Ciclo 5 - Transformemos Educando 10 - Guainia

7/22/2019 Ciclo 5 - Transformemos Educando 10 - Guainia

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Crdmn

4?Crdmn

Lùmu`n fktacrdmn

pdrd ifi`n 1

Lùmu`n fktacrdmn

pdrd ifi`n 1

L ù m u

` n f k t a c r d m n p d r d i f i ` n

1

] r d k s b n r l a l n s A m u i d k m n

4?Crdmn

4?

C u d f k ì d

Qk kuavn buturn pdrd `d amuidifùk

Drtasdkfds nrcdkfzdifùk "dtuld" A` Inin. - Cudfkìd



Asta `fern partakaia d:

Rfvn ak a` rascudrmn,inrracflfaktn n edrrfn:

Ma` lukfifpfn ninrracflfaktn ma:

Mapdrtdlaktn:

Astumfn ink a` YfstaldFktarditfvn ]rdksbnrlalns

Amuidkmn ak`d baihd:



Knlfkdifùk pnr In`nlefd ma` Lfkfsta

ma Ua`difnkas Axtarfnras y Lfkfstarfn

Amuidifùk d` _ralfn QKAYIN

Uay Hdldm efk Fsd D` Ghd`fbd pdrd `

u`fzdifùk ma `ds ]FI ak `d amuidifùk,

saptfalera ma 5?4?



Yfstald Fktarditfvn

]rdksbnrlalns Amuidkmn Ärads fktacrdmds pdrd ifi`n 1

Lùmu`n 4?

_famrds ma _uartn In`nlefd - Uìn Cudfkìd


http://slidepdf.com/reader/full/ciclo-5-transformemos-educando-10-guainia 5/834BQKMDIFÙK _DUD A@ MAYDUUN@@N YNIFD@Gl 8 vìd Encntä @d Idàrd • ]aàbdx (?14) 82?6885

Lùmu`n fktacrdmn pdrd ifi`n 1, ]rdksbnrlalns Amuidkmn 4?

Mfraiifùk pamdcùcfid y inkiaptud`: Ldrìd Durnrd Idrrf``n Cu``n

]axtns: Ärad ma @akcudja y Inlukfidifùk:Earkdrmd Unmrìcuaz Eatdkiur y _dtrfifd Racd

Ärad ma Ifakifds Kdturdàs: _dn`d Unjds y Dràx Cdriìd

Ärad ma Tuìlfid: Ldrthd @f`fdkd _raifdmn y Kdtd`fd ma` Uniìn Ävf`d Ldhaihd

Ärad ma Bìsfid: Nsidr Amud`rmn Cnkzäàz _rdmd, Ldria`d Eakìtaz Lakmfva`sn (ravfsfùk y djusta)

Ärad ma Ldtalätfids: Udbda` Asinedr Ifbuaktas, Ä`vdrn Cutfærraz ma `d Nssd y Custdvn Dmn`bn ma` Uìn _æra(ravfsfùk y djusta)

Uavfsfùk ma` taxtn: Jnsæ @ufs Cdldrrd

Inrraiifùk ma astf`n: Ldrìd Irfstfkd Racd ma Ifiarf

Mfsaôn cräbfin y amftnrfd`: Dkmrad @nzdkn @ùpaz y _d`nlfkn Amftnras

Bntncrdbfd: Idr`ns Cfèartn _uaktas Lajìd

Ya dcrdmaia `d iasfùk ma bntns d: Irfstned` Barkdkmn _æraz, Judk _de`n _rfatn, _amrdzd _rnmuiifnkas, Jdvfar Dldyd,

Mdkfa` Cuzläk, Nldr D`bramn Eustdldkta Unquala y Lusan Inlukftdrfn ma Cudfkìd.

Bukmdifùk pdrd a` Masdrrn``n Ynifd`FYEK:

_rnhfefmd `d raprnmuiifùk pdrifd` n tntd` pnr iud`qufar lamfn sfk dutnrfzdifùk axprasd ma `d Bukmdifùk pdrd a` Masd

rn``n Ynifd` ]rdksbnrlalns

Flprasn ak In`nlefd

Bukmdifùk pdrd a` Masdrrn``n Ynifd`Mfraitnrd Ajaiutfvd y _amdcùcfid: Ldrìd Durnrd Idrrf``n Cu``n

Mfraitnr ma Masdrrn``n Ynifd` y Mfraiifùk Amftnrfd`: Unmn`bn Drmf`d Iuastd

Ùsidr Drldkmn Unmrìcuaz Yäkihaz, Cnearkdmnr ma` Cudfkìd

Ga``y _dn`d _d`difn Lakmnzd, Yairatdrfd ma Amuidifùk y Iu`turd

©



¾_nr quæ uk sfstald fktarditfvn>

A` masdrrn``n ma lú`tfpàs axparfakifds amuidtfvds, ink mfvarsds pne`difnkas, khd lnstrdmn qua d` lfrdr sfstælfidlakta `ns prniasns amuidtfvns denrmdlsu ukfmdm, su c`ned`fmdm y su fktacrfmdm.

Uainrmalns qua a` paksdlfaktn sfstælfin inkifea y astumfd `ns bakùlakinln sfstalds y kn inln dcracdmns ma pdrtas y dmaläs, parifea d` lukmn i

ukd lfrdmd tntd`fzdmnrd y hn`ìstfid.

A` Yfstald Fktarditfvn ]rdksbnrlalns Amuidkmn denrmd d amuidifùk inln ucrdk ram ma ra`difnkas. Astd parspaitfvd parlfta akbdtfzdr dúk läs ukd fktacifùk ma `ns mfvarsns aàlaktns qua d` ra`difnkdrsa inkbnrldk `d astruiturd `ns mfbaraktas prniasns amuidtfvns y ma `ns mfvarsns aktnrkns qua `ns rnmadk

¾_nr quæ uk sfstald fktarditfvn>

A` masdrrn``n ma lú`tfpàs axparfakifds amuidtfvds, ink mfvarsds pne`difnkas, khd lnstrdmn qua d` lfrdr sfstælfidlakta `ns prniasns amuidtfvns denrmdlsu ukfmdm, su c`ned`fmdm y su fktacrfmdm.

Uainrmalns qua a` paksdlfaktn sfstælfin inkifea y astumfd `ns bakùlakinln sfstalds y kn inln dcracdmns ma pdrtas y dmaläs, parifea d` lukmn i

ukd lfrdmd tntd`fzdmnrd y hn`ìstfid.

A` Yfstald Fktarditfvn ]rdksbnrlalns Amuidkmn denrmd d amuidifùk inln ucrdk ram ma ra`difnkas. Astd parspaitfvd parlfta akbdtfzdr dúk läs ukd fktacifùk ma `ns mfvarsns aàlaktns qua d` ra`difnkdrsa inkbnrldk `d astruiturd `ns mfbaraktas prniasns amuidtfvns y ma `ns mfvarsns aktnrkns qua `ns rnmadk

A` sfstald fktarditfvn kn sa matfaka ak `ds idrditarìstfids ma idmd uknma `ns aàlaktns, aktra a``ds `ds lamfdifnkas mfmäitfids n a` inktaxtn,inln ukfmdmas ink ukd astruiturd abfifakta, d iud` yd halns puastn akpräitfid, dhnrd, denrmdkmn astns aàlaktns inln pdrta ma uk sfstaldin`nidlns a` ækbdsfs ak `ds ra`difnkas a fktardiifnkas aktra a``ns, inkukd i`drd fktakifùk amuidtfvd, lamfdkta prniasns aktakmfmns inln ukdld``d ma ra`difnkas mfkälfids, as maifr, fktarditfvds.

A` sfstald fktarditfvn kn sa matfaka ak `ds idrditarìstfids ma idmd uknma `ns aàlaktns, aktra a``ds `ds lamfdifnkas mfmäitfids n a` inktaxtn,inln ukfmdmas ink ukd astruiturd abfifakta, d iud` yd halns puastn akpräitfid, dhnrd, denrmdkmn astns aàlaktns inln pdrta ma uk sfstaldin`nidlns a` ækbdsfs ak `ds ra`difnkas a fktardiifnkas aktra a``ns, inkukd i`drd fktakifùk amuidtfvd, lamfdkta prniasns aktakmfmns inln ukdld``d ma ra`difnkas mfkälfids, as maifr, fktarditfvds.

Yfstald Fktarditfvn ]rdksbnrlalns AmuidkmnYfstald Fktarditfvn ]rdksbnrlalns Amuidkmn



¾Iùln as `d nrcdkfzdifùkma` sfstald fktarditfvn>

@d nrcdkfzdifùk ma` Yfstald Fktarditfvn ]rdksbnrlalnsAmuidkmn astä inkbnrldmd pnr ra`difnkas qua sa mdkaktra sus aàlaktns bukmdktas:

¾Iùln as `d nrcdkfzdifùkma` sfstald fktarditfvn>

@d nrcdkfzdifùk ma` Yfstald Fktarditfvn ]rdksbnrlalnsAmuidkmn astä inkbnrldmd pnr ra`difnkas qua sa mdkaktra sus aàlaktns bukmdktas:

Nrcdkfzdifùk ma` Yfstald Fktarditfvn ]rdksbnrlalns Amuidkmn

Ua`difnkas Idrditarìstfids Nejatfvns

_amdcùcfids

Rfrtudàs

Fktardiifùk

Inktaxtudàs

Lamfdifnkas mfmäitfids

Ua`difnkas fktarditfvds mainlukfidifùk lamfdmd pnr`d taikn`ncìd ma d fkbnrlä-

tfid y `ds inlukfidifnkas.

Fktardiifnkas lntrfias, par-iaptfvds, inckftfvds, npard-

tfvds y ra`difnkas huldkds.

Qkd crdk ram ma ra`difn-kas snifdàs, parsnkdàs,ainkùlfids, aktra luihdsntrds, masma a` inktaxtnhdifd a` sfstald fktarditfvnma dprakmfzdja y vfiavarsd.

Masakidmakdr a` prniasn madprakmar.

Dpnydr n snpnrtdr ns aktnr-kns mastfkdmns d d aksaôdk-

zd y a` dprakmfzdja.

Bdif`ftdr fktardiifnkas aktraastumfdktas, prnbasnras-as-tumfdktas y ma idmd uknma a``ns ink `ns ldtarfdàsmfmäitfins.

Ynpnrtdr y dpnydr `ns prn-iasns amuidtfvns erfkmdkmnsfckfbfidmn y partfkakifd.



Iu`turdifumdmdkdy lu`tfætkfid

Masdrrn``nhuldkn akinlukfmdm

Astrdtacfd iurrfiu`dr: fkiùfr d `ns/`ds astumfdktas ak uk prnyaitn ma ifumdmdkìd ditfvd, lamfdkta a` bnrtdàiflfaktma `d fmaktfmdm parsnkd` y pùrfætkfid, raiupardkmn aàlaktns ma ukd iu`turd mfvarsd qua hdeftd ak uk inktaxtprfvfàcfdmn pnr sus ifriukstdkifds hfstùrfids, `ftardrfds, lusfidàs y turìstfids, pdrd mfkdlfzdr masma d``ì, `d iu`tuifumdmdkd, iradmnrd y prnmuitfvd ak `ns aspdifns ma ditudifùk intfmfdkd ma `ns/`ds astumfdktas y sus inlukfmdma

Inlpnkaktasiurrfiu`dras

Ajas iurrfiu`drasdrtfiu`dmnras

Nejatfvns mfmäitfins Inktakfmns

Nrfaktdk`ns prniasnsamuidtfvns

Inktaxtud`fzdk y mdksaktfmn d `ns inktakfmnsy prniasns amuidtfvns

6 dsfckdturds fktacrdmdsak iudtrn ärads talätfids:@akcudja y Inlukfid-ifùk, Ifakifds Kdturdàsy Ynifdàs, Ldtalätfids.

Uaiupardifùk ma `d la-lnrfd lusfid`, `ftardrfd ahfstùrfid.

Rfsfef`fmdm ma `dmfvarsfmdm.

Dbfdkzdlfaktn ma `dprnpfd fmaktfmdm.

Inlukfmdm ditfvd.

Ifumdmdkìd ditfvd.

Dprakmfzdjas carlfkdàs, sfstælfins yinktaxtud`fzdmns.

Dprakmfzdjas pdrd dbrnktdr `d fkiar-tfmulera.

Inkniflfaktn y rainkniflfaktn mahaihns hfstùrfins bukmdlaktdàs.

Inksifakifd ma `d sfkcu`drfmdm ma `dprnpfd iu`turd.

Inkniflfaktn y rainkniflfaktn ma susvd`nras iu`turdàs y ma ds ntrds iu`turds.

Uainkniflfaktn ma `ds kuavds ra`d-ifnkas aktra a` Astdmn y a` ifumdmdkn.

Uasfckfbfidifùk ma` rn` ma `d lujar.

Uainkniflfaktn ma ns vd`nras maln-irätfins masma a` acdmn ma su iu`turd.

_drtfifpdifùk ifumdmdkd nrcdkfzdmd.

Inkstruiifùk ma ra`difnkas malnirä-tfids fkiùyaktas.

Ajarififn ma `d ifumdmdkìd ditfvd.Masdrrn``n snifd` sustaktdeà y sns-takfeà.Fkiralaktn ma d idpdifmdm ma castfùkma `d inlukfmdm.

Uaspatn d `ds präitfids snifdàs mfvar-sds maktrn ma` ldrin ma rabarakifd ma

Ydearaslu`tfmfsif-p`fkdrfns

Yurcak ma `ds axpaitdtfvds pdrd idmdifi`n y nrfaktdk `d diifùk amuidtfvd

¾Iuä` as `d astruiturd ma` Yfstald Fktarditfvn>

@d astruiturd ma` sfstald fktarditfvn ]rdksbnrlalns Amuidkmn tfaka uk mfsa

iurrfiu`dr eäsfin:

Astäkmdras ma inlpatakifds eäsfidrtfiu`dmns ink ns inlpnkaktas iu`turd ifumdmdkd y lu`tfætkfidmasdrrn``n huldkn ak inlukfmdm

Inkiaptud`fzdifnkas defartds d inkbrnktdifùk, d` dkä`fsfs irìtfin,lfrdmds sfstælfids fktacrdmnrds, inllamfdmnrds aktra a` inkniflfakintfmfdkn y a` inkniflfaktn ifaktìbfi

Lalnrfd hfstùrfid, lusfid` y `ftardrUftns y bastfvfmdmas.Uasfckfbfidifùk ma `d hfstnrfd.

Diifnkas dbfrldtfvds pdrd ds mfvarsatkfds.

Iu`turd ma `ds mfvarsds atkfds.

Maraihns y maearas ifumdmdkns.

Dpnrtas ma `d lujar ak `d iu`turd

Rd`nras malnirätfins y vfmd inmfdkd.

Astruiturd ma` Astdmn

_rnyaitns inlukftdrfns, ma fktacifùk snifd`, fkmfvfmudàs n inàitfvn

Ditfvfmdmas y diifnkas ak a` iurrìi`n ink edsa ak `ns inkniflfaktnsinkiaptud`fzdifnkas trdtdmns ak ärads talätfids.

Uabàxfùk snera ds präitfids snifdintfmfdkds masma `ds kuavds inkia

Inkiaptudàs (sdear: ra`difnkinlpdrdr, mfvarsfbfidr, mfstfkcufr),

prniamflfaktn (hdiar, dp`fidr, lardr y idlefdr), y ma ditftum (sar, dslfr, maifmfr, irftfidr, diaptdr y kac



A` sfstald fktarditfvn ]rdksbnrlalns Amuidkmn as uk sfstald defartn, uk sfstaldefartn ak ukd ra`difùk ma fktaridlefn inkstdkta ink a` inktaxtn mnkma sflpàlaktd. Dmaläs, as uk sfstald inlpàjn, yd qua sus mfvarsns inlpnkaktad` fktarditudr aktra sì y ink a` inktaxtn sa lnmfbfidk y prnmuiak kuavds ra`difnka

@ns suesfstalds qua inkbnrldk a` sfstald fktarditfvn snk:

4. Yfstald ma amuidifùk bnrld` ink ukd ram ma ra`difnkas ak idmd sfstalracfnkd` amuidtfvn y ak a` sfstald kdifnkd` ma amuidifùk.

5. Yfstald ma pdrtfifpdifùk ditfvd ak a` inktaxtn ink ukd ram ma ra`difnkfktrdbdlf`fdr, inlukftdrfd, racfnkd`, kdifnkd` a fktarkdifnkd`.

9. Yfstald ma lamfdifnkas mfmäitfids, ink `ns sfcufaktas suesfstalds:

Lamfdifnkas ma fktardiifùk: ns mniaktas ]rdksbnrldmnras n ]rdksbnrldmnrdastumfdktas y sus inlukfmdmas, denrmdk ns inktakfmns a fktarditúdk ink a``nbrakta d su rad`fmdm, pdrd cakardr fmads y diifnkas qua parlftdk trdksbnrlpnsftfvdlakta su aktnrkn, lfaktrds inktfkúdk dprakmfakmn.

Lamfdifnkas mfmäitfids flprasds: `ds iudàs parlftak cakardr uk aktnrkasirftn y bnlaktdr `d àiturd, ink a` bfk ma prnlnvar `d iu`turd asirftd ak s

vfmd intfmfdkd y `d ma su bdlf`fd, murdkta `d amuidifùk eäsfid y lamfd.

Lamfdifnkas fktarditfvds: a` inlputdmnr, a` taàvfsnr y a` ldtarfd` dumfnvfsud`fktarditfvn, kns parlftak takar kuavds mflaksfnkas ma` inkniflfaktn, bdif`ftd`ns prniasns ma destrdiifùk y `ns fkiùya inln saras ditfvns ak `d ifeariu`tuy a` sfc`n XXF.

=. Yfstald ma inlukfidifùk a fkvastfcdifùk pdrd ratrnd`flaktdr tnmns `n

¾Iuäàs snk `ds idrditarìstfids cakardàs ma` sfstaldfktarditfvn ]rdksbnrlalns Amuidkmn>



• Inlprakmn qua ak uk Astdmn ma Maraihn ds

parsnkds pnmalns pdrtfifpdr ak d iradifùk

n trdksbnrldifùk ma ds ayas y qua æstds sa

dp`fidk d tnmns y tnmds pnr fcud`.

• Inknzin `ns prfkifpfns eäsfins ma` Maraihn

Fktarkdifnkd` Huldkftdrfn (pnr ajalp`n, `d

prntaiifùk d d snifamdm ifvf` ak uk inkb`fitn

drldmn).

• Dkd`fzn irìtfidlakta a` saktfmn ma `ds àyasy inlprakmn `d flpnrtdkifd ma iulp`fr`ds,

dsì kn inlpdrtd d`cukd ma a``ds.

• Dkd`fzn irìtfidlakta y maedtn ink drculak-

tns y avfmakifds snera haihns niurrfmns d

kfva` nid`, kdifnkd` y lukmfd`, y inlprakmn

`ds inksaiuakifds qua æstns puamak takar

snera lf prnpfd vfmd.

• Axprasn alpdtìd dkta crupns n parsnkds

iuyns maraihns hdk sfmn vu`kardmns (pnrajalp`n ak sftudifnkas ma masp`dzdlfaktn) y

prnpnkcn diifnkas sn`fmdrfds pdrd ink a``ns.

• _drtfifpn ak ldkfbastdifnkas pdiìbfids ma

raihdzn n sn`fmdrfmdm dkta sftudifnkas ma

masvaktdjd snifd`, ainkùlfid n ma sdùm qua

vfva `d cakta ma lf racfùk n lf pdìs.

• _drtfifpn ak fkfifdtfvds pn`ìtfids malnirätfids

ak lf lamfn asin`dr n `nid`fmdm.

• Inlprakmn quæ as uk efak púe`fin y pdrtf-

ifpn ak diifnkas qua va`dk pnr su euak usn,

tdktn ak d inlukfmdm asin`dr, inln ak lf

lukfifpfn.

• Inlprakmn qua iudkmn sa ditúd ak bnrld

inrruptd y sa usdk `ns efakas púe`fins pdrd

eakabfifn parsnkd`, sa dbaitdk tnmns `ns

lfalerns ma d snifamdm.

• Inkstruyn ukd pnsfifùk irìtfid brakta d `ds sftud

ifnkas ma mfsirflfkdifùk y axiùsfùk snifd` qua ra

su`tdk ma ds ra`difnkas masfcudàs aktra parsnkds

iu`turds y kdifnkas.

• Uainknzin `ds sftudifnkas ma mfsirflfkdifùk y

axiùsfùk läs dcumds qua sa prasaktdk dhnrd

n sa prasaktdrnk ak a` pdsdmn, tdktn ak a` nrmak

kdifnkd` inln ak a` fktarkdifnkd`7 `ds ra`difnkn

ink `ds mfsirflfkdifnkas qua nesarvn ak lf vfmd

intfmfdkd.

• Inlprakmn qua a` raspatn pnr `d mfbarakifd kn

sfckfbfid diaptdr qua ntrds parsnkds n crupns

vu`karak maraihns huldkns n knrlds inkstftu

ifnkdàs.

• Fmaktfbfin prajufifns, astarantfpns y alnifnkas qua

la mfbfiu`tdk saktfr alpdtìd pnr d`cukds parsnkds

n crupns y axp`nrn idlfkns pdrd supardr`ns.

• Fmaktfbfin y dkd`fzn mfàlds ma `d vfmd ak `ns qua`ns vd`nras ma mfstfktds iu`turds n crupns snifdàs

aktrdk ak inkb`fitn y axp`nrn mfstfktds npifnkas ma

snùifùk, inksfmardkmn sus dspaitns pnsftfvns y

kacdtfvns.

• Drculaktn y maedtn mfàlds ma d vfmd ak ns qua

`ns vd`nras ma mfstfktds iu`turds n crupns snifdàs

aktrdk ak inkb`fitn7 rainknzin `ns lajnras drcu

laktns, dsì kn infkifmdk ink `ns lìns.

Inlpatakifds Ifumdmdkds, Lfkfstarfn ma Amuidifùk Kdifnkd`

_drtfifpdifùk y raspnksdef`fmdmmalnirätfid

_ùrd`fmdm, fmaktfmdm y vd`nrdifùkma `ds mfbarakifds



_drtfifpn inkstruitfvdlakta ak fkfifdtfvds n prnyaitns d bdvnr ma `d kn-vfnàkifd ak a` kfva`

`nid` n c`ned`.

• Inktrfeuyn d qua `ns inkb`fitns aktra parsnkds y aktra crupns sa ldkajak ma ldkard

pdiìbfid y inkstruitfvd lamfdkta `d dp`fidifùk ma astrdtacfds edsdmds ak a` mfä`ncn y `d

kacnifdifùk.

• Qtf`fzn mfstfktds bnrlds ma axprasfùk pdrd prnlnvar y mabakmar `ns maraihns huldkns ak

lf inktaxtn asin`dr y inlukftdrfn.

• Dkd`fzn irìtfidlakta `ds maifsfnkas, diifnkas u nlfsfnkas qua sa tnldk ak a` äleftn

kdifnkd` n fktarkdifnkd` y qua puamak cakardr inkb`fitns n dbaitdr ns maraihns huldkns.

• Dkd`fzn irìtfidlakta `d sftudifùk ma `ns maraihns huldkns ak In`nlefd y ak a` lukmn

y prnpnkcn d`tarkdtfvds pdrd su prnlnifùk y mabaksd.

• Ldkfbfastn fkmfckdifùk (mn`nr, rdefd, raihdzn) ma ldkard pdiìbfid dkta a` subrflfaktn ma

crupns n kdifnkas qua astäk fkvnùirdmds ak inkbrnktdifnkas vfnàktds.

• Rd`nrn pnsftfvdlakta `ds knrlds inkstftuifnkdàs qua hdiak pnsfeà `d prasarvdifùk ma

`ds mfbarakifds iu`turdàs y pn`ìtfids, y qua racu`dk kuastrd inkvfvakifd.

• Inlprakmn qua, pdrd cdrdktfzdr `d inkvfvakifd, a` Astdmn maea inktdr ink a` lnknpn`fn

ma d dmlfkfstrdifùk ma justfifd y ma` usn ma d buarzd, y qua d snifamdm ifvf` maea hdiarà

sacuflfaktn irìtfin, pdrd avftdr deusns.

• Inknzin ds fkstdkifds y sæ usdr ns laidkfslns jurìmfins nrmfkdrfns y d`tarkdtfvns pdrd d

rasnùifùk pdiìbfid ma inkb`fitns: justfifd nrmfkdrfd, juaias ma pdz, iaktrns ma inkif`fdifùk,

inlfsdrìds ma bdlf`fd7 kacnifdifùk, lamfdifùk, dreftrdlaktn.

• Fmaktfbfin mfàlds ma `d vfmd ak `ds qua aktrdk ak inkb`fitn a` efak cakard` y a` efak

pdrtfiu`dr7 dkd`fzn npifnkas ma snùifùk, inksfmardkmn sus dspaitns pnsftfvns y kacdtfvns.

• Drculaktn y maedtn snera mfàlds ma d vfmd ak `ns qua aktrdk ak inkb`fitn a` efak cakard`

y a` efak pdrtfiu`dr, rainknifakmn `ns lajnras drculaktns, dsì sadk mfstfktns d `ns lìns.

• Inknzin y raspatn ds knrlds ma träksftn.

• Inlprakmn `d flpnrtdkifd ma `d mabaksd ma` lamfn dlefakta, tdktn ak a` kfva` `nid`

inln c`ned`, y pdrtfifpn ak fkfifdtfvds d su bdvnr.

Inlpatakifds Ifumdmdkds, Lfkfstarfn ma Amuidifùk Kdifnkd`(inktfkudifùk)



Inlpatakifds `denrdàs masdrrn``dmds ak `ns prniasnsma trdedjn inàitfvn a fkmfvfmud`.

• Uainknzin `ds pnsfeàs bnrlds ma akbraktdr ukd sftudifùk.• Yaàiifnkn ukd ma `ds bnrlds ma ditudr pnsfeàs.• Dsuln ds inksaiuakifds ma lfs maifsfnkas.

• Nesarvn ukd sftudifùk iaridkd d lf aktnrkn (lf idsd, lf edrrfn, lf inàcfnracfstrn fkbnrldifùk pdrd masirfefr`d.

• Dkd`fzn `ds sftudifnkas masma mfstfktns puktn ma vfstd (lfs pdmras, lfs dlfcnparsnkds inknifmds, aktra ntrds).

• Fmaktfbfin `ns inlpnrtdlfaktns dprnpfdmns pdrd idmd sftudifùk (bdlf`fdr, asinìnk pdras).

• Iulp`n `ds knrlds ma inlpnrtdlfaktn mabfkfmds ak uk aspdifn mdmn.

• Uainknzin lfs hdef`fmdmas, mastrazds y tdàktns.• Yuparn lfs maef`fmdmas.• ]akcn ak iuaktd a` flpditn ma lfs alnifnkas y su ldkajn ak lf ra`difùk i

ntrns.

• Uad`fzn lfs fktarvakifnkas raspatdkmn a` nrmak ma `d pd`derd pravfdlakdinrmdmn.

• Axprasn lfs fmads ink i`drfmdm.

• Masdrrn``n tdrads y diifnkas ink ntrns (pdmras, pdras, inknifmns).• Dpnrtn lfs raiursns pdrd d rad`fzdifùk ma tdrads inàitfvds.

• Cakarn ra`difnkas ma inkbfdkzd ink ntrns (pdras).• Uainknzin ds bnrtdàzds y hdef`fmdmas ma `ns ntrns (bdlf`fdras, pdras).

• Axprasn lfs prnpfns fktarasas y lntfvdifnkas.• Eusin bnrlds ma rasn`var `ns inkb`fitns qua akbraktn ak lf aktnrkn iaridkn

• Fmaktfbfin `d fkbnrldifùk raquarfmd pdrd masdrrn``dr ukd tdrad n ditfvfmdm.• Uainàitn mdtns ma sftudifnkas iaridkds d lf aktnrkn (lf idsd, lf edrrfn,

inàcfn).

• Eusin lajnrdr lf bnrld ma ra`difnkdrla ink ntrns ink edsa ak sus dpraiifnkas.

• Yaàiifnkn ns ldtarfdàs qua raqufarn pdrd a` masdrrn``n ma ukd tdrad n diifù• Avftn a` masparmfifn ma `ns ldtarfdàs qua astäk d lf d`ramamnr (lf idsd,

sd`ùk ma i`dsas, `denrdtnrfns, td`àras, aktra ntrns).

• Fmaktfbfin `ds tdrads y diifnkas ak `ds qua `ns ntrns (pdmras, pdras, mniaktasnk lajnras qua yn.

• Masdrrn``n diifnkas pdrd lajnrdr inktfkudlakta ak mfstfktns dspaitns ma vfmd ink edsa ak `n qua dprakmn ma `ns maläs.

• Uainknzin `ns prneàlds qua surcak ma` usn y mfspnsfifùk ma ds mfstfktds i`dsma raiursns ma lf aktnrkn iaridkn (lf idsd, lf edrrfn, lf inàcfn)

• Ldktakcn nrmakdmns y flpfns lf sftfn ma astumfn y lfs flpàlaktns parsnkdà

• Uainknzin `ds kaiasfmdmas ma lf aktnrkn iaridkn (lf idsd, lf edrrfn, inàcfn).

• Fkvaktn snùifnkas iradtfvds pdrd sdtfsbdiar `ds kaiasfmdmas mataitdmds

]fpn mainlpatakifdInlpatakifds

Fktaàitudàs

_arsnkdàs

Fktarparsnkdàs

Nrcdkfzdifnkd`

Alprasdrfdàsy pdrd a`

]nldma maifsfnkas

Iradtfvfmdm

Nrfaktdifùkætfid

Mnlfkfnparsnkd`

Inlukfidifùk

]rdedjnak aqufpn

@fmardzcn

Ldkajnma inkb`fitns

Castfùkma `d

fkbnrldifùk

Nrfaktdifùkd` sarvfifn

Castfùky ldkajn

ma raiursns

Uabarakifdifùkinlpatftfvd

Uaspnksdef`fmdmdlefaktd`

Fmaktfbfidifùk manpnrtukfmdmas pdrdiradr alprasds n

Yueprniasns



426Ifakifds Kdturd`as

Inktakfmn

49@akcudja y Inlukfidifùk

1?=Ldtalätfids

591Tuìlfid

982Bìsfid



Lusan Inluktdrfn ma Cudfkìd.J_C

B n t n d r i h f v n

] r d k s b n r l a l n s

Lùmu`n fktacrdmn pdrd ifi`n 1

]rdksbnrlalns Amuidkmn Ärad ma @akcudjay Inlukfidifùk

4?



Astäkmdras eäsfins ma inlpatakifds ak @akcudja y Inlukfidifùk

_rnmuiifùktaxtud`

Inlpraksfùk afktarpratdifùktaxtud`

• Inlprakmn a` vd`nr ma` àkcudja ak `nsprniasns ma inkstruiifùk ma` inknif-lfaktn.

• Masdrrn``n prniasns ma dutninktrn` y in-rraiifùk `fkcðìstfid ak lf prnmuiifùk mataxtns nrdàs y asirftns.

• Idrditarfzn y utf`fzn astrdtacfds mas-irfptfvds, axp`fidtfvds y dkd`ùcfids ak lf

prnmuiifùk ma taxtns nrdàs y asirftns.• Avfmakifn ak lfs prnmuiifnkas taxtudàsa` inkniflfaktn ma `ns mfbaraktas kfvaàsma `d àkcud y a` inktrn` snera a` usn quahdcn ma a``ns ak inktaxtns inlukfidtfvns.

• A`denrn hfpùtasfs ma fktarpratdifùk dtak-mfakmn d `d fktakifùk inlukfidtfvd y d`saktfmn c`ned` ma` taxtn qua àn.

• Ua`difnkn a` sfckfbfidmn ma `ns taxtns qua

àn ink ns inktaxtns snifdàs, iu`turdàs ypn`ìtfins ak `ns iudàs sa hdk prnmuifmn.• Mfsaôn uk asquald ma fktarpratdifùk,

takfakmn ak iuaktd d` tfpn ma taxtn,tald, fktar`niutnr a fktakifùk inlukf-idtfvd.

• Dsuln ukd ditftum irìtfid brakta d `nstaxtns qua àn y a`denrn, y brakta d ntrnstfpns ma taxtn: axp`fidtfvns, masirfptfvns ykdrrdtfvns.

• Inlprakmn ak `ns taxtns qua àn `dsmflaksfnkas ætfids, astætfids, bf`nsùbfids,aktra ntrds, qua sa avfmakifdk ak a``ns.

• Inlpdrn taxtns ma mfvarsns dutnras, ta-lds, æpnids y iu`turds, y utf`fzn raiursnsma `d tanrìd `ftardrfd pdrd akrfquaiar sufktarpratdifùk.

• Inlpdrn taxtns ma mfvarsns dutnras, ta-lds æpnids y iu`turds, y utf`fzn raiursns

• _rnmuzin taxtns drculak-tdtfvns qua avfmakifdk lfinkniflfaktn ma d akcudy a` inktrn` snera a` usnqua hdcn ma a``d ak ink-

taxtns inlukfidtfvns nrdàsy asirftns.

• Inlprakmn a fktarpratntaxtns ink ditftum irìtfid yidpdifmdm drculaktdtfvd.

• Dkd`fzn irìtfid y iradtfvd-lakta mfbaraktas ldkf-bastdifnkas `ftardrfds maìnktaxtn ukfvarsd`.

Bditnrasma nrcdkfzdifùk

Inlpatakifds Yueprniasns

¾D quæ quaralns àcdr> ¾Iùln maluastrn n dprakmfmn>

@ftardturd



44

Astäkmdras eäsfins ma inlpatakifds ak @akcudja y Inlukfidifùk

Bditnrasma nrcdkfzdifùk

Inlpatakifds Yueprniasns

¾D quæ quaralns àcdr> ¾Iùln maluastrn n dprakmfmn>

ma `d tanrìd `ftardrfd pdrd akrfquaiar sufktarpratdifùk.

• @an taxtns `ftardrfns ma mfvarsd ìkmnàcækarn, talätfid y nrfcak.

• Ak nerds ma d ftardturd ukfvarsd`, fmaktf-bfin a` akcudja, ds idrditarìstfids bnrld-às, `ds æpnids y `ds asiua`ds, `ns astf`ns,`ds takmakifds, ds talätfids, ns cækarns

y `ns dutnras, aktra ntrns dspaitns.

• Fkbfarn `d flp`fidifùk ma `ns lamfns mainlukfidifùk ldsfvd ak `d inkbnrld-ifùk ma ns inktaxtns snifdàs, iu`turdàs,pn`ìtfins, ati., ma` pdìs.

• Dkd`fzn ns laidkfslns fman`ùcfins quasueydiak ak d astruiturd ma ns lamfnsma fkbnrldifùk ldsfvd.

• Dsuln ukd pnsfifùk irìtfid brakta d `ns

aàlaktns fman`ùcfins prasaktas ak asnslamfns, y dkd`fzn su fkifmakifd ak `dsnifamdm ditud`.

• Axp`fin iùln `ns iùmfcns varedàs y knvaredàs sa drtfiu`dk pdrd cakardr saktfmnak nerds ifkaldtncräbfids, idkifnkas yid`fcrdlds, aktra ntrds.

• _rnmuzin taxtns, alpàdkmn àkcudjavared` n kn vared`, pdrd axpnkar lfsfmads n pdrd rairadr rad`fmdmas, inksaktfmn irìtfin.

• Uaspatn `d mfvarsfmdm ma irftarfns y pn-sfifnkas fman`ùcfids qua surcak ak `nscrupns huldkns.

• Qtf`fzn a` mfä`ncn y `d drculaktdifùkpdrd supardr akbraktdlfaktns y pnsfifn-kas dktdcùkfids.

• Fktarpratn ak bnrld irftfid`d fkbnrldifùk mfbukmfmdpnr `ns lamfns ma inlukf-idifùk ldsfvd.

• Uatnln irìtfidlakta `nsàkcudjas kn varedàs pdrdmasdrrn``dr prniasns inlu-kfidtfvns fktakifnkdmns.

• Axprasn raspatn pnr `d mf-varsfmdm iu`turd` y snifd` ma`lukmn inktalpnräkan, ak`ds sftudifnkas inlukfidtf-vds ak `ds qua fktarvakcn.

@ftardturd

Lamfns mainlukfidifùky ntrnssfstaldssfleù`fins

Ætfid ma `dinlukfidifùk



Qkfmdm 4. A` iùmfcn `fkcðìstfin: `ds ldkfbastdifnkas ma` `akcudja 43

Yasfùk 4. A` iùmfcn `fkcuìstfin 43 Yasfùk 5. A` maedta 51 Yasfùk 9. @ds idrtds 9? Yasfùk =. A` fkbnrla 93 Yasfùk 1. A` iuaktn y sus nrìcakas =5 Yasfùk 2. Ldkns d `d nerd 15

Qkfmdm 5. A` pfa ma bntn: d trdkslfsfùk ma `d fkbnrldifùky `ns sfstalds sfleù`fins 1=

Yasfùk 3. _fa ma bntn y astruiturd ma` taxtn asirftn 1= Yasfùk 8. A` pdka` y `d aktravfstd 2= Yasfùk 6. @d `ìrfid vdkcudrmfstd 31 Yasfùk 4?. Ldkns d `d nerd 89

Qkfmdm 9. Inharakifd, inhasfùk vared` y inkinrmdkifd `fkcðìstfid 8=

Yasfùk 44. Inharakifd, inhasfùk vared` y inkinrmdkifd `fkcðìstfid 8= Yasfùk 45. A` salfkdrfn 65 Yasfùk 49. @d kntfifd 68 Yasfùk 4=. A` aksdyn `ftardrfn 4?3 Yasfùk 41. Ldkns d `d nerd 443

Qkfmdm =. Yalfùtfid ma` ifearaspdifn: fktakifnkas inlukfidtfvds,vdrfds bnrlds ma axprasfùk 446

Yasfùk 42. Yalfùtfid ma` ifearaspdifn y taxtn `ftardrfn 446 Yasfùk 43. Lnkù`ncn y sn`f`nqufn 49= Yasfùk 48. Cufùk 4=5 Yasfùk 46. @d æpfid 41?

Ìkm fia



A iùmfcn fkcðìstfin

Qkfmdm 4. A` iùmfcn `fkcðìstfin: `ds ldkfbastdifnkasma` akcudja

Yasfùk

4

A` aspìrftu ma fkvastfcdifùk kn tfaka `ìlftas. Ak `ns Astdmns Qkfmns yak Aurnpd hdk masiuefartn d ú`tflds baihds qua axfsta ukd aspaifa ma

lnkns hfspdkndlarfidkns idpdias ma axprasdrsa pnr asirftn, ræp`fidsqufzä ma` lnkn mf`fcakta qua d buarzd ma tai`adr ukd läqufkd tarlfkdpnr asirfefr ma kuavn, dzdrnsdlakta, `ns snkatns ma Yhdgaspadra. ]d`

insd, inln as kdturd`, ``akd d astds euakds caktasma dsnlern, y kn bd`td qufak trdmuzid kuastrns

`ferns, kf, luihn lakns, nifnsns qua `nsinlprak, inln dktas inlprdedk ds

ideaiftds ramuifmds ma `ns jìedrns.

Hdia läs ma iudtrn sfc`ns quabrdy Edrtn`nlæ ma ds Idsds pumn

inkvakiar d `ns aurnpans maqua ærdlns huldkns y

ma qua takìdlns ukd`ld pnrqua kns

raìdlns7 dhnrd

Majdr ma sar lnkn Ducustn Lnktarrnsn



qufarak inkvakiarsa ma `nlfsln pnrqua asirfeflns.Maifr iùmfcn as hde`dr ma ukcrupn ma aàlaktns (snknrnsn vfsudàs), qua d` inlef-kdrsa parlftak `d inlukfidifùk aktra `ns hnleras. _arn a` iùmfcn`fkcðìstfin as d suld ma vnide`ns n ukfmdmas snknrds qua fktacrdmds mamfbarakta ldkard, parlftak iradr ukd fmad n ukd nrdifùk ink saktfmninlpàtn. @d dusakifd ma asta iùmfcn, qua maea sar rainknifmn pnralfsnr y raiaptnr, brditurdrìd `d inlukfidifùk y dku`drìd `d pnsfef`fmdmma aktakmar asd fmad u nrdifùk d `ds iudàs kns rabarflns.

Ak ntrds pd`derds, `d àkcud as a` iùmfcn `fkcðìstfin qua parlfta main-mfbfidr uk laksdja7 as a` sfstald ma sfckns qua sa dprakmak ak sus mns

bnrlds: nrd` y asirftd.

_nr supuastn, a` iùmfcn astä sujatn d ukds rac`ds y d ukd nrcdkfzdifùk.Idmd mfraitrfz ldrid sus prnpfds idrditarìstfids.

@ds mfbfiu`tdmas ink ds iudàs sa akiuaktrdk ds parsnkds iudkmn usdk aìùmfcn asirftn n a` iùmfcn nrd`, inksfstak ak iraar qua ma `d bnrld inlnsa hde`d sa asirfea7 qua `d suprasfùk ma uk inkaitnr kn d`tard a` sfckfbf-

idmn ma `n qua sa qufara axprasdr7 qua `d inkstruiifùk ma ukd nrdifùkkn axfca uk nrmak ak `ns vnide`ns, sacúk `d bukifùk qua astns iulp`dk.

Aktakmar a` iùmfcn `fkcðìstfin kn as tdk mfspakmfnsn, sù`n raqufaradtakifùk, inlpraksfùk ma `ds rac`ds y dp`fidifùk, y pnr akma, präitfidak su ldkajn, inkniflfaktn. Tufak kn inknia `d harrdlfaktd ink `diud` trdedjd, mfbìif`lakta pnmrä netakar uk prnmuitn ma id`fmdm. _nrasn takcd ak iuaktd:



• Uaqufara a` ldkajn ma rac`ds nrtncräbfids.

• Qtf`fzd uk àkcudja a`denrdmn.

• Axfca uk euak usn ma `ns sfckns ma puktudifùk, pnrqua uk sfcknld` in`nidmn puama d`tardr pnr inlpàtn a` saktfmn ma `d nrdifùk.

• Maldkmd i`drfmdm y praifsfùk ak `ds fmads, puastn qua kn tfaka ukfktar`niutnr fklamfdtn qua a rai`dla ukd axp`fidifùk läs inkiratd.

• _arlfta raa`denrdr `ds nrdifnkas dktas ma qua `àcuak d` raiaptnr,pdrd nbraiar uk laksdja astætfidlakta dtrditfvn.

• Yf efak, kn praifsd rac`ds ma nrtncrdbìd, sì axfca ifartd dtakifùk ak`d inkstruiifùk ma` àkcudja. Qk àkcudja ld` utf`fzdmn inrrnlpa`d àkcud.

• Kn utf`fzd sfckns ma puktudifùk, parn ukd ld`d drtfiu`difùk n usnma` vnide`n, tdlefæk puama d`tardr a` saktfmn ma `n inlukfidmn.

•

_arlfta d fktardiifùk aktra alfsnr y raiaptnr, bdif`ftdkmn d dlp`ftumma` mfsiursn.

• Kn axfca ukd a`denrdifùk ma` `æxfin y pnr astd rdzùk, md idefmd d`àkcudja ma crupn, läs inknifmn inln jarcds.

Iùmfcn asirftn

Iùmfcn nrd`



4

_nr sar `d àkcud uk sfstald ma sfckns, as flpnrtdkta inkniar `d mfvfsfùkqua `ns aspaifd`fstds hdk haihn snera a``ns. @d tanrìd läs diaptdmd as `dprnpuastd pnr Barmfkdkm ma Ydussura (pdmra ma d fkcðìstfid), qufak d` hd-

e`dr ma` sfckn fkcðìstfin, mfstfkcua ak æ`, mns kfvaàs, ukn as a` sfckfbfidmn,d` iud` dtrfeuflns a` inkiaptn qua takalns snera uk aàlaktn7 y a` ntrn asa` sfckfbfidkta, as maifr, d fldcak qua takalns ma asa aàlaktn. Ajalp`n:uk jdrrùk qua puama sar nvd`dmn, ifriu`dr n mabnrla.

@d flpnrtdkifd ma astns mns inlpnkaktas sa maea d su idräitar inkvak-ifnkd` y d su idpdifmdm ma prasaktdr, trds `d avnùifùk ma` tfalpn, ukdlatdlnrbnsfs. Yfk mumd, a` iùmfcn fkcðìstfin sfalpra sarä a` lfsln, parn a`

sfckfbfidmn y a` sfckfbfidkta kn, pnrqua vdrìdk ma diuarmn ink d avnùifùkma `d àkcud y ma` fmfnld.

Uaspnkmd `ds sfcufaktas pracuktds:

4. ¾D quæ sa maea qua `ds pd`derds Astdmns Qkfmns, Aurnpd, Yhdgaspadra, Edrtn`nlæ y Idsds sa asirfedk ink ldyúsiu`ds>

5. ¾Ak iuäktns pärrdbns astä mfvfmfmn a` taxtn ma Lnktarrnsn> ¾Iuäktds nrdifnkarabuarzdk `d fmad qua axprasd>

9. @ad kuavdlakta a` taxtn ma fktrnmuiifùk y mamuzid d ra`difùk qua axfsta akt`d fldcak ma `ns pdìsas saôd`dmns y a` knlera ma Edrtn`nlæ ma `ds Idsds. Kn`vfma a` inktaxtn ak a` iud` astäk uefidmns.

=. Ink sus prnpfds pd`derds y ak bnrld asirftd, axpnkcd `d fmad qua Ducust



5

Uaspnkmdk `ds sfcufaktas pracuktds:4. A` sfcufakta brdclaktn ma` fern A` drta ma dldr, ma Dkmræ Ldurnfs, bua fkta

ifnkd`lakta d`tardmn ak su puktudifùk y ak su nrtncrdbìd. Dmaläs, sa hsuprflfmn d`cukns inkaitnras n pd`derds, ink a` bfk ma qua ustamas nrcdkfia` saktfmn ma `d fmad qua a` dutnr qufsn trdkslftfr. Qk ld` usn ma` iùmf`fkcðìstfin, inln pnmräk inlprnedr, flpfma `d inlpraksfùk y a` p`diar `d àiturd.

‐Ak a` nrfcak dlnr hdy uk ihnqua prnvnidmn pnr `ddmlfrdifùk, sad pnr d`cúk difmakta qua hd rava`dmnukd fkta`fcakifd n haihn uk masan kdiar ak d dusakifd,

a` sar dldmn sa inkvfarta ak uk mfns d` qua pnmalnsdmnrkdr ma tnmd `d parbaiifnkas. Asta trdedjn as `n quaYtakmhd` ``dld ‘`d irfstd`fzdifùk‖. _nr `d irfstd`fzdifùka` nejatn dldmn sa d``ä trdksbnrldmn7 ak uk sar mfba-rakta ma `n quæ as y suparfnr d æ` lfsln. _nr astn aspnr `n qua _rnust mfia qua a` dlnr as suejatfvn, y quadldlns kn d saras, radàs sfkn d saras qua knsntrnsiradlns. Astn majd ma sar varmdm ak idsn ma ukd dmlf-

rdifùk àcìtfld. Astd ``dld kdifakta sa dpdcdrìd prnktnsf d`cúk snp`n ma aspardkzd, pnr `fcarn qua sad, kn `dradkfldsa. Qkd lfrdmd, ukd prasfùk ma `d ldkn, ukdraspuastd uk pnin vfvd `d astflu`dk ak sacufmd. _arnniurra tdlefæk qua d iartfmulera y d sacurfmdm ldtdka` saktflfaktn“.



4

5. Qkd vaz nrcdkfzdmn a` dktarfnr brdclaktn, p`dktaakukd mfsiusfùk snera a` tald y axpnkcdk sus puktnsma vfstd ak uk maedta ak `d sfcufakta i`dsa.

9. Avd`úak `ns arrnras y `ns difartns qua tuvfarnk `nsntrns crupns ak a` ldkajn ma` iùmfcn `fkcðìstfin,y snifd`fiak ink tnmn a` iursn, sus inkiùsfnkas.

=. Idmd lfalern ma` crupn maea asirfefr uk inlak-tdrfn kn ldynr ma 4? `ìkads, snera uk tald ma sufktaræs. Maspuæs, snifd`ìia`n aktra `ns lfalernsma` crupn pdrd sdidr `ds raspaitfvds inkiùsfnkas.

Masdrrn`à ak su iudmarkn:

4. A` iùmfcn `fkcðìstfin bua tdk efak utf`fzdmn pnr Lnktarrnsn ak `d @ai-turd ma fktrnmuiifùk, qua pnr lamfn ma uk iuaktn erava a frùkfin,trdkslftfù ukd fmad d sus àitnras. ¾Iuä` as asd fmad>

5. D pdrtfr ma `ns sfcufaktas vnide`ns, astruitura uk laksdja inharaktaqua puamd sarvfr inln mfsiusfùk: amuidifùk, masprakmfmn, lfamn,asi`dvns, vfmd, crdifds, masan, sdear, masiuefartn, laknr, crdmud`lakta,ldynr, mìd, irua`mdm, pdsfnkas.

9. Masma a` puktn ma vfstd fkcðìstfin, ¾quæ ra`difùk pnmrìd takar a` taxtnqua dided ma a`denrdr, ink `d àiturd ma Ducustn Lnktarrnsn>



=. D inktfkudifùk, akinktrdrä a` brdclaktn qua sa trdedjù ak d ditfvfmdmdktarfnr, tntd`lakta inrracfmn. Dkd`fia idmd ukd ma `ds nrdifnkas yaxp`fqua quæ pd`derds mfarnk ucdr d d astruiturdifùk ma d fmad7 quæ

lnknsì`dens diaktudrnk a` inktakfmn y iuäàs dmjatfvns dbfdkzdrnk`d axp`fidifùk ma` tald.

… Ma haihn a` pdpa` ma` dzdr as td`, qua as luy rdrn qua a` hnleray `d lujar puamdk aàcfr varmdmardlakta, y pnr uk ditn ma vnùktdm

purd, dquæ` qua sarä su inlpdôarn ma vfmd.

Ak a` nrfcak ma tnmn dlnr hdy uk ihnqua prnvnidmn sad pnr `d dm-lfrdifùk, sad pnr d`cúk diifmakta qua hd rava`dmn ukd fkta`fcakifd nhaihn kdiar uk masan. Ak `d dusakifd, a` sar dldmn sa inkvfarta akuk mfns d` qua pnmalns dmnrkdr ma tnmds `ds parbaiifnkas. Asta trd-edjn as `n qua Ytakmhd` ``dld ‘`d irfstd`fzdifùk‖. _nr `d irfstd`fzdifùk a`nejatn dldmn sa hd``d trdksbnrldmn ak uk sar mfbarakta ma n qua as y

suparfnr d æ` lfsln. _nr astn as pnr `n qua _rnust mfia qua a` dlnr assuejatfvn, y qua dldlns, kn d saras radàs, sfkn d saras qua knsntrnsiradlns. Astn majd ma sar varmdm ak idsn ma ukd dmlfrdifùk àcìtfld.Astd ``dld kdifakta sa dpdcdrìd prnktn sf d`cúk snp`n ma aspardkzd,pnr `fcarn qua sad, kn `d radkfldsa. Qkd lfrdmd, ukd prasfùk ma `dldkn, ukd raspuastd uk pnin vfvd d astflu`dk aksacufmd. _arn niurratdlefæk qua `d iartfmulera y `d sacurfmdm ldtdk a` saktflfaktn.



Barmfkdkm ma Ydussura

A` sfc`n XX fkstdurd n qua sa maknlfkd d fkcðìstfidlnmarkd, iuyn bukmdmnr as sfk ùcdr d mumds, a``fkcðfstd sufzn, kdifmn ak Cfkaerd, Barmfkdkm maYdussura (4813-4649).

_drd Ydussura, a` idlpn ma d fkcðìstfid inlprakma tnmds dsldkfbastdifnkas ma` akcudja huldkn, tnmds ds bnrlds axprasf-

vds sfk mfsirflfkdr aktra euakns y ld`ns usns y sfk inksfmardr, a`crdmn ma ifvf`fzdifùk ma sus hde`dktas. @d tdrad ma d `fkcðìstfidas pnr `n tdktn, rad`fzdr `d masirfpifùk a hfstnrfd ma tnmds `dsàkcuds, akinktrdr `ns prfkifpfns cakardàs ma sus sfstalds y,bukmdlaktd`lakta, mas`fkmdrsa y mabfkfrsa a``d lfsld.

• @ùcfid sfleù`fid ma Ldkua` Cdrrfmn• Bukmdlaktns ma `fkcðìstfid ma U. Yflnka• @fkcðìstfid cakard` ma Barmfkdkm ma Ydussura

• @fkcðìstfid cakard` y dp`fidmd ma Ä. @ùpaz Cdriìd• Fktrnmuiifùk d `d `fkcðìstfid ma L. Barkäkmaz _æraz• Edsas pdrd a` astumfn ma` àkcudja ma A. Ldrtìkaz Ia`mräk• Inkniflfaktn y akcudja ma Äkca` @ùpaz Cdriìd y Eadtrfz

_dú`s Cd``drmn• @d sfktdxfs ma `ns ra`difnkdktas suprdnrdifnkdàs ma

I. Buaktas Unmrìcuaz

i ì r i u

` n m a

ait n r a s



Nedld dbfrld qua d`cukns rulnrassnera æ` snk fksu`tdktas pdrd `ns lusu`ldkas Jfl Guhkhakk

As ukd erdsd qua Edrdig Nedld hd trdtdmn ma dpdcdr ukd y ntrd vaz,pdrd var`d drmar ma kuavn sfalpra: vìkiu`ns ink a` fs`dlfsln, rulnrasd`flaktdmns pnr bd`sds dsnifdifnkas a fksfkudifnkas.

Nedld y su idlpdôd radiifnkdrnk buartalakta astd saldkd iudkmnsa pue`fiù ak Fktarkat ukd bntn ma æ` ink uk dtuakmn trfed` snld`ì. V`ns a`ncfns qua raifefù a` mnlfkcn ma @nufs Bdrrdghdk, lfkfstrn ma `dsaitd Kdifùk ma Fs`dl, mfarnk ùcdr d fktarrncdktas ak a` maedta prasf-makifd` ma` ldrtas pnr `d kniha, y tdlefæk ak ukd raukfùk prfvdmd a`bfk ma saldkd ink ukns jumìns prnlfkaktas ma Iàva`dkm.

Ak a` maedta, Nedld rapftfù sus irìtfids snera `ns puktns ma vfstd maBdrrdghdk, qua hdk fkiùfmn kularnsns inlaktdrfns dktfsalftds. Viudkmn sa vfn prasfnkdmn, raihdzù a` raspd`mn ma Bdrrdghdk ak `dinktfakmd prasfmakifd`.

A maedta


Yasfùk

5



5

B n t n s t n l d m d s m a S f g f p a m f d

A` sakdmnr fksfsta ak qua æ` as irfstfdkn, y qua sa aktracù d su idrcn ju-rdkmn snera d Efe`fd ma su bdlf`fd. _arn ak Fktarkat y d`cukns prncrdldsrdmfdàs, y ak ukd prasaktdifùk ma idlpdôd ma LiIdfk astd saldkd,

`n masirfeak bd`sdlakta inln uk lusu`läk ink turefns vìkiu`ns, yakbdtfzdk su sacukmn knlera, Hussafk, qua d` púe`fin à raiuarmd a`ma` mfbuktn mfitdmnr ma Frdg.

‐Yf hdy d`cufak qua tnmdvìd astä inkbukmfmn ink `ns haihns, yn kukidha sfmn lusu`läk“, as mfjn Nedld d ns mfrfcaktas jumìns ak Iàva`dkm,sacúk ukd trdsirfpifùk ma `d sasfùk prfvdmd.

@d bntn ma Nedld ink su fkmulaktdrfd trfed` snld`ì, tnldmd pnr ukbntùcrdbn ma D_ murdkta ukd vfsftd ak a` 5??2 d` pdìs kdtfvn ma supdmra, rasurcfù pnr Fktarkat ak lamfn ma dàcdifnkas kn prnedmdsma qua `d astdedk ifriu`dkmn lfalerns ma `d idlpdôd ma Hf``dryI`fktnk. @d idkmfmdtd y sus dyumdktas mfiak qua kn hdk takfmn kdmdqua var ink asn, parn `d idlpdôd ma Nedld `ns diusd ma mamfidrsad ‐varcnkznsns y nbaksfvns fktaktns

ma fkmuifr talnr“.

A` ldrtas, a` idkmfmdtn rapue`fidkn Jnhk LiIdfk irftfiù ldridmdlaktaukds pd`derds ma fktrnmuiifùk quad`cufak utf`fzù d` prasaktdr`n pnr a`lnmn ak qua sa rabfrfarnk d Nedld.

A` prasaktdmnr Ef`` Iukkfkchdl sarabfrfù d` sakdmnr tras vaias inln‐Edrdig Hussafk Nedld“ y d` fktrn-muifr d LiIdfk fkmfiù qua Nedldard ‐uk pn`ìtfin lariakdrfn, astf`nIhfidcn“.



A` maedta as ukd axpnsfifùk ma tasfs dktd-cùkfids diarid ma uk matarlfkdmn tald,as ukd inkstruiifùk ma drculaktns quasa vdk ma`fkadkmn y dbfdkzdkmn ak `d

lamfmd inln `ds pnsfifnkas ma `ns fk-vnùirdmns puamak malnstrdrsa n pnr a`

inktrdrfn, marruledrsa iudkmn `d sn`fmaz ma`pnmar ma inkvfiifùk ma `ns alfsnras n `d i`drfmdm

ma jufifns as pnera y idrakta ma pasn.

A` maedta as ukd tæikfid qua sa axpdkma läs d``ä ma` aktnrkn didmælfin,

parn ak æ` as luy utf`fzdmd pdrd ajariftdr `d axprasfùk nrd` y asirftd ak `nsastumfdktas, dsì inln pdrd dyumdràs d hf`vdkdr fmads ak bnrld inharakta,dlp`fdr su vnideu`drfn, masdrrn``dr su idpdifmdm drculaktdtfvd y bnlaktdra` trdedjn ma fkvastfcdifùk maktrn y buard ma` du`d.

As flpnsfeà ascrflfr ukns puktns ma vfstd sfk uk dpnyn sarfn. _nr n tdktn,ukd fkvastfcdifùk jufifnsd as `d úkfid drld qua raspd`md `d fktarvakifùkma idmd pdrtfifpdkta.

_nr trdtdrsa ma ukd mfsiusfùk ma pnsfifnkas dktdcùkfids, as flpnrtdkta qua`ns pdrtfifpdktas dsuldk masma a` fkfifn ukd ditftum tnàrdkta y ldkajakukd lakta defartd qua parlftd snpasdr y diaptdr `ns aàlaktns ma jufifnqua a` ntrn hdyd axpuastn, sf astns snk sarfns y nejatfvns.

Ak tnmn maedta sa dspfrd `àcdr d ukd inkiùsfùk. @d lamfdifùk ma uk

tariarn as i`dva pdrd su masdrrn``n y ma d``ì, `d aàiifùk ma uk lnmardmnr,iuyd bukifùk inksfsta ak mdr `d pd`derd d `ns pdrtfifpdktas, id`ldr `ns äkf-lns iudkmn a``ns sa axd`tdk, `àvdr a` maedta pnr uk idlfkn qua pnsfef`ftaukd pnstarfnr inkiùsfùk, ranrfaktdr a` maedta iudkmn tnla ntrn rulen.

]dlefæk maea inktalp`drsa `d pdrtfifpdifùk ma uk sairatdrfn pdrd quatnla kntd ma `n mfsiutfmn y sfrvd ma dpnyn d` lnmardmnr, iudkmn maedaxpnkar `d inkiùsfùk d `d iud` `àcù a` maedta.



Knrlds ak `d prapdrdifùk y rad`fzdifùk

Inln tnmd tæikfid, a` maedta axfca iulp`fr ifartds knrlds qua sa maeaktakar ak iuaktd:

• _uktud`fzdr a` tald qua sa vd d maedtfr.• Fkvastfcdr a` tald y prapdrdr ns snpnrtas pdrd mdr sn`fmaz d` mfsiursn.• Yaàiifnkdr `d dyumds kaiasdrfds sf a` tald `n rai`dld (mfdpnsftfvds,

vfman eadl, ati.).• Avdùdr y takar i`drfmdm snera a` nejatfvn qua sa eusid ak a` maedta.• Astdeàiar `ds rac`ds qua racfräk a` maedta.•

Asincar uk lnmardmnr y uk sairatdrfn.• Nrcdkfzdr d `ns pdrtfifpdktas (aktra iudtrn y nihn parsnkds).• Yfkirnkfzdr a` tfalpn ma idmd fktarvakifùk d bfk ma hdiar aquftdtfvd

`d pdrtfifpdifùk.

_drd takar ak iuaktd

A` maedta kn as ukd puckd ak `d iud` sa ùihd pnr cdkdr `d edtd``d, tnmn `n

inktrdrfn, as ukd npnrtukfmdm pdrd inktrdpnkar inkiaptns y dìdkzdr ukdsnùifùk n aspaiìbfidlakta, ukd inkiùsfùk. _nr `n tdktn, as flpnrtdkta:

• Asiuihdr dktas ma maedtfr.• Yar inkiratn.• Kn inkvartfr `d fktarvakifùk ak uk lnkù`ncn.• _amfr `d pd`derd d` lnmardmnr.• Kn axd`tdrsa, dprakmar d asiuihdr y parlftfr d inkiùsfùk ma d fmad.• Inkstrufr sus drculaktns y utf`fzdr ns snpnrtas iudkmn sad kaiasdrfn.• Kn utf`fzdr `d frnkìd pnrqua puama harfr susiaptfef`fmdmas y prnvnidr

uk akbraktdlfaktn.• Kn raedtfr ink drculaktns djakns d `d fmad qua sa astä p`dktadkmn.• Qtf`fzdr uk vnideu`drfn dmaiudmn d `ds ifriukstdkifds.• A`flfkdr a` àkcudja raeusidmn qua puamd mdr ntrn saktfmn d `ns

puktns ma vfstd n iradr dlefcðamdm.



5

4. Asinjdk ukd ma ds sfcufaktas npifnkas, y nrcdkfiak uk maedta ak a` du`d ma i`ds

d. @ns iaktrns amuidtfvns maeak nrfaktdr d idrrard ma ns astumfdktas masa` sæptfln crdmn. _nr `n tdktn, sacúk `d `ìkad asincfmd (taikn`ùcfid, ifatìbfid, huldkfstd), d`cukds ldtarfds maeak a`flfkdrsa ma` prncrdld.

e. Maearìd sar ne`fcdtnrfd, ukd ldtarfd nrfaktdmd d` inkniflfaktn madcrfiu`turd.

i. D pdrtfr ma` crdmn mæifln, `ns astumfdktas maearìdk raifefr ukd i`dsa i

ækbdsfs ak a` trdedjn ldkud` (idrpfktarìd, dèdôfàrìd, iu`fkdrfd, ati.).

5. Ak suecrupns ma safs parsnkds, mfsiutdk sus npfkfnkas diarid ma ns inlaktdrma `d @aiturd ma fktrnmuiifùk.

9. @d lakifùk ma `ns jumìns ma Iàva`dkm, quæ ra`difùk tfaka ink `d sftudifaxpuastd ak a` taxtn ma Guhkhakk.

=. ¾Iuäàs snk sus pnsfifnkas diarid ma d bfcurd ma Nedld> _rasaktak pnr asir

`ds inkiùsfnkas ma `ns iudtrn puktns.

4. A` drtìiu`n ma Jfl Guhkhakk prasaktd ukd sarfa ma fmads ink ra`difùk dditud` prasfmakta ma `ns Astdmns Qkfmns, Edrdig Nedld. Ak su maedtainln idkmfmdtn, Nedld sa mabfakma dkta ukd sarfa ma inlaktdrfns: ¾quædrculaktns sa axpnkak pdrd cakardr asta maedta>

5. ¾Tuæ prneàlätfid sa asinkma trds `d dbfrldifùk bntncräbfid ma Nedldink uk dtuakmn trfed` snld`ì>

9. ¾@ns inlaktdrfns prasaktdmns raspnkmak d ukd inktfakmd ad` y tnàrdkta=. ¾D quæ inkiùsfùk n snùifùk `àcdrnk `ds pdrtas>

4



Idrtd rabarakifd`

Ak `d idrtd, sa fkiùyak `ds idrtds nbfifdàs y `ds idrtds inlarifdàs. @d idrtd as mniulaktn ldastrn pdrd a` iud` maealns masdrrn``dr varsdtf`fmdm y dcf`fmdm, puasfk flpnrtdr prnbasfùk, nbfifn, mncld, rdzd, axtrdiifùk snifd`, inkmfifùk iu`turd` prabarakifds parsnkdàs, sarä sfalpra pdsn ne`fcdmn pdrd idsf tnmns `ns prniasn

A` dvdkia taikn`ùcfin hd idlefd-

mn a` saktfmn y a` inktakfmn ma`d idrtd. Hny ak mìd, `d mfkälfidma` àkcudja bærtf`, axueardkta yprùmfcn ak sustdktfvns, dmjatfvnsy dmvarefns qua idrditarfzded d didrtd, sa hd ramuifmn d n inkira-tn a flparsnkd` qua mfstfkcua d`d vfmd inktalpnräkad. Dsì puas,dktas sn`ìdlns maifr qua `d idrtdard vftd`, parn hny hde`dlns ma`d idrtd rabarakifd` y su idräitarflprasifkmfeà.

@ds idrtds


Yasfùk

9



_drd dprnpfdrkns ma `d astruiturd pramnlfkdkta ma ukd idrtd rabarakifd`, sfcdl`ds sfcufaktas sucarakifds:

FINK]AI suprflfù a` Dtk n Dtakifùk hdia ukns 4? dôns. Aksu ucdr, sa asirfea Jaba ma Yaiifùk, sf kn sa inknia a` knlerama` raspnksdeà.

BAMAUFIN LÆKMAZMaidkn ma HuldkfmdmasQKFRAUYFMDM JDRAUFDKDMfraiifùk inlpàtdEncntä, M.I.

YaônrBAMAUFIN LÆKMAZMaidkn ma HuldkfmdmasQKFRAUYFMDM DQ]ÙKNLD MA LÆXFINMfraiifùk inlpàtdLæxfin, M.B.

Mnitnr

4. Baihd. Maea fkmfidrsa prflarn `d ifumdm, sacufmd ma ukd inld y ùaa` mìd, a` las y a` dôn. Uainrmalns qua `ns dôns kn `àvdk puktn y q`d àtrd fkfifd` ma `ns lasas sa asirfea ak lfkúsiu`d.

5. Akideazdmns n mfrfcfmns. ]ìtu`n n mfckfmdm ak `d prflard `ìkad. Knleak àtrds ldyúsiu`ds. @uacn vfaka a` idrcn y knlera ma `d alprasdfkstftuifùk ak àtrds ldyúsiu`ds. Bfkd`fzd ink `d mfraiifùk inlpàtd y ntrn rakc`ùk, `d ifumdm ak ldyúsiu`d nrtncräbfid, sacufmd ma M.B. n Msacúk a` idsn. A` akideazdmn puama takar hdstd nihn `ìkads.

Ajalp`ns:

Ajalp`n: Ifumdm ma Læxfin, 42 ma ldrzn ma 5?4?.



9. @ìkad ma aktrdmd n sdùmn. As npifnkd` y pnr `n tdktn, puama nlftfrsa.

=. _rflard `ìkad ma` iuarpn. Maea sdùmdr ak uk tnkn sakif``n y avftdr `

brdsas ma idjùk, pdrd avftdr a` mfstdkifdlfaktn ink a` mastfkdtdrfn y prnpifdrà ifartd ratfiakifd pdrd àar y inlprakmar a` rastn ma `d idrtd. Idmvaz qua sa mfspnkcd d asirfefr ukd idrtd, pfaksa ak a` mastfkdtdrfn y, mpakmfakmn ma qufæk sa trdta, derd a` taxtn ink ukd nrdifùk, uk sdùmn ukd dùsfùk qua sù`n takcdk qua var ink æ`. Astd inkmfifùk à p`dktadsfkiard inrmfd`fmdm y praniupdifùk ma su pdrta hdifd æ`, n iud` ramukmdak eakabfifns d` lnlaktn ma aspardr rasu`tdmns snera a` bfk qua parsfcu

a` inktakfmn ma `d idrtd.

Ajalp`ns: Dpraifdmn saônr Ldkrfqua:

Dpraifdmd mnitnrd Barkdkmd: Uaspatdmd mnitnrd I`drd Fkæs:

Uaspatdmn mnitnr Rdàkifd:

Astfldmn saônr Dpa``fmn:

Ajalp`ns:

• _arlìtdla ba`fiftdr`n dktas qua kdmd, pnr su `úifmn mfsiursn…

• Kn sfk dktas axtakmarà uk dbaitunsn sdùmn, qufarn p`dktadrà…

• Dktas qua kdmd maen ba`fiftdr`n, trds hdear àìmn su drtìiu`n…

1. Iuarpn. Maea astdr inlpuastn ma pärrdbns ma tras n iudtrn `ìkads pdqua `d idrtd sad aktakmfeà räpfmd y i`drdlakta. @ns pärrdbns maeak nbraiar fmads inkifsds y mfraitds axpuastds ink ùcfid y inharakifd. Iudkmn inktakfmn ma ukd idrtd prasaktd mfvdcdifnkas, raftardifnkas n praäleu`n



2. Ifarra n maspamfmd. D` fcud` qua a` sdùmn, a` ifarra maea sarsakif``n n brdtarkd` sacúk sad a` mastfkdtdrfn, y a` ulerd` ma `dbfrld puama nlftfrsa ak `ns idsns iudkmn sa bfkd`fzd ink ukdnrdifùk ma axpaitdtfvd inln: Tuamn d `d aspard ma sus crdtds

kntfifds n Ya maspfma ma ustam, masaäkmnà ns lajnras rasu`tdmnsak a` prnyaitn qua alprakma.

_arn sf kn hdy asta tfpn ma ifarra, a` ulerd` puama sar: Inrmfd`-lakta7 Inrmfd` sdùmn7 Lf` crdifds7 Ma ldkard dtaktd7 Dtaktd-lakta, ati.

3. Bfrld. A` knlera maea asirfefrsa ak `d lfsld bnrld inln sa

asirfefù a` knlera ma` mastfkdtdrfn. Ak d ìkad sfcufakta, a` idrcnn kúlarn ma fmaktfbfidifùk, sf buara a` idsn.

Ajalp`ns:

… asparn qua `d prnpuastd sad ma su aktard sdtfsbdiifùk,

Amudrmn Idktf``n Mfraitnr ma prnyaitns

Inrmfd` sdùmn,

Dldmd Ä`vdraz Innrmfkdmnrd

Ajalp`n:

MDRFM LD]AN @NKMNÔNMfraitnr ma drtas



Ma` asirftnr ihain Brdkz Gdbgd, takalns ukdvarmdmard cdàrìd ma idrtds aktra `ds iudàsastäk ds idrtds d su dlfcn Ldx Ernm, asirftdsmurdkta 5? dôns, masma 46?= d 465=. @dsidrtds d Lfàkd, ntrn `niudz tastflnkfn ma`dlnr púmfin qua aledrcù d Gdbgd murdktatnmd su vfmd, ma `d akbarlamdm pu`lnkdrqua `n lfkù, ma uk mfä`ncn diarid ma `dsftudifùk ainkùlfid, alnifnkd` y `denrd`tnrlaktnsd qua subrfù.

@d idrtd d` pdmra pnr su pdrta, as uk asirftninkbfmakifd`, mascdrrdmnr y `ftardrfdlaktapsfin`ùcfin, ak a` iud` Gdbgd à masirfea dsu pdmra `d fkbùakifd qua æsta ajarifù ak suidräitar. Ya trdtd ma uk mniulaktn qua kuk-id `àcù d ldkns ma` pdmra y inkstd ma ukds4?? päcfkds kdrrdmds ak uk astf`n flpaideà.

Brdkz Gdbgd


rù d uk dlfcn qua lfaktrds asirfeìd, paksded qua asds idrtds pnmr`àcdr d pue`fidrsa maspuæs ma su luarta.

• @ds idrtds ma Idlf`à I`duma`, flpnrtdkta asiu`tnrd, harldkd pnatd y mrdldturcn _du` I`duma` y akdlnrdmd ma` asiu`tnr DucuUnmfk. Astds idrtds buarnk asirftds masma a` ldkfinlfn ak mnkbua inkbfkdmd hdstd su luarta pnr su harldkn, y snk tastflnkfn `d súp`fid qua murdkta 9? dôns à hfzn Idlf`à d _du`, sfk qua buaasiuihdmd jdläs. Idsf tnmd `d nerd ma Idlf`à bua mastrufmd pnr alfsld trds idmd maprasfùk, y `d snlerd qua ajarifù Unmfk ak su vfbua subfifakta pdrd ldtdr`d.



9

Ak pdrajds, masdrrn`àlns uk ajalp`n ma ukd idrtd parsnkd` y ukd idrtd rabarakifd

_drd d prùxfld sasfùk a`denralns iudtrn ajalp`ns ma idrtds ak mnkma hdcd-lns `d sn`fiftum ma uk alpàn, ntrd ak `d qua hdeàlns ma dlnr n dlfstdm,ntrd idrtd inktdkmn uk dinktaiflfaktn flpnrtdkta d uk bdlf`fdr n uk dlfcn,y pnr ú`tfln ukd idrtd mnkma axpnkcdlns ukd rakukifd d uk idrcn ak iud`-qufar alprasd ma su fldcfkdifùk y `ns lntfvns qua sustaktdk astd rakukifd

• @n lajnr pdrd inksacufr a` nejatfvn inlu-kfidtfvn ma ukd idrtd, as alpazdr ink ukd

nrdifùk kn trdmfifnkd`.

• A` drta ma `ncrdr ukd idrtd erava, inrtæs yinkiratd as inksfmardmn pnr luihns inln a`cækarn ftardrfn läs inlpàjn qua axfsta. ¾_nrquæ> @d idrtd pravæ, inktalp`d y kaiasftd mauk fktar`niutnr pdrd iulp`fr su nejatfvn, y akasd lamfmd, idmd nrdifùk maea sar astumfdmd

d inksifakifd, pnrqua `d fktarpratdifùk quaa` mastfkdtdrfn hdcd ma ds pd`derds, as dsuktnqua sa sdà ma `ds ldkns ma` ralftakta ak a`lnlaktn iudkmn `d idrtd tdlefæk `n hdia.

5



A` fkbnrla axfca uk inkniflfaktn axhdustfvn ma` tald qua masdrrn``d,ukd fkvastfcdifùk ink su raspaitfvn prniasn ma inkbrnktdifùk y, pnrinksfcufakta, ukd inlpraksfùk axditd ma` dsuktn qua trdtd. @d rdzùkma mfihd axfcakifd as sflpà: a` fkbnrla, inln `n sucfara a` tærlfknlfsln, as a` snpnrta ink a` iud` sa mdk d inkniar `ns astdmfns pnr `nsiudàs pdsù ukd fkvastfcdifùk hdstd netakar ukds inkiùsfnkas. _arn dsìlfsln, pnmalns aktakmar`n inln a` racfstrn matd``dmn ma uk avaktn.Ak asta saktfmn, maiflns qua a` fkbnrla as rfcurnsn y latùmfin7 as i`drn

ak `d bnrlu`difùk ma fmads y inharakta ak `d suiasfùk ma `ns haihns nhfpùtasfs, y parsfcua ukd bfkd`fmdm inlukfidtfvd inkiratd.

I`dsfbfidifùk

• Fkbnrla `ftardrfn

Astd maknlfkdifùk sa às md d `ns mniulaktns `ftardrfns qua ak su asquakdrrdtfvn alpàdk d tæikfid ma` fkbnrla, efak sad pnr `d saiuakifd mniultd` inln astä p`dktadmn a` ra`dtn n pnrqua a` vd`nr `ftardrfn ma` ra`dtn lfslpnkmard a` fkbnrla. Asta tfpn ma fkbnrla sa puama inkstrufr d pdrtfr ma haih

A fkbnrla


Yasfùk

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• Fkbnrla fkvastfcdtfvn

Astd idtacnrìd sa suemfvfma ak iudtrn i`dsas:

4. Fkbnrla didmælfin. _rnmuifmn ak a` inktaxtn asin`dr n ukfvarsftdrfnQk astumfdkta ma inàcfn n ma ukfvarsfmdm astä ak idpdifmdm ma cakaruk fkbnrla, edsdmn ak ukd talätfid pravfdlakta axpuastd ak i`dsa pna` prnbasnr n hdiar`n d pdrtfr ma d inlpraksfùk ma ukd n vdrfds aiturdn ma ukd fkvastfcdifùk rad`fzdmd.

5. Fkbnrla prniamflaktd`. _rnpfn ma nrcdkfzdifnkas prnmuitfvds. Ya trdma fkbnrlas abaitudmns pnr `ns prnbasfnkdàs, ink edsa ak prniasn

`denrdàs, dmlfkfstrdtfvns, fkvastfcdtfvns, taùrfins n ifaktìbfins, pdpnkar ak ldrihd uk p`dk ma trdedjn, flpàlaktdr inrraitfvns snerprneàlds mataitdmns n prnpnkar tanrìds bf`nsùbfids n ifaktìbfids.

9. Drtìiu`n ifaktìbfin. As prnmuitn ma ukd fkvastfcdifùk ma nrmak aspa

ifd`fzdmn, inln `n puama sar ukd tasfs ma ldastrìd n ukd fkvastfcifùk ma mnitnrdmn, ati. Astns fkbnrlas raifeak a` knlera ma drtìiuifaktìbfin iudkmn snk pue`fidmns pnr ravfstds didmælfids n ifaktìbfid

aspaifd`fzdmds, iuyn irftarfn amftnrfd` astä edsdmn idsf sfalpra, ak inrrnenrdifùk ma ns mdtns axpuastns ak a` fkbnrla n ak d iramfef`fmdma `d iud` cnia a` dutnr ak asa tald aspaiìbfin. Astd i`dsa ma fkbnrlkn raqufara `d saclaktdifùk latnmn`ùcfid qua axfcak a` didmælfina` ifaktìbfin. As maifr, d` sar pue`fidmn ak ukd ravfstd, su inktakfmn aläs inkifsn y inkiùyakta, y a` àkcudja läs bùfmn. _nr `n cakard`, dutnr ma uk drtìiu`n ifaktìbfin as uk axpartn qua hd haihn pue`fidifnkas ma mniulaktns läs axtaksns y prnbukmns d ldkard ma fkbnrlaifaktìbfins.

=. Fkbnrla ifaktìbfin. _uama prnvakfr ma uk drtìiu`n ifaktìbfin iuyd fkvatfcdifùk sa prn`nkcù n sa rdlfbfiù hdstd inkvartfrsa ak ukd prnpuasifaktìbfid ma ldynr trdsiakmakifd. Astns fkbnrlas snk axtaksns maefmd `d inlpàjfmdm qua ravfsta ukd fkvastfcdifùk ifaktìbfid y pnr `n cakard`, snk inlprnedmns pnr pdrta ma ntrns fkvastfcdmnras qua sa dpnydaspaifd`lakta ak `ns lætnmns y prniamflfaktns qua a` fkvastfcdmn



Bdsas ma` fkbnrla

Dukqua d astruiturd ma` fkbnrla sad astrfitd, mfraitd y latfiu`nsd, d suiasfùkma `ds fmads maea takar ukd `ùcfid sfstalätfid y masdrrn``dr a` tald ak bnrldprncrasfvd, axpnkfakmn `ds vdrfdeàs ma ldkard nrmakdmd y inkcruakta.

@n qua dktaiama d` fkbnrla

4. Fmaktfbfidifùk y puktud`fzdifùk ma` tald5. Uainpf`difùk ma `d fkbnrldifùk axfstakta9. Masp`dzdlfaktn d `d fkvastfcdifùk ma idlpn

=. Uad`fzdifùk ma akiuastds y astdmìstfids1. Dkä`fsfs ma` prneàld p`dktadmn y inkbrnktdifùk ink a` puktn ma pdrtfmd

Astruiturd ma` fkbnrla

4. ]ftu`dras. Maea takarsa i`drfmdm snera `n qua sa vd d inlukfidr ak a`fkbnrla, pdrd `ncrdr uk diartdmn tftu`dr qua astdrä inlpuastn pnr ukdktatìtu`n y uk tìtu`n bfaàs d` inktakfmn, sfk fktarpratdifnkas, aubalfslns

kf latäbnrds. Yfk aledrcn, su a`denrdifùk puama sar `d ditfvfmdm bfkd`,iudkmn `d dprnpfdifùk ma` tald astä ak uk euak puktn ma` masdrrn``n.

5. Yfknpsfs n rasulak. _`dktad `d asakifd ma `d fkvastfcdifùk n ma` taldtrdtdmn ak uk lìkfln ma safs `ìkads. _uama prasaktdr uk asquald c`ned`ma` dsuktn fkvastfcdmn, ukd inkiùsfùk n `d bnrlu`difùk ma ukd fkiùc-kftd qua lntfvdrä d` àitnr pdrd qua sa fktarasa pnr `n qua vakmrä ak aìuarpn ma` fkbnrla.

9. Fktrnmuiifùk. Yu axtaksfùk puama bùitudr aktra ds mns y ds 41 päcfkds,mapakmfakmn ma `d axtaksfùk ma` fkbnrla. Maea fkiùfr `d flpnrtdkifdma` tald, ns prnpùsftns ma d fkvastfcdifùk y lnstrdr d`cukns dktaiamak-tas. @ns lætnmns ma fkvastfcdifùk utf`fzdmns murdkta a` prniasn, puamakfkiùfrsa ak `d fktrnmuiifùk n prasaktdr`ns ak a` saclaktn sfcufakta ma`taxtn.



=. Masdrrn``n. A` iuarpn ma` fkbnrla puama fkfifdrsa ink a` p`dktadlfaktnma` prneàld masma su bdsa läs aàlaktd`, uacn sa tanrfzd crdmud`laktalfaktrds sa astdeàia y inkbfrld d hfpùtasfs, hdstd àcdr d ds inkiùsfnkasqua drrnja `d fkvastfcdifùk. @ds hfpùtasfs sa inkiaktrdk ak axpnsfifnkas

inkiaptudàs, dkd`ìtfids n irìtfids, prnmuitn ma` mfsiarkflfaktn qua a`dutnr u ntrns dutnras hdydk haihn snera a` tald. Murdkta a` prniasn ma`masdrrn``n sa pnmrä axpnkar `ds fmads sacúk a` asquald ma `ds pfrälfmasma `d fkbnrldifùk, as maifr, alpazdr ink `n läs aàlaktd` hdstd `àcdr d`ds inkiùsfnkas läs raàvdktas. ]dlefæk sa puama pdrtfr masma `n läsinkiùyakta pdrd masakidmakdr ak `ns dspaitns ma laknr fkifmakifd.

1. Ifarra (sìktasfs y inkiùsfnkas). Qkd vaz astdeàifmn a` prneàld y

p`dktadmn `ds hfpùtasfs, sa masdrrn``d `d fkvastfcdifùk inrraspnkmfakta.Maspuæs, sa prasaktd ukd sìktasfs, as maifr, sa ramnkmad d fmad cakard` ynrcdkfzd uk idpìtu`n ink `ds inkiùsfnkas, dukqua yd `n hdyd haihn ak`d sfknpsfs, ak `d fktrnmuiifùk n d` fkfifdr `d pfrälfma ma` masdrrn``n. Maiud`qufar lnmn, a` dutnr maearä idtd`ncdr ds inkiùsfnkas qua puamakdinlpdôdr idmd brdclaktn, ak idsn ma qua kn sa rasarvak pdrd a` bfkd`.

2. Dkaxns. As tnmn ldtarfd` ma dpnyn qua inktrfeuyd d d lajnr inlpraksfùk

ma d fkvastfcdifùk prasaktdmd. @ns dkaxns sa kulardk ink atrds asirftdsak ldyúsiu`d y maeak sar nrcdkfzdmns pnr a` dutnr. Aktra `ns dkaxns saakiuaktrdk: akiuastds, aktravfstds, astumfns ma idsns, bntncrdbìds, drihfvns,crdedifnkas, iudmrns astdmìstfins y ma lamfifùk, ldpds, ati.

@ns fkbnrlas mdmns d `d ùz púe`fid vdk masma `ns läs puktudàs, inln `nsiaksns ma pne`difùk, hdstd `ns läs fldcfkdtfvns. Iud`qufard qua sad su kd-

turdàzd, a` fkbnrla ldktfaka uk rftln inlúk ak tnmns.

@d dktrnpù`ncd knrtadlarfidkd Ldrcdrat Ladm fktacrd ukd sarfa ma fkvas-tfcdifnkas rad`fzdmds aktra `ns puae`ns prflftfvns ma `ns ldras ma` Yur. A``dhdia ukd inktrfeuifùk d d dktrnpn`ncìd iu`turd` y d d psfin`ncìd snifd` pdrd dinlpraksfùk ma d`cukns ma `ns prneàlds idpftdàs ma kuastrn tfalpn. Astnsastumfns snk pue`fidmns pnr sapdrdmn ink `ns tìtu`ns Dmnàsiakifd y iu`turd7Amuidifùk y iu`turd7 Yaxn y talpardlaktn.



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@adk uk drtìiu`n snera vfnàkifd y ld`trdtn inktrd `d fkbdkifd ak In`nlefdy a`denra uk fkbnrla didmælfin d pdrtfr ma `d àiturd. Fkmfqua quæ buaktautf`fzù y qufæk `n asirfefù.

@ns fkbnrlas vdrìdk ak su inlpàjfmdm y axtaksfùksacúk sad a` tald y, aspaifd`lakta, a` kfva` ak aìud` sa akiuaktra a` astumfdkta. Qk fkbnrla asin`drpuama takar tdk sù`n mns päcfkds, ak tdktn pnsad`ds vdrfdeàs qua `n idtd`ncuak inln td`: prneà-

ld, hfpùtasfs, sìktasfs y inkiùsfnkas. Kn nestdkta,`d raspnksdef`fmdm ma mdr snùifùk d` prneàldp`dktadmn kn raida snera a` fkbnrla. Æsta sù`n saakidrcd ma axpnkar n iuastfnkdr `d sftudifùk y, sfas prnmuitn ma ukd fkvastfcdifùk qua nbrazid `dvfdef`fmdm ma `d snùifùk, æstd sarä fkiùfmd. Qkfkbnrla puama sar prnmuitn ma ukd prn`nkcdmdfkvastfcdifùk qua tnla lasas n dôns.

Ink dyumd ma sus inlpdôarns y su mniakta trdksbnrldmnr n trdksbnrldmnrd insfcdk vdrfns ajalp`ns ma fkbnrlas.

Ma ldkard fkmfvfmud` ravfsa ns fkbnrlas y asirfed ds mfbarakifds aktra a``ns y iùl`ns i`dsfbfidrìd.

4



A` iuaktn ma` inifkarnCanbbray Ihduiar

Qkd vaz vfvìd uk dprakmfz ak kuastrd ifumdm, qua trdedjded ak uk inlar-ifn ma inlastfeàs. Ard läs dàcra qua uk jf`cuarn sua`tn pnr a` ensqua.Ard uk luihdihnta cudpn, parn d`cn edjftn, luy lnrakn y `àvded supa`n kacrn aàcdktalakta pafkdmn.

Edf`ded tdk efak y tdk dkfldmdlakta, qua a dpnmdedk Jdrdkarn _argfk.]nmd ihfid qua sa juktded d æ` takìd suarta, puas æ` astded àkn ma dlnry `dsifvfd inln ukd in`lakd ma lfa`.

Edf`ded y idktded ak tnmds `ds enmds y à takìd läs dbfifùk d `d tdearkdqua d `d tfakmd, puas sfalpra qua hdeìd ukd prniasfùk pnr Ihadpsfmasd`ìd mfspdrdmn ma `d tfakmd trds a``d y kn racrasded hdstd qua hdeìd edf-

`dmn `n suyn y hdeìd vfstn tnmn `n qua hdeìd qua var… Ya raukìd ak ukdid`à n ak ntrd pdrd jucdr d `ns mdmns7 puas kn hdeìd kfkcúk dprakmfz ak`d ifumdm qua aihdsa `ns mdmns lajnr qua _argfk. Dmaläs, ma hurtdmf-``ds, ard uk marrnihdmnr. Astn `n masiuerfù su dln d sus axpaksds, puasluihds vaias sa akinktrù ink a` idjùk ma` mfkarn vdiìn. _nmæfs astdrsacurns qua iudkmn uk dprakmfz `n pdsd tdk efak aihdkmn `ns mdmns,

jucdkmn y ink lujaras, as a` muaôn ma `d tfakmd a` qua `n pdcd ink susidumdàs dukqua kn inlpdrtd a` jn`cnrfn

A iuaktn y sus nrìcakas


Yasfùk

1



Dukqua a` dprakmfz sapd tnidr a` vfn`ìk y `d cuftdrrd, sus juarcds y juacn`ns pdcd a` rnen. _uas, inln pnmæfs var, `d hnkrdmaz y `d euakd vfmdsfalpra dkmdk mfsnifdmns, iudkmn sa trdtd ma cakta pnera.

Dukqua à racdôdedk kniha y mìd y d`cukds vaias ard `àvdmn d enlen

y p`dtf``n d d iäria` ma Kawcdta, a` dàcra dprakmfz parldkaifù ink sumuaôn, hdstd qua idsf tarlfkù su dprakmfzdja. _arn uk mìd, a` muaôn,ravfsdkmn su inktrdtn ma dprakmfzdja, sa dinrmù ma` prnvarefn quarazd: ‐Läs vdà drrnjdr `d ldkzdkd pnmrfmd qua majdr`d qua pumrd d`ds maläs“. @n lfsln niurra ink a` irfdmn prntastùk: as lajnr majdràldrihdr qua parlftfrà qua astrnpaa d `ns maläs irfdmns ma `d idsd.Ma lnmn qua a` muaôn a majù fera y a nrmakù qua sa ldrihdrd, ink

ld`mfifnkas snera su ideazd. Dsì bua inln a` dàcra dprakmfz inksfcufùsu feartdm. Dhnrd pnmrìd hdiar jdrdkd tnmd d kniha, sf dsì a dpataiìd._arn, inln sad qua kn hdy `dmrùk qua kn takcd uk inlpfkiha quaà alpuja d sdquadr y astdbdr d` qua hd rnedmn n astrujdmn, _argfkfklamfdtdlakta akvfù su idld y a` rastn ma su djudr d idsd ma ukinlpdôarn fksapdrdeà qua ard tdk dbfifnkdmn d ns mdmns, d` jn`cnrfny d `d mfsfpdifùk inln æ`…



@ns nrìcakas ma` iuaktn

A` nrfcak ma` iuaktn sa ra-

lnktd d `d dktfcðamdm (läsma =.??? dôns dträs), aktra`ns puae`ns nrfaktdàs su-larfns y acfpifns, fkmfnsy ihfkns, parn kn sa sdeaink praifsfùk a` lnlaktniudkmn dpdraifù `d prflardhfstnrfd. Ya aspaiu`d ink a`

knlera ma` crfacn @uifdknma Ydlnsdtd, kdifmn ak Yf-rfd, qufak asirfefù A` iìkfin yntrn vdstn kúlarn ma ra`dtnsma takmakifd lnrd`7 tdlefæksa lakifnkd d @uifn Dpuàyn, inknifmn ak d ditud`fmdm pnr su nerd: A` dskn ma nr

@n ifartn as qua a` cækarn as uk àcdmn dtrfeufmn d` mfsiursn nrd`, d `d kaiasfmdm minktdr. Dktas ma qua axfstfasak ns d`bdeatns, a` hnlera kdrrded ns haihns, utf`fzdenknldtnpayds pdrd mdrà praifsfùk d `ds fmads (n qufzä pdrd axprasdrsa). @n qua sa sdea, as qua a` ditn ma inktdr bua ukd ditfvfmdm fkbnrld` d `d iud` `àcdrnk `nhnleras prflftfvns maspuæs ma iulp`fr sus bdakds n ma vakfr ma d cuarrd, d`ramamma d hncuard. Ak sus iuaktns, kdrrdedk ds dvakturds y axparfakifds vfvfmds murdka` mìd n murdkta `ns `drcns vfdjas, ink uk tnqua ma ldcfd y bdktdsìd, rasu`tdmn ma sra`difùk ink `n lìtfin.

@ns parsnkdjas ma `ds hfstnrfds ardk pnrtdmnras ma uk paksdlfaktn inàitfvn qurabàjdedk mumd, talnr y snrprasd brakta d `ns bakùlakns kdturdàs qua kn pnmìdaxp`fidr. Astns ra`dtns pdsdedk pnr suiasfvds cakardifnkas, sa akrfquaiìdk, inlp`laktdedk n trdksbnrldedk, crdifds d `d prnbusfùk ma` paksdlfaktn pnpu`dr, maàtdkmn d `ns asiuihds y aksaôäkmnàs d mfbarakifdr `n euakn ma `n ld`n. D tnmn assa suldrnk `ns bfkas ra`fcfnsns, pamdcùcfins y lnrdàs qua tdlefæk hfifarnk la`Ìnk a` pdsdr ma `ns sfc`ns, a` iuaktn bua dmnrkdmn ink kuavds fläcakas sucastfvd



A` iuaktn ak Nrfakta

Ak Ihfkd, a` iuaktn ak bnrld ma bäeu`dmastdiù pnr su fktakifùk sdtìrfid y irìtfidma d snifamdm. Ak Fkmfd, A` _dkihdtdktrd eusiù aksaôdr prfkifpfns lnrdàs d `nshfjns ma` ray Dldrdsdgtf, parn bua ink`ns ärdeas qua kdifarnk `ns iuaktns bdk-tästfins ma D`b @dy`d wd @dy`d, trdmuifmnsedjn a` knlera ma: @ds lf` y ukd kniha

(kniha y kn knihas, inln ma ldkardarrdmd sa sfcua lakifnkdkmn), ak `nsiudàs sa hf`vdkd ukd hfstnrfd trds ntrd,maktrn ma uk lfsln iuaktn, a` ma Yhara-

zdmd qua ink a` bfk ma sd`vdr su vfmd, sainkvfarta ak inktdmnrd ma hfstnrfds pdrda` su`täk (su aspnsn y vfitfldrfn). Crdifdsd `d pd`derd asirftd, luihns ma dqua``nsiuaktns buarnk rainpf`dmns y sfrvfarnkma ajalp`n y lìlasfs pdrd ukd bnrld`ftardrfd qua alpazded d inksn`fmdrsa.

A` àcdmn ma `ns puae`ns nrfaktdàs ink-mflaktù a` inktakfmn ma `n qua hnyinknialns ink asta knlera (sfk inktdr

ink dqua``ds ntrds iu`turds aurnpads iuyndpnrta saktù `ds edsas pdrd `ds sfcufaktascakardifnkas). @d `àcdmd ma pfrdtds nasi`dvns qua rainrrìdk a` Rfajn Lukmn,buarnk dlp`fdkmn `ds varsfnkas y din-lnmäkmn`ds d pdrtfr ma` inktaxtn snifd`,iu`turd` y ra`fcfnsn ma `ds lú`tfpàs snifa-mdmas inktfkaktdàs


A` _dkihdtdktrd.



@ds hfstnrfds ak `d Amdm Lamfd

Murdkta tnmd `d amdm lamfd, a` iuaktn dìdkzù uk aspaifd` sfckfbfidmn. A` fkbdk

mnk Judk Ldkua`, pnr ajalp`n: ak su `fern ma Ajalp`ns qua prnvakìdk ma @ds ly ukd kniha, irad ukd nerd amuidmnrd. Läs d``ä astuvn Ihduiar qua d`fôù ink spdrtfiu`dr tnqua, dqua` astf`n qua sa vakìd bnrldkmn ak ntrd pdrta ma` Inktfkaktaparn bua Eniidiifn qufak à mfn uk cfrn d` inktakfmn y d `d bnrld ma` cækarn. @bdktästfin sa lazi`ù ink `d rad`fmdm y `d hfstnrfd, ink a` hulnr y `d frnkìd irìtfid.

Ak a` sfc`n XRFF, dutnras inln Ihdràs _arrdu`t inlpf`drnk dqua``ns hfstnrfds mfrfcfmd uk púe`fin fkbdktf` qua sa trdtded inln dmu`tn (Idparuiftd Unjd, E`dkid Kfava

_u`cdriftn, ati.), y iuyd fktakifùk pravaktfvd, amuidmnrd y lnrd` sa rabàjded ak lnrdàjd, uk aàlaktn prnpfn ma `ds bäeu`ds.

Uainrmalns ukd ma `ds nrdifnkas ma `d hfstnrfd ma Idparuiftd y su raspaitfvlnrdàjd:

‐Idparuiftd rnjd samaskumù y bua d la-tarsa ak `d idld,mnkma sa quamù luysnrprakmfmd d` variùln ard su deua`dak idlfsùk“.



Lnrdàjd

Ralns dquì qua `ns dmnàsiaktas y läs `ds jnvakiftds aàcdktas,efak haihds y enkftds, hdiak ld` ak nìr d ifartds caktas, y qua knhdy qua axtrdôdrsa ma d ernld ma qua d tdktds a` nen sa ds inld.Mfcn a` `nen, pnrqua asns dkfldàs kn tnmns snk fcudàs: `ns hdyma uk idräitar axiaàkta y hulnr dbdeà, muìa y inlp`difakta,qua sfk rufmn, sfk hfa` kf frrftdifùk parsfcuak d jùvakas mnkia``ds,`àcdkmn maträs ma a``ds d `d idsd y hdstd `d hdeftdifùk. ¾Tufæk

fcknrd qua `nens tdk la`nsns snk `ns läs pa`fcrnsns>

Kn as ma` dkfld` barnz ma` qua maea mabakmarsa Idparuiftd, sfkn ma `didrcd arùtfin-saxud` qua tfaka su ra`difùk ink a` `nen. Hny ak mìd, `dlnrdàjd sa hd suprflfmn ak ds mfbaraktas varsfnkas y insd pdrtfiu`dr, inkuk rasu`tdmn bfkd` desnùtdlakta ba`fz, sa vakma läs `d fmad ma ba`fifmdm

qua `d ma rad`fmdm edjn ukd sn`dpdmd y bd`sd lnrd`.

Ma` sfc`n XRFFF d` sfc`n XX, a` iuaktn dmqufrfù uk kuavn tnkn, dpdraifarnkkuavds lnmd`fmdmas (pn`fifd`, bdktästfin, bfiifùk, rad`fstd, lnmarkfstd ylnmarkn, aktra ntrns), ink uk dutnr qua `ds raprasaktd. Yus idlefnssnk prnbukmns7 a` suecækarn sa ratrnd`flaktd ma ntrds bnrlds kdrrdtfvdsinln d bäeu`d, a` aksdyn, ns lftns, ds ayakmds, ati., mfraiifnkdkmn suinktakfmn hdifd ntrds rad`fmdmas, y iradkmn uk lukmn ma hfstnrfds quasfcuak d`flaktdkmn a` d`ld y `d lakta ma àitnras y kdrrdmnras.

Asta bucdz pdsan pnr `d hfstnrfd ma` iuaktn majd ma `dmn, kn sù`n d ntrdsiu`turds qua à flprflfarnk vdrfdifùk y rfquazd, sfkn d luihns dutnrasqua crdifds d a``ns, astd bnrld `ftardrfd hd pnmfmn niupdr a` ùcdr qua saà md ak `d ditud`fmdm.




4. A` iuaktn ma` inifkarn partakaia d` crupn ma nerds qua `dkzdedk saktakifdlnrdàs ink a` bfk ma dyumdr d amuidr d `ns hnleras. Uaasirfed `ds saktakifqua akiuaktra ak a` ra`dtn y axp`fqua `d fktakifùk ma` dutnr ak idmd ukd ma``ds.

5. Yfcufakmn `d mfkälfid ma `d hfstnrfd ma Ihduiar, tarlfka a` iuaktn qua lfsln majù fkinkiùsn.

9. Uatnla a` iuaktn Idparuiftd Unjd, uefqua `d hfstnrfd ak a` prasakta7 idle`ns rnàs n pdpaàs ma `ns prntdcnkfstds y iraa ukd varsfùk lnmarkd ma` iuakt

=. A` sfcufakta ajalp`n as ukd nerd ma` cudtald`tain Ducustn Lnktarrnsn

¾Iùln pnmrìd i`dsfbfidrsa> ¾Dpù`ncn, bäeu`d, saktakifd, lfkf iuaktn n apcrdba> Fkvastfcua a` saktfmn ma idmd vnide`n y sustakta su raspuastd.

A` pdrdìsn flparbaitn Ducustn Lnktarrnsn

As ifartn mfjn laiäkfidlakta a` hnlera, sfk quftdr `d vfstdma `ds ``dlds qua drmìdk ak `d ihflakad dqua``d kniha mafkvfarkn7 ak a` _drdìsn hdy dlfcns, lúsfid, d`cukns `ferns7`n úkfin ld`n ma frsa d` Ifa`n as qua d``ì a` ifa`n kn sa va.

4



1


4. Asirfed ukd lnrdàjd pdrd ‐A` iuaktn ma` inifkarn.“

5. @ad ukd varsfùk iud`qufard ma` iuaktn E`dkid Kfavas, ramdita suprnpfd lnrdàjd, snifd`fia ink sus inlpdôarns su inktakfmn y inl-

pära`d ink `d varsfùk i`äsfid qua su mniakta às prasaktdrä murdkta`d ditfvfmdm. Uaiuarma qua `ds varsfnkas i`äsfids snk dqua``ds quapnsaak lnrdàjd.

9. A` sfcufakta iuaktn inkiaktrd uk aàlaktn frùkfin, prnpfn ma` astf`nlnmarkn. ¾Ak quæ nrdifnkas sa mataitd asd frnkìd y quæ as `n quaastä frnkfzdkmn a` dutnr>

A` `ninCferdk Ghd`f` Cferdk

@ìedkn: 4889-4694

Ak a` jdrmìk ma uk hnspfifn inkniì d uk jnvak ma rnstrn pä`fmn y harlnsn,

d``ì fktarkdmn. V saktäkmnla juktn d æ` snera a` edkin, à pracuktæ:¾_nr quæ astäs dquì>

La lfrù dsnlerdmn y raspnkmfù:

As ukd pracuktd fkdmaiudmd7 sfk aledrcn, inktastdræ. Lf pdmra qufsn hdiarma lì ukd raprnmuiifùk ma sì lfsln7 tdlefæk lf tìn. Lf ldmra masaded



i ì r i u

` n m

a ait n r a

s

• @d vfumd ma Æbasn ma _atrnkfn• @ds lf` y ukd knihas ma Dkùkfln• @d kdrfz ma Äktnk Ihæjnv• @ns dsasfkns ma Arkast Halfkcwdy• Mfdrfn ma uk `nin ma Cùcn` Kfgn`df• A` psfqufdtrd ma Ba`fseartn Harkäkmaz• @d idrtd rnedmd ma Amcdr D``dk _na• A` Maidlarùk ma Cfnvdkkf Eniidiifn•

]fakmds ma `d idka`d ma Erukn Yihu`tz• @d cd``fkd macn``dmd ma Hnrdifn Tufrncd• Qkd rnsd pdrd Alf`y ma Sf``fdl Bdu`gkar• Iuaktns ma Idktareury ma Canbbray Ihduiar• Mns mataitfvas dkta uk edrrf` ma Ldrg ]wdfk• A` `äpfz y ntrns iuaktns ma Udylnkm Ihdkmàr• @d vfmd ma uk hnlera fkkaiasdrfn ma Läxfln Cnrgf• Bua uk mìd mfstfktn iudkmn ldtdrnk d` iarmn ma Qed`mn Ufeafrn

qua buard `d fldcak ma su fùstra pdmra. Lf harldkd lnstrded d su aspnsnkdvacdkta inln a` ajalp`n parbaitn d sacufr. Lf harldkn paksded quamaeìd sar inln æ`, uk axiaàkta dtàtd. V lfs prnbasnras, inln a` mnitnrma bf`nsnbìd, a` ma lúsfid y a` ma `ùcfid, a``ns tdlefæk buarnk tarlfkdktas, yidmd ukn qufsn qua buard a` rabàjn ma sus prnpfns rnstrns ak uk aspajn. _nrasn vfka d asta ucdr. @n akinktræ läs sdkn. D` lakns puamn sar yn lfsln.

Aksacufmd sa vn`vfù hdifd lì y mfjn:

_arn mfla, ¾ta inkmujarnk d asta ùcdr `d amuidifùk y a` euak inksajn>Kn, sny uk vfsftdkta raspnkmì.Nh dôdmfù æ`, tú aras ukn ma `ns qua vfva ak a` hnspfifn ma` ntrn `dmn ma`d pdram.



Id`f`d y Mflkd as ukd inàiifùk ma iuaktns

idsta``dkns ma 4514 prnedeàlakta qua nrmakùtrdmuifr D`bnksn X a` Ydefn, iudkmn tnmdvìd ardfkbdkta. Aktra luihds ma `ds nerds ra`difnkdmdsink D`bnksn X, Id`f`d a Mflkd as d läs ftardrfdy su ldtarfd kdrrdtfvd prniama ma `d `ftardturdnrfaktd`, prnedeàlakta fkmfd, ma` sfc`n FFF.

Ldkusirftn ma` Id`f`d a Mflkd.



4. Fmaktfbfqua ds bdàkifds qua prasaktd a` ldkajn ma` iùmfcn asirftn aka` sfcufakta ajalp`n, qua hd sfmn d`tardmn d prnpùsftn:

Murdifùk ma` trdedjn

Ak ns pdìsas ak qua idsf tnmds ds lujaras trdedjdk (qua snk d lftdmma` puae`n) y ns hnleras sa mdk d rapnsn dmaläs, ma` crdk kúlarnma sdiarmntas y ra`fcfnsns qua kn prnmuiak kdmd ink sus ldkns, kf`n saônras rfins y haramarns (d ns qua a` vu`cn `dld kneàs y ided`à-

rns), fkiùyækmnà ak astd iuaktd. d tnmd d idtarvd ma `ns qua sfrvakd astns ú`tflns ma aspdmdihfkas y truhdkas, y d `ns, lakmfcns quatakfakmn sdùm bfkcak akbarlamdm pnr hn`cdzdkarìd, hd``dræfs quasnk luihns, `ns qua kn prnmuiak kdmd7 y aktra: `ns qua trdedjdkhdy ukd crdk pdrta qua kn sa niupdk ak insds kaiasdrfds, yd quamnkma tnmn sa inksfcua ink mfkarn as bnrznsn qua hdyd luihdsdrtas tntd`lakta vdkds, qua sù`n sfrvak d` dktnjn y axiasn.

(]nldmn ma @d Qtnpìd, ma ]nläs Lnrn)

5. _rasakta su prnpfn dkä`fsfs ma ukn ma `ns maedtas qua sa rad`fzdrnkak a` du`d ma i`dsa murdkta asta parìnmn.

9. @d sfcufakta idrtd rabarakifd` idraia ma d`cukns dspaitns, parn tdlefækinktfaka mns bnrlds fkinrraitds. Yaôdà `ns (n a`) qua astäk arrdmns y`àka `ns aspdifns `feras.

Ldkns d d nerd


Yasfùk

2



Ya maknlfkd pfa ma bntn d `d àyakmd qua dinlpdôd `d bntn. Asinlpuastn masma ukd n mns pd`derds, hdstd tras n iudtrn `ìkads. @n

pfas snk tdk flpnrtdktas inln `d bntn lfsld a fkiùsn, kukid maea fr ukd bntn sa` inrraspnkmfakta pfa. A``ns sa akidrcdk ma ldtfzdr y dpnydr a` ra`dtn prfkifpd`7 pnasn, `n qua mfcdk `ns pfas ma bntns, kn puama sar axtrditdmn ma` iuarpn ma` ra`dtn

Idrditarìstfids

4. Ya akiuaktrd astruiturdmn ma ldkards axp`fidtfvd, malnstrdtfvd,fktarrncdtfvd, dmlfrdtfvd n sdtìrfid. Yfk flpnrtdr a` saktfmn qua sa àntnrcua d` taxtn, nbraia fkbnrldifùk dmfifnkd` d n qua astä lnstrdkmn`d bntncrdbìd. Astn sfckfbfid qua kn maea rapatfr ak pd`derds, `n qua `dfldcak astä inlukfidkmn pnr sì sn`d, sd`vn sf sa trdtd ma fkmfidr a`knlera ma uk fkmfvfmun, ukd nerd ma drta ati.

5. A` drta ma a`denrdr pfas ma bntns qua kn raftarak n qua mfia d bntncrd-bìd, sa maknlfkd aktrnpìd, as maifr, axtrda `d bdiatd qua kn usdk ntrnslamfns. _nr a` inktrdrfn, iudkmn a` pfa ma bntn iuaktd `n lfsln qua`d fldcak axpnka, sa inknia inln ramukmdkifd. Astd npifùk kn asdinksajdeà, pnrqua makntd pnid iradtfvfmdm y mabfifakta saktfmn ma`d nesarvdifùk y a` dkä`fsfs7 pnr inksfcufakta, masmfia ma `d bartf`fmdmkdrrdtfvd ma qufak `n asirfea.

A` pfa ma bntn

_fa ma bntn y astruiturdifùk

ma taxtn asirftn

Qkfmdm 5. A pfa ma bntn: `d trdkslfsfùk ma `dfkbnrldifùk y ns sfstalds sfleù`fins Yasfùk

3



Ma `d frd

@uifn Dkkan Yækaid

@fern prflarn

F. La axfcfsta, Idrn Knvdtn, qua ta asirf-efasa diarid ma d ldkard ma mnlfkdr dfrd, y iran qua, kn sfk idusd, talas luyprfkifpd`lakta d astd pdsfùk, qua as `dläs snlerìd y masakbrakdmd ma tnmds.@ds ntrds tfakak sfk mumd d`cn ma qufatdsy p`äifmds7 parn astd as tnmd dcftdifùk,masakbrakn ak a` rasaktflfaktn, sam macuarrd, ma sdkcra, ma sup`fifns, drraedtnma burnras snerahuldkns, n`vfmäkmnsama sì lfsld ink td` ma mdôdr d ns maläs,

`dkzäkmnsa ak lamfn ma `ds aspdmds, yävfmd ma vakcdkzds qua d su vaz trdakuk vakcdmnr. _nr astd rdzùk, d`cukns vd-rnkas sdefns mabfkfarnk d frd `dläkmn`d`niurd erava7 pnrqua, flpntakta inlndquæ``d pdrd mnlfkdrsa, n`vfmd tnmdinkvakfakifd, masinknia tnmn dbaitn,as nestfkdmd y tarid ak `n qua sa prn-

pnka, snrmd d `ns inksajns ma `d rdzùk,dcftäkmnsa pnr idusds vdkds, fkhäef` pdrdmfstfkcufr n justn y varmdmarn, pdraifæk-mnsa d asds rufkds qua sa rnlpak sneradqua``n lfsln qua dp`dstdk.

_drd qua ta inkvakzds ma qua kn axfstardzùk ak dqua``ns d qufakas mnlfkd `d

inln d niurd tfaka sus saôdàs ifartbrakta trfsta, dkmdr praifpftdmn, ldkinkvu`sds, taz idlefdkta, raspfrdifdkha`nsd y aktrainrtdmd, dsì tdlefprasaktd astds saôdàs a` hnlera fiukmn. Fkb`äldksa sus njns y iakta`àdfktaksn in`nr rnjn iuera su sale`dkhfarva `d sdkcra ak `ds idvfmdmas ma inrdzùk, tfæle`dkà `ns `defns, dprf`ns mfaktas, a` idea``n sa avdktd y arfsu raspfrdifùk as inrtd y rufmnsd, sus iyukturds irujak y sa ratuariak, cflaruca7 su pd`derd as tnrpa y aktrainrtdm

ihnidk braiuaktalakta sus ldkns, spfas cn`padk a` sua`n, dcìtdsa tnmn iuarpn, y idmd castn as ukd dlakdzdsì sa kns prasakta dqua` d qufak hfkiy masinlpnka `d frd.

Flpnsfeà sdear sf asta vfifn as läs mtastdeà qua mabnrla. _uamak niu`td

`ns maläs, d`flaktdràs ak sairatn7 pa`d frd sa rava`d ak a` sale`dkta, y iudkldynr as, lajnr sa ldkfbfastd. ¾Kn vak tnmns `ns dkfldàs saôdàs praisnrds iudkmn sa dprastdk d` inleddedkmnkdkmn tnmns ns lfalerns d ild ma su ditftum nrmfkdrfd, y axd`täkmsa su barnifmdm> A` jded`ì dkzd aspul



Astruiturdifùk ma` taxtn asirftn

Astruiturdr uk taxtn asirftn as ukd iuastfùk

inkniar `ds harrdlfaktds ink `ds iudàs sa vtrdedjdr y a` prniasn qua sa maea sacufr. _nr npdrta, takar i`drfmdm snera a` tald qua sa vtrdtdr, as d prflard rainlakmdifùk qua sa hddktas ma fkfifdr a` prniasn ma asirfturd. Knpuama hde`dr ma `n qua kn sa sdea n ma `n qsa sdea d lamfds. ]dlpnin sa puama asirfefr takar ak iuaktd quæ as `n qua sa qufara maif

qufæk vd mfrfcfmn y iuä` as `d fktakifùk ma` asirfefakta: ¾dpainkvakiar n maàftdr> Di`drdmds astds pdutds, puama inktfkud`d `denr.

]nmn taxtn (kntd parfnmìstfid, iuaktn, knva`d, aksdyn, pnalati.), pnsaa uk akukifdmn prfkifpd`, uk tald qua maea astdr bukifùk ma n qua sa qufara axprasdr. D su vaz, tnmns ns akukimns saiukmdrfns, cfrdräk d`ramamnr ma` tald n akukifdmn iaktYf sa astä hde`dkmn ma `ds ‐pn`ìtfids ma pdz“ ma uk cnefarkn, sa puama hde`dr ma `ds ú`tflds lamfmds ak ldtarfd ma ain`ncdsì asta sad ukn ma `ns p`dkas ma` prncrdld prasfmakifd`.

A` asirfefakta n alfsnr prasupnka qua sus raiaptnras sdeak tald, parn dúk dsì, maea utf`fzdr uk àkcudja diartdmn snera ajalp`ns y ns dktaiamaktas qua ne`fcdrnk d trdtdr mfihd talätf

Ak a` taxtn ma @uifn Yækaid, Knkdtn sdea n qua as d frd, dsì inltdlefæk n sdeak d`cukns knvdtns sdefns qua d inksfmardk niuYækaid sdea quæ as, pnrqua, inln æ` lfsln n mfia, sa rava`da` sale`dkta y `ds ditftumas. Ynk `ds fkbnrldifnkas dmfifnkdàsakukifdmn, `n qua parlfta dlp`fdrà `d fkbnrldifùk d Knkdtn

Di`drdmds `ds prflards inksfmardifnkas, puama fkfifdr `d astrturdifùk ma uk asirftn, parn dktas, takcd ak iuaktd ns sfcufak



• Avftdr `d suejatfvfmdm ak axiasn.

• Ydear prasaktdr `d fmad iaktrd` snera `d iud` vdk d cfrdr `ns ink-iaptns qua à sarvfräk ma dpnyn.

• Avftdr `d rapatfifùk ma ukd lfsld fmad. Idmd vaz qua sa hdcdrabarakifd d a``d maea sar pdrd dlp`fdr`d y kn pdrd raftardr`d.

• Ldktakar uk nrmak, ukd inharakifd ak `d axpnsfifùk7 pnr `n

tdktn, kn maea trdtdrsa ukd knifùk ukd y ntrd vaz (d lakns qualdktakcd ukd astraihd ra`difùk ink ntrn aàlaktn ma `d ldtarfdqua sa astä inlaktdkmn).

• ]akar prasakta qua a` taxtn as ukd ukfmdm, y inln td`, tnmn `nqua sa mfia maea astdr ra`difnkdmn.

• Iaktrdrsa ak a` taxtn y kn tnldr`n inln axiusd pdrd p`dktadrntrns drculaktns.

• ]akar prasakta a` tfpn ma cækarn qua sa vd d utf`fzdr. As inktrd-prnmuiakta utf`fzdr uk àkcudja `ftardrfn, ldridmn pnr sìlfàs,latäbnrds, hfpærenàs, ati., sf sa astä ramditdkmn uk aksdyn.

• Mabfkfr `d bnrld ma axprasfùk ink `d iud` sa vd d trdedjdr: mas-

irfpifùk, kdrrdifùk, mfä`ncn, drculaktdifùk.

• Matarlfkdr a` tfpn ma kdrrdmnr (prflard, sacukmd n tariard par-snkd).

• ]akar prasakta `d `ìkad qua sa à qufara mdr d` taxtn: rad`fstd,frùkfid, bdktästfid, ifaktìbfid, ati.

Inksajns pdrd `d ramdiifùk ma uk taxtn



Ntrns dspaitns pdrd takar ak iuaktd

Yf `d asirfturd sa aktfakma inln

`d prapdrdifùk pdrd uk mfä`ncnaktra uk alfsnr y uk raiaptnr,`n qua sa mfia maea astdr sujatnd ukd `ùcfid qua kn sù`n sa `n-crd pnr `d i`drfmdm ma `ds fmads,sfkn pnr `d euakd fktardiifùk ma`ns aàlaktns `fkcðìstfins, tdàsinln: ns varens, ns drtìiu`ns, ns

sustdktfvns, `ns dmjatfvns y maläsvnide`ns qua sa vdk d utf`fzdr. A` taxtn maea pnsaar ukd inhasfùk, puasma kn sar dsì, sa mfbfiu`tdrä `d inlprasfùk ma` inktakfmn.

Yf sa lfrd ink matakflfaktn `d bnrld inln a` asirftnr hd astruiturdmnsu asirftn, sa mamuia qua ak prfkifpfn, tnmn taxtn astä inlpuastn pnrnrdifnkas qua d` ukfrsa, bnrldk ns pärrdbns. Idmd pärrdbn maea takar ukd

fmad qua sfrva pdrd bnrtdàiar `d fmad iaktrd` qua a` taxtn astæ trdtdkmn.

_nr supuastn, hdy uk asquald astruiturd` i`äsfin qua inlprakma:fktrnmuiifùk, masdrrn``n, kumn y masak`dia7 parn tnmn mapakmarä ma`tfpn ma taxtn qua sa pratakmd a`denrdr (pamdcùcfin, drculaktdtfvn,parfnmìstfin…).

_nr ú`tfln, kn puama majdrsa ma `dmn a` ldrin n rabarakta ak a` iud`

sa masdrrn``d `d fmad. As maifr, `ns dspaitns ma `d rad`fmdm ak `d iud` safksirfeak a` tald trdtdmn, `d iu`turd qua `n rnmad, `ds fman`ncìds qua `nldridk, `ds pnsfifnkas ætfids y astætfids qua `n ifriukmdk. D astn, samaea inksfmardr qua a` inktaxtn ma` alfsnr y a` ma` àitnr puamak sartntd`lakta mfstfktns. @d àiturd pdrd ukn y ntrn puama sar mfvarcakta,parn d tdrad inksfsta ak diaridrsa n lajnr pnsfeà d asa masinknifmn dqufak vdk mfrfcfmds `ds pd`derds.



3


4. @ad iufmdmnsdlakta a` taxtn ma @uifn Dkkan Yækaid y saôdà:

d. ¾Iùln astä astruiturdmn a` taxtn>

e. ¾Iuäàs snk `ds fmads saiukmdrfds qua inlpàlaktdk a` tald prfkifpd

5. Hdcd ukd `fstd ma `ds pd`derds qua inkbnrldk a` idlpn saläktfin ma` talAs maifr, `ns vnide`ns qua à sfrvak d` dutnr pdrd trdtdr a` tald ma `d frd.

9. I`dsfbfqua a` dktarfnr asirftn. ¾As uk taxtn drculaktdtfvn, ukd kdrrdifùk, uksätfrd n uk sflpà mfä`ncn> Yustakta su raspuastd.

=. Inktaxtud`fia a` taxtn Ma `d frd. Ma sar kaiasdrfn, rad`fia ukd fkvastfcdifùpdrd snpnrtdr sus npfkfnkas.

Masdrrn`àk ak su iudmarkn:

4. A` taxtn sa astruiturd d pdrtfr ma mns tfpns ma rac`ds: ds prnpfds ma` taxtny `ds ma` sfstald ma `d àkcud. Yaàiifnkak ifkin dvfsns pue`fiftdrfns ydkd`fiak `d bnrld inln astds rac`ds sa utf`fzdk ak idmd ukn ma a``ns.

5



5. A`denrak uk dkukifn pue`fiftdrfn, utf`fzdkmn sù`n fläcakas pdrd axpra-sdr su fmad. _uamak utf`fzdr rainrtas ma ravfstds, parfùmfins n mfeujnsma su prnpfd fldcfkdifùk. Axpnkcdk a` tald dkta a` du`d ma i`dsa,

dkd`fzdkmn bnrld y inktakfmn.

9. A` sfcufakta as uk brdclaktn ma` ]rdtdmn snera `d masneamfakifd ifvf`,ma Hakry ]nradu. A` dutnr utf`fzd ukd tæikfid n tæikfids pdrd mdr dinkniar a` inktakfmn ma su taxtn (kdrrdifùk, masirfpifùk, drculaktd-ifùk). Fmaktfbìquak`ds y sustakta su raspuastd ink ajalp`ns axtrdìmnsma` taxtn.

¾Iùln puama uk hnlera inkbnrldrsaink takar sù`n ukd npfkfùk y mfsbrutdr`d>¾Hdy d`cúk cnia ak a``n sf npfkd quabua dcrdvfdmn> Yf su vaifkn à astdbd ukmù`dr, ustam kn sa inkbnrld ink sdearqua `n hdk astdbdmn kf ink maifr qua `nhdk astdbdmn, n kf sfqufard ink pamfràqua à pdcua `n qua à maea, sfkn quafklamfdtdlakta tnld lamfmds inkira-tds pdrd netakar a` flpnrta inlpàtn ypravar qua kn à vua`vdk d astdbdr. @ddiifùk pnr prfkifpfn, d pariapifùk y a`

masalpaôn ma` maraihn, lnmfbfid insdsy ra`difnkas7 as asakifd`lakta ravnù-ifnkdrfd y kn infkifma pàkdlakta inkkdmd ma n qua ard dktas. Kn sn`dlaktamfvfma astdmns a fcàsfds, mfvfma bdlf`fds7sì, mfvfma d` fkmfvfmun sapdrdkmn n mfd-eù`fin ma `n mfvfkn ak æ`.



lamfns ma inlukfidifùk, y hd inkvartfmn d In`nlefd ak uk pdìs inkuk mæbfift fkbnrldtfvn qua prnmuia ukd crdk mfstnrsfùk ak d fkbnrldifùkqua sa mfvu`cd.

Ak asta inktaxtn, `d `flftdifùk ma `ds buaktas ma fkbnrldifùk qua usdk`ns lamfns ma inlukfidifùk, surca inln ukd inksaiuakifd ma` i`fldma fktflfmdifùk y ma `d idlpdôd ma dtdquas inktrd dqua``ns parfnmfstdsqua fktaktdk rad`fzdr ukd `denr ma fkvastfcdifùk. Hdy racfnkas mnkma`ns parfnmfstds snk prasfnkdmns pnr ukn u ntrn ma `ns crupns drldmns d`ldrcak ma `d ày a fkiùsn, pnr raprasaktdktas ma` Cnefarkn `nid` pdrdmfvu`cdr n sfàkifdr ifartd fkbnrldifùk. A` fkbnrla mastdid `d rastrfiifùk

ma` `fera lnvflfaktn inln ntrd `flftdifùk flpnrtdkta d `d `feartdm maaxprasfùk ak In`nlefd. Ak ärads inktrn`dmds pnr `ns crupns drldmns d`ldrcak ma `d ày, `ns parfnmfstds y ntrns inlukfidmnras snifdàs maeaktrds`dmdrsa edjn ds inkmfifnkas flpuastds pnr asns crupns. Dsì lfsln, ak

znkds ma npardifnkas lf`ftdras n ma inledta, `d buarzd púe`fid inktrn`dy rastrfkca `d `feartdm ma lnvflfaktn.

A` fkbnrla tdlefæk saôd`d `d bd`td ma rac`dlaktn y `d pnid trdkspdrakifdak a` prniasn ma dsfckdifùk ma ds pdutds pue`fiftdrfds inln uk prneàldpraniupdkta qua puama mdr ùcdr d `d utf`fzdifùk ma `d pue`fifmdm nbfifdìnk bfkas pn`ìtfins y inln ukd harrdlfaktd ma inktrn` y `flftdifùk d `d`feartdm ma praksd. Dmaläs, a` fkbnrla mastdid d takmakifd ma` Cnefarknditud` ma hdiar usn ma astdmìstfids inln ukd ldkard prnpdcdkmìstfid ysflp`fstd pdrd lajnrdr `d fldcak ma su pn`ìtfid y ma `d sftudifùk ma `nsmaraihns huldkns ak a` _dìs.

Ntrn ma `ns talds iaktrdàs ma` fkbnrla y mfsiutfmn ak a` pdka`, as a` ma`ns sfstalds ma pravakifùk y prntaiifùk qua nbraia a` Astdmn in`nlefdknpdrd cdrdktfzdr d feartdm ma axprasfùk. A` fkbnrla dkd`fzd a` prncrdld maprntaiifùk qua nbraia a` Lfkfstarfn ma` Fktarfnr y Justfifd pdrd parfnmfstdsy ntrns inlukfidmnras snifdàs. Ink ra`difùk d asta prncrdld, d ldynrìdma `ns ditnras aktravfstdmns rainknia su flpnrtdkifd ak ldtarfd ma prn-



taiifùk. Yfk aledrcn, `d Maàcdifùk tdlefæk raifefù uk crdk kúlarn mairìtfids snera d`cukds ärads qua maeak sar lajnrdmds, fkiùfmd `d bd`td mainnrmfkdifùk aktra a` ùrcdkn dsasnr akidrcdmn ma rainlakmdr lamfmds maprntaiifùk y `ds aktfmdmas fkvastfcdtfvds y jumfifdàs ma` Astdmn, `d bd`td mainkbfdkzd ak d abfidifd ma ns asqualds ma sacurfmdm prnpnrifnkdmns y dmalnrd ak `d flpàlaktdifùk ma `ns lfslns. _arn `d ldynr irìtfid hdifdastns prncrdlds ma prntaiifùk, sa iaktrd ak `d bd`td ma vnùktdm pn`ìtfid.As maifr, luihds ma ds parsnkds aktravfstdmds pnr d Maàcdifùk saôd`drnk`d inktrdmfiifùk aktra `d axfstakifd ma astns prncrdlds ma prntaiifùk y a`mfsiursn qua snstfakak d`cukns bukifnkdrfns púe`fins inktrd `d `denr ma`ns inlukfidmnras snifdàs qua kn sù`n astfcldtfzd su trdedjn, sfkn qua

tdlefæk pnka ak pa`fcrn su fktacrfmdm.

Ak kuastrd fkvastfcdifùk, tdlefæk halns fkiùfmn a` pdpa` qua juacd `dMabaksnrìd ma` _uae`n ak ldtarfd ma pravakifùk y prntaiifùk inktrdvfn`difnkas d `ns maraihns huldkns y ak `d ùihd inktrd `d flpukfmdm.Ak pdrtfiu`dr, kns halns iaktrdmn ak a` Yfstald ma Dàrtds ]alprdkdsastdeàifmn ak `d Mabaksnrìd pdrd lnkftnradr y dmvartfr ma sftudifnkas marfascn ma `d pne`difùk ifvf` ak ra`difùk ink a` inkb`fitn drldmn.

Ak asta saktfmn, `d ldynrìd ma `ns ditnras aktravfstdmns lnstrù ukd crdkpraniupdifùk pnr `d bd`td ma sacuflfaktn ma astns fkbnrlas ma rfascn pnrpdrta ma` ùrcdkn akidrcdmn ma hdiar`n ak a` Lfkfstarfn _úe`fin, a` InlftæFktarfkstftuifnkd` ma Dàrtd ]alprdkd (IFD]). @`dld `d dtakifùk `d bd`td maalfsfùk ma dàrtds, d pasdr ma ns fkbnrlas ma rfascn alftfmns pnr d Mabak-snrìd. Ak asta saktfmn, `d Maàcdifùk tdlefæk raifefù irìtfids ra`difnkdmdsink `d bd`td ma innrmfkdifùk ink ntrds mapakmakifds cuearkdlaktdàs, `dmfsiraifnkd`fmdm y `d bd`td ma prniamflfaktn ma` IFD] ak `d tnld ma maif-sfnkas pdrd alftfr `ds lakifnkdmds dàrtds. _nr ú`tfln, a` fkbnrla saôd`d`d praniupdifùk qua cakard `d lf`ftdrfzdifùk ma `d raspuastd astdtd` dkta`ds dàrtds alftfmds pnr a` IFD].

Ntrn ma `ns talds iaktrdàs ma kuastrd fkvastfcdifùk, bua `d `denr ma-salpaôdmd pnr `d Bfsid`ìd ma `d Kdifùk ak `d ùihd inktrd `d flpukfmdm.



4. D pdrtfr ma `d àiturd dktarfnr, asirfed tras fmads qua inksfmara raàvdktas. p`fqua a` saktfmn ma idmd ukd ma a``ds.

5. ¾Tuæ prneàlätfid p`dktadmd ak `d àiturd, sa mas`fkmd ma` inkiaptn ma fpukfmdm>

9. Uad`fia ukd fkvastfcdifùk, dlp`fdkmn a` tald trdtdmn ak a` dktarfnr kular

=. Asirfed su puktn ma vfstd diarid ma` inkiaptn ma` kulard` mns, y d pdrtfr mafkvastfcdifùk rad`fzdmd, prasakta ukd inrtd ramdiifùk pdrd dpnydr sus puktnsvfstd n inlaktdrfns, ink iftds taxtudàs tnldmds ma `d fkvastfcdifùk rad`fzdm

1. Nrcdkfia ink sus inlpdôarns uk pdka` ra`difnkdmn ink ukd talätfid ditinln `d vfnàkifd fktrdbdlf`fdr, a` abaitn ma` fkvfarkn ak `d sdùm púe`fidakbarlamdmas ma trdkslfsfùk saxud`.

@d aktravfstd

As ak rad`fmdm, uk mfä`ncn aktra mnsparsnkds, ak a` iud` ukd ma a``ds ditúdinln aktravfstdmnr y `d ntrd, inln ak-travfstdmn. @d aktravfstd as inksfmardmd

uk cækarn ma `d rapnrtarìd, a` läs aà-laktd` y eäsfin ma` trdedjn parfnmìstfin.A` `ncrn ma ukd euakd aktravfstd mapakma

ma n diartdmds y npnrtukds qua sadk ds pracuktds. @d aktravfstd sa inkstftuya ak a` prfl

pdsn hdifd d inksn`fmdifùk ma iud`qufar ntrn cækarn, sad irùkfid, rapnrtdja, kntfifd, a

Mnlfkdr a` drta ma `d aktravfstd y snera tnmn, ma `d trdksirfpifùk qua sa hdcd a``d, kns md ùz varma hdifd `d iradifùk ma uk astf`n prnpfn ak `d ldkard ma ink

4

Idr`ns _uaktas L



]fpns

4. Aktravfstd ma parsnkdja. ]dlefæk sa inknia inln aktravfstd psfin`ùcfid huldkd. Inkifarka axiùsfvdlakta d` aktravfstdmn, vfstn masma su masalpaôparsnkd`. _nr ajalp`n: `d vfmd ma uk dbdldmn asirftnr, mfsaôdmnr n idktdktaa` quahdiar mfdrfn ma uk drtfstd id`àjarn n ma uk vniadmnr ma parfùmfin, at

5. Aktravfstd talätfid. Ya rabfara d uk aàcfmn aspaiìbfidlakta. _nr ajalp`nA`gfk _dtdrrnyn hde`d snera `ns dma`dktns ifaktìbfins ak @dtfkndlærfid n a` Lkfstrn ma Iu`turd, dkukifd `ds castfnkas qua asd aktfmdm dma`dktdrä pdrd kfôn

y dmnàsiaktas.

Bdsas ma` prniasn pravfn

4. Yaàiifùk ma` tald. Kn saàiifnkdlns

d uk aktravfstdmn, sfk mabfkfr prflarna` tald qua masadlns trdtdr, sd`vniudkmn sa trdtd ma ukd aktravfstd maparsnkdja. Qkd vaz qua hdydlns fmak-tfbfidmn a` tald, nrfaktdlns kuastrddtakifùk d asincar a` parsnkdja quavdlns d aktravfstdr y qua maearä sarfmùkan ak a` dsuktn, sd`vn iudkmn sa

trdtd ma uk haihn trfvfd` y intfmfdkn.

5. Fkvastfcdifùk. Dktas ma aktravfstdr d` parsnkdja qua halns aàcfmn, abaitudl

ukd fkvastfcdifùk lfkuifnsd snera a` tald saàiifnkdmn. Ak asta puktn, raiurrflnd ldtarfd` efe`fncräbfin, kdvacdifùk ak Fktarkat y npfkfnkas ma parsnkds id`fbfidmn aspaifd`fzdmds pdrd snkmadr `ds mfvarsds pnsfifnkas inkiaptudàs. _rniamaln

d tnldr kntd ma` ed`dkia qua halns haihn7 ma` maedta qua täiftdlakta sa hdysusiftdmn aktra `ns mfbaraktas mniulaktns n parsnkds inksu`tdmds7 y, `n läs fl

Idr`ns _uaktas La



Kn as rainlakmdeà fkiùfr tærlfkns in`nqufdàs axprasdmns murdkta `daktravfstd prasakifd`, inln tdlpnin, nrdifnkas parfbærfids d` tald kf rapa-tfifnkas n ramukmdkifds. Ak a` prniasn ma trdksirfpifùk ma `d aktravfstd, `dspracuktds y `ds raspuastds sa mapurdk àvalakta, sfk idusdr lnmfbfidifnkasma idräitar asakifd`. Axfstak sfk aledrcn, ifartds axiapifnkas iudkmn sa trdtdma parsnkdjas iuyd pdrtfiu`drfmdm rasfma justdlakta ak a` àkcudja, inlnpuama sar uk ustrdentds, uk fkmfcakta, uk kdtfvn, uk pnatd, uk bf`ùsnbn, ati.

Yaàiifnka uk tald y uk parsnkdja. Hdcd `d fkvastfcdifùk kaiasdrfd. A`denra `d atravfstd inrraspnkmfakta. _nr ú`tfln, trdksirfed `d aktravfstd ak a` astf`n kúlarnldkajdkmn a` àkcudja d pdrtfr ma `n saôd`dmn ak asta td`àr.

@d fkvastfcdifùk pravfd, prapdrd d` aktravfstdmnrpdrd astdr dàrtd d `ds raspuastds y radiifnkdr inkntrd pracuktd qua inksn`fma `d dktarfnr n quaiuastfnka `d raspuastd mdmd pnr a` aktravfstdmn. @nläs flpnrtdkta, a` parsnkdja puama prasaktdr uk

ldtfz trdsiakmaktd` qua idlefa a` iursn n a` akbnqua ma `d

aktravfstd. _uama prasaktdrsa avaktud`fmdmas inln iudkmn aàktravfstdmn as masinrtæs7 ratfiakta d` tald, dukqua sad ma sumnlfkfn7 prntdcnkfstd ma uk dinktaiflfaktn qua kn bdvnraiasu fldcak n qua pnr iud`qufar lntfvn, kn astæ fktarasdmn akmdr `d aktravfstd d asa aktravfstdmnr. Ak td` idsn, a` aktravfstd-mnr maea takar tditn subfifakta pdrd ldkfbastdr sutf`lakta susaksfef`fmdm brakta d` tald y mastdidr `d kaiasfmdm ma mdr`n dinkniar d ntrds parsnkds.

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‐@ns hard`mns kacrns“Iæsdr Rd``ajn

Hdy cn`pas ak `d vfmd, tdk buartas... ¡Vn kn sæ!Cn`pas inln ma` nmfn ma Mfns7 inln sf dkta a``ns,`d rasdid ma tnmn `n subrfmn

sa alpnzdrd ak a` d`ld... ¡Vn kn sæ!

Ynk pnins7 parn snk… Derak zdkjds nesiurdsak a` rnstrn läs bfarn y ak a` `nln läs buarta.

Yaräk td` vaz `ns pntrns ma eäredrns Dtf`ds7n `ns hard`mns kacrns qua kns ldkmd `d Luarta.Ynk `ds idìmds hnkmds ma `ns Irfstns ma` d`ld,ma d`cukd ba dmnrde`a qua a` Mastfkn e`dsbald.

Asns cn`pas sdkcrfaktns snk `ds irapftdifnkas

ma d`cúk pdk qua ak `d puartd ma` hnrkn sa kns quald. V a` hnlera… _nera… _nera. Rua`va `ns njns, inln

iudkmn pnr snera a` hnlern kns ``dld ukd pd`ldmd7vua`va `ns njns `nins, y tnmn `n vfvfmn sa alpnzd,inln ihdrin ma iu`pd, ak `d lfrdmd.Hdy cn`pas ak `d vfmd, tdk buartas… Vn kn sæ.

@d ìrfid vdkcudrmfstd

Qkfmdm 5. A pfa ma bntn: `d trdkslfsfùk ma `dfkbnrldifùk y ns sfstalds sfleù`fins

Yasfùk

6



‐D`tdznr“ Rfiakta Hufmnern

F

Yny yn D`tdznrAkiarrdmn ak `d jdu`d ma su mastfknAk vdkn la dbarrn d `ns edrrntasma `d avdsfùk pnsfeà

Qkd b`nr ifarrd a` idlfkn V sa àvdktdk inln `d astdtud ma `ds `dlds.

@d avdsfùk flpnsfeàLäs mæef` ldrihn ink lfs dksfdsTua uk ajæriftn sfk ùz ak lamfnma alensidmds

Derì `ns njns ak a` sfc`n

Ak qua lnrìd a` irfstfdkfsln.Uatnrifmn ak su iruz dcnkfzdkta

Vd vd d mdr a` ú`tfln suspfrn¾V ldôdkd quæ pnkmralns ak a` sftfn vdiìn>

_nkmralns uk dèd n uk irapúsiu`n¾V hdy qua pnkar d`cn didsn>@d inrnkd ma aspfkdsIhnrradkmn sus ú`tflds astra``ds sa ldrihftd

Lnrfrä a` irfstfdkfsln qua kn hd rasua`tnkfkcúk prneàldTua sù`n hd aksaôdmn pàcdrfds luartds.

Luara maspuæs ma mns lf` dôns

FF

Kn hdy tfalpn qua parmar Vd vfaka d cn`nkmrfkd lnkntælp

]rda uk diaktn dktìpnmd ma àjdk

qua sa diaridkRfaka cnkmnàdkmn `d cn`nkmrfkd D` hnrftdôd ma `d lnktdznkta@d vfn`nkmrfkd y a` cn`nkiia`nMasin`cdmd astd ldôdkd ma `d ùYa diarid d tnmn cd`npa

Vd vfaka vfaka `d cn`nkmrfkd Vd vfaka vfaka `d cn`nkbfkd

Vd vfaka `d cn`nktrfkd Vd vfaka `d cn`nkifldRfaka `d cn`nkihfkdRfaka `d cn`nki`fld

Vd vfaka `d cn`nkrfld Vd vfaka `d cn`nkrfsd@d cn`nkkfôd@d cn`nkcfrd@d cn`nk`frd@d cn`nkerfsd@d cn`nkihf``d

Vd vfaka `d cn`nkmìd



`d kdturdàzd, d `d luarta, d` dlnr y d Mfns. @n dkaimùtfin y masirfptfvn, dsì inl`n lnrd` y pn`ìtfin buarnk a`flfkdmns ma sus `ìkads ma inlpnsfifùk.

_drd a` pnatd ma vdkcudrmfd, `d pnasìd takìd uk bfk ak sì lfsld y d` pnatd à inrr

pnkmìd `àvdr d iden asd lfsfùk qua ard purfbfidr `d `ftardturd. Yf `d pd`derd astdakidsf``dmd y dmnàiìd ma ukd fkbfkftd pnerazd, ard flprasifkmfeà rnlpar `ds dmurds qua `d `flftdedk.

A` lnlaktn mabfkftfvn infkifma ink a` astd``fmn ma `d prflard cuarrd lukmfd` akdôn ma 464=. Astd cuarrd bua inkmakdmd pnr a` desurmn ma sus sdirfbfifns y inka``d, sa raea`drnk `ns drtfstds ma `d æpnid.

A` surcflfaktn ma `ns ldkfbfastns bua ukd bnrld ma prntastd qua dtdiù `ns dinktalfaktns, pnkfakmn ak ta`d ma jufifn `ns lnma`ns y vd`nras pnr akifld ma `n kuay nrfcfkd`. _arn tdlefæk astns fslns buarnk ldridmns pnr trdksbnrldifnkas akidlpn ifaktìbfin y taikn`ùcfin, d` puktn ma qua d`cukns ma a``ns sa masdrrn``drnpdrtfr ma` mfsiursn y `d bnrld ma `ns aàlaktns qua masdrrn``drnk.

• Yu prfkifpd` latd bua mdr d inkniar a` lukmn fktarfnr ma` hnlera,

pnr `n iud` eusidrnk kuavds astrdtacfds pdrd axprasdr`n.

• A` mastfkn ma `ns hnleras (parsnkdjas), bua ukd ma `ds prfkifpdàspraniupdifnkas talätfids ak `d iradifùk drtìstfid.

• Mabakmfarnk a` ùcdr ma` fkinksifakta ak a` ditn iradtfvn, a` fkmfvf-mud`fsln y a` vd`nr ma `d `feartdm.

@ns fslns läs raprasaktdtfvns

Ak cakard`, `ds vdkcudrmfds snstuvfarnk d`cukns rdscns inlukas qua às mfarnkbnrtdàzd y `d buarzd pdrd ldktakarsa, sar vd`nrdmds y rainknifmds. _nr ajalp`n:



4. Ak su nerd Drta pnætfid, Rfiakta Hufmnern asirfefù `d iæàera nrdifùk: pnatd as uk paquaôn mfns“. Mamuzid a` saktfmn latdbùrfin ma astd nrdifùkaxp`fqua su ra`difùk ink a` lnvflfaktn ma vdkcudrmfd.

5. Axp`fqua a` sfcufakta pnstu`dmn qua hdia pdrta ma` fmadrfn astætfin mdmdìs¾Inksfmard qua astd pnsfifùk fkvftded d `d mastruiifùk ma` fkmfvfmun y su

ifamdm> ¾_nr quæ>

9. A` lnvflfaktn vdkcudrmfstd inkiaktrù uk kúlarn ldynr ma fslns ma `ns ap`fidmns ak `ìkads dktarfnras. D`cukns ma `ds läs flpnrtdktas ak a` idlpn `d `ftardturd y a` drta buarnk: a` mdmdìsln, a` flprasfnkfsln, a` axprasfnkfsla` bduvfsln, a` iuefsln, a` buturfsln y a` astrfmaktfsln.

Asinjd ukd ma astds inrrfaktas drtìstfids, masdrrn`à ukd fkvastfcdifùk y prasasus rasu`tdmns ak ukd axpnsfifùk dkta tnmns `ns lfalerns ma` du`d. Aktracd idmd ukn ma a``ns, uk pnald raprasaktdtfvn ma` lnvflfaktn asincfmn.

=. A` pnald ‐@ns Hard`mns Kacrns“ ma Iæsdr Rd`àjn, makukifd ukns saktflfaki`drns ma` yn pnætfin. ¾Tuæ hdy maträs ma asa dlaktn y pnr quæ lntfvn puamabfkfrsa asa pnald inln raprasaktdkta ma` vdkcudrmfsln>

A` sfstald ma Mfns ns hdrä `feras, rnlpam tnmn. Ynfs `nsdlns ma tnmn `n qua rnlpäfs. @ds àyas, `ds lnrdàs, `dsastætfids sa hdk haihn pdrd qua raspatæfs ds insds bräcfàs.@n qua as bräcf` astä mastfkdmn d sar rntn. _rnedm vuastrdbuarzd ukd sn`d vaz: ns masdbìn d qua maspuæs kn inktf-kuæfs. @n qua kn rnlpäfs ns rnlparä, sarä vuastrn dln.

5



6

@d sfcufakta as `d inksfckd qua dinlpdôù d `nspnatds mdmdìstds ak `d iradifùk ma sus pnalds:

4. A` pnald mdmdìstd suaà sar ukd trdld nsiurd sfk ùcfid, tajfmd pnr ukdsuiasfùk ma pd`derds y snkfmns, ink ukd fki`fkdifùk hdifd `n tarrnrìbf-in a fkifartn, hdifd `n kfhf`fstd y `n bdktdsfnsn. Uatnla a` pnald quasa às aktracù murdkta `ds axpnsfifnkas y dkd`fia ak quæ nrdifnkas saraprasaktdk `ds dktarfnras idrditarfzdifnkas.

5. Ak a` äleftn pue`fiftdrfn ¾quæ tfpn ma fläcakas rainknia qua ma`dtak`d vfcakifd ma d`cukns ma `ns lnvflfaktns ma vdkcudrmfd ak kuastrnstfalpns> Yustakta su raspuastd ink rainrtas ma parfùmfins, dbfihas, ati.

‐_drd hdiar uk pnald mdmdìstd“_nr ]rfstdk ]zdrd

Injd uk parfùmfin. Injd ukds tfjards. Asinjd ak a` parfùmfin ukdrtìiu`n ma `d `nkcftum qua iuaktd mdrà d su pnald. Uainrta a`drtìiu`n. Uainrta aksacufmd, ink iufmdmn, idmd ukd ma ds pd`derds

qua bnrldk a` drtìiu`n y lætd`ds ak ukd en`sd. Dcìta`d sudvalakta. Dhnrd sdqua idmd rainrta ukn trds ntrn. Inpfa inkifakzumdlaktaak a` nrmak ak qua hdydk sd`fmn ma d en`sd. A` pnald sa pdraiaräd ustam. V as ustam uk asirftnr fkbfkftdlakta nrfcfkd` y ma ukd sak-sfef`fmdm haihfzdkta, dukqua fkinlprakmfmd pnr a` vu`cn.



B n t n t n l d m d

m a S f g f p a m f d

A` rnldktfifsln, iuyns pnatds dld-edk `d masaspardifùk sfkiard n bfk-cfmd tuvn uk rfquìsfln drsakd` madmjatfvns sucaraktas, ma iudktn buard

`úcuera, la`dkiù`fin, sn``nzdkta,tnrlaktnsn, uù`dkta, masn`dmn,snlerìn, lamfavd`, irapusiu`dr ybukardrfn. @ns sflen`fstds raukfarnkdmjatfvns avdkasiaktas, crfsäians,dkae`dmns, mfbusns, ralntns, npd-àsiaktas, ak tdktn qua `ns lnmar-kfstds `dtfkndlarfidkns `ns tuvfarnk

ha`ækfins, ldrlùrans, varsd`àsins,aeúrkans, pdkfmds, bdukasins, sdld-rftdkns, pdusdmns ak sus cfrns, sn``n-

zdktas ak sus vfn`nkiha`ns, äurans aksus dèds: ma in`nr desfktfn iudkmnma kapaktas sa trdtded, lfaktrdsàva y dàva sa lnstrded a` d`d ma`àva dedkfin. D` prfkifpfn ma asta

sfc`n, iudkmn a` niu`tfsln sa pusn malnmd ak _drìs, Ydr _a`dmäk `àkdedsus knva`ds ma dmjatfvns qua sucfrfa-rdk `n läcfin, `n id`man, `n asta`dr ydstrd`. Dkdtnà Brdkia, ak sus vfmdsma sdktns, usded luy häef`lakta `ddmjatfvdifùk ma Jdinen ma d Rnräcfkapdrd mdrsa ‐uk tnkn ma æpnid“. @ns

surrad`fstds buarnk cakfdàs ak hd``dry ralnzdr iudktn dmjatfvn pumfardprastdrsa d aspaiu`difnkas pnætfidssnera `n bdktdsld`, dùifkdkta, lfs-tarfnsn, ma`frdkta, bnrtuftn, inkvu`sfvny nkìrfin. Ak iudktn d ns axfstakifd-`fstds ma sacukmd ldkn, prabfarak nspuruàktns a frrftdktas.

Dsì, `ns dmjatfvns sa trdksbnrldk, dìden ma luy pnin tfalpn, ak a`didmalfsln ma ukd takmakifd `fta-rdrfd, ma ukd cakardifùk. ]rds ma `ns

fkvaktnras radàs ma ukd axprasfùk,dpdraiak `ns qua sù`n idptdrnk maa``d `ds tæikfids ma ldtfzdr, in`nradry sucarfr: `d tfktnrarìd ma` nbfifn. Viudkmn hny maiflns qua a` astf`n matd` dutnr ma dyar kns rasu`td fksnpnr-tdeà, kn kns rabarflns d` bnkmn, sfknd ns nrnpaàs, utns, dldkardlfaktns

y nrbaerarìds, ma `d dmjatfvdifùk.

V `d varmdm as qua tnmns `ns crdkmasastf`ns sa idrditarfzdk pnr ukd suldpdrquamdm ak a` usn ma` dmjatfvn. Viudkmn sa vdàk ma æ`, usdk ns dmjatf-vns läs inkiratns, sflpàs, mfraitns,mabfkfmnras ma id`fmdm, inksfstakifd,

astdmn, ldtarfd y äkfln, tdk prabarf-mns pnr qufakas ramditdrnk d Efe`fd,inln pnr qufak asirfefù A` fkcakfnsnhfmd`cn mnk Tufjnta ma @d Ldkihd.



Inhasfùk vared` y sus aàlaktns bnrldàs

@d prnmuiifùk ma uk taxtn as ukd tdrad

qua rai`dld uk lamfdkn inkniflfaktnma` iùmfcn `fkcðìstfin, ma sus rac`ds y vd-rfdktas. Ya asirfea pdrd fkbnrldr, axprasdr,drculaktdr, snifd`fzdr n sflpàlakta, pnra` cnia ma kdrrdr y prnmuifr nerds ftardrfds.

@n ifartn as qua iudkmn sa asirfea, a` alf-snr sulfkfstrd uk pdquata ma pfstds quaà parlftak d` àitnr, dmaläs ma` iùmfcn,fktarpratdr `ds fmads qua sa astäk p`dktadkmn. _drd `ncrdr a` nejatfvn, ak-idmakd pd`derds, nrdifnkas y pärrdbns qua tarlfkdk, bnrldkmn uk tnmncrdifds d` trdedjn ma inktaxtud`fzdifùk qua pdu`dtfkdlakta vd flprflfakmnak a` rainrrfmn qua hdia ma` mfsiursn.

Ldktakar `d `fkad`fmdm y i`drfmdm ma asta mfsiursn, raqufara uk euak

ldkajn ma `d inhasfùk y `d inharakifd, mns aàlaktns idrditarìstfinsma tnmn euak taxtn.

Ya mfia qua hdy inhasfùk taxtud` iudkmn idmd ukd ma ds pdrtas n aàlaktnsbnrldàs ma uk taxtn (sustdktfvns, inkjukifnkas, prapnsfifnkas, dmjatfvns,dmvarefns, tarlfkdifnkas qua fkmfidk inkinrmdkifd ak parsnkd, kúlarn,tfalpn n cækarn), ldktfaka ukd ra`difùk y ukd nrcdkfzdifùk qua às par-lfta cakardr saktfmn.

Inhasfùk sfckfbfid ukfùk, ak asta idsn, ukfùk ma pd`derds qua prnpnrifn-kd ukfmdm d tnmn asirftn. Uasu`td fktarasdkta var iùln ukd hfstnrfd sa vdinkstruyakmn d pdrtfr ma `d axpnsfifùk ma `ns talds qua dinlpdôdk d `dfmad edsa. Asta haihn puama mataitdrsa, sf sa dkd`fzd a` tfpn ma pd`derds,`ns inkaitnras qua sa utf`fzdk (idlpns saläktfins), y a` tfalpn vared` quadinlpdôd d `d kdrrdifùk.



@ns inkaitnras snk dqua``ds pd`derds paquaôds qua sfrvak pdrd ukfr y mdrà saiuaky inharakifd d ns asirftns, y àvdr ak bnrld nrmakdmd, a` p`dktadlfaktn y masdrrnma ds fmads. Nesarva d sfcufakta tde`d qua di`drd ak quæ idsns maeak sar utf`fzdm

Dmfifùk V, ma fcud` bnrld, dmaläs, akifld

Dmvartakifd Lfrd, ¡iufmdmn!, nya, ¡ah!

Inrraiifùk Euakn, raitfbfidkmn, lajnr mfihn

Inkiùsfùk Ak bfk, pnr ú`tfln, ak sìktasfs

Inktrdsta _arn, sfk aledrcn, d pasdr ma, dukqua, kn nestdkta

Mfcrasfùk _nr ifartn, d prnpùsftn

Ajalp`fbfidifùk _nr ajalp`n, fkiùsn, td` inln

Ækbdsfs _uas sì qua, ifartdlakta, i`drn qua, ak asa saktfmn

Axp`fidifùk As maifr, d sdear, astn as

Fktaksfbfidifùk As läs, läxfla, läs dúk

Uastrfiifùk Hdstd ifartn puktn, sf didsn, pasa d qua

Uasulak Ma iud`qufar bnrld, ak rasulak, ak rasulfmds iuaktds

]ald Ak iudktn d, pnr `n iud` sa rabfara d

]rdksfifùk _nr ntrd pdrta, ak ntrn nrmak ma fmads

Idusd _nr td` rdzùk, mdmn qua, ak inksaiuakifd, ma dhì qua

]falpn D` prfkifpfn maspuæs d vaias



Masdrrn``dr ak su iudmarkn:

4. Yaôdà iuäàs snk `ds tasfs qua p`dktad a` taxtn ma Dàjn Idrpaktfar.

5. Uasd`ta ns inkaitnras taxtudàs qua sa akiuaktrak ak a` taxtn ma Fktrnmuiiy axp`fqua `d fmad qua idmd ukn ma a``ns qufsn trdkslftfr.

9. Uanrcdkfia asds lfslds fmads, utf`fzdkmn ntrns inkaitnras taxtudàs.

=. Qtf`fia su mfiifnkdrfn a fkvastfcua a` sfckfbfidmn ma ds pd`derds qua a rasu`tdrmasinknifmds. Ink asta `fstdmn, ramdita uk asirftn pdrd axpnkar su puktn vfstd diarid ma d`cukds ma `ds fmads d``ì axprasdmds. Ynifd`fia dkta a` iursn,trdedjn rad`fzdmn.


4. Uatnlak a` asirftn ma Fktrnmuiifùk a fmaktfbfquak d`cukns aàlaktns crdl

tfidàs qua fkmfquak inkinrmdkifd ak kúlarn, parsnkd, tfalpn y cækarnqua d su vaz ldktakcdk `d maefmd inhasfùk. Ajalp`n: ak a` ú`tfln pärrdbn `d aiturd, d inkjukifùk qua ra`difnkd d pd`derd varmdm ink d pd`derd tnm@d, inln drtìiu`n, dinlpdôd d varmdm, qua as uk sustdktfvn prasaktdkmn ura`difùk ma kúlarn y cækarn7 crdkmas as uk dmjatfvn qua sa ra`difnkd iastf`ns, qua as uk sujatn lakifnkdmn ak tariard parsnkd ma` pùrd`.

5. @d inhasfùk sa md crdifds d` euak usn ma` `æxfin. @ns inkaitnras, p

4

5



Yalfkdrfn fktarkdifnkd`_n`ìtfids púe`fids pdrd `d supardifùk ma `d pnerazd

Iaktrn ma Inkvakifnkas ma `d _`dzd Ldynr ma Lama``ìk

_drtfifpdktas aspaifd`fstds: Uueæk @n Run`n (mfraitnr Iaktrn Fktarmfsifp`fkdrfnpdrd a` Astumfn ma _n`ìtfids _úe`fids Drcaktfkd), _de`n Rf``dtnrn (inksu`tnrMfvfsfùk ma Masdrrn``n Ynifd` y Qkfmdm ma Astumfns Aspaifdàs. IA_D@ Ihf-à), Jnrca Fväk Cnkzäàz (mfraitnr ma` IFM ma `d Qkfvarsfmdm Kdifnkd` maIn`nlefd). @d sftudifùk ma pnerazd qua vfvak läs ma lf` lf``nkas ma parsnkds ak a`lukmn hd ne`fcdmn d paksdr ak mfvarsds astrdtacfds, prncrdlds y p`dkas quadpuktak d su ramuiifùk n arrdmfidifùk7 d mabfkfifùk ma astds astrdtacfds hdraquarfmn nptdr ma bnrld axp`ìiftd n kn, pnr ukd ldkard ma aktakmar a`bakùlakn ma `d pnerazd, sus idusds, idrditarìstfids, `ns ditnras fkvnùird-

mns ak `ds snùifnkas y `ds lamfmds qua hdk ma tnldrsa pdrd akbraktdr`d.

Aktakmar `d pnerazd inln uk prneàld ma lú`tfpàs mflaksfnkas, ra-qufara ma `d dp`fidifùk ma akbnquas inlpàlaktdrfns ak `ds pn`ìtfidsqua pratakmak dbaitdr`d. Ak pdrtfiu`dr `ns dpnrtas ma `ns akbnquas mamaraihns huldkns y a` rainkniflfaktn ma `ds mfbarakifds, fkiùfmn akæsta a` ma cækarn, nbraiak aàlaktns fkmfspaksdeàs qua vfakak sfakmnflpàlaktdmns y prnlnvfmns pnr vdrfns saitnras snifdàs, didmælfins y

A salfkdrfn

Qkfmdm 9. Inharakifd, inhasfùk vared` yinkinrmdkifd `fkcðìstfid

Yasfùk

45



nrcdkfslns fktarkdifnkdàs, parn dúk iuaktdk ink pnid dp`fidifùk ak`ns kfvaàs kdifnkdàs.

A` akbnqua ma `ns maraihns huldkns parlfta hde`dr ma `ds snùifnkas

d `d sftudifùk ma pnerazd masma ukd parspaitfvd ma maraihns y ne`fcd-ifnkas y kn sù`n masma `d dsfstakifd snifd`7 rasd`td a` pdpa` pdrtfifpdtfvnqua maeak jucdr `ds parsnkds ak sftudifùk ma pnerazd ak `d p`dkadifùky ajaiuifùk ma `ds pn`ìtfids y iuaktd ink uk inkjuktn ma vd`nras lnrdàsukfvarsd`lakta rainknifmns y rabnrzdmns pnr ne`fcdifnkas jurìmfids, lu-ihds ma æstds susirftds pnr `d ldynrìd ma `ns Astdmns, inln as a` idsn ma`‘_ditn ma maraihns ainkùlfins, snifdàs y iu`turdàs‖ susirftn pnr läs

ma 41? pdìsas n d Inkvakifùk snera ns maraihns ma` kfôn diaptdmd idsfma ldkard ukfvarsd`. Astns inlprnlfsns maeak cufdr a` inktakfmn ma `dspn`ìtfids d flpàlaktdr.

Qkd lfrdmd mfbarakifdmd ma `ds idusds a flpditns ma `d pnerazd snerahnleras y lujaras `d prnpnrifnkd a` akbnqua ma cækarn, yd qua fkiùyaa` dkä`fsfs snera ns bditnras iu`turdàs qua dsfckdk mfstfktns rnàs y bukifn-kas snifdàs sacúk a` saxn y qua tfakak fkifmakifd ak ldynras n laknras

kfvaàs ma pnerazd.

@d nesarvdkifd ma d mfvarsfmdm iu`turd` mabfka tdlefæk `ds idrditarìstfidsma ds pn`ìtfids ma arrdmfidifùk ma `d pnerazd, puas as kaiasdrfn inkniara` sfckfbfidmn y `ds kaiasfmdmas mfbarakifdmds ma `ds pne`difnkas qua saakiuaktrdk ak astd sftudifùk, fkiùyakmn aspaifbfifmdmas ma ns mfbaraktascrupns ætkfins, yd qua a` crdmn ma mfspnsfifùk ma raiursns n `ds idrdita-rìstfids ma ns lfslns vdrìdk ma diuarmn ink astd mfvarsfmdm. _nr n tdktn,

sarìd uk arrnr aspaifbfidr ukd lamfmd pdrd `d arrdmfidifùk ma `d pnerazdak bukifùk ma uk kfva` hnlncækan n edjn uk irftarfn ma ukfvarsd`fmdm,masinknifakmn `ds pdrtfiu`drfmdmas pne`difnkdàs.

D d uz ma astns akbnquas, sa rad`fzdrä uk ed`dkia ma ds pn`ìtfids ma uihdinktrd `d pnerazd flpàlaktdmds ak Dlærfid @dtfkd ak `ds ú`tflds mnsmæidmds y uk mfä`ncn ink d`cukds fkfifdtfvds ma pn`ìtfid púe`fid ak asta



A` salfkdrfn

A` salfkdrfn as uk ajarififn ma fkvastfcdifùk ak crupn qua parlfta `d axp`nrdifùkprnbukmfzdifùk ma ukd vdrfamdm ma tùpfins ink uk aja iaktrd`, ink fktarvakifùk m

parsnkd` aspaifd`fzdmn ak `ds ärads saàiifnkdmds inln nejatn ma astumfn.

Inktrdrfn d `n qua niurra ink ntrds tæikfids ma axprasfùk nrd`, a` salfkdrfn as ukditfvfmdm aspaifd`fzdmd qua fkiaktfvd d inkstruiifùk ma inkniflfaktn ak a` lfsltfalpn irnkn`ùcfin iudkmn sa astä masdrrn``dkmn.

@ns pdrtfifpdktas kn snk axpnsftnras qua sa uefidk brakta uk púe`fin pdrd sar asiihdmns y raifefr sus fktarvakifnkas. ]dlpnin eusidk idptdr fkbnrldifùk ma tariarnak bnrld pdsfvd. Yu bfkd`fmdm as ajariftdrsa lamfdkta a` astumfn parsnkd` ak uk dpskn ldynr ma mns hnrds. @ns fktacrdktas ma` salfkdrfn sa raúkak ak inlfsfnkas axp`nrdk `ds fmads lamfdkta ukd fktardiifùk raiìprnid. Kn hdy dùlkn kf prnbasn`ds fmads vdk y vfakak, sa inkmaksdk y tnldk bnrld y mfraiifùk.

Uac`ds ma nrcdkfzdifùk

Astds snk `ds rac`ds qua sa maeak takar ak iuaktd ak `d prapdrdifùk ma uksalfkdrfn:

• Knlerdlfaktn ma uk prasfmakta y uk ra`dtnr.

• Ma`flftdrsa a` tald iaktrd` y `ns suetalds, dktas ma aktrdr ak ldtarfd.

• As flprasifkmfeà ma`flftdr a` tfalpn y iulp`fr`n.

•

@ns salfkdrfstds maeak takar uk kfva` hnlncækan ma inkniflfaktns.• A` kúlarn cakard` ma pdrtfifpdktas kn maea axiamar `ds 1? parsnkds.

• Astds 1? parsnkds maeak inkbnrldr inlfsfnkas (suecrupns), y d su vaz,ma`flftdr a` suetald qua idmd ukd vd d trdedjdr.

• Idmd inlfsfùk maea astdr akideazdmd pnr uk innrmfkdmnr y uk saira-tdrfn.

• A` kúlarn ma salfkdrfstds maea nsif`dr aktra iudtrn y 4? parsnkds.



45


4. Ma`flftak y prapdrak aktra tnmns `ns lfalerns ma` du`d y ak inlpdôìd ma smniakta, uk tald ma fktaræs cakard`, sfcufakmn `ds pdutds y knrlds fkmfidmpdrd `d rad`fzdifùk ma uk salfkdrfn.

5. Qkd vaz inkiùfmn a` salfkdrfn, asiuihak dtaktdlakta `d inkiùsfùk qu

prasaktd a` ra`dtnr y tnlak kntd ma tnmns `ns puktns.

9. Mfvfmdk d `ns lfalerns ma` crupn, ak suecrupns ink hdstd iudtrn parsnkdink edsa ak `ns puktns qua àyù a` ra`dtnr, ratnlak a` tald y dkd`fiak: ¾quabaitns takmrìdk ukds lamfmds n ukds inkiùsfnkas mfbaraktas d ds p`dktadmd

=. Avd`úak a` trdedjn masdrrn``dmn pnr idmd lfalern ma` crupn y prasaktak suinkiùsfnkas.


4. Ink edsa ak `d fkbnrldifùk raincfmd ak a` salfkdrfn ma` ]d`àr Inài-tfvn, asirfed ukd kntd parfnmìstfid ak `d iud` rasaôa a` masdrrn``n y `dsinkiùsfnkas ma` lfsln.

5. Fkvastfcua ak Fktarkat, uk salfkdrfn qua hdyd sfmn in`cdmn ak `d ram. Dkd`fia y asirfed `d bnrld inln bua ma`flftdmn.

5



@ns Maraihns Huldkns

Masma su dprnedifùk ak 46=8, `d Mai`drdifùk ma`ns Maraihns Huldkns hd sfmn y sfcua sfakmn ukdbuakta ma fkspfrdifùk ma `ns asbuarzns kdifnkdàsa fktarkdifnkdàs pdrd prnlnvar y prntacar `nsmaraihns huldkns y ds feartdmas bukmdlaktdàs.

Qk aàlaktn asakifd` pdrd d prntaiifùk ma ns maraihns huld-kns, as `d mfbusfùk dlp`fd ma su inkniflfaktn y bnlaktn ma `dinlpraksfùk aktra `ds pne`difnkas, pdrd qua sapdk iuäàs snksus maraihns y iùln puamak mabakmar`ns. Ak `d ditud`fmdm, `dMai`drdifùk astä mfspnkfeà ak läs ma 92? fmfnlds y as a` mn-iulaktn läs trdmuifmn ak a` Lukmn, `n iud` md tastflnkfn masu idräitar y dìdkia ukfvarsdàs.

Maspuæs ma läs ma 2? dôns, rakmflns hnlakdja d `d vfsfùkaxtrdnrmfkdrfd ma `ns ramditnras nrfcfkdàs ma `d Mai`drdifùk y d`ns kularnsns mabaksnras ma `ns maraihns huldkns ak tnmn a`Lukmn, qua hdk ùihdmn pdrd hdiar rad`fmdm su vfsfùk.

Astd Mai`drdifùk partakaia d tnmns y idmd ukn ma knsntrns. Dhnrdkns inrraspnkma àar`d, astumfdr`d, prnlnvar`d y rafvfkmfidr`dinln kuastrd.

9. _rasakta sus prnpfds inkiùsfnkas diarid ma` tald ma `d fkvastfcdifùkrad`fzdmd ak a` dktarfnr kulard`.

=. Fkvastfcua snera uk tald qua à sad dtrditfvn y hdifakmn `ds vaias mara`dtnr, prasakta su fkbnrla.



Yf a` lamfn ma fkbnrldifùk as paquaôn, hderä uk parfnmfstd pdrd idmd `ìkad taltfid. _arn pnr `n cakard`, idmd ukd astä inlpuastd pnr uk aqufpn ma parfnmfsinnrmfkdmns pnr uk amftnr. _nr ajalp`n: a` tald iu`turd` astä saiifnkdmn d su vak `ferns, drtas asiækfids, drtas p`ästfids, lúsfid, ati.

@ds 1S

Hdia uk sfc`n qua `ds 1S ardk `d maknlfkdifùk pnr axiaàkifd pdrd aìaktrn asta cækarn ma `d fkbnrldifùk ak pdrtfiu`dr. @ds 1S snk `ds ifkin

pracuktds eäsfids qua maearäk sar rasua`tds ak d kntfifd: qufæk, quæ, mùkma,iuäkmn y pnr quæ. A` iùln as ukd pracuktd dmfifnkd`, tdlefæk matarlf-kdkta ak a` inkjuktn fktacrd` ma `d kntfifd. @ns fktarrncdktas bukmdlaktdàsmaearäk sar lnstrdmns ak a` àdm, as maifr, ak a` prflar pärrdbn.

@ds buaktas

Ya ``dld buaktas d qufakas sulfkfstrdk `dfkbnrldifùk. Dsì, uk prniasn ma pdz, pnrajalp`n: prnmuifrä kntfifds pn`ìtfids n ma

nrmak púe`fin, y ds buaktas saräk ns vnia-rns masfckdmns pnr a` cnefarkn, pn`ftù`ncnsy raprasaktdktas ma `ns crupns ravnùifn-kdrfns fkvnùirdmns, aktra ntrns. ]nmn `ndktarfnr sa dp`fid d praksd, fkvastfcdifùkdidmælfid a Fktarkat.

Brdkg _adr`, kacnifdmnr ma`Cnefarkn Kdifnkd` ak `ns mfä`ncns

ink `ds BDUI ak @d Hdedkd



• Mùkma: as d fkbnrldifùk ra`difnkdmd ink d uefidifùk cancräbfidak mnkma tuvn ùcdr a` dinktaiflfaktn.

• _nr quæ: as `d pdrta qua ntnrcd `d flpnrtdkifd ma `d kntfifd. Yfa` pnrquæ kn tfaka raàvdkifd, kn tfaka saktfmn inkvartfr ukdfkbnrldifùk ak kntfifd. A` pnrquæ ajaria ukd ma `ds tdrads läsflpnrtdktas ak a` lnlaktn ma inkvnidr d` àitnr.

9. Iuarpn. As a` masdrrn``n ma d kntfifd y masc`nsd idmd ukn ma ns mdtnsaxpuastns ak a` adm. Astn kn sfckfbfid qua a` iuarpn ma d kntfifd maedraftardr d fkbnrldifùk yd sulfkfstrdmd. A` iuarpn maea di`drdr tnmn a`dinktaiflfaktn, inlukfidkmn ak nrmak ma prfnrfmdmas y saiifnkdkmn

`d fkbnrldifùk ak pärrdbns ma iudtrn d safs `ìkads. Idmd pärrdbn maeatakar uk nejatfvn i`drn, as maifr, idmd ukn maea dpnrtdr fkbnrldifùkinharakta a flpnrtdkta. A` iùln as idsf sfalpra, d ldtarfd ma` iuarpn,dukqua tdlefæk sa suaà suldr a` pnrquæ.

=. Ifarra. _uama flp`fidr uk masp`facua ma mns pärrdbns n sar iuastfùk mamns `ìkads. As ukd inkiùsfùk n ukd axpnsfifùk ma `ds inksaiuakifdsqua maldkmd a` dinktaiflfaktn7 tdlefæk puama trdtdrsa ma pravfsfn-

kas n lamfmds tnldmds.

@d pfrälfma fkvartfmd

Iudkmn hde`dlns ma pfrälfmas, quaralns maifr axditdlakta `n qua ukddrquftaiturd pfrdlfmd` sucfara: ukd ifld puktfdcumd iuyn mfälatrn as a`ärad läs ramuifmd ma tnmd `d astruiturd7 ukd bd`md qua d pdrtfr ma `d ifld,

sa vd aksdkihdkmn7 y ukd edsa subfifaktalakta inksfstakta pdrd snpnrtdra` rastn ma `d astruiturd.

A` masdrrn``n ma `d kntfifd sa nrcdkfzd ma fcud` bnrld, axiaptn pnrqua `dpfrälfma as fkvartfmd pdrd nbraiar d` aitnr dktas qua kdmd, ukd dlp`fd edsan p`dtdbnrld qua inktakcd `d asakifd ma `d kntfifd: a` àdm. Maktrn ma a``d,vdlns dcntdkmn ak bnrld pdu`dtfkd, ds mfvarsds iuastfnkas qua mascrdkdk`d kntfifd, hdstd `àcdr d `ns matd`às lakns raàvdktas.



• Maefmn d d kaiasfmdm ma ukd amuidifùk pamdcùcfid inktal-pnräkad, qua asi`drazid dspaitns ra`difnkdmns ink d saxud`fmdmma kfôns y dmnàsiaktas, dided ma sar puastd d mfspnsfifùk ma

`ns àitnras laxfidkns `d nerd Yaxud`fmdm ak `d Amuidifùk, ukinlpakmfn ma tras tnlns qua ink ukd vfsfùk ditud`, md ùiassnera a` tald.

5. @ad d sfcufakta kntfifd y saôdà d` brakta, a` dktatìtu`n, a` tìtu`n, a` àdm,a` iuarpn y a` ifarra, saôd`dkmn aspaiìbfidlakta mùkma alpfazd ytarlfkd æsta ú`tfln.

@d ldjastunsd iukd ma` sdear dktfcun radera sus puartds, trds hdearsapuastn `d prflard pfamrd ak 4688. @d kuavd varsfùk ma `d efe`fntaid,sftudmd ak a` Lamftarräkan, iuaktd ink kularnsds sd`ds, aktra ds iudàs

mastdidk `ds ma lúsfid dktfcud, `ds ma bnkmns ma pdpfrns, parcdlfkns,iùmfias, `ferns rdrns a fkiukdeàs…

@d ifumdm ma Dàjdkmrìd sa vfsta ma cd`d pdrd iaàerdr d rafkducurdifùkma d qua hdia 5.9?? dôns cudrmdrd varmdmarns tasnrns ma` sdear huld-kn, prnmuifmns pnr d cakfd`fmdm ma Drfstùtaàs, Drquìlamas, Aui`fmas,Hfpdtfd, Hfpùirdtas y Cdàkn, aktra luihns ntrns.

Dàjdkmrìd, ùcdr mnkma `d huldkfmdm rainàitù ma ldkard sarfd ysfstalätfid a` inkniflfaktn ma` Lukmn, as ak rad`fmdm `d hfjd ma`flparfn ma `ns _tn`nlans ak Acfptn, iuyns suiasfvns rayas suldedkajalp`dras inpfnsdlakta, inln `ns trdkspnrtdmns ak `ns kdvìns, quaardk ldkusirftns fkidutdmns talpnrd`lakta ak `ns puartns, murdktaa` tfalpn qua tdrmdrd su trdksirfpifùk rad`fzdmd sflu`täkadlakta pnrvdrfns asirfeds, lfaktrds ntrn bukifnkdrfn àìd ak vnz d`td.

Maspuæs ma 4.2?? dôns ak Dàjdkmrìd:YA UAFKDQCQUD @D EFE@FN]AID LÄY C@NUFNYD MA@ LQKMN



@d inkqufstd ma `d ba`fifmdmEartrdkm Uussa``

Inln sa mfia qua d eaefmd y ds idrfifdssnk ds puartds ma d dàcrìd, d cakta saalerfdcd fklamfdtdlakta y prniurdkn mdrsa iuaktd ma `n luihn qua àlnàstdk sus inlpdôarns. Iudkmn hdk

eaefmn läs ma `d iuaktd `ns hnlerasalpfazdk d ``nrdr y d `dlaktdrsa ma`n fkmfckns qua snk lnrd`lakta maìdrfôn ma sus ldmras. ]nmn n qua ink-sfcuak ink a` dìnhn` as `ferdrsa ma `dsaksdifùk ma` paidmn, insd qua d rdzùkinksfcua ak ns lnlaktns läs úifmns.

@d rdzùk ma astds mfstfktds i`dsas mamascrdifd sa hd``d, ak pdrta, ak a` sfsta-ld snifd`, y, ak pdrta, ak `d psfin`ncìdfkmfvfmud` qua as kdturd`lakta, ak ukdprnpnrifùk inksfmardeà, uk prnmuitnma` sfstald snifd`.

@d amuidifùk ak d irua`mdm y ak a` lfa-

mdrsa pnr qufakas snk asi`dvns ma apdsfnkas. Ak `d dmnàsiakifd `d vfmd ard nmfnsd, y astded inktfkudlaktaenrma ma` sufifmfn, ma` iud` la `fecrdifds d` masan ma sdear läs ldtal

tfids… hdear masiuefartn iuäàs a`ds insds qua masaded läs y hdear dqufrfmn crdmud`lakta luihds ma aÀk pdrta as maefmn tdlefæk d hdearmasprakmfmn, ba`fzlakta, ma ifartns msans… parn ak `d ldynr pdrta sa mad `d praniupdifùk idmd mìd laknr,

lì lfsln.

As varmdm qua `ds praniupdifnkas tarfnras trdak `d pnsfef`fmdm ma mn`nrlukmn puama hukmfrsa ak ukd cuarifartds i`dsas ma inkniflfaktns puamsar mfbìifàs ma dìdkzdr, `ns dlfcnspuamak lnrfr. _arn astd i`dsa ma mn

A aksdyn ftardrfn

Qkfmdm 9. Inharakifd, inhasfùk vared` yinkinrmdkifd `fkcðìstfid

Yasfùk

4=



`d vfmd inln `ns qua sa prnmuiak ma`mfscustn inksfcn lfsln. V tnmn fktaræsaxtarkn fkspfrd d`cukd ditfvfmdm qua,lfaktrds a` fktaræs parldkaia ditfvn,

kns pravfaka pnr inlpàtn inktrd a`tamfn. A` fktaræs pnr ukn lfsln, dìnktrdrfn, kn inkmuia d kfkcukd ditfvf-mdm prncrasfvd. ]nmn æxftn sarfn ak uktrdedjn mapakma ma uk fktaræs cakufknpnr a` ldtarfd` ink qua a` trdedjn astära`difnkdmn. A` hnlera d` qua sù`n àpraniupd qua a` lukmn à dmlfra, kn

as prnedeà qua inksfcd su prnpùsftn.@d vdkfmdm iudkmn trdkspnka ifartns`ìlftas, ldtd a` p`diar ma tnmd hdef`fmdmaspnktäkad y inkmuia bdtd`lakta d `dfkmfbarakifd y d` deurrflfaktn.

A` häeftn ma lfrdr d` buturn y ma iraarqua `d vfmd kn tfaka ntrn saktfmn qua a`

ma prnmuifr a` pnrvakfr as parkfifnsn. @dvfmd kn maea inkiaefrsa inln uk la-`nmrdld ak a` iud` a` hærna y `d harnìkddtrdvfasdk mfbfiu`tdmas fkiraìeàs hdstd`àcdr d uk bfkd` mfihnsn. @d rdìz ma` ldàstä ak `d flpnrtdkifd qua sa inkiamad` æxftn ak `d inlpatakifd inln ldynr

buakta ma ba`fifmdm. Vn kn kfacn qua `dinksaiuifùk ma` æxftn bdif`fta a` cnia ma`d vfmd… ]dlpnin kfacn qua a` mfkarn,hdstd ifartn puktn, sad luy idpdz madulaktdr `d ba`fifmdm7 läs d``ä ma ifartnpuktn kn `n iran dsì. @n qua sì dbfrln asqua a` æxftn kn as läs qua uk fkcramfaktama d ba`fifmdm, y qua sa inlprd maldsfd-

pnr inksacufr`n. Dukqua as ifartn quak tnmd prnbasfùk axfsta uk aàlakma inlpatakifd, kn n as lakns qua ksa raspatd praifsdlakta a` æxftn, sfk

`ds iud`fmdmas d `ds qua sa hd maefmn æxftn. Qk hnlera ma ifakifd puama n khdiar mfkarn, parn kn as läs raspatdmsf `n hdia qua sf kn `n hdia.

Ak Dlærfid a` hnlera prnbasfnkd` flfd` hnlera ma kacnifns, y kn inkstftuyinln ak Aurnpd, ukd idtacnrìd dpdrt

Ak `ds i`dsas d`tds kn hdy, pnr `n tdktkdmd qua lftfcua `d ùihd, defartd brdkid, pnr a` æxftn bfkdkifarn. @ns kfôdlarfidkns inlprakmak luy prnkqua astn as `n úkfin qua iuaktd, y ksa praniupdk ma `d amuidifùk qua ktakcd pnsfef`fmdmas paiukfdrfds. Ak sfc`n XRFFF ukd ma `ds idrditarìstfids m

caktàldk ard a` pnmar custdr y aktamar ma `ftardturd, lúsfid y pfkturd.



Yækaid

Nrìcakas y avnùifùk

As mfbìif` astdeàiar `d baihd iudkmn sa

nrfcfkù a` aksdyn. _drd `ns fkvastfcdmn-ras, `ns Mfä`ncns ma _`dtùk, `d _nætfidma Drfstùtaàs, `ds Apìstn`ds Lnrdàsma Yækaid y ntrns asirftns, snk `ds prf-lards buaktas ak `ds iudàs sa fkiueùa` cækarn. Yu avnùifùk prnpfdlaktamfihd kn sa inknia, parn d pdrtfr ma`dôn 418?, dpdraia ukd pue`fidifùkma` brdkiæs Lfiha` ma Lnktdfcka inka` tìtu`n Assdfs. Astns aksdyns kn takìdkntrd prataksfùk pnr pdrta ma` dutnr, sfknmaàftdr y mdr d inkniar d uk crupn madlfcns, sus mfvdcdifnkas diarid ma ukdlu`tfp`fifmdm ma talds.

A` rainkniflfaktn inln cækarn kn sa hfzn ak asa lnlaktn, parn sì samastdiù a` idräitar fktaàitud` ma` asirftn. @d pn`ælfid y `d drculaktdifùkkn snk pdrta ma astns taxtns, inln sì, su mfsiursn in`nqufd` y uk astf`neäsfin qua maspuæs tnldrä ukd bnrld läs rabàxfvd.

@n ifartn as qua masma aktnkias, d pd`derd aksdyn inlakzù d mfkdlfzdrsay id`dr, maefmn d `ns idlefns snifdàs, pn`ìtfins, ainkùlfins y iu`turdàsqua vfvfù Aurnpd ak `ns sfcufaktas dôns.

@ns fktaàitudàs ma aktnkias, sa vfarnk denidmns d `d rabàxfùk, d `d fk-tarfnrfzdifùk ma talds inln `d luarta, `d ra`fcfùk, `d vfmd, y dúk sneradspaitns katdlakta mfmäitfins. @d pdrta suejatfvd ma` asirftnr, su par-snkd`fmdm y sus flprasfnkas aktrdrnk d `d `ftardturd, parn a` aksdyn sù`ndmqufara a` tnkn ink a` iud` sa à rainknia d lamfdmns ma` sfc`n XFX,iudkmn alpfazd d tnrkdrsa läs sarfn.



Rfsfùk inktalpnräkad

As uk cækarn ra`dtfvdlakta lnmarkn qua dedrid ukd lfsia`äkad ma mfsif-p`fkds hatarncækads, `n iud` hdia flpnsfeà mabfkfr`n ak uk sn`n inkiaptn

y mdrà ukd lfsld mfraiifùk. Ak sì, as ukd bnrld mfsiursfvd defartd quaaxtfakma uk dedkfin ma pnsfef`fmdmas y parlfta trdtdr talds bf`nsùbfins,huldkìstfins, pn`ìtfins, snifdàs, ati.

Yu fktakifùk prfldrfd kn as fkbnrldr, sfkn parsudmfr n inkvakiar d` àitnr,mabakmfakmn uk puktn ma vfstd parsnkd`, p`dsldkmn rabàxfnkas a flprasfn-kas y dpnyäkmnsa, d`tarkdlakta ak `ns jufifns y astumfns ma aspaifd`fstds ak

a` tald.

Ak su avnùifùk, kn md idefmd d ntrds bnrlds astætfids inln d ìrfid, pnrquadkta tnmn a` aksdyn as uk cækarn axfcakta qua maldkmd drculaktdifùk,i`drfmdm y rabàxfùk, pnr luy trfvfd` qua sad a` tald qua astæ trdtdkmn.

Dukqua d lazi`d ma cækarns as ukd ma `ds idrditarìstfids ma crdk pdrta ma`ds bnrlds ma asirfturd inktalpnräkad, kn as ifartn qua iud`qufar taxtn,

d` subrfr ukd latdlnrbnsfs, puamd inkvartfrsa ak tnmns. Ak a` bnkmn, idmdcækarn sfcua cudrmdkmn su asakifd. Ynk `ds mfvarsds mfsifp`fkds `ds qua saakidrcdk ma djustdr`n d sus kaiasfmdmas.

A` aksdyn ftardrfn tdlpnin nstaktd uk astf`n aspaiìbfin. Ink ntrds mfsifp`fkdsy ink d ifakifd ak pdrtfiu`dr, inlpdrta a` fktaræs pnr axp`nrdr läs d bnkmn`d rad`fmdm7 fkiursfnkd läs ak `ns `dearfktns ma` sdear ink a` prnpùsftn madprnxfldrsa d `d varmdm ma `ns haihns.



Iùln sa asirfea uk aksdyn

A` aksdyn ldkajd ukd astruiturd edstdkta `fera, ak aspaifd`, sf sa tfaka ak iuak

`d hatarncakafmdm ma mfsifp`fkds qua ldkajd (pn`ìtfid, ra`fcfùk, bf`nsnbìd, `ftardtuati.). _arn ak cakard`, hdy uk hf`n inkmuitnr ma` iud` tnmds sa sfrvak. Ak sus prfla`ìkads, a` aksdyfstd prasaktd uk prneàld qua n àvd d p`dktadr ukd hfpùtasfs diama `ds inksaiuakifds n idusds ma` prneàld7 maspuæs, `àcd d ukd tasfs marfvdmd `d dktarfnr inkjaturd.

Ak asta puktn, a` aksdyfstd sa dtrava d prasaktdr ukd dbfrldifùk qua maea maltrdr murdkta `d axpnsfifùk qua masdrrn``drä ak a` asirftn n iuarpn ma` trdedjn. As

lnlaktn iudkmn a` asirftnr hdia cd`d ma sus inkniflfaktns y sus puktns ma vfsIdmd tasfs eusid sar vd`fmdmd. A` aksdyfstd mamuia, p`dktad, ascrfla, akidmakd fmads, y `n läs flpnrtdkta, drculaktd ma td` bnrld qua puamd vd`fmdr `d fmad prifpd` qua pnstu`ù ak `ds prflards `ìkads.

4. A` brdclaktn ma `d àiturd ma fktrnmuiifùk, axprasd uk puktn ma vfstd parkd` diarid ma` tald ma `d ba`fifmdm. Uatnla tras ma `ds tasfs ak æ` p`dktadmda`denra uk aksdyn ink sus puktns ma vfstd, akrfquaifakmn `d fkbnrldifùk intrds rabàxfnkas.

5. @ad kuavdlakta a` brdclaktn ma fktrnmuiifùk y sustakta `ns lntfvns pnr iudàs puama sar inksfmardmn uk taxtn irìtfin y bf`nsùbfin. Drculakta i

nrdifnkas axtrdìmds ma` lfsln aksdyn.9. ‐@d amuidifùk ak `d irua`mdm y ak a` lfamn as ld`d, parn as `d úkfid q

puama mdrsa pnr qufakas snk asi`dvns ma asds pdsfnkas“. ¾_uama dbfrldrsa qastd nrdifùk ma Uussa`` takfakmn ak iuaktd a` inktaxtn ak a` qua sa axprainktfaka ukd fktakifùk raprasfvd y dkdirùkfid pdrd `ns tfalpns lnmarkn

Drculakta ak sus pd`derds.=. ¾_nmrìd dbfrldrsa qua `ds irìtfids qua prasaktd a` dutnr, vdk mfrfcfmds d uk sfs

ld pn`ìtfin, d` ldkajn ma `ns vd`nras ak `d snifamdm lnmarkd n d `d fkbùak

4



4=


4. @ad d`cukns aksdyns iuyd talätfid à rasu`ta dtrditfvd. Aktra a``ns,asinjd uk aksdyn ifaktìbfin y uk aksdyn ftardrfn iuyds talätfids sadkdbfkas. @æd`ns dtaktdlakta y prasakta uk dkä`fsfs ak pdrdà`n, lns-trdkmn dqua``ns dspaitns qua `ns mfbarakifdk y dqua``ns qua às mdk

hnlncakafmdm inln raprasaktdktas ma` cækarn aksdyìstfin.

5. Uatnla ukd ma `ds fmads p`dktadmds ak iud`qufard ma `ns aksdynstrdedjdmns ak a` kulard` dktarfnr y prasakta su prnpfd axpnsfifùkaksdyìstfid.

9. @ad dtaktdlakta a` sfcufakta brdclaktn y axp`fqua hdstd quæ puktnpuama sar inksfmardmn uk aksdyn n fkmfqua d qua ntrn cækarn pnmrìd

partakaiar.

‐Ak uk ajalp`dr ma` prflar vnùlak ma @ds lf` y ukdkniha (@nkmras, 48=?), ma @dka, qua la inksfcufùlf quarfmn dlfcn _du`fkn Gafks, masiuerflns a` ld-kusirftn qua dhnrd trdmuifræ d` idsta``dkn“. Ink astds

pd`derds, a` asirftnr drcaktfkn Jnrca @ufs Enrcas fkfifdsu Fkbnrla ma Ernmfa, uk taxtn `ftardrfn qua lazi`d d`cækarn aksdyìstfin ink a` iuaktn. @ad a` taxtn saôd`dmna fkmfqua, ink brdclaktns ma` lfsln, ak quæ lnlaktnmajd ma sar iuaktn pdrd ratnldr `ds idrditarìstfids maàksdyn y vfiavarsd.



Eartrdkm Uussa``

Bf`ùsnbn y ldtalätfin erftäkfin, cd`drmnkdmn inka` pralfn Knea`. Yu ækbdsfs ak a` dkä`fsfs `ùcfinrapariutfù snera a` iursn ma `d bf`nsnbìd ma` sfc`nXX. Kdifmn ak ]ra`àig (Cdàs), a` 48 ma ldynma 4835, Uussa`` astumfù ak a` ]rfkfty In`àca ma`d Qkfvarsfmdm ma Idlerfmca. ]rds crdmudrsa ak486=, vfdjù d Brdkifd, Dàldkfd y Astdmns Qkfmns,

y ùacn bua knlerdmn lfalern ma` inksajn macnefarkn ma` ]rfkfty In`àca. Masma luy jnvaklnstrù uk diusdmn saktfmn ma inkifakifd snifd`y d` lfsln tfalpn, sa aspaifd`fzù ak iuastfnkasma `ùcfid y ldtalätfids, ärads snera `ds iudàsmfn inkbarakifds ak luihds fkstftuifnkas ma tnmna` Lukmn. Uussa`` dìdkzù a` æxftn ink su prfla-rd crdk nerd _rfkifpfns ma ldtalätfids (46?5),

ak `d iud` fktaktù trds`dmdr `ds ldtalätfids d`ärad ma `d bf`nsnbìd `ùcfid y mntdr`ds ma uk ldrinifaktìbfin praifsn. In`denrù murdkta nihn dônsink a` bf`ùsnbn y ldtalätfin erftäkfin D`bramKnrth Shftahadm, pdrd a`denrdr `d lnkulak-td` nerd _rfkifpfd Ldtalätfid. Ak su sfcufaktacrdk nerd, @ns prneàlds ma `d bf`nsnbìd (4645),Uussa`` raiurrfù d `d snifn`ncìd, `d psfin`ncìd, `dbìsfid y `ds ldtalätfids pdrd rabutdr `ds mnitrfkdsma` fmad`fsln, `d asiua`d bf`nsùbfid mnlfkdkta akasa tfalpn, qua snstakìd qua tnmns `ns nejatns yaxparfakifds snk brutn ma` fktaàitn. Uussa``, ukdparsnkd rad`fstd, iraìd qua `ns nejatns parifefmnspnr ns saktfmns pnsaak ukd rad`fmdm fkharakta d`ldrcak ma `d lakta.Bntns tnldmds ma Sfgfpamfd



• Diuôdr: inkiaktrdr.• Dbdeà: dcrdmdeà, muìa, sudva ak `d

inkvarsdifùk y a` trdtn.• Dùifkdkta: qua prnmuia saksdifnkas

frradàs.• Dtf`d: jaba ma `ns hukns, eäredrn a fk-

huldkn, iuyn knlera sa dsnifd inkinlpnrtdlfaktns vfnàktns.

• Dvfmaz: dksfd, inmfifd.•

Dzdrnsd: turedmd, talarnsd.• Inkmaksdr: sfktatfzdr, rasulfr, inl-

pakmfdr, `fiudr.• Inyukturd: ifriukstdkifd qua dbaitd

uk dsuktn.• Irapftdr: prnmuifr snkfmns rapatfmns,

räpfmns y sains.• Mairapftum: mfslfkuifùk. Id`fmdm ma

parsnkd dkifdkd ink bdiu`tdmas mfslf-kufmds.

• Mæbfift: bd`td n asidsaz.• Mfraitrfz: qua matarlfkd a` iursn n

mfraiifùk.• A`niuakifd: drta ma hde`dr ak púe`fin.• Arrdmfidr: drrdkidr ma rdìz.• Avdkasiakta: qua sa masvdkaia n

asbuld.• Caktàldk: pd`derd fkcàsd qua masfc-

kd d` ided`àrn fkc`æs ma ifartn rdkcnsnifd` n d` hnlera qua sa à dsalajdak pnrta, inlpnrtdlfaktn y ditftum.

• C`dmfdmnr: ùihdmnr qua ak a` ifrinrnldkn, inledtìd inktrd ntrn n inktrdukd bfard.

• Hurtdmf``ds: ma bnrld burtfvd, sfk quasa knta.

• Fkinktfkakifd: sfk inktakifùk, sfkbrakn.

• Frdiukmn: rdefnsn ak axiasn.

• Jdrdkd: mfvarsfùk eu``fifnsd y dènrn-tdmd.

• Jìedrn: lfalern ma uk puae`n dla-rfkmfn ma d vartfakta nrfaktd` ma Aiud-mnr.

• Jf`cuarn: as ukn ma `ns päjdrns läs``dldtfvns ma Aurnpd. Ya mnlastfidbäif`lakta y puama iruzdrsa ink aìdkdrfn.

•

@dsifvfd: prnpaksfùk d `ns maàftasidrkdàs.• @acdmn: harakifd qua sa majd n trdks-

lfta d `ns suiasnras.• @anktfkd: idmakd latä`fid pdrd in`cdr

a` ra`nj ma en`sf``n.• Lariakdrfn: hnlera qua pdrtfifpd

ak uk inkb`fitn eæ`fin d idlefn ma ukpdcn.

• Lìlasfs: drta ma flftdr lnmn ma

hde`dr, castns y dmaldkas ma ukdparsnkd.

• Kfhf`fsln: fman`ncìd qua kacù tnmnprfkifpfn ra`fcfnsn, pn`ìtfin y snifd`.

• Nkìrfin: ra`dtfvn d `ns suaôns.• Nknldtnpayd: vnide`n qua flftd n

rairad a` snkfmn qua masirfea.• _aiukfdrfd: ra`difnkdmn ink a` mfkarn

ak abaitfvn.• _araiamarn: qua luara.• _arkfifnsn: mdôfkn y parjumfifd`.• Ua`dtnr: parsnkd qua kdrrd haihns n

talds.• Ynpasdr: axdlfkdr a` prn y a` inktrd

ma uk dsuktn.• ]rfed`: partakaifakta n ra`dtfvn d `d

trfeu.• Qù`dkta: qua md crftns n d`drfmns.



9. Ftals kulardmns y vfôatds. @ns `fstdmns snk d`fdmns ma `d rataktfvdra`djdk `d lakta raditfvd (idpdifmdm ma dsflf`dr y radiifnkdr), ma` àitavftdkmn `d praniupdifùk fkinksifakta pnr parmarsa ak `d saiuakifd mafkbnrldifùk.

=. Uasd`tdmns n saôdàs pdrd hfpartaxtns n taxtns inlpàlaktdrfns. Ya masaôd`dr ink ntrn in`nr n ink uk suerdydmn, `ds pd`derds läs flpnrtdkma` mniulaktn n ma` e`nqua ma taxtn. @ds pd`derds tfpn vìkiu`n n hfpvìkiu`n maeak fr ak dzu` y suerdydmds. A` in`nr dzu` `n idptd luy räpfa` njn y ukfvarsd`lakta astä inmfbfidmn inln uk aàlaktn qua rasaläs fkbnrldifùk, `d iud` as sulfkfstrdmd iudkmn sa pu`sd a` lnusa sne`d pd`derd.

Ajalp`n:

A` Ln`fkn Unjn, lusfid` ifkaldtncräbfin ma` mfraitnr Edz @uhrldkk, ashfstnrfd ma` _drìs enhalfn ma bfkdàs ma` sfc`n XFX, iudkmn parsnkdjas inl]nu`nusa-@dutrai vfvìdk ak `d fkiasdkta eúsquamd ma` dlnr, iuyn hd``dzla dtravn d supnkar, à bua kacdmn d æ`, pdrtfiu`drlakta, mdmd su inkifùk ma akdkfsln qua, pdrd bnrtukd ma `d Ea`à æpnqua y ma `d hfstnrfd,

inkmujarnk d asd ldrdvf``nsd buakta ma trdedjn drtìstfin qua tnldrìd vfma àcdmn cfcdkta.

1. Fktartìtu`ns. Maeak sar mfraitns a fkbnrldtfvns, y dpdraiar ink braiuakima ldkard qua sa inkvfartdk ak fkmfidmnras y cuìds ma rainrrfmn mafkbnrldifùk pdrd a` njn.

2. Kn justfbfidr d` iaktrn. Iaktrdr e`nquas ma fkbnrldifùk as inktrdprnmuia

ta, pnrqua sf a` njn kn akiuaktrd `d `ùcfid y a` nrmak ma` taxtn ma ldkafklamfdtd, kn sù`n alpazdrä d bdtfcdrsa, sfkn qua pdsdrä d ntrn saclak

3. Kn usdr ldyúsiu`ds parldkaktas. As ukd mfkälfid qua a` njn kn rasfspnrqua `n ne`fcd d sar inksifakta ma idmd àtrd ak ra`difùk ink `d dktary ink `d sfcufakta. Astn sa maea d qua a` njn astä dinstulerdmn kn sù`n`ds bnrlds fktarkds ma `ds àtrds, sfkn tdlefæk d `ds axtarkds7 y ak `ds lyúsiu`ds `ds bnrlds axtarkds sa tnrkdk `fkadàs



_rfnrfmdmas ak `ns mdtns

qua sa lnktdk ak Fktarkat

Hdy mns aàlaktns fkmfspaksdeàs pdrd bdif`ftdr d aàiifùk ma fkbnrldifùk kaiasdrpdrd astruiturdr ukd päcfkd wae.

4. Jardrquìd. Iudkmn quaralns pnkar fkbnrldifùk ak Fktarkat, maealns dkd`fzrdifnkd`lakta n qua ink axditftum eusidrìd a` usudrfn-àitnr. Ma a``n mapakm`d abaitfvfmdm ma` sftfn wae qua sa rabàjdrä ak a` kúlarn ma usudrfns qua inksu`tak y ak aspaifd`, ak d ratrnd`flaktdifùk qua sa prnmuzid maspuæs. Ak

wae, `n qua inksfmardlns läs flpnrtdkta pdrd a` eakabfifn y `ds kaiasfmdmma` àitnr, `n astdeàialns ak `d prflard aktracd, y `ns bditnras suesfcufakta`ns jardrqufzdlns ink a` lfsln irftarfn. Asa jufifn kn puama sar ntrn sfkn sarvfifn qua quaralns prastdr n `d kdturdàzd rad` ma `n qua nbraialns.

Ajalp`n

A` sftfn sa ``dld Asiua`d Dbrfwae y nbraia iursns snera `d iu`turd dbrfidkd. D

usudrfn a fktarasdräk ns iursns qua nbraia d fkstftuifùk. A` prncrdld as dlp`fparn a` sftfn wae jardrqufzd `ns talds y a`flfkd ma `d prasaktdifùk `ns laknraàvdktas, y rasarvd d`cukns pdrd iudkmn a` usudrfn hdcd inktditn.

5. INKIUAIFÙK. Maea sar idrditarìstfid ma `d ramdiifùk y ma tnmns `ns bditnraqua fktarvfakak ak d astruiturd ma d wae. @ds pd`derds i`dva snk a` fkmfidtfvma` `fstdmn ma pd`derds ink `ds iudàs iraalns qua a` usudrfn pnmrä akinktrkuastrn sftfn wae. Asa `fstdmn sa hdia, supnkfakmn `n qua a` àitnr eusidrä, paksdkmn ak `n qua quaralns qua æ` akiuaktra.

Ajalp`n

Qk usudrfn eusid fkbnrldifùk snera a` drta rupastra ma Dlærfid @dtfkd. @dpd`derds ink `ds iudàs pnsfeàlakta, sn`fiftdrä astd fkbnrldifùk saräk:



4. Astdeàzid uk aqufpn ma fktacrdktas pdrd a` sfcufakta trdedjn ma idlpn:

• Iraak d inlpnsfifùk talätfid ma uk parfùmfin fkstftuifnkd` pdrd Fktarkqua takcd iudtrn päcfkds n pdktd``dzns.

• A`denra sfata saclaktns ma dvdkias pdrd mfstrfeufr ak `d prflard päcfink sus raspaitfvns tftu`dras.

• Asirfed brdclaktns fkbnrldtfvns qua sfrvdk pdrd fksartdr ak `ds rastdk

tras päcfkds.

• Masdrrn`à d`cukds ma ds kntds qua buarnk dkukifdmds ak ns dvdkias, ldkard qua puamd sustaktdr `ds tras päcfkds dmjuktds.

• Hdcd bntncrdbìds n eäja`ds ma Fktarkat pdrd dpnydr `d fkbnrldifùk quavd d mfstrfeufr ak tnmn a` parfùmfin.

• Iraak a` knlera ma` parfùmfin y cakarak uk fstdmn ma 4? pd`derds i`d

• Drta prain`nlefkn• Drta rupastra• Drta ak pfamrd• _atrnc`fbns• Bnrlds drtìstfids ak Yumdlærfid• Bnrlds drtìstfids ak Iaktrndlærfid• _fkturds rupastras• Hd``dzcns drquan`ùcfins• Drta lnef`fdrfn• @ftnasiu`turd• Lurdàs ak pfamrd• Drta `dtfkndlarfidkn• Rastfcfns ma pfamrd

4



‐Ed`tdsdr Cærdrm (4111-4185)“ Judk Jnsæ Drran`d

Fr d ldtdr d` prìkifpa ma Nrdkca. Frd ldtdr`n y inerdr ùacn `ns vafk-tfifkin lf` asiumns qua nbraifùBa`fpa FF pnr su ideazd. Fr d pfa,

sn`n, sfk raiursns, sfk pfstn`d, sfkiuihf``n, iradkmn a` cækarn ma `nsdsasfkns qua pfmak d su vìitfld a`mfkarn qua hdia bd`td pdrd inlprdra` drld ma` irflak, td` bua `d hd-

zdôd ma Ed`tdsdr Cærdrm, uk jnvakidrpfktarn ma Mùà.

D trdvæs ma ukd paknsd parsaiu-ifùk pnr `ns _dìsas Edjns, luartnma hdlera y ma bdtfcd, pdmaifakmnfkinktdeàs malnrds aktra `ns ajær-iftns aspdônàs y b`dlakins, `ncrùderfrsa pdsn hdstd su vìitfld. Akmumds, rnmans y ratrniasns fkvfrtfù

tras dôns y tuvn qua snpnrtdr `dvajdifùk ma qua Cdspdr Dôdstrn àtnldrd `d ma`dktard.

A` pnrtucuæs Cdspdr Dôdstrn, in-larifdkta ma pdôns, kn idraiìd ma

fldcfkdifùk, snera tnmn dkta uksaôua`n ma vafktfifkin lf` asiumns.Hnlera praidvfmn, a`fcfù iufmdmn-sdlakta a` prniamflfaktn y d baihd

ma` irflak. _arn d ú`tfld hnrd ma-ifmfù pnkar uk fktarlamfdrfn aktrasu iaraern y a` drld: Judk Jäuracuf`d alpuôdrìd pnr æ`.

Judk Jäuracuf, jnvakzua`n ma vafk-ta dôns, ard tìlfmn ma pnr sì. _arn

Dôdstrn `ncrù talp`dr su d`ld hdstd

a` harnìsln, lamfdkta uk sfstald masutfàs indiifnkas iuyd sairatd i`dvasa kns asidpd. ]d` vaz n derulù inkàiturds harnfids7 td` vaz n prnvayùma td`fsldkas7 td` vaz `n `àvù la-tùmfidlakta hdifd uk inksifaktasufifmfn.

@n úkfin qua sdealns ink iartazdas qua a` mìd saôd`dmn pnr su pdtrùk(48 ma ldrzn ma 4185), y murdkta`ns bastfvdàs iaàerdmns ak Dlearaspdrd hnkrdr d` muqua ma Dkjnu ak su



_dutds pdrd a`denrdr uk dkä`fsfs `ftardrfn

]nmn dkä`fsfs `ftardrfn maea inktalp`dr `d nerd ak su inkjuktn. Qkd axp`fidifù

brdclaktdrfd qua sa prasakta inln uk `fstdmn, kn as uk dkä`fsfs sfkn ukd eurmra`difùk ma inktakfmns.

A` varmdmarn dkä`fsfs axfca d` àitnr, ra`difnkdr, inlpdrdr, fktacrdr, masifbrdr y p`dldr `n àìmn edjn ukd pnsfifùk mnkma su vfsfùk parsnkd` as mabfkfmd, efak sad ed`d bnrld ma uk aksdyn n ukd rasaôd. @d tìpfid lakifùk ma `ds pdutds ak sn`ftdrfn,`d ldkard ma uk `fstdmn, `fqufmdk tnmn varmdmarn dkä`fsfs.

]dlefæk as flpnrtdkta takar ak iuaktd, qua `d efncrdbìd ma` dutnr as axtarfnr d nerd. As frraàvdkta pratakmar mfùifmdr, inlprakmar a fktarpratdr uk asirftn pnr vfvakifds ma` dutnr, pnr su idräitar n su parsnkd`fmdm. @d nerd maea axp`fidrsa pnsì lfsld y pnr `ds fmads qua sueydiak ak tnmn mfsiursn, läs dúk, sf asta mfsiursas `ftardrfn.

Dktas ma fkfifdr a` dkä`fsfs, sa maea fmaktfbfidr `ds sfcufaktas pdutds lìkflds:

4. ]ald5. Drculaktn9. _arsnkdjas=. ]alds i`dva1. @nid`fzdifùk cancräbfid2. ]falpn hfstùrfin

3. Uaiursns `ftardrfns: tfpn ma kdrrdmnr, astf`n, tfalpn fktarkn, tfpns mamasirfpifùk y bfcurds `ftardrfds

A` sfcufakta ajalp`n kn as ukd suld ma mdtns, sfkn ukd ra`difùk ma aàlaktn(fmaktfbfidifùk ma `ns parsnkdjas, inktaxtud`fzdifùk hfstùrfid ma `d nerd, dkä`fsfs inlaktdrfn ma` puae`n ma Inld`d, ati.), qua sa akiuaktrdk maktrn ma `d nerd7 ukaxpnsfifùk inlaktdmd ma` àitnr qua hd sdefmn idptdr dspaitns ma `d asakifd qu



42


4. @d masirfpifùk as ukn ma ns aàlaktns läs flpnrtdktas ak kularnsdsnerds `ftardrfds. Qtf`fzdkmn uk àcudja `ftardrfn, masirfed a` ùcdr mnkmasa masdrrn``drnk ns haihns. @ad kuavdlakta d @aiturd ma fktrnmuiifùky hdcd saktfr d su buturn àitnr, `d ea`àzd, lfstarfn u hnrrnr ma` ùcdrmnkma niurrfù `d hfstnrfd, ak uk asirftn dkd`ìtfin ma 4? `ìkads.

5. @ad kuavdlakta `d hfstnrfd ma Ed`tdsdr Cærdrm, iaktra su dtakifùk aka` parsnkdja prfkifpd` y axp`fqua iuäàs huefardk sfmn `ns rasu`tdmnsma `ns dinktaiflfaktns vfvfmns, sf a` parsnkdja huefasa tnldmn ntrdmaifsfùk y ntrn rulen.

9. @ns haihns kdrrdmns ak Mùà, ¾puamak ra`difnkdrsa ink d`cúk dinkta-iflfaktn vfvfmn ak kuastrn _dìs ak `ns ú`tflns dôns> Axp`fqua.


4. ¾_nr quæ a` ra`dtn ma Drran`d sa inksfmard uk taxtn `ftardrfn>

5. Yaôdà tras raiursns `ftardrfns utf`fzdmns pnr a` dutnr. Axp`fqua ak quæ inksfidmd ukn ma a``ns.

9. Fmaktfbfqua d` parsnkdja iaktrd` ma `d nerd y dkd`fia `ds idrditarìstfids qua

mabfkak inln td`.=. Matarlfka `ns tras aàlaktns qua mabfkak `d astruiturd ma` ra`dtn.

4



‐Lnkù`ncn ma` fksulfsn“(Brdclaktn)

Judk Jnsæ Drran`d

_nsaì d `d huærbdkd `d kniha lfsld ak qua va`äedlns d su pdmra d `dùz pdrpdmadkta ma `ns ifrfns (¡Nh, sf pumfard maifr astn lfsln ink ntrdspd`derds!).

Inln tnmn sa sdea ak asta lukmn, `d insd `àcù d nìmns ma` vfajaif``nqua lfrd kuastrn sfc`n d trdvæs ma sus ld`fifnsns quavamns. La rabfarn d

asa dkifdkn saônr qua prasfma `ds àtrds laxfidkds tnidmn ink a` cnrrnma mnrlfr ma `ns lalnrfd`fstds, y qua la vdpuàù ak pàkd id`à ink suakburaifmn edstùk, dkta `d fkabfidifd ma `d pn`fiìd ifumdmdkd. Uaifeì tdl-efæk ukd inrrnsfvd `ùvfd ma fkjurfds prnbarfmds ink vnz dcumd y burfnsd.

V tnmn, crdifds d qua a` fkinrraitn pdtrfdrid ¡a` mfde`n sa `n `àva! astdedakdlnrdmn ma `d muìa luihdihd qua masma dhnrd la denrraia.

¡Dy ma lì! Vd la denrraia hdstd d dvdkmard, d pasdr ma kuastrns iäkmfmnsy mf`dtdmns dlnras. V `d ea``d inkbfmakta, d qufak a` maifr pnpu`dr saôd`dinln lf Muìfkad, kn qufsn nìr yd `ds quajds ma` inrdzùk mn`fakta ma supnatd. Iran qua la maspraifdk hdstd `ns parrns.

_nr bnrtukd, astds fkbdlas hde`dmurìds kn puamak `àcdr hdstd lf quarfmnpúe`fin. Vn idktn pdrd uk dumftnrfn inlpuastn ma raidtdmds saônrftds y maalpn`vdmns vfajftns pnsftfvfstds. D a``ns `d dtrnz aspaifa kn `àcd7 astäk

Lnkù`ncn y sn f nqufn

Qkfmdm =. Yalfùtfid ma` ifearaspdifn: fktakifnkasinlukfidtfvds, vdrfds bnrlds ma axprasfùk

Yasfùk

43



Ak su vfmd, tnmd parsnkd d`cukd vaz, ldktuvn uk mfä`ncn inksfcn lfsld n `dkzuk sfkkúlarn ma rai`dlns y mfdtrfeds d uk fktar`niutnr qua asiuihded ak bnrlrasfckdmd y pdsfvd. Astds bnrlds ma axprasfùk raifeak a` knlera ma lnkù`ncn sn`f`nqufn. Astds bnrlds ma axprasfùk nrd` tdlefæk partakaiak d` idlpn ma `d tardturd y `ds hd alpàdmn inln raiursn `ftardrfn ak `d kdrrdtfvd y `d mrdldturcfd


@ns sapu`turarns axhuldk a` iräkan ma Vnrfig,

a` eubùk pnr Aucèka Ma`dirnfx (i. 4896)

@d bfcurd ma Hdlàt astä buartalakta `fcdmd

Asiakds ma Hdlàt ma Sf``fdl Yhdgaspadra.

Yn`f`nqufn

As uk mfsiursn qua alfta uk parsnkdjapdrd sì lfsln, pnr lamfn ma mfvdcd-

ifnkas alnifnkdàs n bf`nsùbfids. Ua-bàxfnkd, sdefækmnsa a` fktar`niutnr masì lfsln, inksifakta ma `d kaiasfmdmma akinktrdr ukd pnsfeà raspuastd dsus mumds a fktarrncdktas. A` sn`f`nqufnp`dktad uk mfàld qua sdiuma `d fktf-lfmdm ma` fktar`niutnr y qua kn as läsqua `d inksifakifd ma qufak `n alfta.

A` ajalp`n läs raprasaktdtfvn masn`f`nqufn ak `d `ftardturd, as Hdlàtma Yhdgaspadra, nerd ak `d iud` a`parsnkdja axprasd su `dlaktn braktad `d maiapifùk y dkcustfd qua à hdprnvnidmn a` inlpnrtdlfaktn ma suldmra qua kn cudrmù subfifakta mua-

`n dkta `d luarta ma` aspnsn y sa hdidsdmn kuavdlakta.

A` sn`f`nqufn as ukd bucd ma `drcnspaksdlfaktns qua bùyak y sa fktar-inkaitdk ak ukd sfktdxfs idrcdmd maaxi`dldifnkas. Ajalp`n: ak a` taxtnma D`lds luartds ma Kfgn`äf Cncn`.



Lnkù`ncn

@ns asirftnras y mrdldturcns `n usdk läs qua a` sn`f`nqufn. A` lnkù`ncn as uk m

iursn qua bnrlu`d uk sujatn qua ak bnrld inksifakta, pakatrd ak su fkinksifay axprasd sus saktflfaktns y saksdifnkas läs prnbukmds. ¾Tufæk as su fktar`niut_nr n cakard`, ntrn parsnkdja qua kn sa prnkukifd kf sa rava`d dkta ds pd`derds mmfsiursn. A` hde`dkta fktarpa`d, diusd, axpnka ak uk diaàrdmn bùjn qua akidmasfk tracud, ukd fmad trds ntrd.

@d ftardturd deukmd ak ajalp`ns ma lnkù`ncns y ns akinktrdlns masma a` sfc`n nrn: A` parrn ma nrn ma @npa ma Racd7 Lrs Mdf``nwdk ma Rfrcfkfd Snn`b, Dktas masdyukn ma N. Ka``y, @d läs buarta ma Ducust Ytfkearc, @d vnz huldkd ma JaInitadu, Ynera a` mdôn qua hdia a` trdedjn ma Dktnk Ihæjnv, Lnkù`ncn ma LnE`nnl ak Q`fsas ma Jdlas Jnyia, aktra ntrns.


4. ¾D qufæk sa mfrfca a` lnkù`ncn qua sa prasaktd ak d @aiturd ma fktrnmuiifù

5. ¾Axfsta ukd fktakifùk ldkfpu`dmnrd pnr pdrta ma` alfsnr ma` lnkù`ncn> Yf as dsì, ¾d quæ dpuktdk sus mfcrasfnkas>

9. ¾Tuæ tfpns ma pd`derds parlftak fkbarfr a` astdmn dkìlfin ma` parsnkdja>

=. @ns drculaktns ak ns iudàs a` ditnr-parsnkdja dpnyd sus quajds, sa edsdk ukd matarlfkdmd sftudifùk: ¾quæ tfpn ma sftudifùk as> ¾Hdy uk nrmak `ùcfak sus nrdifnkas> Axp`ìqua`ds.

4



‐A` cnrrfùk ak a` tajdmn“Cfnvdkkf _dpfkf

_draia flpnsfeà, parn asns erutns cfcdktas ma mns pfarkds pdraiak iradmnsdpnstd pdrd kuastrn idstfcn. N kns hdiak prfsfnkarns, n kns ldtdk, y, kninktaktns ink astn, la bdstfmfdk a` suaôn.

Kn aktfakmn kdmd ma `n qua pdsd. @uz drrfed y ùz dedjn. _draia qua saastä hdifakmn ma mìd y, sfk aledrcn, æsta kn as a` id`nr ma sn`.

A` haihn as qua astd kniha kn as pnsfeà mnrlfr ak pdz.

La pdraia qua hdia pnin ha racrasdmn d` kfmn y ak astd æpnid ma` dôn dsknihas kn tarlfkdk kukid. Kn puama sar `d ldôdkd. Dquì hdy uk lfsta-rfn. Dedjn ak a` astde`n nfcn vnias7 drrfed ak a` ifa`n ntrds vnias, kn sæ maqufæk. ¾Yarä pnsfeà qua `ns hnleras sa hdydk puastn ma rapakta d vn`drinln knsntrns> ¡Yarìd kuastrd rufkd!


4. @adk kuavdlakta ns ajalp`ns prasaktdmns ma lnkù`ncn y sn`f`nqufn. Dkd`fiaak matd`à ns brdclaktns, y raspnkmdk masma a` puktn ma vfstd fkcðìstfin, ¾qu`ns diarid y quæ `ns mfbarakifd>

5. @ns sfcufaktas pärrdbns snk uk ajalp`n ma lnkù`ncn iuyn nrmak hd sfmn d`tardm

fktakifnkd`lakta pdrd a` ajarififn. Uaasirfedk a` taxtn, eusquak su inharakiy axp`fquak quæ fmads às sucfrfù a` lnkù`ncn ak masnrmak.

5



5. Asirfed uk sn`f`nqufn qua axpnkcd su masdzùk dkta `d fkidpdifmdm madìdkzdr uk masan qua hd ldktakfmn murdkta luihn tfalpn.

9. A`denra uk fstdmn ma pnsfeàs talds qua n fkqufatdk n aktusfdsldk yqua qufsfard axpnkar d ntrns. Uamdita su prnpfn lnkù`ncn, asincfakmnukn ma `ns dktarfnras dsuktns.

Lnrfr…, mnrlfr7 kn läs y ink uk suaôn sdear qua mflns bfkd `ds inkcnjds, y d `ns lf` snerasd`tns kdturdàs qua inlpnkak`d harakifd ma `d idrka, inksuldifùk as æstd qua ink ruacnssa puama masadr. Lnrfr, mnrlfr…“.

Sf``fdl Yhdgaspadra

Asirftnr, pnatd, dutnr tadtrd` y mrdldturcn fkc`æs4

412= Kdia ak Ytrdtbnrm-upnk-Dvnk. As a` tariar hfjn ma JnhkYhdgaspadra y Ldry Drmak.

4185 Ya idsd ink Dkka Hdthdwdy. D` dôn sfcufakta kdia suhfjd Yusdk y, mns dôns maspuæs, `ns cala`ns Jumfth yHdlkat.

4188-86 Ya fkstd`d ak @nkmras, dedkmnkdkmn d aspnsd a hfjns, yasirfea sus prflards nerds.

4169-6= _ue`fid `ns pnalds Rakus y Dmnkfs y @d vfn`difùk ma@uiraifd, mamfidmns d` inkma Hakry Srfnthasày maYnuthdlptnk, su prntaitnr.

416= Uadparturd ma ns tadtrns. Yhdgaspadra as yd lfalern ma`d lajnr inlpdôìd ma d æpnid, d Inlpdôìd ma Ditnrasma @nrm Ihdlear`dfk.

4163 Bd`àia su hfjn Hdlkat. Yu euakd sftudifùk ainkùlfidinln alprasdrfn ma `d inlpdôìd à parlfta dmqufrfrKaw-_`dia, ukd idsd ak Ytrdtbnrm.

4. Astd fkbnrldifùk as tnldmd taxtud`lakta ma d päcfkd wae:http://www efncrdbfdsyvfmds inl/lnkncrdbfd/shdgaspadra/irnkn`ncfd htl



Atdpds ma `d prasaktdifùk ma` cufnk

Iudkmn takalns `d fmad ma `d hfstnrfd, prasaktdlns a` cufùk ak tras atdpds eäsfi

@d astrdtacfd m

idrdin`, pa`ìiu

ma` in`nlefdk

Y f I e

4. Yfknpsfs (iarid ma mns päcfkds). Inksfsta ak asirfefr ma ldkard sfk-tætfid, `d hfstnrfd qua sa pratakma inktdr ma prfkifpfn d bfk, fkiùfmns`ns kumns eäsfins ma `d trdld.

5. Asidàtd (iarid ma ifkin päcfkds). As a` lfsln p`dktadlfaktn ma `d

sfknpsfs, parn sa dlp`ìd y masc`nsd `d hfstnrfd ak asiakds, ma bnrldrasulfmd.

9. ]rdtdlfaktn (iarid ma 9? päcfkds). Astdeàia d a`denrdifùk inlpàtda fktacrd` ma `ns cufnkas tæikfin y `ftardrfn. A` `ftardrfn prasaktd tnmns`ns mfä`ncns y a` tæikfin axp`fid ak bnrld lfkuifnsd, idmd diifùk ma`ds asiakds y sus inlpàlaktns: lnvflfaktns ma iäldrd, aktrdmds ma

`d edkmd snknrd, fùlfkdifùk, p`dkn d p`dkn, ati. As `d tariard pdrtama `d asirfturd ma` cufnk ak `d iud` sa matd``dk tnmds `ds asiakds, inkasenzns ma `ns pdr`dlaktns y ink `d idrditarfzdifùk ma idmd asiakd.Asta cufnk sa mfstrfeuya d tnmn a` aqufpn huldkn qua fktarvfaka ak`d rad`fzdifùk ma `d prnmuiifùk.



Ajalp`n: ]rdln ma uk cufnk

Axtarfnr. Mìd. Idlpus ukfvarsftdrfn

Udfk y Cdea edjdk pnr `d asid`fkdtd ma `d bdiu`tdm y idlfkdk, sacufmnspnr ukd iäldrd.

Cdea. ]u sacukmn iuaktn, masma ùacn, as tdk fktarasdkta inln a`prflarn. La pdraifù ldrdvf``nsn.Udfk. ¡Nh, bdktästfin!Cdea. La flprasfnkù. Yì.Udfk. La sfaktn alnifnkdmd. Astny tdk inktaktd ma qua ta hdydcustdmn.

Cdea. Yì.Udfk. As uk crdk astìlu`n pdrd lì. Tufarn qua `n sapds.Cdea. Kn, kn… quæ tnktarìd. Kn as läs qua ukd npfkfùk, `d lìd.La flprasfnkù d lì.Udfk. Vd sæ. _arn tú aras `d npfkfùk.Cdea. @d vfmd kn flftd d` drta, flftd d `d ld`d taàvfsfùk.Udfk y Cdea ma matfakak y sa lfrdk. Ufsds.

Snnmy D`àk, Ldrfmns y lujaras

Inùlkd ma `d hfstnrfd

@ds mfvfsfnkas axfstak ink i`drfmdm y snk `n qua sa inknia inln ditns qua knrld

lakta, snk ma tras d ifkin. @ns ditns snk `ds atdpds i`dva ma` ra`dtn dumfnvfsud` qusa suemfvfmak ak asiakds ink sus lnlaktns ma i`ìldx, tdlefæk ``dldmns cfrns qua hdiak `ns ækbdsfs alntfvns ak `d hfstnrfd.

D` hdiar a` cufùk, astns iäìu`ns ma tfalpn eusidk `d dmaiudmd prnpnrifùk ma `bdsas, ma ldkard qua tdlefæk `d aspfkd mnrsd` qua inkmuia `d saiuakifd ma `ds aiakds, astæ snlatfmd d` aquf`ferfn qua inksfsta ak qua a` p`dktadlfaktn kn puamsar luy prn`nkcdmn kf tdk bucdz qua a` aspaitdmnr kn takcd tfalpn pdrd fmaktfbfi



• _UFLAU DI]N (51-91 LFKQ]NY)

_`dktadlfaktn: prasaktd a` astdmn ma aquf`ferfn y a` surcflfaktn ma

`d d`tardifùk. As a` ditn qua läs fkbnrldifùk sulfkfstrd.

• YACQKMN DI]N (31-81 LFKQ]NY)

Masdrrn``n: sa md `d ùihd pnr raiupardr a` astdmn ma aquf`ferfn. Aàspaitdmnr maefù quamdr inkvakifmn ma` p`dktadlfaktn, ma td` bnrldqua a` sacukmn maea mnsfbfidr y abaitudr ds idmakds aktra ns paqua-ôns lntfvns y a` nejatfvn bfkd`. @ns parsnkdjas sfalpra astäk ditfvns,

dukqua sad ak bnrld pntakifd`.

• ]AUIAU DI]N (41-5? LFKQ]NY)

Ifarra: sa prasaktd a` i`ìldx. Ya raiupard a` astdmn ma aquf`ferfn n sadmqufara ukd kuavd inkmfifùk qua puama sar fkiùsn, d aktrdmd d ukkuavn inkb`fitn. @n ifartn as qua a` i`ìldx bfkd` kn as a` úkfin, sfknqua idmd asiakd maearìd n pnmrìd takar uk lnlaktn ldridmn pnr

`d alnifùk7 d prflard asiakd tdlefæk maea sar flpditdkta, dukquakn as ukd rac`d fkquaerdktdeà. Ya rainlfakmd, sfk aledrcn, qua `didrcd alnifnkd` kn quama raàcdmd d` ú`tfln lnlaktn ma d pa`ìiu`d.

4. Nestäiu`n: as ma idräitar ifriukstdkifd` y astätfin.

Ajalp`ns: takar d` sar dldmn d` ntrn `dmn ma` Hfld`dyd, masinkniar

A` túka` ma` masdrrn``n

Inrraspnkma d` saclaktn fktarlamfn ma` ra`dtn, as maifr, d `ns cfrns ma `d ùihdmasdrrn``n, y akldrid tras tfpns ma mfbfiu`tdmas:



radàs n bfitfifds, `d hfstnrfd astä iaktrdmd ak uk hærna n harnìkd qua sa lnvad pdrtfr ma:

• Qkd lntfvdifùk prfkifpd` qua as d rdzùk ma sar ma` ra`dtn, d qua fkmud ditudr.

• Qkds fktakifnkas qua snk ds maifsfnkas y ns pdsns qua md a` parsnkdak su fktaktn pnr supardr a` inkb`fitn y raiupardr a` aquf`ferfn.

• Qk nejatfvn prfkifpd` qua sa `ncrd maspuæs ma hdear iulp`fmn `ns netfvns saiukmdrfns qua sa akidrcdk ma fktrnmuifr suspaksn y axpaitdtfvAs `n qua sa eusid dìdkzdr.

5. Cuìd ldtarfd`

A` stnry endrm as `d cuìd pdrd masc`nsdr `ds fläcakas y a` snkfmn ma uk inlifd` ma taàvfsfùk n ifka. Iudkmn sa trdtd ma ukd pa`ìiu`d n uk mniulaktd`,inknia inln cufnk tæikfin.

Hdcd uk cufnk tæikfin ak mns inùlkds ma ifkin bf`ds, pdrd masirfefr a` mfä`ncn yfldcak ma ifkin asiakds ra`difnkdmds ink ds idusds ma` idàktdlfaktn c`ned`. Q`ns parsnkdjas ma su aàiifùk y idrditarìia`ns eravalakta, tdktn sf nptd pnr `àv

Fldcak ma Cderfa` _æraz Irfsdktn www.lu`tfla

Ytnry endrm.

4



Cufùk ak tras ditns

• Uatnlak a` crupn ma trdedjn qua astdeàifarnk ak a` lùmu`n ma @akcudifkaldtncräbfin pdrd a` td`àr inàitfvn qua masdrrn``drnk. Astumfdr `d sknpsfs qua p`dkadrnk aktnkias, y ns rnàs ink sus raspaitfvds prnpuastiradtfvds.

•

Astdeàzidk `d idrditarfzdifùk psfin`ùcfid, castud` y bìsfid ma tnmns `nparsnkdjas fkvnùirdmns.

• Masirfedk `ns tras ditns inktukmaktas qua inkbnrldräk `d inùlkd vataerd` ma `d hfstnrfd: fktrnmuiifùk, kumn n i`ìldx, ifarra n masak`dia.

• Asirfedk `d asidàtd ink edsa ak `ds prnpuastds qua `ns mfbaraktas rnàdsulfmns pnr ns fktacrdktas ma` aqufpn hdk mfsaôdmn, y ukd vaz puastn

ak inksfmardifùk y dprnedmns ns bditnras ra`difnkdmns ak mfihd asidàtfkfifdr `d a`denrdifùk ma` cufnk tæikfin-`ftardrfn qua masc`nsdrä tnmns `nmatd`às tæikfins, ns mfä`ncns y a` masdrrn``n ma ds asiakds pdrd tras ditn

4



48

Idrditarfzdifùk ma parsnkdjas

_drd mdrà vfmd y inkbnrldifùk d uk parsnkdja, as kaiasdrfn mabfkfr sukfva` ma prntdcnkfsln: prfkifpd` n saiukmdrfn, sfk mfslfkufr a` ækbdsfs, `di`drfmdm y buarzd qua maed flprflfrsa ak a` parsnkdja7 dsì, uk parsnkdjaqua aktra tìlfmd y ldrcfkd`lakta ak `d hfstnrfd murdkta ukns sacukmns,puama inktakar a` lntfvn fktarkn ma tnmd `d hfstnrfd. @d idrditarfzdifùkma `ns parsnkdjas hdia pdrta ma` àkcudja ifkaldtncräbfin, pnrqua tnmninkiaptn aldkdmn ma iud`qufar dspaitn ma` parsnkdja matarlfkd a` rulenma `d hfstnrfd.

E`nig. Ak ukd hfstnrfd, ns parsnkdjas snk tras jùvakas. Astdeàzid su idrdi-tarfzdifùk, takfakmn ak iuaktd psfin`ncìd, dspaitn, tfpn ma fkmulaktdrfd,kfva` amuidifnkd`, lnmdàs, bnrld ma fktarditudr y nejatns qua pnrtdk.Maspuæs, asirfed `d prflard aktracd ma` cufùk: sfknpsfs.

A` Dvfdmnr as ukd

pa`ìiu`d prntdcnkfzdmd

pnr @ankdrmn MfIdprfn

qua mrdldtfzd `d vfmd ma

Hnwdrm Huchas, pfnkarn

ma `d dvfdifùk. Kdrrd su

vfmd masma `d mæidmd ma

465? hdstd `d mæidmd

ma 46=?, æpnid ak qua

Huchas mfrfcìd y prnmuiìd

sus prnpfds pa`ìiu`ds ak

Hn``ywnnm y tdlefæk

pf`ntded sus prnpfnsprntntfpns dærans.



Dpn`n masma _ærcdln, bua d npnkærsaà pnrqua masaded qua `ns tauirnscdkdrdk `d vfitnrfd. Akinkträrnksa dleds mafmdmas ak `d akifkd7 y a` sn-eardkn Dpn`n, hfjn ma Zaus, hde`ù mfifakmn:

¾_nr quæ, akdrmaifmd kuavdlakta, nh hfjd ma` crdk Zaus, vfakas ma`N`flpn> ¾Tuæ pnmarnsn dbaitn ta luava> ¾Didsn qufaras mdr d ns dquans`d fkmaifsd vfitnrfd> _nrqua ma `ns tauirns kn ta inlpdmaiarìds, dukquaastuvfasak paraifakmn. Yf qufaras inkmasiakmar ink lf masan y sarìd `nlajnr suspakmaralns pnr hny a` inledta y `d paàd7 y ùacn vn`varäkd edtd``dr hdstd qua `ncrak drrufkdr d F`fùk, yd qua ns p`dia d `ds mfnsdsmastrufr astd ifumdm.

Uaspnkmfnà Dtakad, `d mfnsd ma `ns erf``dktas njns:

Yad dsì, Bàihdmnr7 ink asta prnpùsftn vfka ma` N`flpn d` idlpn ma `nstauirns y ma `ns dqufvns. Lds ¾pnr quæ lamfn hds paksdmn suspakmar `dedtd``d>

Inktastù a` sneardkn Dpn`n, hfjn ma Zaus:

Hdcdlns qua Hæitnr, ma inrdzùk buarta, mnldmnr ma ided``ns, prnvnquad `ns mäkdns d paàdr ink æ` ak tarrfeà y sfkcu`dr inledta7 a fkmfckdmns`ns dquans, ma harlnsds craeds, susiftak d d`cufak qua lfmd sus drldsink a` mfvfkn Hæitnr.

Dsì mfjn, y Dtakad, d mfnsd ma ns erf``dktas njns, kn sa npusn. Haàkn, hfjn

dldmn ma _rìdln, inlprakmfù d` puktn `n qua ard crdtn d `ns mfnsas quainkvarsdedk, y `àcäkmnsa d Hæitnr, à mfrfcfù astds pd`derds:

¡Hæitnr, hfjn ma _rìdln, fcud` ak prumakifd d Zaus! ¾Tuarräs hdiar `nqua ta mfcd yn, qua sny tu harldkn> Ldkmd qua suspakmdk `d paàd`ns tauirns y `ns dquans tnmns, y ratd d` läs vd`fakta ma æstns d ùihdrinktfcn ak tarrfeà inledta, puas dúk kn hd mfspuastn a` hdmn qua



luards y `àcuas d` tærlfkn bdtd` ma tu vfmd. Ha nìmn qua dsì `n maiìdk `nssalpftarkns mfnsas.

Ak tdàs tærlfkns hde`ù. Nyùà Hæitnr ink fktaksn p`diar, y inrrfakmn dìaktrn ma dlens ajæriftns ink `d `dkzd incfmd pnr a` lamfn, matuvn `ds bd-`dkcas trnydkds, qua d` lnlaktn sa quamdrnk qufatds. Dcdlakùk inktuvnd `ns dquans, ma harlnsds craeds7 y Dtakad y Dpn`n, a` ma` drin ma p`dtd,trdksbfcurdmns ak euftras, sa pnsdrnk ak `d d`td akifkd ma` pdmra Zaus, qua`àvd `d æcfmd, y sa maàftdedk ak inktalp`dr d `ns cuarrarns iuyds maksdsbf`ds dpdraiìdk arfzdmds ma asiumns, idsins y dkzds. Inln a` Iæbfrn, idyak-mn snera a` ldr, akiraspd `ds n`ds, y a` pnktn kacrad7 ma salajdkta lnmnsaktärnksa ak `d ``dkurd `ds hfàrds ma dqufvns y tauirns. V Hæitnr, puastnaktra ukns y ntrns, mfjn:

¡Nìmla tauirns y dquans, ma harlnsds craeds, y ns mfræ n qua ak a` paihnlf inrdzùk la mfitd! A` axia`sn Irnkfùk kn rdtfbfiù kuastrns jurdlaktns, ysacufrä idusäkmnkns ldàs d ukns y d ntrns, hdstd qua tnlæfs `d tnrradmdF`fùk n suiuleäfs juktn d `ds kdvas qua dtrdvfasdk a` pnktn. Aktra vnsntrns

sa hd``dk ns läs vd`faktas dquans7 dqua` d qufak a` äkfln fkifta d inledtfrinklfcn, dma`äktasa y sarä idlpaùk ink a` mfvfkn Hæitnr. _rnpnkcn `nsfcufakta y Zaus sad tastfcn: Yf dquæ`, ink su ernkia ma drcd puktd, inksfcuaquftdrla d vfmd, maspùjala ma ds drlds, `ævasa`ds d ds iùkidvds kdvas, yaktracua lf iuarpn d ns lìns pdrd qua ns trnydkns y sus aspnsds n suedkd d pfrd7 y sf yn a ldtdra d æ`, pnr inkiamarla Dpn`n td` c`nrfd, la àvdræsus drlds d `d sdcrdmd F`fùk, `ds in`cdræ ak a` talp`n ma` bàihdmnr Dpn`n,

y akvfdræ a` idmävar d `ns kdvìns ma luihns edkins, pdrd qua `ns dquans,ma `drcd idea`àrd, à hdcdk axaqufds y à arfjdk uk túlu`n d nrf``ds ma` as-pdifnsn Haàspnktn. V mfrä d`cukn ma `ns buturns hnleras, dtrdvasdkmn a`vfknsn ldr ak uk edja` ma luihns ùrmakas ma ralns…



]atfs, trds `d iùàrd ma Dqufàs, sup`fid d Zaus

pdrd qua æsta parlftd qua `ns trnydkns

dmqufardk vaktdjd (@d F`fdmd).

Jadk Ducusta Mnlfkfqua Fkcras

Bntns tnldmds ma Sfgfp

Luarta ma Hæitnr pnr Dqufàs (@d F`fdmd).

_atar _du` Uueaks.

Lusan Enyldks vnk Eaukfkcak.

Unttarmdl.

@d æpfid as a` cækarn ftardrfn qua axd`td dc`nrfd ma `ns hærnas ak uk lukmn ma bdk-tdsìd y mfvfkfmdmas, ma inkjurns y bùrlu`dssdcrdmds qua à mdk vfmd d su rad`fmdm.

A` cækarn æpfin qua sa fkiùya ak `ds bf`dsma `d pnasìd, sa akiuaktrd ak a` nrfcak ma`ns puae`ns prflftfvns, hdifakmn pdrta masu avnùifùk iu`turd`. _artakaia d d atdpdma bnrldifùk ma `d inàitfvfmdm, kn ma `dfkmfvfmud`fmdm.

A` hærna æpfin as uk sar inàitfvn quamastdid aktra a` inkc`nlardmn pnr subuarzd, su vd`nr y su hnknr, parn tdlefækas uk hærna qua eusid a` dp`dusn ma susinkcækaras. Ma td` ldkard qua sus ditnsraspnkmak d d kaiasfmdm ma sar a` prfla-rn aktra tnmns pdrd qua asd snifamdm `naksdìa.

Asta hærna as raprasaktdmn ak ds inlpnsf-ifnkas n suecækarns qua hdiak pdrta ma dæpfid, inln d apnpayd, a` pnald æpfin na` idktdr ma castd, aktra ntrns. Ak tnmds, a`hærna masp`facd sus hdef`fmdmas y dstuifds,

Lamfdkta sucastfvds masirfpifnkas, a`kdrrdmnr kns luastrd a` aktnrkn qua `nrnmad, `d rfquazd ma sus drlds, su ea-`àzd y `d ma `ns parsnkdjas y mfnsas qua`n dinlpdôdk, dsì inln `ns lnlaktnsiudkmn sa tnrkd dvdsd``dmnr, úkfin, kn pnrnrcu``n, sfkn pnr ukd ày flp`ìiftd qua `dlfsld snifamdm d `d iud` partakaia à hd



Ak d apnpayd, suecækarn ma d æpfid crfacd, rainknialns uk drquatfpn ma hnleiuyd pdrtfiu`dr fktardiifùk ink `ds mfvfkfmdmas y a` Qkfvarsn, `n mabfkìdk y à ntncdedk ukd inkiapifùk ma` Lukmn y ma `d vfmd luy pdrtfiu`dr.

_drd asta hærna y su inlukfmdm, a` Lukmn ard uk tnmn nrmakdmn y parldkakracfmn pnr àyas mfvfkds qua dktavakìdk ak a` astdeàiflfaktn ma `ds insds y ak

mastfkn ma `ns hnleras. @ns masfckfns ma `ns mfnsas ardk fkbàxfeàs y a` hnlera kpnmìd hdiar d`cn inktrd a``ns, axiaptn diaptdr`ns ak bnrld pdsfvd. As läs, ak ukfvarsn ma `d apnpayd, `d suarta n bnrtukd ma` hnlera ardk susiaptfeàs ma ukinktfkud latdlnrbnsfs7 ma d``ì, `d dbfrldifùk ma qua kfkcúk hnlera ard muaôn msu prnpfn mastfkn.

Yu pariapifùk ma` nrmak y ma` aquf`ferfn ma` Inslns, trdtded a` saktflfaktn ma ma

cdrrdlfaktn ma` hnlera ma hny. Yu saktfmn ma n träcfin ard läs efak ma axtrdôaz`n iud` axp`fidrìd a` lntfvn pnr a` iud` su vfmd nsif`ded aktra d rfcurnsfmdm, a` maey a` raspatn d `ds àyas ukfvarsdàs.

]dàs fmads rava`dk a` pnrquæ ma `ds crdkmas apnpayds, astns lftns ukfvarsdàs quiulp`ìdk ak ú`tflds, ukd lfsfùk knrldtfvd y ma dlnkastdifùk.

Dúk ink astd vfsfùk ma` Lukmn, puama dbfrldrsa qua a` hnlera crfacn idraiìd m

@ns idktns æpfins d ns iudàs kns rabarflns (fkmapakmfaktas ma` aspdifn cancräbfin ma `d iu`turd d `d iud` partakazidk), snk a` rabàjn ma ukd inkiapifùk ak `d iua` fkmfvfmun-hærna astä ne`fcdmn d dìdkzdr `ds läs d`tds vfrtumas. _nr astd rdzùk, hærna as dstutn, häef`, mfastrn y rfcurnsn. A` hærna æpfin ùihd y vfva pnr a` rainkniflfaktn y ak asa dbäk ma c`nrfd, bukma `n harnfin ink `n sdkcrfaktn.

¾Ma mùkma vfaka asta parsnkdja> Rfaka ma `d d`td kneàzd y asta as uk haihn quma dktaldkn, à hdia saktfr su maraihn pdrd niupdr su ùcdr ak `d snifamdm.

@d apnpayd crfacd



ma Hnlarn, raàd a` Idktn F y mamuzid: ¾D iuä` ma ds tras dktarfnras idtacnrìsa suenrmfkd a` taxtn>

5. Mfjflns qua `d apnpayd mastdid pnr `ds lú`tfpàs masirfpifnkas qua prasakt

Uaàd a` Idktn RFF ma d fktrnmuiifùk y trdksirfed dqua``ns dpdrtdmns qua sfrvdma ajalp`n. ¾Tuæ bukifùk iulpàk asns dpdrtdmns ak asta idpìtu`n (rainkniflfaktn ma` hærna, su aktnrkn, sus drlds)> Yustakta su raspuastd.

9. ¾Tufæk as a` hærna æpfin ma @d F`ìdmd y pnr quæ> Uaspd`ma su raspuastd ink àiturd qua hfzn ma `d nerd

=. ]akfakmn ak iuaktd d i`dsfbfidifùk qua hfzn Gdysar snera d apnpayd, fkvastfcupnr idmd idtacnrìd, mns tfpns ma apnpayd ak a` trdksiursn ma `ns sfc`ns.


4. Fkvastfcuak iuä` bua a` inktaxtn hfstùrfin ak a` iud` sa masdrrn``drnk `ds mnapnpayds hnlærfids.

5. ¾Tuæ mfnsas pdrtfifpdk ak a` Idktn RF y quæ raprasaktdk aktra a` crupn m

mfvfkfmdmas> Fkvastfcuak.

9. ¾Iùln sa axprasd n snerakdturd` y n läcfin ak ns idktns ma @d F`ìdmd> ¾Tuapfsnmfns raspd`mdk sus raspuastds> Axp`ìquak`ns.

=. ¾Iùln sa rabàjd `d fktrnlfsfùk (in`denrdifùk), ma `ns mfnsas ak `ns suiasnqua vfvak `ns parsnkdjas ma `d F`ìdmd> ¾Yu pdrtfifpdifùk ldrid a` rulen ma `n

5



46

4. ]rdksirfed iudtrn nrdifnkas ma` Idktn RF, ak `ds iudàs `d dmjatfvdifùksa nesarva ink i`drfmdm.

5. ¾Tuæ bukifùk iulpà asd dmjatfvdifùk ak `ds nrdifnkas>9. ¾@d suarta y `d bnrtukd ma `ns hnleras sa rabàjd ak `ns idpìtu`ns ma `d

nerd> ¾Tuæ tfpn ma bnrtukd as asd> _rasakta uk ajalp`n.=. ¾Iùln bua ld`trdtdmn a` hnknr ma` hærna æpfin ma @d F`ìdmd>

Hnlarn (sfc`n RFFF d. I.), as a` knlera ma` pnatd y rdp-snmd crfacn dktfcun d qufak trdmfifnkd`lakta sa à dtrf-euya `d dutnrìd ma `ds prfkifpdàs pnasìds æpfids crfacds@d F`ìdmd y @d Nmfsad. Masma a` parìnmn haàkìstfin, sahd iuastfnkdmn qua hdyd sfmn a` dutnr ma dleds nerds

æpfids7 sfk aledrcn, dktarfnrlakta kn hdeìd mumds, sfkn qua @d F`ìdmd y

@d Nmfsad. ardk inksfmardmns ra`dtns hfstùrfins radàs.

A` knlera Hnlarn as ukd vdrfdkta jùkfid ma` aù`fin Hnldrns y sfckfbfidrahæk, prakmd n cdrdktìd. Hdy ukd tanrìd qua snstfaka qua asta knleraprnvfaka ma ukd snifamdm ma pnatds `dldmns Hnlarfmdf qua ftard`lak-ta sfckfbfid hfjns ma rahakas, as maifr, masiakmfaktas ma prfsfnkarns macuarrd. Mdmn qua astns hnleras kn ardk akvfdmns d d cuarrd, pnr mumdrma su àd`tdm ak a` idlpn ma edtd``d, kn lnrìdk ak æ`. _nr `n tdktn, sa

às inkbfded a` trdedjn ma rainrmdr d pnasìd æpfid nid` pdrd rainrmdr nssuiasns pdsdmns, ak tfalpns dktarfnras d `d `ftardturd asirftd. ]dlefæksa hd sucarfmn qua a` knlera Hnlarns pnmrìd sar uk juacn ma pd`derdsmarfvdmn ma `d axprasfùk hn-la-hnrùk, qua sfckfbfid a` qua kn va.

Diarid ma` ùcdr mnkma lurfù, axfsta ukd trdmfifùk dtastfcudmd d` laknsmasma a` sfc`n R d. I., ma qua sa prnmujn ak `d fs`d ma Ìns. _dusdkfds ra-inca astd trdmfifùk y hde`d snera ukd astdtud ma Hnlarn qua vfn y uknräiu`n qua àyù ak a` ]alp`n ma Dpn`n ak Ma`bns



Qkfmdm 4

Yasfùk 4. Iùmfcn `fkcðìstfin

Fmaktfbfqua `ds bdàkifds qua prasaktd a` ldkajn ma` iùmfcn asirftn ak a`

sfcufakta ajalp`n qua hd sfmn d`tardmn d prnpùsftn:

Murdifùk ma` trdedjn

Ak `ns _dìsas ak qua idsf tnmds `ds lujaras trdedjdk (qua snk `d lftdm ma`puae`n) y ns hnleras sa mdk d rapnsn dmaläs, ma` crdk kúlarn ma sdiar-mntas y ra`fcfnsns qua kn prnmuiak kdmd ink sus ldkns, kf n saônras rfins y

haramarns (d ns qua a` eu`cn `dld kneàs y ided`àrns), fkiù``ækmnsa ak astdiuaktd. d tnmd d idtarvd ma `ns qua sfrvak d astns ú`tflns ma aspdmdihfkasy truhdkas, y d `ns, lakmfcns qua takfakmn sdùm bfkcak akbarlamdm pnrn`cdzdkarìd, hd``dræfs qua snk luihns, ns qua kn prnmuiak kdmd7 y aktra:`ns qua trdedjdk hdy ukd crdk pdrta qua kn sa niupdk ak insds kaiasdrfds,yd qua mnkma tnmn sa inksfcua ink mfkarn as bnrznsn qua hd``d luihdsdrtas tntd`lakta vdkds, qua sù`n sfrvak d` hdktnjn y axiasn.

(]nldmn ma @d Qtnpìd, ma ]nläs Lnrn)

Yasfùk 5. Maedta

_rasakta su prnpfn dkä`fsfs snera ukn ma ns maedtas qua sa rad`fzdrnk ak a`du`d ma i`dsa murdkta asta parìnmn.

Ldkns d d nerd

Qkfmdm =. Yalfùtfid ma` ifearaspdifn: fktakifnkasinlukfidtfvds, vdrfds bnrlds ma axprasfùk

Yasfùk

5?



Yasfùk =. Fkbnrla

Ak crupn, a`denrak uk fkbnrla snera a` rftln ma d i`dsa, a` dlefakta asin`dr,sus masans, pntakifd`fmdmas y prnyaiifnkas prnbasfnkdàs.

Ydktn Mnlfkcn, 42 ma akarn ma 5?49

YAÔNU

JDFUN HAUKÄKMAZ

JABA MA _UAKYD FKY]F]Q]N MA DU]A V IQ@]QUD

Mfraiifùk inlpàtdYdktn Mnlfkcn, Uapúe`fid Mnlfkfidkd

Uaspatdmn saônr Harkäkmaz:^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^, masan pnkar ak inkniflfaktnsuyn ds frracu`drfmdmas mataitdmds pnr a` inlftæ suparvfsnr ak a` prncrd-

ld ma rdmfn, ink a` prnpùsftn ma qua sa sfrvd a`denrdr `ns inlukfidmnsqua astd sftudifùk raqufara. Dmjuktn akinktrdrä fkbnrla qua matd``d `nsuiamfmn.Ak aspard ma qua ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^, sa susirfea maustam,

Dtaktdlakta,

JNHDKD YDL_AU Dumftnrd Lfkfstarfn ma Iu`turd

Yasfùk 9. Idrtds

@d sfcufakta idrtd rabarakifd` idraia ma d`cukns dspaitns, parn tdlefækinktfaka mns bnrlds fkinrraitds. Yaôdà `ns (n a`) qua astäk arrdmns y `àka`ns aspdifns `feras.



Idpìtu`n XRFFMa `d irua`mdm y `d iàlakifd7 y sf as lajnr sar

Dldmn qua talfmn, n sar talfmn qua dldmn(]nldmn ma A` _rìkifpa ma Ldqufdva`n)

_dsn d `ds ntrds iud`fmdmas yd iflaktdmds y mai`drn qua tnmns `nsprìkifpas maeak masadr sar takfmns pnr iàlaktas y kn pnr iruaàs.

V, sfk aledrcn, maeak iufmdrsa ma alpàdr ld` astd iàlakifd,Iæsdr Enrcfd ard inksfmardmn irua`, pasa d `n iud` bua su irua`mdm

astuvfard prapdrdkmn pdrd ukd prùxfld pnkakifd. Yustakta su raspuastdink sftudifnkas inktaxtud`fzdmds ak `d ifumdm y ak a` pdìs qua hdeftd.

5. Eusqua ukd aktravfstd ak d`cukn ma `ns mfdrfns ma `d ifumdm, nesarvaukd ak `d taàvfsfùk kdifnkd` n fktarkdifnkd` y asiuiha ntrd ak rdmfn.Hdcd uk pdrdà`n, ldridkmn `ds idrditarìstfids ma aktrdmd ma idmdlamfn, as maifr, d ldkard pdrtfiu`dr inln idmd lamfn ma fkbnrldifùkfkfifù `d aktravfstd n hfzn `d prasaktdifùk ma` aktravfstdmn.

Yasfùk 6. @ìrfid vdkcudrmfstd

@ad ink dtakifùk ukd ma `ds bäeu`ds ma Asnpn y mastdqua sf `d fktakifùk ma`dutnr bua lnrd`, ra`fcfnsd, mfmäitfid, frùkfid n fkbnrldtfvd. Yustakta.

Qkfmdm 9

Yasfùk 44. Inharakifd, inhasfùk vared` y inkinrmdkifd `fkcðìstfid

Ma` sfcufakta brdclaktn, saôdà a` akukifdmn iaktrd`7 axp`fqua a` usn qua saà md d `d puktudifùk7 fkmfqua `ds fmads saiukmdrfds qua dpnydk a` asirftn7saôdà ds pd`derds qua a mdk inhasfùk d` pärrdbn7 rasd`ta tras nrdifnkas qualdktakcdk `d inharakifd ma` asirftn.



Yasfùk 45. Yalfkdrfn

Dsfstd d uk salfkdrfn ma ns inkiartdmns pdrd asta dôn, d bfk ma inklalnrdruk dôn läs ma` kdiflfaktn ma Ihdràs Mdrwfk, y prasakta uk fkbnrla snera`d ldkard inln mfihn salfkdrfn sa `àvù d iden.

Yasfùk 49. Kntfifd

Ak a` àkcudja y astruiturd ma `d kntfifd, raspnkmd `ds sfcufaktas pracuktds:

• Ak `d fkbnrldifùk, ¾ak quæ inksfsta `d tanrìd ma `d pfrälfma fkvartfmd>

• ¾D quæ kns rabarflns d` hde`dr ma `ds 1S>

• ¾Iuä` ma ds 1S suaà sar rasua`td ak a` iuarpn ma d kntfifd> ¾_nr quæ>

• ¾Iuäàs snk `ds mns idrditarìstfids prfkifpdàs ma` cækarn kntfifd>

`d qua flpusn a` nrmak ak `d Unldôd, `d qua `ncrù su ukfùk y `dqua `d vn`vfù d `d pdz y d `d ba. Tua, sf sa axdlfkd efak, sa varä qua

Enrcfd bua luihn läs iàlakta qua a` puae`n b`nraktfkn, qua pdrdavftdr sar tdihdmn ma irua`, majù mastrufr d _fstnyd. _nr `n tdktn, ukprìkifpa kn maea praniupdrsa pnrqua `n diusak ma irua`, sfalpray iudkmn su irua`mdm takcd pnr nejatn a` ldktakar ukfmns y bfaàsd `ns súemftns7 pnrqua ink pnins idstfcns ajalp`dras sarä läs ià-lakta qua dqua``ns qua, pnr axiasfvd iàlakifd, majdk lu`tfp`fidr`ns masùrmakas, idusds ma ldtdkzds y sdquans qua parjumfidk d tnmdukd pne`difùk, lfaktrds qua `ds lamfmds axtralds dmnptdmds pnr

a` prìkifpa sù`n vdk ak inktrd ma ukn. V as snera tnmn uk prìkifpakuavn a` qua kn maea avftdr ns ditns ma irua`mdm, puas tnmd kuavdmnlfkdifùk trda inksfcn fkbfkfmdm ma pa`fcrns.



Yasfùk 4=. Aksdyn `ftardrfn

Yaôdà quæ hdia qua a` sfcufakta brdclaktn ma Ìtd`n Id`vfkn, sa inksfmara

uk aksdyn `ftardrfn.

A` ra`dtn bdktästfin pdrta ma uk mfsiursn rad`fstd qua as sdiumfmn pnruk avaktn masinknifmn a fksù`ftn, qua d`tard `d rad`fmdm intfmfdkd._nr a``n, pdrd maknlfkdr d uk taxtn inln bdktästfin as kaiasdrfn quaæsta ne`fcua d` aitnr d inksfmardr a` lukmn ma ns parsnkdjas inln

uk lukmn ma parsnkdjas radàs, y d vdif`dr aktra ukd axp`fidifùkkdturd` y ukd axp`fidifùk snerakdturd` ma `ns dinktaiflfaktns quasuiamak ak `d hfstnrfd.

@d `ftardturd bdktästfid sa mfstfkcua pnr `d parpàjfmdm brakta d ukhaihn fkiraìeà y ukd diaptdifùk dkta `n snerakdturd`. @d asakifdma `d `ftardturd bdktästfid as `d rairadifùk ma `n qua sa va, ma insdsaxtrdnrmfkdrfds qua fldcfkdlns qua puamak àcdr d suiamar, insds

inrrfaktas qua td` vaz asinkmak edjn `d dpdrfakifd ukd sacukmdkdturdàzd fkqufatdkta, lfstarfnsd, tarrfeà.

(]nldmn ma @ns iuaktns bdktästfins ma` sfc`n XFX )

Qkfmdm =

Yasfùk 42. Yalfùtfid ma` ifearaspdifn y taxtn `ftardrfn

• Aktra ak Fktarkat y hd`à ifkin mfraiifnkas iuyn mfsaôn fkbnrldtfvnprasakta `ds inkmfifnkas y idrditarìstfids kaiasdrfds ma` inkiaptn maramdiifùk Sae.



Yasfùk 43. _uastd ak asiakd: lnkù`ncn, sn`f`nqufn, tadtrn

• A`denra uk lnkù`ncn, hdifakmn ækbdsfs ak `d masirfpifùk psfin`ùcfid

ma` parsnkdja.

• Ak mns iudrtf``ds, asirfed uk sn`f`nqufn ak a` iud` a` prntdcnkfstd ma`d hfstnrfd sad su d`tar acn. Dvarfcða a` sfckfbfidmn ma` tærlfkn pra-vfdlakta.

• A`fjd ukd ma ds mns bnrlds dktarfnras (lnkù`ncn n sn`f`nqufn), y lnkta`d asiakfbfidifùk tadtrd` pdrd 4? lfkutns y prasækta`d d` crupn.

Yasfùk 48. Cufnk

A`denra `d asidàtd ak ifkin asiakds, ma uk cufùk mniulaktd` snera `dslazi`ds fktariu`turdàs a fktarrdifdàs qua hny ak mìd dkfmdk ak `d inkiap-ifùk ma ifumdmdkns ma` lukmn ak uk _`dkatd c`ned`fzdmn. Yfcd a` asqualdprnpuastn d inktfkudifùk:

Yasfùk 46. Æpfid

A` hærna ma d æpfid pnsaa ukns vd`nras y ukd vfsfùk ma` Lukmn luy aspaiì-bfins. Masirfed iuä` sarìd a` dktfhærna ma ns tfalpns lnmarkns. Drculaktasu raspuastd.

]falpn _arsnkdjas Fldcak Dumfn

Asiakd 4.



Iùmfcn `fkcðìstfin

• CDUUFMN, Ldkua`. @ùcfid sfleù`fid. Ldmrfm: ]aikùs, 4681.

• BQAK]AY UNMUÌCQAZ, I. @d sfktdxfs ma `ns ra`difnkdktas suprdnrd-ifnkdàs. Ldmrfm: Drin @ferns, 4668.

• BAUKÄKMAZ _ÆUAZ, L. Fktrnmuiifùk d d @fkcðìstfid, Edria`nkd: Drfa`,4666.

• LDU]ÌKAZ I. A. Edsas pdrd a` astumfn ma` àkcudja. Edria`nkd: Nitda-mrn, 4661.

• YFLNKA, U. Bukmdlaktns ma fkcðìstfid. ]rdmuitnrd: Lª ma` _. UnmrìcuazUafkd. Edria`nkd: Drfa`, 4669.

Maedta, salfkdrfn y pdka`

•

LAMDQUD, N`cd y LNKBDUUA@@, D`fifd. ]æikfids crupdàs y dprak-mfzdja dbaitfvn. Euakns Dfras: @ulak, 5??8.

• DKMAU-ACC, Azaqufa`. Hde`dr ak púe`fin y sdear inlukfidr. Euakns Dfras: @ulak, 5??2.

• EDRFN, Idrlak y IÆY_AMAY, Inrd. @akcud. Euakns Dfras: Gdpaùsz, 5??4.

• YDKZ _FKVN@, C`nrfd. Inlukfidifùk abaitfvd ak a` du`d. ]æikfids ma

axprasfùk nrd` pdrd mniaktas. Edria`nkd: Crdù, 5??1.

Iuaktn

• LD]N, Mdkfa`. Iùln inktdr iuaktns. Idrdids: Lnkta Ävf`d, 4668.

• _DY]NUFZD MA A]IHAEDUKA, Mnrd. A` drta ma kdrrdr: uk nbfifn n`vf-mdmn. Euakns Dfras: Cudmdùpa, 4668.

Efe`fncrdbìd



• _A@ACUÌK, Dkd. @d dvakturd ma nfr iuaktns y lalnrfds ma d trdmfifùknrd`. Ldmrfm: Ifkia`, 4685.

• UNMDUF, Cfdkkf. Crdlätfid ma `d bdktdsìd: fktrnmuiifùk d` drta mafkvaktdr hfstnrfds. Edria`nkd: ma Ernkia, 4662.

• NKC, Sd`tar. Nrd`fmdm y asirfturd. Læxfin: Bnkmn ma Iu`turd Ainkù-lfid, 4662.

Astruiturdifùk ma` taxtn asirftn

• RDK MFJG, ]. Asirfturd y bukifnkas ma` mfsiursn. Ldmrfm: Iätamrd, 468?.

• INUNLFKDY, Ausaefn y UQEFN, Idrlak. ]æikfids ma asirfturd. Edr-ia`nkd: ]afma, 4686.

• ID_DUUÙY, Jnsæ Mnlfkcn. Fktrnmuiifùk d` inlaktdrfn ma taxtns. Ld-mrfm: Lfkfstarfn ma Amuidifùk y ifakifd, 4681.

• ID@RFKN, Ìtd`n. @ns iuaktns bdktästfins ma` sfc`n XFX. Edria`nkd: Yfrua`d,4664.

@ìrfid

• IFU@N], @nurmas. @ds i`dvas ma `ds vdkcudrmfds drtìstfids ma` sfc`n XX.Edria`nkd: Drfa`, 4688.

• UDLÌUAZ, Judk Dktnkfn. A` drta ma ds vdkcudrmfds. Ldmrfm: Dkdyd, 4668.

• D_N@@FKDFUA, Cuf``dula. Id`fcrdlds. Edria`nkd: Iätamrd, 5??1.

• CUÐKBA@M, Lfhdf`. Dktn`ncìd ma `d pnasìd `dtfkndlarfidkd ma vdk-

cudrmfd. Euakns Dfras: Hfpdrfùk, 4661.

• BAUKÄKMAZ Lnrakn, Iæsdr. Dlærfid @dtfkd ak su `ftardturd. Læxfin:Yfc`n XXF, QKAYIN, 4688.

• _DIHAIN, Jnsæ Alf`fn. @aiturd irìtfid ma `d `ftardturd dlarfidkd, vdk-cudrmfds y tnld ma pnsasfùk. Ak: Efe`fntaid Dydiuihn, ]. 461, Rn`. FFF.Idrdids, 4663.




]rdksbnrlalns Amuidkmn

Ärad ma IfakifdsKdturd`as

4?

Iarrn Lnkn Uìn, Cudfkìd



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B d i t n r a s m a n r c d k f z d i f ù

k

¾ I ù l n m a l u a s t r n ` n d p r a k

m f m n >

I n l p a t a k i f d s

¾ D q u æ

q u a r a l n s

` ` a c d r >

A x p

` f i n

` d

m f v a r s

f m d

m

e f n ` ù c

f i d

i n l n

i n k -

s a i u a k i

f d

m a i d l

e f n s

d l

e f a k

t d ` a s ,

c a k

æ t f i n s

y r a

` d i

f n k a s

m f k ä l

f i d s

m a k

t r n

m a

` n s a i n s

f s -

t a l d s .

U a

` d i

f n k n

` d a s

t r u i

t u r d

m a

` d s l n

` æ i u

` d s n r c

ä -

k f i d s a

f k n r c

ä k

f i d s i n k

s u s p r n p

f a m d

m a s

b ì s f i d s y

q u

ì l f i d s y s u i d p d i

f m d

m

m a i d l

e f n q u

ì l f i n .

A x p

` f i n

` d s

b u a r z d s a k

t r a

n e j a t n s i n l n

f k t a r d i i

f n -

k a s

m a

e f m d s d

` d i d r c d

a ` æ i

t r f i d y d

` d l d s d .



•

A x p

` f i n

d p

` f i d i

f n k a s

t a i k n

` ù c

f i d s

m a

`

l n

m a

` n m a l a i

ä k

f i d

m a

b ` u f m n s

•

D k d

` f z n a

` p n

t a k i

f d ` m a

` n s r a i u r s n s k d -

t u r d

` a s a k

` d n e

t a k i

f ù k

m a a k a r c

ì d p d r d

m f b a r a k

t a s u s n s .

•

A s t d

e ` a z i n r a

` d i

f n k a s a k

t r a a

` m a p n r t a y

` d s d

` u m b ì s f i d y

l a k

t d ` .

•

A x p

` f i n i d l

e f n s q u

ì l f i n s a k

` d i n i

f k d ,

` d f k m u s t r f d y a `

d l

e f a k

t a

•

D r c u l a k

t n ` d f l

p n r t d k i

f d m a

` d s l a

m f m d s

m a p r a v a k i

f ù k

m a

` a l

e d r d z n y

m a

` d s

a k

b a r l a

m d

m a s

m a

t r d k s l

f s f ù k s a x u d

` a k

a ` l d k

t a k

f l f a k

t n m a

` d s d

` u m f k m f v f m u d

`

y i n

` a i

t f v d .

A s t ä k

m d r a

s e ä s f i n s

m a i n l p a t a

k i

f d s a k

I f a k i

f d s

K d t u r d

` a s

( i n k

t f k u d i

f ù k

)

A k t n r k n b ì s f i n

I f a k i f d ,


y s n

i f a m d m



A k t n r k n v f v n

•

N e s a r v n y

b n r l u

` n p r a c u k

t d s a s p a i

f b f i d s s n

e r a d p

` f i d i

f n k a s

m a

t a n r ì d s i

f a k

t ì b f i d s

•

B n r l u

` n h f p ù t a s f s i n k

e d s a a k a

` i n k n i

f l

f a k

t n i n

t f m f d k n ,

t a n r ì d s y l n

m a

` n s i

f a k

t ì b f i n s

•

F m a k

t f b f i n v d r f d

e ` a s q u a

f k b ` u y a k a k

` n s r a s u

` t d m n s

m a u k a x p a r f l a k

t n

•

_ r n p n k c n l n

m a

` n s p d r d p r a

m a i

f r ` n s r a s u

` t d m n s

m a u k a x p a r f l a k

t n

•

U a d

` f z n l a

m f i f n k a s i n k

f k s t r u l a k

t n s y a q u

f p n s d

m a i u d

m n s

•

U a c

f s t r n l

f s n

e s a r v d i

f n k a s y r a s u

` t d m n s u t

f ` f z d k

m n a s q u a l d s , c r ä

b f i n s y

t d e ` d s

•

U a c

f s t r n l

f s r a s u

` t d m n s a k

b n r l d n r c d k

f z d

m d y s f k d

` t a r d i

f ù k d

` c u k d

•

A s t d

e ` a z i n

m f b a r a k i

f d s a k

t r a m a s i r f p i

f ù k , a

x p

` f i d i

f ù k ,

y a v

f m a k i

f d

•

A s t d

e ` a z i n

m f b a r a k i

f d s a k

t r a l n

m a

` n s ,

t a n r

ì d s ,

` a y a s a

h f p ù t a s f s

•

U a i n k n z i n

` n s d p n r t a s

m a i n k n i

f l f a k

t n s m

f b a r a k

t a s d

` i

f a k

t ì b f i n

•

U a i n k n z i n q u a

` n s l n

m a

` n s

m a

` d i

f a k i

f d i d l

e f d k i n k a

` t f a l p n y q u a v d r f n s p u a

m a k

s a r v

ä ` f m n s s f l u

` t ä k a d l a k

t a .

•

I u

f m n ,

r a s p a

t n ,

y a x

f j n r a s p a

t n p n r l

f i u a r p n y p n r a

` m a

` d s

m a l

ä s p a r s n k d s

•

] n l n

m a i

f s f n k a s r a s p n k s d

e ` a s y i n l p d r t f m

d s s n

e r a l

f s a x u d

` f m d

m

•

D k d

` f z n i r ì t f i d l a k

t a ` n s p d p a

` a s

t r d m f i f n k d

` a s

m a c

æ k a r n a k k u a s t r d i u

` t u r d i n k r a s p a i

t n d

` d s a x u d

` f m d

m y

` d r a p r n

m u i i

f ù k

•

A x p

` f i n

` d

n e t a k i

f ù k

m a a k a r c

ì d

k u i

` a d r d

p d r t f r

m a

` d d

` t a r d i

f ù k

m a

` d a s t r u i

t u r d

m a

` ä t n l n .

•

A x p

` f i n

` d t r d k s b n r l d i

f ù k

m a

a k a r c

ì d l a

i ä k

f i d a k a k a r c

ì d

t æ r l

f i d .

Q t f ` f z n l n

m a

` n s

e f n ` ù c

f i n s ,

b ì s f i n s y q u

ì l f i n s p d r d a x -

p ` f i d r

` d

t r d k s

b n r l d i

f ù k y

i n k s a r v d i

f ù k

m a

` d a k a r c

ì d .

F m a k

t f b f i n

d p

` f i d i

f n k a s

m a

m f b a r a k

t a s l n

m a

` n s

e f n ` ù

-

c f i n s , q u

ì l f i n s y

b ì s f i n s a k

p r n i a s n s

f k m u s

t r f d ` a s y a k

a ` m a s d r r n

` ` n

t a i k n

` ù c

f i n 7

d k d

` f z n i r ì t f i d l a k

t a ` d s

f l -

p ` f i d i

f n k a s

m a s u s u s n s .


¾ D q u æ

q u a r a l n s

` ` a c d r >

B d i t n r a s m a n r c d k f z d i f ù k

¾ I ù l n m a l u a s t r n ` n d p r a

k m f m n >

L a d p r n x f l n d `

i n k n i f l f a k t n i n l n

i f a k t ì b f i n ( d ) k d t u r d `

M a s d r r n ` ` n

i n l p r n l f s n s

p a r s n k d ` a s

y s n i f d ` a s



Ìkm fiaQkfmdm 4. @ns ainsfstalds 439

Yasfùk 4. Akarcìd y ldtarfd ak `ns ainsfstalds 439

Yasfùk 5. ]arlnmfkälfid 431

Yasfùk 9. @d bntnsìktasfs 438

Yasfùk =. Kfva`as trùbfins 483

Yasfùk 1. Ua`difnkas aktra `ds inlukfmdmasma uk ainsfstald 464

Yasfùk 2. D`cukns ifi`ns efncanquìlfins 463

Yasfùk 3. Ldkns d `d nerd 5?5

Qkfmdm 5. @ns nrcdkfslns y su raspuastd dkta `ns astìlu`ns ma` lamfn 5?2

Yasfùk 8. A` sfstald karvfnsn 5?2

Yasfùk 6. A` sfstald akmnirfkn 55?

Yasfùk 4?. Ldkns d `d nerd 556



4

Bùjn ma akarcìd

@ns saras vfvns kaiasftdk ma akarcìd pdrd pnmar rad`fzdr tnmds sditfvfmdmas vftdàs (masp`dzdlfaktn, masdrrn``n, iraiflfaktn a iùsn `d lfsld d`flaktdifùk).

4. Fmaktfbfqua ak a` sfcufakta mfeujn, `ns aàlaktns efùtfins y defùtfins, dsì inl`ds pnsfeàs ra`difnkas qua puamdk axfstfr aktra a``ns.

5. Masirfed iùln y ma mùkma netfakak akarcìd ns sfcufaktas nrcdkfslns: d dea`d vdid, a` äcuf`d, a` edcra, `d sarpfakta inrd` y ären` ma ldkcn.

Ya pnmrìd dbfrldr, qua ink luy pnids axiapifnkas, tnmns `ns nrcdkfslns

ma` _`dkatd mapakmak ma d akarcìd ma` Yn` pdrd sneravfvfr. _arn ¾`ns sarasvfvns iùln inksfcuak dprnvaihdr astd akarcìd> @ns d`flaktns qua ns sarashuldkns y ntrns nrcdkfslns inksulak ¾astäk ra`difnkdmns ink d akarcìdprnmuifmd pnr kuastrn dstrn Uay> _drd raspnkmar astds y ntrds pracuktdsra`difnkdmds ink a` bùjn akarcætfin ak `ns ainsfstalds, ak astd ukfmdm,sa varä ak matd`à, a` prniasn lamfdkta a` iud` `d akarcìd sn`dr snstfaka `dvfmd ak `d ]farrd.

Akarcìd y ldtarfd ak ns ainsfstaldsQkfmdm 4. @ns ainsfstalds Yasfùk

4



4

]rdedjn ak suecrupns.

Idmd suecrupn dkd`fzdrä `ds sfcufaktas pracuktds7 ùacn, snifd`fzdrä dkta sus inpdôarns y mniaktas `s inkiùifnkas d `ds qua hdyd `àcdmn

• Yf `d akarcìd kn sa irad kf sa mastruya, ¾iùln as qua pf`ds, edtarìds ma ia-ù`dras, y ntrns drtabditns sflf`dras, cakardk akarcìd a`æitrfid y maspuæs ma

uk tfalpn majdk ma bukifnkdr>

• @d ldynr pdrta ma d akarcìd a`æitrfid ak In`nlefd, as prnmuifmd pnr p`dktds hfmrna`æitrfids. A` prniasn lamfdkta a` iud` sa netfaka `d akarcìd asra`dtfvdlakta sakif``n: a` dcud ma rìns y aled`sas sa majd idar ak bnrld maidsidmd snera crdkmas turefkds aspaifd`lakta mfsaôdmds pdrd qua d` cfrdprnmuzidk aàitrfifmdm. ¾Iùln as qua uk rìn n uk crdk iuarpn ma dcudak rapnsn puama takar akarcìd> ¾Ma mùkma `d hdk netakfmn>

@d prflard ày ma `d tarlnmfkälfid sa inknia inln `d ày ma`d inksarvdifùk pnrqua dbfrld qua `d akarcìd kn sa irad k

sa mastruya, sfkn qua sa trdksbnrld.

]arlnmfkälfid as d ifakifd qua astumfd ds trdksbnrldifn-kas ma `d akarcìd.

@d tarlnmfkälfid

Qkfmdm 4. @ns ainsfstalds Yasfùk

5



Crdk pdrta ma `dakarcìd quanetfakak `ns

ldlìbarns y `ds dvasma `ns d`flaktns quainksulak, as usdmdpdrd prnmuifr id`nr.

@d akarcìd tntd` ma uk sfstald y `d ma sus d`ra-

mamnras sa ldktfaka inkstdkta. D inktfkudifùk,

dkd`fialns d`cukns ajalp`ns qua kns parlftdk

inlprakmar lajnr `d dbfr ldifùk dktarfnr.

Iudkmn `d akarcìd a`æitrfid `àcd d uk enlef``n,a` bf`dlaktn ma tukcstakn qua sa akiuaktrd ak sufktarfnr, sa hdia fkidkmasiakta, as maifr, prnmuiaùz d` dulaktdr su talpardturd. Ak asta idsn aspnsfeà dpraifdr qua `d akarcìd fkfifd` kn sa mas-truya, ak rad`fmdm parldkaia inkstdkta, sn`n qua

sa trdksbnrld ak ùz y id`nr.

Ma bnrld sflf`dr, niurra ink `ns nrcdkfslns. @dùz sn`dr as trdksbnrldmd maktrn ma `ns i`nrnp`ds-tns ma `ds p`dktds ak akarcìd a`æitrfid, y ùacn akakarcìd quìlfid pnr lamfn ma `d bntnsìktasfs. @nsprnmuitns qua sa netfakak ak asta prniasn inlniaù`nsd y d`lfmnkas, sfrvak ma d`flaktn pdrd ntrns

nrcdkfslns qua inkvfartak astd akarcìd quìlfid aklnvflfaktn (akarcìd laiäkfid), id`nr (akarcìd tær-lfid), n flpu`sns a`æitrfins (akarcìd a`æitrfid), ati.

@d sacukmd ày ma `d tarlnmfkälfid dbfrld qua sfalpra qua sa rad`fzdukd trdksbnrldifùk ma akarcìd, pdrta ma a``d kn puama sar dsflf`dmd. Asflpnrtdkta takar ak iuaktd qua astd brdiifùk ma akarcìd kn sa pfarma(inln yd sa mfjn), sfkn qua kn puama usdrsa pdrd rad`fzdr uk trdedjn útf`.

Radlns uk ajalp`n:

Ydealns qua iarid ma` 1?% ma `d ùz sn`dr dìdkzd `d suparbfifa tarrastra,y qua a` rastn as frrdmfdmn pnr d dtlùsbard d` aspdifn. _drta ma d idktfmdmqua ncrd fkcrasdr d d ]farrd, as rabàjdmd pnr sus suparbfifas i`drds n sa mfsfpdsflpàlakta inln id`nr. Ya astfld qua sù`n a` ?.4% ma `d akarcìd sn`drqua `àcd d `d suparbfifa ma `d ]farrd, as dprnvaihdmd pnr `ns nrcdkfslns.



5

@ds p`dktds tdlpnin inksfcuak dprnvaihdr d` 4??% `d akarcìd sn`dr7d`cukns ma `ns rdyns ma ùz snk rabàjdmns sflpàlakta pnr `ds lfsldshnjds, y su akarcìd kn puama sar dprnvaihdmd.

Astumfns raifaktas hdk malnstrdmn qua ma tnmd d uz qua àcd d ukd znkdma vacatdifùk deukmdkta inln ukd sa`vd, úkfidlakta ma` 4 d` 9% as usdmnpdrd `d bntnsìktasfs.

@ns dkfldàs hareìvnrns inksulak p`dktds pdrd netakar akarcìd y pnmarrad`fzdr sus bukifnkas, parn ukd pdrta ma astd akarcìd sa inkvfarta ak id`nr7dsì qua iudkmn asta dkfld` as inksulfmn pnr ntrn, kn à trdksbarfrä tnmd

`d akarcìd qua netuvn ma `d p`dktd, sfkn `d brdiifùk qua hdeìd quamdmninktakfmd ak sus tajfmns.

Fkvastfcualns:

d. ¾Iuäktds àyas ma `d tarlnmfkälfid axfstak>

e. Ak sus prnpfds pd`derds mabfkd: ¾Tuæ as tarlnmfkälfid y qua bakùlakaxp`fid>

@d idktfmdm ma akarcìd útf` vd mfslfkuyakmn

d lamfmd qua sa pdsd ma uk kfva` trùbfin d ntrn.



Yf efak sa dbfrld qua ns saras vfvns mapakmak ma d uz sn`dr pdrd su suparvfvakif

sù`n ukd pdrta ma a``ns, inksfcua trdksbnrldr astd bnrld ma akarcìd ak d`flaktn. Akt`ns nrcdkfslns idpdias ma bderfidr sus prnpfds sustdkifds kutrftfvds, sa akiuaktrd`ds p`dktds, `ds d`cds y d`cukds editarfds.

@ns nrcdkfslns bntnsfktatfzdmnras pnsaak sustdkifds idpdias ma desnrear d uz, `dldmds pfclaktns. Aktra ns läs inknifmns, sa akiuaktrdk d i`nrnbf`d qua a ntnrca` idrditarìstfin varma d ds p`dktds7 y ns idrntakns, pfclaktns rnjns, dkdrdkjdmnsdldrf``ns, qua puamak dpraifdrsa bäif`lakta pnr ajalp`n, ak d`cukns ma `ns tajfmnma` tnldta y `d zdkdhnrfd. @ns pfclaktns prasaktas ak `ns auidrfntds bntnsfktat

zdmnras, sa hd``dk maktrn ma `ns tf`dinfmas (lalerdkds fktarkds ink dpdrfakifd msdin dp`dkdmn)7 ak `ns prnidrfntds idpdias ma rad`fzdr `d bntnsìktasfs, `ns tf`dinfmakn sa akiuaktrdk ak `ns i`nrnp`dstns, inln yd vflns7 `ns nrcdkfslns prnidrfntdidraiak ma nrcdka`ns mabfkfmns pnr lalerdkd.

A` in`nr varma ma `d i`nrnbf`d dpdraia pnrqua a` pfclaktn desnrea `ds `nkcftumas m

nkmd vfn`atd, rnjn y dzu`, y ak idlefn, rab`ajd `ds `nkcftumas ma nkmd varma.

@d bntnsìktasfs


9

@u`n prnmuifmn ak Cudfkìd



4. Ak uk raifpfakta ink d`inhn`, in`nqua `ds hnjds y trftúra`ds ink a`

lnrtarn.

5. Rfartd `d lazi`d netakfmd ak a` sacukmn raifpfakta.

9. Fktrnmuzid ak `d lazi`d, pdrta ma` pdpa` bf`trn.

=. Maja saidr a` pdpa`.

_rniamflfaktn:

Masirfed matd``dmdlakta `ds idrditarìstfids qua prasaktda` pdpa` y inlakta `ds inki`usfnkas snera `d axparfakifd.



Ak `d prflard atdpd ma `d bntnsìktasfs, d`cukns bntnkas (pdrtìiu`ds qua inlpnk`d ùz), fkcrasdk ak `d p`dktd d trdvæs ma `ds hnjds. Mfihds pdrtìiu`ds snk desnrefmpnr `d i`nrnbf`d qua sa akiuaktrd ak `ns tf`dinfmas7 d lamfmd qua `d i`nrnbf`d raibntnkas, vd `feardkmn aàitrnkas qua mfbaraktas tfpns ma ln`æiu`ds idptdk y trdpnrtdk. Inkbnrla `ns aàitrnkas snk `àvdmns d kfvaàs läs edjns, vdk `feardkakarcìd qua sa utf`fzdrä pnstarfnrlakta pdrd a`denrdr D]_ (Dmaknsfkd ]rfbnsbdtln`æiu`d pnrtdmnrd ma akarcìd, ma crdk flpnrtdkifd ak `ns prniasns qua rad`fz

`ns saras vfvns. D` bfkd` ma` prniasn, `ns aàitrnkas snk idptdmns pnr `d ln`æitrdkspnrtdmnrd KDM_+.

@ds ln`æiu`ds maKDM_+snk ramuifmds, as maifr cdkdk aàitrnkas ma d sfcufakta bnrl

@d bntnsìktasfs sa rad`fzd ak mns atdpds: ak `d prflard, sa idpturd `d ùz7 y ak`d sacukmd, niurrak d`cukns prniasns quìlfins qua kn raqufarak prasakifdma ùz.

KDM_+ KDM_H



_ + DM_ D]_

Inln puama dpraifdrsa ak d bfcurd, ukn ma ns prnmuitns ma` prniasn as a` D]_, qusa bnrld iudkmn d ln`æiu`d ma Dmaknsfkd Mfbnsbdtn (DM_), raifea uk bnsbdtn. A` D]sa bnrld, crdifds d `d akarcìd qua `feardk `ns aàitrnkas d` masiakmar ma kfva`.

Ak `d bntnsìktasfs, `ns inlpnkaktas ma` dcud snksapdrdmns pdrd usdr`ns ak ntrns prniasns, pnrajalp`n: a` nxìcakn as `feardmn d` dlefakta,lfaktrds qua a` hfmrùcakn hdrä pdrta ma ln`æ-iu`ds inln `d KDM_H.

Ak d prflard atdpd ma d bntnsìktasfs, sa puamanesarvdr `d ldkard inln `d akarcìd as trdks-bnrldmd:

4. @d akarcìd ulìkfid sa trdksbnrld ak akar-

cìd a`æitrfid, crdifds d` bùjn ma aàitrnkas.

5. @d akarcìd a`æitrfid sa trdksbnrld akakarcìd quìlfid, iudkmn quamd d`ldia-kdmd ak ds ln`æiu`ds ma KDM_H y D]_.

Akarcìd ùlìkfid

Akarcìd ùlìkfin

I`nrnp`dstn

Akarcìdquìlfid

KDM_H D]_



5

Ak asta puktn ma `d bntnsìktasfs, `d p`dk-td hd `ncrdmn inkvartfr `d akarcìd sn`drak akarcìd quìlfid qua puama utf`fzdrpdrd bderfidr dzúidras inln `d cùinsd:I2H45N2. _arn ns nrcdkfslns bntnsfktæ-tfins kaiasftdk idrenkn pdrd bderfidr`ds ln`æiu`ds ma cùinsd. ¾Ma mùkmanetfakak a` idrenkn, nrcdkfslns inln`ds p`dktds n ds d`cds qua sa akiuaktrdksularcfmds ak a` dcud>

@ds p`dktds netfakak a` idrenkn ka-iasdrfn pdrd bderfidr sus dzúidras, ma`mfùxfmn ma idrenkn qua sa akiuaktrd ak a` dfra. Ak idlefn, ns nrcdkfslnsbntnsfktætfins qua sa akiuaktrdk sularcfmns, inln d`cds y ntrds p`dktds,desnreak a` idrenkn mfsua`tn ak a` dcud.

A` idrenkn ncrd fkcrasdr ak ds iæù`ds bntnsfktætfids ma ds p`dktds, pnr lamfnma astnlds qua snk `ns pnrns qua pnsaak `ds p`dktds ak sus hnjds y td``ns.


Inktastak ak a` iudmarkn:

4. ¾Ma mùkma prnvfaka a` mfùxfmn ma idrenkn prasakta ak a` dfra n mfsua`tn a` dcud y qua desnreak `ds p`dktds>

5. ¾As eakæbfin pdrd `ns maläs nrcdkfslns, qua `ds p`dktds desnredk ma` lam

B`nrd cudfkfdkd



@d cùinsd as d akarcìd quìlfid prnmuitn ma d bntnsìktasfs, qua dpnrtd`d akarcìd kaiasdrfd pdrd qua ds iæù`ds rad`fiak dmaiudmdlakta susbukifnkas. Dmaläs, as d edsa pdrd d inkstruiifùk ma ln`æiu`ds läsinlpàjds inln idrenhfmrdtns, `ìpfmns y prntaìkds.

Ak `ds sfcufaktas päcfkds, axfstak dkfldifnkas ra`difnkdmds ink `dbntnsìktasfs y a` ifi`n ma Id`vfk:

• http://www.efn`ncfd.amu.dr/p`dktds/bntnsfkt5.htl• http://www.ldph=6.cdànk.inl/bntn/nvarvfaw.htl`• http://wae.amuidstur.prfkidst.as/prnyaitns/efncan^nv/Dkf-

ldifnkas/Fkmfia^dkfl.htl

@d bruitnsd, `d rfensd y `d cùinsd, snk lnknsdiärfmns pnrqua pnsaak ukd sln`æiu`d ma dzúidr7 ak idlefn, ns mfsdiärfmns astäk inlpuastns pnr mns ln`æiusflpàs ma dzúidr7 ajalp`ns: `d sdidrnsd n dzúidr ma `d idôd y `d `ditnsd n dzúma `d àiha. Iudkmn vdrfds ln`æiu`ds ma dzúidr sflpà sa ukak aktra sì (inln a` idsn ma `ds ln`æiu`ds qua inkbnrldk `d iaù`nsd ma `ds p`dktds), sa hde`d



9

@ns nrcdkfslns hdk avnùifnkdmn pdrd d`ldiakdr `ds sustdkifds kutrftfvds qua kraqufarak ak a` lnlaktn, parn puamak utf`fzdr maspuæs. Ajalp`n: a` d`lfmùk

uk pn`fsdiärfmn qua `d ldynrìd ma `ds p`dktds utf`fzd inln rasarvd d`flaktfifd. AIn`nlefd, d`cukds ma `ds p`dktds d`flaktfifds läs pnpu`dras pnr su inktakfmn md`lfmùk snk d pdpd, d yuid, a` trfcn, d iaedmd, a` ldìz, a` sdcú ma pd`ld, d dihfra` p`ätdkn, `ns cdredkzns, `ds àktajds, `ds dùefds y ntrds läs.

Ink `d fkbnrldifùk raifefmd y takfakmn ak iuaktd a` crdk kúlarn ma pd`derdkuavds qua halns asiuihdmn y/n àìmn, vdlns d rad`fzdr uk iruifcrdld ak `d ids_drd a``n, maealns hdiar uk `fstdmn ma 45 pd`derds kuavds qua hdcdk rabarakifd `d sasfùk ma hny:

Bntnsìktasfs: Ink asta fstdmn idmd ukn maearä trdar haihn, ak ukd hnjd e`dkid, uiruifcrdld qua fkvnùira astds 45 pd`derds kuavds y sus sfckfbfidmns. Yad iradtfvy hdcd a` iruifcrdld läs nrfcfkd` pnsfeà.

_nr sar ukd sustdkifd ma rasarvdprnmuifmd d pdrtfr ma` dzúidr, a`d`lfmùk pnsaa uk crdk inktakfmnakarcætfin y pnr td` rdzùk, as luyflpnrtdkta fkiùfr`n ak pnrifnkasdmaiudmds ak `d mfatd mfdrfd.

A` cùiùcakn as `d bnrldinln `d ldynrìd ma `ns dkf-ldàs d`ldiakd a` dzúidr. Ak`ns vartaerdmns, sa akiuaktrdprfkifpd`lakta ak a` hìcdmn yak `ns lúsiu`ns.



Maefmn d qua ak idmd kfva` trùbfin `dakarcìd útf` as laknr, a` kúlarn manrcdkfslns qua puamak dprnvaihdr`dtdlefæk mfslfkuya. Ma td` ldkard quaa` lajnr lnma`n qua raprasaktd asta ba-kùlakn, as d bfcurd trfdkcu`dr qua sa ahd maknlfkdmn pfrälfma ain`ùcfid.

D` fcud` qua `ds pfrälfmas ma Acfptn,`ds pfrälfmas ain`ùcfids kaiasftdkma ukd edsa pdrd snstakar a` rastn ma

su astruiturd7 ak `ns ainsfstalds, `nsnrcdkfslns prnmuitnras snk `ns quaniupdk a` prflar kfva` trùbfin. Astnssaras vfvns inln su knlera `n fkmf-id, snk idpdias ma a`denrdr su prnpfnd`flaktn d pdrtfr ma d trdksbnrldifùkma `d akarcìd sn`dr ak akarcìd quì-lfid y pnr `n tdktn, tdlefæk sa `asmaknlfkd dutùtrnbns. @ds p`dktds,`ds d`cds y `ds editarfds bntnsfktætfidshdiak pdrta ma asta flpnrtdkta kfva`.



Crdifds d `d idpdifmdm qua tfakak `ns nrcdkfslns dutùtrnbns maprnmuifr su prnpfn d`flaktn, `ns hatarùtrnbns (nrcdkfslns quasa d`flaktdk ma ntrns pdrd netakar akarcìd), puamak sneravfvfr y

hdiar pdrta ma `d pfrälfma ain`ùcfid.

Nrcdkfslns inksulfmnras (hatarùtrnbns), y su kfva` trùbfin:

Yacukmn

kfva` trùbfin

Inksulfmnras maprflar nrmak

Nrcdkfslns hareìvnrns. Ajalp`n

aàbdkta, vdid, vakdmn, nrucd, id-ed``n, jfrdbd, drmf``d y inkajn.

• Idrkìvnrns qua inksulak har-eìvnrns.

• Nrcdkfslns qua sa d`flaktdk mafksaitns (fksaitìvnrns) Ajalp`nàùk, nsn, end, znrrn, nen, rdkd`dcdrtfjd y nsn hnrlfcuarn.

Inksulfmnras masacukmn nrmak

]ariar kfva`

trùbfin

Iudrtn kfva`

trùbfin

Idrkìvnrns qua inksulak fksai-tìvnrns u ntrns idrkìvnrns. Ajalp`n: äcuf`ds y sarpfaktas qua sad`flaktdk ma rdkds, inldmrajds y`dcdrtfjds.

Inksulfmnras matariar nrmak

Nrcdkfslns qua sa d`flaktdk ma nsrastns ma ntrns (rdlds, hnjds y trnk-ins ma ärenàs y p`dktds luartdsrastns ma pfa`, asquaàtns, haiasati.). Ajalp`ns: euftras, idkcrajnsy d`cukns asidrdedjns.

Matrftìvnrns n idrrnôarns



=

@ns masinlpnkamnras n macrdmdmnras d` fcud`qua `ns matrftìvnrns, netfakak `d akarcìd ma `nsrastns nrcäkfins. Yfk aledrcn, snk idpdias mautf`fzdr sustdkifds qua a` rastn ma dkfldàs knpuama dsflf`dr, inln pnr ajalp`n: `d iaù`nsdy ns masaihns kftrncakdmns. Dmaläs, snk luyflpnrtdktas pdrd a` ainsfstald pnrqua mavua`-vak kutrfaktas d` sua`n, iudkmn inkvfartak `dldtarfd nrcäkfid qua prnvfaka ma `ns rastns ma`ns nrcdkfslns, ak ldtarfd fknrcäkfid.

]rdedjn fkmfvfmud`.

@àka a` sfcufakta iudmrn ink nrcdkfslns prnpfns ma su racfùk y ùacn, mfeúja`nak ukd pfrälfma ain`ùcfid.

_rflarkfva` trùbfin

Yacukmnkfva` trùbfin

]ariarkfva` trùbfin

Iudrtnkfva` trùbfin

_rnmuitnras

Inksulfmnras maprflar nrmak

Inksulfmnras masacukmn nrmak

Inksulfmnras matariar nrmak

Matrftìvnrns n idrrnôarns

Bntn tnldmd ma Sfgfpam



Masdbnrtukdmdlakta, `d bdukd y `d b`nrd ma kuastrn _dìs kn snk djakdsd astd prneàlätfid. D inktfkudifùk, sa ra`difnkdk d`cukns ma `ns idsnsqua ajalp`fbfidk `d fktrnmuiifùk ma aspaifas axùtfids ak `ns ainsfsta-lds in`nlefdkns, y a` d`tn crdmn ma dlakdzd qua raprasaktdk pdrd`d efnmfvarsfmdm kdifnkd`.

Ak `d ditud`fmdm, a` enidihfin as ukn ma `ns paias läs raprasaktdtfvnsma `d bdukd in`nlefdkd y inrra a` rfascn ma masdpdraiar, maefmn d `dfktrnmuiifùk ma `d tf`dpfd n lnjdrrd ak su häeftdt. A` ‐paz fkvdsnr“ buatrdìmn d bfkas ma `ns dôns 3? masma Äbrfid a fktrnmuifmn ak `ds dcuds ma`Ldcmdàkd, pdrd trdtdr ma rastdeàiar ns raiursns pasquarns ma` rìn qua

pnr asd æpnid, sa vaìdk luy mfslfkufmns. Ak abaitn, pdrta ma` nejatfvnsa iulp`fù pnrqua a` kúlarn ma tf`dpfds sa fkiralaktù sustdkifd`lakta7parn aspaifas inln a` enidihfin qua as akmælfid n prnpfd ma` ùcdr,mfslfkuyù inksfmardeàlakta.

Masma aktnkias, lú`tfpàs fkvastfcdmnras hdk inlprnedmn qua a` mas-iaksn ma d`cukds ma `ds aspaifas ma paias akmælfids ma` rìn Ldcmdàkd,as inksaiuakifd mfraitd ma `d fktrnmuiifùk ma `d lnjdrrd. @ns astumfns

hdk rava`dmn tdlefæk, qua a` æxftn ma `d aspaifa fktrnmuifmd sa maea dsu räpfmd raprnmuiifùk (idmd tras lasas, ak inlpdrdifùk ink `ns mnsdôns y lamfn qua maea aspardr a` enidihfin), d `d ldynr rasfstakifd d `dinktdlfkdifùk y pnrqua idraia ma mapramdmnras kdturdàs.

B n t n t n l d m d m a S f g f p a m f d

]f`dpfdEnidihfin



1


A`denrdr ink ns inlpdôarns, uk fstdmn ma rainlakmdifnkas akidlfkdmds d pravaky inrracfr a` prneàld ma `d fktrnmuiifùk ma aspaifas axùtfids ak `ns ainsfstal

Yflefnsfs

Lutud`fsln

Ua`difùk ak `d iud`dleds aspaifas saeakabfifdk. Ajalp`n:`fquak (dsnifdifùkma d`cds y hnkcns):`ns hnkcns erfkmdksustrdtns y `ds d`cdsa` d`flaktn.

Ua`difùk ak `d iudùkd aspaifa sa eaka-bfifd y `d ntrd kn raif-

ea mdôn kf eakabfifn.Ajalp`n: `d cdrzdeuayard sa eakabfifdma` cdkdmn vdiukn,qua d` masp`dzdrsa,aspdktd `ns fksaitns.

Ua`difùk ak `d iudùkd aspaifa sa ea-kabfifd y parjumfid d`d ntrd. Ajalp`n: `dtakfd n nlerfz sn`ftd-rfd qua sa d`njd ak a`fktastfkn ma`cdmn ma`hnlera y sa d`flak-td ma `ds sustdkifdskutrftfvds qua d``ì saakiuaktrdk. _uama

dìdkzdr hdstd mfazl ma nkcftum maktrnma` fktastfkn y prn-muifr käusads, mn`nrdemnlfkd`, mfdrrad ypærmfmd ma pasn.

Inlaksd`fsln _drdsftfsln

@d fktardiifùk aktra nr-cdkfslns ma mfbarakta as-paifa qua vfvak juktns, sainknia inln sflefnsfs.



4

Eusidr ntrns tras ajalp`ns pdrd idmd ra`difùk sflefùtfid.

@d ifriu`difùk ma sustdkifds fknrcäkfids d trdvæs ma` ain-sfstald inln dcud, bùsbnrn, kftrùcakn y ldckasfn, aktrantrns, sa inknia inln ifi`n efncanquìlfin pnrqua ak æ`fktarvfakak bditnras can`ùcfins y efn`ùcfins.

A` dcud as ukn ma `ns aàlaktns läs flpnrtdktas aktra `nsbditnras defùtfins ma `ns ainsfstalds. Ifriu`d d trdvæs ma `ddtlùsbard, `d hfmrùsbard y `d inrtazd tarrastra, rad`fzdkmn aìfi`n ma` dcud.

@ds paquaôds pdrtìiu`ds ma dcud qua rasu`tdk ma `d avdpn-

rdifùk ma` dcud suparbfifd` ma ldras, rìns, `dcns, `dcukds yntrns iuarpns hìmrfins, dsifakmak d d dtlùsbard, parmfakmn

crdmud`lakta su id`nr, `n iud` pnsfef`ftd su inkmaksdifùk ak bnrld ma cntds qua d` bfkd`, bnrldk `ds kueas7 iudkmn`ds cntds dìdkzdk uk tdldôn ra`dtfvdlakta crdkma, sapraifpftdk ak bnrld ma `ùvfd. Ak cakard`, a` dcud `ùvfdsfalpra takmrä mns mastfkns: ratnrkdr d ns iuarpns hìmrfinsma mnkma sa avdpnrù n pdsdr d bnrldr pdrta ma` inkjuktnma dcuds suetarräkads.

D`cukns ifi`ns efncanquìlfins


2



Ak d ú`tfld atdpd `dldmd dsflf`difùk, `ds p`dktds pnr lamfn ma sus rdìiasdesnreak prfkifpd`lakta a` kftrùcakn ak bnrld ma kftrdtn, dukqua d`cukdsp`dktds puamak utf`fzdr a` dlnkfn ak bnrld mfraitd. Maktrn ma d p`dktd, a`

dlnkfn sa inlefkd ink inlpuastns qua inktfakak idrenkn pdrd prnmuifrinlpuastns nrcäkfins inln `ns dlfknäifmns.

]rdedjn fkmfvfmud`.

Asirfefr y rasn`var `ds sfcufaktas pracuktds ak a` iudmarkn:

4. ¾Iùln iraa ustam qua `d td`d ma ensquas dbaitd a` ifi`n kdturd` ma` dcud

5. ¾_nr quæ snk tdk flpnrtdktas `ns lfirnnrcdkfslns pdrd `d bartf`fmdm ma `n

F l d c a k

t n l d m d m a S f g f p a m f d

Ifi`n ma` kftrùcakn

5



A` ifi`n ma` idrenkn as ntrn flpnrtdkta ifi`n maktrn ma ns ainsfstalds. Aìdrenkn as uk aàlaktn qua sa akiuaktrd ak a` dfra y ak a` dcud, mfsua`tnak bnrld ma mfùxfmn ma idrenkn, prnmuitn ma `d raspfrdifùk ma `ns saras

vfvns, inleustfnkas y ntrds radiifnkas quìlfids. Inln pumn dpraifdrsaak crdk pdrta ma` masdrrn``n ma astd Qkfmdm, `ds p`dktds pnr lamfn ma`d bntnsìktasfs, tfakak `d idpdifmdm ma desnrear a` mfùxfmn ma idrenkn ytrdksbnrldr`n ak idrenhfmrdtn. Luihns nrcdkfslns sa d`flaktdk ma astdsp`dktds y aktnkias, a` mfùxfmn ma idrenkn sa vua`va d `feardr d` aktnrknpnr lamfn ma d raspfrdifùk, d masinlpnsfifùk ma sustdkifds ma masaihnma `ns nrcdkfslns n `d putrabdiifùk ma sus prnpfns iuarpns d` lnrfr.

F l d c a k t n l d m d m a w w w . g d

` f p a m f d . i n

l

Ifi`n ma`

idrenkn

Fkvastfcdr a` nrfcak ma ds trdksbnrldifnkas ma` idrenkn ak inleustfeà bùsf`

@d ldynr pdrta ma` idrenkn sa akiuaktrd inktakfmd edjn

`d suparbfifa tarrastra ak bnrld ma idreùk y patrùàn.

9



Ldkns d d nerd


34. Yù`n a` 1?% ma `d ùz sn`dr inksfcua `àcdr d `d suparbfifatarrastra maefmn d:

d. Tua a` rastn ma `d ùz quamd razdcdmd ak a` idlfkn.

e. @d bnrld dihdtdmd ma `d ]farrd.

i. Tua as rabàjdmd d` aspdifn axtarfnr n as desnrefmd pnr aà-laktns prasaktas ak `d dtlùsbard.

m. @d mfstdkifd aktra a` Yn` y `d ]farrd.

a. @d va`nifmdm ma `d ùz.

5. Axp`fqua iùln `ns rdyns sn`dras puamak dtrdvasdr läs bäif`lakta `ddtlùsbard qua `ns rdyns fkbrdrrnjns.

9. Axp`fqua d prflard ay ma d inksarvdifùk, vd`fækmnsa ma uk ajalp`n.

=. D` nesarvdr `d raprasaktdifùk cräbfid ma ukd pfrälfma ain`ùcfid, aspnsfeà dpraifdr d mfslfkuifùk ma` kúlarn ma nrcdkfslns d lamfmdqua sa dsifakma ak `ns mfbaraktas kfvaàs trùbfins. Axp`fqua pnr quæ

niurra asta bakùlakn.1. Asirfed sf as bd`sn (b) n varmdmarn (v):

d. @ds p`dktds y `ds d`cds tfakak `d idpdifmdm ma rad`fzdr bntn-sìktasfs ( )

e. @ns pfclaktns snk sustdkifds idpdias ma desnrear `d ùz ( ) i. A` in`nr varma ma `ds p`dktds sa maea ak crdk pdrta d `d



6. Uaprasakta ukd pfrälfma ain`ùcfid, edsäkmnsa ak `d ram trùbfid ma`puktn dktarfnr.

4?. Inlpàta `ns sfcufaktas akukifdmns:

d. @ns nrcdkfslns suaàk inlpatfr pnr raiursns inln ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .

e. @d inlpatakifd ma nrcdkfslns ma vdrfds aspaifas pnr a` dcudma uk astdkqua as uk i`drn ma ajalp`n ma inlpatakifd ^^^^

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .

i. @d inlpatakifd ^^^^^^^^^^^^^^^^^^^ niurra aktra nrcdkfs-lns ma ^^^^^^^^^^^^^^^^^^^^^âspaifa.

m. @d pramdifùk as ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .

a. @d fktardiifùk aktra nrcdkfslns ma mfbarakta aspaifa qua vfvak juktns, sa inknia inln ^^^^^^^^^^^^^^^^^^^^^^^ .

b. @d ra`difùk ak `d iud`, dleds aspaifas sa eakabfifdk sa ``dld^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .

c. A` inlaksd`fsln niurra iudkmn ^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .

h. @ds pu`cds y cdrrdpdtds sa inksfmardk nrcdkfslns ^^^^^^^^^^^^^^^^^^^^^^^ pnrqua sa d`flaktdk d axpaksds ma ntrnsy às idusdk mdôn.



5_drtas ma `d kaurnkd

I`dsfbfidifùk ma `ds kaurnkds sacúk su pn`drfmdm

Kaurnkd ukfpn`dr

Yu snld tfaka ukdsn`d prn`nkcdifùk(dxùk).

Kaurnkd efpn`dr

Ma uk axtraln ma suiuarpn iaù`dr sa prn-yaitd ukd makmrftd yma` ntrn uk dxùk.

Kaurnkd lu`tfpn`dr

_nsaa lú`tfpàs prn-`nkcdifnkas aktra `dsiudàs sa akiuaktrdk ukdxùk y vdrfds makmrftds.



D mfbarakifd ma `d p`dkdrfd,`ns dkæ`fmns inln `d `nlerfzma tfarrd, pnsaak uk inrmùkkarvfnsn mneà (prnmuitn ma`d busfùk ma mns inrmnkas),qua rainrra d pdrta vaktrd` masu iuarpn. A` sfstald karvfnsntdlefæk sa inlpnka ma mnscdkc`fns mnrsdàs `nid`fzdmnsak `d racfùk iabä`fid, y ku-larnsns cdkc`fns ma laknrtdldôn qua sa akiuaktrdk d

`n `drcn ma` inrmùk karvfnsn(aspaiìbfidlakta uk pdr ma cdkc`fns pnr saclaktn). Astns nrcdkfslns pnsaak vdrfntfpns ma iæù`ds saksnrfdàs, aktra `ds iudàs sa akiuaktrdk: `ds laidknrraiaptnrd

(tditn), idpdias ma parifefr fkiùsn, `ds vferdifnkas ma` sua`n7 `ds iæù`ds bntnsaks

eàs (saksfeàs d `d ùz), ma crdk dyumd pdrd `ds `nlerfias ma tfarrd qua idraiak mvfstd7 y raiaptnras ma hulamdm qua parlftak d` dkfld`, mfstfkcufr ukd znkd saima ukd húlamd.

A` sfstald karvfnsn ma nrcdkfslns inl`ns fksaitns, `ns idkcrajns, `ds drdôdsntrns drtrùpnmns, inlpdrtak d`cuksflf`ftumas ink a` sfstald karvfnsn m`ds `nlerfias ma tfarrd, tdàs inln prasakifd ma uk inrmùk karvfnsn vatrd` mneà, crdkmas cdkc`fns ak d racfùiabä`fid y uk pdr ma paquaôns cdkc`fnpnr idmd saclaktn. Yfk aledrcn, `ndrtrùpnmns d mfbarakifd ma ns dkæ`fmnpnsaak tras pdras ma cdkc`fns mnrsdàk `d ideazd qua bnrldk ukd aspaima paquaôn iaraern, d mnkma àcdksa dsnifdk ns astìlu`ns qua prnvfaka

Drdôd `nen.



_drtas ma` akiæbd`n

A` akiæbd`n as `d pdrta iaktrd` ma` sfstald karvfnsn y astäinkbnrldmd pnr a` iaraern7 a` iaraea`n as uk ùrcdkn läspaquaôn qua a` iaraern y sa uefid ak `d pdrta pnstarfnr ma `didvfmdm irdkadkd7 y a` trnkin iaraerd` as `d astruiturd quainlukfid d` iaraern ink `d læmu`d aspfkd`. ]nmn a` akiæbd`n

sa akiuaktrd maktrn ma` iräkan.



5

]rdedjn fkmfvfmud`.

Ak su iudmarkn, axp`fqua ds prfkifpdàs mfbarakifds aktra a` sfstald karvfnsn iaktry a` sfstald karvfnsn parfbærfin.

_rnpdcdifùk ma` flpu`sn karvfnsn

D sujatdr uk nejatn, pnr ajalp`n: uk luôain ma paùiha, ds kaurnkds sak-snrfdàs parifeak asa astìlu`n y `n inkmuiak d `d læmu`d aspfkd . Qkd vazd` ì, a flpu`sn sfcua uk idlfkn hdstd a iaraern, rainrrfakmn `d astruiturdma `ds kaurnkds ma prnyaiifùk y `ds fktarkaurnkds. Ak a` iaraern, sa

prniasd `d fkbnrldifùk y ak asta idsn pdrtfiu`dr, as `d saksdifùk maastdr dpratdkmn uk nejatn sudva. @d maifsfùk ma dpratdr a` nejatn inkluihd läs buarzd, vfdjd ak bnrld ma flpu`sn karvfnsn masma a` iara-ern, pdsd pnr `d læmu`d aspfkd` (d trdvæs ma kaurnkds ma prnyaiifùka fktarkaurnkds), y d``ì hdia sfkdpsfs ink ukd kaurnkd lntnrd pdrdkd`lakta trdslftfr a` flpu`sn abaitnr d `ns lúsiu`ns ma `d ldkn.

]nmns `ns flpu`sns kn sfcuak `d lfsld rutd. Ak nidsfnkas, a` astìlu`nqua prnvfaka ma `ds kaurnkds saksnrfdàs `àcd d `ds fktarkaurnkds, ypdsd mfraitdlakta d ds kaurnkds lntnrds (kn vfdjd hdstd a` iaraern).Asta tfpn ma raspuastd fkvnùktdrfd, sa inknia inln rabajn. @d radi-ifùk fkstdktäkad ma ratfrdr `d ldkn d` pfkihdrsa ink ukd aspfkd, asuk ajalp`n qua maluastrd asta bakùlakn. Idsf sflu`täkadlakta,`ds kaurnkds ma prnyaiifùk ratrdkslftak d fkbnrldifùk d` iaraern,mnkma as rainknifmn y avdùdmn pdrd qua a` fkmfvfmun tnla `ds la-mfmds d` raspaitn



Astruiturd y bukifnkas ma` sfstald karvfnsn dutùknln

_ dr d s f l p ä

t f i n

Y f l

p ä t f i n



Inln pumn dpraifdrsa murdkta pdr-ta ma asta idpìtu`n, d læmu`d aspfkdàs luy flpnrtdkta pnrqua d trdvæsma `ns karvfns qua `d inkbnrldk,ifriu`dk flpu`sns karvfnsns aktraa` akiæbd`n y a` rastn ma` iuarpn.Yfk aledrcn, ak nidsfnkas `d trdks-lfsfùk ma mfihns flpu`sns puamadbaitdrsa maefmn d trduldtfslnsnidsfnkdmns ak astd ma`fidmd znkd.

Iudkmn `ds àsfnkas snk tntdàs, `ns

laksdjas kn puamak sar trdkslftfmnspnr a` iaraern y `àcdr d su mastfkn(n vfiavarsd), lfaktrds qua ak `dsàsfnkas pdrifdàs, d`cukns ma `nsflpu`sns karvfnsns puamak dìdkzdrd `ds mfbaraktas pdrtas ma` iuarpn.Axfstak dmaläs, `ns mascdrrns pdr-ifdàs n inlpàtns ma `d læmu`d

(trdksaiifnkas), qua sacúk a` crdmnma trduldtfsln, puamak nidsfnkdrmasma mfsidpdifmdmas parldkaktashdstd `d luarta.

Yù`n ns karvfns uefidmns pnr maedjnma `d àsfùk rasu`tdk dbaitdmns7 pnr

`n tdktn, uk trduldtfsln idusdräldynr pærmfmd ma bukifnkas, iudktnläs iarid ma d ideazd sa d`nja. _nrajalp`n: d pdrdpàjfd as nidsfnkdmdpnr ukd àsfùk ak a` ärad ùledr nsdird (aspd`md edjd)7 `d parsnkd inkastd fkidpdifmdm pfarma `d saksfef`f-mdm y pnr inksfcufakta, d lnvf`fmdmak `d pdrta fkbarfnr ma su iuarpn. @dtatrdpàjfd (dktas ``dldmd iudmrfpà-

jfd), as uk tfpn ma asfùk luihn läscrdva, qua rasu`td ma ukd inktusfùk

ak a` ärad iarvfid` (iua``n), y inl-prnlata `d lnvf`fmdm ma `ds iudtrnaxtralfmdmas a fkiùsn, tdlefæksuaà dbaitdrsa d bukifùk raspfrdtnrfd,pnr n iud` as kaiasdrfn a` usn ma ukraspfrdmnr drtfbfifd`.

Fldcak tnldmd ma Akifi`npamfd Læmfid D.M.D.L

@asfnkas ma `d læmu`d aspfkd`



Bukifnkdlfaktn ma` sfstald akmnirfkn

D mfbarakifd ma` sfstald karvfnsn qua edsd su bukifnkdlfaktn ak `d trdkslfsfùk m

flpu`sns karvfnsns (saôdàs a`æitrfids), d trdvæs ma kaurnkds, a` sfstald akmnirfk`feard masma ds c`äkmu`ds, sustdkifds `dldmds hnrlnkds qua ditúdk snera iæùàspaiìbfids ``dldmds iæù`ds e`dkin, pdrd cakardr uk abaitn snera a``ds.

Ntrd mfbarakifd aktra ns mns sfstalds, as d rdpfmaz ink d iud` trdkslftak sus laksdjas7 `d kdturdàzd a`æitrfid ma `ns flpu`sns qua cakard a` sfstald karvfnsn, supaak crdk lamfmd `d va`nifmdm ma `ds hnrlnkds qua vfdjdk masma `ds c`äkmu`ds hdst`ds iæù`ds e`dkin7 sfk aledrcn, `ds hnrlnkds puamak ditudr ak tnmn a` iuarpn d

Dmaläs ma hdear ma-sdrrn``dmn a` sfstaldkarvfnsn, idpdz maparifefr y prniasdr `dfkbnrldifùk fktarkd y

axtarkd, crdifds d `davnùifùk, `ns dkfldàs hdk dmquf-rfmn astruiturds fktarra`difnkdmdspdrd ldktakar `ds bukifnkas vftdàs.]d` as a` idsn ma` sfstald akmnirfkn

qua pnmrìd ``dlärsaà ink justd rdzùk«a` cudrmfäk ma kuastrn iuarpn· (duk-qua kn as axiùsfvn ma `ns huldkns),

maefmn praifsdlakta d `d parldkaktaravfsfùk y racu`difùk ma ds ditfvfmdmasbfsfn`ùcfids.

A sfstald akmnirfkn

Qkfmdm 5. @ns nrcdkfslns y su raspuastd dkta `nsastìlu`ns ma` lamfn

Yasfùk

6



]fpns ma c`äkmu`d ma` sfstald akmnirfkn

C`äkmu`ds axnirfkds

@feardk sus sairaifnkas pnrlamfn ma uk inkmuitn d nstajfmns qua inlukfidk inka` axtarfnr (tajfmns iutäkans,y d`cukns tajfmns ma` sfstald

mfcastfvn). Ajalp`n: ds c`äk-mu`ds sumnrìpdrds ma `d pfa`huldkd.

C`äkmu`ds akmnirfkds

Idraiak ma inkmuitn y `fea-rdk sus sairaifnkas mfraitd-lakta d` tnrrakta sdkcuìkan,mnkma snk trdkspnrtdmds hds-td ns tajfmns y iæ`u`ds e`dkin.

Ajalp`n: `d tfrnfmas sairatdukd hnrlnkd inknifmd inlntfrnxfkd, qua sa akidrcd maastflu`dr a` latden`fsln.

C`äkmu`d sumnrìpdrd C`äkmu`d tfrnfmas



_rfkifpdàs c`äkmu`ds akmnirfkds

Fkiralaktdk `d braiuak-ifd ma `ns `dtfmns ma`

inrdzùk, dulaktdk `dtaksfùk drtarfd`, inktrdakn mf`dtdk ns vdsns sdkcuì-kans y aàvdk ns kfvaàsma dzúidr ak `d sdkcra._nr `n cakard`, asta ink-

juktn ma radiifnkas niu-rra iudkmn hdy raspuastdfklamfdtd. Ajalp`n: ukdsftudifùk ma pa`fcrn

C`äkmu`d(s) Idrditarìstfids Hnrlnkd/bukifùk prfkifpd`

Ya `nid`fzd ak a` hfpn-tä`dln. Dukqua pa-quaôd, astd c`äkmu`d

ink bnrld y tdldôn mabrìjn`, inktrn`d `ds buk-ifnkas ma luihds ntrdsc`äkmu`ds akmnirfkdsma` iuarpn. Ya mfvfmaak dmaknhfpùbfsfs n `ù-eu`n dktarfnr, kaurnhf-pùbfsfs n ùeu`n pnstarfnry `ùeu`n fktarlamfn.

@ds c`äkmu`ds suprd-rrakdàs sa sftúdk ak `dpdrta suparfnr ma `nsrfônkas. Idmd ukd astäbnrldmd pnr ukd znkdfktarkd ``dldmd læmu`dy ukd idpd axtarkd ``d-ldmd inrtazd.

Hfpùbfsfs

n pftuftdrfd

Yuprdrra-

kdàs

(læmu`d)

Astflu`d `d c`äkmu`d tf-rnfmas

Astflu`d `d prnmuiifùkma àiha

Hnrlnkd ma` iraif-lfaktn

_rnmuia `ds inktrdiifn-kas ma` útarn y astflu`d`d sairaifùk ma àiha dtrdvæs ma `ds ldlds.

Astflu`d `d radesnrifùkma dcud ma `ns rfônkas.

Astflu`d `d inrtazd su-prdrrakd`.

Astflu`dk `ds c`äkmu`dssaxudàs.

]YH4

_rn`ditfkd

Ynldtn-trnbfkd

Nxftnifkd

DMH

DI]H

BYH y @H

Dmrakd`fkdy knrdmra-kd`fkd



C`äkmu`d(s) Idrditarìstfids Hnrlnkd/bukifùk prfkifpd`

Astä sftudmd juktn d`fktastfkn ma`cdmn. @f-eard akzflds (bukifùkaxnirfkd), d` fktastfknpdrd inktrfeufr ink `dmfcastfùk.

]dlefæk pnsaa iæù`dsaspaifd`fzdmds maktrnma `ns fs`ntas ma @dk-carhdks ma` päkirads,

qua prnmuiak fksu`f-kd y cùidcùk (bukifùkakmnirfkd), hnrlnkdsakidrcdmds ma racu`dra` latden`fsln ma `dcùinsd.

_dr ma ùrcdkns raprn-muitfvns balakfkns `n-id`fzdmns d idmd dmn ma`útarn.

_dr ma ùrcdkns ldsiu-`fkns qua sa akiuak-trdk `nid`fzdmns ak aàsirntn.

_äkirads

Nvdrfns

]astìiu`ns

_rnluava `d desnrifùk

ma cùinsd pnr pdrta ma`ds iæù`ds, pdrd mfslf-kufr su inkiaktrdifùk ak`d sdkcra.

Astflu`d `d `feardifùk ma`d cùinsd (d`ldiakdmdak a` hìcdmn ak bnrld macùiùcakn), d `d sdkcra.

Masdrrn``dk `ns ùrcdknsraprnmuitnras balakfkns

y prnluavak `d dpdrf-ifùk ma va``n púefin ydxf`dr, iraiflfaktn ma `dsldlds y dlp`ftum ma dsidmards.

_rnluava a` iraiflfaktnma` tdpfz ma` útarn pdrdraifefr a` ùvu`n.

Astflu`d d bnrldifùk maasparldtnznfmas y prn-luava `d dpdrfifùk ma`ds idrditarìstfids lds-iu`fkds: masdrrn``n ma`paka, iraiflfaktn mava``n púefin y bdifd`, ytnkn ma vnz läs crdva

Fksu`fkd

Cùidcùk

Astrùcakns

_rncastarnkd

]astnstarnkd



6

D`cukds c`äkmu`ds ma` iuarpn

Fläcakas tnldmds ma Akifi`npamfd Læmfid D.M.D.L

• Dukqua ak `d sasfùk dktarfnr inlakzdlns ink a` tald ma `ds c`äkmu`ds,partfkakta rapdsdr uk pnin snera su uefidifùk. _drd a``n maealns inksacuk fldcak ma` iuarpn huldkn mnkma pnmdlns uefidr idmd ukd ma `ds c`ämu`ds qua lakifnkdlns ak i`dsa, pdrd a``n puama id`idr, mfeujdr, rainrtdpacdr7 `n flpnrtdkta as qua uefqua ak uk iuarpn huldkn `d ldynr idktfmma c`äkmu`ds qua puamd.

• Fkvastfcua quæ ntrns ùrcdkns ma` iuarpn huldkn prnmuiak hnrlnkds. Axp`fq

Nvdrfn

knrld`

Nvdrfn

pn`fquìstfin



=

Ak d sfcufakta päcfkd wae, sa puama hd``dr fkbnrldifùk ra`difn-kdmd ink ds akbarlamdmas ma` sfstald akmnirfkn: http://www.k`l.kfh.cnv/lam`fkapùs/spdkfsh/akmnirfkamfsadsas.htl`


Idmd suecrupn maea asincar uk trdstnrkn ma` sfstald akmnirfkn, rainàitdr ldynr idktfmdm ma fkbnrldifùk ra`difnkdmd ink a` tald, y axpnkar`d dkta prnbasnr y inlpdôarns ma i`dsa.

@d mfdeatas, ukd akbarlamdm ma` sfstald akmnirfkn

_drd inkniar lajnr `ds idrditarìstfids ma asta trdstnrkn ma` sfstald ak-mnirfkn, prflarn inknzidlns iùln a` nrcdkfsln inksfcua ldktakarastdeàs `ns kfvaàs ma cùinsd ak `d sdkcra.

@ds iæù`ds eatd ma ns fs`ntas ma @dkcarhdks ak a` päkirads, snk ds akidr-cdmds ma sacracdr `d hnrlnkd ``dldmd fksu`fkd. Astd sustdkifd as `feardmdiudkmn `d inkiaktrdifùk ma dzúidr as d`td ak a` tnrrakta sdkcuìkan, ma

KDRACQALNY AK FK]AUKA]



bnrld qua prnluava `d desnrifùk ma `d cùinsd pnr pdrta ma `ds iæù`dspdrd qua su kfva` sa astdef`fia. @d hnrlnkd cùidcùk rad`fzd tnmn `n ink-trdrfn, pnrqua prnluava `d macrdmdifùk ma cùiùcakn (cùinsd d`ldia-kdmd ak a` hìcdmn), d cùinsd pdrd `feardr`d d `d sdkcra y dsì, dulaktdr a`kfva` ma dzúidr.

Ak nidsfnkas, `d prnmuiifùk ma fksu`fkd pnr pdrta ma` päkirads puamamfslfkufr (mfdeatas tfpn 4), `n iud` dbaitd `d desnrifùk ma cùinsd pnrpdrta ma `ds iæù`ds y quamd crdk pdrta ma su inktakfmn ak `d sdkcra. @drasfstakifd ma ds iæù`ds d` abaitn ma d fksu`fkd, tdlefæk suaà cakardr a`lfsln abaitn (mfdeatas tfpn 5). Ak dlens idsns, su inksaiuakifd as ukfkiralaktn ak d inkiaktrdifùk ma cùinsd ak d sdkcra, trdstnrkn qua sainknia inln mfdeatas la``ftus.

Aspaifd`lakta ak `ds parsnkds dbaitdmds ink `d mfdeatas tfpn 4, suaàkprasaktdrsa sìktnlds inln pærmfmd ma pasn, käusads, vùlftn, bdtfcdlusiu`dr, sam y hdlera inkstdktas. _nr `n cakard`, `ns pdifaktas inkastd akbarlamdm snk mfdcknstfidmns d talprdkd amdm (kfôaz), y maeakinktrdrrastdr `d sfktnldtn`ncìd, fkyaitäkmnsa fksu`fkd mfdrfdlakta pnr a`

rastn ma su vfmd. @ns sìktnlds ma `d mfdeatas tfpn 5, snk sflf`dras d `ns ma`d mfdeatas tfpn 4, dukqua luihds vaias, kn prasaktd sfckns avfmaktaspdrd qufak d pdmaia7 dsì qua crdk idktfmdm ma parsnkds kf sfqufard sdeakqua `d tfakak. @d dpdrfifùk y `d avnùifùk ma asta trdstnrkn astäk luydsnifdmds d `d neasfmdm y d `d bd`td ma ajarififn. @d fksu`fkd n sustdkifdsdkä`ncds d `d lfsld, dsì inln dktfmfdeætfins nrdàs, snk `d lajnr bnrldma inktrn`dr `d mfdeatas ma asta tfpn.

@d lamfifùk ma `ds inkiaktrdifnkas ma cùinsd ak sdkcra y nrfkd, snk`d lajnr bnrld ma mataitdr `d akbarlamdm. Maspuæs ma mfdcknstfidrsa`d mfdeatas, a` nejatfvn prfkifpd` ma` trdtdlfaktn as rastdeàiar a` kfva`knrld` ma d cùinsd ak d sdkcra, pdrd avftdr inlp`fidifnkas pnstarfnrasinln fksubfifakifd rakd`, pærmfmd ma d vfsfùk maefmn d mdôns ak d ratfkd,d`tardifnkas ifriu`dtnrfds ak erdzns y pfarkds (qua puama `àvdr d `d dl-putdifùk ma `ns lfalerns), akbarlamdmas idrmìdids, prneàlds iaraernvdsiu`dras y inld mfdeætfin.



_drtas ma `d kaurnkd

4. ¾Tuæ as ukd kaurnkd> ¾Iuäàs snk sus bukifnkasprfkifpdàs>

5. Ak `d sfcufakta fldcak, fmaktfbfqua `ds prfkifpdàspdrtas ma `d kaurnkd.

9. Maedjn ma idmd kaurnkd, asirfed su inrraspnkmfakta i`dsfbfidifùk pn`dr(ukfpn`dr, efpn`dr, lu`tfpn`dr).

Ldkns d d nerd

Qkfmdm 5. @ns nrcdkfslns y su raspuastd dkta `nsastìlu`ns ma` lamfn

Yasfùk

4?



4?

Fkvastfcua:

• ¾Tuæ iufmdmns maea takar ukd parsnkd qua subra ma mfdeatas>• ¾Tuæ ntrds akbarlamdmas hd asiuihdmn qua sa maedk d` ld` bukifnkdlfa

ma ukd c`äkmu`d>• ¾Iùln sa puama mataitdr qua hdy uk ld` bukifnkdlfaktn ma `ds c`äkmu`ds

a` iuarpn>

1. A`denra uk iudmrn inlpdrdtfvn aktra a` sfstald karvfnsn iaktrd` y a`sfstald karvfnsn parfbærfin.

2. ¾Iuä` as `d prfkifpd` mfbarakifd aktra `d prnpdcdifùk ma uk flpu`snkarvfnsn inlúk y uk rabàjn>

3. Inlpàta `ns aspdifns ak e`dkin ink `ns tærlfkns inrraspnkmfaktas:

d. A` sar huldkn pnsaa ^^^^^^^^ pdras ma karvfns irdkadàs.

e. A` hnlera tfaka ^^^^^^^^^^^ pdras ma karvfns aspfkdàs.

i. Aktra sus lú`tfpàs bukifnkas, a` sfstald karvfnsn dutùkn-

ln pdrdsflpätfin sa akidrcd ma ^^^^^^^^^^^ `d pupf`d,

^^^^^^^^^^^^^ `d sd`fvdifùk, ^^^^^^^^^^^^^ `d vajfcd7

lfaktrds qua a` sfstald sflpätfin ^^^^^^^^^^ `ns ernkqufns,

^^^^^^^^^^^^ d pupf`d, ^^^^^^^^^^^^^^ d ditfvfmdm mfcas-tfvd y ^^^^^^^ ^^^^^^^ a` flpu`sn idrmìdin.



8. Astdeàzid `ds prfkifpdàs mfbarakifds aktra a` sfstald karvfnsn y a`sfstald akmnirfkn:

6. Uasua`vd a` iruifcrdld ma `d päcfkd sfcufakta ink `ds i`dvas qua saprasaktdk d inktfkudifùk:

4. Cakard ak a` nrcdkfsln, uk inkjuktn ma radiifnkas qua niurrakiudkmn sa kaiasftd ukd raspuastd fklamfdtd.

5. Astflu`d `d radesnrifùk ma dcud ma `ns rfônkas.

9. Astflu`d `d prnmuiifùk ma àiha.=. Fkiralaktd a` kfva` ma idìfn ak `d sdkcra.

1. Mfslfkuya `d inkiaktrdifùk ma dzúidr ak `d sdkcra.

2. Inktrn`d a` latden`fsln ma crdsds y idrenhfmrdtns. _rnluava dmacrdmdifùk y sìktasfs ma `ds prntaìkds.

3. Mfslfkuya `d inkiaktrdifùk ma idìfn ak `d sdkcra.

8. Astflu`d `d `feardifùk ma cùinsd ak `d sdkcra.

6. Uacu`d ds bukifnkas ra`difnkdmds ink ns parìnmns mfurkn y kni-turkn.

4?. Masdrrn``dk `ns ùrcdkns raprnmuitnras balakfkns.

44. _rnluava `d dpdrfifùk ma `ds idrditarìstfids ldsiu`fkds.

45. _rnluava a` iraiflfaktn ma` tdpfz ma` útarn.

49. Astflu`d a` iraiflfaktn inrpnrd`.

4=. Astflu`d `d sairaifùk ma àiha d trdvæs ma `ds ldlds.



Hnrlnkds ma` iuarpn huldkn



Efe`fncrdbìd

• SF@YNK, 4666 AK _UFLDIG, U. 5??4. Bukmdlaktns mainksarvdifùk efn`ùcfid: parspaitfvds dtfkndlarfidkds. Bnkmnma Iu`turd Ainkùlfid. Læxfin M.B.

• IQU]FY, H. EDUKAY, K. 5???. Efn`ncìd. Amftnrfd` _dkd-larfidkd. Euakns Dfras.

• _AUAZ, A. 4612. _`dktds útf`as ma In`nlefd. @ferarfdIn`nlefdkd - Idldihn Un`mdk (Iìd. @tmd.). Encntä.



Lùmu`n fktacrdmn pdrd ifi`n 1]rdksbnrlalns Amuidkmn

Ärad Tuìlfid 4?

Inlukfmdm inrracflfaktn _uartn In`nlefd



A s t ä k m d r a s e ä s f i n s

m a i n l p a t a k i f d s a k

T u ì l f i d


B d i t n r a s m a n r c d k f z d i f ù k

¾ D q u æ

q u a r a l n s

` ` a c d r >

U a ` d i f n k n ` d a s t r u i t u r d m a

` d s l n ` æ i u ` d s f k n r c ä k f i d s

i n k s u s p r n p f a m d m a s b ì s f i d s

y q u ì l f i d s y s u i d p d i f m d m

m a i d l e f n q u ì l f i n .

¾ I ù l n m a l u a s t r n ` n d p r a k m f m n >


I f a k i

f d ,


y

s n i f a m d m


•

F m a k t f b f i n i d l e f n s q u ì l f i n s a k ` d

v f m d i n t f m f d k d y a k a ` d l e f a k

t a .

•

A x p ` f i n ` n s i d l e f n s q u ì l f i n s

m a s m a

m f b a r a k t a s l n m a ` n s .

•

R a r f b f i n a ` a b a i t n m a p r a s f ù k

y t a l -

p a r d t u r d a k ` n s i d l e f n s q u ì l

f i n s .

•

Q s n ` d t d e ` d p a r f ù m f i d p d r d m a t a r l f -

k d r p r n p f a m d m a s b ì s f i d s y q u ì l

f i d s m a

` n s a ` a l a k t n s .

•

U a d ` f z n i ä ` i u ` n s i u d k t f t d t f v n s a k

i d l e f n s q u ì l f i n s .

•

F m a k t f b f i n i n k m f i f n k a s p d r d i n

k t r n ` d r

` d v a ` n i f m d m m a i d l e f n s q u ì l

f i n s .

•

I d r d i t a r f z n i d l e f n s q u ì l f i n s a k

i n k m f i f n k a s m a a q u f ` f e r f n .

•

A x p ` f i n ` d a s t r u i t u r d m a ` n s ä t n l n s d

p d r t f r m a m f b a r a k t a s t a n r ì d s .

•

A x p ` f i n ` d r a ` d i f ù k a k t r a ` d a s t r u i t u r d

m a ` n s ä t n l n s y ` n s a k ` d i a s q u a r a d -

` f z d .

•

U a ` d i f n k n ` d a s t r u i t u r d m a ` i d r e n k n

i n k ` d b n r l d i f ù k m a l n ` æ i u ` d

s n r c ä -

k f i d s .

•

U a ` d i f n k n c r u p n s b u k i f n k d ` a s

i n k ` d s

p r n p f a m d m a s b ì s f i d s y q u ì l f i d s m a ` d s

s u s t d k i f d s .

A j a s t a l ä t f i n s

A x p ` f i n ` d s b u a r z d s a k t r a

n e j a t n s i n l n f k t a r d i i f n k a s

m a e f m d s d ` d i d r c d a ` æ i t r f -

i d y d ` d k d t u r d ` a z d m a ` d

l d t a r f d .

•

I d l e f n s b ì s f i n s y q u ì l

f i n s ( u k f m d m 4 ,

Y a s f ù k

4 )

•

] d e ` d p a r f ù m f i d ( Q k f m

d m = ,

Y a s f ù k = )

•

U a d i i f n k a s q u ì l f i d s

( Q k f m d m 2 ,

Y a s f ù k 3 )

•

A s t a q u f n l a t r ì d ( Q k f m

d m 2 ,

Y a s f ù k 3 )

•

I f k æ t f i d q u ì l f i d ( Q k f m d m 2 ,

Y a s f ù k 3 )

•

A q u f ` f e r f n q u ì l f i n ( Q

k f m d m 8 ,

Y a s f ù k 4 ? )

•

@ a y a s m a ` n s c d s a s ( Q k f m d m 3 ,

Y a s f ù k 8 )

•

Ä t n l n ( Q k f m d m 9 , s a s f ù k 9 )

•

A k ` d i a q u ì l f i n ( Q k f m

d m 1 ,

Y a s f ù k 1 )

•

B u k i f n k a s y k n l a k i ` d t u r d f k n r c ä k f i d ( Q k f -

m d m 1 ,

Y a s f ù k 2 )

•

Y n ` u i f n k a s ( Q k f m d m 8

, Y a s f ù k 6 )

•

A x p ` f i

n i d l e f n s q u ì l f -

i n s a k

` d i n i f k d ,

` d f k m u s -

t r f d y a

` d l e f a k t a .



Qkfmdm 4. Flpnrtdkifd ma `d quìlfid 596

Yasfùk 4. Ldtarfd, quìlfid y aktnrkn 596

Qkfmdm 5. A` pdtfn: kuastrn `denrdtnrfn 514

Yasfùk 5. @denrdtnrfn ma quìlfid 514 Qkfmdm 9. Inkstftuifùk ma `d ldtarfd 525

Yasfùk 9. Ätnln 525

Qkfmdm =. @d tde`d parfùmfid 535

Yasfùk =. ]de`d parfùmfid y parfnmfifmdm 535

Qkfmdm 1. @ns inlpuastns 585

Yasfùk 1. Ak`dia quìlfin 585

Yasfùk 2. Inlpuastns y knlaki`dturd fknrcäkfid 569

Qkfmdm 2. Uadiifnkas quìlfids 94?

Yasfùk 3. Astaqufnlatrìd 94?

Qkfmdm 3. Cdsas 99=

Yasfùk 8. Cdsas 99=

Qkfmdm 8. Yn`uifnkas 914

Yasfùk 6. Yn`uifnkas 914

Ì km f i a



]ùlasa ukns lfkutns pdrd paksdr ma bnrld fkmfvfmud` snera `ds sfcufaktaspracuktds:

Ya hd pracuktdmn d`cukd vaz:

¾_nr quæ a` inktakfmn ma` huavn pdsd ma sar `ìqufmn d sù`fmn yidlefd ma sdenr iudkmn sa inifkd>

¾_nr quæ `d pu`pd ma `d ldkzdkd sa nsiuraia iudkmn quamd ax-puastd d` dfra>

¾_nr quæ sa prnmuia d`inhn` iudkmn sa lazi`d dzúidr ink dcud ysa majd pnr vdrfns mìds>

¾_nr quæ a` `flùk as äifmn y `d kdrdkjd as mu`ia>

¾_nr quæ ak uk mìd ma id`nr a` hfa`n sa marrfta, parn a` dcud, ns jucns, `d cdsansd n `d iarvazd kn sa avdpnrdk>

Ldtarfd, quìlfid y aktnrknQkfmdm 4. Flpnrtdkifd ma `d quìlfid Yasfùk

4



@d quìlfid as `d ifakifd qua sa akidrcd ma` astumfn ma `ns bakùlakns ma `d kdturdàzd, ra`difnkdmns ink `d inlpnsfifùk, fktardiifùk, trdksbnrldifnkas y prnpfamdmas ma `d ldtarfd, td` inlsa dpraifd ak a` ldpd inkiaptud`.

Dsì, d quìlfid kn as sn`dlakta d`cn qua sa hdia ak a` denrdtnrfsfkn qua `d akinktrdlns d kuastrn d`ramamnr tnmn a` tfalpn

iudkmn raspfrdlns, iudkmn inlalns, ak `d rnpd qua usdlns, ak `ns prnmuitns mdsan qua alpàdlns, ak a` ldtarfd` ma `ds harrdlfaktds y utaksf`fns qua usdlnak kuastrn trdedjn y ak a` hncdr, ak `ns lamfidlaktns qua inksulflns, ak `d lkard inln inifkdlns kuastrns d`flaktns, ak `ns idlefns ma in`nr, n`nr y sdenr m`ds brutds, a` quasn, `d àiha y `ds varmurds, ak a` bukifnkdlfaktn ma `ns idrrns, `dlntns, `ns dvfnkas, y uk sfkbìk läs ma avaktns.

D kfva` kutrfifnkd` d quìlfid as vftd`, yd qua ns kutrfaktas, inln ns c`úifmns, ìpfm(crdsds y diaftas), prntaìkds, lfkardàs y vftdlfkds sa akiuaktrdk ak `ns d`flaktnqua inksulflns d mfdrfn y sa hdk bnrldmn d` fktarfnr ma `ns lfslns, crdifds d uksarfa ma prniasns quìlfins qua sa `àvdk d iden maktrn ma `ds iæù`ds y ak `n läprnbukmn ma `d tfarrd, as maifr, ak a` ldcld vnìäkfin.

LD]AUFD

Astdmns ma dcracd

Ya i`dsffflidksacúk

Yu astruiturdinkstftufmd pnr ätnlns

Inkstftuìmns pnraàitrnkas, kautrnkas,

prntnkas, qudrgs, lunkas,àptnkas, barlfnkas y läs

pdrtìiu`ds suedtùlfids

_uama sar fnkas sf pfarma ncdkd aàitrnkas7 n fsùtnpns sf

vdrìdk `d idktfmdm ma kautrnkasak a` kúiàn

Bnrldk nsAàlaktns

@d ukfùk ma vdrfns aàlaktnsmfbaraktas md nrìcak d `ns

INL_QAY]NY

@d ukfmdm läs paquaôd sainknia inln LN@ÆIQ@D y

puama astdr bnrldmd pnr mns nläs ätnlns fcudàs n mfbaraktas

Lazi`ds

Hnlncækads

Qkd sn`d bdsa, kn samfstfkcuak inlpn-

kaktas

Ya sapdrdk pnrmastf`difùk,

irnldtncrdbìd,sue`fldifùk yirfstd`fzdifùk

Ya sapdrdk pnrldckatfzdifùk,maidktdifùk n

ffl`trdifùk

Rdrfds bdsas nesarvdeàs

Hatarncækads Cds

@ìqufmn

Yù`fmn

InEn

Y



_drd pnmar masdrrn``dr sus ditfvfmdmas mfdrfds, tnmns ns saras vfvns kaiasftdk akarcÆstd as netakfmd lamfdkta `d fkcastfùk ma ifartds sustdkifds quìlfids qua prnvkak ma `ns d`flaktns y qua sa maknlfkdk kutrfaktas. D` aktrdr ak a` nrcdkfsln, kutrfaktas snk dsflf`dmns, y ma `ns d`flaktns y qua sa maknlfkdk kutrfaktas. @kutrfaktas d` aktrdr ak a` nrcdkfsln sa dsflf`dk y pdrta ma a``ns sa d`ldiakd hds

LD]AUFD

Yù`fmns @ìqufmns n cdsas

Rn`úlak

l@, il9, @

Ldsd _asn

Kawtnk (K)lc, c, `e, Gc

_nsaa

Idlefns

Bìsfins Tuìlfins

]rdksbnrldifùk msustdkifds ak ntrds,

UADIIFNKAY TQÌ

Idlefn ak d dpdrfakifdbìsfid ma ds sustdkifds, parn

kn ak su inlpnsfifùk

Qkfmdmas ma lamfmd

_rnpfamdmas

Bìsfids

N`nr, in`nr, sdenr, maksfmdm,puktn ma busfùk y aeu``fifùk

Fkstdldef`fmdm, nxfmdifùk Mapakmak ma d idktfmdmma ldtarfd

Kn mapakmak ma d idktfmdmma sustdkifd

Tuìlfids Axtaksfvds Fktaksfvds

D_@FIDIFNKAY TQÌLFIDYIN]FMFDKDY

Tuìlfid ma `ns d`flaktns



Dmaläs, ns saras vfvns kaiasftdk inkstrufr y rapdrdr tajfmns pdrd pnmar masdrrn``drsa y iraiar.

@ns ldtarfdàs kaiasdrfns pdrd iulp`fr ink astd

bukifnkas tdlefæk snk prnpnrifnkdmns pnr `nd`flaktns.

@ns kutrfaktas qua prnpnrifnkdk `ns d`flaktns qua snk fkmfspaksdeàs pdrd inksarvdr d vfmd sn`ns idrenhfmrdtns, `ns ìpfmns, y prntaìkds, qua sn`ns raspnksdeàs ma` dpnrta ma tnmd `d akarc

qua kaiasftdlns d mfdrfn, pdrd a` masdrrn``n ma tnmds kuastrds bukifnkas v

tdàs. ]dlefæk astäk `ds vftdlfkds y lfkardàs `ns iudàs, sf efak kn tfakak kfkcukfkifmakifd ak a` dpnrta id`ùrfin, snk fkmfspaksdeàs pdrd qua ds radiifnkas quìlfiinrpnrdàs sa `àvak d iden.

D `ns idrenhfmrdtns n c`úifmns `ns akinktrdlns ak `ds brutds, vacatdàs, crdkns, iaradàs y àiha ak bnrld ma dzúidras, d`lfmnkas y hdrfkds, y ak `ds idrkas, ak ukln`æiu`d inknifmd inln cùiùcakn. Ynk flpnrtdktas, yd qua a``ns inkstftuyak 1?% ma `d mfatd mfdrfd, dpnrtdkmn `d lftdm ma `d akarcìd qua kaiasftdlns mìd d mì

pdrd a` masdrrn``n ma kuastrds ditfvfmdmas vftdàs y intfmfdkds.

@ns ìpfmns snk ds lfslds crdsds, diaftas y inàstarn` y, d` fcud` qua `ns c`úifmns, snma nrfcak vacatd` n dkfld`. Ynk alpàdmns inln ldtarfd` ma rasarvd akarcætfiinrpnrd`, inln inkstftuyaktas ma `ds lalerdkds iaù`dras y inktrn`dmnras ma talpardturd inrpnrd`. _drtfifpdk ak `d sìktasfs ma hnrlnkds, inln `d prncastarnky `d tastnstarnkd y snk raspnksdeàs ak d`cukns idsns ma `ns in`nras ma d`cukns dlaktns, inln `d zdkdhnrfd, rfid ak idrntaknfmas, qua snk uk tfpn ma `ìpfmns qudyumdk ak `ns huldkns d prntacar `d pfa` inktrd `d rdmfdifùk u`trdvfnàtd (pnr a`snk usdmns ak d bderfidifùk ma e`nquadmnras sn`dras) y ak d sìktasfs ma ratfkn`, quas `d lfsld Rftdlfkd D, qua iufmd `d sdùm ma `ns njns.

@ds prntaìkds sa utf`fzdk ak `d sìktasfs ma tajfmns inln `ns lúsiu`ns, `d sdkcra, idea``n, `ds uôds y `d pfa`.

@d vdrfamdm ma sdenras, in`nras,

n`nras y kutrfaktas ak `ns

d`flaktns as a` rasu`tdmn ma

prniasns quìlfins

pdrtfiu`dras.



@d prnmuiifùk ma dktfefùtfins, vdiukds sfktætfids

y bärldins hd lajnrdmn kuastrd sdùm.

@d quìlfid y `d sdùm

Ditud`lakta snk fkinktdeàs `ns prniasns quì -lfins qua sa `àvdk d iden pdrd trdksbnrldrsustdkifds ma nrfcak dkfld`, vacatd` n sfktætfin,pdrd trdksbnrldr`ds ak ldtarfd prflds, pdrd a`d-enrdr nejatns ma usn intfmfdkn, mrncds y drtìiu`nsfkmustrfdàs.

Lamfdkta prniasns quìlfins

sa netfakak parbulas.

@n dktarfnr sa hd `ncrdmn crdifds d` inkniflfaktn

ma d quìlfid, parlftfakmn dsì a` dvdkia ma d tai-kn`ncìd y `ds ifakifds, cakardkmn kuavns idlpnsma astumfn ak efnquìlfid, lamfifkd, efntaikn`n-cìd, fkcakfarìd cakætfid, efn`ncìd lnàiu`dr, inl-eustfeàs, ati., inlprakmfakmn dsì d flpnrtdkifdma `d quìlfid ak kuastrd prnpfd axfstakifd.

@d ifakifd hd masaktrdôdmn a`

harlnsn lfstarfn ma` DMK.



Luihds ma ds mrncds qua sa inksulak inln trdtdlfaktns læmfins snk prnmuifmpnr prniamflfaktns quìlfins (dktfefùtfins, dkbatdlfkds, dktffkb`dldtnrfns, ati.). netakifùk ma vdiukds sfktætfids y `d prnmuiifùk ma dktfiuarpns lnkni`nkdàs hdlajnrdmn `d fklukfmdm pne`difnkd`. @d quìlfid dsnifdmd d ntrds ifakifds inln efn`ncìd y `d fkcakfarìd cakætfid hd lajnrdmn kntdeàlakta `d sdùm ma `ns pnemnras ma `d ]farrd.

@d prnmuiifùk ma masfkbaitdktas d kfva`læmfin y `d utf`fzdifùk ma sustdkifds marfvd-mds ma` i`nrn, snmd iäustfid, dlnkfdin, ati., h dsfmn útfàs ak d a`flfkdifùk ma vfrus, editarfds,hnkcns y prntnzndrfns, inktrdprnmuiaktas

pdrd `d sdùm ma `ds p`dktds, `ns dkfldàs y a`hnlera.

_arn d quìlfid kn sù`n sa usd pdrd d a`denrd-ifùk ma lamfidlaktns y masfkbaitdktas, sfknqua dmaläs dyumd d axp`fidr y inlprak-mar a` pnrquæ ma luihds akbarlamdmas,`n qua d su vaz hdia pnsfeà `d fkvastfcdifùk

ak a` tarrakn ma `d quìlfid bdrldiæutfid y a` surcflfaktn ma kuavns trdtdlfaktlæmfins trdmfifnkdàs n d`tarkdtfvns.

@d quìlfid prnmuia dktfefùtfin

d crdk asid`d.

Fkcakfarìd cakætfid: iæù`ds huldkds ak

`ds iudàs d`cukds prntaìkds sa busfnkdk in

prntaìkds varmas bùnrasiaktas pdrd parl



Inleustfùk: as uk prniasn ak a` iud` d ldtarfd

sa nxfmd, ak prasakifd ma` nxìcakn u ntrn dcaktanxfmdkta buarta, `feardkmn crdkmas idktfmdmasma akarcìd, qua sa ldkfbfastd ak bnrld ma id-`nr n buacn. _drd qua astn sa mæ, sa raqufara `dprasakifd ma uk dcakta inleurakta, qua saakidrcd ma nxfmdr d` inleustfeà (pnr ajalp`na` nxìcakn). Qk ajalp`n ma inleustfùk sa mdd` akiakmar ukd astubd n iudkmn sa prakma a`

lntnr ma uk idrrn, qua ak mfihns idsns sa mdpnr d nxfmdifùk ma` cds kdturd` y ma d cdsn`fkd.

Lazi`ds abarvasiaktas: as uk bakùlakn ak a`qua ukd sustdkifd cdsansd asidpd ma uk ìqufmny sa md pnr mns rdznkas: pnr fksnùef`fmdm ma`cds, inln ak a` idsn ma `ds cdsansds, n inlnprnmuitn ma radiifnkas quìlfids, inln a`

D`gd-Ya`tzar ak dcud.Barlaktdifùk: as uk prniasn quìlfin prnpfnma `d ldtarfd nrcäkfid, ak `d iud` æstd sa nxfmdak prasakifd ma lfirnnrcdkfslns, inln `dàvdmurd, mdkmn nrfcak d inlpuastns inln a`dìnhn`, sf a` prniasn sa ldktfaka dàjdmn ma`dfra, n vfkdcra sf sa majd axpuastn d` lamfn dl-efakta. _nr a``n, a` vfkn sa dvfkdcrd y a` quasn y

`d àiha sa vua`vak rdkifns.Masinlpnsfifùk ma d inlfmd: as `d radiifùkma editarfds y lfirnnrcdkfslns, qua ditúdkinln macrdmdmnras (inksulfmnras) ma `ds sus-tdkifds quìlfids qua inlpnkak `ns d`flaktns,iuyns masaihns latdeù`fins mdk ùcdr d idl-efns ak a` n`nr, in`nr, sdenr, taxturd y dspaitn

@d quìlfid y d`cukns bakùlakns d kuastrnd`ramamnr



YQY]DKIFD IN@NU FKFIFD@

A` fkmfidmnr y `ds sustdkifds:

4. Ldrqua 2 vdsns ma p`ästfin trdkspdrakta ink `ns knleras: jucn ma `flùk jdeùk ak pn`vn, `aiha ma ldckasfd, sd`, dzúidr y vfkdcra.

5. In`nqua ak idmd vdsn paquaôds idktfmdmas ma `d sustdkifd fkmfidmd ydcud. Læzi`a`ns hdstd qua sa mfsua`vdk y dknta ak `d tde`d qua akinktrdrä dedjna` in`nr ma idmd ukd.

9. Dmfifnka uk ihnrrn ma` dcud ma rapn``n ak idmd vdsn y racfstra sus nesarvdifnkas ak `d tde`d sfcufakta:

=. ¾@ns idlefns ma in`nr nesarvdmn snk prnmuitn ma idlefns bìsfins n quìlfins> Axp`fqua su raspuastd.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

IN@NU INK A@FKMFIDMNU

Jucn ma `flùk

Jdeùk ak pn`vn

@aiha ma ldckasfd

Yd`

Dzúidr

Rfkdcra



Inln sa vfn ak `d ukfmdm dktarfnr, `d quìlfid astä d kuastrn d`ramamnr, parnluihns ma `ns prnmuitns qua usdlns d mfdrfn hdk sfmn sfktatfzdmns n lajn-rdmns ak `ns `denrdtnrfns, yd qua `d quìlfid sa idrditarfzd pnr sar ukd ifakifdd`tdlakta axparflaktd`. Dsì, ak astd sasfùk inkniaralns d`cukns ldtarfdàs,aqufpns y usns ma `ns lfslns ak a` `denrdtnrfn ma quìlfid, dktas ma pdsdr d`d axparflaktdifùk. ]dlefæk denrmdralns `ds knrlds ma sacurfmdm qua samaeak sacufr, yd qua sfalpra axfstak rfascns ak d ldkfpu`difùk ma sustdkifds,ldtarfdàs y aqufpns.

LD]AUFD@AY MA@ @DENUD]NUFN

Ynk `ns qua sa alpàdk pdrd sujatdr, lamfr, d`ldiakdr n idàktdr y kn bukifnkink aàitrfifmdm. Ya i`dsfbfidk ink edsa ak a` ldtarfd` ma` iud` astäk inkstftufmsf sa puamak idàktdr n kn y, sf sa puama hdiar lamfifnkas ink a``ns (var ldinkiaptud` 5).

@d ldmard sa alpàded dktfcudlakta inln ld-tarfd` pdrd sujatdr ldtarfdàs inln `ns tuens maaksdyn, ak crdmf``ds n pfkzds pdrd tuen, parn majùma usdrsa maefmn d qua puama inktdlfkdrsa inklfirnnrcdkfslns y masinlpnkarsa7 tdlefæk puamaqualdrsa ink bdif`fmdm. Maefmn d a``n, sa prnpnkak`ns lfslns ldtarfdàs, parn bderfidmns ak p`ästfin

@ns dpnrtas ma `d quìlfid d `d snifamdm

@denrdtnrfn ma quìlfidQkfmdm 5. A` pdtfn: kuastrn `denrdtnrfn Yasfùk

5



Ak iudktn d` vfmrfn, `ns ldtarfdàs sa bderfidkak æsta, puastn qua parlfta `àvdr d iden radi-ifnkas quìlfids ak `ds qua sa desnrea n `feardakarcìd ak bnrld ma id`nr, sfk qua subrdk luihnsmdôns. _nr a``n sa as i`dsfbfid inln rabrditdrfnsn kn rabrditdrfns.

Bfkd`lakta, `ns ma pnria`dkd sa usdk pdrd masdrrn``drprniasns ak `ns qua sa raqufarak talpardturds luyd`tds, qua a` vfmrfn kn snpnrtd, tdàs inln `d bukmfifùk

ma latdàs y d`cukds sdàs.

Bukifùk ma d`cukns ldtarfdàs

]uen ma aksdyn: ak æ` sa `àvdk d iden radiifn-

kas quìlfids d paquaôd asid`d. _uamak sar nkn rabrditdrfns7 as maifr, qua d`cukns sa puamakidàktdr sfk qua a` vfmrfn sa astd`à. Ntrns, pnra` inktrdrfn, kn sa maeak axpnkar d` buacn pnrkfkcúk lntfvn.

Aràklayar: sa dsalajd d` eadgar, parn sa mf-barakifd ak qua ak `d pdrta suparfnr tfaka ukiua``n dkcnstn, pnr `n qua as fmad` pdrd hdiarradiifnkas quìlfids vfnàktds ak su fktarfnr, pra-vfkfakmn qua `ns prnmuitns ma radiifùk sd`cdkvn`dkmn y idfcdk snera a` dkd`fstd, dstfläkmn`n.As rabrditdrfn.



Rdsn ma praifpftdmn n eadgar: tfaka lú`tfpàsbukifnkas, qua vdk masma a` idàktdlfaktn ma`ìqufmns, hdstd sar a` raifpfakta pdrd lazi`drsustdkifds y hdiar radiifnkas quìlfids. D pasdr

ma takar ukd asid`d crdmudmd, kn as fmad` pdrdlamfr ìqufmns ink praifsfùk, yd qua d asid`d knas tdk matd``dmd inln d ma d prneatd y dmaläs,pnrqua as uk ldtarfd` qua sa axpnka d` id`nrinkstdktalakta.

_`did ma idàktdlfaktn: ldtarfd` ma uk vfmrfn

rabrditdrfn luy pntakta, qua sa in`nid snera a`trìpnma, pdrd sarvfr ma snpnrta d `ns ldtarfdàsqua sa id`faktdk, inln a` eadgar n a` Aràklayar.

_fpatd: as uk tuen d`drcdmn y ma`cdmn qua saalpàd pdrd `d axtrdiifùk y lamfifùk ma `ìquf-

mns. _uama sar crdmudmd n dbnrdmd. @d mfbarakifdrdmfid ak qua, lfaktrds ukds iuaktdk ink asid`dkulærfid y lfmak vdrfamdm ma vn`úlakas, `dsntrds tfakak sù`n ukd `ìkad (inknifmd inln a`dbnrn) qua fkmfid a` vnùlak tntd` ma `d pfpatd,pnr `n qua sa usdk pdrd lamfr vn`úlakas aspa-iìbfins. Kn as rabrditdrfd.

_rneatd: as uk tuen `drcn dpnydmn snera ukdedsa, qua iuaktd ink ukd asid`d crdmudmd, pnr nqua sa alpàd pdrd lamfr a` vnùlak ma `ìqufmnsy cdsas y kn sa maea idàktdr.



Lnrtarn: as ukd vdsfjd paquaôd ma pnria`dkd, quasa usd pdrd trfturdr sustdkifds.

_fpatadmnr: utaksf`fn ma p`ästfin qua sa in`nid ak

`d enid ma `d pfpatd pdrd suiifnkdr `ìqufmns, avf-tdkmn d suiifùk ink d enid, pravfkfakmn ma astalnmn `d fkcastd ma cdsas y sustdkifds inrrnsfvds ytùxfids, inln `ns äifmns y a` latdkn`.

Crdmf``d: sa usd pdrd in`nidr `ns tuens ma aksdynmurdkta `ds pruaeds._fkzd pdrd tuen ma aksdyn: sa alpàd pdrd incar

`ns tuens y avftdr dsì qualdmurds pnr id`nr n pnrabaitn ma `ns raditfvns.

Laiharn ma Euksak: fkstrulaktn latä`fin quabukifnkd ink cds y sa usd pdrd akiakmar buacn yidàktdr sustdkifds.

Ynpnrta ukfvarsd`: inkstd ma ukd edsa, ak d quasa fkirustd uk tuen `drcn. Ya alpàd pdrd sujatdrldtarfdàs ma vfmrfn, ink `d dyumd ma pfkzds.

Aspätu`d: harrdlfaktd qua iuaktd ink uk ldkcnp`ästfin y ukd `älfkd latä`fid p`dkd ak a` ntrn

axtraln, qua sfrva d lnmn ma iuihdrd, pdrd ax-trdar sù`fmns.

]rìpnma: ldtarfd` latä`fin qua, inln su knlera`n fkmfid, iuaktd ink tras pdtds, qua snpnrtdk ukdrn. Ynera æsta sa in`nid d p`did ma idàktdlfak-tn.



Ldpd inkiaptud` 5: I`dsfbfidifùk ma `ns ldtarfdàs ma `denrdtnrfn

LD]AUFD@AY MA @DENUD]NUFN

YA I@DYFBFIDK

Yacúk suinlpnsfifùk

Ldmard Rfmrfn _nria`dkd Latd` _`ästfin

_fkzd pdrd tuen maaksdyn

Rdsn mapraifpftdmns

Lnrtarn Aspätu`d Cntarns

Yacúk su bukifùk

Rnùlætrfins

Kn vnùl

Dcftd

Dbnrdmn Kn dbnrdmn Uabrditdrfns Kn rabrditdrfns

Ldtrdz _fpatd ]uen ma aksdyn _fikùlatrn

ATQF_NY MA @DENUD]NUFN

Ynk dqua``ns qua bukifnkdk ink aàitrfifmdm y rad`fzdk ditfvfmdmas qua rasu`tdmalnrdmds n mfbìifàs pnr ntrns lamfns. @ns läs flpnrtdktas snk:

Ed`dkzd: alpàdmd pdrd lamfr `d ldsd ma `ds

sustdkifds qua sa utf`fzdk ak a` `denrdtnrfn. Hdyma vdrfns tfpns, qua vdk masma `ds ldkudàs (ed-`dkzds crdlards), hdstd dqua``ds qua pasdk crdknspaquaôns (ed`dkzds dkd`ìtfids).

Astubds: d` fcud` qua ds takalns ak idsd, sa usdkpdrd idàktdr7 d mfbarakifd as qua kn inifkdlnsink astds.

_ntakifùlatrn: sa alpàd pdrd d matarlfkdifùkma` pH ma `ds sustdkifds.

Lub`d: as uk hnrkn qua ldkajd talpardturdsluy d`tds, pdsdkmn pnr `ns 2??¿I.

Hnrkn: as sflf`dr d `ns hnrkns inkvakifnkdàs (kn `ns lfirnnkmds) y sa usdk pd

Fldcak tnldmd ma a` Mautsiha Bntnthag ma `d

Efe`fntaid ma` Astdmn ma Ydjnkfd (Y@QE)



8. Kn lazià `ds sustdkifds quìlfids qua kn inknia y qua kn astæk ak `nsprniamflfaktns, yd qua d`cukds radiifnkas puamak axp`ntdr y `feardr vdpnrastùxfins, idusdkmn àsfnkas qua puamak sar parldkaktas.

6. Kn inksuld d`flaktns n eaefmds maktrn ma` `denrdtnrfn.

4?. Kn inrrd kf juacua ak a` `denrdtnrfn.

44. Ak idsn ma fkiakmfn usa axtfkcufmnras, kukid dcud, yd qua luihns ra-ditfvns sa akifakmak ink ldynr dcrasfvfmdm ak prasakifd ma æstd.

45. Ak idsn ma diifmakta diumd fklamfdtdlakta d` mniakta qua mfrfca a``denrdtnrfn `n läs prnktn pnsfeà.

49. @ad ink matakflfaktn `ns prniamflfaktns dktas ma fr d` `denrdtnrfn, inka` bfk ma takar i`drfmdm snera `n qua sa vd d rad`fzdr y ramuifr dsì d` lìkfln di -ifmaktas y cdstns fkkaiasdrfns ma raditfvns.

4=. Kn fkcrasdr ink ldàtds kf ink diiasnrfns inln dkf``ns, eubdkmds, ra`njas,

pu`sards n idmakds, yd qua æstns puamak radiifnkdr n aktrdr ak inktditn ink`ns raditfvns y a` buacn.

41. Dpdcua a` iaù`dr7 `ds vferdifnkas ma æsta puamak cakardr ihfspds y inka``ds, buacn.

42. Kn usdr ldquf``dja ak `ds uôds y `ns njns. @ns sfckns ma akvakakdlfaktnsa avfmakifdk ak `ns pärpdmns y `ds uôds.

43. ]akar a` idea``n raincfmn.

48. Kn usdr àktas ma inktditn, yd qua `ns quìlfins sa puamak d`njdr maktrnma æstns, idusdkmn mdôns ak `ns njns.



d. Ua`difnkdkmn `ns ldtarfdàs ink utaksf`fns ma usn intfmfdkn:

Inlpàta `d sfcufakta tde`d, in`nidkmn ak `d idsf``d brakta d idmd ldtarfd` dquaùtaksf`fns ma `d idsd n a` trdedjn ink a` qua puamd raalp`dzdr`ns. Yf kn axfstafkvakta `ns qua kaiasfta. _nr ajalp`n, a` tuen ma aksdyn puama raalp`dzdrsa iukd n``d ma vfmrfn rabrditdrfn n ukd inlúk y inrrfakta.

]uen ma aksdyn

Rdsn ma praifpftdmns

_fpatd

Rfmrfn ma ra`nj

Aspätu`d

Aràklayar

_fkzds

Lnrtarn

Crdmf``d

Aleumn

_rneatd

4



e. Jucdkmn ink `d quìlfid:

Uad`fia `ns sfcufaktas axparflaktns, takfakmn ak iuaktd `ds knrlds ma sacurfmdmasirftds ak `d sasfùk:

_rapdra ukd snùifùk ma 4?? l@., qua inktakcd ukd pdrta ma dìnhn` atì`finsafs ma dcud. Yularjd ak astd lazi`d uk pdôua`n ma ta`d, säqua`n y axprìld`n. Aifækmdà buacn hdstd qua æsta sa dcnta, y inlpàta `d tde`d.

In`nqua 5? l@. ma vfkdcra ak ukd enta``d p`ästfid ma cdsansd ma tdldôn lamfdk(91? l@.). Lfaktrds tdktn pnkcd, ink dyumd ma uk aleumn, mns iuihdrdmds ma eidrenkdtn ma snmfn ak uk c`nen (enled). Iufmdkmn qua a` pn`vn ma` efidrenkdkn idfcd ak a` vfkdcra, in`nqua d enid ma` c`nen ak d enid ma d enta``d y dsacúraink ifktd pacdkta, ink ukd iuarmd n ink uk iduihn. Qkd vaz takcd a` sfstald, ma

idar a` efidrenkdtn ak a` vfkdcra y nesarva `n qua niurra ink a` c`nen.

Masmneà uk i`fp a fktrnmúzid`n maktrn ma uk `flùk, dsacuräkmnsa qua parbn`d iäsidrd y aktra inln lìkfln 4? il. Hdcd `n lfsln ink uk d`dlera ma inerma lnmn qua `ns axtralns ma `ns ideàs quamak d ukd mfstdkifd ma 41 il. aktrsì. Injd a` `flùk ink `d ldkn y in`nqua `d àkcud ak `ns axtralns `feras ma `ns mnd`dleras.

Injd uk edkdkn pa`dmn y hulamazid ukd ma `ds mns puktds ak dìnhn` atì`fin

Qkd vaz qua `n hdcd, akifakmd `d puktd ink uk bùsbnrn y luarmd a` ntrn axtralnsnp`dkmn d` lfsln tfalpn a` buacn snera ukds uvds pdsds. Iùjd`ds ink uk takamnsùpà`ds, ``æva`ds d `d enid y iùld`ds.

Injd ukd idrtu`fkd, iùrta`d ak vdrfns iudmrns fcudàs y tnla ukn ma a``ns. Indyumd ma uk pfkia` n uk dcftdmnr asirfed `n qua qufard snera a``d, usdkmn inltfktd äifmn su`búrfin inkiaktrdmn. Mæja`n rapnsdr ukns fkstdktas y, iudkmn saquaxpnkcd `d ntrd idrd ma `d idrtu`fkd d `d ``dld, dsacuräkmnsa qua a` buacn pdsa pa` ùcdr mnkma ustam asirfefù, sfk qua sa quala a` pdpa`. Nesarva `n qua niurr

ink `n qua asirfefù.

In`nqua ak uk snpnrta ukfvarsd` uk drn ink kuaz y uefqua ak a` nrfbfifn ma æsuk vdsn ma pdpa` ink dcud ak su fktarfnr, n iua`cua ak a` drn uk c`nen àkn ma dcuIufmdkmn kn qualdrsa ink `d ``dld, diarqua ak `d pdrta ma dedjn ma` vdsn n mc`nen ukd va`d akiakmfmd y mæja`d d``ì hdstd qua a` dcud hfarvd y pnstarfnrlaktaeu``d, as maifr, hdstd qua a` dcud alpfaia d eureujadr.



5

In`nqua ak uk vdsn ma praifpftdmns (n vdsn ma p`ästfin trdspdrakta) mns n tras cnma d`cúk in`nrdkta rnjn y snera æsta dmfifnka dcud, hdstd `d lftdm ma `d idpdifmma` vdsn, dcftdkmn hdstd qua tnmd `d lazi`d tnla in`nr. Ink uk cntarn dmfifnukds cntds ma e`dkquadmnr idsarn hdstd qua hdyd d`cúk idlefn.

AX_AUFLAK]N UAYQ@]DMN ¾_NU TQÆNIQUUA AY]N>

d. ¾A` buacn kn quald>

e. Axpdksfùk

i. ¾V mùkma quamù `d pf`d>

m. ¾Brìn n id`fakta>

a. ¾Fkvfsfe`a>

b. ¾_dpa` n iduihnrasfstakta d` buacn>

c. In`nr:¾trdkspdrakta>

Qtf`fzdkmn `ns ldtarfd`as ma `denrdtnrfn, prnpnkcd mns latnmn`ncìds pdrdsapdrdr ukd lazi`d ma dcud y tfarrd.



]ùlasa ukns lfkutns pdrd paksdr mabnrld fkmfvfmud` snera `ds sfcufaktaspracuktds:

¾Ydea ma quæ astä inlpuastd `d ldtarfd>

Yf ustam tnldrd ukd hnjd ma iudmarkn, `d mne`drd d `d lftdm, `d pdrtfardy incfard ukd ma `ds lftdmas, `d mne`drd y pdrtfard ma kuavn, y dsì hfifa -

rd ink tnmds `ds lftdmas ma `d hnjd qua netakcd, ¾iraa qua `àcdrìd d ukpuktn ak a` qua kn puamd rnlpar läs `d hnjd> ¾_nmrìd mfvfmfr `d hnjdfkbfkftdlakta>

¾Tuæ sfckfbfid `d pd`derd ätnln>

¾Ydea ak quæ pdìs y ak quæ æpnid sa hde`ù pnr prflard ma vaz ma `ns ätnlns>

¾_nr quæ as flpnrtdkta a` astumfn ma `ns ätnlns ak quìlfid>

_drd tnmds `ds ifvf`fzdifnkas, sfalpra hdk sfmn lntfvn ma iurfnsfmdm `ns idlefny inlpnsfifùk ma `d ldtarfd. Ak Craifd, pnr ajalp`n, dprnxfldmdlakta hdifd dôn 2?? d. I., sa iraìd qua a` ukfvarsn astded inlpuastn pnr dcud, tfarrd, buacndfra, pnr a``n murdkta `d d`quflfd (fkfifns ma `d quìlfid) `ns ifaktìbfins trdtdedk mnetakar nrn d pdrtfr ma inlefkdifnkas ma astns aàlaktns ink ntrns latdàs ]d`

Lnma`ns dtùlfins

ÄtnlnQkfmdm 9. Inkstftuifùk ma `d ldtarfd Yasfùk

9



axparflaktns kn tuvfarnk æxftn, sfk aledrcn sì `ncrdrnk netakar kuavns inlpuasy parlftfarnk a` fkfifn ma `d lamfifkd (Fdtrnquìlfid).

@auifpn ma Jnkfd p`dktaù qua ds sustdkifds sa puamak mfvfmfr parn kn fkbfkftdlaky as Malùirftn, fcud`lakta hdifd a` 2?? d.I., qufak dpnyd astd tanrìd y mfia q`d ldtarfd astä inlpuastd pnr paquaôds pdrtìiu`ds ‐fkmfvfsfeàs“ d `ds qua edutinln ätnlns.

@d quìlfid dpdraia pnr prflard vaz ink Dktnfka @dvnfsar, qufak hdia ukd axprflaktdifùk läs rfcurnsd, fktrnmuifakmn `d ed`dkzd ak a` dkä`fsfs ma `ds sustdkifakinktrdkmn qua ak `ns prniasns quìlfins kukid hdy pærmfmd ma ldtarfd7 `n qniurra as qua æstd sa inlefkd ma kuavds ldkards, ldktakfakmn sfalpra `ds idk

mdmas fkfifdàs. D astn sa `n ``dlù `d @ay ma `d Inksarvdifùk ma `d Ldsd y as `d qhfzn avfmakta qua d` pdraiar `d ldtarfd sì maea astdr inkbnrldmd pnr pdrtìiupaquaôds y mfbaraktas aktra sì, `n qua parlfta axp`fidr, pnr ajalp`n, a` pnr quk cds sa puama inlprflfr y prfkifpd`lakta a` pnr quæ `d ldtarfd sa lazi`d mfvarsds bnrlds.

Astn `àvd d` quìlfin Fkc`æs Jnhk Md`tnk d prnpnkar `d ]anrìd Dtùlfid, ink `ns cufaktas pnstu`dmns

• @ns aàlaktns astäk inlpuastns pnrpdrtìiu`ds luy paquaôds a fkmfvfsfeàs(ätnlns) sflf`dras d `ns masirftns pnrMalùirftn.

• ]nmd `d ldtarfd astä inlpuastd pnrätnlns.

• @ns ätnlns ma uk lfsln aàlaktnsnk fcudàs.

• @ns ätnlns ma mfstfktns aàlaktns snkmfbaraktas.

• @ns ätnlns ma uk lfsln aàlatn tfakak a` lfsln tdldôn, ldy bnrld.

• @ns inlpuastns quìlfins sa bldk pnr `d ukfùk ma mns n li`dsas ma ätnlns mfbaraktas. inlefkdrsa ätnlns ma aàlaktmfstfktns ak prnpnrifnkas sflp`sa netfakak `ns inlpuastns.



Ink edsa ak `d tanrìd dtùlfid, bfkd`lakta `dinlukfmdm ifaktìbfid diaptd d` ätnln inln `dukfmdm inkstftuyakta ma `d ldtarfd. Yfk aledr-cn, dúk hdy fkbùakifd ak `ds iraakifds dktfcuds,

inln pnr ajalp`n a` kn iraar ak a` vdiìn, `nqua `àvd d` p`dktadlfaktn ma` prflar lnma`ndtùlfin.

Ak 46?= Jnsaph ]hnlsnk prnpnka a` Lnma`nma` Eumìk ma _dsds, a` iud` inksfsta ak ukd as-paifa ma tnrtd idrcdmd pnsftfvdlakta (dúk samasinkniìd `d axfstakifd ma `ns prntnkas), ak

`ns qua b`ntdedk `ns aàitrnkas, dsalajdkmn d uk pumìk ma pdsds.

Inln `d quìlfid as axparflaktd`, tnmn `n qua sa mfcd maea sar malnstrdmn7 ainksaiuakifd, a` lnma`n ma ]hnlsnk maeìd inlprnedrsa. _nr a``n, Arkast Uutharbnrad`fzd uk axparflaktn, qua inksfsta ak enledrmadr ink pdrtìiu`ds d`bd ukd älfkma nrn, rnmadmd ink ukd pdktd``d ma su`burn ma zfki. Ink asta axparflaktn pumdpraifdr qua `d ldynrìd ma `ds pdrtìiu`ds d`bd dtrdvasdedk mfraitdlakta `d `älfksfk masvfdrsa ma su trdyaitnrfd7 ntrds subrìdk ukd paquaôìsfld masvfdifùk7 y ntrd

ak idlefn, sa mfsparsdedk ink crdkmas äkcu`ns a fkiùsn sa mavn`vìdk d `d buakma pdrtìiu`ds, as maifr qua raentdedk.

Lnma`n dtùlfin ma ]hnlsnk

Axparflaktn ma Uutharbnrm.



Lnma`n dtùlfin ma Uutharbnrm

Astn hfzn qua, ak vaz ma inkbfrldr a` lnma`nma ]hnlsnk, sa idlefdrd pnr inlpàtn, ydqua `n qua sa asparded ard qua `ds pdrtìiu`dsd`bd dtrdvasdrdk `d `älfkd ink pnin n kdmd

ma masvfdifùk. Ak inksaiuakifd, Uutharbnrmp`dktad qua a` ätnln inksfsta ak mns pdrtas:

d. Qk kúiàn, ak a` qua sa akiuaktrd tnmd`d idrcd pnsftfvd ma` ätnln.

e. Qkd inrtazd dtùlfid ak `d qua nreftdk `ns aàitrnkas.

_arn a` lnma`n ma Uutharbnrm kn sù`n masdbìd d ]hnlsnk, sfkn dmaläs d ns crfacyd qua sucfara qua `d ldynrìd ma` aspdifn ma` ätnln astä vdiìn, `n qua bdif`ftdpdsn mfraitn ma `d rdmfdifùk, sfk qua astd sa masvìa.

D pasdr qua a` lnma`n parlfta mdr rdzùk d ns rasu`tdmns ma` axparflaktn, kn axppnr quæ a` kúiàn d`ldiakd d idrcd pnsftfvd y pnr quæ ns aàitrnkas ink idrcd kacdt

kn snk dtrdìmns pnr a` kúiàn ma` ätnl

Edsäkmnsa ak a` ätnln ma hfmrùcaknbìsfin mdkæs Kfa`s Enhr sucfara su prnlnma`n, inkiùyakmn qua ns aàitrnnreftdk d`ramamnr ma` kúiàn ak kfvaiudktfzdmns ma akarcìd (as maifr, i

akarcìds aspaiìbfids), y inln inkiuakifd, `ns aàitrnkas tdlefæk astiudktfzdmns. Dsì, iudkmn sa luavaksus kfvaàs kn frrdmfdk akarcìd7 pnrinktrdrfn, iudkmn uk aàitrùk pdsd uk kfva` ma akarcìd d`tn d ukn lakakarcætfin, `feard uk bntùk, qua as u

pdrtìiu`d ma uz, n sf pdsd ma uk vfka` lakns akarcætfin d ukn ldynr, desnrea ifa

Lnma`n dtùlfin ma Enhr



Ntrd dp`fidifùk ma asta lnma`n as `d pù`vnrd: ¾sa hd pracuktdmn d`cukd vaz iùlhdiak `ns bderfidktas ma `d pù`vnrd pdrd mdràs asds in`nrdifnkas tdk idrditarìstfid `ns juacns pfrntæikfins> As luy sflpà: `n `ncrdk ink `ns aspaitrns ma alfsfùInln yd sa lakifnkù, snk pdrtfiu`dras d idmd aàlaktn7 ma haihn, `ns aspaitr

snk a` aqufvdàkta d kuastrds hua``ds mfcftdàs. Dsì, pnr ajalp`n, a` in`nr dldrf`sa maea d` snmfn, a` rnsdmn d` pntdsfn, a` kdrdkjd as pnr a` idìfn, dzu` pnr a` inerrnjn pnr a` astrnkifn y a` varma pnr a` edrfn.

Asta lnma`n parlftfù astdeàiar qua uk ätnln astä inkstftufmn pnr uk kúiàn, ak qua sa akiuaktrdk ns kautrnkas y prntnkas y d`ramamnr ma` kúiàn astäk ns kfva`ma akarcìd iudktfzdmns, ak `ns qua sa luavak `ns aàitrnkas.

Crdifds d` lnma`n ma Enhr, bua pnsfeà inlprakmar bakùlakns inln `d `feardifùn desnrifùk ma akarcìd, parn a` qua `n hdcd kn flp`fid qua `d ifakifd pdra. Dinktrdrfn, as dsì inln dpdraia a` lnma`n läs raifakta: a` Lnma`n Iuäktfin, quinlpàlaktd `ns hd``dzcns ma Enhr y kns mfia qua:

4. @ns aàitrnkas astäk iudktfbfidmns, d` fcud` qua a` kfva` ma akarcìd d` iupartakaiak7 sfk aledrcn, a``ns nreftdk ak znkds luy aspaiìbfids ma` kfva`, d` qua maknlfkd nreftd` dtùlfin, y kn sa luavak pnr tnmn a` kfva` inln sa iraìd dktas



5. @d akarcìd, pnsfifùk, uefidifùk y lnvflfaktns ak a` aspdifn ma `ns aàitrkas kn neamaiak d @ayas ma `d Bìsfid Kawtnkfdkd (a``n bnrzù d `d fkvakifùk mabìsfid iuäktfid, ak su ldynrìd bnrlu`dmd pnr Dèart Afkstafk) y sa maea raiurrfr d ldtalätfids pdrd su inlpraksfùk.

9. A` aàitrùk tfaka inlpnrtdlfaktn mud`, as maifr qua sa puama ldkfbastdr inlpdrtìiu`d (as maifr ink ldsd) n inln akarcìd (iudkmn sa luava). Ak inksaiuakisf sa qufara matarlfkdr `d pnsfifùk läs prnedeà ma` aàitrùk ak ukd racfùk maspdifn, as flpnsfeà hd``dr `d va`nifmdm ink `d qua sa luava, y sf `n qua sa qufaas matarlfkdr `d va`nifmdm, kn sa puama idìu`dr `d pnsfifùk. D asta bakùlakn sainknia inln _rfkifpfn ma Fkiartfmulera.

Ak inksaiuakifd, ink a` lnma`n a` ätnln sa nrcdkfzd ink edsa ak `ns kúlariuäktfins:

Kúlarns iuäktfins

Inln sa dided ma lakifnkdr, a` kuavn lnma`n sa edsd ak `ds ldtalätfids y prpnka d` ätnln ink edsa ak `ns sfcufaktas kúlarns:

d. Kúlarn iuäktfin prfkifpd` (k): fkmfid `d idktfmdm ma kfvaàs ma akarcìd psaktas ak uk ätnln. Rdk ma` kúlarn 4 hdstd a` 3.

e. Kúlarn iuäktfin dzflutd` (`): axp`fid `d bnrld ma `ns nreftdàs, mnkma akiuaktrdk `ns aàitrnkas. Ya idìu`d rastäkmnà 4 d` k, pnr ajalp`n:

k < 4 ` < 4 ’ 4 < ? < nreftd` s

k < 5 ` < 5 ’ 4 < 4 < nreftd` p y ` < 4 ’ 4 < ? < nreftd` s

k < 9 ` < 9 ’ 4 < 5 < nreftd` m7 ` < 5 ’ 4 < 4 < nreftd` p y ` < 4 ’ 4 < ?nreftd` s

k < = ` < = ’ 4 < 9 < nreftd` b7 < 9 ’ 4 < 5 < nreftd` m7 < 5 ’ 4 < 4 < nre



i. Kúlarn iuäktfin ldckætfin (l`): axp`fid `ds nrfaktdifnkas, as maifr, `mflaksfnkas ak a` aspdifn ak `ds qua sa hd``dk `ns nreftdàs. Ya idìu`d tnldkma` vd`nr ma` kúlarn dzflutd`, pdsdkmn asa lfsln vd`nr pnr `ns kúlarn kacdtfvnhdstd `àcdr d` lfsln kúlarn, parn ak pnsftfvns, dsì:

Iudkmn:

` < ? l` < ? (inln sù`n hdy uk kúlarn, fkmfid qua sù`n axfsta ukd pnsfifùk aa` aspdifn).

` < 4 l` < -4, ?, +4 (hdy tras kúlarns, tras pnsfifnkas: pX, pV y pZ).

` < 5 l` < -5, -4, ?, +4, +5 (1 pnsfifnkas: mXV, mVZ, mXZ, mX5V5, mZ5).

` < 9 l` < -9, -5, -4, ?, +4, +5, +9 (3 pnsfifnkas: Bz9, bXZ5, bVZ5, bX(X5 ’ 9V5bV(V5 ’ 9X5), bXVZ, bZ(X5 ’ 9V5).



m. Kúlarn iuäktfin aspìk (s): fkmfid `ns saktfmns ma cfrn ma `ns aàitrnkas, sù`n ink mns pnsfef`fmdmas: ak a` saktfmn ma `ds ldkaif``ds ma` ra`nj, n ak inktrd

Inkbfcurdifùk aàitrùkfid

Ink edsa ak a` lnma`n iuäktfin sa puama matarlfkdr iùln sa akiuaktrdk uefmns idmd ukn ma `ns aàitrnkas ma uk ätnln y ak quæ nrmak sa `àkdk idmd ukn

`ns kfvaàs ma akarcìd, ink sus raspaitfvns nreftdàs, pnr lamfn ma `d inkbfcurdifaàitrùkfid:

Ak d mfstrfeuifùk aàitrùkfid ma iud`qufar aàlaktn, sa suaà asirfefr a` kúlarn aàitrnkas inln axpnkaktas, qua d` sar suldmns ak su tntd`fmdm kns md a` kúla



ma` cräbfin, sdefakmn qua a` kúlarn d` qua sa maea `àcdr as a` kúlarn dtùlfipdrtfiu`dr d idmd aàlaktn.

Ajalp`n:

N8 < 4Y5 5Y55_=

@d inkbfcurdifùk kn sù`n kns mfia iuäktns aàitrnkas hdy y ak quæ ucdras, sfkn qudmaläs kns parlfta inkniar a` kfva` ma akarcìd läxfln ma` ätnln, qua ak d tdeparfùmfid sa inknia inln parìnmn. Yacúk `d idktfmdm ma aàitrnkas uefidmns aasta lfsln kfva`, as pnsfeà matarlfkdr a` crupn ma `d tde`d d` iud` partakaiak, tinln sa puama var ak `ns ajalp`ns sfcufaktas:

Aàlaktn Yìlen`n Kúlarn Inkfcurdifùk _arìnmn Crupn Uacfùk dtùlfin aàitrùkfid

Earf`fn Ea = 4 s5 5s5 5 FF s

Enrn E 1 4 s5 5s5 5p4 5 FFF p

Idrenkn I 2 4 s5 5s5 5p5 5 FR p

Kftrùcakn Kf 3 4 s5

5s5

5p9

5 R p Nxìcakn N 8 4 s5 5s5 5p= 5 RF p

Ntrns inlpnkaktas ma` ätnln

Ink a` masdrrn``n ma `d enled dtùlfid (ukd i`drd malnstrdifùk ma qua a` ätnlsì puama mfvfmfrsa) sa hfzn avfmakta a` pntakifd` ma `d akarcìd dtùlfid y iùln sinrraitn usn pnmrìd eakabfifdr d `d huldkfmdm, yd qua astd akarcìd puama inks

mardrsa inln `flpfd, puastn qua sf sa inktrn`d rfcurnsdlakta su prnmuiifùk, khderìd inktdlfkdifùk y erfkmdrìd tdktd akarcìd, qua fkiùsn `àcdrìd d sar nesnàta` usn ma` patrùàn.

Kn sù`n as a` fktaræs pnr `d akarcìd `n qua inkmuia d `ns ifaktìbfins ak su idlfkditud`, sfkn tdlefæk `d axp`fidifùk ma` nrfcak ma` ukfvarsn. _nr a``n sa iradrnk `ndiaàrdmnras ma pdrtìiu`ds, qua sf efak dúk kn `ncrdk rap`fidr a` Efc-Edkc d paqu



9

pdrtìiu`ds, dktas masinknifmds pdrd `d ifakifd, iuyds bukifnkas snk `d bnrldifùk `ns aàitrnkas, kautrnkas y prntnkas. Ynk `ds cakardmnrds ma `ds buarzds kuiàdqua à mdk astdef`fmdm d` ätnln y avftdk qua a` kúiàn in`dpsa inln rasu`tdmn `ds buarzds ma rapu`sfùk aktra `ns prntnkas, y snk tdlefæk `ds mfraitds raspnksdema `ds buarzds crdvftdtnrfds ma` aspdifn.

D`cukds pdrtìiu`ds snk `ns qudrgs (inlpnkak d `ns kautrnkas y prntnkas), `ns katrfkns, ensnkas, barlfnkas, àptnkas, lunkas, aktra ntrds, `n qua sfckfbfid quaätnln kn sù`n sa masinlpnka ak aàitrnkas, kautrnkas y prntnkas, sfkn qua dmalpnmrìd hdiar`n ak `ds pdrtìiu`ds inkstftuyaktas ma æstns y ak ntrds läs.

Uad`fia `d inkbfcurdifùk aàitrùkfid pdrd a` B, Id, D` y _e, uefiäkmn`ns ak `d tdparfùmfid.


4. ¾As inrraitn a` tærlfkn ätnln> ¾_nr quæ>

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

5. Uad`fia `d inkbfcurdifùk aàitrùkfid ma` H, Kd, N, K, Lc, I` y I y pramfcdparìnmn y crupn ma `d tde`d parfùmfid ak `ns qua sa akiuaktrdk.

4



]ùlasa ukns lfkutns pdrd paksdr ma bnrldfkmfvfmud` snera `ds sfcufaktaspracuktds:

¾Tuæ as `d tde`d parfùmfid>

¾Inknia ustam d quæ hdia rabarakifd a` tærlfkn parfnmfifmdm>

¾Ya hd pracuktdmn d`cukd vaz pnr quæ `d tde`d parfùmfid tfaka asd nrcdkfzdifùktdk pdrtfiu`dr>

¾Iuä` as `d flpnrtdkifd ma` kúlarn dtùlfin ink raspaitn d `d tde`d parfùmfid>

Inln sa vfn ak `d sasfùk dktarfnr, `d inkbfcurdifùk aàitrùkfid as luy flpnrtdktyd qua kns md rdzùk ma `d idktfmdm ma aàitrnkas prasaktas ak uk ätnln, a` lnmak qua æstns astäk mfstrfeufmns y ak pdrtfiu`dr, pdrd a` astumfn ma astd sasfùk, kmd fmad ma `d bnrld inln astä nrcdkfzdmd `d tde`d parfùmfid, yd qua, inln sa vpravfdlakta, a` kfva` ma akarcìd as `n lfsln qua a` parìnmn ak `d tde`d y `d sultntd` ma `ns aàitrnkas ak mfihn kfva` kns md a` crupn.

]de`d parfùmfid

]de`d parfùmfid y parfnmfifmdmQkfmdm =. @d tde`d parfùmfid Yasfùk

=



Hfstnrfd ma `d tde`d parfùmfid

Ak `d æpnid ma `d d`quflfd, `ns ifaktìins kn pnmìdk inlpdrtfr susinkniflfaktns pnr talnr d lnrfr ak d hncuard. Iudkmn àcd a` kma` Nsiurdktfsln, sa masiuerak luihìsflns aàlaktns y ink `ddiaptdifùk ma `d tanrìd dtùlfid, æstns snk rainknifmns inln td`.Yfk aledrcn, snk tdktns `ns kuavns aàlaktns, qua kn hdy uk ink-saksn snera sus knleras, sìlen`ns pdrd raprasaktdr`ns y luihn

lakns, d`cúk irftarfn pdrd i`dsfidr`ns y nrmakdr`ns.

Jnhk Md`tnk, qufak prnpusn `d tanrìd dtùlfid, tdlefæk sa md d `dtdrad ma raprasaktdr ink sìlen`ns d `ns ätnlns. Ink a` tfalpn,æstns dmqufarak `d bnrld ditud`:

]rdedjn ma Jnhk Md`tnkpdrd raprasaktdr d `ns



sa dprnxflded d `d lamfmd drftlætfid ma `ds ldsds dtùlfids ra`dtfvds maidmd ukn ma `ns aàlaktns, maknlfkäkmn`ns trìdmds.

Qk ajalp`n as a` sfcufakta:A` i`nrn tfaka uk pasn dtùlfin ma 91.1 y a` ynmn ma 452.67 d` suldr`ns ymfvfmfr`ns aktra mns, sa netfaka 84.5, qua as luy iaridkn d` pasn rad` maèrnln (36.6). Yfk aledrcn, astd sf-tudifùk as läs ukd idsud`fmdm quaukd rac`d7 ak inksaiuakifd, kn asdmaiudmd pdrd nrcdkfzdr d `ns aà-laktns.

Ak 4829 Jnhk Kaw`dkms (fkc`æs),in`niù `ns aàlaktns ak crupns manihn, d æstns às mfn a` knlera manitdvds, yd qua idmd nihn aàlak-tns prasaktdedk prnpfamdmas sflf-`dras. Ak 4826 Mflftrf Lakmaàfav(rusn), mfn d inkniar `d nrmakdifùk

Ak 4849, Jnhks Jdine Earza`fus (sua-in), i`dsfbfiù ns aàlaktns quìlfinsinknifmns ak aàitrnpnsftfvns y

aàitrnkacdtfvns. Hdifd 4856, JudkSn`bcdkc Mnearafkar (dàläk), sa-ôd`ù pnr prflard vaz `d axfstakifdma ukd ra`difùk sfckfbfidtfvd aktra dsprnpfamdmas ma `ns aàlaktns y susraspaitfvds ldsds dtùlfids ra`dtfvds.

Yus fkvastfcdifnkas n àvdrnk d ne-

sarvdr d prasakifd ma crupns ma trasaàlaktns, ak ns iudàs, d ldsd dtù-lfid ra`dtfvd ma` aàlaktn iaktrd`,

Jnhks Jdine Earza`fus

Jnhk Kaw`dkms

B n t n t n

l d m d m a w f g f p a m f d

B n t n t n l d m d m a w f g f p a m f d



Mflftrf Fväknvfih Lakmaàfav,pdmra ma `d tde`d parfùmfid.

Uatrdtn ink `d tncd ma idtamrätfin ma `dQkfvarsfmdm ma Amfleurcn. Diudra`d

snera pdpa` Cdàrfd astdtd` ]ratfdgnv, Lnsiú

läs inlpàtd ma `ns aàlaktns, edsäkmnsa ak `ds prnpfamdmas quìlfids,inln bukifùk ma` kúlarn dtùlfin.

A` crdk difartn y lærftn sa bukmdlaktù ak prama-ifr aàlaktns kn masiuefartns tnmdvìd, pdrd `nsiudàs rasarvù uk aspdifn ak `d tde`d y läs dúkdma`dktù sus prnpfamdmas.

@d tde`d lnmarkd astä inkstftufmd pnr 48 inùlkds, maknlfkdmds crupns n bdlf`fqua raprasaktdk d idktfmdm ma aàitrnkas qua hdy ak a` kfva` ma vdàkifd, y qua s`ns aàitrnkas qua avaktud`lakta puamak fktarvakfr ak uk ak`dia. Ya mfvfmak `ds bdlf`fds D (aàlaktns raprasaktdtfvns) y E (aàlaktns ma trdksfifùk), kulardmink ns dktfcuns kúlarns rnldkns7 sfk aledrcn, hny ak mìd sa kulardk ma` 4 d`

]dlefæk tfaka parìnmns, rabarfmns d `d idktfmdm ma kfvaàs ma akarcprasaktas ak idmd ätnln fkmfvfmud`, lntfvn pnr a` qua hdy 3 parìnmnQkd idrditarìstfid ma astd bnrld ma nrcdkfzdifùk, as qua `ns aàlaktns tfakak ppfamdmas bìsfids y quìlfids sflf`dras, tdktn ak `ns crupns, inln ak `ns parìnm

@d tde`d parfùmfid tdlefæk sa mfvfma ak iudtrn znkds, mapakmfakmn ma` ú`tflnreftd` dtùlfin ma `d inkbfcurdifùkaàitrùkfid7 as maifr, sa iuaktd ink d

znkd s inkbnrldmd pnr ns aàlaktnsdìd`fkn y dìd`fkntærrans7 `d znkd p,inlprakmfmd pnr `ns aàlaktns ma`crupn FFF hdstd a` RFFF D7 `d znkd m ak`d qua astäk tnmns `ns aàlaktns matrdksfifùk (crupn E inlpàtn) y `d

znkd b , inrraspnkmfakta d `ns `dktä-kfmns y ditìkfmns.



A` sfstald parfùmfin astdeàia ukd mfvfsfùk kdturd` ma `ns aàlaktns `feras,latdàs qua snk a` 8?% y `ns kn latdàs a` 5?%.

Latdàs

@nid`fzdifùk ma `ns aàlaktns ak `d tde`d parfùmfidLatdàs y kn latdàs



Niupdk `d ú`tfld inùlkd ma `d maraihd ak `d tde`d. Ya maknlfkdk inln kne`maefmn d qua ak su ú`tfln kfva` ma akarcìd iuaktdk ink 8 aàitrnkas, `n qua inkbfara läxfld astdef`fmdm y `ns hdia pnin n kdmd raditfvns. ]nmns a``ns axfs

ak d`cukd prnpnrifùk ak `d dtlùsbard tarrastra, dukqua su inkiaktrdifùk, axia`d ma` drcùk, as axtrdnrmfkdrfdlakta edjd.

Ak æstns, d lamfmd qua dulaktd a` kúlarn dtùlfin, `ns aàitrnkas vdk d uk kffktarfnr ak vaz ma fr d` kfva` läs axtarkn. _nr a``n, tfakak ak nreftd` m fkinlpàt

Ynk tnmns dqua``ns aàlaktns ak iuyd inkbfcurdifùk aàitrùkfid nrmakdmd, a` pkú`tfln suekfva` as =b n 1b. @ns aàlaktns ma trdksfifùk fktarkd sa in`nidk dpdak `d tde`d parfùmfid ak mns crupns n sarfas ma aàlaktns.

Cdsas kneàs

Aàlaktns ma trdksfifùk

@dktäkfmns y ditìkfmns

Kaùk, cds kneà alpàdmn ak dùlerdmn y pue`fifmdm



_arfnifmdm quìlfid

Inln sa lakifnkù, `ns aàlaktns inlpdrtak prnpfamdmas sflf`dras, tdktn ak `ncrupns inln ak `ns parìnmns. D`cukds ma a``ds snk: rdmfn dtùlfin, akarcìd ma fnk

zdifùk, dbfkfmdm aàitrùkfid y aàitrnkacdtfvfmdm.

A` rdmfn rad` ma uk ätnln kn sa hd pnmfmn iudktfbfidr, parn sì sa hdk astdeàifmtdldôns ra`dtfvns, dprnvaihdkmn d matarlfkdifùk ma ds mfstdkifds fktar- kuiàdrak `ns inlpuastns.Ya inksfmard inln a` vnùlak ma `d maksfmdm aàitrùkfid tntd`, d`ramamnr mkúiàn. Astd lamfmd as sù`n iartard ak uk 6?%, ydqua dúk kn sa hd pnmfmn lamfr ink rfcurnsfmdm,pnr `n qua sa raiurra d matarlfkdr`n ink edsa ak`ds mfstdkifds fktar-kuiàdras aktra ns aàlaktns akuk inlpuastn. D lamfmd qua a` parìnmn dulaktd,fcud` `n hdia a` rdmfn dtùlfin7 ak idlefn, aktraldynr sad a` crupn, laknr a` tdldôn dtùlfin.

A` pntakifd` ma akarcìd ma fnkfzdifùk, as d akarcìd raquarfmd pdrd quftdrà uk aàitrùd uk ätnln kautrn ak astdmn cdsansn. @d matarlfkdifùk axparflaktd` ma` pntakifma fnkfzdifùk sa abaitúd ak tuens ma masidrcd. Aàitrnkacdtfvfmdm: sa mabfka inl`d idpdifmdm qua tfakak `ns ätnlns pdrd dtrdar `ns aàitrnkas ma ntrns ätnlns, a

uk ak`dia quìlfin. D laknr rdmfn dtùlfin, ldynr aàitrnkacdtfvfmdm, ak inksiuakifd, d lamfmd qua dulaktd a` parìnmn, laknr aàitrnkacdtfvfmdm, y ldynlfaktrds sa dvdkzd ak `ns crupns

]dldôn dtùlfin

Akarcìd ma fnkfzdifùk y dbfkfmdm aàitrùkfid

L (c) + akarcìd ma fnkfzdifùk L (c ) + a‖ ätnln kautrn fùk pnsftfvn aàitrùk

+

Ajalp`n:



Nrcdkìiasa ak suecrupns ink sus inlpdôarns. @uacn: 4. Uaspnkmdk: ¾pnr quæ rdzùk d lamfmd qua dulaktd a` rdmfn dtùlfin `d a`trnkacdtfvfmdm mfslfkuya>

5. Nrmakak `ns sfcufaktas aàlaktns ink edsa ak su kúlarn dtùlfin7 matlfkak iuä` sarìd a` läs aàitrnkacdtfvn, iuä` a` läs aàitrnpnsftfvn, iuä` as a` lcrdkma y iuä` a` läs paquaôn ak tærlfkns ma rdmfn dtùlfin. Aàlaktns: N, I, Kf, Ba, Kd, H y Id.

Uaspnkmd `ds pracuktds d inktfkudifùk, ink edsa ak `d fkbnrldifùk sulfkfstrdmAk `d tde`d parfùmfid, `ns aàlaktns sa nrcdkfzdk ak crupns y parìnmns, ma diuard` kúlarn dtùlfin, ink prnpfamdmas bìsfids y quìlfids sflf`dras. @ns aàlaktnsi`dsfbfidk inln latdàs, kn latdàs y salflatdàs y sa uefidk ak `d tde`d inlnluastrd ak `d sfcufakta bfcurd:

4



• Aàitrnkacdtfvfmdm: 5.1

• Aàitrnkas ma vdàkifd: 4

• Kn inkmuitfvfmdm ak su bnrld

dtùlfid, d`td ak bnrld fùkfid

• Crupn D



• D`td inkmuitfvfmdm

• Crupn E


• Aàitrnkas ma vdàkifd: =

• D`td inkmuitfvfmdm

• Crupn D

• Aàitrnkacdtfvfmdm: 4.?


• D`td inkmuitfvfmdm• Crupn D

D E

I M

Ma diuarmn d `d fkbnrldifùk, raspnkmd:

4. @ns aàlaktns latä`fins inrraspnkmak d:

d. ]nmnse. D, E y Ii. D, E y Mm. D, I y M

5. A` aàlaktn E kn inkmuia `d aàitrfifmdm pnr sar:

d. Dìd`fkne. Ma trdksfifùki. Hd`ùcakn

@ds sfcufaktas bfihds luastrdk fkbnrldifùk snera `ds prnpfamdmas bìsfids y quìlfidma iudtrn aàlaktns, ma` parìnmn 1:



9. A` nrmak ma` tdldôn dtùlfin, ma laknr d ldynr inrraspnkma d:

d. D, E, I, Me. E, M, I, D

i. E, D, I, Mm. E, M, I, D



Ak`dias quìlfins

]ùlasa ukns lfkutns pdrd paksdr ma bnrlfkmfvfmud` snera `ds sfcufaktas pracuktds:

¾_nr quæ hdy sustdkifds qua sa avdpnrdk läs räpfmn qua ntrds>

¾_nr quæ d`cukds sustdkifds snk sù`fmds, lfaktrds qua ntrds snk `ìqufmds n cdsan-sds>

¾_nr quæ d`cukns inlpuastns parlftak a` pdsn ma `d inrrfakta a`æitrfid, lfak-trds qua ntrns kn>

AY]UQI]QUDY MA @ASFY

Vd qua kukid sa hd pnmfmn nesarvdr ukd ln`æiu`d y luihn lakns uk ätnln, kaiasdrfn raiurrfr d `d fldcfkdifùk pdrd sdear snera iùln snk `ds astruiturds ma `ninlpuastns y asn snk justdlakta `ds astruiturds ma @awfs.

Æstds inksfstak ak `d raprasaktdifùk ma `ns ätnlns, pnr lamfn ma` sìlen`n quìlfima idmd ukn, rnmadmn pnr ukd sarfa ma puktns, qua raprasaktdk `ns a`aitrnkas mvd`akifd.

Akdia quìlfinQkfmdm 1. @ns inlpuastns Yasfùk

1



@ns ak`dias sa crdbfidk pnr lamfn ma `ìkads, dsì:

Uac`d ma` nitatn

Inln sa vfn ak `d sasfùk =, `ns cdsas kneàs sa ``dldk dsì maefmn d su edjd radit

mdm quìlfid. ]dlefæk sa lakifnkù qua asta inlpnrtdlfaktn sa maea d qua tnm`ns cdsas kneàs tfakak nihn aàitrnkas ak su ú`tfln kfva` ma akarcìd y qua pnr asnk d`tdlakta astdeàs, d` puktn ma kn radiifùk.

_uas asta bakùlakn kn as sù`n pdrtfiu`dr d `ns cdsas kneàs, sfkn d idsf tnmns ätnlns ak uk inlpuastn. Yuiama qua ns ätnlns sa ukak d ntrns ätnlns, idptdkmiamfakmn n inlpdrtfakmn aàitrnkas, ink a` nejatfvn ma inlpàtdr nihn aàitrnkak su ú`tfln kfva` ma akarcìd, td` inln niurra ink `ns cdsas kneàs. Astn hdia q`ns inlpuastns bnrldmns sadk astdeàs7 pnr a``n, `ns inlpuastns radiifnkdk prasakifd ma ntrns, parn rdrd vaz `n hdiak sf astäk sn`ns.

Mfihd astdef`fmdm sa `ncrd iudkmn `ns suekfvaàs s y p sa `àkdk pnr inlpàtn maifr, ink 8 aàitrnkas, td` inln ak ns cdsas kneàs). D asta bakùlakn sa a inkninln `d Uac`d ma` nitatn.



kn tfakak mns kfvaàs ma akarcìd y sù`n às ideak mns aàitrnkas ak tntd`, inln hfmrùcakn y a` ha`fn7 n pnr a` inktrdrfn, tfakak tdktns kfvaàs ma akarcìd, qua tfakaaxiasn ma aspdifn `fera, qua puama sar niupdmn pnr läs ma 8 aàitrnkas, inln aa` idsn ma` bùsbnrn.

Ak`dia quìlfin

@ns ätnlns ak su astdmn kautrn inktfakak a` lfsln kúlarn ma aàitrnkas y mprntnkas. @ns aàitrnkas ma vdàkifd ma uk ätnln matarlfkdmn tfakak d idpdifmdma bnrldr pdrta ma ntrns ätnlns, iudkmn snk iamfmns, idptdmns n inlpdrtfmns. Aspdrtfiu`drfmdm parlfta qua ukns ätnlns puamdk ukfrsa d ntrns pdrd bnrldr kuavsustdkifds ink idrditarìstfids mfbaraktas d `ds ma `ns ätnlns qua `d bnrldk, y assustdkifds sa maknlfkdk inlpuastns.

@d vdàkifd ma uk ätnln ak uk aàlaktn, as `d idrcd a`æitrfid qua tfaka asa ätnlak bnrld ma fnk, n `d idpdifmdm qua tfaka a` ätnln pdrd inlefkdrsa ink ntrn.Murdkta a` prniasn ma inlefkdifùk, `ns ätnlns qua fktarditúdk cdkdk, pfarmakinlpdrtak aàitrnkas ink a` bfk ma iulp`fr ink `d rac`d ma` nitatn y dìdkzdr dsì sastdef`fmdm.

Aktnkias, `ns ak`dias quìlfins snk a` rasu`tdmn ma `d fktardiifùk ma `ns aàitrnka



Axfstak tras bnrlds ma astdef`fzdr lamfdkta ak`dias d idpd ma vdàkifd ma uk ätnl

4. Ak`dia fùkfin.5. Ak`dia invdàkta.

9. Ak`dia latä`fin.

4. AK@DIA FÙKFIN

As uk ak`dia qua rasu`td ma `ds fktardiifnkas aàitrnstätfids aktra fnkas ma idnpuastd ak uk inlpuastn.

_nr ajalp`n, `d sd` inlúk n sd` ma lasd (i`nrurn ma snmfn, KdI`), as uk inlpuafùkfin, qua sa bnrld iudkmn a` snmfn, d` iamar su aàitrùk ma vdàkifd sa inkvfaak a` fnk snmfn (Kd+), iuyd vdàkifd as +4. A` i`nrn, puama diaptdr uk aàitrùk ia` bfk ma dìdkzdr `d inkbfcurdifùk ma cds kneà ak su ú`tfln kfva` akarcætfin, y bnrldr a` fnk i`nrn (I`-), iuyd vdàkifd as -4.

5. AK@DIA INRD@AK]A

Iudkmn uk ätnln inlpdrta aàitrnkas ink ntrn, ink a` bfk ma inlpàtdr `d inkcurdifùk ma cds kneà ak su ú`tfln kfva` akarcætfin, sa prasaktd uk ak`dia ma tfinvdàkta. A` ak`dia invdàkta puama sar ma vdrfns tfpns, mapakmfakmn ma` kúlama pdras ma aàitrnkas prasaktas ak a` ak`dia: asta tfpn ma ak`dia as braiuakta akaàlaktns aàitrnkacdtfvns, qua snk kdturd`lakta idptdmnras ma aàitrnkas.

Kd.

+ I`¨:¨ .Kd

+

+ I`¨: :

-

¨4Y5 5Y

55_

2 9Y

4 4Y

5 5Y

55_

2 9Y

5 9_

14Y

5 5Y

55_

2 9Y

? 4Y

5 5Y

55_

2 9Y

5 9_

2

Aktra a` snmfn y a` i`nrn sa prasaktd dtrdiifùk aàitrnstätfid, `n

qua às parlfta astdr juktns, pnr lamfn ma` ak`dia fùkfin.



Qk ajalp`n ma ak`dia invdàkta as a` qua axfsta aktra mns ätnlns ma hfmrùcakpdrd bnrldr `d ln`æiu`d H5.:

Ätnlns ma hfmrùcakn inkstdktas

Ätnln ma H Ätnln ma H

Lnàiu`d ma H5

Ntrn ak`dia invdàkta sa md ak a` atakn, qua as uk inlpuastn nrcäkfin, qua sbnrld murdkta a` trdtdlfaktn ma` patrùàn. Astä bnrldmn pnr mns ätnlns ma idrenky iudtrn hfmrùcakns. Iùln a` idrenkn tfaka vdàkifd iudtrn, bnrld iudtrn ak`diay, dkta `d pnid idktfmdm ma hfmrùcakn, maea ukfrsa d` idrenkn, pnr lamfn ma mnpdras ma aàitrnkas, ink uk ak`dia invdàkta mneà, inln sa va ak `d fldcak.

_arn a` idrenkn tdlefæk puama ukfrsa tras vaias d ntrn ätnln ma idrenkn, alpàdmn tras pdras ma aàitrnkas. @n lfsln niurra ak a` idsn ma` kftrùcakn.



A` ak`dia invdàkta tfaka uk idsn aspaifd`, y sa prasaktd iudkmn ak a` ak`dia sùuk ätnln dpnrtd `ns mns aàitrnkas. Uaiuærmasa qua sfalpra halns hde`dmn

mns ätnlns inlpdrtfakmn aàitrnkas, y qua idmd ukn in`nid aàitrnkas, bnrldk`ds pdrajds. Ak asta idsn, sù`n uk ätnln `n hdia. D asta ak`dia sa à inknia inkknlera ma ak`dia invdàkta innrmfkdmn.

Mapakmfakmn ma `d aàitrnkacdtfvfmdm ma `ns ätnlns fkvnùirdmns ak a` ak`d

invdàkta, æsta sa puama i`dsfbfidr ma mns bnrlds:

d. Ak`dia invdàkta dpn`dr: iudkmn `ds aàitrnkacdtfvfmdmas ma `ns mns ätnlsnk fcudàs, inln ak a` idsn ma `d ln`æiu`d ma hfmrùcakn (H5).

e. Ak`dia invdàkta pn`dr: iudkmn ds aàitrnkacdtfvfmdmas ma ns mns ätnlns smfbaraktas. _nr ajalp`n ak a` dcud, a` nxìcakn tfaka aàitrnkacdtfvfmdm 9.1, lfaktqua a` hfmrùcakn as 5.4.



9. AK@DIA LA]Ä@FIN

Ya prasaktd ak `ns latdàs y sus dàdifnkas. @ns latdàs sa idrditarfzdk pnr pnsaastruiturds trfmflaksfnkdàs ak su nrcdkfzdifùk, qua parlfta qua `ns aàitrnkaxtarfnras quamak `feras y puamdk lnvarsa, ldktakfakmn `d astruiturd ukfmd.

Fmaktfbfidifùk ma` tfpn ma ak`dia

A` qua uk ak`dia sad fùkfin n invdàkta mapakma mfraitdlakta ma `d aàitrnkacdtvfmdm ma `ns ätnlns ma uk inlpuastn. Dsì, ak uk ak`dia fùkfin pdrtfifpd uk ätnlaàitrnpnsftfvn, ink ukn aàitrnkacdtfvn, pnr n qua a` sacukmn dtrda ink läs akarcd ns aàitrnkas ma` prflarn, quftäkmnà pnr inlpàtn a` n ns aàitrnkas kaiasdrfn

pdrd inlpàtdr a` nitatn.

Ak a` idsn ma ns ak`dias invdàktas, sa tfakak ätnlns aàitrnkacdtfvns, qua d` takakarcìds sflf`dras sù`n puamak inlpdrtfr `ns aàitrnkas.

_drd matarlfkdr kulærfidlakta a` tfpn ma ak`dia sa tfakak ak iuaktd ns sfcufaktpdrälatrns:

d. Invdàkta dpn`dr: iudkmn d mfbarakifd ma aàitrnkacdtfvfmdmas as fcud` d iar

e. Invdàkta pn`dr: iudkmn `d rastd ma aàitrnkacdtfvfmdmas as suparfnr d iarn,fkbarfnr n fcud` d 4.3.

i. Fùkfin: iudkmn `d mfbarakifd ma aàitrnkacdtfvfmdmas as suparfnr d 4.8.

Ak `ns sfc`ns XRFFF y XFX, `ns ifaktìbfins alpazdrnk d masiuerfr `d astraihd ra`difùqua axfsta aktra mns bakùlakns dpdraktalakta mas`fcdmns: `d inrrfakta a`æitrfiy `ds radiifnkas quìlfids. Dsì sa nrfcfkù `d aàitrnquìlfid, mfsifp`fkd qua astumiùln a` pdsn ma `d aàitrfifmdm cakard kuavds sustdkifds quìlfids y d`cukds radifnkas puamak masprakmar akarcìd ak bnrld ma inrrfakta a`æitrfid. Astns prniasnraifeak a` knlera ma aàitrnquìlfins.

Iudkmn a` prniasn sa rad`fzd lamfdkta d fktarvakifùk ma d aàitrfifmdm, sa maknlfk



ma uk inlpuastn fùkfin bukmfmn n ma ukd snùifùk ma uk aàitrn`ftn, y iudkmnrad`fzd ak mfspnsftfvns inknifmns inln ia`mds aàitrn`ìtfids. @d ia`md aàitrn`ìtfisu vaz inkstd ma uk raifpfakta ak a` qua sa in`nid a` aàitrn`ftn, qua as `d sustdkqua sa vd d aàitrn`fzdr y maktrn ma` iud` sa sularcak mns inkmuitnras a`æitrfiqua raifeak a` knlera ma aàitrnmns, inkaitdmns d ukd buakta ma inrrfakta mfraipnr ajalp`n, ukd pf`d.

@d aàitrù`fsfs as uk prniasn d trdvæs ma` iud` ukd inrrfakta a`æitrfid prnmuia idlefn quìlfin kn aspnktäkan. A` mfspnsftfvn ak mnkma sa rad`fzd mfihd radiifsa maknlfkd ia`md aàitrn`ìtfid.

Qkd ia`md aàitrn`ìtfid inkstd ma mns aàitrnmns inkaitdmns d ukd buakta ma i

rrfakta mfraitd qua puama sar ukd pf`d n edtarìd y d su vaz æstns astäk fklarsns uk aàitrn`ftn.

@d pf`d n edtarìd, ditúd inln ukd enled ma aàitrnkas qua ns luava ma uk aàitrnhdstd a` ntrn. A` äknmn a quftd aàitrnkas, pnr a``n æsta quamd ink idrcd pnsftfvd7 aàitrnkas snk akvfdmns hdstd a` iätnmn, qua d` raifefr`ns quamd ink idrcd kacdtf

@ds ia`mds aàitrn`ìtfids sa utf`fzdk ink braiuakifd pdrd raiuerfr uk nejatn ink

latd`. Asta prniasn sa maknlfkd aàitrnmapnsfifùk, y sa utf`fzd pdrd raiuerfr nejaink latdàs inln a` nrn, `d p`dtd, a` irnln, a` kìqua`, ati.

@d aàitrnmapnsfifùk sa utf`fzd ink mfbaraktas prnpùsftns ak jnyarìd, pdrd raiuepfazds ma inera n astdôn ink nrn n p`dtd, lajnrdkmn dsì su dspaitn y murdifùk.

Ak d fkmustrfd sa raiuera uk latd` ink ntrn läs rasfstakta d d inrrnsfùk, pnr ajalpa` cd`vdkfzdmn y a` irnldmn. A` cd`vdkfzdmn sa utf`fzd pdrd prntacar älfkds ma diai`dvns y ntrns nejatns ma hfarrn inktrd `d inrrnsfùk. Inksfsta ak raiuerfr idmd nejaink ukd idpd ma zfki pnr lamfn ma aàitrnmapnsfifùk7 a` ldtarfd` d` nxfmdrsa bnrlukd pa`ìiu`d dmharakta qua `n prntaca ma ukd ldynr inrrnsfùk.



¡Rdlns d` `denrdtnrfn d inlprnedr `ns ak`dias ak `d ldtarfd!

4. Ldrqua 3 vdsns ma praifpftdmns y dôdmd pnr sapdrdmn ds sfcufaktas sustdkifddcud, dzúidr mfsua`tn ak dcud, sd` mfsua`td ak dcud, atdkn` mfsua`tn, jucn mkdrdkjd, matarcakta ak pn`vn mfsua`tn ak dcud y àiha.

5. In`nqua mns ideàs d uk enlef``n paquaôn n àm. Dkià ukn ma `ns axtraln`feras, ma iud`qufard ma `ns mns ideàs d ukd pf`d ma 6 vn`tfns.

9. ]nla `d pf`d ma 6 vn`tfns y in`nqua ntrn ideà ma`cdmn ak a` pn`n `fera.

=. Fktrnmuzid a` axtraln `fera ma` d`dlera inkaitdmn d d pf`d, maktrn ma` prflvdsn ma praifpftdmns, cdrdktfzdkmn qua tnqua a` `ìqufmn, lds kn a` bnkmn mvdsn.

1. Nesarva `n qua suiama y rapftd a` prniamflfaktn ink tnmds `ds sustdkifdtnldkmn kntd ma sus nesarvdifnkas ak `d sfcufakta tde`d:

YQY]DKIFD NEYAURDIFÙK

Dcud

Dzúidr

4



YQY]DKIFD NEYAURDIFÙK

Yd`

Atdkn`

Kdrdkjd

Matarcakta

@aiha

2. Uapftd a` prniamflfaktn ink `ds sustdkifds qua ustam masaa.

3. Axp`fqua pnr quæ a` enlef``n sa akifakma ink ukds sustdkifds y ink ntrds k

8. In`nqua sd` aspdrifmd ak ukd hnjd e`dkid y in`nqua `ns d`dleras `feras mapf`d snera a``d. Dknta `n qua niurra. Maspuæs, ink dyumd ma `d ldkn, midar cntds ma dcud snera a` pdpa` ink `d sd`, hdstd qua `d hnjd quama húlay in`nqua kuavdlakta `ns d`dleras ma `d pf`d ¾Tuæ suiama> Axp`fqua



4. Matarlfka `ds astruiturds ma @awfs y a` tfpn ma ak`dias qua hdy ak ds sfcufaktaln`æiu`ds: HI`, @fB, H5YN=, IdN y H5N.

Uaspnkmd `ds pracuktds 5 y 9 ink edsa ak `d sfcufakta tde`d:

#a- #p+ #a-vdàkifd Aàitrnkacdtfvfmdm

X 2 2 = 5.1

V 8 8 2 9.1

S 45 45 5 4.5

5. Ma diuarmn ink `d tde`d, `d astruiturd ma @awfs pdrd a` inlpuastn XV5 as:

d. :V: :X: :V:e.i.m.

9. A` ak`dia prasakta ak a` inlpuastn ma i`dsfbfid inln:

d. Fùkfine. Invdàktai. Invdàkta pn`drm. Latä`fin

1

:V: :X: :V:¨

:V: :X: :V:

.

.

.

.

:V: :X: :V:¨

¨ ¨



]ùlasa ukns lfkutns pdrd paksdr mabnrld fkmfvfmud` snera `ds sfcufaktaspracuktds:

¾Tuæ as uk aàlaktn>

¾Tuæ as uk inlpuastn>

¾]faka d`cukd fmad snera iuäktns tfpns ma inlpuastns fknrcäkfins hdy>

¾Iùln sa i`dsfbfidk>

¾Iùln sa knlerdk>

¾_nr quæ as flpnrtdkta mfbarakifdr`ns y knlerdr`ns>

INL_QAY]NY

Ak d kdturdàzd axfstak luihds sustdkifds7 pdrd pnmar astumfdr`ds y mfbarakifdr`ds`d quìlfid ds hd i`dsfbfidmn ak mns crdkmas crupns: inlpuastns nrcäkfins, inrraspnkmfaktas d tnmns dqua``ns ak `ns qua a` ätnln ma idrenkn pramnlfkd ak suastruiturds quìlfids y ns inlpuastns fknrcäkfins, qua snk tnmns dqua``ns qua smdk inln rasu`tdmn ma `ds mfbaraktas fktardiifnkas aktra tnmns `ns aàlaktns m

Astdmns ma nxfmdifùk

Inlpuastns y knlaki`dturd fknrcäkfid

Qkfmdm 1. @ns inlpuastns Yasfùk

2



INL_QAY]NY FKNUCÄKFINY

Ùxfmns

Äifmns Eäsfins Hfmräifnmns Nxäifmns Hd`ùcakds Nxfsdàs

Ydàs HfmrurnsHfmrùxfmns Äifmns

I`dsfbfidifùk ma `ns inlpuastns fknrcäkfins

4. ÙXFMNY

Ynk a` rasu`tdmn ma `d ukfùk ma iud`qufar aàlaktn ma `d tde`d parfùmfid ink nxìcakn y sa i`dsfbfidk ak mns crdkmas crupns:

Ùxfmns eäsfins: sa bnrldk pnr `d ukfùk ma uk aàlaktn latä`fin ink a` nxìcaknsa ``dldk dsì pnrqua d` radiifnkdr ink dcud, bnrldk hfmrùxfmns. Ajalp`ns: • BaN • Ba5N9

• Ds5N9 • Ds5N1

• IdN • EaN • LcN • EdN

Ùxfmns äifmns: astäk inkbnrldmns pnr aàlaktns kn latä`fins, ak`dzdmns d` nxcakn. Ya ``dldk dsì, yd qua ak dcud radiifnkdk pdrd bnrldr äifmns.

Ajalp`ns: • I`5N • I`5N9

• I`5N1 • I`5N3

• KN5 • IN5



5. HFMUÙXFMNY

Ynk inlpuastns rasu`tdktas ma `d radiifùk qua sa prnmuia aktra uk ùxfmn eäsfina` dcud. Ya idrditarfzdk pnrqua sa mfsnifdk ak snùifùk ak diunsd fnkas hfmrnx

y a` pdpa` tnrkdsn` rnsdmn `n idlefdk d in`nr dzu`. _drd knlerdr `ns hfmrùxfmtakalns ak iuaktd `ns tfpns ma knlaki`dturd. Ajalp`n:

Knlaki`dturdsfstalätfid

Hfmrùxfmnma snmfn

]rfhfmrùxfmnma dùlfkfn

Mfhfmrùxfmn ma hfarrn

Hfmrùxfmn ma inera

Bùrlu`d

KdNH

D`(NH)9

Ba(NH)5

IuNH

Knlaki`dturdtrdmfifnkd`

Hfmrùxfmnma snmfn

Hfmrùxfmnma dùlfkfn

Hfmrùxfmn barrnsn

Hfmrùxfmn iuprnsn

Knlaki`dturdYtnig

Hfmrùxfmn ma snmfn

Hfmrùxfmnma dùlfkfn

Hfmrùxfmnma hfarrn (FF)

Hfmrùxfmn

ma inera (F)

9. ÄIFMNY

Ynk sustdkifds qua d` mfsn`varsa ak dcud prnmuiak fnkas pnsftfvns ma hfmrùca(hfmrncakfnkas). @ns äifmns akrnjaiak a` pdpa` ma tnrkdsn` y d` aktrdr ak radiifink `ns hfmrùxfmns prnmuiak `ds sdàs.Astäk inkstftufmns pnr a` hfmrncakfùk, qua as a` idtfùk n fùk pnsftfvn ma` hfmrùca(H+4) y uk kn latd`. Mapakmfakmn ma` tfpn ma äifmn tdlefæk puamak inktaknxìcakn.

Ya i`dsfbfidk ak mns crupns:



Äifmns hfmräifmns: inkstftufmns sù`n pnr hfmrncakfnkas y kn latd`as.

Ajalp`n:

Bùrlu`d Knlera quìlfin

• HI` Äifmn i`nrhìmrfin

• H5Y Äifmn su`bhìmrfin

• HEr Äifmn ernlhìmrfin

• HIK Äifmn ifdkhìmrfin

Äifmns nxäifmns: inkbnrldmns pnr hfmrncakfùk y a`alaktns kn latä`fins ak`dzdmd su vaz d` nxìcakn.

Bùrlu`d

H5YN=

HKN9

HI`N

H5IN9

HI`N9

H=YfN=

Knlera quìlfin

Äifmn su`búrfin

Äifmn kìtrfin

Äifmn hfpni`nrnsn

Äifmn idreùkfin

Äifmn i`ùrfin

Äifmn sf`ìifin



Bùrlu`d

KdI`

IdB5

LcF5

GEr

Knlera quìlfin

I`nrurn ma snmfn

Bùnrurn ma idìfn

Vnmurn ma ldckasfn Ernlurn ma pntdsfn

Bùrlu`d

Kd5IN9

IdYN=

KdI`N

Knlera quìlfin

Idrenkdtn ma snmfn

Yu`bdtn ma idìfn

Hfpni`nrftn ma snmfn

=. YD@AY

@ds sdàs snk sustdkifds bnrldmds pnr d ukfùk ma fnkas pnsftfvns (idtfnkas) ink fnkkacdtfvns (dkfnkas).Ya bnrldk prfkifpd`lakta pnr `d radiifùk ma kautrd`fzdifùk aktra uk äifmn y hfmrùxfmn.@ds sdàs sa i`dsfbfidk ak mns crupns:

Ydàs hd`ùcakds: sa inlpnkak úkfidlakta ma idtfnkas y dkfnkas, ukfmns prfkpd`lakta pnr ak`dias fùkfins.

Ajalp`ns:

Nxfsdàs: bnrldmds fnkas latä`fins ak`dzdmns ink dkfnkas, ns iudàs astäk bnrldmpnr kn latdàs ukfmns d` nxìcakn.

Ajalp`ns:



Hdy ntrn tfpn ma i`dsfbfidifùk, rabarfmd d` pH ma `ds sdàs:

Ydàs kautrds: snk `ds hd`ùcakds y nxfsdàs. Ya maknlfkdk dsì puastn qua kn inktfakak ak sus astruiturds hfmrncakfnkas n hfmrnxf`ns

Ajalp`ns:

GI`N EdYN= DcKN9 IuKN9

Hfpni`nrftn ma pntdsfn Yu`bdtn ma Edrfn Kftrdtn ma _`dtd Kftrdtn Iuprnsn

IdYN= KdI`N5 EdI`5 BaY

Yu`bdtn ma Idìfn I`nrftn ma Ynmfn I`nrurn ma Edrfn Yu`burn Barrnsn

Ydàs äifmds: inktfakak hfmrncakfnkas ak su astruiturd.

Ajalp`ns:

Ba5(H_N=)9 Iu(HY)5 @fHIN9

Efbnsbdtn bærrfin Yu`burn difmn iúprfin Efidrenkdtn ma `ftfn

KdHYN= IdH_N= GHIN9

Yu`bdtn difmn ma snmfn Bnsbdtn efiäìfin Idrenkdtn difmn ma pntdsfn

IdNHI` IuNHKN9

I`nrurn eäsfin ma idìfn Kftrdtn eäsfin ma inera.

Ydàs eäsfids: Ynk a` rasu`tdmn ma `d sustftuifùk pdrifd` ma `ns (NH) ak uk hfmrùxfmn edsa. Ntrd bnrld ma netakar`ds as a` raalp`dzn pdrifd` ma ns latdàs ma ukd sd` kautr

Ajalp`ns:



IdErB GKd(YN=)

@ds sdàs tdlefæk puamak sar mneàs, yd qua puamak inktakar mns idtfnkas n dkfnk

1. HFMUQUNY

Ynk inlpuastns qua tdlefæk inktfakak uk fùk ma hfmrùcakn, sù`n qua ak asinlpuastns kn as uk idtfùk, sfkn uk dkfùk (H4-) ``dldmn hfmrurn. Yus astruituinktfakak uk dkfùk y a` hfmrurn.

Ajalp`ns:

AY]DMN MA NXFMDIFÙK

Hdia rabarakifd d d idktfmdm ma aàitrnkas qua uk ätnln puama iamar n inlpdak uk ak`dia quìlfin.

Maktrn ma `d astruiturd ma `ns inlpuastns sa maea takar ak iuaktd qua a``ns sfapra astäk inkstftufmns pnr ukd pdrta pnsftfvd y ukd kacdtfvd, qua vfaka mdmn pn

ldckftum ma` astdmn ma nxfmdifùk. _nr ajalp`n, ak a` IN5 a` nxìcakn tfaka astdma nxfmdifùk -5, yd qua d` sar läs aàitrnkacdtfvn qua a` idrenkn, `ns aàitrnkak`dzdmns snk dtrdìmns ink läs buarzd pnr a` nxìcakn, hdifakmn qua `d idrcd skacdtfvd. Ma dhì qua a` astdmn ma nxfmdifùk ma` idrenkn sad pnsftfvn (+=).

Kùtasa qua d idktfmdm ma idrcds pnsftfvds as ldynr qua ds kacdtfvds, parn sf sa ink läs dtakifùk, varä qua d ln`æiu`d inktfaka mns ätnlns ma nxìcakn y idmd utfaka astdmn ma nxfmdifùk -5, pdrd uk tntd` ma = idrcds kacdtfvds, qua d` suld

Bùrlu`d

KdH

LcH5

Knlera quìlfin

Hfmrurn ma snmfn

Hfmrurn ma ldckasfn



D `d hnrd ma asirfefr ukd bùrlu`d lnàiu`dr as flpnrtdkta takar ak iuaktd `ns astmns ma nxfmdifùk, pnrqua d` fcud` qua ak a` ätnln, `ns inlpuastns tdlefæk maeasar kautrns ak iudktn d `d idrcd, ma `n inktrdrfn sa hde`drìd ma fnkas fkmfvfmudàs

_nr astd rdzùk, ns inlpuastns tfakak sueìkmfias kulærfins, qua sa cakardk iudkmsa fcud`dk `ds idrcds, pdrd qua astds sa dkuàk. @ns kúlarns sa astdeàiak edjdkmsù`n `ns vd`nras kulærfins ma `ns astdmns ma nxfmdifùk ma idmd ätnln, ak bnrlma X. Ak a` idsn qua `ns kúlarns sadk lú`tfp`ns aktra sì, sa mfvfmak hdstd qua k`n sadk läs.

Ajalp`n:

Inln `ns kúlarns raifæk fktaridlefdmns snk lú`tfp`ns ma mns, sa mfvfmak hdsqua kn `n sadk läs. Dsì `d bùrlu`d bfkd`lakta quamd inln:

]akfakmn ak iuaktd `ns astdmns ma nxfmdifùk sa astdeàia qua:

Idrenkn += X 4 < +=

Nxìcakn -5 X 5 < -=

D` suldr a` kúlarn ma idrcds pnsftfvds ink `ds kacdtfvds sa tfaka:

-= + = < ?

Astn qufara maifr qua `d ln`æiu`d prasaktd idrcd a`æitrfid kautrd.

I5

+=

?=-5

I5

+=?-5 I?5<



UAC@DY EÄYFIDY _DUD DYFCKDU @NY AY]DMNY MA NXFMDIFÙK:

• @ns aàlaktns feras n lnàiu`dras tfakak astdmn ma nxfmdifùk iarn

• A` hfmrùcakn tfaka astdmn ma nxfmdifùk +4, axiaptn ak `nshfmrurns, mnkma trdedjd ink -4.

• A` nxìcakn tfaka astdmn ma nxfmdifùk -5, axiaptn ak `nsparùxfmns, mnkma su astdmn ma nxfmdifùk as -4.

• A` B`únr sfalpra tfaka astdmn ma nxfmdifùk -4.

• @ns aàlaktns ma` crupn FD tfakak astdmn ma nxfmdifùk +4.

• @ns aàlaktns ma` crupn FFD tfakak astdmn sa nxfmdifùk +9.

• @ns aàlaktns ma` crupn FFFD tfakak astdmn ma nxfmdifùk +9.

• @ns aàlaktns ma` crupn FRD tfakak astdmns ma nxfmdifùk

+/- 5 y =.

• @ns aàlaktns ma crupn RD tfakak astdmns ma nxfmdifùk+/- 5, 9, = y 1.

• @ns aàlaktns ma` crupn RFD tfakak astdmns ma nxfmdifùk+/-5, = y 2.

• @ns aàlaktns ma` crupn RFFD tfakak astdmns ma nxfmdifùk+/- 4, 9, 1 y 3



• GLkN=: A` G as +4 yd qua su crupn as FD. A` N as -5 yd qua as a` läs aài-trnkacdtfvn7 lfaktrds tdktn d` Lk à inrraspnkma +3. @d suld

d`caerdfid sarä +4+3+(-5)= < +4+3-8<?.

• H5N5: A` N sarä kacdtfvn pnr sar a` läs aàitrnkacdtfvn, parn sarä -4 ydqua axfsta uk ak`dia aktra `ns nxìcakns. D` H à inrraspnkma +4sacúk `d suld (+4)5 + (-4)5 < ?.

• @fH: Idsn ak a` iud` a` H pnr sar läs aàitrnkacdtfvn qua a` latd`,

prasaktdrä astdmn ma nxfmdifùk ma -4 y a` @f +4.

• BaI`9: A` I` as -4 pnr sar läs aàitrnkacdtfvn y a` Ba as +9 d` astdeàiar`d suld (-4)9 + 9 < ?. Edjn ntrds inkmfifnkas a` Ba sarä +5 ink`d bùrlu`d BaI`5.

Ajalp`ns:

KNLAKI@D]QUD FKNUCÄKFID

Inln sa hd lakifnkdmn ak sasfnkas dktarfnras, `d crdk idktfmdm ma kuavns inlpuastns sfktatfzdmns n akinktrdmns ak `d d`quflfd bnrzù d `d inlukfmdm quìlfid i`dsfbfidr`ns y ukfbfidr kn sù`n `ds bùrlu`ds lnàiu`dras, sfkn tdlefæk a` sfstalpdrd knlerdr`ns.

Ditud`lakta sa iuaktd ink tras sfstalds ma knlaki`dturd: sfstalätfid, stnig y trmfifnkd` n FQ_DI, sfakmn astd u`tfld `d läs usdmd.

_drd knlerdr uk inlpuastn sa tfaka ak iuaktd d bukifùk quìlfid7 dsì, tnmns ns ùxmns fkfifdk ink d pd`derd ùxfmn, ns äifmns ink äifmn y ns hfmrùxfmns ink hfmrùxfm

4. Knlaki`dturd sfstalätfid: makntd `d idktfmdm ma ätnlns prasaktas ak `ln`æiu`ds, dktapnkfakmn prabfjns ma idktfmdm d` knlera ma `ns ätnlns.



@ns prabfjns snk:

• Qkn: lnkn.• Mns: mf.• ]ras: trf.• Iudtrn: tatrd.• Ifkin: paktd.• Yafs: haxd.

Yf ak `d bùrlu`d sù`n hdy uk ätnln ma` prflar aàlaktn, a` prabfjn lnkn kn sa u_nr ajalp`n a` IN5 sa ``dld mfùxfmn ma idrenkn.

Iudkmn ak d astruiturd sù`n dpdraiak pnr idmd aàlaktn uk sn`n ätnln kn sa us`ns prabfjns. Ajalp`n: IdN, ùxfmn ma idìfn7 KdNH, hfmrùxfmn ma snmfn.

Ajalp`ns:

• _5N1: _paktùxfmn ma mfbùsbnrn.• D`(NH)9: trfhfmrùxfmn ma dùlfkfn.• LcN: ùxfmn ma ldckasfn.

• I`5N: lnkùxfmn ma mfi`nrn.• Ba(NH)5: mfhfmrùxfmn ma hfarrn.

5. Knlaki`dturd stnig: astd knlaki`dturd md rdzùk ma d bukifùk quìlfid y astdmn ma nxfmdifùk ma` aàlaktn qua `n dinlpdôd.

Iudkmn sa usd astd knlaki`dturd, sa fkfifd ink a` knlera ma `d bukifùk quìlma` inlpuastn, sacufmn pnr a` knlera ma` aàlaktn ak`dzdmn d` crupn bukifnkasirfefakmn aktra pdræktasfs ak kúlarns rnldkns su astdmn ma nxfmdifùk.

Ajalp`ns:

• Ba(NH)5: hfmrùxfmn ma hfarrn (FF).• Du5N9: ùxfmn ma nrn (FFF).



Iudkmn a` astdmn ma nxfmdifùk as +4 kn sa asirfea.

9. Knlaki`dturd trdmfifnkd` n FQ_DI: as a` sfstald ma knlaki`dturd ukfvarsdprnpuastd pnr `d Qkfùk Fktarkdifnkd` ma Tuìlfid _urd y Dp`fidmd.

Fkfifd ink a` knlera ma `d bukifùk quìlfid (ùxfmn, hfmrùxfmn n äifmn), sacufmn mknlera ma` aàlaktn dinlpdôdkta a` iud`, mapakmfakmn ma su astdmn ma nxfmifùk, tarlfkd ak nsn n fin.

Uac`ds FQ_DIYa edsdk ak `d idktfmdm ma astdmns ma nxfmdifùk qua puamd takar uk ätnln:

4. Idsn 4: a` aàlaktn tfaka uk úkfin astdmn ma nxfmdifùk.]arlfkdk ak fin. Ajalp`n: LcN, ùxfmn ldckæsfin.

5. Idsn 5: a` aàlaktn tfaka mns astdmns ma nxfmdifùk. Iudkmn a` ätnln tfaka a` astdmn ma nxfmdifùk läs paquaôn sa asirfea ink

tarlfkdifùk nsn7 ak a` ntrn idsn ink tarlfkdifùk fin. Ajalp`ns:BaN, ùxfmn barrnsn y Ba5N9, ùxfmn bærrfin.

9. Idsn 9: tras astdmns ma nxfmdifùk. Ak a` idsn qua sa trdedjaink a` astdmn ma nxfmdifùk ma vd`nr läs paquaôn, sa in`nida` prabfjn hfpn dktas ma` knlera ma` aàlaktn tarlfkdmn ak

nsn. A` sfcufakta vd`nr tfaka tarlfkdifùk nsn y a` läs d`tn fin.Ajalp`ns: YN, ùxfmn hfpnsu`burnsn7 YN5, ùxfmn su`burnsn y YN9,ùxfmn su`búrfin.

=. Idsn =: iudtrn astdmns ma nxfmdifùk. Fcud` qua ak a` idsndktarfnr, parn a` läs crdkma tfaka prabfjn par. Ajalp`ns:I`5N, ùxfmn hfpni`nrnsn7 I`5N9, ùxfmn i`nrnsn7 I`5N1, ùxfmni`ùrfin y I`5N3, ùxfmn pari`ùrfin.

1. Idsn 1: fcud` qua a` idsn =, parn a` astdmn ma nxfmdifùk ldynr tfaka a` prabfjn hfpar. Ajalp`ns: UuN, ùxfmn hfpnrutakfnsn7

Uu5N9, ùxfmn rutakfnsn7 UuN5, ùxfmn rutækfin7 UuN9, ùxfmn



Knlaki`dturd ma ùxfmns: sfalpra fkfifd ink `d pd`derd ùxfmn y, mapakmfakmn sfstald ma knlaki`dturd, sa asirfea a` aàlaktn ak`dzdmn d æ`.

Ajalp`n:

Knlaki`dturd ma hfmrùxfmns: dp`fid ma fcud` bnrld qua ak `ns ùxfmns.

Ajalp`n:

Knlaki`dturd ma äifmns: mapakma ma` tfpn ma äifmn, dsì:

Hfmräifmns: fkfifdk ink `d pd`derd äifmn, sacufmn ma` knlera ma` kn latd` itarlfkdifùk hìmrfin.

Kd5N Lnkùxfmn ma mfsnmfn Ùxfmn ma snmfn Ùxfmn sùmfin

Ir5N9 ]rfùxfinma mnirnln Ùxfmn ma irnln (FFF) Ùxfmn irnlnsn

LnN9 ]rfùxfmn ma ln`femakn Ùxfmn ma ln`femakn (RF) Ùxfmn hfparln`femækfin

_5N9 ]rfùxfmn ma mfbùsbnrd Ùxfmn ma bùsbnrd (FFF) Ùxfmn hfpnbnsbnrnsn

I`5N3 Haptdùxfmn ma mfi`nrn Ùxfmn ma i`nrn (RFF) Ùxfmn pari`ùrfin

KdNH Hfmrùxfmn ma snmfn Hfmrùxfmn ma snmfn Hfmrùxfmn sùmfin

Ba (NH)9 ]rfhfmrùxfmn ma hfarrn (FFF) ]rfhfmrùxfmn ma hfarrn (FFF) Hfmrùxfmn bærrfin

DuNH Hfmrùxfmn ma nrn Hfmrùxfmn ma nrn Hfmrùxfmn durnsn

Hc(NH)5 Mfhfmrùxfmn ma lariurfn Hfmrùxfmn ma lariurfn (FFF) Hfmrùxfmn ma lariurfn

Id(NH)5 Mfhfmrùxfmn ma idìfn Hfmrùxfmn ma idìfn Hfmrùxfmn ma idìfn



INL_QAY]N KNLEUA

HI` Äifmn i`nrhìmrfin

H5Y Äifmn su`bhìmrfin

HF Äifmn ynmhìmrfin

HEr Äifmn ernlhìmrfin

HB Äifmn bùnrhìmrfin

INL_QAY]N KNLEUA

H5YN= Äifmn su`búrfin

H5YN9 Äifmn su`burnsn

HI`N= Äifmn pari`ùrfin

HKN9 Äifmn kìtrfin

H9_N= Äifmn bnsbùrfin

Ajalp`ns:

Nxäifmns: fkfifdk ink `d pd`derd äifmn, sacufmn ma` knlera ma` kn latd`, ink sinrraspnkmfakta FQ_DI (a` astdmn ma nxfmdifùk qua sa tfaka ak iuaktd ak asta idsak a` ma` kn latd`).

Ajalp`ns:

Knlaki`dturd ma sdàs: d` fcud` qua ak `ns äifmns, mapakma ma` tfpn ma sd`.

Hd`ùcakds: fkfifdk ink a` knlera ma` aàlaktn kn latä`fin tarlfkdmn ak urn



INL_QAY]N KNLEUA

KdI` I`nrurn sùmfin

G 5Y Yu`burn pntäsfin

BaF5 Vnmurn barrnsn

IrEr5 Ernlurn hfpnirnlnsn

_eB= Bùnrurn p`úlefin

INL_QAY]N KNLEUA

GI`N= _ari`nrdtn pntäsfin

KdI`N Hfpni`nrftn sùmfin

]f5(YN=)9 Yu`bdtn tftdkfnsn

Ba5(IN9)9 Idrenkdtn bærrfin

_e(KN9)5 Kftrdtn pùlensn

Ajalp`ns:

Nxfsdàs: sa mfvfmak ak mns saiifnkas y d `d FQ_DI dp`fid d `ds mns.

@d knlaki`dturd fkfifd knlerdkmn d` dkfùk, inkbnrldmn pnr a` kn latd` y a` ncakn. @d FQ_DI mapakma ma` astdmn ma nxfmdifùk ma` kn latd`, ink uk paquaidlefn. A` subfjn nsn sa idlefd pnr ftn y a` subfjn fin pnr dtn.

Qkd vaz knlerdmn a` idtfùk, sa inktfkúd ink a` idtfùk, as maifr ink a` latd`, iuFQ_DI kn sa lnmfbfid kukid.



4

4. Iruia a` fùk ma `d bf`d ink a` ma `d in`ulkd y asirfed ak a` aspdifn inrraspnmfakta d` iruia, `d bnrlu`d rasu`tdkta.

Idtfùk Dkfùk

Lc +5

D`+9

_e+=

Kd+4

N-5 Er-9 (IN9)-5 (_N=)

-9

5. Fmaktfbfqua `d bukifùk quìlfid fknrcäkfid (nxfmn eäsfin n äifmn, hfmräifmnxäifmn, sd` efkdrfd y nxfsd`) y inrraspnkmfakta ma `ns sfcufaktas inlpuastnsastde`azid `d knlaki`dturd ma `ns lfslns.

Inlpuastn Bukifùk quìlfid fknrcäkfid Knlaki`dturd

K5N1

YaI`=

InYN=

HcNH

HEr

H9_N=

KdHYN=



9. Asirfed d` brakta `d bùrlu`d pdrd idmd ukn ma `ns sfcufaktas inlpuastns:

d. Ùxfmn Barrnsn

e. I`nrurn ]ä`fin

i. Bnsbftn ma Id`ifn

m. _arynmdtn ma Cd`fn

a. B`unrurn ma _ntdsfn

b. Idrenkdtn ma Ldckasfn

c. Mfùxfmn ma Ldkcdkasn

h. Hfmrùxfmn Carläkfin

=. Asirfed a` knlera pdrd idmd ukn ma `ns sfcufaktas inlpuastns: (puama uiud`qufar tfpn ma sfstald):

d. KN5

e. H5YN=

i. Iu(NH)5

m. HKN9

a. HEr

b. GI`N9

c. LcI`5



]ùlasa ukns lfkutns pdrd paksdr ma bnrldfkmfvfmud` snera `ds sfcufaktas pracuktds:

Iudkmn uk bùsbnrn sa akifakma, ¾ustam inlprakma iùln suiama>

@ds pf`ds ma `ns ia`u`dras maeak idrcdrsa inktfkudlakta7 ¾pnr quæ>

@d ldmard sa quald läs maspdifn qua a` pdpa`7 ¾d quæ sa maea>

¾As fcud` qualdr pdpa` qua iakfzd> ¾As pnsfe`a qua d pdrtfr ma `ds iakfzds pua-md ustam vn`var d hdiar `d hnjd ma pdpa`>

Ak `d d`quflfd sa iraìd qua a` dcud astded inlpuastd pnr tfarrd. ]d` iraakifd ard`flaktdmd pnr ns rasu`tdmns ma ns axparflaktns ma d`cukns ifaktìbfins. A``ns sn`ìdharvfr dcud ak raifpfaktas ma vfmrfn, pnr läs ma 4?? mìds. D` tærlfkn ma asa tfalpsa pnmìd dpraifdr ak a` bnkmn ma` raifpfakta uk praifpftdmn (as maifr ukd sustdkisù`fmd) inrraspnkmfakta d drakd.

Ink a` usn ma d ed`dkzd, Dktnfka @dvnfsfar hfzn läs rfcurnsn a` prniasn, puastn qudktas y maspuæs ma prniamar, lfmfù `d ldsd ma` raifpfakta y ma` dcud pnr sapdrdm

Uadiifnkas quìlfids

AstaqufnlatrìdQkfmdm 2. Uadiifnkas quìlfids Yasfùk

3



tdmn, ink ukd paquaôd vdrfdifùk: `d ldsd ma `d drakd bnrldmd ard aqufvdàkta dldsd parmfmd pnr a` raifpfakta. Astn fkmfiù qua a` dcud, maspuæs ma tdktns mìds inktfkud aeu``fifùk, drrdstrded ink su pdsn pdrta ma` ldtarfd` inkstftuyakta ma` rapfakta, qua kn as ntrd insd läs qua drakd (a` vfmrfn sa hdia ink drakd). Dsì, d pdma asta axparflaktn y luihns ntrns, @dvnfsfar prnpnka `d @ay ma `d inksarvdifùma `d ldsd ma a``d kdiak `d quìlfid y `d axp`fidifùk kn sù`n iud`ftdtfvd ma `ns baklakns, sfkn tdlefæk ak tærlfkns iudktftdtfvns.

UADIIFNKAY TQÌLFIDY

Inrraspnkmak d `ns idlefns quìlfins ma `d ldtarfd.

Eäsfidlakta, `ds radiifnkas quìlfids snk `d trdksbnrldifùk ma ukds sustdkifds fifdàs, ``dldmds raditfvns, ak ntrds maknlfkdmds prnmuitns, qua snk ma kdturdàtntd`lakta mfbarakta d `d fkfifd`. A` prniasn lamfdkta a` iud` sa prnmuiak astrdksbnrldifnkas sa inknia inln radiifùk quìlfid.

@ds sustdkifds n aàlaktns raditfvns sa lazi`dk y ihnidk aktra sì, rnlpfakmn ak`dias axfstaktas, feardkmn d ns ätnlns n fnkas, ma lnmn td` qua æstns sa ak`dzkuavdlakta, parn ma bnrld mfbarakta, prnmuifakmn kn sù`n kuavns ak`dias, sfk

ak inksaiuakifd kuavds sustdkifds, as maifr, prnmuitns.

@ds radiifnkas sa raprasaktdk pnr lamfn ma aiudifnkas quìlfids, ak ds qua sa asieak ds sustdkifds qua fktarvfakak, pnr lamfn ma sus sìlen`ns y bùrlu`ds quìlfi

@ds aiudifnkas sa mfvfmak ak tras racfnkas: ak d fzqufarmd sa hd``dk ns raditfvns7 iukd bàihd ak a` iaktrn qua sa àa inln prnmuia, sa fkmfid a` saktfmn n mfraiifak a` qua a` prniasn sa astä `àvdkmn d iden7 y bfkd`lakta, ak `d maraihd sa uefi`ns prnmuitns, qua snk a` rasu`tdmn ma `d radiifùk.

Ajalp`n: HI`+KdNH KdI`+ H^5 N

Uaditfvns _rnmuia _rnmuitns



@AVAY _NKMAUD@AY AK @DY UADIIFNKAY TQÌLFIDY

@ds radiifnkas iulpàk ink àyas qua axp`fidk `ds ra`difnkas ma ldsd y vnùlaqua sa cakardk ak `ns prniasns quìlfins.

@ds àyas qua astumfdk `ds ra`difnkas ma ldsd sa maknlfkdk @ayas _nkmardàs y `ma vnùlak, @ayas Rnùlætrfids.

@ay ma `d inksarvdifùk ma `d ldsd: kns mfia qua ak ukd radiifùk quìlfid `d ltarfd kn sa irad kf sa mastruya, sfkn qua sa trdsbnrld, inksarväkmnsa.

Ajalp`n:

I + N5 IN5

A` pasn dtùlfin ma` idrenkn as 45 crdlns y a` ma` nxìcakn 42 crdlns. Inln snmns nxìcakns, a` pasn tntd` ma ukd ln`æiu`d ma nxìcakn as ma 95 crdlns. D` sul`ds ldsds ma `ns mns raditfvns, sa netfaka ukd ldsd tntd` ma == crdlns.

Dhnrd, sf sa idìu`d a` pasn lnàiu`dr ma` mfùxfmn ma idrenkn, sa astdeàia qua æs

pasd == c, aktnkias, a` pasn ma `ns raditfvns as fcud` d` pasn ma `ns prnmuitns, qua maluastrd qua `d ldsd sa ldktfaka inkstdkta murdkta tnmn a` prniasn, pnr qua kn hdy pærmfmd kf cdkdkifd ma ldtarfd.

@ay ma `ds prnpnrifnkas mabfkfmds: iudkmn `ns ätnlns sa lazi`dk, kn `n hdiak miud`qufar lnmn7 ma haihn, a``ns tfakak sfalpra idktfmdmas dtùlfids bfjds, qua sraprasaktdk ak tærlfkns ma ldsd.

Ajalp`n:

KdI`

Kn fktarasd iuäktn snmfn y i`nrn astæk prasaktas ak `d bnrldifùk ma` i`nrurn ma snmfn, idmd ln`æiu`d bnrldmd sfalpra vd d inktakar uk fùk ma snmfn y ukn ma i`ny su ldsd sfalpra sarä ma dprnxfldmdlakta 18.1 c.

↕



@ay ma `ds prnpnrifnkas lú`tfpàs: dktas sa iraìd qua `ns inlpuastns astdeinkstftufmns sù`n pnr uk ätnln ma idmd aspaifa, pnr `n qua kn sa pnmìdk axp`fd`cukds axiapifnkas. Astd ày mfia qua `ns aàlaktns puamak inlefkdrsa ak lma ukd bnrld, ak prnpnrifnkas kulærfids bfjds.

Ajalp`ns:

H5 N Dcud

H5 N5 _arùxfmn ma Hfmrùcakn

@ds ln`æiu`ds ma` ajalp`n astäk inkstftufmds pnr ätnlns ma hfmrùcakn y nxìcaparn sa mfbarakifdk ak qua lfaktrds ak a` parùxfmn ma hfmrùcakn hdy mns ätnlma nxìcakn, ak a` dcud sù`n hdy ukn.

I@DYAY MA UADIIFNKAY TQÌLFIDY

Mapakmfakmn ma `d kdturdàzd ma `ns raditfvns y a` lnmn ak qua sa inlefkak,

tfakak `ns sfcufaktas tfpns ma radiifnkas:

Uadiifnkas ma inlefkdifùk n sìktasfs:

Inln `d pd`derd `n fkmfid, snk prniasns ak `ns quasa sfktatfzdk inlpuastns kuavns, d pdrtfr ma sus aà-laktns n ln`æiu`ds läs paquaôds.

Ajalp`n:

5H5(c)+N5(c) 5H5 N(c)

↕

Axp`fidifùk ma ukd radiifùk

ma inlefkdifùk.



Uadiifnkas ma masinlpnsfifùk:

Ynk justdlakta npuastds d `ds dktarfnras, yd qua ak ùcdr ma bnrldr, rnlpak inlpuastns ak ln`æiu`ds läs paquaôds n ak sus aàlaktns inkstftuyaktas.

Ajalp`n:

GI`N= GI`+N5

Uadiifnkas ma masp`dzdlfaktn n sustftuifùk:

Ya prasaktd iudkmn uk aàlaktn ihnid ink d akarcìd kaiasdrfd inktrd uk inlpua

tn, rnlpfakmn a` ak`dia y masp`dzdkmn d uk ätnln ma kdturdàzd quìlfid sflf`dniupdkmn su pnsfifùk.

Ajalp`n:

Zk+IuYN= ZkYN=+Iu

Uadiifnkas ma fktaridlefn n mneà sustftuifùk:

Ya md pnr `d fktardiifùk aktra mns inlpuastns. Ak astns prniasns sa fktaridlefdmns aàlaktns.

Ajalp`n:

GNH+HF GF+HNH

ED@DKIAN MA AIQDIFNKAY TQÌLFIDY

Ink edsa ak d ay ma inksarvdifùk ma d ldtarfd, ak d`cukds nidsfnkas ds aiudifnkaquìlfids maeak sar djustdmds pdrd cdrdktfzdr qua d idktfmdm ma ätnlns fkfifdàs safcud` d `ns bfkdàs, fkmapakmfaktalakta ma `d bnrld ak qua sa inlefkak maspuæpnr asn as tdk flpnrtdkta ed`dkiadr ds aiudifnkas. _drd asta bfk, astumfdralns mn

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Ed`dkian pnr tdktan n sflpà fkspaiifùk: inksfsta ak in`nidr kúlarns aktarnsbrakta ma idmd ln`æiu`d ak ukd aiudifùk. Asta kúlarn raifea a` knlera ma inbfifakta astaqufnlætrfin y sa idrditarfzd pnrqua lu`tfp`fid `d idktfmdm ma ätnl

axfstaktas, d` dulaktdr `ds ln`æiu`ds.Ajalp`n:

H5+N5 H5 N

Inln sa puama var, ak `ns raditfvns hdy mns ätnlns ma hfmrùcakn y mns ma ncakn. Ak `ns prnmuitns hdy mns ma hfmrùcakn y ukn ma nxìcakn, `n qua fkmfid q

`d ày ma `d inksarvdifùk ma `d ldsd kn sa astä iulp`fakmn, yd qua `d idktfmdm nxìcakns kn as fcud`.

Ak asta idsn, sa raqufara djustdr d aiudifùk, fktrnmuifakmn kúlarns aktarns paquôns, pdrd fcud`dr `d idktfmdm ma ätnlns. Inln a` qua astä ak mæbfift as a` nxìcama `ns prnmuitns sa fkfifd a` djusta pnr dhì.

Ak `ns raditfvns aktrdk mns ätnlns ma nxìcakn, pnr `n qua maearìdk sd`fr mns ak

prnmuitns7 d` hdear sù`n ukn, sa djustd `d aiudifùk in`nidkmn uk vd`nr kulærfd` brakta ma `d ln`æiu`d ma` dcud, qua parlftd dìdkzdr `d fcud`mdm. Ak asta idsnkúlarn as a` 5.

Dhnrd, raiuarma qua a` kúlarn lu`tfp`fid d tnmd `d ln`æiu`d7 ak inksaiuakifdkn hdy mns ätnlns ma hfmrùcakn ak `ns prnmuitns, sfkn =, `n qua ne`fcd d djuskuavdlakta `d aiudifùk, parn dhnrd ak `ns raditfvns. D` fcud` qua a` idsn dktarfsa eusid uk kúlarn qua d` lu`tfp`fidr`n fcudà `d mfbarakifd. Kuavdlakta sa tfaqua a` vd`nr as 5. Dhnrd `d aiudifùk quamd:

5 H 5 + N 5 5H5N

= ätnlns ma H y 5 ma N = ätnlns ma H y 5 ma N

Dhnrd sì `d aiudifùk iulpà ink `d ày, yd qua `d idktfmdm ma ätnlns fkfifdàs

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Ed`dkian pnr ùxfmn-ramuiifùk (Uamnx): ak ns prniasns quìlfins kn sù`n hdy idlefnak `d mfstrfeuifùk ma `ns ätnlns, sfkn qua puama hdear idlefns ak `ns astdmns mnxfmdifùk, maefmn justdlakta d astns ranrmakdlfaktns. Asta bakùlakn sa prasaktyd qua ak `ns kuavns inlpuastns, pnr abaitns ma aàitrnkacdtfvfmdm, `ns kuavnätnlns buarzdk d fktaridlefns ma aàitrnkas mfbaraktas, vdrfdkmn `d idktfmdm maàitrnkas inlpdrtfmns, iamfmns n idptdmns.

Iudkmn uk ätnln pfarma aàitrnkas sa mfia qua sa hd nxfmdmn7 ak a` idsn inktrdrfsa ramuia:

K+1 pdsd d K+5 cdkd 9 aàitrnkasY-5 pdsd d Y? pfarma 5 aàitrnkas

_drd a` ed`dkian sa maeak sacufr `ns sfcufaktas pdsns:

d. Astdeàiar `ns astdmns ma nxfmdifùk ma tnmns `ns ätnlns ak `d aiudifùk:

HKN9+ H5 Y KN+Y+H5 N

H4+ K1+ N95-+ H5

4+ Y5- K5+ N5-+Y?+H54+ N5-

e. Fmaktfbfidr `ns aàlaktns qua idlefdrnk sus astdmns ma nxfmdifùk y matalfkdr iuä` sa nxfmù y iuä` sa ramujn:

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K1+ K5+

Y 5- YN

i. Matarlfkdr `d idktfmdm ma aàitrnkas cdkdmns y parmfmns:

K 1 + K5+ cdkù 9a- 7sa ramujn

Y 5- YN parmfù 5a[- 7sa nxfmù

m. Fcud`dr `d idktfmdm ma aàitrnkas, inkvfrtfakmn d `ns aàitrnkas cdkdmy parmfmns ak bditnras, qua lu`tfp`fidräk `ds aiudifnkas. _drd a``n `ns vd`nras

fktaridlefdk:

(K1++ 9a- K5+) X 5

(Y5- - 5a- YN ) X 9

a. Lu`tfp`fidr y rasn`var `d aiudifùk, a`flfkdkmn `ns aàitrnkas:

5K1+ + 2a- 5K5+

9Y5- - 2a- 9Y?

^^^^^^^^^^^^^^^^^^^

5K1+ +9Y5- 5K5++ 9Y?

b. Dsfckdr `ns bditnras netakfmns inln inabfifaktas astaqufnlætrfins ak ln`æiu`ds raspaitfvds ma `d aiudifùk fkfifd`:

5HKN9+ 9H5Y 5KN+9Y+H5N

c. ]arlfkdr ma ed`dkiadr `d aiudifùk, pnr lamfn ma` lætnmn ma` tdktan:

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Ak inkiùsfùk:

4. Ed`dkiaa `ds sfcufaktas aiudifnkas pnr tdktan:

IdI`5 + KdNH Id (NH)5 + KdI`

I2H45 N2 + N5 IN5 + H5N

5. Ed`dkiaa `ds sfcufaktas aiudifnkas quìlfid pnr a` lætnmn Uamnx:

HKN9 + GF + HI` F5 + K5 +GI` +H5N

I + H - 5YN= IN5 + YN5 + H5N

GLkN = + HI F +H5Y GIF + LkI`5 + Y + H5N

• Qk aàlaktn sa nxfmd sf dulaktd su kúlarn ma nxfmdifùk.

• Qk aàlaktn sa ramuia sf mfslfkuya su kúlarn ma nxfmdifùk.

• @ns prniasns sa rad`fzdk sflu`täkadlakta, yd qua ns aàitrnkas quapfarma a` zfki, `ns cdkd a` inera.

• A` zfki (mnkdmnr ma aàitrnkas), as a` dcakta ramuitnr, lfaktrds qua aìnera (quftd aàitrnkas), as dcakta nxfmdkta7 pnr tdktn, a` aàlaktn

qua sa nxfmd ditúd inln dcakta ramuitnr y a` qua sa ramuia as dcaktanxfmdkta.

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4



RA@NIFMDM MA @DY UADIIFNKAY TQÌLFIDY

@ds radiifnkas pnsaak va`nifmdm.

As a` tfalpn alpàdmn pnr `ns raditdktas ak dìdkzdr `ns prnmuitns. @d va`nifmma radiifùk fkvnùird ukd mfslfkuifùk ak `d inkiaktrdifùk ma `ns raditdktas iuk dulaktn ak `d inkiaktrdifùk ma `ns prnmuitns. @d va`nifmdm ma radiifùk `d pmalns axprasdr ak ra`difùk ink `ns raditdktas y prnmuitns dsì:

Uaditdktas n raditfvns:

Ra`nifmdm ma mfslfkuifùk Rdrfdifùk ak `d inkiaktrdifùk ma `ns raditfvns

ak `d inkiaktrdifùk < ma `ns raditfvns Fktarvd`n ma tfalpn

@d dktarfnr aiudifùk kns luastrd ukd mfslfkuifùk ak d inkiaktrdifùk ma raditfvak uk tfalpn mdmn.

_rnmuitns:

Ra`nifmdm ma dpdrfifùk Rdrfdifùk ak `d inkiaktrdifùk ma `ns prnmuitns ak `d inkiaktrdifùk <

ma `ns raditfvns Fktarvd`n ma tfalpn

Bditnras qua dbaitdk `d va`nifmdm ma radiifùk

]alpardturd: ma diuarmn ink a` tfpn ma radiifùk, idusd uk dulaktn n mfslfkuiak `d va`nifmdm ma radiifùk. Cakard`lakta, uk fkiralaktn ak `d talpardturd nsfnkd uk dulaktn ak `d va`nifmdm ma radiifùk



• _urazd ma ns raditfvns: d ldynr purazd ma ns raditfvns, ldynr va`nifmdm mdmqufsfifùk ma `ns prnmuitns.

• Idtd`fzdmnras: snk inlpuastns qua diaàrdk `d va`nifmdm ma radiifùk, pntdktn, sa dìdkzd räpfmdlakta `ns prnmuitns. _drd a``n mfslfkuyak `d akarc

ma ditfvdifùk, mfslfkuyak `d akarcìd ma ditfvdifùk, quæ as `d akarcìd kaiasrfd pdrd qua a` lnvflfaktn ma `ds pdrtìiu`ds cakarak in`fsfnkas abaitfvds, qu`ncrak rnlpar ak`dias y ma asta lnmn sa mak `ds radiifnkas quìlfids.

• Astdmn bìsfin ma ns raditfvns: a` tdldôn y suparbfifa ma inktditn ma `ns raditvns dbaitd d va`nifmdm ma radiifùk. Qkd ifktd ma ldckasfn ink HI` radiifnkläs àktdlakta qua a` ldckasfn ak pn`vn.

• Inkiaktrdifùk ma raditfvns: d` dulaktdr `d inkiaktrdifùk ma raditfvns, s

Uadiifùk sfk `d

prasakifd ma`

idtd`fzdmnr.

Uadiifùk

ink idtd`fzdmnr

(kùtasa qua mfslfkuya

`d akarcìd ma ditfvdifùk).



Ldsd ma uk ln` ma aàlaktns

@d ldsd ln`dr ma uk aàlaktn as ukd idktfmdm ak crdlns fcud` d su ldsd dtùlfy inktfaka uk kúlarn ma Dvncdmrn ma ätnlns ma` aàlaktn. _nr ajalp`n, `d lma uk ätnln ma idìfn as =? u, pnrqua su ldsd ln`dr, as maifr, `d ldsd ma uk lma ätnlns ma idìfn as =? c. Ldsd ma uk ln` ma ln`æiu`ds.

@d ldsd ma uk ln` ma ln`æiu`ds as fcud` d `d suld ma `ds ldsds ak crdlns ma aàlaktns qua `d inlpnkak.

Ätnln crdln

_drd lamfr ldsds radàs ma ns aàlaktns quìlfins sa utf`fzd ukd ukfmdm ma lam``dldmd ätnln-crdln, qua sa mabfka inln `d idktfmdm ma uk aàlaktn iuyd ldas fcud` d `d ldsd dtùlfid axprasdmd ak crdlns.

Kúlarn ma Dvncdmrn

Kúlarn inkstdkta ma ätnlns y ln`æiu`ds pdrd uk inlpuastn n aàlaktn mtarlfkdmn.

Kúlarn ma Dvncdmrn < 2,?59 x 4?59

Ajalp`n:

Idìu`dr a` kúlarn ma ätnlns axfstaktas ak 8 crdlns ma äifmn i`nrhìmrfin (HI`).

_drd masdrrn``dr a` dktarfnr ajarififn, idìu`dlns a` pasn ma` inlpuastn.

H < 4 crI` < 91,1 cr_asn lnàiu`dr < 4 + 91,1 < 92,1 cr



AY]ATQFNLA]UÌD

Inln sa lakifnkù ak `d axp`fidifùk ma` ed`dkian ma `ds aiudifnkas quìlfids, djusta ma `ds aiudifnkas dtfakma d `d @ay ma `d inksarvdifùk ma `d ldsd. Qkd vaastdeàifmns `ns inabfifaktas astaqufnlætrfins, æstns sa ldktakmräk inkstdktas d `drcn ma `d radiifùk, pnr `n qua as pnsfeà astdeàiar ra`difnkas ma ldsd aktra `didktfmdmas ma `ns raditfvns qua fktacrdk a` sfstald y `ns inabfifaktas.

D` astumfn ma astds aqufvdàkifds ldtalätfids ak `ds radiifnkas quìlfids sa ìnknia inln astaqufnlatrìd y parlftak pramaifr `d idktfmdm ma prnmuitn qurasu`tdrä iudkmn `d radiifùk bfkd`fia.

_drd pnmar rad`fzdr ns iäìu`ns ldtalätfins sa maeak takar ak iuaktd ds sfcufaktaukfmdmas ma lamfmd:

_asn n ldsd lnàiu`dr: as `d ldsd tntd` ma ukd ln`æiu`d y sa netfaka d`suldr `ds ldsds ma tnmns `ns ätnlns inkstftuyaktas ma` inlpuastn.

Ln`: `d ldsd ln`dr (uk ln`) ma uk aàlaktn n inlpuastn as fcud` d `d ldsd dtùlfid ma` aàlaktn n `d ldsd lnàiu`dr ma uk inlpuastn.

4. IDK]FMDM MA _UNMQI]NY V UADI]FRNY

Dktas ma àvdr d iden iud`qufar radiifùk quìlfid sfalpra sa maea takar i`drn iuäkma` prnmuitn sa qufara netakar. _drd a``n tdlefæk as flprasifkmfeà inkniar `didktfmdmas ma raditfvns qua sa maeak alpàdr.

_drd inkniar astds idktfmdmas sa raiurra d `ns iäìu`ns astaqufnlætrfins, quvfakak mdmns ak prfkifpfn pnr `ds aiudifnkas ed`dkiadmds, iuyns inabfifaktaastaqufnlætrfins sa ldktfakak inkstdktas ak tnmn a` prniasn, parlftfakmastdeàiar ra`difnkas ma ldsd aktra `ds idktfmdmas ma raditfvns usdmds y mprnmuitns netakfmns.

_drd asta iäìu`n sa alpàdk tras lætnmns:



Lætnmn crdln d crdln: sf sa inkniak `ds idktfmdmas ma ldsd ak crdlns maraditfvns ak `d aiudifùk quìlfid, as pnsfeà hd``dr `ns crdlns ma prnmuitn quanetakmrä ak `d radiifùk. Dquì sa usdk `ds ldsds lnàiu`dras:

Ajalp`n:

5H5 + N5 5H5 N

¾Iuäktns crdlns ma dcud sa prnmuiak ink 36 c. ma hfmrùcakn>

_drd pnmar raspnkmar d pracuktd sa maea ak prflar ucdr varfbfidr qua d aiudiastæ ed`dkiadmd inrraitdlakta.

D inktfkudifùk sa idìu`dk `ds ldsds lnàiu`dras ma ds sustdkifds fkvnùirdmds`d pracuktd, dsì:

Idmd ätnln ma hfmrùcakn tfaka ukd ldsd dtùlfid ma 4c, yd qua idmdln`æiu`d ma hfmrùcakn tfaka mns ätnlns y a` inabfifakta la fkmfid qua

hdy mns ln`æiu`ds7 ak inksaiuakifd, ak tntd` hdy = ätnlns ma hfmrùcakn

iuyd ldsd inrraspnkma d = crdlns:

5X(4cX5)<=c

@d ln`æiu`d ma` dcud pnr su pdrta pasd 48c, puastn qua `ns mns ätnlnsma hfmrùcakn pasdk 5c y a` ma nxìcakn 42c qua d` suldr`ns md 48,parn d` fcud` qua ak a` idsn dktarfnr, hdy mns ln`æiu`ds, pnr `n qua `dldsd tntd` ma` dcud as 92c.

5X((4cX5)+42c)<92

@ns iäìu`ns vd`nras dktarfnras sfckfbfidk qua =c ma hfmrùcakn prnmuiak92c ma dcud. Æstd ra`difùk ma ldsd astaqufnlætrfid sa inknia inlnbditnr ukftdrfn.

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Dhnrd sa ra`difnkdk `ds idktfmdmas ma ldsd qua radiifnkdk ak `d rad`fmdm, ink `nbditnras ukftdrfns.

92cH5 N

=cH5

Lætnmn ln` d ln`: ak astns iäìu`ns `d ldsd sa idìu`d úkfidlakta ak tærlfknln`dras. Yfcufakmn ink a` lfsln ajalp`n:

@ns inabfifaktas astaqufnlætrfins snk aqufvdàktas d kúlarn ma lnàs ma idmdsustdkifd7 dsì, mns lnàs ma hfmrùcakn radiifnkdk ink ukd ln` ma nxìcakn, pdrd

prnmuifr mns lnàs ma dcud. Ak asta idsn a` bditnr ukftdrfn sa astdeàia aktra `dslnàs ma hfmrùcakn y `ds ma dcud:

Mns lnàs ma H prnmuiakta 5 lnàs ma H5N

Inln `ns iäìu`ns sa hdiak ak tærlfkns ln`dras, maea inkvartfrsa `d ldsd ma raditfvn d lnàs, dsì:

4ln`H5

5cH5

Bfkd`lakta sa ra`difnkdk `ds lnàs qua radiifnkdk ink a` bditnr ukftdrfn:

96.1ln`H5 *

Lætnmn ln`/crdln: inln sa vfn ak `ns idsns dktarfnras, as pnsfeà matarlfkdr a

< 334cH5 N

<96.1ln`H5

36cH5 *

36cH5 *

5ln`H5 N

5ln`H5

<96.1ln`H5 N



inabfifaktas astqufnlætrfins. Ak inksaiuakifd, as pnsfeà hdiar ra`difnkas crdlln` n ln`/crdln.

_nr ajalp`n: 5 lnàs ma H, prnmuiak 92c ma dcud, dsì:

96.1ln`H5*

5. UADI]FRN @ÌLF]A

¾@a hd pdsdmn d`cukd vaz qua d` prapdrdr uk D`gd-sa`tzar ak nidsfnkas raqufara difnkdr ldynr idktfmdm ma dcud, pnrqua kn tnmn a` lamfidlaktn sa lazi`d y radiifnkd ink a` dcud> Fkiùsn, ak ntrns idsns sa raqufara in`nidr ntrd pdstf``d ak dcud, pnrqua a` lamfidlaktn as fksubfifakta pdrd `d idktfmdm ma dcud.

@ns ajalp`ns dktarfnras sa maeak d` raditfvn `ìlfta. Ak tnmn prniasn sfalpra hde uk raditfvn qua astæ ak laknr idktfmdm (prnpnrifùk) ink raspaitn d`(ns) ntrn(s

D astd sustdkifd sa a inknia inln raditfvn ìlfta y sa idrditarfzd pnrqua sa inkla pnr inlpàtn, lntfvn pnr a` iud`, d` dcntdrsa brakd `d radiifùk, `flftdkmn `didktfmdm ma prnmuitn bnrldmn.

Ajalp`n:

5H5 + N5 5H5 N

41c ma H radiifnkdk ink 8 lnàs ma N7 ¾iuäktds lnàs ma dcud sa netfakak>

Hdstd a` lnlaktn as inlpàtdlakta masinknifmn iuä` ma `ns mns raditfvns as `ìlfta7 pnr a``n sa idìu`d d ldsd ma dcud prnmuifmd, ink idmd ukn ma ns raditfvy a` rasu`tdmn qua mæ laknr idktfmdm as a` inrraitn y a` raditfvn ink a` qua sa h

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92cH5N

5ln` H5

<344cH5N



prnmuiifùk ma dcud7 pnr a``n `d idktfmdm ma H5N bnrldmd as pnid.

Ak iudktn d` nxìcakn, æ` as a` raditfvn ak axiasn, n qua qufara maifr qua d` bfkd`fzd`d radiifùk hderä d`cn ma nxìcakn sfk radiifnkdr.

5ln`H5N

=cH5

5ln` H5N

4ln` N5

9. _QUAZD

_drtfakmn ma `d edsa ma qua kn tnmds `ds sustdkifds ink qua sa rad`fzdk radiifnkaquìlfids snk tntd`lakta purds, as flpnrtdkta takar ak iuaktd a` crdmn ma purazdma ns raditfvns ak ns iäìu`ns astaqufnlætrfins, yd qua kn tnmd d ldsd ma raditfvalpàdmd inrraspnkma d æ`.

Ajalp`n:

5H5 + N5 5H5N

¾Iuäktns crdlns ma dcud sa prnmuiak d pdrtfr ma 51c ma H d` 61% ma purazd>

Dktas ma idìu`dr a` dcud prnmuifmd sa maea astdeàiar `d idktfmdm rad` ma hfmrùcakn qua radiifnkù, yd qua a` pnriaktdja fkmfid qua a` 61% ma` raditfvn usdmn in-

<3.1ln`H5N41cH5*

8ln` N5* <42ln` H5N

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51c

4??%

@d idktfmdm ma hfmrùcakn qua radiifnkd as 59,8c y kn 51. Dhnrd sì as pnsfeà iiu`dr `d ldsd ma dcud bnrldmd

59.8cH5*

92cH5N

<54=.5c H5N

=. UAKMFLFAK]N MA UADIIFÙK N _NUIAK]DJA MA _UNMQIIFÙK

Ak `d rad`fmdm luihns bditnras inln `d talpardturd, id`fmdm y purazd ma `nsraditfvns, dbaitdk `d idktfmdm ma prnmuitn bnrldmn y luihns prniasns kn sa ajiutdk d` 4??%.

Ajalp`n:

¾Iuä` as a` pnriaktdja ma rakmflfaktn ma `d radiifùk sf sa prnmuiak 5?? crdlnma dcud, d pdrtfr ma 51c ma H>

5H5 + N5 5H5N

_drd pnmar matarlfkdr a` pnriaktdja ma rakmflfaktn as flpnrtdkta hd``dr a` raklfaktn taùrfin, qua inrraspnkma d` vd`nr ma dcud prnmuifmd sf d radiifùk sa àvdriden d` 4??%. Asta iäìu`n as a` lfsln ma `d idktfmdm ma prnmuitns y raditfvns:

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<59.31 <59.8cH561%*

=cH5



51cH5*92cH5 N

=cH5

5??cH5N*4??%

551cH5N

_rapdrdifùk ma cd`àtds ma ldktaquf``d:

4. _asa uk raifpfakta ma p`ästfin `flpfn.

5. In`nqua ak a` raifpfakta 5??c ma ldktaquf``d d talpardturd dlefakta, in21c ma dzúidr. Lazià hdstd qua kn sa dpraifak crulns ma dzúidr. _rabarfe`lakta usa dzúidr pdrd aspn`vnradr.

9. Dcracua pnin d pnin 2?c ma bæiu`d ma ldìz, lazi`dkmn inktfkudlakta.

=. Dôdmd 4=?c ma hdrfkd ak mns tdkmds ma 3?c idmd ukd, lazi`dkmn inkstdktlakta, hdstd netakar ukd ldsd `fsd y sfk crulns.

1. In`nqua 5?c ma d`lakmrds pfidmds y 5 iuihdrdmds ma ihfps ma ihnin`dta (aspdsn as npifnkd`).

2. _asa tnmn a` inktakfmn ma` raifpfakta y pnr mfbarakifd astdeàzid `d idktfmd

<551cH5N<4??% Uakmflfaktn ]aùrfin

<88.88 < 88.6% Uakmflfaktn ma radiifùk

5



3. Iuerd ukd edkmajd latä`fid ink pdpa` idìdkta n pdrdbfkdmn iuefartn ldktaquf``d. Ink dyumd ma ukd iuihdrd in`nqua ldsd snera `d edkmajd, m

jdkmn aspdifns prumaktas aktra `ds cd`àtds, puastn qua æstds vdk d iraiar i`d iniifùk.

8. Inifka ak uk hnrkn praidàktdmn d 41?¿I, murdkta 41 lfkutns n hdstd q`ds cd`àtds astæk àvalakta mnrdmds.

6. Maja rapnsdr `ds cd`àtds ak uk ùcdr sain y brasin. Qkd vaz brìds, pæsa`dastdeàzid a` pnriaktdja ma rakmflfaktn.

4?. Uaspnkmd `ds sfcufaktas pracuktds: ¾pnr quæ idlefd `d inksfstakifd ma d lds

¾a` idlefn qua niurra as uk idlefn bìsfin, quìlfin n `ns mns>

44. @d lajnr pdrta: ¡inlpdrtd `ds cd`àtds ink sus bdlf`fdras y/n inlpdôarns i`dsa!

4. A` dùlfkfn radiifnkd ink a` äifmn su`búrfin y prnmuia su`bdtn ma dùlfkfn l

hfmrùcakn cdsansn. Yf 5? crdlns ma dùlfkfn sa dmfifnkdk d ukd snùifùk q

inktakcd 441 c ma äifmn, rasua`vd:

d. Asirfed `d aiudifùk quìlfid ed`dkiadmd d pdrtfr ma `d fkbnrldifùk m

prneàld.

e. ¾Iuä` as a` raditfvn `ìlfta>

i. ¾Iuäktds lnàs ma hfmrùcakn sa bnrldräk>

m. ¾Iuäktns crdlns ma su`bdtn ma dùlfkfn sa bnrldräk>

3



a. ¾Iuäktns crdlns snerdräk ma` raditfvn ak axiasn>

9. A` i`nrurn ma tftdkfn (FR) radiifnkd ink dcud pdrd prnmuifr mfùxfmn ma tftdk

y äifmn i`nrhìmrfin.

d. Asirfed `d aiudifùk quìlfid ed`dkiadmd ma` prniasn quìlfin.

e. Yf inlfakzd ink 4= l` ma i`nrurn ma tftdkfn (FR) (m < 4,= Gc/@) ¾Tuæ ld

ma dcud, ak crdlns, sa raqufara pdrd ukd radiifùk tntd`>

i. ¾Tuæ idktfmdm ma prnmuitn sa netakmrä, sf dhnrd sa pdrta ma 9? l` m

i`nrurn ma tftdkfn (FR) y ?.?9 Gc ma dcud7 sf a` rakmflfaktn ma `d radiifù

bua ma` 68% y `d purazd00 ma `ns raditfvns snk ma` 8? y 31% raspa

tfvdlakta>

5. Ed`dkiaa ds sfcufaktas aiudifnkas pnr ùxfmn-ramuiifùk y i`dsfbfqua ds sfcufaktradiifnkas quìlfids:

d. IdI`5 + KdNH Id(NH)5 + KdI`

e. KN + N5 KN5

i. HcN Hc + N5

m. I2H45N2 + N5 IN5 + H5N

a. Kd + H5N Kd(NH) + H5

9. @d barlaktdifùk as uk prniasn quìlfin qua sa alp`ad ak `d a`denrdifùk m



eaefmds dìnhù`fids, inln a` vfkn y `d iarvazd.

I2H45N2 5I5H1NH + 5IN5

Cùinsd Atdkn`

=. Yf sa alpàdk 1??,=c ma cùinsd ¾iuäktn atdkn` sa netakmrä pnr lamfn

asta prniasn>

@d mfslfkuifùk ma `d idpd ma nznkn as uk tald luy praniupdkta aktra `dinlukfmdm ifaktìbfid y ak cakard` pdrd tnmns, puastn qua su mastruiifùkparlfta a` fkcrasn ma `ns rdyns u`trdvfnàtd (QR) ma` sn`, qua kn sù`n cakard

prneàlds ak `d pfa`, sfkn qua dmaläs idusdk a` marratflfaktn ma `ns pn`nYa iraa qua a` nznkn radiifnkd ink a` KN axpu`sdmn pnr `ns dvfnkas maprnpu`sfùk. @d radiifùk as:

N9 + KN N5+KN5

Yf ?.3=?c ma N9 radiifnkdk ink ?.23?c ma KN, ¾iuäktns crdlns

KN5 saprnmuifräk>, ¾iuä` inlpuastn as a` raditfvn ìlfta> Idìuà a` kúlarn ma lnma` raditfvn ak axiasn qua snerdräk ak a` prniasn.

4. @d radiifùk aktra a` snmfn y a` dcud prnmuia `d edsa ma` latd`, juktn ink a`

masprakmflfaktn ma hfmrùcakn ak bnrld cdsansd, inln sa luastrd d inktfkudifù

Kd(Y)+H5N(`) KdNH(di) + H5(c)

↕

↕

↕



5. Ink edsa ak astd fkbnrldifùk raspnkmd `ds sfcufaktas pracuktds:

@d aiudifùk inrraitdlakta ed`dkiadmd as:

d. K d ( Y ) + H5N(`) KdNH(di) + H5(c)

e. 5 K d ( Y ) +H5N(`) 5KdNH(di) +H5(c)

i. 5 K d ( Y ) +5H5N(`) 5KdNH(di) +H5(c)

m. K d( Y )

+5H5N

(`) KdNH

(di) +5H

5(c)

9. @d idktfmdm rad` ma snmfn qua radiifnkd as:

d. 51c e. 59.8c i. 55.6c m. 5?.1c

=. A` raditfvn `ìlfta ak asta prniasn as:

d. H5N e. KdNH i. H5 m. Kd

1. @d idktfmdm ak ln`as ma KdNH bnrldmns inrraspnkma d:

d. ?,65ln` e. 4,1=ln` i. 5,?4ln` m. 4,?9ln`

↕

↕

↕

↕



2. @d idktfmdm ak crdlns ma hfmrùcakn bnrldmn as:

d. ?,81c e. 4,?9c i. 4,6?c m. 5,54c

3. Yf ak `d rad`fmdm sa bnrldk 91c ma KdNH, a` rakmflfaktn ma `d radiifùk

inrraspnkma d`:

d. 4??%

e. 61% i. 6?% m. 81%



]ùlasa ukns lfkutns pdrd paksdr ma bnrld fkmfvfmud` snera `ds sfcufaktaspracuktds:

¾_nr quæ rdzùk ukd pfpatd ma cds kn astd``d>

¾Yf sa nprfla a` sprdy ma ukd enta``d ma parbula ak ukd asqufkd ma` sd`ùk, a`n`nr ma` parbula sa saktfrìd ak `d asqufkd npuastd> ¾_nr quæ>

¾Tuæ bnrld tfaka uk cds> ¾As if`ìkmrfin inln `d pfpatd ma cds> ¾V sf `d pfpatdbuard trfdkcu`dr n iudmrdmd>

¾Tuæ vn`ulak tfaka uk cds>

A` cds as uk astdmn ma `d ldtarfd qua sa idrditarfzd pnr `d pnid fktardiifùk y dtrd-iifùk aktra `ds ln`æiu`ds, hdifakmn qua æstds astæk luy sapdrdmds aktra sì.A` inlpnrtdlfaktn ma `ns cdsas sa axp`fid masma `d ]anrìd Ifkætfid Ln`aiu`dr:

Qk cds astä inlpuastn pnr ln`æiu`ds luy sapdrdmds ukds ma ntrds, ink mfstdkifdqua snerapdsdk `ds mflaksfnkas ma `ds pdrtìiu`ds inln td`.

@ds pdrtìiu`ds inkstftuyaktas ma ns cdsas sa luavak inkstdktalakta ak mfraiifnka

CdsasQkfmdm 3. Cdsas Yasfùk

8



`fsfnkak aktra sì ak ihnqua a`ästfins, puastn qua ds pdrtìiu`ds maspuæs ma d in`fsraentdk, lntfvn pnr a` qua kn hdy radiifùk aktra a``ds.

@ds ln`æiu`ds ak uk cds kn tfakak buarzds ma dtrdiifùk n rapu`sfùk aktra a``ds.

@d akarcìd ifkætfid ma uk cds mapakma ma `d talpardturd d `d qua sa akiuaktra.

A` vnùlak ma uk cds kn as mabfkfmn, yd qua `ds pdrtìiu`ds niupdk tnmn a` aspdimfspnkfeà ma` raifpfakta qua `ds inktfaka, sfk qua a``n flp`fqua radiifùk quìld`cukd.

@ns cdsas snk inlprasfeàs. Astd prnpfamdm inksfsta ak mfslfkufr a` aspdifn vdi

qua hdy aktra `ds ln`æiu`ds.

@ns cdsas dmnptdk `d bnrld ma` raifpfakta qua `ns inktakcd.

Maefmn d su edjd maksfmdm, a` prniasn ma mfbusfùk as läs räpfmn qua ak `ns ntrnastdmns.

_rasfùk ma `ns cdsas

Inln sa vfn ink `d ]anrìd Ifkætfid Lnàiu`dr, `ds pdrtìiu`ds ma uk cds kukid astqufatds7 d` inktrdrfn, a``ds sa luavak inkstdktalakta ihnidkmn ink pdrtìiu`ds cds y ma` raifpfakta ak a` qua a` cds sa akiuaktrd, ajarifakmn buarzds.

Inln mfihds buarzds (B) sa cakardk snera ukd suparbfifa (ärad), astds buarzds sa tmuiak inln prasfùk:

_ <

B

D



Qk ajalp`n ma `d prasfùk `n akinktrdlns d` vfdjdr. @ns nìmns snk `ns ùrcdkns maaquf`ferfn ma` iuarpn y snk luy saksfeàs d `ns idlefns ma prasfùk7 pnr a``n, uprflar sìktnld qua kns fkmfid qua `d prasfùk hd idlefdmn as dqua` maknlfkdmninln nìmn tdpdmn.

Ntrn ajalp`n as `d prasfùk dtlnsbærfid, quaas `d pras fùk qua ajaria `d dtlùsbard

snera `ns iuarpns y vdrìd sacúk a` sftfn ma `dtfarrd. @d ldynr prasfùk dtlnsbærfidsa akiuaktrd d kfva` ma` ldr y mfslfkuya ink `dd`turd, pdrd lamfr`d utf`fzdlns a` edrùlatrnfkvaktdmn ak 422= pnr Avdkca`fstd ]nrrfia`f, bìsfinftd`fdkn.

D kfva` ma` ldr, `d prasfùk lamfmd ak a` edrùlatrn sa à maknlfkd, ukd dtlùsbard ma prasfùk (4 dtl), y aqufvdà d:

4 dtl < 32 il Hc < 32? ll Hc < 32? tnrr. 4 dtl < 32? tnrr.

@d prasfùk ak `ns cdsas

as prnmuifmd pnr a` ihnqua

ma `ds ln`æiu`ds

ma` cds aktra sì y inktrd `ds pdram

ma` raifpfakta.

@ds ln`æiu`ds ma uk cds ihnidk aktra sì ink `ds

pdramas ma` raifpfakta iradkmn `d prasfùk.

Astd enta``d p`ästfid bua sa``dmd dd`turd ma =523 l., ùacn edjdmd dd`turd ma 53=9, y bfkd`lakta d ukd rd ma 9?1 l. _uama nesarvdrsa iùlidlefn ak `d prasfùk ma` dfra `d dp`d



Yf prasfùk as buarzd pnr ukfmdm ma ärad. Aktnkias:

_ < B/D < Mfkds/ il5 , Kawtnk/ l5 < _dsid`

A` _dsid` as ukd ukfmdm ma lamfmd ak a` Yfstald Fktarkdifnkd`

4 dtl < 4,?49x4?9 _dsidàs (_d)

Ajalp`n:

¾D iuäktns lf`ìlatrns ma lariurfn aqufvdàk: 9 dtlùsbards y 4 _dsid`>

@AVAY TQA UFCAK A@ INL_NU]DLFAK]NMA @NY CDYAY

@ay ma Enyà

Ak a` sfc`n XRFF a` Tuìlfin y Bf`ùsnbn erftäkfin Uneart Enyà astumfù a` inlpnrtdlfatn ma `ns cdsas, ra`difnkdkmn a` idlefn ma `d prasfùk brakta d` vnùlak, iudk`d idktfmdm ma pdrtìiu`ds y `d talpardturd ak `d qua sa hd``dk snk inkstdkt

Ak sus astumfns, Enyà ncrù matarlfkdr qua d prasfùk ma uk cds as fkvarsdlakta prnpifnkd` d su vnùlak7 as maifr, qua lfaktrds ukd dulaktd, `d ntrd maea mfslfku



_nr ajalp`n: ustam inca ukd jarfkcd, à quftd `d dcujd y suiifnkd dfra. Dhnrd, sf in`nid su mamn snera `d enid ma `d jarfkcd, nestruyakmn `d aktrdmd n sd`fmd ma` dfy alpfazd d edjdr a` ælen`n, sfk majdr sd`fr a` cds, varä qua a` vnùlak vd mflfkuyakmn, parn idmd vaz tfaka qua dp`fidr ldynr buarzd7 as maifr, ldynr prasfùk snera a` ælen`n pdrd sacufr inlprflfakmn a` cds. Yf quftd a` mamn räpmdlakta, a` sfstald raiupard su vnùlak fkfifd` y `d prasfùk mfslfkuy

]d` bakùlakn sfalpra as fcud` ak tnmns ns cdsas, ma dhì qua sa mfcd qua astd ra`difùk prsfùk/vnùlak sad inkstdkta. _nr a``n, pnmalns trdksbnrldr d aiudifùk dktarfnr ds



@ay ma Ihdràs

A` bìsfin brdkiæs Jdiquas Dàxdkmra Iasdr Ihdràs eusiù d ra`difùk ma` vnùlak intalpardturd, iudkmn `d prasfùk y `d idktfmdm ma ldsd parldkaiak inkstdk

Ink edsa ak sus astumfns astdeàifù qua `d ra`difùk R Rs ] as mfraitdlakta prnifnkd`, astn sfckfbfid qua sf ukd ma `ds mns vdrfdeàs dulaktd `d ntrd tdlefækhdia, n pnr a` inktrdrfn, sf ukd mfslfkuya, d ntrd tdlefæk n hdrä, yd qua d ra`disfalpra as inkstdkta.

Maspajdkmn, sa netfaka `d aiudifùk ma Ihdràs:



Asta inlpnrtdlfaktn sa ra`difnkd ink `d akarcìd ifkætfid, yd qua d` dulaktdr talpardturd, sa fkiralaktd a` lnvflfaktn ma `ds pdrtìiu`ds y ink æ` a` aspdifn quniupdk `ds pdrtìiu`ds.

@ay ma Cdy-@ussdi

Jnsaph @ufs Cdy-@ussdi ard uk bdkätfin ma ns c`nens darnstätfins y sa fktarasù pnr

astumfn ma `ns cdsas, iudkmn `d prasfùk y `d talpardturd vdrìdk, ldktakfakmn a`vn`ulak y `d ldsd inkstdktas.

Æsta quìlfin y bìsfin brdkiæs akinktrù qua, d` dulaktdr d talpardturd, sa fkiralak`d prasfùk7 pnr a` inktrdrfn, sf mfslfkuya `d talpardturd, `d prasfùk tdlefæk maidaak ukd ra`difùk mfraitdlakta prnpnrifnkd`:

@ns c`nens darnstätfins sa fkb`dk id`aktdkmn a` dfra

inktakfmn ak `d en`sd.



Maspajdkmn:

@ay ma Dvncdmrn

Ak 4844 a` ftd`fdkn Dldman Dvncdmrn pue`fiù uk astumfn ak a` qua axp`fid `d ra

ifùk fkharakta aktra a` vnùlak y `d idktfmdm ma pdrtìiu`ds, iudkmn `d ] y `d _ sinkstdktas. Ak a` astumfn di`drd qua `d ra`difùk aktra a` vnùlak y `ds pdrtìiu`dsmfraitdlakta prnpnrifnkd`:

A` bukifnkdlfaktn ma `ds n``ds d prasfùk sa

axp`fid ak pdrta ink astd ày. Yf efak dquì hdypærmfmd ma ldtarfd ak bnrld ma cds, `ns d`f-

laktns sa inifkdk maefmn d` fkiralaktn ma `d

prasfùk, pnr abaitns ma `d talpardturd.



@ay ma Ihdràs-Enyà n inlefkdmd

Inln yd sa hd astdeàifmn, `d prasfùk puama ra`difnkdrsa mfraitdlakta ink a` vnùlak y æsta d su vaz ink `d talpardturd. Uapdsdkmn, sa sdea qua a` vnùlak asfkvarsdlakta prnpnrifnkd` d `d prasfùk y mfraitdlakta prnpnrifnkd` d `d talpardturd, dsì:

Mfihd ra`difùk as ukd inkstdkta, aktnkias:

@ay ma `ns cdsas fmadàs

Uasulfakmn `ds àyas dktarfnras, takalns `n sfcufakta:

Inln puama varsa, `ds tras àyas tfakak ak inlúk d` vnùlak7 ak inksaiuakifdastds aiudifnkas puamak ra`difnkdrsa dsì:



D` fcud` qua ak `ds maläs àyas, astds ra`difnkas snk inkstdktas:

Mnkma U as `d inkstdkta ma `ns cdsas fmadàs.

Inln sa trdtd ma cdsas fmadàs, ns vd`nras pdrd rasn`var d aiudifùk y hd``dr a` vdma `d inkstdkta snk:

_rasfùk: 4dtl

Rnùlak: 55.=@

Lnàs (k): 4ln`

]alpardturd: 539G. A` ga`vfk as ntrd ukfmdm ma lamfmd pdrd `d talpardturd y saidìu`d ink `d sfcufakta aiudifùk:

Maspajdkmn ink `ns vd`nras kulærfins `d aiudifùk ma cdsas fmadàs sa tfaka:

Uaiuarma qua `d ra`difùk ma astns bditnras as inkstdkta7 ma dhì `d rdzùk pnr `d isa idìu`ù a` vd`nr ma U.

Inkiùyakmn, `d aiudifùk ma `ns cdsas fmadàs as fcud` d:

4dtl * 55.=@

4ln` * 539G<?.?89 dtl.@

ln`.G



Astd aiudifùk sa alpàd iudkmn tnmns `ns bditnras astäk ra`difnkdmns aktra sì.

_drd kn n`vfmdr a` nrmak ma `d aiudifùk, puama utf`fzdr astd dyumd:

_ R < k U ] _dtns Rn`dkmn fcud` d` Kúlarn ma Udtnkas ]rntdkmn

- Iäìu`ns ma maksfmdm: maspajdkmn d aiudifùk ma ns cdsas fmadàs as pnsfe

matarlfkdr `d ldsd, a` pasn lnàiu`dr y maksfmdm ma ukd sustdkifd:

Mnkma l as `d ldsd n idktfmdm ma cds qua fktarvfaka ak a` prniasn y L su ldsdlnàiu`dr:

Uainrmdkmn qua:



Mnkma m as `d maksfmdm ma `d sustdkifd, dsì `d aiudifùk quamd:

@ay ma Md`tnk ma `d _rasfnkas _drifd`as

A` dfra, pnr ajalp`n as a` rasu`tdmn ma ukd lazi`d ma sustdkifds cdsansds inln nxìcakn, lnkùxfmn y mfùxfmn ma idrenkn, ùxfmns ma kftrùcakn y dzubra, vdpnr mdcud, latdkn, kftrùcakn y luihns läs. Ak inksaiuakifd, d prasfùk dtlnsbærfid as raspnksdef`fmdm ma ukd sn`d ma ds sustdkifds inkstftuyaktas ma` dfra, sfkn ma tnmd` lfsln tfalpn, yd qua idmd inlpuastn ajaria su prnpfd prasfùk.

Dsì, `d @ay ma Md`tnk kns mfia qua `d _rasfùk tntd` ma uk sfstald as d suldtnrfd

`ds prasfnkas pdrifd`as qua idmd cds ajaria snera æ`.



A` pasn ma `ds ln`æiu`ds y `ds nesarvdifnkas ma Crdhdl ]hnlds

Crdhdl ak 4858 nesarvdkmn `ds ln`æiu`ds ma `ns cdsas kntù qua:• @ns cdsas ink ln`æiu`ds pasdmds sa mfbukmak àktdlakta.

• @ns cdsas ink ln`æiu`ds `fvfdkds sa mfbukmak räpfmdlakta.

Crdhdl tnldkmn inln edsa astns pnstu`dmns y ntrds nesarvdifnkas inkiùyù:

‐@d va`nifmdm ma mfbusfùk ma `ns cdsas as fkvarsdlakta prnpnrifnkd` d `d rdìz iumrdmd ma sus ldsds n maksfmdmas“.

Bùrlu`d ma `d ày

Ak `d bùrlu`d dktarfnr nesarvdlns `ds va`nifmdmas (4-5) y `ds maksfmdmas (4-5) m

mns cdsas mfbaraktas:



Ak `d cräbfid dktarfnr, `ds ln`æiu`ds ma` sfstald ukn sa mfbukmak läs räpfmn qua ma` sfstald mns, yd qua prasaktdk ukd laknr maksfmdm.

4. @denrdtnrfn

A` abaitn ma `d prasfùk dtlnsbærfid.

Ldtarfd`as:

• @dtd ma cdsansd vdiìd • _fkzds qua puamdk snstakar `d `dtd. • Laiharn n astubd

• Uaifpfakta latä`fin, p`ästfin n ma pnria`dkd.

_rniamflfaktn:

d. In`nqua ak d dtd ukd idktfmdm ma dcud qua kn supara ns 1il. ma d`tu dp`fidkmn `ns prfkifpfns ma `ns cdsas.

e. Yf d präitfid sa rad`fzd ak a` denrdtnrfn, utf`fia a` trìpnma y d ld``d ma dseapdrd id`aktdr. Ak su mabaitn usa `d astubd.

i. _rapdra a` raifpfakta latä`fin. Asta maea takar dcud subfifakta pdrd tdp`d `dtd läs n lakns hdstd uk iudrtn.

m. Iudkmn a` dcud astæ hfrvfakmn, tnla `d pfkzd y ink luihd praiduifvn`taa räpfmdlakta `d `dtd ak a` raifpfakta.

4



Dkä`fsfs:

d. ¾_nr quæ suiamfù asta bakùlakn>

e. Qsdkmn `d tanrìd ma `ns cdsas, ¾iùln axp`fid `n suiamfmn>

i. Uad`fia uk cräbfin ma `n qua prnedeàlakta a niurrfù d `d `dtd.

m. Yf kn sa rad`fzd räpfmdlakta a` prniamflfaktn ma vn`tadr `d `dtd,¾suiama a` lfsln abaitn>

5. Uasua`vd:

4. Qk tdkqua ma 4? ftrns ma ha`fn sa àkd d ukd prasfùk ma 41? dtlùsbards. ¾Iuäktc`nens ma jucuata ma 4.1? ftrns puamak sar fkb`dmns d ukd prasfùk ma 4 dtlùsbaink a` ha`fn ma` tdkqua> Yupnkcd qua kn hderä idlefn ma talpardturd ak tdkqua.

4. Qk tdkqua ma 4? `ftrns ma ha`fn sa `àkd d ukd prasfùk ma 41? dtlùsbard¾Iuäktns c`nens ma jucuata ma 4.1? `ftrns puamak sar fkb`dmns d ukd prasfùma 4 dtlùsbard ink a` ha`fn ma` tdkqua> Yupnkcd qua kn hderä idlefn mtalpardturd ak a` tdkqua.

5. A` vnùlak ma ukd luastrd ma cds d 5?¿I as 5,1 `ftrns. Yupnkcd qua `d pr

sfùk sa ldktfaka inkstdkta. d) ¾Iuä` as a` vnùlak ma` cds d 5??¿I> e) ¾D qutalpardturd (ak ¿I) sarä a` vnùlak ma 9 `ftrns> i) ¾D qua talpardturd (ak ¿Isarä a` vnùlak ma 4 `ftrn>

9. Qk cds tfaka ukd maksfmdm ma ?,135 c/`ftrn d 6?¿I y ukd prasfùk ma ?,1 dtl¾Iuä` as a` pasn lnàiu`dr ma` cds>

=. Qkd luastrd ma ?,9?? c ma uk `ìqufmn bua vdpnrfzdmd d 41?¿I. A` vdpnr niup

8



48? l` edjn ukd prasfùk ma ?,668 dtl. ¾Iuä` as a` pasn lnàiu`dr ma` `ìqufmn

1. A` ifdkurn ma hfmrùcakn, uk inlpuastn d`tdlakta vakaknsn, sa prapdrd ilarifd`lakta lamfdkta `d sfcufakta radiifùk rad`fzdmd d d`td talpardturd `d prasakifd ma uk idtd`fzdmnr.

IH= (c) + N5 (c) + KH9 (c) HIK (c) + H5N (c)

2. Ak a` euian rairadtfvn sa alpàd dfra inlprflfmn hdstd prnbukmfmdmas iaridkd 2? pfas. Iudkmn sa alpàd ukd lazi`d ma cdsas ``dldmd Kftrnx (qua inktfahdstd 92% ma N5) `ns euzns puamak parldkaiar d prnbukmfmdmas ma asta tfpnr uk parfnmn ldynr. Yfk aledrcn, pdrd masiakmar duk läs, maeak alpàlazi`ds aspaifdàs ma cdsas inln a` ]rflfx. Æstd as ukd lazi`d raspfrdtnqua inktfaka nxìcakn, ha`fn y kftrùcakn. Axp`fqua utf`fzdkmn `ns prfkifpfns `ns cdsas `ds fkbnrldifnkas dktarfnrlakta lakifnkdmds.

3. Qstam tfaka uk c`nen tntd`lakta a`ästfin ink uk vnùlak ma 1 ftrns. Axp`fqtras bnrlds mfbaraktas ak ds iudàs pnmrìd dulaktdr a` vnùlak ma mfihn c`ndp`fidkmn `ns prfkifpfns ma `ns cdsas.

Qkd bdlf`fd vfdjù ma Idrtdcakd d Encntä. D` `àcdr `ns kaulätfins ma` dutnlùvfsa astd``drnk sfk axp`fidifùk dpdrakta, pnr a``n hfifarnk `d sfcufakta `fstd ma pnsef`fmdmas pdrd axp`fidr `n niurrfmn

D. Qkd tdihua`d ak a` idlfkn, qua pfkihù ukd ma `ds ``dktds

E. Fkb`drnk `ds ``dktds d` läxfln ak Idrtdcakd

I. Qk huain

M. A` euak i`fld d` `àcdr d Encntä



4. @d axp`fidifùk dmaiudmd as:

d. D

e. E

i. I

m. M

5. A` bakùlakn sa axp`fid pnr `d @ay ma:

d. Enyà

e. Ihdràs

i. Cdy @ussdi

m. Cdsas fmadàs

9. @ds vdrfdeàs qua fkbùyarnk ak `d axp`nsfùk ma `ds ``dktds buarnk:

d. Rnùlak y talpardturd

e. Rnùlak y idktfmdm ma ldtarfd

i. Rnùlak y prasfùk

m. _rasfùk y talpardturd

=. Inlakta ink sus inlpdôarns iùln fkbùyarnk ds vdrfdeàs pdrd qua ds `dktaxp`ntdrdk.



]ùlasa ukns lfkutns pdrd paksdr ma bnrlfkmfvfmud` snera `ds sfcufaktas pracuktds:

¾_nr quæ ds eaefmds cdsansds pfarmak a` cds ink läs rdpfmaz ak i`flds id`fakta

¾_nr quæ as pnsfeà sd`dr ukd snpd sfk dmfifnkdr läs sd`, sù`n avdpnrdkmn a` dcuma `d lfsld>

¾_nr quæ sa mfia qua ak a` ldr Luartn tnmn b`ntd>

¾_nr quæ iudkmn sa inla uk d`flaktn luy sd`dmn ukn sfakta sam>

¾_nr quæ sumdlns>

@ds snùifnkas sa i`dsfbfidk inln lazi`ds hnlncækads, inlpuastds ma mnsn läs sustdkifds, qua kn puamak fmaktfbfidrsa d sflpà vfstd y qua kn radi-ifnkdk aktra sì

_rnpfamdmas in`fcdtfvds ma `ds mfsnùifnkas

YnùifnkasQkfmdm 8. Ynùifnkas Yasfùk

6



Qkd mfsnùifùk n snùifùk as ukd lazi`d hnlncækad ma mns n läs sustdkifds7 aa``ds kn puamak mfstfkcufrsa sus inlpnkaktas. @ds snùifnkas snk edstdkta inlukasd mfdrfn takalns inktditn ink a``ds. A` dfra qua raspfrdlns, a` dcud ma ldr, a` dtùa` ernkia y a` nrn inkstftuyak ajalp`ns ma æstds. @ds snùifnkas astäk inlpuastpnr mns sustdkifds: a` snùtn y a` mfsn`vakta.

• A` snùtn as d sustdkifd qua sa mfsua`va. _nr n cakard`, astä prasakta ak lakidktfmdm qua a` mfsn`vakta.

• A` mfsn`vakta as a` lamfn ma mfsparsfùk ma` snùtn.

A]D_DY MA @D BNULDIFÙK MA QKD MFYN@QIFÙK

@ds mfsnùifnkas sa i`dsfbfidk sacúk a` kúlarn ma inlpnkaktas ak:

• Efkdrfds, bnrldmds pnr mns inlpnkaktas.• ]arkdrfds, bnrldmds pnr tras inlpnkaktas.• Iudtarkdrfds, bnrldmds pnr iudtrn inlpnkaktas.

@ds mfsnùifnkas prasaktdk idrditarìstfids aspaiìbfids inln ds sfcufaktas:

• Yu dspaitn as ukfbnrla, as maifr, qua sus inlpnkaktas kn sa puamak mfstfkcud sflpà vfstd.

• @ds pdrtìiu`ds kn sa praifpftdk ink a` trdksiurrfr ma` tfalpn iudkmn a` snùsa hd mfsua`tn tntd`lakta



• A` snùtn ma ukd mfsnùifùk puama astdr prasakta ak mfbaraktas prnpnrifnk

• @ds mfsnùifnkas, pnr `n cakard`, snk trdkspdraktas.

• @ns inlpnkaktas ma `ds mfsnùifnkas kn idlefdk su inlpnsfifùk quìlfid

• A` snùtn ma ukd mfsnùifùk puama pdsdr d trdvæs ma iud`qufar bf`trn, pnr n tdtn, kn sa puama sapdrdr pnr bf`trdifùk7 astn sa maea d` tdldôn ma `ds pdrtìiuqua `d inlpnkak.

@ds dktarfnras idrditarìstfids mfstfkcuak d `ds snùifnkas ma `ds lazi`ds hatarnckads, iuyd inlpnsfifùk kn as `d lfsld ak tnmns `ns puktns, y sus inlpnkaktaspuamak mfstfkcufr ink bdif`fmdm.

D` inksfmardr `d idktfmdm ma snùtn prasakta ak `d mfsnùifùk, sa puamak mfstfkcvdrfns tfpns ma snùifnkas sacúk su inkiaktrdifùk: fksdturdmds, inkiaktrdmds, sdrdmds y snera sdturdmds.

]fpns ma snùifùk

Qkd snùifùk mfùfmd as dqua``d ak d iud` d ink-

iaktrdifùk (idktfmdm) ma snùtn as ra`dtfvdlakta

edjd ak ra`difùk ink `d idktfmdm ma mfsn`vakta.

Ynùifùk inkiaktrdmd, as d qua inktfaka ldynr

idktfmdm ma snùtn qua ukd mfùfmd.

Ynùifùk sdturdmd, as dqua``d ak `d iud` `d

idktfmdm ma snùtn qua sa puama mfsn`var d ukd

talpardturd mdmd `àcd d` läxfln vd`nr.

Ynùifùk snerasdturdmd, as dqua``d qua inktfaka

ldynr idktfmdm ma snùtn ma n qua knrld`lakta

puama inktakar d ukd matarlfkdmd talpardturd.



_UN_FAMDMAY A@AI]UN@Ì]FIDY MA @DY YN@QIFNKAY

@ns snùtns sa puamak i`dsfbfidr ak mns crupns: dqua``ns qua d` mfsn`varsa snk idpdiama inkmuifr d aàitrfifmdm, `dldmns aàitrn`ftns y dqua``ns qua kn, kn aàitrn`ftns

D su vaz, `ns aàitrn`ftns puamak sar buartas n mæefàs y mapakma ma `d idpdifmdqua tfakak æstns pdrd mfsn`varsa, yd qua `ns prflarns, d` aktrdr ak inktditn ink asn`vakta, sa mfsnifdk pnr inlpàtn ak sus fnkas, lfaktrds qua ns sacukmns, sf efasa mfsua`vak, kn sa mfsnifdk d` 4??% .

Dhnrd as pnsfeà axp`fidr lajnr `ns rasu`tdmns netakfmns ak a` `denrdtnrfn ma `sasfùk 1:

I`dsfbfidifùk ma `ds sustdkifds ak mfsnùifùk diunsd

Mfsnùifnkas sù`fmds:

Qkd snùifùk kn sa inlpnka sù`n ma `ìqufmns mfsua`tns ak dcud. @ds snùifnkapuamak sar ma vdrfns tfpns:

Aàitrn`ftn buarta Aàitrn`ftn mæef` Kn aàitrn`ftn

HI` IH9INN (KH

5 )

5IN úrad

HKN9 HB IH

9NH Latdkn`

IH`N= HKN5 I5H1NH Atdkn` H5YN

= KH

9I

2H

45N

2 Cùinsd

KdNH H5N I

45H

55N

44 Ydidrnsd

Ed (NH)5

KdI` y inlpuastns

fùkfins



Inlpnkakta 4 Inlpnkakta 5 Astdmn bfkd` ma `d snùifùk Ajalp`ns

Cds Cds Cds Dfra Cds @ìqufmn @ìqufmn Cdsansds Cds Yù`fmn Yù`fmn Hfa`n

@ìqufmn @ìqufmn @ìqufmn Iarvazd Yù`fmn @ìqufmn @ìqufmn Dcud Yd`dmd Yù`fmn Yù`fmn Yù`fmn Hfarrn

Dukqua `ds mfsnùifnkas ak su ldynrìd snk `ìqufmds, axfstak snùifnkas qua sa aiuaktrdk ak astdmn sù`fmn7 æstds sa maknlfkdk dàdifnkas, ak `ds iudàs uk sù`fsa akiuaktrd mfsua`tn ink ntrn, n, dld`cdlds qua snk dàdifnkas ma latdàs inl`d p`dtd n a` astdôn ink a` lariurfn. ]nmds `ds lazi`ds ma sù`fmns, `ìqufmns n cds

mfsua`tns ak uk sù`fmn sa maknlfkdk mfsnùifnkas sù`fmds.

Ldtarfdàs inln a` ernkia (inera y astdôn), a` diarn (hfarrn, idrenkn, ldkcdkakìqua`, vdkdmfn), a` `dtùk (inera y zfki), snk ajalp`ns ma mfsnùifnkas sù`fmds.

Mfsnùifnkas ìqufmds

@ds mfsnùifnkas `ìqufmds snk `ds läs inknifmds y alpàdmds, sa bnrldk d` lazi

ukd sustdkifd sù`fmd, `ìqufmd n cdsansd ak uk `ìqufmn.

Ynùtn

Cds

@ìqufmn

Yù`fmn

Mfsn`vakta

@ìqufmn

@ìqufmn

@ìqufmn

Ajalp`n

Eaefmds cdsansds (mfùxfmn ma idrenkn ak dcud).

A` vfkdcra (äifmn diætfin ak dcud).

Yd` ak dcud.

Mfsnùifnkas cdsansds

Iudkmn sa mfùya ak uk lamfn cdsansn iud`qufar sustdkifd sù`fmd, ìqufmd n cdsansa bnrldk `ds snùifnkas cdsansds. Ya puamak knlerdr inln ajalp`ns ma asta tfma snùifnkas, a` dfra y a` cds qua sa usd ak `ds astubds.



Ynùtn Mfsn`vakta Ajalp`n

Cds Cds A` dfra.

@ìqufmn Cds I`nrnbnrln avdpnrdmn ak kftrùcakn.

Yù`fmn Cds Hfa`n sain sue`fldmn ak kftrùcakn.

BDI]NUAY TQA DBAI]DK @D YN@QEF@FMDM

Inln `d snùef`fmdm hdia rabarakifd d `d idktfmdm ma snùtn qua sa mfsua`va ak usn`vakta d ukd talpardturd aspaiìbfid, as pnsfeà d`tardr`d idlefdkmn `ds inkmfifnkas ak `ds qua sa prapdrdk `ds snùifnkas. Hdy mns bditnras qua fktarvfakak ak snùef`fmdm: `d talpardturd y `d prasfùk.

- ]alpardturd:

Iudkmn sa dulaktd d talpardturd ma uk sfstald, sa fkiralaktd d akarcìd ifkætfima` lfsln, maefmn d qua `ds pdrtìiu`ds sa luavak läs y ink ldynras va`nifmdmaAstn flp`fid qua as läs bäif` mfsn`var ukd sustdkifd sf `d talpardturd as aàvdmd7 aidlefn, `ds insds sa inlp`fidk d edjds talpardturds.

_nr `d lfsld rdzùk qua, d ldynr talpardturd, hdy ldynr lnvflfaktn ma `ds pdrtiu`ds, a` idsn dktarfnr kn dp`fid d ns cdsas. Uaiuærmasa qua æstns snk lakns maksnqua `ns `ìqufmns y sf `d talpardturd sa fkiralaktd, a` lnvflfaktn ma `ds pdrtìiu`cdsansds tdlefæk n hdrä, ma dhì qua a``ds sa asidpak ma d snùifùk d talpardturläs d`tds.

- _rasfùk:

@n qua sì bdvnraia `d snùef`fmdm ma uk cds as `d prasfùk. D ldynr prasfùk, ldyn



IN y IN5 dlefaktdàs, yd qua astns cdsas snk d`ldiakdmns pnr `ns niædkns y updrta ma a``ns ncrd radiifnkdr quìlfidlakta, bnrldkmn äifmn idreùkfin, d`tardk`ds inkmfifnkas kdturdàs ma` ainsfstald ldrfkn.

_UN_FAMDMAY IN@FCD]FRDY N IN@AI]FRDYYnk prnpfamdmas axtaksfvds, puastn qua mapakmak ma `d idktfmdm ma pdrtìiu`ds snùtn (kn ma su kdturdàzd), prasaktas ak `d mfsnùifùk y snk prnpfds ma snùifnkfksdturdmds (mfùfmds).

- Mfslfkuifùk ma `d prasfùk ma vdpnr:

]akcd ak iuaktd qua `ds pdrtìiu`ds qua inkbnrldk `d ldtarfd kukid astäk qufatak pdrtfiu`dr sf sa trdtd ma uk `ìqufmn n cds.

Ak a` idsn pdrtfiu`dr ma `ns `ìqufmns, sus pdrtìiu`ds sa luavak ak tnmds `ds mfraiikas y d`cukds ma `ds qua astäk ak `d suparbfifa `ncrdk asidpdr ma` sfstald ak bnrlma cds, lfaktrds qua `ds qua astäk ak astdmn cdsansn, pnr abaitns ma `d dmhasfùvua`vak d` astdmn `ìqufmn. Dsì, iudkmn `d va`nifmdm ma avdpnrdifùk as fcud` d `d inkmaksdifùk, sa tfaka `d prasfùk ma vdpnr ma uk `ìqufmn.

Iudkmn uk snùtn as kn vn`ätf`, dbaitd mfraitdlakta d prasfùk ma` mfsn`vakta, puaqua à mfbfiu`td `d `feardifùk ma pdrtìiu`ds ak bnrld cdsansd, d` hdear ldynr dmhsfùk, mfslfkuyakmn `d prasfùk ma vdpnr ma` sfstald.

- Aàvdifùk ma` puktn ma aeu``fifùk:

A` puktn ma aeu``fifùk as uk bakùlakn ak a` qua `d prasfùk ma vdpnr ma uk `ìqufas fcud` d `d prasfùk axtarkd. Ink `d dmfifùk ma uk snùtn kn vn`ätf` `d prasfùk vdpnr mfslfkuya. Ak inksaiuakifd, as läs mfbìif` `ncrdr fcud`dr astd prasfùk inkma `ns d`ramamnras, lntfvn pnr a` qua a` puktn ma aeu``fifùk sa fkiralaktd.

- Mfslfkuifùk ma` puktn ma inkca`difùk:

Ak `ns pdìsas mnkma kfavd, as usud` racdr `d kfava ink sd`, yd qua æstd sa marr



A` dcud y luihns ntrns ìqufmns sa akiuaktrdk luy astdeàs ak asta astdmn ma dcracdifùk, inln inksaiuakifd ma `ns puaktas ma hfmrùcakn. Æstns snk fktardiifnkaa`æitrfids qua sa prasaktdk aktra `ds ln`æiu`ds, inln inksaiuakifd ma `ds idrcdqua sa cakardk pnr abaitns ma `d dtrdiifùk ma `ns aàitrnkas ak uk ak`dia (aàitrnkacdtfvfmdm). @ns puaktas ma hfmrùcakn snk läs buartas d talpardturds dlefaktalaknras7 pnr asn, pdrd avdpnrdr a` dcud as kaiasdrfn idàktdr`d.

Iudkmn sa dmfifnkd uk snùtn, ak pdrtfiu`dr ukd sd`, ds ln`æiu`ds ma` ìqufmn hfmrtdk `d sd`, as maifr, `ds pdrtìiu`ds ma` `ìqufmn rnmadk `ns fnkas pnsftfvns y kacdtfvnma `d sd`, mfslfkuyakmn `d idktfmdm ma puaktas ma hfmrùcakn, hdifakmn läs mfbìisn`fmfbfidr a` `ìqufmn.

- _rasfùk nslùtfid:

@d ùslnsfs as uk bakùlakn prnpfn ma `ds lalerdkds iaù`dras, qua inksfsta ak pdsn sù`n ma dcud hdifd a` fktarfnr n axtarfnr ma `d iæù`d y sa ditfvd mapakmfakmma `d inkiaktrdifùk (idktfmdm) ma sustdkifds mfsua`tds ak a` iftnp`dsld iaù`dr.

Iudkmn `d iæù`d tfaka axiasn ma aàitrn`ftns ak a` iftnp`dsld, parlfta a` pdsn m

dcud d su fktarfnr, ink a` nejatfvn ma mfsn`var `ns fnkas y dsì mfslfkufr su inkiaktrdifùk, `àväkmn`d d kfvaàs knrldàs. _nr asta lntfvn as qua saktflns sam iudkmfkcarflns d`flaktns luy sd`dmns.

Ak a` idsn inktrdrfn, iudkmn hdy mabfifakifd ma fnkas ak a` iftnp`dsld, d iæù`d masd`fr dcud pdrd inkiaktrdr ns aàitrn`ftns. Asta bakùlakn as prnpfn ma d sumnrdifùIudkmn sumdlns, `d iæù`d kaiasftd parmar aàitrn`ftns pdrd qua æstns dyumak ak trdkslfsfùk ma ns flpu`sns karvfnsns, ak d inkvarsfùk ma ns kutrfaktas ak akarcy pdrd qua `ns lúsiu`ns puamdk lnvarsa. D` parmar aàitrn`ftns, `d iæù`d raqufafcud`dr d inkiaktrdifùk fkfifd` pdrd qua bukifnka inrraitdlakta, aktnkias ditfvd sd`fmd ma dcud, ak bnrld ma sumnr, pnr asn asta kn sù`n inktfaka dcud, sfkn dmaläsd`7 ma dhì su sdenr idrditarìstfin.



@NY IN@NFMAY

@ns in`nfmas snk lazi`ds fktarlamfds aktra `ds mfsnùifnkas y `ds suspaksfnkas. Ak umfsnùifùk, `ds pdrtìiu`ds ma snùtn astäk mfsparsds ma ldkard hnlncækad y kn subrsamflaktdifùk d` quamdr ak rapnsn, maefmn d qua æstds sa akiuaktrdk pdrifd`laukfmds d `ds ln`æiu`ds ma` sn`vakta. Ak `ds suspaksfnkas sì sa prasaktd samflaktdifùmaefmn d qua `ds pdrtìiu`ds snk ra`dtfvdlakta crdkmas.

@ds pdrtìiu`ds ma `ns in`nfmas snk läs crdkmas qua `ds ln`æiu`ds qua bnrldk mfsnùifnkas7 sfk aledrcn, kn sa prasaktd samflaktdifùk d` majdr`ns ak rapnsn.

@ns in`nfmas sa akiuaktrdk bnrldmns pnr mns pdrtas:

Bdsa mfsparsd: aqufvdà d` snùtn ak ds mfsnùifnkas7 astä inkstftufmd pnr ln`æiu`ds sak``ds n ln`æiu`ds cfcdktas inln a` d`lfmùk. _uama ditudr inln uk inkjuktn ma pdrtìiufkmapakmfaktas n qua sa dcrupdk pdrd bnrldr astruiturds ldynras y efak nrcdkfzdm

Bdsa ma mfsparsdkta: as d sustdkifd ak d iud` ds pdrtìiu`ds in`nfmdàs astäk mfstrfeufm

Yacúk a` astdmn bìsfin ak a` qua sa akiuaktrak d bdsa mfsparsd y a` lamfn mfsparsdk`ns in`nfmas puamak sar:

Alu`sfùk (diafta y dcud)

@fnbùefins n `fùbnens, iudkmn `ds pdrtìiu`ds mfsparsds tfakak pnid dbfkfmdmink a` lamfn mfsparsdkta. Astns in`nfmas snk pnin astdeàs, ajalp`n ma a``nsnk `ds alu`sfnkas, inln `d bnrldmd d` dcftdr ukd lazi`d ma dcud y diafta.

@fnbì`fins, iudkmn `ds pdrtìiu`ds mfsparsds tfakak ukd buarta dbfkfmdm ink a`

lamfn ma suspaksfùk, pnr ajalp`n, jdeùk mfsua`tn ak dcud.



I`dsas ma in`nfmas

FL_NU]DKIFD MA @NY IN@NFMAY

Luihns ma ns d`flaktns qua inksulflns inln a` quasn, d ldktaquf``d y d jdàdsnk in`nfmas.

@ds alu`sfnkas inkstftuyak lamfidlaktns, inln pnr ajalp`n `d Alu`sfùk ma Yintt.

Ak d fkmustrfd sa utf`fzdk pdrd d bderfidifùk ma iarälfids, p`ästfins, taxtfàs, pdpapa`ìiu`ds bntncräbfids, tfktds, ialaktns, cnlds, iuarns, ùerfidktas, jdenkas, fksaitfifmds dcrìin`ds y matarcaktas, aktra ntrns.

I`dsa ma in`nfma Bdsa mfsparsd Bdsa mfsparsdkta Ajalp`ns

Aspuld Cds @ìqufmn Irald edtfmd

Aspuld sù`fmd Cds Yù`fmn _famrd pùlaz

Darnsn` @ìqufmn Cds Kueas

Alu`sfùk @ìqufmn @ìqufmn Ldynkasd, àiha, prntnp`dsld iaù`dr

Alu`sfùk sù`fmd @ìqufmn Yù`fmn Tuasn, ldktaquf``d

Huln Yù`fmn Cds Huln, pn`vn ma` dfra

Yn` Yù`fmn @ìqufmn Akcrumn, jdàds

Yn` sù`fmn Yù`fmn Yù`fmn Ifartds dàdifnkas



_UN_FAMDMAY MA @NY IN@NFMAY

• Abaitn ]ykmd``: sa prasaktd iudkmn d trdvæs ma uk in`nfma sapuama var `d trdyaitnrfd ma uk rdyn ma ùz, maefmn d qua `dspdrtìiu`ds suspakmfmds `d rabàjdk.

• Lnvflfaktn Ernwkfdkn: masirfea a` lnvflfaktn inktfkunma `ds pdrtìiu`ds ma uk in`nfma.

• Dmsnrifùk: d` pnsaar ukd crdk ärad suparbfifd`, `ds pdrtìiu`ds

ma `ns in`nfmas dtrdak y ratfakak sustdkifds ak su suparbfifa.

• Mfä`fsfs: prniasn ma sapdrdifùk ma fnkas y ln`æiu`ds ma pdr-tìiu`ds in`nfmdàs d trdvæs ma lalerdkds salfparladeàs.

Mfsnùifnkas diunsds y su inkiaktrdifùk

Iudkmn ak ukd snùifùk a` mfsn`vakta as a` dcud, sa bnrld `ds mfsnùifnkas diuns_nr `n cakard`, ak asta tfpn ma snùifnkas a` snùtn sa akiuaktrd prasakta ak lakprnpnrifùk qua a` sn`vakta.

D`cukns ajalp`ns ma snùifnkas diunsds qua sa utf`fzdk d mfdrfn snk: `d àiha, rabrasins, a` idbæ fkstdktäkan ak dcud, a` vfkdcra, ns matarcaktas ìqufmns, ns ìqufm

pdrd `flpfdr vfmrfns, `d lfa`, ati.

Ynùef`fmdm

@d snùef`fmdm as `d prnpfamdm qua tfaka ukd sustdkifd ma mfsn`varsa n mfùfrsa ntrd. Masirfea `d idktfmdm ma snùtn qua as mfsua`td ak ukd idktfmdm ma sn`vak_drd lamfr `d snùef`fmdm ma ukd sustdkifd, sa idìu`d `d idktfmdm ak crdlns ma snùtn kaiasdrfn pdrd sdturdr ifak crdlns ma uk sn`vakta matarlfkdmn, d ukd ta



Ajalp`n:

88 crdlns ma kftrdtn ma snmfn sa mfsua`vak ak 4?? crdlns ma dcud d 5?ºI, pinksfcufakta, `d snùe`fmdm ma astd sd` as ma 88 c ma kftrdtn/4?? c ma dcud.

QKFMDMAY MA INKIAK]UDIFÙK

Iudktdtfvdlakta, d inkiaktrdifùk ma ds mfsnùifnkas sa axprasd dtakmfakmn d` tfpma ra`difùk qua axfsta aktra `ds idktfmdmas axditds ma snùtn y mfsn`vakta.

_nriaktdja: as `d ra`difùk ma ldsd n vnùlak aktra a` snùtn y a` sn`vakta atærlfkns ma pnriaktdja:

Ajalp`n:

Yf 91c ma KdI` sa mfsua`vak ak 4?1c ma dcud, ¾iuä` as a` pnriaktdja ma KdI` ak snùifùk>

Ynùifùk:

@ns mdtns sulfkfstrdmns pdrd a` ajarififn snk:

• Ynùtn: KdI`

• Idktfmdm ma snùtn: 91 c

• Mfsn`vakta: Dcud

• Idktfmdm ma mfsn`vakta: 4?1 c



• % ma KdI` ak `d snùifùk < >

_nr `n tdktn, `d mfsnùifùk prapdrdmd inktfaka ukd inkiaktrdifùk ma` 51% (ldldsd) ma KdI`. Asta vd`nr sfckfbfid qua ak `d snùifùk hdy 51c ma KdI` pnr id4??c ma snùifùk.

A` pnriaktdja vnùlak d vnùlak, sa alpàd pdrd axprasdr `ds inkiaktrdifnk

ma `ìqufmns. Ya mabfka inln a` vnùlak ma snùtn ak uk vnùlak ma 4?? l` snùifùk. Dsì, ukd snùifùk d` 41% ak vnùlak ma dìnhn` ak dcud, inktfaka l@ ma dìnhn` pnr idmd 4??l@ ma snùifùk (a`flfkdr 31l@ ma dcud). A` pnriaktvnùlak d vnùlak sa idìu`d utf`fzdkmn `d sfcufakta axprasfùk ldtalätfid:

Ajalp`n:

¾Iuä` as a` pnriaktdja vnùlak d vnùlak ma ukd mfsnùifùk qua inktfaka 1 lma dìnhn` ak 51 l` ma dcud>

Ynùifùk:

Mdtns ma` ajarififn.



• Yn`vakta: 51 l` (dcud)

Rnùlak tntd` ma `d mfsnùifùk:

51% l` ma dcud + 1 l` ma dìnhn` < 9? l` ma snùifùk.

_nr `n tdktn, a` pnriaktdja ak vnùlak ma dìnhn` ma ukd mfsnùifùk qua inktfak1 l` ma dìnhn` ak 51 l` ma dcud as 42,22%.

- Brdiifùk ln`dr (X): raprasaktd `d ra`difùk ma mns idktfmdmas salajdktas. Yaxprasd inln XD y sa idìu`d dsì:

D` bfkd`, `d suldtnrfd ma `ns pnriaktdjas ma idmd sustdkifd qua bnrld `d snùifùmaea sar fcud` d` 4??%

- Ln`drfmdm (L): hdia rabarakifd d `d idktfmdm ma lnàs ma snùtn prasaktaak uk `ftrn ma snùifùk:

- Ln`d`fmdm (l): as `d idktfmdm ma lnàs ma snùtn pnr idmd gf`ncrdln ma snvakta:

1 l` ma dìnhn`

9? l` ma snùifùk% ak Rnùlak < x 4?? < 42,22



- Knrld`fmdm (K): idktfmdm ma aqufvdàktas-crdln (Aq-c) ma snùtn ak uk fma snùifùk:

@ns aqufvdàktas snk mfbaraktas, mapakmfakmn ma `d sustdkifd, dsì:

• Aqufvdàkta-crdln pdrd äifmns:

_nr ajalp`n, idìuà `ns aqufvdàktas crdln ma 36c ma H5YN=:

• Aqufvdàkta-crdln pdrd hfmrùxfmns:

• Aqufvdàkta-crdln pdrd hfmrùxfmns:



• Aqufvdàkta-crdln pdrd sdàs u ùxfmns:

@denrdtnrfn ma snùifnkas:

d. Ùslnsfs

4. In`nqua 9?l@ ma ukd snùifùk ma d`lfmùk d` 1% ak uk Aràklayar m4??l@. Iuerd d enid ma` Aràklayar ink pdpa` ia`nbäk ma bnrld ukfbnrlama lnmn td` qua d` vn`tadr`n kn sa marrdla a` d`lfmùk (puama dldrrdr a

ia`nbäk ink dyumd ma uk iduihn).

5. Uapftd a` lfsln prniamflfaktn ak ntrn Aràklayar ma` 4??l@, parn avaz ma dmfifnkdr d`lfmùk, in`nqua 9?l@ ma Fsnmfka n iud`qufar dktfsæptfid edsa ma ynmn. _uama usdrsa @ucn` sf hdy ak a` `denrdtnrfn.

9. ]nla mns vdsns ma praifpftdmns ma 51?l@ y in`nqua ak a` prflar4??l@ ma `d snùifùk ma d`lfmùk d` 1%. D` sacukmn dmfifùkaà 4??l@ mFsnmfka.

=. Fktrnmuzid ma bnrld fkvartfmd a` Aràklayar ink a` d`lfmùk ak a` vdsqua inktfaka Fsnmfka.

1. Uapftd a` prniamflfaktn dktarfnr, parn astd vaz in`nqua a` Aràklayaink Fsnmfka snera a` vdsn ink d`lfmùk.

4



2. In`nqua ak uk tuen ma aksdyn 4?l@ ma snùifùk ma d`lfmùk y maja idsnera æstd uk ihnrrftn ma Fsnmfka. ]akcd prasakta d in`nrdifùk qua tnldsnùifùk pdrd qua puamd dkd`fzdr `n qua niurrfrä ink a` axparflaktn.

3. Fkfifa `d sfcufakta präitfid (prapdrdkmn snùifnkas) y iudkmn tarlfink a``d nesarva `ns idlefns qua sa prasaktdrnk ak `ns Aràklayars n `ns vdsns ma praifpftdmns.

8. Inlakta ink sus inlpdôarns ak pàkdrfd.

e. _rapdrdkmn snùifnkas:

6. Ldrqua 4? vdsns ma p`ästfin ink kúlarns.

4?. Dcracua d idmd ukn 5??l@ ma dcud.

44. Dmfifnka d idmd vdsn `ds sfcufaktas idktfmdmas ma rabrasin ak pn`vink dyumd ma ukd iuihdrftd:

Rdsn Idktfmdm ma rabrasin

4 @n qua injd ink `d puktd ma ukd iuihdrftd 5 Lamfd iuihdrdmftd 9 Qkd iuihdrdmftd = Qkd iuihdrdmftd y ukd pfzid läs

1 Iuihdrdmftd y lamfd 2 Mns iuihdrdmftds 3 Mns iuihdrdmftds y lamfd 8 9 iuihdrdmftds 6 = iuihdrdmftds4? 3 iuihdrdmftds



45. Lazià `ds snùifnkas hdstd `d läxfld mfsnùifùk7 kn fksfstd ink `dqua kn sa mfsua`vak.

49. _ruaea idmd ukd ma `ds lazi`ds y ink edsa ak a` sdenr matarlfka qu

tfpn ma snùifùk as. Dknta sus nesarvdifnkas ak `d sfcufakta tde`d:

Rdsn

45

9=1238

64?

Ydenr ]fpn ma snùifùk

Hd`à `ds sfcufaktas ukfmdmas ma inkiaktrdifùk:

4. Ya prapdrd ukd snùifùk qua inktfaka 51c ma KdI` ink 5??c ma dcudIdìuà d) `d brdiifùk ln`dr ma `ns inlpnkaktas y e) `d ln`d`fmdm ma `d snùifùk.

5 Idìuà a` pnriaktdja ma idmd ukd ma `ds sfcufaktas snùifnkas: d) 81

6



ma dzúidr ak 5??l@ ma snùifùk, e) 38c ma inera ink 4??c ma snùifùk,9? l@ ma atdkn` ak 51?l@ ma snùifùk.

9. Idìuà a` vnùlak ma snùifùk qua maea lamfrsa pdrd prapdrdr u

snùifùk ma dzúidr ma lasd (sdidrnsd I45H55N44) 5L, d pdrtfr ma 5?ma` dzúidr.

=. Idìuà a` pnriaktdja, `d L y `d K ma ukd snùifùk ma 98c ma KdI` 41?l@ ma snùifùk.

1. Idìuà a` pnriaktdja, `d L y `d K ma ukd snùifùk ma 65c ma H9_N= 51?l@ ma snùifùk.

Qk astumfdkta rad`fzd uk axparflaktn ak a` qua tnld tras vdsns mapraifpftdmns ink 4?? c ma dcud d 5?¿I y sfcua a` prniamflfaktn qua samasirfea d inktfkudifùk:

D` vdsn 4 a dcracd 41 c ma GI` y dcftd. @uacn, dcracd uk irfstd` dmfifnkdma GI` qua sa mfsua`va. D` vdsn 5 à dcracd 91 c ma GI` y dcftd. D` idenma uk tfalpn, dcracd uk irfstd` dmfifnkd` ma GI` qua ida d` bnkmn. Dvdsn 9 à dcracd 1? c ma GI`, id`faktd hdstd 3?¿I y `n majd rapnsdr pdrd

mfslfkufr d talpardturd aktdlakta. Maspuæs ma uk tfalpn, dcracd ukirfstd` dmfifnkd` ma GI`, a` iud` alpfazd d iraiar dc`nlardkmn d idktfmdmma snùtn qua astä ak axiasn.

@d tde`d qua lajnr raprasaktd `d inkiùsfùk ma` astumfdkta snera a` tfpnma snùifùk qua sa netfaka ak idmd ukn ma `ns vdsns as:



Rdsn Inkiùsfùk

4 @d snùifùk sa akinktrded sdturdmd pnrqua kn

mfsua`va läs sd`.

5 @d snùifùk as snerasdturdmd pnrqua kn mfsua`va läs

sd` y parlfta bnrldr irfstdàs.

9 @d snùifùk as kn sdturdmd pnrqua dúk puama mfsn`var

läs sd`.

Rdsn Inkiùsfùk




läs sd`.

9 @d snùifùk sa akinktrded sdturdmd pnrqua kn mfsua`

va läs sd`.

d.

e.



Rdsn Inkiùsfùk


läs sd`.


mfsua`va läs sd`.



Rdsn Inkiùsfùk

4 @d snùifùk as snerasdturdmd pnrqua kn mfsua`va lässd` y parlfta bnrldr irfstdàs.


mfsua`va läs sd`.


läs sd`.

i.

m.

Astumfdktas ]rdksbnrlalns,ink a` Yfstald Fktarditfvn.



]ùlasa ukns lfkutns pdrd paksdr ma bnrldfkmfvfmud` snera `ds sfcufaktas pracuktds:

¾Tuæ as `d cdstrftfs>, ¾quæ lamfidlaktns suaàs usdrsa pdrd trdtdr astd akbarla-mdm>, ¾iùln bukifnkdk quìlfidlakta asns bärldins>

¾_nr quæ `d Inid-In`d quftd a` ùxfmn ma `ns latdàs>

D`cukns ma ns prniasns quìlfins ma` iuarpn y d fkmustrfd sa àvdk d iden pnr lamma radiifnkas äifmn-edsa, inknifmds tdlefæk inln radiifnkas ma kautrd`fzdifùk

Inln vflns ak `d sasfùk 2, `ns äifmns snk sustdkifds inkbnrldmds pnr `d ukfùk m

uk hfmrncakfùk (H+) ink uk aàlaktn kn latä`fin, qua d vaias puama astdr dinlpdôdmn pnr nxìcakn.

Axfsta ntrd mabfkfifùk pdrd äifmns, inln dqua``ns qua d` aktrdr ak inktditn ink dcud sa fnkfzdk, `feardkmn prntnkas (H+) d` lamfn. Asta inkiaptn bua prnpuastpnr Drrhakfus, qufæk dmaläs pnstu`ù qua ukd sustdkifd eäsfid as idpdz ma fnkfzdrsak dcud, `feardkmn fnkas hfmrnxf`ns (NH)-4.

Äifmns, edsas y sdàs

pH y aquf ferfn quìlfinQkfmdm 8. Ynùifnkas Yasfùk

4?



• Buartas: sa mfsnifdk ak uk 4??% ak dcud.

• Mæefàs: sa mfsnifdk pdrifd`lakta.

Aquf`ferfn äifmn-edsa

_drd `d quìlfid, `ns aquf`ferfns sa mdk iudkmn `ds va`nifmdmas ma `ns prniasns sfcudàs. Ak a` idsn ma ukd radiifùk quìlfid, a` aquf`ferfn sa `ncrd iudkmn `d va

ifmdm ma `d radiifùk ma `ns raditfvns pdrd bnrldr prnmuitns as fcud` d `d va`nifmma radiifùk ma `ns prnmuitns pdrd bnrldr d `ns raditfvns. D asta tfpn ma radiifnktdlefæk sa às ``dld radiifnkas ravarsfeàs, yd qua kn vdk ak uk sn`n saktfmn, sfqua puamak mavn`varsa ma `ns prnmuitns d `ns raditfvns7 sa raprasaktdk ink bàihd ma mneà saktfmn n ink mns bàihds ak saktfmn inktrdrfn.

Qk ajalp`n ma asta tfpn ma radiifùk as `d qua sa md aktra `ns äifmns y `ds edsas

@d bàihd kns fkmfid qua a` sfstald astä ak aquf`ferfn y pnmalns raiurrfr d `ds ltalätfids pdrd hd``dr ukd inkstdkta ak `d qua asta bakùlakn sa md. D mfihn vdsa à inknia inln `d inkstdkta ma aquf`ferfn (G) y sa idìu`d dsì:



pH inln lamfmd ma `d difmaz

A` tærlfkn pH makntd ukd ukfmdm ma lamfmd ma `d inkiaktrdifùk ma `ns prntnkaak ukd snùifùk. Ink a` pH as pnsfeà matarlfkdr iuäkmn `ds sustdkifds snk äifmdeäsfids n kautrds7 pdrd a``n as flpnrtdkta astumfdr ak prflar ùcdr ukd sustdki

qua inktfaka tdktn prntnkas inln hfmrnxf`ns y qua as a` ldrin ma rabarakifd ma nvd`nras ma pH. Asta inlpuastn as a` dcud.

D pasdr ma sar uk aàitrn`ftn mæef`, a` dcud axparflaktd ukd paquaôd fnkfzdifùk ds

Ink edsa ak asta sfstald, `d inkstdkta ma aquf`ferfn ma dutnfnkfzdifùk ma` dcud a

Maefmn d qua sù`n ukd paquaôd idktfmdm ma` dcud sa fnkfzd, idsf qua `d inkiaktrifùk ma` dcud kn idlefd7 aktnkias:



Ak inksaiuakifd, iudkmn:

Crdifds d astds ra`difnkas ldtalätfids as qua sa hd `ncrdmn astdeàiar d` pH inlukfmdm ma lamfmd ma `d difmaz ma `ds sustdkifds y sa idìu`d dsì:

Ink edsa ak `n dktarfnr sa tfaka qua:

Ma fcud` bnrld qua ink a` pH, tdlefæk as pnsfeà hdiar d lfsld ra`difùk ldtaltfid ink `ns hfmrnxf`ns, aktnkias:

Dhnrd, sf sa dp`fid a` `ncdrftln kacdtfvn d` vd`nr ma `d Gw ma` dcud sa netfaka:



Dhnrd:

Lu`tfp`fqua pnr -4 d `ns mns `dmns ma `d fcud`mdm:

Asta vd`nr parlftfù astde`aiar ukd asid`d kulærfid ma pH, qua vd masma a` 4 hds4=, mnkma a` 3 as kautrn, dktas ma asa vd`nr as äifmn y maspuæs ma 3 as eäsfin:

Asid`d ma pH

pH äifmnpH kautrn

pH eäsfin

4 5 9 = 1 2 3 8 6 4? 44 45 49 4=



Kautrd`fzdifùk

@ds rdiifnkas ma kautrd`fzdifùk sa rad`fzdk aktra äifmn y eäsas. Ynk aspaifas radiifnkas ma sustftuifùk. A` äifmn i`nrhìmfin (HIF) radiifnkd ink a` hfmrùxfmn

snmfn (KdNH) pdrd prnmuifr i`nrurn ma snmfn (sd` kautrd):

Astds radiifnkas raifeak td` knlera, maefmn d qua `ns prnmuitns ma `d radiiftfakak pH kautrn, td` inln sa puama var ak a` ajalp`n, mnkma a` i`nrurn ma snm

y a` dcud snk sustdkifds kautrds.

Ak a` dkä`fsfs quìlfin sa sdea qua sa hd `ncrdmn kautrd`fzdr uk äifmn ink ukd ediudkmn a` fkmfidmnr ma pH (dmfifnkdmn d` äifmn dktas ma mdr fkfifn d `d radiifùidlefd ma in`nr.

@ns fkmfidmnras snk sustdkifds luy saksfeàs d `ns idlefns ma pH, puastn qua sidpdias ma ukfrsa d `ns prntnkas y `ns hfmrnxf`ns y mapakmfakmn d qufæk astæk u

mns, takmräk in`nrdifnkas luy aspaiìbfids7 pnr a``n snk fmadàs ak `ds vd`nrdifnkäifmn-edsa.

Fkmfidmnras

Aktra `ns fkmfidmnras äifmn - edsa läs usudàs takalns:

d. A` pdpa` tnrkdsn` dzu` y rnjn. e. A` pdpa` fkmfidmnr ukfvarsd`.

@ns fkmfidmnras snk sustdkifds quìlfids qua sa usdk pdrdinkniar d difmaz n edsfifmdm ma ukd snùifùk, a` lnlaktn

iudkmn sa rad`fzd ukd radiifùk ma kautrd`fzdifùk n puktnbfkd` ma ukd tftu`difùk.



m. A` dkdrdkjdmn ma latf`n. a. Dzu` ma erlntfln`. b. Rarma ma ernlnirasn`.

D`cukns fkmfidmnras sa puamak prapdrdr ak a` denrdtnrfn d pdrtfr ma vacatd`as inl`d in` lnrdmd, `d iaen``d rnjd n `d b`nr ma jdldfid harvfmds ak dcud.

@d pnsfef`fmdm ma lamfr a` pH kn sù`n tfaka vd`nr quìlfin. @d inkstdkifd ma` pH a`ns sfstalds efn`ùcfins as i`dva pdrd su bukifnkdlfaktn.

A` pH ma `d sdkcra as dprnxfldmdlakta 3,9 edjn matarlfkdmds inkmfifnkas, pnajalp`n, ink a` ld` bukifnkdlfaktn ma uk ùrcdkn, a` pH knrld` ma d sdkcra puam

varsa dbaitdmn. Yf a` pH as laknr qua 3,9 sa prnmuia `d difmnsfs latdeù`fid, ukakbarlamdm qua puama dbaitdr a` sfstald karvfnsn iaktrd` y inkmuifr d uk astdmma inld.

B n t n t n l d m d m a w f g f p a m f d

Ak `d ditud`fmdm axfstak `d-enrdtnrfns d`tdlakta aspa-ifd`fzdmns pdrd a` dkä`fsfs masdkcra

Yf pnr a` inktrdrfn, a` pH ma d sdkcra duklaktd, efak sad pnr pærmfmd ma jucn cästrfiak vùlftns raiurraktas, pnr `d fkcastfùk ma bärldins dktfäifmns n pnr dbaiifnkas

rfônk, puama prnmuifrsa d`id`nsfs latdeù`fid, dbaiifùk qua idusd `d mfslfkuifùma` rftln raspfrdtnrfn, aspdslns lusiu`dras y inkvu`sfnkas.

Astds mns d`tarkdtfvds ma pH iudkmn snk savards, puamak idusdr `d luarta.



Fkmfidmnras ma pH kdturdàs:

4. In`nidr 9?l@ ma atdkn` ak 9 vdsns ma praifpftdmns.

5. Dmfifnka ak a` vdsn ukn uk puôdmn inksfmardeà ma pætd`ns ma rnsds rnjds, a` vdsn mns irfsdktalns y ak a` vdsn tras ldrcdrftds.

9. Id`fakta d buacn edjn pnr 1 lfkutns idmd vdsn, hdstd qua a` dìnhn` sa in`nr

ink `ns pætd`ns ma `ds b`nras.

=. Enta `ns pætd`ns y cudrma `ns `ìqufmns. Kn n`vfma ldridr `ns vdsns pdrd qua sa inkbukmd ma fkmfidmnr.

1. ]nla 4? tuens ma aksdyn y dcracua:

D` tuen 4: 5?l@ ma jucn ma `flùk. D` tuen 5: 5?l@ ma vfkdcra. D` tuen 9: 5?l@ ma dcud. D` tuen =: 5?l@ ma matarcakta ak pn`vn mfùfmn. D` tuen 1: 5?l@ ma snùifùk sd`fkd. D` tuen 2: 5?l@ ma àiha. D` tuen 3: 5?l@ ma àiha ma ldckasfd. D` tuen 8: 5?l@ ma ihdlpú mfùfmn.

D` tuen 6: 5?l@ ma dzúidr mfsua`td ak dcud. D` tuen 4?: 5?l@ ma Inid-In`d.

2. D idmd tuen dmfifnka 4l@ ma` fkmfidmnr netakfmn ink ns pætd`ns ma `ds rns

3. Uapftd a` pdsn 1 y 2 ink a` fkmfidmnr ma `ns irfsdktalns y ùacn ink a` ma ldrcdrftds. @àka `d tde`d.

4?



Yustdkifd In`nrnrfcfkd`

Fkmfidmnr rnsds

Fkmfidmnrirfsdktalns

Fkmfidmnrtu`fpdkas

Jucn ma `flùk

Rfkdcra

Dcud

Matarcakta

Yd`

@aiha

@aiha ma ldckasfd

Ihdlpú

Dzuidr

Inid-In`d

8. Axp`fqua ink edsa ak `ns in`nras iùln ditúdk `ns tras fkmfidmnras.



4. Nesarva `d sfcufakta cräbfid ma `d asid`d ma pH y `ns raspaitfvns vd`nras md`cukds sustdkifds ma usn idsarn.

Asinjd ifkin sn`uifnkas ma usn inlúk,inln d`flaktns, `flpfdmnras, jdenkas,ati. Qeìqua`ds maktrn ma astd asid`d ma

pH y ra`difnka d`cukds ma sus prnpfamd-mas bìsids, inln in`nr sdenr, n vn`dtfmdmink su pH.

5. A` asquald luastrd a` pH ma d`cukds sustdkifds ma usn braiuakta inkn ihdlpú, dsì inln d`ckns b`ufmns efn`ùcfins inln `d sdkcra, fkmfidkmn pdrd idm

ukn, `d inkiaktrdifùk ma hfmrncakfnkas (WH+\).

Ink edsa ak `d bfcurd fkmfqua:

d. ¾Iuä` as `d sustdkifd läs äifmd> ¾Iuä` as su pH>

e. ¾Iuä` sustdkifd prasaktd uk pH kautrn>, ¾pnr quæ>

4?



i. ¾Tuæ pdsd ink `d inkiak- trdifùk ma hfmrncakfnkas d

lamfmd qua dulaktd a` pH>

m. ¾Iuä` as `d sustdkifd maldynr edsfifmdm>, ¾iuä` as supH>

9. Inlp`ata `d sfcufakta tde`d:

Yustdkifd Inkiaktrdifùk (L) pH pNH WH+\ WNH-\

HKN9 ?.?4

Lc(NH) 4?

HIF ?.51

KdNH 9

H5

YN=

4X4?-9



Uaspnkmd `ds pracuktds ink edsa ak `d sfcufakta fkbnrldifùk:

Murdkta a` latden`fsln iaù`dr sa bnrld IN5 qua as `feardmn d `d sdkcra y atrdkspnrtdmn pnr `ds vakds. D` sar uk ùxfmn äifmn, radiifnkd ink a` dcud pdrbnrldr äifmn idreùkfin, a` iud` fktarvfaka ak a` aquf`ferfn äifmn edsa sdkcuìkadpnr lamfn ma `ds sfcufaktas radiifnkas:

@d sfcufakta tde`d luastrd d`cukds mabfkfifnkas ma äifmns y edsas:

4. Ma diuarmn ink `d fkbnrldifùk dktarfnr, a` fnk efidrenkdtn, HIN9-4, ditú

ak `d aiudifùk:

d. 5, inln ukd edsa pnrqua tfaka ätnlns ma H ak su astruiturd.e. 9, inln ukd edsa pnrqua mnkd d` lamfn uk pdr ma aàitrnkas `feras.

Ernkstamy @nwry

Äifmn: sustdkifd idpdz ma mnkdr prntnkas (H+4)Edsa: sustdkifd idptdmnrd ma prntnkas

Äifmn: sustdkifd qua diaptd pdras ma aàitrnkas `ferasEdsa: sustdkifds mnkdmnrd ma pdras ma aàitrnkas `feras

@awfs



i. 9, inln uk äifmn pnrqua `feard d` lamfn prntnkas (fnkas H+).m. 5, inln uk äifmn pnrqua puama diaptdr prntnkas (fnkas H+) ma` lamfn.

5. A` pH as ukd lamfmd fkmfraitd ma `d inkiaktrdifùk ma prntnkas, fnkas H+, aukd sn`uifùk. Aktra ldynr as `d idktfmdm ma prntnkas, laknr as a` pH. Madiuarmn ink `ds aiudifnkas dktarfnras, a` fkiralaktn ma IN5 ak `d sdkcra:

d. Fkiralaktd `d inkiaktrdifùk ma prntnkas (fnkas H+) y mfslfkuya a` pH:e. Masp`dzd a` aquf`ferfn hdifd `d fzqufarmd a fkiralaktd `d inkiaktrdifùk ma

prntnkas.i. Fkiralaktd d inkiaktrdifùk ma prntnkas (fnkas H+) sfk lnmfbfidr a` aquf`ferfm. Mfslfkuya `d inkiaktrdifùk ma prntnkas (fnkas H+) y masp`dzd a` aquf`ferfn

hdifd `d maraihd.

9. Qk trdtdlfaktn utf`fzdmn knrld`lakta pdrd mfslfkufr d difmalfd latdeù`fin difmaz ma` p`dsld as a` sulfkfstrn ma` fnk efidrenkdtn HIN9

-4. Ma diuarmink ds aiudifnkas 4 y 5, a` trdtdlfaktn ma d difmalfd latdeù`fid inksfsta adulaktdr `d inkiaktrdifùk ma HIN9

-4ak a` aquf`ferfn pdrd:

d. Mfslfkufr `d inkiaktrdifùk ma IN5 y dulaktdr a` pH.

e. Masp`dzdr d `d fzqufarmd a` aquf`ferfn y dulaktdr a` pH.i. Kautrd`fzdr `d inkiaktrdifùk ma H+ y mfslfkufr a` pH.m. Dulaktdr `d inkiaktrdifùk ma H5N y mfslfkufr a` pH.



Efe`fncrdbìd

• Drfds _äaz, Harkdkmn. 463=. Cuìd mfmäitfid pdrd a``denrdtnrfn ma quìlfid fknrcäkfid. Qkfvarsfmdm Kdifnkd` maIn`nlefd. Mapdrtdlaktn ma Tuìlfid. Encntä

• Edenr, Jnsaph D`eart. 4689. Tuìlfid cakard` lnmarkd: ukdfktrnmuiifùk d `d Tuìlfid bìsfid y d `d Tuìlfid masirfptfvdsuparfnr (Fknrcäkfid, Nrcäkfid y Efnquìlfid) trdmuifmd,dmdptdmd y dlp`fdmd pnr J. Fedrz. Amftnrfd` Ldrìk. Encntä.

• Earkdrm, Ldurfia. 4661. Iursn ma quìlfid fknrcäkfid7 trd-muiifùk Vn`dkmd Brdkifs C. Amftnrfd` Inktfkaktd`, Læxfin.

• Idstrn Kdrväaz, Ydkmrd _dtrfifd. 5??1. _räitfids ma `denrd-tnrfn: quìlfid fknrcäkfid F. Qkfvarsfmdm Ydktfdcn ma Id`f,QYI. Id`f.

• Ihdkc Udylnkm (5??5). Tuìlfid. Am 3¿. Læxfin: LiCrdwHf``

• Lfkfstarfn ma Amuidifùk Kdifnkd` (5?45). Ydear 44¿ 5?45.Iudmarkf``n ma pracuktds sdear 44¿. In`nlefd: FIBAY. _p.=1 ’ 15.

• (5??=). Astäkmdras eäsfins ma inlpatakifds ak ifakifds kd-tur`as. Bnrldr ak ifakifds: ¡A` masdbìn! @n qua kaiasftdlnssdear y sdear hdiar. In`nlefd: Idrcrdphfis. _p. 55-59

• Nsnrfn U. y Cùlaz D (5??=). Axparflaktns mfvartfmns maquìlfid pdrd jùvakas. Lama``ìk: Qkfvarsfmdm ma Dktfnqufd.

• ]rfdkd Cderfa` (5??4). Tuæ bäif` as `d quìlfid. _räitfids ma`denrdtnrfn. Encntä: Bnkmn ma _ue`fidifnkas ma` CflkdsfnLnmarkn.





Ärad Bìsfid 4?



A s t ä k m d r a s e ä s f i n s

m a i n l p a t a k i f d s a k

B ì s f i d


I f a k i f d

, t a i k n ` n c ì d

y s n i f a m d m


•

A x p ` f i n ` d a s t r u i t u r d m a ` n s ä t n l

n s d

p d r t f r m a m f b a r a k t a s t a n r ì d s .

•

R a r f b f i n a ` a b a i t n m a p r a s f ù k y

t a l -

p a r d t u r d a k ` n s i d l e f n s q u ì l f

i n s .

•

U a d ` f z n i ä ` i u ` n s i u d k t f t d t f v n

s a k

i d l e f n s q u ì l f i n s .

•

A x p ` f i n ` n s i d l e f n s q u ì l f i n s m

a s m a

m f b a r a k t a s l n m a ` n s .

•

Q s n ` d t d e ` d p a r f ù m f i d p d r d m a t a

r l f -

k d r p r n p f a m d m a s b ì s f i d s y q u ì l f i d s m a

` n s a ` a l a k t n s .

•

I d r d i t a r f z n i d l e f n s q u ì l f i n

s a k

i n k m f i f n k a s m a a q u f ` f e r f n .

•

A x p ` f i n ` d n e t a k i f ù k m a a k a r c ì d

k u i ` a d r d p d r t f r m a ` d d ` t a r d i f ù k m a

` d a s t r u i t u r d m a ` ä t n l n


•

A s t d e ` a z i n r a ` d i f n k a s a k t r a ` d s m f b a r a k t a s

b u a r z d s q u a d i t ú d k s

n e r a ` n s i u a r p n s

a k r a p n s n n a k l n v f l f a k t n r a i t f ` ì k a n

u k f b n r l a y a s t d e ` a z i n

i n k m f i f n k a s p d r d

i n k s a r v d r ` d a k a r c ì d l

a i ä k f i d .

•

L n m a ` n l d t a l ä t f i d l a

k t a a ` l n v f l f a k t n

m a n e j a t n s i n t f m f d k n s d p d r t f r m a ` d s b u a r -

z d s q u a d i t ú d k s n e r a a

` ` n s .

•

A s t d e ` a z i n r a ` d i f n k a s a k t r a a s t d e f ` f m d m y

i a k t r n m a l d s d m a u k

n e j a t n .

•

A s t d e ` a z i n r a ` d i f n k a s a k t r a

` d i n k s a r v d -

i f ù k m a ` l n l a k t n ` f k a

d ` y a ` f l p u ` s n a k

s f s t a l d s m a n e j a t n s .

•

A s t d e ` a z i n r a ` d i f n k a s a

k t r a a ` l n m a ` n m a `

i d l p n c r d v f t d i f n k d ` y ` d ` a y m a ` d c r d v f t d -

i f ù k u k f v a r s d ` .

•

U a ` d i f n k n l d s d , m f s t d k i f d y b u a r z d m a

d t r d i i f ù k c r d v f t d i f n k d ` a k t r a n e j a t n s .

•

A x p ` f i n ` d t r d k s b n r l d i f ù k m a a k a r c ì d l a -

i ä k f i d a k a k a r c ì d t æ r l

f i d

U a ` d i f n k n ` d a s t r u i t u r d m a

` d s l n ` æ i u ` d s n r c ä k f i d s a

f k n r c ä k f i d s i n k s u s p r n -

p f a m d m a s b ì s f i d s y q u ì l f i d s

y s u i d p d i f m d m m a i d l e f n

q u ì l f i n .

A x p ` f i n ` d s b u a r z d s a k t r a

n e j a t n s i n l n f k t a r d i i f n k a s

m a e f m d s d ` d i d r c d a ` æ i t r f i d

y d ` d l d s d .

Q t f ` f z n l n m a ` n s e f n ` ù c f i n s ,

b ì s f i n s y q u ì l f i n s

p d r d

a x p ` f i d r ` d t r d k s b n r l d i f ù k y

B d i t n r a s m a n r c d k f z d

i f ù k

¾ I ù l n m a l u a s t r n ` n d p

r a k m f m n >


¾ D q u æ

q u a r a l n s

` ` a c d r >



A s t ä k

m d r a s e ä s f i n s m a i n l

p a t a k i f d s a k B ì s f i d ( i n k t f k u d i f ù k )

•

N e s a r v n y b n r l u ` n p r a c u k t d s a s p a i f b f i d s s n e r a d p ` f i d i f n k a s m a t a n

r ì d s i f a k t ì b f i d s

•

B n r l u ` n h f p ù t a s f s i n k e d s a a k

a ` i n k n i f l f a k t n i n t f m f d k n , t a n r ì d s y l n m a ` n s i f a k t ì b f i n s

•

F m a k t f b f i n v d r f d e ` a s q u a f k b ` u y a

k a k ` n s r a s u ` t d m n s m a u k a x p a r f l a k t n

•

_ r n p n k c n l n m a ` n s p d r d p r a m a

i f r ` n s r a s u ` t d m n s m a u k a x p a r f l a k t n

•

U a d ` f z n l a m f i f n k a s i n k f k s t r u l a k t n s y a q u f p n s d m a i u d m n s

•

U a c f s t r n l f s n e s a r v d i f n k a s y r a s u ` t d m n s u t f ` f z d k m n a s q u a l d s , c r ä b f i n s y t d e ` d s

•

U a c f s t r n l f s r a s u ` t d m n s a k b n r l

d n r c d k f z d m d y s f k

d ` t a r d i f ù k d ` c u k

d

•

A s t d e ` a z i n m f b a r a k i f d s a k t r a m a

s i r f p i f ù k , a x p ` f i d i f ù k , y a v f m a k i f d

•

A s t d e ` a z i n m f b a r a k i f d s a k t r a l

n m a ` n s , t a n r ì d s , ` a y a s a h f p ù t a s f s

•

U a i n k n z i n ` n s d p n r t a s m a i n k n i f l f a k t n s m f b a r a k t a s d ` i f a k t ì b f i n

•

U a i n k n z i n q u a ` n s l n m a ` n s m a ` d i f a k i f d i d l e f d k i n k a ` t f a l p n y q u a v d r f n s p u a m a k s a r v ä ` f m n s s f l u ` t ä k a d l a k t a .

•

I u f m n , r a s p a t n , y a x f j n r a s p a t n

p n r l f i u a r p n y p n r a ` m a ` d s m a l ä s p a r s n k d s

•

] n l n m a i f s f n k a s r a s p n k s d e ` a s

y i n l p d r t f m d s s n e r a l f s a x u d ` f m d m

•

D k d ` f z n i r ì t f i d l a k t a ` n s p d p a ` a s t r d m f i f n k d ` a s m a c æ k a r n a k k u a s t r d i u ` t u r d i n k r a s p a i t n d ` d s a x u d ` f m d m y ` d r a p r n -

m u i i f ù k

•

] n l n m a i f s f n k a s s n e r a d ` f l a k t d i f ù k y p r ä i t f i d m a a j a r i f i f n q u a b d v n r a z i d k l f s d ` u m

•

A x p ` f i n d p ` f i d i f n k a s t a i k n ` ù c f i d s m a ` l n m a ` n

m a l a i ä k f i d m a b ` u f m n s

•

D k d ` f z n a ` p n t a k i f d ` m a ` n s r a i u r s n s k d t u r d ` a s a k

` d n e t a k i f ù k m a a k a r c ì d p d r d

m f b a r a k t a s u s n s .

•

A s t d e ` a z i n r a ` d i f n k a s a k t r a a ` m a p n r t a y ` d s d ` u m

b ì s f i d y l a k t d ` .

•

A x p ` f i n i d l e f n s q u ì l f i n s

a k ` d i n i f k d , ` d

f k m u s t r f d y a ` d l e f a k t a

•

D r c u l a k t n ` d f l p n r t d k i f d m a ` d s l a m f m d s m a

p r a v a k i f ù k m a ` a l e d r d z n y m

a ` d s a k b a r l a m d -

m a s m a t r d k s l f s f ù k s a x u d ` a k a

` l d k t a k f l f a k t n

m a ` d s d ` u m f k m f v f m u d ` y i n ` a i

t f v d .


I f a k i f d ,

t a i k n ` n c

ì d

y s n i f a m d m



F m a k t f b f i n d p ` f i d i f n k a s m a

m f b a r a k t a s l n m a ` n s e f n ` ù -

c f i n s , q u ì l f i n s y b ì s f i n s a k

p r n i a s n s f k m u s t r f d ` a s y a k

a ` m a s d r r n ` ` n t a i k n ` ù c f i n 7

d k d ` f z n

i r ì t f i d l a k t a ` d s

f l p ` f i d i f n k a s m a s u s u s n s .

B d i t n r a s m a n r c d k f z d

i f ù k

¾ I ù l n m a l u a s t r n ` n d p

r a k m f m n >


¾ D q u æ

q u a r a l n s

` ` a c d r >

L a d p r n x f l n d ` i n -

k n i f l f a k t n i n l n

f a k t ì b f i n ( d ) k d t u r d `

M a s d r r n ` ` n

n l p r n l f s n s

p a r s n k d ` a s y s n i f d ` a s



Ì k m f i a

Qkfmdm 4. Ifkalätfid 96?

Yasfùk 4. Iudktfbfidifùk ma` lukmn bìsfin 96? Yasfùk 5. Lnvflfaktn F =41 Yasfùk 9. Lnvflfaktn ak a` p`dkn =95

Qkfmdm 5. Mfkälfid. A` lnvflfaktn y sus idusds ==3

Yasfùk =. Buarzd ==3

Qkfmdm 9. Astätfid =39

Yasfùk 1. Aquf`ferfn ma `ns iuarpns =39

Qkfmdm =. Akarcìd =88

Yasfùk 2. ]rdedjn, pntakifd y akarcìd

Qkfmdm 1. Hfmrnlaiäkfid 1?3

Yasfùk 3. Laiäkfid ma b`ufmns 1?3 Yasfùk 8. _räitfid ma hfmrnlaiäkfid 152

Qkfmdm 2. ]arlnmfkälfid 195

Yasfùk 6. Id`nr y talpardturd 195Yasfùk 4? _räitfid ma id`nr y talpardturd 1=3



Iudktfidifùk ma` lukmn bìsfin

Qkfmdm 4. Ifkalätfid Yasfùk

4

Ldcfd y lftn

A` sur ma Brdkifd as ukd tfarrd id`fzd suridmd pnr vfajns rìns y hnrd-mdmd pnr fkkulardeàs iuavds. Hdia 5?? sfc`ns kuastrns dktapd-sdmns, ns hnleras ma Irnldôùk, hfifarnk ldcfd ak asds crdkmasiuavds. @ns ùcdras sairatns ma` rftud` astäk `àkns ma ldckìbfinslurdàs pn`firnlns ma hnleras y dkfldàs. _fktdmns d `d ùz ma`ds älpdrds ma pfamrd d`flaktdmds ink crdsd, astds fläcakas snk`ns rastns ma `ns rftns läcfins ma idzd ma `d amdm ma pfamrd.

Jdlas Brdzar, ak `d rdld mnrdmd, hde`d ma `d ``dldmd ày ma `d sflf`ftum.‐Qk abaitn sa pdraia d su idusd“. Iudkmn a` erujn ma Irnldôùk drrnjdedsu `dkzd snera ukd fldcak pfktdmd ak `d pdram, sdeìd qua sf `d ldcfd ma`lnlaktn kn à bd``ded, a` dkfld` inkjurdmn sarìd idzdmn ink tnmd sacu-rfmdm. As ukd ldcfd sflpätfid qua prasupnka qua `ds insds ditúdk ukdssnera ntrds d mfstdkifd, d trdvæs ma ukd dbfkfmdm sairatd trdkslftfækmnsa`ns flpu`sns ma ukd d ntrd. _draia qua axfsta tdlefæk ntrd i`dsa ma ldcfdsflpätfid, ra`difnkdmd ink `d ày ma` inktditn, ‐`ds insds qua hdk astdmn

ak inktditn d`cukd vaz, inktfkúdk ditudkmn aktra sì. Qk ldknjn ma pa`nn uk pamdiftn ma uôd as tnmn `n qua kaiasftd a` erujn pdrd astdeàiar `dinktfkufmdm y, d pdrtfr ma æstd, a` inktrn`.

A` masan ma fkbùfr ak `d kdturdàzd idprfihnsd, yd sad vakifakmn a` nsn ma`ds idvarkds n inksfcufakmn uk eakabfifn mfbìif`, pdraia edstdkta huldkn.‐Euakd suarta“, ‐Iruzd ns mamns“, ma iud`qufar bnrld d ldcfd akvn`vfù d`lukmn praifvf`fzdmn flprackù tnmds `ds iu`turds hfstùrfids y sa ldktfaka



Qkd vaz rad`fzdmd `d àiturd, raspnkmd `ds sfcufaktas pracuktds:

_racuktds Uaspuastds¾D`cukd vaz hd haihn ldcfd > ¾Tuætfpn ma ldcfd>Masirfed pdsn d pdsn iùln hfzn`d ldcfd.¾Iraa qua asd ldcfd astä ra`difnk-dmd ink d ifakifd> ¾Ma quæ bnrld>¾Tuæ axparflaktns inknia qua sa

puamak ra`difnkdr ink `d ldcfd>Axprasa ink sus pd`derds `n quaaktfakma iudkmn a` dutnr dbfrld:‐@d ifakifd y `d ldcfd snk aspìrftusma `d lfsld bdlf`fd“.

Fktrnmuiifùk d `d bìsfid

Masma hdia luihn tfalpn ds parsnkds hdk trdtdmn ma aktakmar a` pnr quæ ma d kdtu-

rdàzd y ns bakùlakns qua ak a``d sa nesarvdk: a` pdsn ma ds astdifnkas, ns bakùlakns

i`flätfins, a` lnvflfaktn ma ns iuarpns y ma ns dstrns, ati. @d huldkfmdm sfalpra sahd pracuktdmn snera `d bnrld ma fktardiifùk ma `ds pdrtìiu`ds, y snk luihds `ds axp`f-

idifnkas qua masma `d ifakifd y `d bf`nsnbìd sa akiuaktrdk d` raspaitn. Dsì, `ns bf`ùsnbns

crfacns astdeàiìdk dkd`ncìds aktra a` iuarpn huldkn, sus ra`difnkas y `ns bakùlakns

kdturdàs, `n iud` às parlftìd hdiar pramfiifnkas. _nr ajalp`n, a` ldckatfsln pnmìd

masirfefr `d ldkard inln `ds parsnkds sfaktak dtrdiifùk aktra a``ds y qua kn as fcud

pdrd tnmds. @ns inkiaptns ma dtrdiifùk y rapu`sfùk ardk iaktrdàs ak d ifakifd pra- dr

Bukmdlaktn taùrfin



B n t n

t n l d m d m a S f g f l a m f d

Drfstùtaàs bukmdlaktù d bìsfid ak iudtrn prfkifpfns eäsfins: d kacdifùk ma` vdiìn

`d axfstakifd ma ukd idusd abfifakta ak tnmn idlefn, a` prfkifpfn ma `d diifùk

pnr inktditn, y `d axfstakifd ma uk prflar dcakta fklùvf`. ]dlefæk i`dsfbfiù alnvflfaktn kdturd` y vfnàktn, mdkmn axp`fidifùk d `n qua sa pnmìd nesarvd

ak asa tfalpn, y dbfrlded qua a` lnvflfaktn surcìd ma d kdturdàzd ma` nejatn

sf `d kdturdàzd ma æsta ard astdr qufatn, parldkaiìd qufatn, n ak idsn ma `ns

nejatns iaàstas, astdr ak lnvflfaktn. A` lnvflfaktn vfnàktn ard cakardmn pn

ukd buarzd qua sa flpnkìd d uk nejatn pdrd qua æsta sa lnvfard.

Ak d ditud`fmdm, tnmdvìd as flpnrtdkta a` lnvflfaktn ma d ldtarfd y a` sdeaa` pnr quæ sa inlpnrtd ma matarlfkdmds ldkards. _nr asn, pdrd inlprak

mar `d bìsfid y a` inlpnrtdlfaktn ma `ds insds qua nesarvdlns y ink `ds qua

fktarditudlns mìd d mìd, as euakn inlprakmar a` lnvflfaktn ma uk nejatn

y iùln sa masirfea. Iudkmn sa nesarvd uk nejatn idlefdr ma ukd pnsfifùk

d ntrd, n cfrdr ak uk tfalpn matarlfkdmn, sa mfia qua astä ak lnvflfaktn

Yf ak asa tfalpn sa inksarvd ak su pnsfifùk, maiflns qua astä ak rapnsn7

sf sa luava ink va`nifmdm inkstdkta (pnr ajalp`n, `ns iuarpns iaàstas), sa

maea sar iufmdmnsn pdrd mabfkfr sf uk nejatn astä ak rapnsn n ak lnvflfaktn

_drd astumfdr a` lnvflfaktn ma

`ns iuarpns, àd a` sfcufakta idsn

y nesarva a` vfman:

Fldcfka qua astä ak ukd mfsinta-

id7 tnmds `ds vaktdkds astäk iarrd-

mds y pfktdmds ma kacrn7 `d puartd

tdlefæk astä iarrdmd, pnr n qua d

úkfid buakta ma uz as uk strnvar n

ùz rnentfzdmd uefidmd ak ukd ma



Knlera: ]d`àr 4: Lnvflfaktn y prneàlätfid.Murdifùk 4:5= lfkutns

Ma diuarmn d `n qua nesarvù, raspnkmd `ds sfcufaktas pracuktds

@d bìsfid as d ifakifd qua sa akidrcd ma` astumfn ma d ldtarfd, d akarcìd

ma` ukfvarsn y `d fktardiifùk aktra `ds lfslds7 astumfd `ds prnpfamdmas

ma `d ldtarfd, `d akarcìd, a` tfalpn, a` aspdifn y sus fktardiifnkas. @d

bìsfid astumfd pnr n tdktn uk dlp`fn rdkcn ma idlpns y bakùlakns kdtu-

rdàs, masma `ds pdrtìiu`ds suedtùlfids hdstd `d bnrldifùk y avnùifùkma` ukfvarsn, dsì inln `d lu`tftum ma bakùlakns kdturdàs intfmfdkns,

y ukn ma sus nejatfvns as masirfefr `ds rac`ds qua rfcak kuastrn ukfvarsn.

@d bìsfid as `d läs eäsfid y bukmdlaktd` ma tnmds `ds ifakifds. Astumfd

`d kdturdàzd ma dspaitns tdk aàlaktdàs inln a` lnvflfaktn, `ds

buarzds, `d ldtarfd, `d akarcìd, a` snkfmn, `d ùz y `d inlpnsfifùk ma `ns

ätnlns y sus dp`fidifnkas, ns iudàs hdk ajarifmn ukd crdk fkbùakifdak a` prncrasn ma `d snifamdm. Yfrva ma edsa d ntrds ifakifds läs aspa-

ifd`fzdmds inln `d quìlfid, `d efn`ncìd, d dstrnknlìd, `d taikn`ncìd, `d

fkcakfarìd, ati. @d quìlfid alpàd `ds àyas ma `d bìsfid pdrd astumfdr `d

bnrldifùk ma `ds ln`æiu`ds y `ds bnrlds präitfids ma trdksbnrldr ukds

d. ¾Iraa qua `d pa`ntd ak `d mfsintaid sa luava d` dzdr, n tfaka uk

pdtrùk ma lnvflfaktn>

e. ¾Tuæ hdrìd ustam pdrd sdear d qufæk à pacdrä `d pa`ntd ak `d

mfsintaid>

i. Yf tuvfard qua racfstrdr a` idlfkn qua sfcua d pa`ntd ma uk ucdr

d ntrn, ¾iùln `n hdrìd>



sustdkifds ak ntrds, ak `ds radiifnkas quìlfids. @d efn`ncìd, d su vaz,

mapakma ak euakd pdrta ma `d bìsfid pdrd pnmar axp`fidr luihns ma`ns prniasns qua niurrak ak `ns saras vfvns. @d dstrnknlìd raqufara

ma `ds àyas ma `d bìsfid pdrd axp`fidr a` lnvflfaktn ma `ns p`dkatds y

ntrns iuarpns iaàstas y `ns bakùlakns qua niurrak ak a``ns. @d dp`f-

idifùk ma `ns prfkifpfns ma `d bìsfid d `d snùifùk ma `ns prneàlds

taikn`ùcfins, tdàs inln `d inkstruiifùk ma amfbfifns, ldqufkdrfds,

vahìiu`ns, prniasns fkmustrfdàs, ati., hd mdmn ùcdr d `ds mfbaraktas

rdlds ma `d fkcakfarìd.

@d bìsfid as flpnrtdkta kn sù`n pnrqua kns dyumd d inlprakmar ns prn-

iasns qua niurrak ak `d kdturdàzd, sfkn tdlefæk pnrqua hd parlftfmn

masdrrn``dr tæikfids y lætnmns axparflaktdàs qua sa dp`fidk ak ukd

crdk vdrfamdm ma ditfvfmdmas huldkds. Edstd ink vfsftdr uk hnspftd`, uk

nesarvdtnrfn dstrnkùlfin, uk denrdtnrfn canbìsfin n latanrn`ùcfin, ukdfkmustrfd, ati., pdrd mdrsa iuaktd ma ns kularnsns aqufpns edsdmns ak

prfkifpfns bìsfins qua sa utf`fzdk ak mfihns ùcdras.

@d bìsfid rasu`td asakifd` y sfrva ma dpnyn d ntrds ifakifds7 pnr a``n,

pnmalns aktakmar lajnr ntrds ifakifds sf dktas aktakmalns `d bìsfid.

_nr ntrd pdrta, ns inkiaptns bìsfins y sus ra`difnkas inkstftuyak d edsa

ma crdk pdrta ma` masdrrn``n taikn`ùcfin qua idrditarfzd d snifamdm. Qkdmaiudmn dprakmfzdja ma d ldtarfd parlftfrä inlprakmar astns bukmd-

laktns, dsì inln d`cukds inksaiuakifds ma asta masdrrn``n, bdvnraifakmn

ukd rabàxfùk irìtfid y bukmdlaktdmd snera d fkifmakifd ma` masdrrn``n

taikn`ùcfin ak a` lamfn kdturd`, snifd` y dlefaktd`.



Yf ukn ma `ns nejatfvns bukmdlaktdàs as masiuerfr `ds rac`ds qua rfcak

kuastrn ukfvarsn, maealns alpazdr pnr fkvastfcdr n qua suiama d kuastrn

d`ramamnr7 astn as, pnkarkns ak inktditn ink a` lukmn axtarfnr, y astn `n

hdialns d trdvæs ma kuastrns saktfmns.

_drd a``n utf`fzdlns `ns inkiaptns ma lamfmd, yd qua astns kns parlftak

astdeàiar ra`difnkas iudktftdtfvds pdrd `d masirfpifùk ma` sfstald bìsfin.

Aktra `ds ldckftumas bfsids takalns:

_drd axprasdr ds mfbaraktas lamfifnkas rad`fzdmds, d bìsfid utf`fzd a` Yfstald

Fktarkdifnkd` ma Lamfmds.

A` Yfstald Fktarkdifnkd` ma Lamfmd

Masma `ds æpnids prflftfvds, a` sar huldkn tuvn `d kaiasfmdm ma lamfr: lamfr `nkcftumas, lamfr ldsd, lamfr tfalpn, ati. V `d prflard harrdlfaktd n fkstrulaktnma lamfifùk bua su iuarpn, `d `nkcftum ma su pfa, ma su erdzn, ma sus ldkns n atdldôn ma sus mamns, qua à parlftìd `àvdr inksfcn su prnpfn pdtrùk ma lamfmd@ns idlefns ma ùkd, `d lfcrdifùk ma `ds dvas y `ns idlefns i`flätfins à prnpnr-ifnkdedk ukd fmad ma `d vdrfdifùk ma `ns mìds (lamfmd ma tfalpn)7 sa inlpdrdrnk`ds idktfmdmas ma pfamrds, rnids, rdlds, inkihds, ati., ink ntrns aàlaktns pdrdmatarlfkdr `d ldsd.



Ink a` pdsn ma` tfalpn, sa hfzn kaiasdrfn ukfbfidr sfstalds ma lamfmd qua parl

ardk `d inlarifd`fzdifùk ma prnmuitns aktra `ns puae`ns, `d matarlfkdifùk ma ä

ma tarrakns pdrd maldridr tarrftnrfns, `d murdifùk ma uk vfdja aktra mns ifumd

ati. Astds aktra ntrds, buarnk ds idusds prflnrmfdàs qua mfarnk pfa d d iradifù

uk sfstald fktarkdifnkd` ma lamfmd.

• @nkcftum: as `d ldckftum bukmdlaktd` pdrdlamfr mfstdkifds n mflaksfnkas ak a` aspdifn.

• Ldsd: sa utf`fzd pdrd masirfefr `d idktfmdm ma

ldtarfd qua pnsaa uk iuarpn.

• ]falpn: as uk inkiaptn mfbìif` ma mabfkfr7sa inksfmard inln ukd sarfa ma suiasns quaniurrak ak bnrld akidmakdmd sfalpra hdifddma`dkta. D`cukns n inksfmardk inln d axp`f-idifùk d d axfstakifd ma ukd iudrtd mflaksfùk._drd su lamfifùk, axfstak fkstrulaktns idmdvaz läs snbfstfidmns y ma ldynr praifsfùk, parn

kn snk `d harrdlfaktd pdrd mabfkfr`n (fktaktamabfkfr`n).

A` sfstald ics qua tfaka inln ukfmdm pdtrùk ma d nkcftum, a` iaktìlatrn7ma `d ldsd, a` crdln7 y ma` tfalpn, a` sacukmn.

A` sfstald fkc`æs qua tfaka inln ukfmdm pdtrùk ma `d `nkcftum, a` pfa7 ma`d ldsd, a` sùc7 y ma` tfalpn, a` sacukmn.

A` sfstald LGY qua tfaka inln ukfmdm pdtrùk ma d `nkcftum, a` latrn7 ma`d ldsd, a` Gf`ncrdln7 y ma` tfalpn, a` sacukmn. Ya à maknlfkd YfstaldFktarkdifnkd` ma Lamfmd (YF).

Ak `d ditud`fmdm, axfstak vdrfns sfstalds ma lamfmds:



Ya puama rad`fzdr inkvarsfùk ma lamfmds aktra `ns mfbaraktas sfstalds, takfakmn akiuaktd `ds ra`difnkas qua axfstak y sa luastrdk ak `d sfcufakta tde`d:

Ak cakard`, a` Yfstald Fktarkdifnkd` ma Lamfmd inksfmard sfata ukf-mdmas eäsfids qua inrraspnkmak dsfata idktfmdmas qua snk: @nkcftum

- latrn (l)7 Ldsd - Gf`ncrdln (Gc)]falpn - sacukmn (s)7 Inrrfaktaa`æitrfid - Dlparas (D)7 ]alpardturd - Crdmns Ga`vfk (ºG)7 idktfmdm masustdkifd - lnàs (ln`)7 fktaksfmdmùlfknsd - Idkma`ds (im).

Latrn(l)

Iaktìlatrn(il)

_fa(bt)

(l) 4 4?? 9.58

(il) ?.?4 4 ?.?958

(bt) ?.9?1 9?.1 4

Yacukmn(s)

Lfkutn(l)

Hnrd(h)

(s) 4 4/2? 4/92??

(l) 2? 4 4/2?

(h) 92?? 2? 4

Gf`ncrdln(gc)

Crdln(c)

Yùc(Yc)

(gc) 4 4.??? ?.?28

(c) ?.??4 4 2.81x4?-1

(Yc) 4=.18 4=18= 4

Ajalp`n:Inkvartfr `d va`nifmdm ma 512 Gl/h d l/s.

Ynùifùk: pdrd snùifnkdr asta ajarififn sa takmräk ak iuaktd `ns sfcufaktas

puktns:

4. Ya maea takar ak iuaktd `ds tde`ds ma inkvarsfùk (ak asta ajarififn sa ak-iuaktrdk mns ukfmdmas ma inkvarsfùk, ukd ma `nkcftum y ntrd ma tfalpn)

5. Ya maeak idlefdr `ns gf`ùlatrns d latrns y `ds hnrds d sacukmns (pdrd astn

as kaiasdrfn takar ak iuaktd `ns bditnras ma inkvarsfùk ):

4Gl < 4???l 4h < 92??s



@d kntdifùk ifaktìbfid

Ya utf`fzd pdrd axprasdr idktfmdmas ldynras n laknras qua 4, lamfdkta d pnta(pnsftfvd n kacdtfvd), ma mfaz inrraspnkmfakta.

Yf `d idktfmdm as ldynr qua 4,

sa utf`fzdk ds pntakifds pnsftfvdsma 4?, ak `ds iud`as a` axpn-kakta inrraspnkmarä d` vd`nrpnsfifnkd` ma `d idktfmdm, dsì:

Yf `d idktfmdm as laknr qua 4,

sa utf`fzdk `ds pntakifds kacdtf-vds ma 4?, ak `ds iud`as a` ax-pnkakta inrraspnkmarä d` vd`nrpnsfifnkd` ma `d idktfmdm dsì:

_nmalns rad`fzdr npardifnkas ma suld, rastd, lu`tfp`fidifùk y mfvfsfùk ink kúl

?,4 < 4?-4 7 ?,?4 < 4?-5 7 ?,??4 < 4?-

?,???4 < 4?-= 7 ?,????4 < 4?-1

4 < 4?? 7 4? < 4?4 7 4?? < 4?5 74??? < 4?9 7 4?.??? < 4?=

9. Ya asirfea `d idktfmdm qua sa vd d inkvartfr y sa asincak `ns bditnras minkvarsfùk qua idkia`dk `ds ukfmdmas

Yf qufara prditfidr astns ajarififns, nesarva a` vfman:

Knlera: Inkvarsfùk ma ukfmdmas. Murdifùk: 1:5=



Ak `d lu`tfp`fidifùk, sa rad`fzd a` prnmuitn aktra `ds pdrtas maifldàs7 ùacn sa lutfp`fidk `ds pntakifds ma 4?, takfakmn ak iuaktd `d prnpfamdm ma `d pntakifdifùpdrd edsas fcudàs y axpnkaktas mfbaraktas (iudkmn sa lu`tfp`fidk pntakifds ma edsfcudàs y axpnkaktas mfbaraktas, sa majd `d lfsld edsa y sa suldk `ns axpnkaktas

Ak `d mfvfsfùk, sa mfvfmak prflarn `ds pdrtas maifldàs y ùacn `ds pntakifds ma 4?

takfakmn ak iuaktd `d prnpfamdm pdrd edsas fcudàs y axpnkaktas mfbaraktas ak inifakta (iudkmn sa mfvfmak mns pntakifds ma edsas fcudàs y axpnkaktas mfbaraktasa majd `d lfsld edsa y sa rastdk `ns axpnkaktas).

( 4,98 x 4? 9 ) x ( 9,25 x 4?-6 ) < =,6612 x 4?-2

2,18 x 4?= / 5,5= x 4?-6 < 5,693 x 4?49

Ak a` idsn ma `d suld y `d rastd,sa maea asirfefr fkfifd`lakta `dspdrtas maifldàs inln bditnrasma `d lfsld pntakifd ma 4?.@uacn, sa dp`fid `d prnpfamdmmfstrfeutfvd ma` prnmuitn raspai-tn ma `d dmfifùk n sustrdiifùk.

9,51 x 4?= + 5,54 x 4?= <( 9,51 + 5,54 ) x 4?= < 1,=2 x 4?=



_rnpnrifnkd`fmdm

Ak d vfmd intfmfdkd sa utf`fzd a` tærlfkn ma prnpnrifùk ink mfbaraktas sfckfbfidmn

• Iudkmn maiflns qua d`cn astä efak prnpnrifnkdmn mdlns d asta

tærlfkn uk saktfmn ma drlnkìd y astætfid: ‐Asta kfôn hd iraifmn

luihn, parn astä efak prnpnrifnkdmn“.

• Yf inlaktdlns qua a` æxftn ma ukd parsnkd as prnpnrifnkd` (n

astä ak prnpnrifùk) d su trdedjn, quaralns maifr qua hdy ukd

inrra`difùk aktra astds mns vdrfdeàs: æxftn y trdedjn.

Ak d bìsfid y d ldtalätfid astd pd`derd tfaka uk sfckfbfidmn läs rastrfkcfmn, pua

qua ra`difnkd ldckftumas lamfeàs7 dsì, iudkmn ukd rdzùk sa fcud`d d ntrd, sa m

@ds ifbrds sfckfbfidtfvds

@ds ifbrds sfckfbfidtfvds ma ukd lamfmd inrraspnkmak d` kúlarn ma mìcftns sacrns läs a` mìcftn mumnsn. _nr ajalp`n: sf `d `nkcftum ma ukd edrrd ma dùlfk

as ma 1,=2 il, astn kns cdrdktfzd qua `ns mns prflarns kúlarns (1 y =) sn

sacurns, parn puama axfstfr uk arrnr ak a` ú`tfln, a` 2 qua pnmrìd sar 1 n 37 p

`n tdktn, takalns tras ifbrds sfckfbfidtfvds. Astn mapakma luihn ma` fkstrulak

ma lamfifùk utf`fzdmn7 sf `d lamfmd buard 1,=2?, `d fkiartfmulera astdrìd ak

kúlarn ?, parn takmrìdlns iudtrn ifbrds sfckfbfidtfvds qua inrraspnkmak d u

lamfmd läs praifsd.

Ak `d inkvarsfùk ma ukfmdmas, as flpnrtdkta utf`fzdr `d kntdifùk ifaktìbfid ink

äkfln ma avftdr inkbusfnkas d` asirfefr `ns rasu`tdmns ma uk mdtn axparflaktd`, y

rasu`tdmn takmrä a` lfsln kúlarn ma maifldàs qua a` kúlarn ma laknr praifsfù



Qk dutnlùvf` dvdkzd =?gl hdifd a` knrta ak ukd hnrd.d. Matarlfka `d rdzùk aktra idmd mfstdkifd y su raspaitfvn tfalpn ak 2

hnrds.

e. ¾Tuæ tfpn ma prnpnrifnkd`fmdm tfakak astds vdrfdeàs>

]falpn (h) 4 5 9 = 1 2

Mfstdkifd (gl) =? 8? 45? 42? 5?? 5=?

Ra`nifmdm (l/s) =? =? =? =? =? =?

Ajalp`n:

d. @d rdzùk aktra idmd mfstdkifd y su raspaitfvn tfalpn sa idìu`d dsì:

Ynùifùk:

e. @ds ldckftumas snk mfraitdlakta prnpnrifnkdàs, pnrqua d rdzùk aktra

sus raspaitfvns vd`nras as inkstdkta a fcud` d =?l/s.

Ak `d cräbfid pnmalns nesarvdr qua sa astäk ra`difnkdkmn `ds mns vdrfdeàs:mfstdkifd (gl) y tfalpn (t)



• Mfraitd

Mns ldckftumas tfakak prnpnrifnkd-`fmdm mfraitd, sf d` dulaktdr a` vd`nrma ukd, dulaktd tdlefæk a` vd`nr ma`d ntrd. Dmaläs, snk mfraitdlaktaprnpnrifnkd`as, sf su cräbfid inrras-pnkma d ukd ìkad raitd qua pdsd pnra` nrfcak.

• Mfraitd d` iudmrdmn

Ya prasaktd iudkmn su cräbfid inrras-pnkma d ukd iurvd ma nrfcak pdrd-eù`fin y `d ra`difùk sa inkvfarta ak`fkad` iudkmn `d sacukmd ldckftum saaxprasd d` iudmrdmn.

• Fkvarsd

Mns ldckftumas tfakak prnpnrifnkd`f-mdm fkvarsd, sf d lamfmd qua dulaktda` vd`nr ma `d prflard, mfslfkuya a`vd`nr ma `d sacukmd. _uama sar `fkad`n iudmrätfid.



Id`ferdmnr

Latrn

@nkcftum

Ldsd

Irnkùlatrn

]falpn

Buarzd

Mfkälnlatrn

Lfirùlatrn

Ed`dkzd mainlpdrdifùk

Crdlard

Ed`dkzd matras erdzns

_räitfid ma `denrdtnrfn: dktas ma fkfifdr a` trdedjn ma `denrdtnrfn, as flpnrtdkrainkniar d`cukns fkstrulaktns ma lamfmd pdrd `nkcftum, ldsd, tfalpn y buarzd

4



Ldtarfdàs

Iuarmd n pftd ma 4,5 l, 2 ldsds paquaôds mfbaraktas, id`ferdmnmfmäitfin (sa inkstruya), irnkùlatrn, ed`dkzd (sa inkstruya)snpnrta y asiudmrd.

]de`d 4.9

@nkcftum # ma nsi. _arìnmn Braiuakifd @nkcftum # ma nsi. _arìnmn Braiuakifd

4? 2?

5? 3?

9? 8?

=? 6?

1? 4??

_rniamflfaktn

4. Nrcdkfzdr a` aqufpn ma trdedjn.

5. Yujatdr ukd ldsd paquaôd dàxtraln ma d pftd y d inktfkud-ifùk, hdiar ldridifnkas snera`d iuarmd, idmd 4? il d pdrtfrma` puktn mnkma sa sujatù `dldsd y hdstd `àcdr d 4?? il, inlakzdkmn ak `d `nkcftum ma 4? il.Masp`dzdr `d ldsd d uk `dmn ma` puktn bfjn hdstd qua `d iuarmd quama

inlpàtdlakta hnrfznktd`7 sn`tdr `d ldsd y matarlfkdr a` kúlarn mansif`difnkas (lnvflfaktn ma fmd y vua`td ma `d ldsd), murdkta 9? s.Uapatfr `d axparfakifd pdrd `nkcftumas ma 5?, 9?, =?, 1?, 2?, 3?, 8?,6? y 4?? il. @àvdr `ns mdtns d `d tde`d 4.9.



]atrdamrn

_arìnmn (]): tfalpn kaiasdrfn pdrd rad`fzdr ukd 3?ª nsif`difùkinlp`atd (9? s/kúlarn ma nsif`difnkas).

Braiuakifd (b): kúlarn ma nsif`difnkas ak `d ukfmdm ma tfalpn(kúlarn ma nsif`difnkas /9? s).

d. A`denrdr d cräbfid ma nkcftum inktrd parìnmn (]) y matarlfkdra` tfpn ma prnpnrifnkd`fmdm.

e. A`denrdr `d cräbfid ma `nkcftum inktrd braiuakifd (b) y matar-lfkdr a` tfpn ma prnpnrifnkd`fmdm. 9. Matarlfkdr a` parìlatrn y a` ärad ma mns pn`famrns racu`dras, a`

tatrdamrn y a` axdamrn (uk pn`famrn as uk sù`fmn `flftdmn pnr pn-`ìcnkns racu`dras qua d su vaz, snk bfcurds p`dkds ma `dmns fcud`asinln trfäkcu`n, iudmrdmn, paktäcnkn, ati.).



Axdamrn

]atrdamrn

Axdamrn

=. Inkstrufr `ns sù`fmns prnpuastns y matarlfkdr a` vnùlak ma idmdukn.

1. Inlpàtdr `d tde`d 4.=.

Rnùlak_n`famrn

Latrn

Maiìlatrn

_fa

Latrn

Maiìlatrn

_fa

_arìlatrnYfstald

ma lamfmd Ärad

]de`d 4.=



]de`d 4.1

Gf`ncrdlns Crdlns YùcLdsd

DônsAvaktnssaàiifnkdmns Yacukmns Lfkutns Hnrds Mìds

]de`d 4.2

2. Ma sar kaiasdrfn, inkstrufr ukd ed`dkzd ma d ldynr axditftum pnsf-eà, y pnr inlpdrdifùk ink ukd n vdrfds ldsds inknifmds, matarlfkdra` vd`nr ma ntrds ldsds (pnr `n lakns =). Axprasdr a` rasu`tdmn ak

Gc, c y sùc (tde`d 4.1).

3. Yaàiifnkdr tras avaktns mfbaraktas ma inrtd n lamfdkd murdifùk,matarlfkdr a` tfalpn ma idmd ukn y axprasdr`n ak sacukmns, lf-kutns, hnrds, mìds y dôns, utf`fzdkmn `d kntdifùk ifaktìbfid ak `dtde`d 4.2.



4

Ynùifùk:

_rneàlds ma dp`fidifùk

4. Ya inksfmard qua d mfstdkifd lamfd ma d ]farrd d` Yn` as ma 4=6.163.83? @ds lamfifnkas inktalpnräkads sa hdiak ink tæikfids `äsar n ma rdmdr, ukd praifsfùk ma ukn n mns gf`ùlatrns. Axprasdr ak kntdifùk ifaktìbfid mfstdkifd ak latrns, ak iaktìlatrns y ak pfas.

A` bditnr ma inkvarsfùk ma Gl d l as 4.??? pnrqua uk Gl aqufvdà d4.??? l. _nr `n tdktn, maealns lu`tfp`fidr a` vd`nr prnpuastn, pnr lf`pdrd axprasdr `d raspuastd ak latrns.

4=6.163.83? Gl X 4.??? < 4=6.163.83?.??? l < 4,=616383? X 4?44l

A` bditnr ma inkvarsfùk ma l d il as 4?? pnrqua uk l aqufvdà d 4??il. _nr `n tdktn, maealns lu`tfp`fidr a` vd`nr ak latrns pnr ifak pdrdnetakar `d raspuastd ak iaktìlatrns.

4,=616383? X 4?44latrns X 4?? < 4,=616383? X 4?49 il

A` bditnr ma inkvarsfùk ma l d pfas as 9,58 pnrqua 4 l aqufvdà d 9,58bt. _nr `n tdktn, maealns lu`tfp`fidr a` vd`nr ak latrns pnr 9,58 pdrdnetakar `d raspuastd ak pfas (bt).

4,=616383? X 4?44 latrns X 9,58 < =,6?284?492 X 4?44bt.



Ynùifùk:

_drd inkvartfr ukfmdmas ldynras d laknras salu`tfp`fid7 y ma laknras d ldynras sa mfvfma

pnr a` bditnr ma inkvarsfùk.

5. Inln `d va`nifmdm ma `d ùz as ma 9??.??? Gl/s, ¾iuäktds hnrds, iuäktnslfkutns y iuäktns sacukmns tdrmdrä `d ùz ma` Yn` pdrd `àcdr d `d suparbfifama `d ]farrd>

Inln `d ùz rainrra 9??.??? Gl ak uk sacukmn y `d mfstdkifd ma` Yn` d

`d ]farrd as ma 4=6.163.83? Gl, a` tfalpn kaiasdrfn as:

ts <

tlfk <

th <

]akar ak iuaktd qua a` bditnr ma inkvarsfùk ma hnrds d lfkutns y ma lf-kutns d sacukmns as 2?. _nr `n tdktn, pdrd axprasdr hnrds ak sacukmns, samaea lu`tfp`fidr pnr 9.2??.



l(lc) ? ?,1 4,? 4,1 5,? 5,1 9,?

](sac) ? 9? 2? 6? 45? 41? 48?

h(il) ?

t(sac) ? 9? 2? 6? 45? 41? 4

Ynùifùk:

9. Ya inksfmard qua `d ldsd ma `d @ukd as dprnxfldmdlakta 3,9=6 Ó 4?55

Axprasdr asta vd`nr ak crdlns y sùc.

A` bditnr ma inkvarsfùk ma Gc d c as 4.???, pnrqua uk Gc aqufvdà d 4.???c. _nr `n tdktn, maealns lu`tfp`fidr a` vd`nr prnpuastn ak Gc pnr 4.???pdrd netakar `d raspuastd ak crdlns.

3,9=6 X 4?55 Gc X 4.??? < 3.9=6 X 4?51 c

A` bditnr ma inkvarsfùk ma Gc d sùc as ?,?28, pnrqua uk Gc aqufvdà d?,?28 sùc. _nr `n tdktn, maealns lu`tfp`fidr a` vd`nr prnpuastn ak Gcpnr ?,?28 pdrd netakar `d raspuastd ak sùc.

3,9=6 X 4?55 Gc X ?,?28 < =6,6395 X 4?5? sùc

=. Ak ukd präitfid ma denrdtnrfn, sa dcracù d uk raifpfakta iùkfin, ukd sustd`ìqufmd ma 4? il9 idmd 9? sacukmns murdkta tras lfkutns. Ak idmd idsnmatarlfkù `d ldsd y `d d`turd dìdkzdmds pnr a` `ìqufmn y sa astdeàifarnksfcufaktas tde`ds ma mdtns.

]de`d 4.4 ]de`d 4.5



D pdrtfr ma `d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y ns prniasnsrad`fzdmns, matarlfkdr `d axp`fidifùk bìsfid pdrd idmd avaktn sa`aiifnkdmn.

Dkä`fsfs ma rasu`tdmns

4. _rnpnrifnkd`fmdm 5. Ärads y parìlatrns 9. Rn`úlakas =. Inlpdrdifùk ma ldsds 1. Dkä`fsfs ma tfalpn

t(sac)

t(sac)

A`denrdr `d cräbfid inrraspnkmfakta pdrd idmd tde`d y matarlfkdr quæ tfpn ma prnpnrifnkd`fmdm sa prasaktd ak idmd idsn.

Cräbfid 4 Cräbfid 5

Ldsd y tfalpn snk mfraitdlaktaprnpnrifnkd`as.

Udmfn y tfalpn tfakak prnpnr-ifnkd`fmdm mfraitd d` iudmrdmn.



D inktfkudifùk, ukd sarfa ma ajarififns ma dp`fidifùk qua dyumdräk d ukd lajninlpraksfùk y dprnpfdifùk ma` tald trdtdmn. Ak `n pnsfeà, hdiar `d snùifùk

ak bnrld fkmfvfmud`.

4. ]akfakmn ak iuaktd ns prniamflfaktns dmaiudmds pdrd d inkvarsfùkma ukfmdmas ma lamfmd ma `nkcftum, ldsd y tfalpn, inlpàtdr `dssfcufaktas tde`ds, justfbfidkmn idmd raspuastd (prniamflfaktn).

Asirfed `ns prniasns ak su iudmarkn.

Uad`fialns ntrns ajarififns

45

Hnrds Lfkutns Yacukmns

45

45

45Latrns Iaktìlatrns _fas

45

45

45Gf`ncrdlns Crdlns Yùc

45

45

5. Qtf`fzdkmn uk rasnrta n edkmd a`ästfid, uk snpnrta y ldsds mfbarak-tas, prnpnkar y dp`fidr uk prniasn bìsfin qua à parlftd astdeàiar `dprnpnrifnkd`fmdm mfraitd a fkvarsd, y hdiar d malnstrdifùk lamfdkta

`d utf`fzdifùk ma cräbfids axp`fidtfvds.

9. Uad`fzdr `ds sfcufaktas npardifnkas:

d. =,=1 x 4?9 + 8,=9 x 4?= <

e. 8,?2 x 4?1 X ?,21 x 4?-9 <

i. 9,=86 x 4?-5 / 2,842 x 4?= <

m (9 x 4?5 X 6 5 x 4?-9) / = ?3 x 4?2 <



Inkiùsfnkas

Dutnavdùdifùk

Axp`fidr `d flpnrtdkifd y dp`fidifnkas ma `ns talds trdtdmns ak `d cuìd, pdrd

snùifnkdr sftudifnkas bìsfids radàs.

_drd fr inksn`fmdkmn a` prniasn ma dprakmfzdja, sa prnpnka astd ditfvfmdmiuyd bfkd`fmdm as raidpfùtdr n trdedjdmn hdstd asta puktn. Dsì sa prnluavak`ns prniasns ma latdinckftfvns qua a dyumdräk d praifsdr difartns y mfbfiu`-

tdmas ak a` dprakmfzdja, `ns iudàs maea dkd`fzdr y dyumdr d sn`vaktdr pnrlamfn ma ntrn tfpn ma ditfvfmdmas. @d fmad as qua trdedja fkmfvfmud`lakta,parn sf `n inksfmard, puama snifd`fzdr ink sus inlpdôarns. D inktfkudifùkhdy ukd sarfa ma pracuktds7 `n fkvftdlns d raspnkmar`ds: • ¾Inksfmard qua `ns inkniflfaktns y `d prasaktdifùk ma fkbnrldifùk

buarnk `ns dmaiudmns>Yf ^^^^ Kn ^^^^ ¾_nr quæ>

• Asirfed mns kuavns inkniflfaktns qua hdyd netakfmn: d. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ e. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

• ¾Tuæ mfbfiu`tdmas tuvn d` rad`fzdr `ds ditfvfmdmas p`dktadmds ak astdukfmdm>

• ¾_drtfifpù ditfvdlakta ma tnmds `ds ditfvfmdmas n à bd`tn pnkar läsfktaræs ak d`cukd atdpd ma` prniasn>

Uacrasa d `ds pracuktds ink qua fkfifdlns astd ukfmdm, ravfsa susraspuastds y inktasta `ds sfcufaktas pracuktds:

• ¾Iuä` ma `ns inkiaptns d``ì p`dktadmns à bd`td dúk pnr ravfsdr>, ¾tfaka



Lnvflfaktn F

DQ]NY / HNUDY MA ENCN]Ä _A]UNEUDY-LN]NU

Kn sa ‘dcuù‖ `d bfastd ak ]nidkifpä

@NY _F@N]NY tuvfarnk qua snrtadr `d `ùvfd y `d kfae`d qua inefjù a` dutù-mrnln ak `d tdrma y `d kniha ma` säedmn.

Barkdkmn Drfzd-A@ ]FAL_N.

Yf ldkajdr uk dutnlùvf` aksus `ìlftas murdkta safs hnrds asyd uk ratn baknlakd`, hdiar`n

edjn ukd `ùvfd tnrrakifd`, snera`älfkds ma crdkfzn, pdrihas makfae`d y murdkta ukd euakd pdrtaak d kniha, ds 2 Hnrds _atrnerdsLN]NU bua `d idrrard läs murd,mfbìif`, prnedtnrfd y dzdrnsd quasa hd inrrfmn ak `d hfstnrfd ma`Dutùmrnln ma ]nidkifpä.

_arn asd inktfkcakifd kn àraedjù uk äpfia d` aktusfdsln inka` iud` ukd kutrfmd inkiurrakifddinlpdôù `d idrrard. A` rapartnrfn ma trnlpns, mas-`fzdmds, sd`fmds ma pfstd, dutnsfkukmdmns, diifmaktas buartasdukqua sfk inksaiuakifds mfba-raktas d `ns mdôns laiäkfins,ak lamfn ma `ns iudàs `d hd-

ef`fmdm, tdàktn y rfascn ma `ns pdrtfifpdktas qua sneravfvfarnkma ns 34 qua fkfifdrnk d pruaed

edjn uk sn` rdmfdkta, buarnk ukdtaksd inkstdkta d `n `drcn ma `d

dcntdmnrd jnrkdmd. Bfkd`lakta, d `ds 8:?? p.l., ak puktn, asidlpù, justn pdrd sdùmdrd `ns cdkdmnras ma `d mrdlätfididrrard. Yaedstfäk y Ju`fäk Ldr-tìkaz, ak uk prntntfpn Udmfid` ma`d idtacnrìd fera, buarnk qufakasläs vua`tds `ncrdrnk hdiar aktratnmns, ink uk dutn astupakmn parnmasiuefartn, sfk prntaiifùk inktrd

`d ùvfd, n iud` hfzn läs vd`fnsnsu rftln ma pruaed. _nr su pdrta ]nläs Ytauar,Dàjdkmrn @fkia y Jnrca Inrtæssa flpusfarnk ak a` crupn ma asta

tfpn ma dutns ink lntnras hdstd5??? i.i. Ma pdsn, Inrtæs dkntùsu vfitnrfd 4= ak `ds 2 Hnrds. A` lajnr ma `ns turfslns hdstd5??? i.i. bua a` I`ìn ma Ydktfdcny Mfacn Barkdkmn Lajìd qua vak-ifù d` _aucant ma ns aiudtnrfdkns@drrad, Lnyd y Inrrad, qufakas`ncrdrnk hdstd a` lnlaktn a`lajnr rasu`tdmn ma uk aqufpn

axtrdkjarn. A` Ywfbt ma `d bdlf-`fd _uyn ma Lama``ìk hfzn ukdflpaideà prasaktdifùk y bua a`lajnr i`dsfbidmn ma `ns turfslns

y ma d idtacnrìd hdstd 4=?? i.i.,

lfaktrds qua _arafrd cdkù lara-ifmdlakta a` crupn ma dutns inklntnras ma sn`n 8 vä`vu`ds inkJudk Idlf`n y Jhnk DàxdkmarUfvard. Bfkd`lakta, `d sarfa ma`]I 5.??? `d cdkù a` Hyukmdf maUnkd`m Qrrad, Dkmræs Ufdôn yJdfla Cdriìd.

JNYÆ I@N_D]NBYGV


5



Bukmdlaktn taùrfin

D pdrtfr ma `d àiturd dktarfnr, raspnkmd `ds sfcufaktas pracuktds:

_racuktds Uaspuastds¾Iùln iraa qua sa bukifnkd a`

lnvflfaktn ma `ns idrrns>¾Iraa ustam qua dbaitd ak d`cn a`

lnvflfaktn iudkmn hdy ùvfd, crdkfzn

n kfae`d> ¾_nr quæ>

_ärasa brakta d ukidlfkn, id` à n

dvakfmd y matarlfka

`d va`nifmdm ma:

Qk idrrn /Qkd efifiàtdQkd parsnkd

Qk dkfld`

Masirfed a` prniasn qua rad`fzù pdrd

idìu`dr idmd ukn ma `ns lnvflfaktns

Lnvflfaktn

As a` idlefn ma pnsfifùk ma uk iuarpn ink raspaitn ma uk puktn n ldrinma rabarakifd7 astn kns fkmfid qua a` lnvflfaktn as ra`dtfvn, mapakmama` puktn ma rabarakifd qua tnla a` nesarvdmnr. Astn qufara maifr, quapdrd ukd parsnkd, uk nejatn puama astdr ak lnvflfaktn, lfaktrds quapdrd ntrd, uefidmd ak ntrn puktn ma rabarakifd, a` lfsln nejatn puamapdraiar ak rapnsn.



Aàlaktns ma` lnvflfaktn

Idktfmdmas asid`dras: snk ds idktfmdmas qua sù`n raqufarak ma uk vd`nr (ldc

kftum), pdrd sar inlpàtdlakta axp`fidmds. _nr ajalp`n: a` tfalpn, `d ldsy `d talpardturd.

_drd a` idsn ma` lnvflfaktn, sa inksfmardk asid`dras:

• ]rdyaitnrfd: as a` idlfkn rainrrfmn y rasu`td ma d ukfùk ink saclaktnma raitd ma tnmns y idmd ukn ma `ns puktns pnr mnkma hdyd pdsdmn a

iuarpn.

• Udpfmaz: as `d rdzùk aktra `d `nkcftum n aspdifn rainrrfmn y a` tfalpnutf`fzdmn pdrd rainrrar`n.

• Udpfmaz lamfd: as `d rdzùk aktra a` idlfkn tntd` rainrrfmn y a` tfalptntd` qua tnlù rainrrar asd mfstdkifd ∂t.

v < < m m

∂ t t 5 - t

4

rdpfmaz lamfd < mfstdkifd rainrrfmd

tfalpn tntd`

• Mfstdkifd: as d nkcftum tntd` ma` idlfkn rainrrfmn, iudkmn uk nejatnsa masp`dzd ma uk ùcdr (puktn ma pdrtfmd), d ntrn (puktn ma `àcdmd)

• Idktfmdmas vaitnrfdàs: snk ds idktfmdmas qua raqufarak ma d ldcktum y mfraiifùk pdrd sar axp`fidmds. _nr ajalp`n: buarzd y diaàrdifùk



_drd a` idsn ma` lnvflfaktn, sa inksfmardk vaitnrfd`as:

• Ra`nifmdm: as a` aspdifn rainrrfmn ak `d ukfmdm ma tfalpn. Yf sainksfmard ak uk fktarvd`n ma tfalpn qua tfakma d iarn, sa inksfmardfkstdktäkad y pdrd fktarvd`ns ma tfalpn ldynr, sa inksfmard inlnva`nifmdm lamfd.

• _nsfifùk: sa ra`difnkd ink a` ldrin ma rabarakifd utf`fzdmn y `dsinnrmakdmds (x, y), ak mnkma sa akiuaktrd ink raspaitn ma` nrfcak

(vaitnr pnsfifùk).

• Masp`dzdlfaktn: as `d mfstdkifd ak `ìkad raitd, aktra a` puktn mapdrtfmd y a` puktn ma ``acdmd ma` nejatn (vaitnr masp`dzdlfaktn).

v < < x

5 - x

4 ∂ x

t 5 - t

4 ∂ t

Ra`nifmdm lamfd <masp`dzdlfaktn (latrns)

tfalpn (sacukmns)

Masp`dzdlfaktn

]rdyaitnrfd



Lnvflfaktn ukfbnrla

Ya prasaktd iudkmn a` iuarpn rainrra aspdifns fcudàs ak tfalpns fcudàs. Yf `dyaitnrfd as `fkad`, a` lnvflfaktn sa maknlfkd Uaitf`ìkan Qkfbnrla. @d cräbfid

aspdifn inktrd tfalpn as ukd raitd ink ifartn crdmn ma fki`fkdifùk, y `d cräbfidva`nifmdm inktrd tfalpn as ukd raitd pdrdà`d d` aja hnrfznktd`.

Y (l)

t (s)

t (s)

R (l/s)

v <s

5 - s

4

t 5 - t

4

Aspdifn vs. tfalpn

Ak `d cräbfid ma aspdifn inktrdtfalpn, `d pakmfakta ma `d raitdinrraspnkma d `d ldckftum ma `dva`nifmdm.

Ra`nifmdm vs. tfalpn

Ak `d cräbfid ma va`nifmdm inktrdtfalpn, a` ärad edjn d raitd aquf-vdà d` aspdifn tntd` rainrrfmn.

s < v . t



Lnvflfaktn vdrfdmn

Niurra iudkmn a` iuarpn rainrra aspdifns mfbaraktas ak idmd ukfmdm ma tfalpn, yhdy vdrfdifùk ak `d va`nifmdm (diaàrdifùk). Yf `d va`nifmdm vdrìd idktfmdmas fcud-às ak fktarvd`ns ma tfalpn fcudàs, aktnkias sa maknlfkd Lnvflfaktn QkfbnrlaRdrfdmn. @d cräbfid ma aspdifn inktrd tfalpn as ukd salfpdräen`d, `d ma va`nifmdminktrd tfalpn as ukd raitd ink ifartn crdmn ma fki`fkdifùk, y d ma diaàrdifùk inktrd

Ajalp`n:

Qk dtàtd qua aktrakd mfdrfdlakta, rainrra ukd mfstdkifd ma 51?gl ak 5hnrds. ¾Tuæ va`nifmdm ak l/s rainrra a` dtàtd pnr mìd>

Ynùifùk: pdrd snùifnkdr asta tfpn ma prneàlds sa maeak sacufr astns pdsns:

d) ]nldr `ns mdtns mdmns pnr a` ajarififn.

e) Ynùifnkdr `d aiudifùk.

i) Yf a` ajarififn `n pfma, hdiar `d inkvarsfùk ma ukfmdmas.

MD]NY:

Y(l)<51?gl

t(s)< 5h

Aiudifùk



Y (l)

t (

R (l/s)

t (

t (s)

d (l/s5

)

Aspdifn vs. tfalpn

Ra`nifmdm vs. tfalpn

Diaàrdifùk vs. tfalpn

@d pakmfakta ma `d raitd tdkcakta d `diurvd ak uk puktn ‐p“, aqufvdà d `d

ldckftum ma d va`nifmdm ak mfihn puktn.

A` ärad edjn `d iurvd aqufvdà d` aspdifntntd` rainrrfmn.

@d cräbfid ma diaàrdifùk inktrd tfalpn,raprasaktd ukd diaàrdifùk inkstdkta

v5 < vn

5 + 5 d.x

@d pakmfakta ma `d raitd ak `d cräbfid mava`nifmdm inktrd tfalpn, inrraspnkma d`d ldckftum ma `d diaàrdifùk.

Nesarva `ns sfcufaktas ajalp`ns.

Qkd parsnkd D rainrra 6 gl ak 49? lfkutns7 `d parsnkd E rainrra 41?? l

ak 6?? s7 y `d parsnkd I `àvd ukd va`nifmdm ma 1 gl/h. ¾Iuä` ma `ds tras

parsnkds as `d läs räpfmd>



Yf `d parsnkd D rainrra 6 gl ak 49? lfkutns, `d E 41??l ak 6?? s, y `d I ukdva`nifmdm ma 1Gl/h, `n inkvakfakta as pdsdr ns vd`nras ma mfstdkifd y tfalpn d `dlfsld ukfmdm ma lamfmd.

Ajalp`n:

Qk trak qua vfdjd fkfifd`lakta d 5?l/s diaàrd d rdzùk ma 1l/s5 ak `d lfsldmfraiifùk. ¾Tuæ tdk àjns vfdjdrä ak =? s> ¾Iuä` sarä su va`nifmdm bfkd`>

Ynùifùk: d takar ak iuaktd:

m) ]nldr `ns mdtns mdmns pnr a` ajarififn. a) Aàcfr `d aiudifùk dmaiudmd y snùifnkdr`d. MD]NY:vn < 5?l/sd < 1l/s5t < =?ss <>

vb < >

Aiudifùk_drd sdear quæ tdk àjns vfdjd a` trak ak =?s sa utf`fzd `d aiudifùk:

@d va`nifmdm bfkd` sa hd``d d pdrtfr ma `d aiudifùk:

6gl< 6???l

1Gl< 1???l

49? lfkutns< 38?? s

4 hnrd< 92?? s

Dhnrd sa puama inlpdrdr:@d parsnkd D takmrìd ukd va`nifmdm ma 6???/38??(l/s)< 4.41 (l/s)@d parsnkd E takmrìd ukd va`nifmdm ma 41??/6??(l/s)< 4.23 (l/s)@d parsnkd I takmrìd ukd va`nifmdm ma 1???/92??(l/s)< 4.96 (l/s)

D` inlpdrdr ns vd`nras dktarfnras, sa puama astdeàiaqua d parsnkd läs räpfmd as d E, pnrqua su va`nifmdmas ldynr.



Lnvflfaktn ma idìmd `fera

Yacúk Drfstùtaàs, `d va`nifmdm ma `ns iuarpns d` idar, sa ra`difnkd ink su pa

as maifr, aktra läs pasdmn sad a` nejatn, läs räpfmn ida. Cd`fàn inksfmarqua `d rasfstakifd ma` dfra pnmìd ratdrmdr `d idìmd ma d`cukns iuarpns `fcarnscrdk suparbfifa, parn bfkd`lakta Kawtnk rasn`vfù a` prneàld, maspraifdkmbrfiifùk ink a` dfra, y inkiùyù qua tnmns `ns iuarpns idak ink `d lfsld diaìfùk, sfk flpnrtdr su bnrld, ldsd, in`nr, ati. Idìu`ù dmaläs, `d diaàrdifùk axparflaktd uk iuarpn edjn `d diifùk ma `d buarzd ma crdvamdm qua aqufvdàprnlamfn d 6.8 l/s5.

•

Aiudifnkas ma` lnvflfaktn ukfbnrlalakta diaàrdmn:

d.t 5x < vf.t +

5

vb < vf + d.t

d < vb vf t

x: mfstdkifdvf: va`nifmdm fkfifd`t: tfalpnd: diaàrdifùk

• Ak `ds aiudifnkas ma` lnvflfaktn maidìmd `fera, `d diaàrdifùk as inkstdktay aqufvdà d c < 6,8 l/s5 y a` aspdifnrainrrfmn x as `d d`turd h. @d va`nifmdmfkfifd` kn sa tfaka ak iuaktd pnrqua as ?.

h: d`turdc: crdvamdm

c.t 5

h <

5

vb < c.t



Ajalp`n:

Qk nejatn sa majd idar masma ukd d`turd ma 8l ak uk tfalpn ma 5s. Ma-

tarlfka su va`nifmdm.

Ynùifùk:

MD]NY:

vn < ?l/s

d < c < 6.8l/s5

h < 8l

t < 5s

vb < >

Aiudifùk: pdrd matarlfkdr `d va`nifmdm ma idìmd utf`fzdlns `d sfcufakta

aiudifùk:

Uavfsa a` sfcufakta `denrdtnrfn vfrtud`:http://www.xtai.idt/~nidsa``d/dppàts/idfcumd/dppàtsn`5.htl,



_räitfid ma `denrdtnrfn

Ldtarfd`as

Irnkùlatrns, maiälatrn, asiudmrd y pdpa` iudmrfiu`dmn n lf-`flatrdmn.

_rniamflfaktn

4. Nrcdkfzdr a` aqufpn ma trdedjn y sa`aiifnkdr ma inlúkdiuarmn, d` lajnr mapnrtfstd.

5. Ynera uk aspdifn dmaiudmn, matarlfkdr ukd mfstdkifd ak

`ìkad raitd ma 1? l, fkmfidkmn uk saclaktn ma 4? l ma`nkcftum.

9. Ak idmd ukn ma `nspuktns saôd`dmns,uefidr uk irnknla-trfstd pdrd qua ra-cfstra `ns tfalpns maidmd inlpatfmnr d`lnlaktn ma pdsdrbrakta d æ`.

5



=. Inksaiutfvdlakta a` raprasaktdkta ma idmd aqufpn (mapnrtfstd), maeatnldr d pdrtfmd, ldktakfakmn ukd rdpfmaz inkstdkta murdkta tnmn a`rainrrfmn (kn as kaiasdrfn inrrar).

1. Ak a` sacukmn fktaktn edjn `ds lfslds inkmfifnkas, maea dulaktdrprncrasfvdlakta su va`nifmdm hdstd qua d` bfkd`, masdrrn`à d läxfld.

2. @d inlpatakifd qua sa prasaktd inksfsta ak netakar d pdrtfr ma` masp`d- zdlfaktn ma` inrramnr ak idmd idsn, d lajnr cräbfid inrraspnkmfaktad uk lnvflfaktn raitf`ìkan y d uk lnvflfaktn ukfbnrla diaàrdmn.

3. @ns mdtns netakfmns ak `ns crupns, sa maeak inksfckdr ak d tde`d 5.4.

8. A`denrdr `ds cräbfids inrraspnkmfaktas d aspdifn vs. tfalpn, va`nifmdmvs. tfalpn, diaàrdifùk vs. tfalpn, y matarlfkdr iuä` bua a` aqufpncdkdmnr (`d cräbfid läs dprnxfldmd d` lnvflfaktn fmad`).

]de`d 5.4


D pdrtfr ma d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y ns prniasns

]1]4 ]5 ]9Knlera ]=



Dutnavdùdifùk

_drd fr inksn`fmdkmn a` prniasn ma dprakmfzdja, sa prnpnka astd ditfvf-mdm iuyd bfkd`fmdm as qua raidpftuà `n trdedjdmn hdstd asta puktn. Dssa prnluavak `ns prniasns ma latdinckftfvns qua à dyumdräk d praifsdrdifartns y mfbfiu`tdmas ak a` dprakmfzdja, `ns iudàs maea dkd`fzdr y dyumdrd sn`vaktdr pnr lamfn ma ntrn tfpn ma ditfvfmdmas. @d fmad as qua trdedjafkmfvfmud`lakta, parn sf `n inksfmard, puamak snifd`fzdr ink sus inlpdôa-

rns. D inktfkudifùk hdy ukd sarfa ma pracuktds7 n fkvftdlns d raspnkmar`ds:

Rd`nra sus dprakmfzdjas. _drd a``n, ldrqua ink ukd X a` pnriaktdja quaastfla dmaiudmn:

Idtacnrìd _racuktd ?% 5?% =?% 2?% 8?% 4??%

Iulp`flfaktn y

raspnksdef`fmdm

¾Iulp`fù ink ds aiturds

dsfckdmds, ds ditfvfmdmasmasdrrn``dmds ak i`dsa

y `d aktracd ma tdrads y

trdedjns fkmfvfmudàs>

Iradtfvfmdm y

id`fmdm

¾Dpnrtù fmads y æstds

buarnk sfckfbfidtfvds>

¾Uad`fzù sfk arrnr d`cukn`ds tdrads y/n `ns trdedjns

dsfckdmns>

Dprakmfzdja ydpnrtdifùk ma

inkniflfaktns

¾Tuæ tdktn dprakmfù y

quæ tdktns inkniflfak-tns dpnrtù ak `ds i`dsas,

ak `ds tdrads y/n `ns trd-

edjns rad`fzdmns>



s < v . t < 5 l/s . 51 s < 1? l

v < < < ?,?41 l/ss ?,53 l

t 48 s

s < 53 il < < ?,53 l53 il

4??

v < < 5 l/s3,5 Gl/h

9,2


Lnvflfaktn Uaitf`ìkan Qkfbnrla

4. Axprasdr ak l/s, `d va`nifmdm ma uk lùvf` qua rainrra 53 il ak 48 s:

Ynùifùk: `d va`nifmdm sa ma-bfka inln a` inifakta aktra aàspdifn rainrrfmn y a` tfalpnutf`fzdmn, d mfstdkifd rainrrfmd

`d axprasdlns ak latrns:

5. Axprasdr ak l, d mfstdkifd rainrrfmd pnr uk lùvf` murdkta 51 s, sf su va`nifmdmas ma 3,5 Gl/h.

Ynùifùk: a` aspdifn rainrrfmninrraspnkma d` prnmuitn ma`d va`nifmdm pnr a` tfalpn7axprasdlns `d va`nifmdm maGl/h d l/s, mfvfmfakmn aktra9,2 (bditnr ma inkvarsfùk).

5



9. Matarlfkdr a` tfalpn kaiasdrfn pdrd qua uk vahìiu`n rainrrd 9 gf`ùlatrnsu va`nifmdm as ma 45 l/s.

Ynùifùk: a` tfalpn tntd` aquf-vdà d` inifakta aktra a` aspd-ifn rainrrfmn y `d va`nifmdm,axprasdlns d mfstdkifd ak l:

=. Ynera ukd idrratard raitd, mfstdktas 5?? Gl, astäk uefidmns mns vahìi D y E ink va`nifmdmas ma 91 l/s y 1= Gl/h raspaitfvdlakta. Matarlfkdmfstdkifd qua rainrra idmd ukn dktas ma iruzdrsa.

s < 9 Gl . 4.??? < 9.??? l

t < < 51? s9.??? l

45 l/s

v < < 41 l/s1= Gl/h

9,2

Ynùifùk: tnmns `ns vd`nras maeak astdr ak a` lfsln sfstald ma lamfmd.

Axprasalns fkfifd`lakta `dva`nifmdm ak l/s:

5?? Gl

D v < 91 l/s Ev < 1= Gl/h



t < < < =.??? s s 5??.??? l

v U

1? l/s

@d mfstdkifd ak latrns: s < 5?? Gl . 4.??? < 5??.??? l

@d va`nifmdm rasu`tdkta aktra`ns mns vahìiu`ns iudkmn samfrfcak ukn hdifd a` ntrn,aqufvd`a d d suld ma ds va`n-ifmdmas ma idmd ukn ma a``ns.

v U < v

D + v

E <

91 l/s + 41 l/s < 1? l/s

A` tfalpn qua raqufara uk lùvf` ink astd va`nifmdm pdrd rainrrar `d mfs-tdkifd fkmfidmd as:

A` vahìiu`n D ak asa tfalpnrainrra:

s D < v

D . t <

91 l/s . =.??? s < 4=?.??? l

A` vahìiu`n E ak asa tfalpnrainrra:

s E

< v E . t <

41 l/s . =.??? s < 2?.??? l



h < vf . t +

c . t 5

5

t < < < < 4?? s5 < 4? s5 . h 5 x =6? l 68? l

c 6,8 l/s5 6,8 l/s5

Lnvflfaktn Qkfbnrla Diaàrdmn:

1. Matarlfkdr a` tfalpn qua tdrmd uk nejatn ak idar masma ukd d`turd ma l. ¾Ink quæ va`nifmdm `àcd>

Ynùifùk: d pdrtfr ma `daxprasfùk:

Inksfmardkmn qua `d va`nifmdm fkfifd` vf < ?, maspajdlns t pdrd netakar:

_drd matarlfkdr `d va`nifmdm qua tfaka d` `àcdr d` pfsn, utf`fzdlns ukdaxprasfùk qua kns parlftd ra`difnkdr va`nifmdm, diaàrdifùk y tfalpn:

v b < v

f + c . t < ? + 6,8 l/s5 x 4? s < 68 l/s



Uac`dlaktn

Ya `dkzd masma uk pd-sf``n ma ukd dkihurdma = latrns, didedmnak uk drin ma 8 latrns

ma rdmfn. A` saitnr ma idìmd astdrä ldr-idmn ink mns ìkads e`dkids ma 1 il madkihurd, ma td` lnmn qua sf `ns enrmas

fktarkns ma `ds `ìkads sa prn`nkcdsakmaearìdk pdsdr pnr `ds mns fktarsaiifn-kas ma `ns enrmas fktarfnras ma` driny `ds `ìkads pdrdà`ds qua ma`flftdk a`pdsf``n ma flpu`sn y qua sa iruzdk aka` puktn iaktrd` ma` iìriu`n, ma` iud` a`drin bnrld pdrta. A` saitnr takmrä dsì 56º dprnxfldmdlakta.

_drd rad`fzdr idmd fktaktn, a` dtàtd tfakauk lfkutn. Knrld`lakta, idmd dtàtdrad`fzd tras fktaktns.

@d jded`fkd maea incarsa pnr `d akinr-mdmurd (d` lakns `d ldkn ma` dtàtdmaea tnidr`d), y `dkzdrsa pnr akifld

ma` hnlern n ma` erdzn ma dkzdr7 kn saparlfta dkzdr`d ak rntdifùk kf puama a

dtàtd mdr `d aspd`md d` saitnr ma idìmddktas ma sn`tdr `d jded`fkd7 `ns astf`nskn i`äsfins kn astäk dutnrfzdmns. Yf `d

jded`fkd sa rnlpa ak a` fktaktn n ak adfra kn sa inktdrä inln ku`n7 tdlpninsf `d rnturd hdia parmar a` aquf`ferfn ddtàtd y prnvnid qua tnqua buard madrin7 ak asta idsn sa a parlftfrä vn`var d

inlakzdr. Ak d idìmd, d puktd latä`fidmaea tnidr a` sua`n dktas qua iud`qufantrd pdrta ma `d jded`fkd.

A` idlpaùk n`ìlpfin, Arfg @allfkc, ak `d pruaedma jded`fkd ma `ns Juacns N`ìlpfins ma 46?8.A` `dkzdlfaktn ma jded`fkd as ukd pruaed

ma` dtàtfsln ditud` ak qua sa `dkzd ukd jded`fkd

@dkzdlfaktn ma jded`fkd9

B n t n t n l d m d m a S f g f p a m f d

Lnvflfaktn ak a` p`dkn


9



Idrditarìstfids ma `d jded`fkd

@d jded`fkd as uk vakde`n d`drcdmn ink`d puktd latä`fid. @d `nkcftum ma `d jd-

ed`fkd as ma 52?-53? il ak idtacnrìdldsiu`fkd y 55?-59? il ak idtacnrìdbalakfkd, y uk pasn läxfln ma 8?? cpdrd `ns hnleras y 2?? c pdrd `ds lu-

jaras. ]faka uk dsfmarn, bderfidmn inkinrma`, ma ukns 41 il ma `drcn, quasa akiuaktrd dprnxfldmdlakta ak aìaktrn ma crdvamdm ma `d jded`fkd.

D `n `drcn ma `d hfstnrfd sa hd vakfmndiaridkmn d `d puktd a` iaktrn ma crd-vamdm ma `ds jded`fkds, pdrd hdiar quaidfcdk dktas, yd qua sa inlakzdedk drad`fzdr ldrids qua axiamìdk a` drcn ma`ns idlpns ma idìmd, ink a` inksfcufakta

pa`fcrn.

]æikfids ma `dkzdlfaktn

A` nejatfvn ma abaitudr uk euak `dlfaktn tæikfin as a` ma qua `d jded

takcd `d ldynr va`nifmdm pnsfeàa` lnlaktn ma sar `dkzdmd, duktdlefæk fkbùyak ntrns dspaitns puamak sar inktrn`dmns, inln a` äkma sd`fmd n a` d`fkadlfaktn ma d jdedink `ns hnlerns.Masma a` fkfifn ma`dkzdlfaktns ak `d ard lnmarkd, axfstfmn vdrfds tæikfids ma dkzdlfa

axfstfakmn fkiùsn murdkta d`cúk tfpn ukd tæikfid rntdtnrfd marfvdmd`dkzdlfaktn ma edrrd, qua sa prdiak a` _dìs Rdsin. Astd tæikfid ard lpa`fcrnsd sf kn sa mnlfkded parbalakta, puastn qua axfstìd d pnsfef`ma qua d jded`fkd sd`fard hdifd ntrn qua kn buard `d znkd ma `d idìmd in

inksfcufakta pa`fcrn.

n l d m d m a S f g f p a m f d




_racuktds Uaspuastds

¾Tuæ tfpn ma lnvflfaktn rad`fzd d jded`fkd ak a` `dkzdlfaktn>

¾Tuæ vdrfdeàs iraa ustam qua maeatakar uk mapnrtfstd ma dkzdlfaktnma jded`fkd pdrd netakar uk euaktfrn>

¾Ink qua ntrn mapnrta ra`difnkd a``dkzdlfaktn ma jded`fkd>

Rdyd d ukd idkihd ma edsquaten`.Masma a` iaktrn ma` drin, `dkia `dpa`ntd hdifd d iastd. Yf kn tfaka di-iasn d ukd idkihd ma edsquaten`,trdta ma akiastdr ukd en`d ma pdpa`n ukd pa`ntd ak ukd idkaid, n akuk nejatn sflf`dr. Axp`fqua quæ tfpnma lnvflfaktn rad`fzù (tnla `ds

lamfmds qua sadk kaiasdrfds pdrddrculaktdr su hfpùtasfs).

Lnvflfaktns inln `ns masirftns ak `d ài-

turd sa puama prasakifdr y axparflaktdr ak

mfbaraktas tfpns ma avaktns n sftudifnkas._nr ajalp`n, dktas sa utf`fzdedk drlds ma

inledta qua sa ``dldedk idtdpu`tds, `ds

iudàs drrnjdedk rnids cfcdktas pdrd mar-

rfedr d` akalfcn7 su rainrrfmn raprasaktd

uk lnvflfaktn pdrdeù`fin.



¾Tuæ tfakak ak inlúk `ns `dkzdlfaktns qua sa hdiak ink `d ldkn, ink uk id

y ink ukd hnkmd>

Nesarva a` sfcufakta vfman, ak a` iud` sa prasaktd ukd sftudifù

sflf`dr d` `dkzdlfaktn ma prnyaitf`as:

Knlera: ]d``ar 5. @dkzdlfaktn ma tnrtdsMurdifùk: 4:58 lfkutns

Ma diuarmn d `n qua nesarvù ak a` vfman, raspnkmd `ds sfcufaktas pracuktds

¾Tuæ idlfkns sacufrìd a` pdsta` sf n dkzd d ifartd mfstdkifd d ukn ma sus dlfcn

¾Iraa qua pdrd qua sa luavd a` pdsta` tfaka qua parldkaiar ukd buarzd qu



Bukmdlaktn taùrfin

Lnvflfaktn pdrdeù`fin

Ya maknlfkd lnvflfaktn pdrdeù`fin d` qua rad`fzd uk nejatn iuyd trdyaitnrfd mas-irfea ukd pdräen`d. Inrraspnkma d d trdyaitnrfd fmad` ma uk prnyaitf` qua sa luavaak uk lamfn qua kn nbraia rasfstakifd d` dvdkia y qua astä sujatn d uk idlpn crdvftdtnrfn ukfbnrla. ]dlefæk as pnsfeà malnstrdr qua puama sar dkd`fzdmn inln `dinlpnsfifùk ma mns lnvflfaktns, uk lnvflfaktn raitf`ìkan ukfbnrla (hnrfznktd`)y uk lnvflfaktn ma idìmd `fera (vartfid`).

• A` lnvflfaktn ma lamfdpdräen`d n salfpdrdeù fin(`dkzdlfaktn hnrfznktd`):sa puama inksfmardr inln

`d inlpnsfifùk ma uk dvdk-ia hnrfznktd` raitf`ìkanukfbnrla y `d idìmd `fera.

• A` lnvflfaktn pdrdeù`f-in inlpàtn: sa puamainksfmardr inln `d inl-pnsfifùk ma uk dvdkiahnrfznktd` raitf`ìkan ukf-bnrla y uk `dkzdlfaktnvartfid` hdifd drrfed, qua asuk lnvflfaktn raitf`ìkanukfbnrlalakta diaàrdmnhdifd dedjn (LUQD), pnr`d diifùk ma `d crdvamdm.

Rx

Rf



Ak inkmfifnkas fmadàs ma rasfstakifd ku`dd` dvdkia y idlpn crdvftdtnrfn ukfbnrla,`n dktarfnr flp`fid qua:

4. Qk iuarpn qua sa majd idar feralak-ta y ntrn qua as `dkzdmn hnrfznktd`-lakta masma `d lfsld d`turd, tdrmdka` lfsln tfalpn pdrd `àcdr d` sua`n.

5. @d fkmapakmakifd ma `d ldsd ak `didìmd `fera y a` `dkzdlfaktn vartfid`

as fcud` ma vä`fmd ak ns lnvflfaktnspdrdeù`fins.

9. Qk iuarpn `dkzdmn vartfid`laktahdifd drrfed y ntrn pdrdeù`fidlaktainlpàtn qua dìdkia d lfsld d`turdtdrmd a` lfsln tfalpn ak idar.

Astds aiudifnkas sa puamak netakar d pdrtfr ma` prfkifpfn ma fkmapakmakifd ma vflfaktns, tdktn ak a` saktfmn hnrfznktd` (aja x), inln ak a` saktfmn vartfid` (aja

Ak a` saktfmn hnrfznktd`, sa hdia prasakta a` lnvflfaktn raitf`ìkan ukfbnrla yparlfta akinktrdr a` dìdkia hnrfznktd`.

x < v

b . t

Ak a` saktfmn vartfid`, sa inksfmard a` lnvflfaktn ma idìmd `fera, y kns parmatarlfkdr a` tfalpn ma idìmd (t ), `d va`nifmdm d` `àcdr d` pfsn v

b y `d d`turd ma

mnkma bua sn`tdmn a` nejatn (h)7 sa inksfmard qua vf < ?.

c t5 5 h

Aiudifnkas ma` lnvflfaktn salfpdrdeù`fin (lsp)



Ajalp`n:

Ya majd idar ukd pa`ntd ink ukd va`nifmdm fkfifd` ma 2l/s, masma `d suparbfifa

ma ukd lasd p`dkd qua tfaka ukd d`turd ma 4.1l. Matarlfka: d) `d pnsfifùk ma

`d pa`ntd d ns ?.9 sacukmns maspuæs ma` dkzdlfaktn, e) d pnsfifùk ma d pa`ntdd` ihnidr ink a` pfsn y i) `d va`nifmdm ma `d pa`ntd dktas ma tnidr ink a` pfsn.

Yn`uifùk:

MD]NY:

vn < 2l/s

d < c < 6.8l/s5h < 4.1l

t < ?.9s

vb < >

Aiudifùk: pdrd matarlfkdr d va`nifmdm ma idìmd utf`fzdlns d sfcufakta aiudifùk:

d.

e. pdrd matarlfkdr `d pnsfifùk d` ihnidr a`

pfsn maealns matarlfkdr a` tfalpn d`

ihnidr a` pfsn prflarn

i. pdrd hd``dr `d va`nifmdm ak a` aja x as fcud` y ak a` aja y takalns:



Aiudifnkas ma lnvflfaktn pdrdeù`fin

]dlefæk ``dldmn lnvflfaktn ma prnyaitfàs, pnrqua tnmn nejatn `dkzdmn va`nifmdm fkfifd` y ink ifartn crdmn ma fki`fkdifùk raspaitn ma` dìdkia hnrfzn

masirfea ukd trdyaitnrfd ma idrditarìstfids sflf`dras. Dmaläs, `n lfsln qua alnvflfaktn lsp, axfsta fkmapakmakifd ma lnvflfaktn y pnr `n tdktn, pnmasfktatfzdr su astumfn, matarlfkdkmn ds inlpnkaktas raitdkcu`dras ma d va`niv

x , v

y `d d`turd läxfld H

l, a` tfalpn ma vua`n t, y a` dìdkia hnrfznktd` x.


4. Masma n d`tn ma uk didktf`dmn ma 1? l, as mfspd-rdmn uk prnyaitf` ink va`nifmdm hnrfznktd` ma 41l/s. Matarlfkdr a` tfalpn ma vua`n, a` dìdkia

hnrfznktd` y `d va`nifmdm d` `àcdr d` dcud.

Ynùifùk: inknifakmn `d d`turd, as pnsfeàmatarlfkdr a` tfalpn ma idìmd:

As flpnrtdkta rainrmdr qua ak `d d`turd läxfld, `d v y as iarn.

A` tfalpn qua tdrmd a` nejatn ak suefr, as a` lfsln qua fkvfarta ak edjdr hdstlfsld d`turd ma mnkma sa `dkzù.

t < < < < 4? 5?= s5 < 9 46= s5 . h 5 x 1? l 4?? l

vn

5 . sak5δ 5vnsakδ v

n

5 . sak5δ

5.c c cv

x

< v . insδ 7 v y

< v . sakδ 7 H l < 7 t < 7 x <

9



Inknifmn a` tfalpn y d va`nifmdm hnrfznktd`, pnmalns matarlfkdr a` d`idkia hnrfznktd`

_drd matarlfkdr a` vd`nr ma `d va`nifmdm bfkd`, sa raqufara matarlfkdr a` vd`nr ma `dva`nifmdm vartfid` d` lnlaktn ma hdiar inktditn ink a` dcud.

v y < c . t < 6,8 l/s5 . 9,46= s < 94,9?4 l/s

@d va`nifmdm bfkd` sarä aktnkias:

5. Matarlfkdr `ds inlpnkaktas raitdkcu`dras, `d d`turd läxfld, a` tfalpn mavua`n y a` d`idkia hnrfznktd` ma uk prnyaitf` qua hd sfmn mfspdrdmn d` kfvama` pfsn ink va`nifmdm fkfifd` ma 44? l/s y uk äkcu`n ma fki`fkdifùk ma 9?º.

x < v x . t < 41 l/s . 9,46= s < =3,64 l

v b < v

x

5 + v y

5 < (41 l/s)5 + (94,9?4l/s)5 < 45?=,315l/s < 9=,34 l/s



vn

5 . sak5δ (44? l/s)5 . sak59? º 45.4?? x ?,51 9.?51

5.c 5 x 6,8 l/s5 46,2 46,2 H

l < < < < < 41=,99

5vn .sakδ 5(44? l/s) . sak9? º 55? . ?,1 l/s 44? l/s

c 6,8 l/s5 6,8 l/s5 6,8 l/s5

x < < < < < 4?26,5= v

n

5 . sak5δ (44? l/s)5 . sak5 x9? º 45.4?? xsak 2?º 4?.=38,2

c 6,8 l/s5 6,8 6,8

Yn`uifùk: inlpnkakta hnrfznktd`

v x

< v . insδ < 44? l/s . ins9? º < 44? l/s . ?,822 < 61,52 l/s

Inlpnkakta vartfid`

v y

< v . sakδ < 44? l/s . sak9? º < 44? l/s . ?,1 < 11 l/s

D`turd läxfld

]falpn ma vua`n

t < < < < < 44,5

D`idkia hnrfznktd`



4. _rflarn, nrcdkfzdr crupns ma trd-edjn pdrd inkstrufr ukd idtdpu`-td. _ravfdlakta, fkvastfcdr quæ

as, su hfstnrfd= y `ns ldtarfdàskaiasdrfns pdrd inkstrufr`d.

5. Inlprnedr su bukifnkdlfaktn y axditftum pdrd ukd mfstdkifd ma 9 l.9. Ak `d präitfid, sa rad`fzdräk ifkin `dkzdlfaktns pdrd diartdr snera uk td-

eàrn ma tfrn d` e`dkin, in`nidmn pravfdlakta ak a` pfsn y d `d mfstdkifdprnpuastd.

=. A`denrdr ukd cräbfid masirfptfvd ma d trdyaitnrfd ma` prnyaitf` masma a` ln-laktn ma` dkzdlfaktn hdstd a` lnlaktn ma hdiar inktditn ink a` tdeàrn.

Ldtarfdàs

Ifktd lætrfid, ed`fkas, idtdpu`td, tdeàrn pdrd tfrn d` e`dkin(sa puama mfsaôdr ak uk p`facn ma idrtu`fkd, pdpa` parfùmfinn aspuld murd).


_rniamflfaktn


=. www.as.wfgfpamfd.nrcwfgfIdtdpu`td59g,ma`dgrngatd.wnmprass.inl

=

Fldcak lnmfbfidmd ma www.ma`dgrngatd.wnrmprass.inl

Uavfsa a` sfcufakta `denrdtnrfn vfrtud`:http://www.xtai.idt/~nidsa``d/dppàts/lnvpdrde/dppàtsn`5.htl



Ynùifnkdr ns sfcufaktas prneàlds, utf`fzdkmn ns inkiaptns, ds bùrlu`dsy `ns prniamflfaktns dmaiudmns pdrd idmd ukn.

• A`denrdr `d cräbfid ma aspdifn inktrd tfalpn (s vs t), dkd`fzdr yinkiùfr snera `d ra`difùk qua axfsta aktra s y t, `d pakmfaktama `d raitd y su saktfmn bìsfin.

• A`denrdr d cräbfid ma va`nifmdm inktrd tfalpn (v vs t), dkd`fzdry inkiùfr snera `d ra`difùk aktra v y t, a` ärad edjn `d raitd ysu saktfmn bìsfin.

4. @ns mdtns racfstrdmns d pdrtfr ma` lnvflfaktn ma uk vahìiu`n snera

ukd pfstd p`dkd y raitd drrnjdrnk `ns sfcufaktas rasu`tdmns:

5. Axprasdr ak Gl/h `d va`nifmdm ma uk lùvf` qua rainrra ?,?91 Gl ak 41 s.

9. Iuä` as a` aspdifn rainrrfmn (ak l), pnr uk lùvf` qua sa masp`dzd

ink ukd va`nifmdm ma 58,8 Gl/h murdkta 9 lfkutns.

=. Iuäktn tfalpn tdrmd ak rainrrar 3? gl, uk lùvf` qua vfdjd ink ukdva`nifmdm ma 3 l/s. Axprasdr `d raspuastd ak sacukmns.

=1s (l) ? 1 4? 41 5? 51 9? 91 =?

6t (s) ? 4 5 9 = 1 2 3 8



@ns sfcufaktas ajarififns sa rasua`vak edjn a` sfcufakta akukifdmn: mns vahìiu-`ns mfstdkifdmns pnr 4?? Gl tfakak va`nifmdmas ma 5? l/s y =? Gl/h ras-paitfvdlakta. Matarlfkdr d mfstdkifd qua ns sapdrd d` iden ma 5 hnrds sf:

4. _drtak ma` lfsln ùcdr, d `d lfsld hnrd y ak `d lfsld mfraiifùky saktfmn.

5. _drtak ma` lfsln ùcdr, d `d lfsld hnrd y ak `d lfsld mfraiifùkparn ak saktfmn inktrdrfn.

9. _drtak ma sus raspaitfvds astdifnkas d` lfsln tfalpn, D hdifd E yE hdifd D.

=. _drtak ma sus raspaitfvds astdifnkas D hdifd E y E hdifd D, parn Dsdà ukd hnrd maspuæs.

1. _drtak ma sus raspaitfvds astdifnkas d` lfsln tfalpn, D hdifd E y

E ak a` lfsln saktfmn ma D.

2. D puama dìdkzdr d E, sf pdrtak ma sus raspaitfvds astdifnkas d`lfsln tfalpn, D hdifd E y E ak a` lfsln saktfmn ma D. Yf as dsì,iuäktn tfalpn raqufara D pdrd dìdkzdr d E.

3. Matarlfkdr `d d`turd ma uk amfbfifn, sf masma su puktn läs d`tn sa

majd idar ukd asbard qua tdrmd 3,1 sacukmns ak `àcdr d` pfsn.

8. Ink quæ va`nifmdm `àcd `d asbard ma` ajarififn dktarfnr.

6. Masma ukd d`turd ma 5? l, sa `dkzd hdifd drrfed uk nejatn inkva`nifmdm ma 5? l/s. Matarlfkdr `d d`turd läxfld qua puamadìdkzdr, a` tfalpn qua tdrmd ak `àcdr d` pfsn y `d va`nifmdm ma`àcdmd




snùifnkdr sftudifnkas bìsfids radàs ma `d vfmd mfdrfd.

Inkiùsfnkas

Avdùdifùk

¾Tuæ dprakmfù ink `d ditfvfmdm>Rd`nrdr a` trdedjn rad`fzdmn, d prasaktdifùk y masdrrn``n ma d cuìd, d dp`fid-ef`fmdm ma d aiturd, y ma sar pnsfeà, prnpnkar lnmfbfidifnkas pdrd lajnrd

Qtf`fzdr ds axprasfnkas vfstds y ns prniasns ldtalätfins dmaiudmns pdrdsnùifnkdr `ns sfcufaktas prneàlds:

4. Qkd asbard latä`fid as `dkzdmd masma ukd d`turd ma 5 l ink va`n-ifmdm hnrfznktd` ma = l/s. Matarlfkdr:

d. A` tfalpn qua tdrmd ak idar.e. A` dìdkia hnrfznktd`.i. @d va`nifmdm vartfid` d` `àcdr d` pfsn.m. @d va`nifmdm bfkd`.

5. Qk dvfùk vfdjd ink va`nifmdm hnrfznktd` ma 45? l/s d ukd d`turd ma5 Gl7 ak asa fkstdkta, sua`td uk nejatn qua maea idar ak uk puktnsnera `d ]farrd d ukd mfstdkifd ma 5.=?? l. Edjn astds inkmfifnkas,¾sarä pnsfeà iulp`fr a` nejatfvn>

9. _drd netakar d ldynr abfifakifd ak uk dkzdlfaktn ma mfsin, a` dtàtdmaea idìu`dr a` lajnr äkcu`n pdrd su dkzdlfaktn. Yf supnkalns qua`d va`nifmdm ink `d iud` as `dkzdmn as ma 9? l/s, idìu`dr a` dìdkia

hnrfznktd` pdrd 9?º, =?º, =1º, 1?º y 2?º, y matarlfkdr ink iuä` maastns äkcu`ns sa netfaka a` ldynr dìdkia. ¾Yuiamarä n lfsln ink`d d`turd läxfld> ¾Tuæ pdsd ink a` tfalpn>



Dutnavdùdifùk

UAB@AXFNKN YNEUA LF _UNIAYN MA D_UAKMFZDJA

Ditfvfmdmas ma dprakmfzdja qua masdrrn``æ Dprakmfzdjas

DitfvfmdmLa

custùKn lacustù

Luymfbìif`

Mfbìif` Bäif` Dprakmì

d`cn KuavnAstn yd`n sdeìd

_drd fr inksn`fmdkmn a` prniasn ma dprakmfzdja, sa prnpnka astd ditfvf-mdm iuyd bfkd`fmdm as qua raidpftuà `n trdedjdmn hdstd asta puktn. Dsìsa prnluavak `ns prniasns ma latdinckftfvns qua à dyumdräk d praifsdrdifartns y mfbfiu`tdmas ak a` dprakmfzdja, `ns iudàs maea dkd`fzdr y dyumdrd sn`vaktdr pnr lamfn ma ntrn tfpn ma ditfvfmdmas. @d fmad as qua trdedjafkmfvfmud`lakta, parn sf `n inksfmard, puamak snifd`fzdr ink sus inlpdôa-

rns. D inktfkudifùk hdy ukd sarfa ma pracuktds7 n fkvftdlns d raspnkmar`ds:

_faksa ak `ds ditfvfmdmas qua rad`fzù ak astd ukfmdm y raspnkmd:

• ¾Iuäàs snk `ns dpnrtas läs vd`fnsns ma astd ukfmdm>

• ¾Ak quæ ifriukstdkifds puama dp`fidr d`cukns ma `ns inkiaptns dprak-mfmns ak astd ukfmdm> Mæ ajalp`ns.

• Masirfed ma quæ ldkard `ncrù inlprakmar lajnr `ns talds masdrrn`-`dmns ak astd ukfmdm. Qtf`fia `d sfcufakta rajf``d:



Buarzd

Qkfmdm 5. Mfkälfid. A lnvflfaktn y sus idusds Yasfùk

=

Dtrdiifùk bdtd`

@d inlukfmdm ifaktìbfid inksfmard qua tnmd `d ldtarfd maùkfvarsn astä sujatd d iudtrn buarzds bukmdlaktdàs: `d crd-

vamdm, a` aàitrnldckatfsln y `ds buarzds kuiàdras buartasy mæefàs. @d fktardiifùk kuiàdr buarta ldktfaka juktns `nsprntnkas y `ns kautrnkas ak a` kúiàn dtùlfin, d pasdr ma

`d rapu`sfùk aktra `ns prntnkas ma idrcd pnsftfvd qua ma ntrn lnmn `nshdrìd sapdrdrsa. @d buarzd kuiàdr mæef` ’ukd mflfkutd pdrta (4?-59) ma`d fktardiifùk kuiàdr buarta’ as d qua rnlpa ns kautrnkas, bnrldkmnuk prntùk y axpu`sdkmn uk aàitrùk ak bnrld ma rdmfnditfvfmdm eatd.

@d inlprasfùk ma astds iudtrn buarzds eäsfids hd sfmn fkbùakifdmd pnr`d tanrìd iuäktfid, sacúk `d iud` `d rdmfdifùk sa alfta n kn ak nkmdsinktfkuds, sfkn ak paquaôns pdquatas ma akarcìd maknlfkdmns iudktns.Astd fmad sa dp`fiù pnr prflard vaz d `ns idlpns aàitrnldckætfins, y`d tanrìd iuäktfid ma d aàitrnmfkälfid inksfmard tnmds ds rdmfdifnkasaàitrnldckætfids ak tærlfkns ma iudktns ``dldmns bntnkas, qua snkdesnrefmds y alftfmds pnr `ns aàitrnkas.

Idmd buarzd pdraia takar su prnpfd pdrtìiu`dlaksdjard inln a` bntùk. @d buarzd kuiàdrmæef` as trdkspnrtdmd pnr `ds pdrtìiu`ds Sy Z7 `d fktardiifùk kuiàdr buarta, pnr `nspfnkas. @d crdvamdm pnr `ns crdvftnkas, dúksfk mataitdr.



Ink a` masiuerflfaktn ma `ns TQDUGY, `ds pdrtìiu`ds qua bnrldk `nsprntnkas y ns kautrnkas, sa masdrrn``n d tanrìd irnln mfkälfid iuäktfid(TIM), pdrd axp`fidr `ds buarzds qua ditúdk aktra a``ns.

Ak `d tanrìd iuäktfid aàitrnmfkälfid sn`n axfsta uk tfpn ma pdrtìiu`dlaksdjard: a` bntùk, sfk aledrcn ak `d TIM axfstak kn lakns ma nihn``dldmns C@QNKAY qua trdkslftak `d buarzd y ‐pacdk“ d `ns qudrgs.

@d buarzd kuiàdr mæef` as `d qua mfvfma `ns kautrn-

kas, idusdkmn `d rdmfnditfvfmdm eatd. Astd buarzd astrdkspnrtdmd pnr ds pdrtìiu`ds S y Z. Mdmn qua astdspdrtìiu`ds snk luy crdkmas, d buarzd kuiàdr mæef` asabaitfvd sn`n ak mfstdkifds axtraldmdlakta inrtds.

Iudkmn ak uk kúiàn dtùlfin uk kautrùk sa masinlpn-ka ak uk prntùk y uk aàitrùk (ukd pdrtìiu`d eatd), ukdpdrtìiu`d S pdsd akarcìd aktra ds pdrtìiu`ds. @d pdrtìiu`d

eatd sa alfta masma a` kúiàn ma` ätnln ak a` qua a`kautrùk astä idlefdkmn. Ma `d masinlpnsfifùk eatdsa masprakma tdlefæk uk dktfkautrfkn, ukd lfstarfnsdpdrtìiu`d sfk ldsd, dukqua pnrtdmnrd ma ukd akarcìdqua kn tfaka idrcd.

@d fktardiifùk kuiàdr buarta ldktfaka ukfmn `ns prn-tnkas y kautrnkas ak a` kúiàn, d pasdr ma qua `ns

prntnkas ma idrcd pnsftfvd sa rapaàk. Ak astd buarzd, dakarcìd, trdkslftfmd pnr pfnkas, ditfvd ds enleds kuiàdras y ldktfakaakiakmfmds d `ds astra``ds. As abaitfvd snera ukd mfstdkifd inrtd, dsì quapuama dpratdr pnmarnsdlakta `ns kúiàns läs paquaôns. @ns kúiànsläs crdkmas kn astäk ukfmns tdk buartalakta, y snk fkastdeàs maefmnd `d rapu`sfùk dmfifnkd` aktra crdkmas kúlarns ma prntnkas.



trfifmdm, y sa akidrcd ma ldktakar d `ns aàitrnkas sapdrdmns y ak ùreftdd`ramamnr ma` kúiàn. Ya trdkslfta pnr pdrtìiu`ds maknlfkdmds bntnkas

vfrtudàs. Dukqua ns idlpns aàitrnldckætfins kn snk tdk crdkmas inln`ns ma `d crdvamdm, a` ma `d ]farrd sa axpdkma pnr lfàs ma gf`ùlatrnshdifd a` aspdifn axtarfnr.

@d crdvamdm as `d buarzd qua kns ldktfaka snera `d ]farrd, d `d @ukd akùreftd, d `ns p`dkatds cfrdkmn d`ramamnr ma` Yn` y d `ds cd`dxfds ukfmds. As`d lakns inlprakmfmd ma `ds iudtrn buarzds eäsfids, as prnedeà qua sa

trdkslftd pnr pdrtìiu`ds ``dldmds crdvftnkas, dukqua æstds kukid sadkmataitdmds, puas kn pdraiak takar abaitn snera ntrd ldtarfd. As `d läsmæef` ma `ds iudtrn buarzds1.

1 Dutnr Ifakifd axp`fidmd Encntä: Rnùktdm



Bukmdlaktn taùrfin

Inln saclaktn ma raitd mfrfcfmd, su raprasaktdifùk cräbfidas ukd bàihd. A` puktn ma mnkma pdrta, matarlfkd a` puktnma dp`fidifùk y `d puktd fkmfid a` saktfmn.

Raitnr

Ak tærlfkns cakardàs, uk vaitnr as uk saclaktn ma raitd mfrfcfmn iuyd `nkcftum asa` vd`nr ma `d ldckftum vaitnrfd` qua raprasaktd, y iuyd nrfaktdifùk kns fkmfid `dmfraiifùk y a` saktfmn ma dquæ``d.

Qkd vaz rad`fzdmd `d àiturd dktarfnr, raspnkmd `ds sfcufaktas pracuktds:

_racuktds Uaspuastds¾Ya hd pracuktdmn quæ buarzdsditúdk snera `ns dvfnkas pdrd quasa ldktakcdk ak a` dfra>¾Iraa ustam qua uk iuarpn puamaparldkaiar ak lnvflfaktn sfkqua ditúa kfkcukd buarzd snera æ`>Axp`fqua.¾Iùln iraa qua ditúd `d buarzdma `d crdvamdm pdrd qua `d ùkd saldktakcd ak ùreftd y `ns p`dkatdscfrak d`ramamnr ma` sn`>Alpuja uk `dmrf``n ak ukd su-parbfifa p`dkd. ¾_nr quæ `d idjdmfslfkuya su va`nifmdm> Axp`fqua.



Ak iudktn d d kntdifùk ldtalätfid ds idktfmdmas vaitnrfdàssa raprasaktdk ink bàihd snera a` knlera ma` vaitnr. _nrajalp`n: a` vaitnr buarzd as:

Axfstak vaitnras qua tfakak a` lfsln puktn ma dp`fidifùk y samaknlfkdk inkiurraktas. V sf dmaläs, inlpdrtak ldckftum,mfraiifùk y saktfmn, snk aqufpnàktas. Qk vaitnr npuastn dntrn as a` qua tfaka a` lfsln puktn ma dp`fidifùk, lùmu`ny mfraiifùk, parn saktfmn inktrdrfn. _nr ajalp`n: pdrd a`vaitnr su npuastn as - .

Npardifnkas ink vaitnras

Yuld ma vaitnras

Lætnmn ma` pdrdà`ncrdln



Ya puama suldr vaitnras pnr mns lætnmns cräbfins: a` ma` pdrdà-`ncrdln qua inksfsta ak raprnmuifr ns mns vaitnras inkiurraktasinktrdrfns, bnrldkmn uk pdrdà`ncrdln. A` rasu`tdmn sa netfakad` ukfr a` puktn ma inkiurrakifd y a` puktn iaktrd` hdifd mnkmasa juktdk ds raprnmuiifnkas ma ns mns vaitnras fkfifdàs. V a` ma`

pn`ìcnkn inksfsta ak uefidr idmd vaitnr ukn d inktfkudifùk ma`ntrn7 a` vaitnr rasu`tdkta sa netfaka d` ukfr a` fkfifn ma` prflarvaitnr ink a` bfkd` ma` ú`tfln.

Lætnmn ma` pn`ìcnkn

Uastd ma vaitnras

@d rastd ma mns vaitnras as `d suld ma` prflarn ink a` npuastnma` sacukmn. _drd hdiar `d mfbarakifd ma mns vaitnras, edstd ink

dp`fidr D - E < D + (-E), astn as, suldr a` vaitnr npuastn.



_rnmuitn pnr uk asid`dr

Lu`tfp`fidr uk vaitnr pnr uk asid`dr as tnldr a` vaitnr tdktds vaias inln fkmfa` asid`dr, `n iud` as vä`fmn tdlefæk, ak `ns idsns iudkmn a` asid`dr as brdiifnk

n kacdtfvn.

Inlpnkaktas raitdkcu`dras ma uk vaitnr

Qk vaitnr sa puama masinlpnkar ak mns inlpnkaktas: `d inlpnkakta `d inlpnkakta y:

D x

< D . insδ 7 D y

< D . sakδ

Buarzd

As `d diifùk qua sa ajaria snera uk iuarpn pdrd idlefdr su astdmn ma lnvflfa

ma rapnsn n pdrd prnmuifr mabnrldifnkas ak a` lfsln. _nr ukd buarzd, pnma

pnkar ak lnvflfaktn uk iuarpn, idlefdr su mfraiifùk ma masp`dzdlfaktn n m

kar`n, `n lfsln qua dp`fidr ukd prasfùk pdrd mabnrldr`n.



@d buarzd sa inksfmard ukd idktfmdm vaitnrfd` pnrqua pdrd inlprakmar su abaitnbìsfin, sa raqufara inkniar kn sù`n su ldckftum sfkn tdlefæk, su mfraiifùk y sak-tfmn. D` dp`fidr ukd buarzd snera uk e`nqua qua sa akiuaktrd snera ukd suparbfifahnrfznktd`, sf `d mfraiifùk ma `d buarzd infkifma ink `d suparbfifa y astä mfrfcfmdhdifd `d maraihd, a` nejatn sa lnvarä ak a` lfsln saktfmn. Yf idlefdlns a` sak-tfmn ma `d buarzd hdifd `d fzqufarmd, parn inksarvdkmn su mfraiifùk y ldckftuma` nejatn sa lnvarä hdifd `d fzqufarmd.

Iudkmn snera uk lfsln iuarpn ditúdk vdrfds buarzds, a` nejatn sa lnvarä ak a

saktfmn qua fkmfid a` vaitnr ma `d buarzd rasu`tdkta.

Ya dp`fidk mns buarzds: D y E.

@d buarzd rasu`tdkta sa netfaka d pdrtfr ma `d suld vaitnrfd` ma tnmds `ds buarzdsdp`fidmds.

A` nejatn sa luava ak a`saktfmn ma `d buarzd rasu`tdkta.

D E

Br



Buarzds laiäkfids

_asn ( ): as `d buarzd qua ajaria `dcrdvamdm snera uk iuarpn7 sa mabfkainln a` prnmuitn ma `d ldsd pnr `dcrdvamdm. Astn sfckfbfid qua a` pasnpuama vdrfdr, sacúk a` vd`nr ma `dbuarzd ma `d crdvamdm.

]aksfùk (]): as d buarzd qua sa ajariapnr lamfn ma ukd iuarmd fkaxtaksfe`a,ma ldsd maspraifde`a ak ra`difùk ink`d ldsd ma` iuarpn `fcdmn d a``d.

Knrld` (K): as `d buarzd parpakmfiu-`dr d `d suparbfifa qua rasu`td inln

radiifùk d ukd buarzd dp`fidmd akasa lfsln puktn, pnr diifùk ma ukiuarpn dpnydmn snera a``d. Iudkmn dsuparbfifa as hnrfznktd`, tfaka `d lfs-ld ldckftum ma` pasn7 sf d suparbfifaas fki`fkdmd, d knrld` infkifma ink dinlpnkakta vartfid` ma` pasn.



B n t n S f g f p a m f dUnzdlfaktn (Br): as `d buarzd qua axfsta

aktra mns suparbfifas ak inktditn. Axfstakmns i`dsas: a` rnzdlfaktn astätfin qua

sa prasaktd iudkmn ukd buarzd axtarkdtrdtd ma masp`dzdr `ds suparbfifas7 tfaka `dlfsld ldckftum qua `d buarzd axtarkd ysaktfmn inktrdrfn7 a` rnzdlfaktn ifkætfin saprasaktd iudkmn hdy lnvflfaktn ra`dtfvnaktra `ds mns suparbfifas ak inktditn.

Buarzd a`ästfid raiupardmnrd: as d buarzdajarifmd pnr uk rasnrta, lua``a n edkmda`ästfid qua as mabnrldmd (dulaktn nmfslfkuifùk ma su `nkcftum fkfifd`), astämfrfcfmd ak saktfmn inktrdrfn d d mabnrld-ifùk y su ldckftum mapakma ma d vdrfdifùk

ma d nkcftum y d inkstdkta ma a`dstfifmdmG. @d ra`difùk aktra `d buarzd dp`fidmd y `d`nkcftum ma `d mabnrldifùk astä mdmd pnr@d `ay ma Hnng.

Buarzd iaktrìpatd: inrraspnkma d `dinlpnkakta rdmfd` ma `d buarzd rasu`tdktaqua ditúd snera uk iuarpn qua masirfeaukd trdyaitnrfd ifriu`dr.

Buarzd iaktrìbucd: sa inksfmard inln ukdbuarzd ma radiifùk d `d buarzd iaktrìpatd,iudkmn æstd as prnmuifmd pnr `d pdrtìiu`dqua cfrd ink lnvflfaktn ifriu`dr snera a`dcakta qua nidsfnkd a` lnvflfaktn

B n t n S f g f p a m f d



@ay ma `d fkarifd:

@ns trdedjns masdrrn``dmns pnr Cd`fàn a prnpnrifnkdrnk`d edsa pdrd d prflard ay ma Kawtnk. Cd`fàn majù idar`feralakta nejatns pdrd nesarvdr d diifùk ma d crdvamdm,y pdrd nesarvdr lajnr a` bakùlakn, majù rnmdr asbards pnruk p`dkn fki`fkdmn. @d asbard masiakmìd y uacn dsiakmìd pnr ntrnp`dkn ink mfstfktd fki`fkdifùk d` prflarn, `n iud` matarlfkù qua `d asbarddìdkzded sfalpra `d lfsld d`turd, parn rnmded hnrfznktd`lakta luihnläs àjns iudkmn a` äkcu`n ma fki`fkdifùk ma` sacukmn p`dkn ard laknr.Inkiùya qua tnmns `ns nejatns tfakmak d ldktakar su astdmn fkfifd` malnvflfaktn. Kawtnk `ncrù ra`difnkdr a` inkiaptn ma fkarifd ink `d ldsd ydsì akukifd su prflard ày ‐tnmn iuarpn tfakma d parldkaiar ak su astdmnma rapnsn n ma lnvflfaktn raitf`ìkan ukfbnrla ak a` qua sa akiuaktrahdstd iudkmn ukd buarzd axtarkd ditúa snera æ` pdrd idlefdr mfihn astdmn.

D` hde`dr ma fkarifd sa fkvnùird a` inkiaptn ma psaumnbuarzd, inksfmardmdinln dqua``d buarzd ma `d iud` sa inknia su abaitn bìsfin parn kn su nrfcakkf puktn ma dp`fidifùk

@ayas ma Kawtnk

Fsddi Kawtnk kdifù ak a` dôn 42=5, a` lfsln dôn iudkmn luara Cd`fàn. Idsf tnsus dôns ma iradtfvfmdm `ns iulp`fù ak `d Qkfvarsfmdm ma Idlerfmca, Fkc`dta

_rflarn inln astumfdkta y maspuæs, inln prnbasnr d`tdlakta mfstfkcufmn. Kusa idsù, y su parsnkd`fmdm inktfkúd fktrfcdkmn d `ns astumfnsns hdstd kuastrns mrasarvdmn, d vaias irìptfin, akramdmn ak rfôds parsnkdàs ink `ns arumftns, inkmfù su dtakifùk kn sù`n d `d bìsfid y `ds ldtalätfids, sfkn tdlefæk d `d ra`fcfùk d`quflfd.

@n úkfin ak `n iud` tnmn a` lukmn astä ma diuarmn as ak su erf``dkta tdàktn. prneàlds fktrfcdedk d `ns ifaktìbfins ak `ns tfalpns ma Kawtnk: `ds àyas ma` l

lfaktn, ds ayas ma ds ùreftds p`dkatdrfds y d ldtalätfid ma d vdrfdifùk inktfkuidktfmdmas, uk idlpn qua sa inknia ditud`lakta inln: iäìu`n mfbarakifd` a fkta_uama dbfrldrsa ink justfifd, qua Kawtnk bua a` prflarn ak rasn`var ns tras prneàl



_rfkifpfn bukmdlaktd` ma `d mfkälfid:

Kawtnk astdeàia d ra`difùk mfraitd aktra d buarzd dp`fidmd y d vdrfdifùkak d va`nifmdm (diaàrdifùk), qua axparflaktd ukd ldsd qua parldkaiainkstdkta.

_nr `d dktarfnr ra`difùk, pnmalns matarlfkdr `ds ukfmdmas ma buarzd dsì:

Ak a` sfstald LGY, `d ukfmdm ma buarzd as a` kawtnk (K) y ak a` sfstaldics, as `d mfkd. Ya inksfmard qua 4 K < 4??.??? mfkds.

¾Hd paksdmn d`cukd vaz quæ maea hdiar pdrd qua uk iuarpn inlfakia d lnvarsa>

¾Tuæ sa maea hdiar pdrd qua uk iuarpn maja ma lnvarsa>

A` sfcufakta vfman prasaktd `d flpnrtdkifd qua tfaka `d prflard @ay ma Kawtnk

pdrd d laiäkfid. Astd ay astdeàia `ns ldrins ma rabarakifd fkarifdàs y d bnrld

p`dkd ma` aspdifn7 dmaläs, d trdvæs ma a``d sa puama mabfkfr `d ldsd fkarifd`.

Ak a` sfcufakta ak`dia hdy uk vfman snera `d prflard ày ma Kawtnk:

Knlera: ]d`àr 9 4rd @ay ma KawtnkMurdifùk: 4=:58 lfkutns



@ay ma diifùk y radiifùk

Fkfifd`lakta, sa puama dbfrldr qua pdrd tnmd diifùk axfsta ukd radiifùk,y masma a` puktn ma vfstd ma` dkä`fsfs ma buarzd, Kawtnk inkiùyù qua sfsa dp`fid ukd buarzd snera ukd suparbfifa ak uk puktn _ (diifùk), fkla-mfdtdlakta dpdraia ukd buarzd ma `d lfsld ldckftum parn ma saktfmninktrdrfn (radiifùk), d d buarzd dp`fidmdak a` lfsln puktn ma `d suparbfifa. Dastds buarzds sa às maknlfkd pdras mabuarzd. _nr ajalp`n: uk iuarpn in`nidmnsnera ukd suparbfifa hnrfznktd` ajariapnr diifùk ma su pasn, ukd buarzd snera`d suparbfifa, fklamfdtdlakta d suparbf-ifa ajaria ukd buarzd ma ldckftum fcud`y ak saktfmn npuastn d `d prflard ak a`lfsln puktn ma dp`fidifùk.

Uaspnkmd d `ds sfcufaktas pracuktds:

- ¾Ak a` aspdifn, àjns ma iud`qufar buakta ma crdvftdifùk, uk

aàbdkta y uk rdtùk takmrìdk a` lfsln pasn> ¾_nr quæ>

Yf masma ukd kdva aspdifd` mfspdrd ukd ed`d ma idôùk hdifd a`

aspdifn sfk brfiifùk, ¾sdeas iuäktd buarzd hdy qua ajariar snera

`d ed`d pdrd qua sa ldktakcd ak lnvflfaktn>



Flpu`sn:

Inrraspnkma d` prnmuitn ma `d buarzd dp`fidmd snera uk nejatn pnr uktfalpn matarlfkdmn. Ak a` sfstald LGY sa lfma ak K/s y ak a` sfstaldics, sa lfma ak mfkds/s. _nr sar a` prnmuitn ma uk vaitnr pnr uk asid`dr,a` rasu`tdmn as uk vaitnr.

Idktfmdm ma lnvflfaktn `fkad`:

]nmn iuarpn qua sa akiuaktrd ak lnvflfaktn pnsaa ukd idktfmdm malnvflfaktn qua aqufvd`a d` prnmuitn ma su ldsd pnr `d va`nifmdm.

@ds ukfmdmas ak a` sfstald LGY snk `ns kawtnks, y ak a` sfstald ics, `dsmfkds.

Yf quaralns matarlfkdr `d idktfmdm ma lnvflfaktn ma uk sfstaldma pdrtìiu`ds, maealns akinktrdr `d suld vaitnrfd` ma `d idktfmdm malnvflfaktn ma idmd pdrtìiu`d ak cakard`.

Knlera: ]d``ar 9: 5md @ay ma KawtnkMurdifùk: 48:=5 lfkutns

Asta vfman fktaktd raspnkmar d `d pracuktd: ¾quæ

inksaiuakifds tfaka d fktardiifùk ink ns nejatns

bìsfins>



Lùmu`n ma laidkfzdmn edsdmn ak lntnras `fkad-às masdrrn``dmn ak Fmagn, ink va`nifmdmas ma 4??

l/lfk y diaàrdifnkas ma 4? l/s5.

B n t n h t t p : / / w w w . f k t a r a l p r a s d s . k a t

Ma fcud` bnrld, `d buarzd qua ajaria a` ldrtf``n snera `d puktf``d, y `d qua

ajaria d puktf``d snera a` ldrtf``n, snk buarzds ma diifùk-radiifùk. Idmd ukd

ma astds buarzds ditúd snera mfbaraktas iuarpns: ukd snera d puktf``d y d ntrd

snera a` ldrtf``n7 iud`qufard ma æstds puama sar `d diifùk y ntrd `d radiifùk.

Uaspnkmd ds sfcufaktas sftudifnkas ma diuarmn d n qua nesarvd mfdrfdlakta:

• Axp`fqua n qua suiama iudkmn mns parsnkds lnktdmds snera pdtfkas

sa alpujdk `d ukd d `d ntrd.

• Yf astä snera ukd pfstd ma hfa`n y pratakma dkzdr uk nejatn, ¾quæ iraa

qua suiamarä>

Knlera: ]d`àr 9: 9ard @ay ma KawtnkMurdifùk: 8:=1 lfkutnsAk æsta vfman sa md raspuastd d `d pracuktd: ¾Iùln fktarditúdk




Ldtarfdàs

_dpa` pdrd pàcdmn, ifktd lætrfid,tfzd n ldridmnr, p`dkn, e`nquama ldmard, pdpa` `fjd, pnàd bfjd,4,1 l ma pftd, ldsds ma 4?? c,1? c, 5? c y 4?c, cdkihns i`fpsldrfpnsd, cdkihns i`fps inrrfaktasy trdkspnrtdmnr.

_rniamflfaktn

4. Nrcdkfzd uk aqufpn ma trdedjn ink ifkin astumfdktas.

5. Idmd ukn, inkstrufr ukd rdkd ma pdpa` ak nrfcdlf.

9. Yaàiifnkdr `d qua sd`ta lajnr.

=. Mfeujdr uk p`dkn idrtasfdkn snera a` pfsn.

1. Qefidr d rdkd ak a` nrfcak y mdrà mfaz flpu`sns, inksarvdkmn sfal-pra `d mfraiifùk qua fkmfqua `d ideazd ma `d rdkd.

2. Uacfstrdr `ns puktns (pdrajds nrmakdmds), ma `d pnsfifùk pdrd idmd

flpu`sn.

3. A`denrdr ukd cräbfid d asid`d 4:1? ak pdpa` lf`flatrdmn, y matarlfkdr

`d `nkcftum ma idmd vaitnr.

8. Akinktrdr `d trdyaitnrfd (suld ma ldckftumas ma `ns vaitnras).

1

F l d c a k l n m f b f i d m d m a w w w . t d r f k

c d . k a t .



6. Akinktrdr a` vaitnr masp`dzdlfaktn.4?. Mfspnkar a` p`dkn, a` trdkspnrtdmnr, `d pnàd bfjd y `d iuarmd, ma td`

bnrld qua sa puamd vdrfdr a` äkcu`n ma fki`fkdifùk (bfcurd 4), ink

bdif`fmdm.

44. _acdr a` pdpa` `fjd ak ukn ma `ns `dmns ma` e`nqua ma ldmard.

45. Matarlfkdr `d ldsd ak gc y `d buarzd ak K, kaiasdrfds pdrd qua aè`nqua sa mas`fia snera a` p`dkn hnrfznktd` (fkfifd`lakta pdrd ldmard-ldmard y ùacn pdrd `fjd-ldmard). Matarlfkdr ink dktarfnrfmdm `dldsd ma `ns mfbaraktas aàlaktns utf`fzdmns.

_`dkn fki`fkdmn ]rdkspnrtdmnr_nàd

@fjd



49. In`nidr a` e`nqua ma ldmard snera uk axtraln ma` p`dkn y àvdktdràktdlakta a` lfsln axtraln, hdstd ncrdr qua a` e`nqua inlfakia dmas`fzdrsa snera d suparbfifa. Matarlfkdr a` vd`nr ma` äkcu`n (prflarnldmard - ldmard y ùacn ldmard `fjd).


D pdrtfr ma d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y ns prniasnsrad`fzdmns matarlfkdr `d axp`fidifùk bìsfid pdrd idmd avaktn astumfdmn

Matarlfkdr d inlpnkakta vartfid` ma` pasn, d inlpnkakta hnrfznktd` ma`pasn y d buarzd ma rnzdlfaktn astätfin, supnkfakmn qua a` inabfifakta marnzdlfaktn as ± < ?,9.

Buarzd marnzdlfaktn

Inlpnkaktavartfid` ma` pasn

Inlpnkaktahnrfznktd` ma` pasn Knrld` Äkcu`n



=

Yn`uifùk:

Yn`uifùk:

Ajarififns ma dp`fidifùk

4. Matarlfkdr cräbfidlakta a` vaitnr rasu`tdkta d pdrtfr ma `ns sfcufavaitnras:

5. Qk vaitnr tfaka ukd ldckftum ma 8 il y prasaktd ukd fki`fkdifùk inkpaitn ma `d hnrfznktd` ma 9?º. Matarlfkdr `ds inlpnkaktas raitdkcu`d

D x

< D . insδ < 8 ins 9?N < 8 x ?,822 < 2,658

D y

< D . sakδ < 8 sak 9?N < 8 x ?,1 < =



9. Ak a` sfcufakta sfstald, matarlfkdr sf `d ldsd l4 sa luava, y sf as dsì, ma-tarlfkdr `d diaàrdifùk: l4 < 1 Gc7 l5 < = Gc. ± < ?,9.

Ynera l4 ditúdk = buarzds: a` pasn,`d knrld`, `d taksfùk maefmn d` pasnma l5 y a` rnzdlfaktn d` fktarditudrink `d suparbfifa.

Ynùifùk:

@d knrld` y a` pasn tfakak a` lfsln vd`nr pnrqua astäk d`fkadmds pnrakinktrdrsa l4 snera ukd suparbfifa hnrfznktd`. _nr `n tdktn, `d buarzd

rasu`tdkta aktra `ds mns as fcud` d iarn (?).

Matarlfkalns dhnrd, d buarzd rasu`tdkta aktra d taksfùk y a` rnzdlfaktn:l4 sù`n sa luava, sf `d prflard as ldynr qua `d sacukmd.

@d suldtnrfd ma `ds buarzds hnrfznktdàs as:

l4

l5



Ynùifùk:

D pdrtfr ma` prfkifpfn bukmdlaktd` ma d mfkälfid (sacukmd ay ma Kawtnk),pnmalns matarlfkdr a` vd`nr ma `d diaàrdifùk:

=. Qk ifi`fstd sa masp`dzd snera ukd idrratard raitd ink ukd va`nifmdm maGl/h. Yf su ldsd as ma 15 Gc y `d ma `d efifiàtd as ma 4? Gc, matarla` vd`nr ma `d idktfmdm ma lnvflfaktn.

`d ldsd tntd` ma` sfstald aqufvdà d `d suld ma `d ldsd ma` ifi`fstd y `d ldsdma `d efifiàtd, y `d va`nifmdm `d axprasdlns ak l/s:

Dp`fidlns `d ày ma Hnnga:

1. Matarlfkdr `d inkstdkta ma a`dstfifmdm ma uk rasnrta qua raqufara buarzd ma 9 K pdrd dulaktdr su `nkcftum ak ?,1 l.

Ynùifùk:



4. Ak `ds sfcufaktas cräbfids qua raprasaktdk sftudifnkas intfmfdkds,matarlfkdr ds buarzds qua ditúdk snera idmd iuarpn y raprasaktdr`dsink vaitnras snera idmd mfeujn.



9. Matarlfkdr ds inlpnkaktas raitdkcu`dras ma ns sfcufaktas vaitnras

• Ldckftum fcud` d 9 il fki`fkdifùk ma 9?º.

• Ldckftum fcud` d 1 il fki`fkdifùk ma =1º.

• Ldckftum fcud` d 8 il fki`fkdifùk ma 2?º.

5. Matarlfkdr ak bnrld cräbfid y utf`fzdkmn a` lætnmn qua inksfmarainkvakfakta, a` vaitnr rasu`tdkta ak idmd idsn:



=. Ak ns sfcufaktas sfstalds ma iuarpns fcdmns, matarlfkdr d buarzdrasu`tdkta snera d ldsd 4 y akinktrdr su dia`ardifùk ak idmd idsn:

l4 < 9 Gc7 l5 < 1 Gc7 l9 < 8 Gc7 ± < ?,9



1. Qk rasnrta subra ukd vdrfdifùk ma = il ak su `nkcftum, d` dp`fidràukd buarzd ma ?,9 K. Matarlfkdr a` vd`nr ma `d inkstdkta ma a`ds-tfifmdm.

2. ¾Tuæ buarzd maea hdiarsa snera uk rasnrta pdrd vdrfdr su nkcftumak 1 il, sf su inkstdkta ma a`dstfifmdm as ma 26 K/l>

3. ¾Iuä` as d inkstdkta ma a`dstfifmdm rasu`tdkta d` in`nidr ns rasnrtasma `ns ajarififns 1 y 2 ak sarfa>

Axp`fidr `d flpnrtdkifd y dp`fidifnkas ma `ns talds trdtdmns ak `d cuìd, pdrdsnùifnkdr sftudifnkas bìsfids radàs ma `d vfmd mfdrfd.

Inkiùsfnkas

Avdùdifùk

¾Tuæ dprakmfù ink `d ditfvfmdm>

Rd`nrdr a` trdedjn rad`fzdmn, d prasaktdifùk y masdrrn``n ma d cuìd, d dp`fid-ef`fmdm ma d aiturd, y ma sar pnsfeà, prnpnkar lnmfbfidifnkas pdrd lajnrd`d netakifùk ma `ns `ncrns prnpuastns.

@ns sfcufaktas ak`dias à dyumdräk d rabnrzdr `d talätfid vfstd y d p`dktadr sakif``ds

axparfakifds ma `denrdtnrfn.

_UFLAUD @AV MA KAS]NK:

http://axparflaktnsidsarns.kat/5?4?/4?/axparflaktn-prflard-ày-ma-kawtnk/

http://axparflaktnsidsarns.kat/5?4?/4?/fkarifd-y-àyas-ma-kawtnk/

]AUIAUD @AV MA KAS]NK:

http://axparflaktnsidsarns kat/5?4?/4?/axparflaktns-tariard-ày-ma-kawtnk/



Dutnavdùdifùk

A` sfcufakta asquald ma avdùdifùk rabàjd `ns dspaitns d vd`nrdr ma sutrdedjn y, snera tnmn, ma sus dprakmfzdjas murdkta astd ukfmd. @d id`fbfid-ifùk lìkfld sarä ma 1, y d läxfld ma 5? puktns, pnr n qua d puktudifùklamfd inksfmardmd kaiasdrfd pdrd dprnedr ds ditfvfmdmas sarä, ak asta idsnma 4? puktns.

Asidsn

dprakmfzdja4

Dprakmfzdja

lamfn5

Euak dprakmf-

zdja9

Axiaàkifd ak

a` dprakmfzdja=

Kntdifùkkulærfid

Inlprak-sfùk ma `nsinktakfmns

B d ` t d m ainlprak -sfùk ma `nsinktakfmns.

Asidsd inlp-raksfùk ma `dsfkmfidifnkasmdmds pdrd `drad`fzdifùk.

I n l p r a k m aeäsfidlakta`ds fkmfidifnkasmdmds pdrd `drad`fzdifùk.

Euakd inlp-raksfùk ma `dsfkmfidifnkasmdmds pdrd `drad`fzdifùk.

Eúsquamdma `d fkbnr-ldi fùk yutf`fzdifùkma `ns ra-iursns akFktarkat

Kn hd utf-` fzdmn mabnrld sdt-f s b d i tn r f d`ns raiursnsr ai nl ak -mdmns.

Ak nidsfnkaskn hd utf`fzdmnma bnrld sdt-fsbditnrfd `nsraiursns rain-lakmdmns

Hd utf`fzdmn nsraiursns rain-lakmdmns mabnrld sdtfsbdi-tnrfd.

Hd utf`fzdmn nsraiursns rain-lakmdmns mabnrld sdtfsbdi-tnrfd.

Hd alpàdmnntrns raiursnskn rainlak-mdmns ma bnrldfkjustfbfidmd

Hd alpàdmnntrns raiursnskn rainlak-mdmns ma bnrldfkjustfbfidmd.

Ya hd `flftdmnd alpàdr `nsraiursns rain-lakmdmns pdrd`d rad`fzdifùkma `ds ditfvf-mdmas.

Dmaiudifùkma `ds tdradsd` prniasnraquarfmn

@ds tdradskn sa ra-d ` fzdk td `y inln saprnpnkak.

Ak pnids nid-sfnkas rad`fzdk`ds tdrads td` yinln sa prn-pnkak.

Idsf sfalpra`ds tdrads sadjustdk d` prn-iasn prnpuas-tn.

@d rad`fzdifùkma `ds tdradssa djustdk d `nprnpuastn.



4Aquf`ferfn ma `ns iuarpns

Qkfmdm 9. Astätfid Yasfùk

1

Yua`n: murdkta uk ajarififn ma sua`n, tnmda` ärad ma` dpdrdtn maea sar iuefartd pnr a`cflkdstd. A` ajarififn inkstd prfkifpd`laktama tras d ifkin mfdcnkdàs (sarfas dirneätf-ids rad`fzdmds d `n `drcn ma ukd mfdcnkd`ma` sua`n), `àvdmds d iden ak mfbaraktasmfraiifnkas. @ns aàlaktns ma trdksfifùk(lnvflfaktns cflkästfins qua sa rad`fzdk

aktra `ds mfdcnkdàs), maeak sar ajaiutdmnsink a` rftln y d drlnkìd dprnpfdmns. A` äradma` dpdrdtn inlprakma 45 pnr 45 latrns.

Ided``n ink drins: a` cflkdstd maea iuerfrink su ajarififn `ds tras ärads ma` pntrn, a`lamfn y dlens axtralns, lfaktrds rad`fzdinktfkuns lnvflfaktns ifriu`dras fktarrul-pfmns sù`n pnr ds raquarfmds tfjards. @ds úkf-ids pdrtas ma` iuarpn qua puamak tnidr a`dpdrdtn snk `ds ldkns. A` ided``n ink drinslfma 441 il ma d`tn y a` ided``n ak sì, lfma91 il ma dkihn pnr 42? il ma `drcn. @dscrupds ma` ided``n maeak astdr sapdrdmds ma=? d =1 il.

Cflkdsfd2



Dkf``ds: a` ajarififn ma dkf``ds maeafkiùfr d` lakns mns pdrdmds maldkns: ukd, ajaiutdmd pnr lamfnma `d buarzd y `d ntrd, d trdvæs ma`

ed`dkian. D` lakns uk aàlaktnma buarzd maea sar `àvdmn d idenmurdkta mns sacukmns. Ajalp`ns maastns aàlaktns ma buarzd snk aÌrfstn, d iruz fkvartfmd n d p`dkihd.

Yd`tn: idmd sd`tn astä i`dsfbfidmn aka` iùmfcn ma puktudifùk, qua ntnrcd

`d kntd sacúk a` aàlaktn qua sa`àvd d iden murdkta a` ajarififn, asmaifr, d idmd tfpn ma sd`tn. A` cflkdstd tfaka qua supardr ukdd`turd y ukd mfstdkifd lìkflns akidmd sd`tn. A` dtarrfzdja maea sar

bfrla, sfk kfkcúk pdsn ma snerd yak `ìkad ink a` pntrn.

Edrrds pdrdà`ds: uk ajarififn mapdrdà`ds inksfsta eäsfidlakta akaàlaktns ma ed`dkian y vua`n.

Inlpnkaktas ma buarzd puamak saralpàdmns ak `d rutfkd, dukqua knsnk kaiasdrfns.

Ya axfca qua a` cflkdstd ajaiuta mnsaàlaktns ma ed`dkian: ukn dpnyd-mn y a` ntrn in`cdkmn ma `ds edrrds.

@ds edrrds pdrdà`ds sa sftúdk d 461il ma d`tn. Idmd edrrd lfma 41? ilma drcn y d sapdrdifùk aktra dledspuama sar djustdmd ma =5 d 15 il.

Edrrd bfjd: a` ajarififn ma edrrd bfjdinksfsta axiùsfvdlakta ma aàlak-tns ma ed`dkian sfk pdrdmds. Ya àaxfca d` cflkdstd qua ajaiuta pnr`n lakns uk lnvflfaktn ak a` iud`sua`ta `d edrrd y ùacn sa vua`vd d

dcdrrdr d a``d (ukd ‘‖sua`td‖‖), y tdl-efæk maea àvdr d iden uk ed`dkian(swfkc), mnrsd` (ink `d aspd`md maidrd d `d edrrd). @d edrrd bfjd sa sftúdd 531 il ma d`tn. Lfma 5=? il ma`drcn y tfaka 5,8 il ma mfälatrn.




_racuktds Uaspuastds¾Ya hd pracuktdmn iùln as qua puamaldktakarsa ma pfa> ¾V iùln as qua tn-mns ns iuarpns qua astäk d su d`ramamnrsa ldktfakak ak aquf`ferfn> ¾Iuä` as suaxp`fidifùk d astns bakùlakns>¾Tuæ tfpn ma aquf`ferfn utf`fzdk ns cfl-kdstds pdrd kn idarsa> ¾Iraa ustam quaasta mapnrta astä `fcdmn d `d bìsfid> ¾Maquæ ldkard>

_ùkcdsa ma pfa ink `ns erdzns defartnsy matarlfka mnkma astä su iaktrn maaquf`ferfn. Axp`fqua su raspuastd.

Qefqua a` iaktrn ma crdvamdm ma iudtrnnejatns qua ustam asinjd (pnr ajalp`n:ukd brutd, uk `fern, uk zdpdtn, ati.).

Uavfsa a` sfcufakta `denrdtnrfn vfrtud`:

http://www.xtai.idt/~nidsa``d/dpp`ats/p`dfki`/dpp`atsn`5.htl,

Bukmdlaktn taùrfin

Aquf`ferfn ma `ns iuarpns

Qk iuarpn sa akiuaktrd ak aquf`ferfn, iudkmn `d suldtnrfd vaitnrfd` ma tnmdbuarzds qua ditúdk snera æ`, as fcud` d iarn, as maifr, `d buarzd rasu`tdkta as fcuiarn. _drd qua astn sa iulp`d maeak axfstfr mns inkmfifnkas: `d prflard, qua ak aquf`ferfn trds`difnkd`7 y d sacukmd, qua astæ ak aquf`ferfn rntdifnkd`. Qk iuapuama astdr ak aquf`ferfn trds`difnkd` sfk takar uk aquf`ferfn rntdifnkd` y vfiava



Aquf`ferfn trds`difnkd`: uk iuarpn astä ak aquf`ferfn trds`difnkd` iudkmn d suldtnrfdma tnmds ds buarzds inkiurraktas (buarzds qua ditúdk snera uk lfsln puktn), sneraæ`, as fcud` d iarn.

Aquf`ferfn rntdifnkd`: uk iuarpn astä ak aquf`ferfn rntdifnkd` iudkmn `d suld ma`ns tnrquas n lnlaktns ma tnrsfùk qua ditúdk snera æ`, as fcud` d iarn, as maifr,iudkmn mns n läs buarzds pdrdà`ds (kn inkiurraktas), aktra sì, ditúdk snera ukiuarpn y puamak hdiar qua a` iuarpn cfra n rnta snera uk aja y prnmuzid uk tnrquan lnlaktn ma tnrsfùk snera a` lfsln.

Ya inksfmard qua a` tnrqua n lnlaktn ma tnrsfùk ma ukd buarzd, as a` prnmuitn ma`d fktaksfmdm ma `d buarzd pnr `d mfstdkifd parpakmfiu`dr masma a` puktn n aja marntdifùk hdstd su `ìkad ma diifùk.

@d suld vaitnrfd` ma ds buarzds sa ncrd, akinktrdkmn fkfifd`lakta ds inlpnkaktasraitdkcu`dras ‐x“ y ‐y“ pdrd ùacn, rad`fzdr `d suldtnrfd inrraspnkmfakta y d` bfkd`,hd``dr a` vaitnr rasu`tdkta.

(tanrald ma _ftäcnrds )

As rainlakmdeà a`denrdr `d cräbfid ma `ns vaitnras ditudktas, ink a` äkfln mainlprakmar ink ldynr bdif`fmdm a` sfstald.

I`dsas ma aquf`ferfn

Ak iudktn d` aquf`ferfn trds`difnkd`, axfstak tras i`dsas ma aquf`ferfn qua sa inksf-mardk pdrd mns inkmfifnkas mfbaraktas ak `ds iudàs sa puama akinktrdr uk iuarpn



Iuarpn suspakmfmn: `d inkmfifùk pdrd qua uk iuarpn suspakmfmn astæaquf`ferfn as qua `d vartfid` qua pdsd pnr a` puktn ma suspaksfùk maea pdsdr pniaktrn ma crdvamdm ma` iuarpn.

Iaktrn macrdvamdm _uktn ma

suspaksfùk

Iaktrn macrdvamdm

_uktn masuspaksfùk

_uktn masuspaksfùk

Iaktrnma crdvamdm

• Aquf`ferfn astde`a: sa prasak

a` puktn ma suspaksfùk astä akifld ma` iaktrn ma crdvamYa idrditarfzd pnrqua a` ned` sar sapdrdmn ma su pnsfifùkaquf`ferfn, d` majdr ma ditudbuarzd, vua`va d su pnsfifùk fkf

• Aquf`ferfn fkastde`a: sa prasa

sf a` puktn ma suspaksfùk astämaedjn ma` iaktrn ma crdvamdmidrditarfzd pnrqua a` nejatn dsapdrdmn ma su pnsfifùk ma a`ferfn, d` majdr ma ditudr d buakn vua`va d su pnsfifùk fkfifd

•

Aquf`ferfn Fkmfbarakta: sa prastd sf a` puktn ma suspaksfùk iifma ink a` iaktrn ma crdvamdmidrditarfzd pnrqua a` nejatn dsapdrdmn ma su pnsfifùk ma a`ferfn, d` majdr ma ditudr d buadmnptd ukd pnsfifùk sflf`dr dpnsfifùk fkfifd`.



Iuarpns dpnydmns: `d inkmfifùk pdrd qua uk iuarpn dpnydmn astæ ak aquf`ferfnas qua `d vartfid` qua pdsd pnr su iaktrn ma crdvamdm idfcd maktrn ma `d edsa masustaktdifùk n sad `d pdrta snera `d iud` masidksd a` iuarpn.

Iaktrn ma crdvamdm ma uk iuarpn

As a` puktn mnkma sa supnka qua ditúd `d buarzd ma crdvamdm. Ak uk nejatn rìcfmna` iaktrn ma crdvamdm as uk puktn bfjn ink raspaitn ma` nejatn, dukqua kn astækaiasdrfdlakta `nid`fzdmn ak a` lfsln nejatn.

Läqufkds sflpàs

Ynk dqua``ds läqufkds qua bdif`ftdk `d rad`fzdifùk ma uk trdedjn pnrqua parlftak

• Aquf`ferfn astdeà: iudkmn d` sapdrdra` iuarpn ma su pnsfifùk ma aquf`ferfn,vua`va d raiupardr`d pnr sì lfsln.

• Aquf`ferfn fkastdeà: iudkmn d` sapdrdra` iuarpn ma su pnsfifùk ma aquf`ferfn, `dpfarma mabfkftfvdlakta.

• Aquf`ferfn fkmfbarakta: iudkmn d` sapdrdr

a` iuarpn ma su pnsfifùk ma aquf`ferfn,dmqufara iud`qufar pnsfifùk y sfcua ink-sarvdkmn `d qua takìd dktas.



_d`dkid: as ukd edrrd bfjd rasfstakta, qua puama cfrdr d`ramamnr ma uk puktn ]faka tras aàlaktns: d pntakifd (_), d rasfstakifd (U), y a` buìrn n puktn ma dp( ). Yacúk `d uefidifùk ma` buìrn, `ds pd`dkids sa puamak i`dsfbfidr ak tras cæka

• _d`dkid ma prflarcækarn: sa idrdi-tarfzd pnrqua a`buìrn sa akiuaktrdaktra `d pntakifdy `d rasfstakifd.

Ajalp`n: `ds tfja-rds, `ns d`fidtas, `dspfkzds, ati.

• _d`dkid ma sacukmncækarn: sa idrditarfzdpnrqua `d rasfstakifdastä aktra a` puktn madpnyn y `d pntakifd.Ajalp`n: `d idrratf``d,a` mastdpdmnr.

• _d`dkid ma tariar cækarn: sa idrditarfzd pnrqua `dpntakifd astä aktra d rasfs-takifd y a` puktn ma dpnyn.Ajalp`n: a` mapf`dmnr, `dspfkzds pdrd a` pdk n pdrda` hfa`n.



_nàds: inkstdk ma ukd ruamd didkd`dmd qua puama cfrdr snera su aja, mfslfku-yakmn d` läxfln a` rnzdlfaktn, y idlefdkmn `d mfraiifùk ma `d buarzd (taksfùk),qua sa dp`fid snera d iuarmd qua pdsd pnr su idkd`. Axfstak `ds sfcufaktas i`dsas:

• _nàd bfjd: sa idrditarfzd pnrqua suaja sa akiuaktrd bfjn d `d edrrd qua `duka d` snpnrta pdrd ldktakar`d sus-pakmfmd. Yu bukifùk as sflpàlaktaidlefdr d mfraiifùk y kn d ldckftumma `d buarzd.

Ajalp`n: sf hdy ukd pnàd bfjd y k lùvfàs, `d cdkdkifd laiäkfid qua sa netfakaastä mdmd pnr 7 sf hdy vdrfds bfjds y vdrfds lùvfàs `d cdkdkifd laiäkfid as

• _nàd lùvf`: su aja sfrva inln snpnrtapdrd `d rasfstakifd y sa snstfaka snera`d iuarmd snera `d iud` sa dp`fid `dbuarzd, `n iud` hdia qua `d buarzd sad`d lftdm ma `d rasfstakifd aqufvdàktad ukd cdkdkifd laiäkfid.

• _n`fpdstns: as uk sfstald ma pnàdslùvfàs ink ukd n vdrfds pnàds bfjds

Yacúk `d inkbfcurdifùk qua sa à mæsa netfaka ldynr n laknr cdkdkifdlaiäkfid.



_rniamflfaktn

4. Nrcdkfzdr a` aqufpn ma trdedjn y inkstrufr ak idrtu`fkd ds bfcurds prnpuastds.

5. Matarlfkdr a` iaktrn ma crdvamdm y a` iaktrn ma ldsd ma idmd bfcurd

Inksu`tdr snera a` lætnmn dprnpfdmn pdrd `ncrdr`n.

9. Qefidr tras puktns mfbaraktas ak idmd bfcurd, akifld, snera y maedjnma` iaktrn ma crdvamdm.

=. Yuspakmar ink a` hf`n y `d dcujd, `ds bfcurds ak bnrld inksaiutfvd maidmd ukn ma `ns puktns saôd`dmns, y matarlfkdr `d i`dsa ma aquf`ferfnak idmd idsn.


Ldtarfdàs

]rfäkcu`n fsùsiaàs, trfäkcu`n asidàkn, iudmrdmn, raitäkcu`npaktäcnkn racu`dr, paktäcnkn frracu`dr, haxäcnkn racu`drhaxäcnkn frracu`dr, iìriu`n, dcujd, hf`n, inkn mfkdlùlatrnldsds mfvarsds, 5 l ma pftd (iuarmd), trdkspnrtdmnr, 9 pnàdsbfjds y 9 pnàds lùvfàs.

2



1. Inkstrufr uk inkn ak idrtu`fkd y in`nidr`n ak `ds tras pnsfifnkas pnsf-eàs pdrd matarlfkdr `ds tras i`dsas ma aquf`ferfn. Ya puama prnpnkary inkstrufr ntrd bfcurd pdrd inksacufr a` lfsln abaitn dktarfnr.

2. Ak a` iuarpn huldkn, sa akiuaktrdk `ds tras i`dsas ma pd`dkids, ¾akmùkma sa akiuaktrd idmd ukd> Uad`fzdr a` mfeujn inrraspnkmfakta afkmfidr ak idmd idsn, `d uefidifùk ma `ns tras aàlaktns inkstftutfvns:rasfstakifd, pntakifd y puktn ma dpnyn.

3. Ink a` aqufpn ma trdedjn, raukfr `d ldynr idktfmdm ma nejatns quatakcdk dp`fidifùk ma pd`dkids.

8. I`dsfbfidr`ns ma diuarmn ink su cækarn (4º, 5º, 9º).

6. Ak ukd idrtaàrd, rad`fzdr `ns mfeujns inrraspnkmfaktas, fkmfidkmn `duefidifùk ma `d pntakifd, `d rasfstakifd y a` puktn ma dpnyn ak idmdidsn.

4?. Hdiar ukd axp`fidifùk d` rastn ma` iursn ink malnstrdifùk präitfid.

44. Qtf`fzdkmn mfbaraktas lnktdjas a fkfifdkmn ink d pnàd bfjd, matarlfkdrak bnrld präitfid, `d vaktdjd laiäkfid ma idmd ukn. A`denrdr cräbfidsy malnstrdr`d ak bnrld kulærfid.

45. A`denrdr `ds cräbfids ma idmd lnktdja.


D pdrtfr ma `d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y `nsprniasns rad`fzdmns, matarlfkdr `d axp`fidifùk bìsfid pdrd idmd avaktnnesarvdmn



1

=1º?2?º

y

B4

B5

x


4. Ya raqufara ldktakar suspakmfmd ukd ldsd ma 1? gc pnr lamfn ma mns imds qua bnrldk ink `d hnrfznktd`, äkcu`ns ma 2?º y =1º. ¾Iuä` as a` vd`n`d buarzd qua sa maea ajariar ak a` axtraln ma idmd iuarmd>

Yn`uifùk: snera a` p`dkn idrtasfdkn sa raprasaktd a` sfstald ma buarzds,mnkma ? inrraspnkma d` puktn (?,?)



_drd qua a` iuarpn astæ ak aquf`ferfn, `d suldtnrfd ma `ds buarzdsmaea sar ?. ]akfakmn ak iuaktd `ds inlpnkaktas raitdkcu`dras y `dnrfaktdifùk ma idmd ukd, pnmalns p`dktadr mns aiudifnkas:

Ya maspajd ak `d prflard aiudifùk y sa raalp`dzd ak `d sacukmd:

Uasn`vfakmn d aiudifùk pdrd sa matarlfkd qua < 918,34 K . Inkasta vd`nr, pnmalns matarlfkdr : < 512,554 K

Ynùifùk: pdrd àvdktdr`d idrratf``d y pnkar`dak lnvflfaktn, a` sfs-tald maea quamdr akaquf`ferfn. _nr `n tdktn,`d suld ma `ns tnrquasmaea sar fcud` d iarn.

_

U

5. Iuä` as `d buarzd kaiasdrfd pdrd pnmar trdkspnrtdr snera ukd idrratf``d, ukpasn ma 68 K. @d mfstdkifd ma` aja ma `d ruamd (buìrn), d `d buarzd ma` pasn asma 1? il7 y ma` buìrn d` puktn ma dp`fidifùk ma `d pntakifd, as ma 4,9 l.



Fcud`dkmn `ns mns tnrquas y maspajdkmn _, sa puama matarlfkdr suvd`nr:

9. _drd suefr hdstd ifartd d`turd, ukd ldsd ma 91 Gc, sa utf`fzd uk pn`fpdstnmns pnàds lùvfàs y ukd bfjd. ¾Iuä` sarä d buarzd kaiasdrfd pdrd suefr d l

Ynùifùk: maefmn d `d ldsd ma 91 Gc, `d rasfstakifd aqufvdà d su pasn:

U < 91Gc . 6,8 l/ sac 5 < 9=9 Kaw.

Ink mns pnàds lùvfàs y ukd bfjd, d vaktdjd laiäkfid qua sa netfaka as:



4. Ynera uk iuarpn, sa dp`fidk trasbuarzds ma fcud` ldckftum B4 <B5 < B9 < 5 K, inln sa fkmfidak `d bfcurd. Matarlfkdr cräbfidy kulærfidlakta, a` vd`nr ma `dbuarzd rasu`tdkta y sf as mfbarakta

ma iarn, astde`aiar d dia`ardifùkqua axparflaktd a` iuarpn.

5. Matarlfkdr d buarzd kaiasdrfd pdrd ldktakar a` sfstald ak aquf`ferfn,sf `d ldsd as ma 5? Gc.

B2?º

9. _drd avdktdr uk pasn ma 48 K, sa iuaktd ink ukd edrrd ma hfarrn ma 4,1

l ma nkcftum dpnydmd snera ukd pfamrd. Yf d mfstdkifd aktra a` nejatn

y `d pfamrd as ma 1? il, ¾Iuä` sarä `d buarzd kaiasdrfd pdrd lnvar`n.

=. Qk mastdpdmnr ma akvdsa tfaka ukd `nkcftum ma 45 il7 `d tdpd ma

`d cdsansd tfaka uk rdmfn ma 4,5 il y npnka ukd rasfstakifd ma ?,9



1. Iuä` as d buarzd kaiasdrfd pdrd suefr ukd ldsd ma =1 Gc, qua utf`fzd:

Uaprasaktdr ak bnrld cräbfid, a` lnktdja ak idmd ukn ma ns idsns dktarfnr

• Qkd pnàd bfjd

• Qkd pnàd lùvf`

• Qkd pnàd bfjd y ukd lùvfàs

• Qkd pnàd bfjd y mns lùvfàs

• Qkd pnàd bfjd y tras lùvfàs

Dutnavdùdifùk

Inlpàta `d sfcufakta tde`d pdrd vd`nrdr `ds ditfvfmdmas prnpuastds y rad`fzdmds hdstd a` lnlaktn. _drd a``n, ldrqua ink ukd X a` pnriaktdja quastfla dmaiudmn.


Iulp`flfaktn y

raspnksdef`fmdm

¾Iulp`fù ink ds aiturds

dsfckdmds, ds ditfvfmdmas

prnpuastds ak astd ukf-

mdm y `ns trdedjns fkmf-

vfmudàs n pnr aqufpn>

Iradtfvfmdm yid`fmdm

¾Dpnrtù fmads> ¾Astdsbuarnk sfckfbfidtfvds>

¾Uad`fzù sfk arrnr d`cukn`ds tdrads y/n `ns trdedjnsdsfckdmns>

Dprakmfzdja ydpnrtdifùk mainkniflfaktns

¾Tuæ tdktn dprakmfù yquæ tdktns inkniflfak-tns dpnrtù ak `ds i`dsas,ak `ds tdrads y/n `ns trd-edjns rad`fzdmns>



Akarcìd kuiàdr3

Akarcìd kuiàdr: as dqua``dqua sa `feard inln rasu`td-mn ma ukd radiifùk kuiàdr. Ya puamanetakar pnr a` prniasn ma Bfsfùk Kuiàdr(mfvfsfùk ma kúiàns dtùlfins pasdmns) nefak pnr Busfùk Kuiàdr (ukfùk ma kúiànsdtùlfins luy `fvfdkns). Ak `ds radiifnkaskuiàdras sa `feard ukd crdk idktfmdm ma

akarcìd maefmn d qua pdrta ma `d ldsd ma`ds pdrtìiu`ds fkvnùirdmds ak a` prniasn,sa trdksbnrld mfraitdlakta ak akarcìd. @ndktarfnr sa puama axp`fidr edsäkmnsa ak`d ra`difùk Ldsd-Akarcìd prnmuitn ma `dcakfd`fmdm ma` crdk bìsfin Dèart Afkstafk.

Ink ra`difùk d d feardifùk ma akarcìd, ukd radiifùk kuiàdr as uk lf``dr mavaias läs akarcætfid qua ukd radiifùk quìlfid. _nr ajalp`n: `d cakardmdpnr `d inleustfùk ma` inleustfeà bùsf` ma` latdkn.

Bfsfùk kuiàdr: as ukd radiifùk kuiàdr qua tfaka ùcdr pnr `d rnturd ma ukkúiàn pasdmn d` sar enledrmadmn pnr kautrnkas ma ifartd va`nifmdm. Drdìz ma astd mfvfsfùk a` kúiàn sa sapdrd ak mns brdclaktns dinlpdôdmn maukd alfsfùk ma rdmfdifùk, `feardifùk ma 5 ù 9 kuavns kautrnkas y ma ukdcrdk idktfmdm ma akarcìd (5?? LaR) qua sa trdksbnrld bfkd`lakta ak id`nr.

Dèart Afkstafk,bdlnsn ifaktìbfin dàläk.

B n t n S f g f p a

m f d

4]rdedjn, pntakifd y akarcìd

Qkfmdm =. Akarcìd Yasfùk

2



Qsns pdiìbfins ma `d akarcìd kuiàdr

Crdifds d` usn ma raditnras kuiàdras hny ak mìd as pnsfeà netakar flpnr-tdktas idktfmdmas ma ldtarfd` rdmfditfvn d edjn instn. As dsì inln masmabfkdàs ma `ns dôns =?, sa prnmuia ukd axpdksfùk ak a` alpàn pdiìbfinma mfvarsns tfpns ma Fsùtnpns Udmfditfvns ak mfvarsds ärads ma` quahdiarifaktìbfin y prnmuitfvn ma` hnlera.

Dcrfiu`turd y d`flaktdifùk: inktrn` ma p`dcds: ink `d taikn`ncìd kuiàdras pnsfeà dp`fidr `d ``dldmd ‐]æikfid ma `ns Fksaitns Astærfàs (]FA)“, quainksfsta ak sulfkfstrdr d`tds alfsfnkas ma rdmfdifùk fnkfzdkta d uk ifartncrupn ma fksaitns ldihns ldktakfmns ak `denrdtnrfn. @uacn `ns ldihnsastærfàs sa majdk ak feartdm pdrd bdif`ftdr su dpdradlfaktn ink ns fksaitnshalerd. Kn sa prnmuia, pnr akma, `d kaiasdrfd masiakmakifd. Ma astalnmn, ùacn ma suiasfvds y rfcurnsds rapatfifnkas ma` prniasn, as pnsfeà

inktrn`dr y mfslfkufr su pne`difùk ak ukd matarlfkdmd racfùk cancräbfid.

Lutdifnkas: `d frrdmfdifùk dp`fidmd d salf``ds, maspuæs ma flpnrtdktasy rfcurnsns astumfns, parlfta idlefdr `d fkbnrldifùk cakætfid ma ifar-tds vdrfamdmas ma p`dktds y vacatdàs ma inksuln huldkn. A` nejatfvnma `d tæikfid, as `d netakifùk ma kuavds vdrfamdmas ma aspaifas inkidrditarìstfids pdrtfiu`dras qua parlftdk a` dulaktn ma su rasfstakifd yprnmuitfvfmdm

A` prniasn ma `d bfsfùk parlfta a` bukifnkdlfaktn ma `ns Uaditnras Ku-iàdras qua ditud`lakta npardk ak a` lukmn.

Busfùk kuiàdr: `d busfùk kuiàdr niurra iudkmn mns kúiàns dtùlfinsluy `fvfdkns sa ukak, bnrldkmn uk kúiàn dtùlfin läs pasdmn ink ld-ynr astdef`fmdm. Astds radiifnkas `feardk akarcìds tdk aàvdmds qua ak `dditud`fmdm sa astumfdk bnrlds dmaiudmds pdrd ldktakar `d astdef`fmdm yinkbfkdlfaktn ma `ds radiifnkas.



Inksarvdifùk ma d`flaktns: `ds rdmfdifnkas snk utf-`fzdmds ak luihns pdìsas pdrd dulaktdr a` parìnmnma inksarvdifùk ma luihns d`flaktns. As flpnrtdkta

saôd`dr, qua d tæikfid ma frrdmfdifùk kn cakard abaitnssaiukmdrfns ak `d sdùm huldkd, sfakmn idpdz ma ra-muifr ak bnrld inksfmardeà a` kúlarn ma nrcdkfslnsy lfirnnrcdkfslns pdtùcakns prasaktas ak vdrfdmnsd`flaktns ma inksuln ldsfvn.

Hfmrn`ncìd: crdifds d` usn ma `ds tæikfids kuiàdras aspnsfeà masdrrn``dr mfvarsns astumfns ra`difnkdmns inkraiursns hìmrfins. Ak astumfns ma dcuds suparbfifdàsas pnsfeà idrditarfzdr y lamfr `ds inrrfaktas ma dcuds`ùvfds y ma kfava7 idumdàs ma rìns, bucds ak aled`sas,`dcns y idkdàs y `d mfkälfid ma `dcns y mapùsftns. Akastumfns ma dcuds suetarräkads as pnsfeà lamfr `nsidumdàs ma ds kdpds, fmaktfbfidr a` nrfcak ma ds dcudssuetarräkads, su amdm, va`nifmdm, mfraiifùk, bùjn, ra`d-

ifùk ink dcuds suparbfifdàs, inkaxfnkas aktra diuìbarns,pnrnsfmdm y mfsparsfùk ma diuìbarns.

Rdiukds: sa hdk a`denrdmn rdmfn vdiukds pdrd inledtfrakbarlamdmas pdrdsftdrfds ma` cdkdmn y qua dbaitdk `dprnmuiifùk paiudrfd ak cakard`. @ns dkfldàs snla-tfmns d` trdtdlfaktn snpnrtdk murdkta uk parìnmn läsprn`nkcdmn a` pa`fcrn ma ra fkbaiifùk sfalpra `dtakta

ak su lamfn kdturd`.

Lamfifkd kuiàdr: sa hd axtakmfmn ink crdk rdpfmaza` usn ma rdmfdifnkas y ma rdmfnfsùtnpns ak lamfifkdinln dcaktas tardpæutfins y ma mfdckùstfin. Ak a` mfdc-kùstfin sa utf`fzdk rdmfnbärldins pdrd mfvarsns astumfnsma: tfrnfmas, hìcdmn, rfôùk, latden`fsln, ifriu`difùk



Ak tardpfd læmfid: ink `ds tæikfids kuiàdras sa puama inledtfr ifartnstfpns ma iäkiar. Ink braiuakifd sa utf`fzdk trdtdlfaktns ak edsa d frrdmfd-ifnkas ink rdyns cdlld prnvakfaktas ma buaktas ma Ined`tn-2?, dsì inln

tdlefæk, asbards fktarkds rdmfditfvds, dcujds a hf`ns ma Ined`tn rdmfditfvn.Inlefkdkmn a` trdtdlfaktn ink ukd dmaiudmd y praldturd mataiifùk maìäkiar, sa netfakak tardpfds ink axftnsns rasu`tdmns.

Lamfn dlefakta: ak astd ärad sa utf`fzdk tæikfids kuiàdras pdrd `d matai-ifùk y dkä`fsfs ma mfvarsns inktdlfkdktas ma` lamfn dlefakta. @d tæikfidläs inknifmd raifea a` knlera ma Dkä`fsfs pnr Ditfvdifùk Kautrùkfid,edsdmn ak `ns trdedjns masdrrn``dmns ak 4692 pnr a` ifaktìbfin húkcdrn J.C.Havasy, _ralfn Knea` ma Tuìlfid ak 46==. @d tæikfid inksfsta ak frrdmfdrukd luastrd, ma td` bnrld, ma netakar d pnstarfnrf `ns aspaitrns cdlldqua a``d alfta, pdrd bfkd`lakta prniasdr `d fkbnrldifùk ink dyumd inl-putdifnkd`. @d fkbnrldifùk aspaitrd` fmaktfbfid `ns aàlaktns prasaktas ak`d luastrd y `ds inkiaktrdifnkas ma `ns lfslns.

Fkmustrfd a fkvastfcdifùk

]rdzdmnras: sa a`denrdk sustdkifds rdmfditfvds qua snk fktrnmuifmds ak uk

matarlfkdmn prniasn. @uacn sa mataitd d trdyaitnrfd ma `d sustdkifd crdifdsd su alfsfùk rdmfditfvd, n qua parlfta fkvastfcdr mfvarsds vdrfdeàs prnpfdsma` prniasn. Aktra ntrds vdrfdeàs, sa puama matarlfkdr idumdàs ma bùfmns,bf`trdifnkas, va`nifmdmas ak tuearìds, mfkälfid ma` trdkspnrta ma ldtarfdàs,idlefns ma bdsa ma `ìqufmn d cds, va`nifmdm ma mascdsta ma ldtarfdàs, ati.

Fläcakas: as pnsfeà netakar fläcakas ma pfazds ink su astruiturd fktarkdutf`fzdkmn rdmfncrdbìds ak edsa d rdyns cdlld n efak ink uk bùjn ma kau-

trnkas. Astds fläcakas raifeak a` knlera ma Cdlldcrdbìd y Kautrncrdbìdraspaitfvdlakta, y snk ma crdk utf`fmdm ak `d fkmustrfd inln lætnmn knmastruitfvn ma inktrn` ma id`fmdm. Ink astns lætnmns sa puama inlprnedr did`fmdm ak sn`mdmurds astruiturdàs, ak pfazds latä`fids bukmfmds, ak pfazdsiarälfids, pdrd dkä`fsfs ma hulamdm ak ldtarfdàs ma inkstruiifùk, ati.

Ak a` äleftn ma `d efn`ncìd, `d fktrnmuiifùk ma inlpuastns rdmfditfvnsldridmns hd parlftfmn nesarvdr ds ditfvfmdmas efn`ùcfids hdstd ak sus läs



@d akarcìd d trdvæs ma `d hfstnrfd

A` sar huldkn, masma sus prflarns pdsns ak `d ]farrd y d trdvæs ma `d

hfstnrfd, sfalpra hd eusidmn bnrlds ma utf`fzdr `d akarcìd pdrd netakar

ukd lajnr id`fmdm ma vfmd. _drd a``n, hd haihn usn ma mfvarsds bnrlds

ma akarcìd: buacn (akarcìd quìlfid), va`ds y ln`fkns (akarcìd ma` vfaktn

n aù`fid), ruamds hfmräu`fids (akarcìd ma` dcud n hfmräu`fid), idreùk (ak-

arcìd quìlfid), patrùàn (akarcìd quìlfid), kuiàdr (akarcìd kuiàdr), ati.

- 91?.??? d. I.: a` sar huldkn masiuera

a` buacn. Astn a parlftfù idàktdrsa, in-

ifkdr ns d`flaktns y dàjdr d ds eastfds.

- 6.??? d. I.: a` sar huldkn mnlastfid

dkfldàs pdrd pnmar inlar y pdrd utf-

`fzdr`ns inln dyumd ak a` trdedjn.

- 9.1?? d. I.: a` sar huldkn fkvaktd `d

ruamd, ntrd bnrld ma alpàdr d akarcìd

ak eakabfifn prnpfn.

- 5.??? d. I.: a` sar huldkn fkvaktd `d



va`d, ukd bnrld ma dprnvaihdr d akarcìdaù`fid pdrd kdvacdr.

- 1? d. I.: a` sar huldkn fkvaktd `d

ruamd hfmräu`fid y a` ln`fkn ma vfaktn,

`n qua supnka ukd bnrld ma dprnvaihdr

`d akarcìd hfmräu`fid ma` dcud y d aù`fid

ma` vfaktn.

- 4.345: sa fkvaktd d läqufkd ma vdpnr.

Astn supnka uk aknrla dvdkia ak `d fkmustrfd y ak a` trdkspnrta.

- 4.6??-4.639: aktra 46?? y 4643, a` inksuln ma akarcìd dulaktd aknr-

lalakta, sfakmn a` idreùk `d prfkifpd` buakta ma akarcìd. Aktra 4643 y4639 mfslfkuya a` inksuln ma idreùk y dulaktd kntdeàlakta a` ma

patrùàn. A` patrùàn, dmaläs, ard buakta ma luihds ntrds sustdkifds.

- 4.639-4.681: buarta irfsfs akarcætfid: a` patrùàn inlfakzd d dcntdrsa




_racuktds Uaspuastds

Inksu`ta: ¾pnr quæ as tdk flpnr-tdkta ak kuastrds vfmds `d akarcìd

kuiàdr>¾Iraa qua as pnsfeà trdksbnrldr

akarcìd laiäkfid ak ntrn tfpn ma

akarcìd> Axp`fqua su raspuastd.Knlera ifkin nejatns ma su idsd

mnkma sa trdksbnrla `d akarcìd aktrdedjn. Axp`fqua.¾Tuæ tfpn ma akarcìd iraa ustam as

`d qua prnmuia a` buacn>Iudkmn `ns idrrns astäk ak lnv-

flfaktn astäk prnmuifakmn uk tfpn

ma akarcìd. ¾Tuæ tfpn ma akarcìd as>

y sa inlfakzdk d usdr ntrds akarcìds:

kuiàdr, hfmrna`æitrfid, aù`fid, sn`dr, ati.

2. ]nldmn ma: http://raiursnstfi.amuidifnk.as/saiukmdrfd/amdm/=asnbfsfidquflfid/flprasns/qufkiakd2.pmb



]rdedjn

As uk prniasn ma trdksbarakifd ma akarcìd lamfdkta a` iud` sa prnmuia uk idlma pnsfifùk ma ukn n vdrfns iuarpns, as maifr, rad`fzdr uk trdedjn flp`fid dp`fidrbuarzd y uk masp`dzdlfaktn ‐mfbarakta ma iarn“.

4J < 4?3 a

4 ju`fn aqufvdà d 4 Kawtnk

pnr latrn,

4 arcfn aqufvdà d 4 mfkd pnr

iaktìlatrn,

Bukmdlaktn taùrfin

A` trdedjn (S) sa mabfka aktnkias, inlna` prnmuitn aktra `d buarzd rasu`tdktadp`fidmd y a` masp`dzdlfaktn ma` iuar-pn snera a` iud` sa dp`fid mfihd buarzd.

A` trdedjn as ukd idktfmdm asid`dr qua

sa axprasd ak a` sfstald LGY ak K/l7astd ukfmdm sa maknlfkd ju`fn (J).

Ak a` sfstald ics, a` trdedjn as `d buarzdrasu`tdkta aqufvdàkta d ukd mfkd qua

ditúd snera uk iuarpn pdrd masp`dzdr`nuk iaktìlatrn y sa à maknlfkd arcfn.

Axfsta ukd aqufvdàkifd aktra `ds mnsukfmdmas:



_ntakifd

D pdrtfr ma `d aiudifùk, pnmalns akinktrdr qua d ukfmdm ma

pntakifd ak a` sfstald LGY as Ju`fn / sacukmns qua aqufvdàd` vdtfn (S), n pntakifd ma `d läqufkd qua àvdktd uk pasnma 4 K d ukd d`turd ma uk l ak uk sacukmn.

Ntrd ukfmdm ma pntakifd as a` ided``n ma buarzd (H_), quaaqufvdà d 3=2 S, a` gf`nvdtfn hnrd qua as a` trdedjn qua rad`fzdukd läqufkd iuyd pntakifd as ma uk gf`nvdtfn murdkta ukdhnrd ma bukifnkdlfaktn.

Axfsta ra`difùk aktra d pntakifd y d va`nifmdm pdrd fktarvd`ns matfalpn lìkflns (‐t“ tfakma d iarn), qua sa puama axprasdr inln:

_ < B . v . ins δ

Aqufvdà d` trdedjn (S) rad`fzdmn pnr ukfmdm ma tfalpn (t). Akcakard`, ukd läqufkd takmrä läs pntakifd ak d lamfmd inlnrad`fzd uk trdedjn ak a` laknr tfalpn pnsfeà.

Qk kfôn drrdstrd ukd idrratd ink ukd buarzd ma 2?K, ak ukd mfstdkifd ma =?lbnrldkmn uk äkcu`n ma 9?º ink `d hnrfznktd`.¾Tua trdedjn rad`fzd asta>

Ynùifùk:

Mdtns:

B < 2?K

x < =?l

θ < 9?º

Ajalp`n:

w< B(ins?).x :

w< 2?K (ins9?º).(=?l) < 5?38.=2K.l



Akarcìd

@d akarcìd dsnifdmd d` lnvflfaktn sa maknlfkd akarcìd laiäkfid y inrraspnd `d suld ma `d akarcìd ifkætfid y `d akarcìd pntakifd`.

@d akarcìd ifkætfid d pnsaak tnmns`ns iuarpns ak vfrtum ma` lnvflfak-tn, y iudkmn `d trdksbfarak d ntrniuarpn ak rapnsn, sa mfia qua sarad`fzù uk trdedjn. _nr `n tdktn, a`trdedjn rad`fzdmn aqufvdà d d mfba-

rakifd aktra d akarcìd ifkætfid bfkd`y `d akarcìd ifkætfid fkfifd`.

Bntn Sfgfpamfd

@d akarcìd pntakifd` crdvftdifnkd` `d pnsaa ukiuarpn ak vfrtum ma `d d`turd mnkma sa akiuaktrdink raspaitn ma` kfva` ma` pfsn.

Ap < l . c . h

Mnkma l as `d ldsd, c `d diaàrdifùk maefmd d `dcrdvamdm y h d d`turd mnkma sa akiuaktrd d ldsd

@d akarcìd pntakifd` a`ästfid `d pnsaak `ns rasnrtas y `dsedkmds a`ästfids.

G as `d inkstdkta ma a`dstfifmdm ma` rasnrta n edkmd a`ästfid, x inrraspnkma`d vdrfdifùk ma d nkcftum qua axparflaktd a` rasnrta n edkmd a`ästfid iudkmsa às dp`fid ukd buarzd B .

@d akarcìd d` fcud` qua a` trdedjn, sa axprasd ak ju`fns (J) pdrd a` sfstald LG



@ns idrrns ma ukd lnktdôd rusd dìdkzdk suläxfld akarcìd ifkætfid iudkmn astäk ak a`

bnkmn ma su trdyaitnrfd.

B n t n w f g f p a m f d

B n t n w f g f p a m f d

@ay ma inksarvdifùk ma `d akarcìd

@d akarcìd kn sa irad kf sa mastruya, sfknqua sa trdksbnrld. Ak a` idsn ma `d akar-

cìd laiäkfid, pnmalns dbfrldr qua akuk sfstald ma buarzds inksarvdtfvds, `dakarcìd parldkaia inkstdkta, as maifr,`d akarcìd laiäkfid fkfifd` as fcud` d `dakarcìd laiäkfid bfkd`.

Qk iuarpn qua sa akiuaktrd d ifartd d`tu-rd (h) pnsaa akarcìd pntakifd` crdvftdifn-kd`, as maifr, d` sar `feardmn, inlfakzd didar pnr diifùk ma `d buarzd ma crdvamdmy `d akarcìd pntakifd` crdvftdifnkd` satrdksbnrld prncrasfvdlakta ak akarcìdifkætfid. As ma kntdr qua ak asta idsn, sasupnka uk sfstald fmad` iuyn rnzdlfaktninktrd a` dfra as ku`n.

Qk sfstald inksarvdtfvn fkvnùird buarzdsqua mdk nrfcak d `d akarcìd pntakifd` crd-vftdifnkd` n d `d akarcìd pntakifd` a`ästfid,inln ukd bukifùk qua mapakma axiùsf-vdlakta ma `d pnsfifùk fkfifd` y bfkd` maìuarpn y kn ma `d trdyaitnrfd sacufmd pnra` lfsln.

Idsf tnmd d akarcìd utf`fzdmd pnr d huldkfmdm sa hd nrfcfkdmn d pdrtfr ma d rdmfdifùksn`dr `àcdmd d `d ]farrd. Qk 62% ma `ds kaiasfmdmas akarcætfids quamdk sdtfsbaihdspnr `d inleustfùk ma idreurdktas bùsfàs inln idreùk, patrùàn y cds kdturd`, quaraprasaktdk `d akarcìd quìlfid d`ldiakdmd ak `d ]farrd. Iudkmn astds buaktas sahdydk dcntdmn, sa maearä eusidr idmd vaz ink ldynr mamfidifùk `ns idreurdktaskuiàdras (busfùk kuiàdr y bfsfùk kuiàdr), `d akarcìd ma crdvftdifùk ak `ds ldrads y



3

Ldtarfdàs

Eäsiu`d, ifktd lætrfid y irnkùlatrn.

_rniamflfaktn

4. Inkbnrldr a` aqufpn ma trdedjn.

5. Qtf`fzdr `d ifktd lætrfid pdrd matarlfkdr ukd mfstdkifd ma 5? l.

9. Ma inlúk diuarmn, saàiifnkdr d uk inlpdôarn pdrd rad`fzdr`d präitfid.

=. Qefidr mns fktacrdktas ma` aqufpn ak a` puktn fkfifd` y mns ak a`

puktn bfkd`. A` qufktn maea ldkajdr a` irnkùlatrn.

1. @d tdrad ma` astumfdkta saàiifnkdmn as trds`dmdr d sus inlpdôarnsd` ùcdr npuastn ma mnkma sa akiuaktrdk fkfifd`lakta, ma uknak ukn y ak a` laknr tfalpn pnsfeà.

2. A` irnknlatrfstd maea matarlfkdr ns tfalpns pdrifdàs pdrd idmdrainrrfmn.




3. @ns mdtns sa racfstrdk ak `d tde`d 4 lnma`n (sa raqufara inkniar `dldsd ma idmd ukn).

8. ]akfakmn ak iuaktd a` trdedjn rad`fzdmn, `d pntakifd y `d akarcìdraquarfmds ak a` ajarififn, matarlfkdr a` kúlarn ma id`nrìds yinksu`tdr snera `ns pnsfe`as d`flaktns qua `as parlftfrìdk raiupa-rdr asds id`nrìds. A`denrdr uk `fstdmn ma pnr `n lakns, tras lakúsmfbaraktas, ak ukd tde`d inln `d lnma`n.

]de`d 4

MfstdkifdAkarcìdifkætfid

]rdedjn _ntakifd]falpn


D pdrtfr ma d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y ns prniasnsrad`fzdmns matarlfkdr `d axp`fidifùk bìsfid pdrd idmd avaktn astumfdmn

Lakú 4 Lakú =Lakú 5 Lakú 9

]de`d 5



2


4. Qk e`nqua ma ldmard ma 5 Gc sa akiuaktrd snera ukd suparbfifa hnrfztd`, a` inabfifakta ma rnzdlfaktn as ma ?,9 y sa dp`fid ukd buarzd ma 4pdrdà`d d `d suparbfifa d trdvæs ma ukd iuarmd. Yf a` e`nqua ma ldmarmasp`dzd d ukd mfstdkifd ma 1? il, matarlfkdr a` trdedjn rad`fzdmn.

Ynùifùk: fkfifd`lakta sa maea matarlfkdr a` vd`nr ma d buarzd rasu`tdkta:

A` trdedjn rad`fzdmn as:

< 6,45 K x ?,1 l < =,12 J

5. ]akfakmn ak iuaktd a` ajarififn dktarfnr, sf `d buarzd kn as hnrfznktd`

qua prasaktd ukd fki`fkdifùk ma 2?º ink raspaitn ma `d hnrfznktd`, malfkdr a` trdedjn rad`fzdmn.

Ynùifùk:



Dsiaksnr

Inktrdpasn

_nàd

9. Matarlfkdr d pntakifd, axprasdmd ak ided``ns ma buarzd, ma` lntnr pdrd ukdsiaksnr ma ldsd fcud` d 1?? Gc, qua pnsaa uk inktrdpasn ma 5?? Gc, ukdidpdifmdm pdrd suefr ukd idrcd ma =8? Gc (8 parsnkds ink uk prnlamfn ma2? Gc idmd ukd), y suefr ma` pfsn 4 d 4? ak 51 s. @d d`turd ma idmd pfsn ama 5,8 l.

Ynùifùk: sa matarlfkd fkfifd`lakta `d ldsd tntd`:

@d buarzd qua maea rad`fzdr a` lntnr maea sar prnpnrifnkd` d` pasn ma `dldsd tntd`:

A` trdedjn tntd` rad`fzdmn as: (pdrd `àcdr ma` 4º d` 4?º pfsn a` dsiaksnr ra-inrra 6 pfsns).

< 32== K x 51,5 l < 465.258,8 J



@d pntakifd ak vdtfns (S) as:

@ns vdtfns sa axprasdk ak ided``ns ma buarzd (H_)

=. Ak a` axtraln suparfnr ma uk p`dkn fki`fkdmn ma 4 l ma `nkcftum y fki`fkdifùk ma =1º, sa sua`td uk e`nqua ma ldmard ma 1 Gc ma ldsd. Ymas`fzd snera `d suparbfifa sfk rnzdlfaktn, ink quæ va`nifmdm `àcd d` bma` p`dkn.

Ynùifùk: Fkfifd`lakta sa matarlfkd d d`turd

mnkma sa akiuaktrd a` nejatn.

h < 4 l . sak =1n < 4 l . ?,3? < ?,3? l

Dhnrd sa puama matarlfkdr d akarcìd pntakifd`.

A p < l . c . h < 1 Gc . 6,8 l/s5 x ?,3? < 9=,9 J

_nr a` prfkifpfn ma inksarvdifùk ma `d akarcìd y inksfmardkmn qua kn hdyrnzdlfaktn, `d akarcìd pntakifd` sa hd inkvartfmn ak akarcìd ifkætfid d``àcdr d` bfkd` ma` p`dkn. Yf maspajdlns `d va`nifmdm, pnmalns snùifnkdra` prneàld:



4. Matarlfkdr a` trdedjn rad`fzdmn ak `ns sfcufaktas idsns:

• Ynera ukd suparbfifa hnrfznktd`, ukd buarzd tdlefæk hnrfznktd`ma 4? K drrdstrd ukd ldsd ma ?,1 Gc y a` inabfifakta marnzdlfaktn as ma ?,51.

• @d lfsld buarzd ma` ajarififn dktarfnr sa dp`fid ink uk äkcu`nma 9?º.

• Ya dp`fid ukd buarzd ma 8 K pdrd hdiar suefr ukd ldsd ma ?,1Gc snera uk p`dkn fki`fkdmn 9?º, ink ukd `nkcftum fcud` d 4l sfk rnzdlfaktn.

5. Mns trdedjdmnras tfakak d lfsfùk ma àvdr idmd ukn hdstd a` tariarpfsn ma ukd inkstruiifùk, 4? eu`tns ma pacdkta pdrd ed`mnsd maàkihdpa ma `d inifkd. Idmd eu`tn tfaka ukd ldsd ma 51 Gc y `dmfstdkifd prnlamfn as ma 9 l pnr pfsn. A` prflarn suea ma eu`tnak eu`tn, lfaktrds qua a` sacukmn suea ak `ns tras prflarns vfdjasma d tras eu`tns y ak a` ú`tfln suea tdlefæk a` ú`tfln eu`tn. ¾Tufækrad`fzù läs trdedjn>

9. Qkd pd`d laiäkfid àvdktd ukd rnid ma 5=? Gc ma ldsd hdstd ma-pnsftdr`d snera a` p`dtùk ma ukd vn`quatd qua astä d 9 l ma d`turd,y tdrmd ak a` ajarififn ?,59 s. Matarlfkdr a` vd`nr ma `d pntakifd ma`d läqufkd.

=. Ak a` ajarififn 5, a` prflar trdedjdmnr sa malnrù 41 lfkutns y a`sacukmn 49 lfkutns. ¾Iuä` as `d pntakifd masdrrn``dmd pnr idmdukn>



1. Masma ukd d`turd ma 51 l, sa majd idar uk nejatn ma ldsd fcud`4? Gc. Matarlfkdr `d akarcìd ifkætfid y `d va`nifmdm d` lnlaktnma hdiar inktditn ink a` pfsn.

2. Masma a` axtraln suparfnr ma uk p`dkn fki`fkdmn =1º y ma 4,5 l,sa mas`fzd ukd ldsd ma 41 Gc sfk rnzdlfaktn. D` `àcdr d` bfkd` ma`p`dkn sa mas`fzd snera ukd suparbfifa hnrfznktd` iuyn inabfifaktama rnzdlfaktn as ma ?,9 qua as `d va`nifmdm d` `àcdr d` bfkd` ma`p`dkn. ¾Tuæ mfstdkifd dìdkzù d rainrrar dktas ma matakarsa>

< =1º

L 4

h

Avdùdifùk

¾Tuæ dprakmfù ink `d ditfvfmdm>Rd`nrdr a` trdedjn rad`fzdmn, d prasaktdifùk y masdrrn``n ma d cuìd, d dp`fid-ef`fmdm ma d aiturd, y ma sar pnsfeà, prnpnkar lnmfbfidifnkas pdrd lajnrdr


snùifnkdr sftudifnkas bìsfids radàs ma `d vfmd mfdrfd.

Inkiùsfnkas



Dutnavdùdifùk

D` tarlfkdr astd ukfmdm as flpnrtdkta rad`fzdr `d avdùdifùk ma tus dprak-mfzdjas. _drd a``n, asirfed ak a` mfeujn ma` iuarpn huldkn ak a` ùcdrfkmfidmn `ds raspuastds d `ns sfcufaktas fktarrncdktas:

d. Ak `d ideazd: ¾quæ dprakmfù ak astd ukfmdm>e. Ak a` iua``n: ¾pdrd quæ a sfrva d talätfid denrmdmd ak astd ukfmdm>i. Ak ukn ma `ns erdzns: ¾ak quæ ifriukstdkifds puama dp`fidr d`cukns

ma `ns inkiaptns dprakmfmns ak astd ukfmdm>m. Ak a` ntrn erdzn: ¾quæ pdrta ma `d talätfid sa à mfbfiu`tù>

a. Ak a` astùldcn: ¾quæ nestdiu`fzù su dprakmfzdja>b. Ak a` paihn: ¾quæ tdktn à custù `n qua dprakmfù>c. Ak `ns pfas: ¾quæ inksajn sa mdrìd d sì lfsln pdrd sar a` lajnr astu-

mfdkta ma astd i`dsa>



4Yasfùk

Kuavds taikn`ncìds

ak `d fkmustrfd d`flaktdrfd8

A` masdrrn``n ma kuavds taikn`ncìdsak `d Fkmustrfd D`flaktdrfd ink `dbfkd`fmdm ma netakar d`flaktnslìkfldlakta prniasdmns d `d vazqua sacurns y qua inksarvak sus

iud`fmdmas kutrfifnkd`as y nrcdkn-`æptfids, astä parlftfakmn d`drcdr dvfmd útf` ma luihns prnmuitns y sd-tfsbdiar `ns custns ma` inksulfmnr.

@d dpdrfifùk ma prnmuitns lìkfldlakta prniasdmns astä dsnifdmd d idlefn`ns häeftns ma inksuln. Ynk prnmuitns qua prasaktdk uk vd`nr dôdmfmn y ukdid`fmdm kutrftfvd y saksnrfd`, qua cakard`lakta sa inksulak irumns n ink uk tr

lfaktn tærlfin sudva. _nr asta lntfvn, rasu`td flprasifkmfe`a inkniar a` abaitn`ds mfstfktds taikn`ncìds ma inksarvdifùk ak su id`fmdm.

@ns ldynras dvdkias ak asta idlpn sa hdk inksacufmn ink a` masdrrn``n ma slds bìsfins, qua dbaitdk `d vfdef`fmdm ma `ns lfirnnrcdkfslns, sfk uk fkirala

8 HAUUAUN D L y UNLAUN MA ÄRF@D L M Kuavds taikn`ncìds ak `d fkmustrfd d`flaktdrfd Qkfva

Laiäkfid ma ufmnsQkfmdm 1. Hfmrnlaiäkfid Yasfùk

3

A`denrdifùk ma id



sustdkifd` ma d talpardturd ma` d`flaktn. Astns lætnmns‐kn tærlfins“ kn dbaitdk, n n hdiak lìkfldlakta d `dsidrditarìstfids kutrftfvds y saksnrfdàs ma `ns d`flaktns.

D`tds prasfnkas

Ditud`lakta, axfstak mns prniamflfaktns: `d prasfùk mf-kälfid, tnmdvìd kn utf`fzdmn d kfva` fkmustrfd` y d prasfùkastätfid, qua as `d qua hny tfaka dp`fidifùk präitfid.

Ak `d d`td prasfùk mfkälfid a` fkiralaktn ma prasfùk sanrfcfkd ak uk tfalpn luy inrtn (lf`æsflds ma sacukmn)inln inksaiuakifd ma ukd axp`nsfùk qua cakard ukdnkmd ma ihnqua, maknlfkdmd nkmd ma ihnqua hfmrn-mfkälfid. Astd taikn`ncìd inksfcua `d fkditfvdifùk malfirnnrcdkfslns y a` de`dkmdlfaktn ma ifartns tajfmns,inln idrka, pnr rupturd ma d astruiturd iaù`dr. Asta prn-iamflfaktn sa akiuaktrd ak bdsa ma astumfn y masdrrn``n.

@d dp`fidifùk ma d`td prasfùk astätfid sa edsd ak snlatard uk prnmuitn d aàvdmns kfvaàs ma prasfùk hfmrnstätfid(4??-4??? L_d) ma bnrld inktfkud murdkta uk ifartntfalpn (vdrfns lfkutns). D asta tfpn ma taikn`ncìd sa `dmaknlfkd inlúklakta d`tds prasfnkas hfmrnstätfids(Hfch _rassura _rniassfkc, H_). @d utf`fzdifùk ma d`tdsprasfnkas hfmrnstätfids sa rfca, bukmdlaktd`lakta pnr

mns prfkifpfns: d) @a Ihdta`far, akukifd qua iud`qufarbakùlakn (radiifnkas quìlfids, idlefns lnàiu`dras,ati.), qua vd dinlpdôdmn ma mfslfkuifùk ma vnùlaksubra uk fkiralaktn d` dulaktdr d prasfùk, y vfiavarsdy e) `d ày ma _dsid`, sacúk `d iud` ukd prasfùk axtarkddp`fidmd d uk bùfmn inkbfkdmn sa trdkslfta ma bnrldukfbnrla a fkstdktäkad ak tnmds `ds mfraiifnkas. Madiuarmn ink asta ú`tfln prfkifpfn astd taikn`ncìd puama



prnmuitn akvdsdmn sularcfmns ak uk bùfmnma prasurfzdifùk (ma edjd inlprasfef`fmdm).@d prasfùk dp`fidmd d` sfstald parlftfrìd uktrdtdlfaktn fsnstätfin y ukfbnrla fkmapak-mfaktalakta ma` tdldôn, bnrld y vnùlak

ma` ldtarfd` prniasdmn.

Ak a` laridmn puamak akinktrdsa prnmuitnsprasurfzdmns inln larla`dmds zulns, jd-àds, inkiaktrdmns y puræs ma brutds, pnstrasprnmuitns `äitans marfvdmns iärkfins iurdmns y inifmns `nkihadmns y prapdrd`fstns pdrd su inksuln Ink bfkas mfstfktns d `d inksarvdifùk, `d dp`fidifùk ma

prasfnkas hfmrnstätfids parlfta netakar mfstfktns tfpns ma caàs ma pasidmn, idhuavn y àiha. Dsì lfsln, astd taikn`ncìd diaàrd `d mfbusfùk ma snùtns ak mfvad`flaktns, `d snùef`fzdifùk ma cdsas y `ns prniasns.

Q`trdsnkfmns

@ns u`trdsnkfmns puamak mabfkfrsa inln nkmds diústfids fkdumfeàs ma ukd brai

ifd suparfnr d 5? gHz. _drd `d inksarvdifùk ma `ns d`flaktns, snk läs abfidiankmds u`trdsùkfids ma edjd braiuakifd (48-4?? gHz7 < 4=1 ll) y d`td fktaks(4?-4??? S/il5). A` abaitn inksarvdmnr ma `ns u`trdsnkfmns astä dsnifdmn d `nkùlakns inlpàjns ma idvftdifùk cdsansd, qua axp`fidk `d cakardifùk y avnùma lfirn eureujds ak uk lamfn `ìqufmn. Kn nestdkta, a` abaitn ma `ns u`trdsnksnera ns dcaktas d`tardktas ma ns d`flaktns as flftdmn y mapakmfakta ma lú`tbditnras pnr a``n, su dp`fidifùk sa hd akidlfkdmn hdifd d inlefkdifùk, sflu`tdn d`tarkd, ink ntrds fkknvdifnkas ak a` prniasn ma d`flaktns.

Frrdmfdifùk

Ak `d Fkmustrfd D`flaktdrfd, a` tærlfkn ma ‐frrdmfdifùk“ sa utf`fzd pdrd rabad trdtdlfaktns ak `ns qua `ns d`flaktns sa axpnkak d `d diifùk ma rdmfdifnfnkfzdktas murdkta uk ifartn tfalpn. Ak a` sfstald fktarkdifnkd`, `d mnsfs de



Ak mfvarsds fkvastfcdifnkas sa hd puastn ak avfmakifd qua iudkmn `d mnsfs desnr-efmd as m“ d 4? gCy `d bnrldifùk ma inlpuastns rdmfn `ìtfins kn supnka rfascnpdrd `d sdùm.

Idlpns a`æitrfins ma d`td fktaksfmdm

A` abaitn snera `ns lfirnnrcdkfslns sa edsd ak `d d`tardifùk n mastruiifùk ma `d pd-

ram iaù`dr iudkmn sa dp`fid ukd fktaksfmdm ma idlpn a`æitrfin qua md ùcdr d ukdmfbarakifd ma pntakifd` aktra dlens `dmns ma `d lalerdkd (pntakifd` trdkslal-erdkd). Iudkmn astd mfbarakifd ma pntakifd` dìdkzd uk vd`nr irìtfin matarlfkdmn,qua vdrìd ak bukifùk ma` tfpn ma lfirnnrcdkfsln, nrfcfkd `d bnrldifùk ma pnrnsfrravarsfeà ak d lalerdkd iaù`dr (aàitrnpnrdifùk) y ak inksaiuakifd d pærmfmdma su fktacrfmdm, fkiralaktn ma `d parladef`fmdm y bfkd`lakta mastruiifùk ma `diæù`d dbaitdmd. As ukd ma ds lajnras d`tarkdtfvds d ns lætnmns inkvakifnkdàs mapdstaurfzdifùk, `n qua hfzn qua sa maknlfkdrd pdstarfzdifùk brìd.

Yu usn astä flftdmn d prnmuitns enleadeàs, idpdias ma inkmuifr d aàitrfifmdm yaxaktns ma lfirnnrcdkfslns aspnru`dmns. Yfk aledrcn, kn prnmuia kfkcúk abaitnsnera akzflds. @ns d`flaktns läs fmùkans pdrd asta trdtdlfaktn snk: àiha, huavn`ìqufmn, zulns ma brutds y inkiaktrdmns, snpds y axtrditns ma idrka.

Idlpns ldckætfins nsif`dktas

@d talpardturd murdkta a` prniasdmnsa ldktfaka aktra ?ºI y 1?ºI. A` abaitninksarvdmnr sa maea, bukmdlaktd`lakta,d mns bakùlakns: (d) d `d rupturd ma `dln`æiu`d ma DMK y ma ifartds prntaìkds,y (e) d `d rnturd ma ak`dias invdàkta ak



@ns d`flaktns läs fmùkans pdrd snlatarsa d astaprniasn ma inksarvdifùk snk: zulns, larla`dmds,brutns trnpfidàs ak snùifnkas dzuidrdmds, marfvdmnsiärkfins, prnmuitns inifmns, akvdsdmns y `fstns pdrdsu inksuln.

@uz e`dkid ma d`td fktaksfmdm

@d dp`fidifùk ma pu`sns ma ùz e`dkid ma d`td fktaksf-mdm as uk trdtdlfaktn `flftdmn d `d suparbfifa ma `nsprnmuitns, qua puama utf`fzdrsa pdrd d pdstaurfzdifùkma `ìqufmns trdkspdraktas y d`flaktns akvdsdmns akldtarfdàs trdkspdraktas. ]dlefæk puama dp`fidrsapdrd `d astarf`fzdifùk ma suparbfifas ma ldtarfdàs yaqufpns. @d murdifùk ma idmd pu`sn as ma 5??-9?? ls

y `d braiuakifd as ma 4 d 5? s-4 (447 45).

Asta trdtdlfaktn prnmuia idlefns bntnquìlfins y bn-tntærlfins. @ns prflarns nrfcfkdk lnmfbfidifnkas aka` DMK, ak ds lalerdkds iaù`dras y ak ns sfstaldsma rapdrdifùk y akzflätfins. @ns sacukmns prnmuiakuk fkiralaktn ma d talpardturd lnlaktäkan ak dsuparbfifa trdtdmd qua, pnr d inrtd murdifùk ma` pu`-sn, kn dbaitd d `d talpardturd c`ned` ma` prnmuitn.@ns aqufpns utf`fzdmns prasaktdk iäldrds ak `ds quamasta``dk, ink `d braiuakifd raquarfmd, `älpdrds macdsas (xakùk n grfptùk) ma d`td fktaksfmdm y abfidifd._rnmuitns trdtdmns, ink rasu`tdmns edstdkta sdtfsbdi-tnrfns, snk bfàtas y pnrifnkas ma idrka y pasidmn,cdleds, idrka ma pn``n y sdìhfihds.



D pdrtfr ma `d àiturd qua rad`fzù, raspnkmd `ds sfcufaktas pracuktds:

_racuktds Uaspuastds¾Tuæ d`flaktns ink akvdsas

prasurfzdmns inknia> Lakifnka

ifkin.Yacúk `d àiturd, ¾ink quæ bfk sa

utf`fzdk `ns akvdsas prasurfzdmns>¾Tuæ tfaka qua var d hfmrnlaiäkf-

id ink `ns akvdsas prasurfzdmns>¾_nr quæ iudkmn uk euzn astä

maktrn ma` dcud kn sa hukma kf

b`ntd>¾Tuæ pdsd iudkmn ukd parsnkd

fkcrasd d` dcud sfk kfkcúk aqufpnaspaifd`fzdmn pdrd euiadr>

Dvdkias ak akvdsdmn ma d`flaktns

A` akvdsa tfaka uk pdpa` bukmdlaktd` ak d inksarvdifùk ma ns d`flaktns

y ak `ds ú`tflds mæidmds sa hdk rad`fzdmn inksfmardeàs fkknvdifnkas, akldtarfdàs y sfstalds ma akvdsdmn, ink fkmumdeà raàvdkifd ak d inlar-

ifd`fzdifùk ma d`flaktns läs sacurns, sdùmdeàs y dpataifeàs.



Bukmdlaktn taùrfin

Yustdkifd Maksfmdm ak Gc/l9 Maksfmdm ak c/il9

Diafta 65? ?,65

Diarn 3.8?? 3,8

Dcud 4.??? 4

Dìnhn` 84? ?,84

Dùlfkfn 5.3?? 5,3

Inera 8.6?? 8,6

C`fiarfkd 4,52 45,2?

Hfarrn 3.8?? 3,8

Ldmard 6?? ?,6

Lariurfn 49.2?? 49,2

Nrn 46.9?? 46,9

Hfmrnstätfid

As a` astumfn ma `ns bùfmns ak rapnsn. @ns bùfmns snk `ds sustdkifds qua tfakaprnpfamdm ma bùfr ma uk raifpfakta d ntrn, dmnptdkmn `d bnrld tntd` n pdrifd`kuavn raifpfakta, `n iud` sa maea d qua `ds buarzds lnàiu`dras aktra `ns mfbarainkstftuyaktas snk mæefàs. Ya inksfmardk bùfmns `ns `ìqufmns y `ns cdsas.

Maksfmdm: ldckftum bìsfid (τ) qua sa mabfka inln a` inifakta aktra `d ldsdma uk iuarpn y su vnùlak (v). Ak a` sfstald fktarkdifnkd` (YF) sa lfma ak Gc/l

Ak `d sfcufakta tde`d, sa puama dpraifdr `d maksfmdm ak c/il9 y ak Gc/l9 d talrdturd ma 5?º iaktìcrdmns:



_rasfùk: aqufvdà d `d buarzd parpakmf-iu`dr (B) dp`fidmd pnr ukfmdm ma ärad (D).

Ak a` YF, sa axprasd ak K/l5

, ukfmdm quasa maknlfkd pdsid` (_d), qua ak bnrlddprnxfldmd aqufvdà d `d prasfùk quaajaria snera a` sua`n ukd `älfkd ma 4?5 c ma ldsd ak 4 l5 ma suparbfifa.

_rasfùk ak ns ìqufmns: tdlefæk sa a ma-knlfkd prasfùk hfmrnstätfid. As `d buarzd

ajarifmd pnr uk ìqufmn ak aquf`ferfn par-pakmfiu`dr d `d suparbfifa ma` raifpfaktaqua `n inktfaka n d `d suparbfifa ma uksù`fmn sularcfmn ak æ`.

Aiudifùk bukmdlaktd` ma `d hfmrnstätfid

Luastrd qua `d prasfùk ak uk puktn kn mapakma ma` vnùlak ma` `ìqufmn quahdy pnr akifld ma mfihn puktn y as prnpnrifnkd` d `d maksfmdm (τ) ma` `ìqufmn, `ddiaàrdifùk ma `d crdvamdm (c) ma` sftfn y `d prnbukmfmdm (h) d `d iud` sa akiuaktrdmfihn puktn. As maifr, mns puktns sftudmns d `d lfsld prnbukmfmdm ak a` fktarfnma uk `ìqufmn, astäk snlatfmns d `d lfsld prasfùk.

_ < τ . c . h

Kfva` ma` `ìqufmn_rnbukmfmdm



Mns raifpfaktas ma mfbaraktas bnrlds snk `àkdmns ink cdsn`fkd

hdstd qua a` kfva` ma` bùfmn as ma 9?il pnr akifld ma `d idsa maidmd ukn. @ds ärads ma ds edsas ma ns raifpfaktas snk ma 5?il9 y

4?il raspaitfvdlakta. Inlpdrd `d prasfùk y `d buarzd tntd` snera

`d edsa ma idmd raifpfakta.

Ynùifùk: _drd snùifnkdr asta ajarififn maealns takar ak iuaktd

`d maksfmdm ma `d cdsn`fkd

Mdtns:

p < 28?gc/l9

c < 6,8l/s5

h < 9?il ?.9l

D4 < 5?il5 5x4?-9l5.

D5 < 4?il5 4x4?-9l5

Ajalp`n:

r4 r5

_ < pch < (28?gc/l9)(6.8l/s5)(?.9l) < 4666.5_D

B < _D4 < (4666.5 _d)(5x4?-9l5)<9.66K

B < _D5 < (4666.5 _d)(4x4?-9l5)<4.66K



_rfkifpfn ma Drquìlamas

]nmn iuarpn sularcfmn ak uk ìqufmn, axparflaktd uk alpuja vartfid` hdifd drrfed,fcud` d` pasn ma` vnùlak ma` `ìqufmn masp`dzdmn. Asta prfkifpfn tfaka dp`fidifnkas

ak `d darnstätfid y ak `d fkmustrfd àihard ink a` maksìlatrn pdrd matarlfkdr `dpurazd ma `d àiha, ati.

Yf a` iuarpn sa akiuaktrd inlpàtdlakta sularcfmn y a` alpuja qua axparflaktdas ldynr qua su pasn, mabfkftfvdlakta suefrä d `d suparbfifa y a` alpuja snera `dpdrta sularcfmd ma vnùlak vs sarä fcud` d` pasn ma` iuarpn.

_rfkifpfn ma _dsid`

@ns ìqufmns trdkslftak ak tnmds mfraiifnkasy ink `d lfsld fktaksfmdm, `ds prasfnkas

qua sa ajariak ak matarlfkdmd racfùk maa``ns. Dp`fidifnkas ma asta prfkifpfn snk: `dpraksd hfmräu`fid, `ns sfstalds ma brakns madutnlùvfàs, ati.

Ak a` idsn ma `d praksd hfmräu`fid, sadprnvaihd `d mfbarakifd aktra a` mfälatrnma` ælen`n mnkma sa dp`fid `d buarzd y a`mfälatrn ma` ælen`n mnkma sa ajaria `d prasfùk7 snera a` pfstùk ma` ärad D4 sadp`fid `d buarzd B4, @d prasfùk ajarifmd aqufvdà d B4 /D47 astd prasfùk sa trdkslfta dtnmns `ns puktns ma` `ìqufmn y ma fcud` bnrld d uk pfstùk ma` ärad D 5. _drd netakarukd buarzd B5, `d ra`difùk ma ärads as D4 0 D5. _nr `n tdktn, inln _4 < _5 aktnkias:



@d prasfùk dtlnsbærfid as `d prasfù

ajarifmd pnr a` dfra ak iud`qufar pukt

ma d dtlùsbard. Knrld`lakta sa raar

d d prasfùk dtlnsbærfid tarrastra, par

a` tærlfkn as axtaksfeà d d dtlùsbar

A` fkstrulaktn qua sa utf`fzd pdrd lamfr `d prasfùk ma uk `ìqufmn as a` Ldkùlqua inksfsta ak uk tuen ak bnrld ma Q qua inktfaka `ìqufmn ma maksfmdm () bukifnkdlfaktn sa md, sf ukn ma sus axtralns sa inkaitd ink a` raifpfakta iprasfùk sa masad dvarfcudr.

_N < p + τ . c . h

_rasfùk dtlnsbærfid

A` pasn ma` dfra ajaria prasfùk snera`d suparbfifa tarrastra. D mfbarakifd ma`ns ìqufmns, ns cdsas snk inlprasfeàs

y inln su maksfmdm puama vdrfdr, `dsidpds suparfnras ma d inùlkd ma dfrainlprflak d `ds läs edjds. _nr astdrdzùk, a` dfra d kfva` ma` ldr as läsmaksn y d lamfmd qua dsiakmalns savd akrdraifakmn hdstd qua sa masvdka-ia d ukd d`turd dprnxfldmd ma =? Gl.

@d idpd edjd trnpnsbard ma 44 Glinktfaka a` 8?% ma` dfra tntd` ma `ddtlnsbard y prasaktd `ds inkmfifnkaskaiasdrfds pdrd `d vfmd. @d prasfùkdtlnsbærfid bua matarlfkdmd pnr aìfaktìbfin ftd`fdkn Avdkca`fstd ]nrrfia``fak 42=9. Qkd dtlùsbard aqufvdà d 32?

Ak a` sfcufakta ak`dia akinktrdrä uk `denrdtnrfn vfrtud` ma` prfkifpfn ma

quìlamas:

http://www.ldthsnk`fka.in.ug/knklalears/cdlasrnnl/sfls/drihf/drihf=.ht



Hfmrnmfkälfid

Aiudifùk ma inktfkufmdm

As a` astumfn ma `ns bùfmns ak lnvflfaktn. Astalnvflfaktn nrfcfkd uk bùjn qua as tureuàktniudkmn `ds pdrtìiu`ds qua inkbnrldk a` bùfmn,

masirfeak trdyaitnrfds qua sa iruzdk aktra sì ymdk nrfcak d raln`fkns7 y a` bùjn `dlfkdr iuydspdrtìiu`ds ma` lamfn sa masp`dzdk ink trdyaitnrfdspdrdà`ds.

_drd a` astumfn ma` lnvflfaktn ma `ns bùfmns,sa inksfmardk ifartds idrditarìstfids pdrtfiu`dras:d. Yar dlfkdr pdrd qua tnmds ds pdrtìiu`ds ma ukbùfmn takcdk d lfsld va`nifmdm d` pdsdr pnr ukpuktn matarlfkdmn7 e. Kn vfsinsn pdrd maspra-ifdr a` rnzdlfaktn ink ds pdramas ma` tuen qua ntrdkspnrtd n aktra `ds idpds ma bùfmns y kn hdydpærmfmd ma akarcìd laiäkfid7 i. Fkinlprasfeàpdrd cdrdktfzdr qua d maksfmdm ma` bùfmn sa ldk-takcd inkstdkta. _nr astn as flpnrtdkta sapdrdr

a` astumfn ma ns `ìqufmns (qua snk präitfidlaktafkinlprasfeàs), y ma `ns cdsas qua sì sa puamakinlprflfr n axpdkmfr (kaulätfid).

Iudkmn pnr a` fktarfnr ma uk tuen sa luava uk bùfmn fkinlprasfeà, `d va`nifmdmas ldynr ak `d lamfmd inln a` mfälatrn ma` tuen sad laknr, y mfslfkufrä ak `dlamfmd inln dulakta su mfälatrn. As maifr, `d ra`difùk aktra `d va`nifmdm mabùfmn y a` ärad ma `d saiifùk trdksvarsd` ma` tuen snk fkvarsdlakta prnpnrifnkdàs

D4

. v4

< D5

. v5



@d dp`fidifùk ma `d aiudifùk ma inktfkufmdm sa dpraifd bäif`lakta iudkmn d` zdr ukd ldkcuard y masadlns qua a` ihnrrn takcd uk ldynr dìdkia, nestrupdrifd`lakta `d sd`fmd ma` dcud (mfslfkuflns a` ärad ma `d saiifùk trdksvarsd` mldkcuard), pdrd `ncrdr`n.

]anrald ma Earknu``f

Uaprasaktd `d ày ma inksarvdifùk ma `d akarcìd laiäkfid ak uk bùfmn ak llfaktn. A` trdedjn katn aqufvdà d `d suld ma `d vdrfdifùk ma `d akarcìd ifkæt`d vdrfdifùk ma `d akarcìd pntakifd`.

A` trdedjn as buarzd pnr mfstdkifd, . Ak tærlfkns ma prasfùk aqufvdà d

Qkd dp`fidifùk ma` tanrald ma Earknu``f as a` dtnlfzdmnr qua pnr mfbarakifdprasfnkas aktra `d pdrta suparfnr ma` tuen y `d suparbfifa ma` `ìqufmn qua inktfaæsta suea y `d inrrfakta ma dfra `n mfsparsd @n lfsln a` tuen n inktdmnr ma Rak

p . D .∂ x < p . ∂R

Astn kns parlfta axprasdr d prasfùk ak tærlfkns ma trdedjn y vdrfdifùk ma vnù

, inln `d netakalns ma dquì sa netfaka `d bncakard` ma `d aiudifùk ma Earknu``f:

Skatn < ∂ Ai+ ∂ A p



Yustaktdifùk ma dvfnkas. Maefmn d `d bnrld, hdy vdrfdifùk ak `d va`nif-mdm ma` dfra drrfed y maedjn ma `ds d`ds ma ns dvfnkas, n iud` cakard ukdmfbarakifd ma prasfùk qua nrfcfkd d maknlfkdmd buarzd ma sustaktdifùk.

Yfk aledrcn, a` prfkifpfn ma Earknu``f kn sa dp`fid d astd sftudifùk, ma-efmn d qua ak æ` sa inksfmard a` bùjn ma bùfmns fmadàs y inksarvdifùkma d akarcìd maktrn ma` sfstald, `n iud` kn sa iulpà ak ds inkmfifnkasma vua`n.

@ay ma Hdcak-_nfsauf`à. _drd ukd vfsinsfmdm inkstdkta ak uk bùjn dlf-kdr fkinlprasfeà, d tdsd prnlamfn ma bùjn as fkvarsdlakta prnpnrifnkd`d `d vfsinsfmdm y d `d `nkcftum ma` tuen qua `n trdkspnrtd, y mfraitdlaktaprnpnrifnkd` d `d vdrfdifùk ma prasfùk aktra mns puktns mfbaraktas ma`tuen inkmuitnr y a` rdmfn ma `d saiifùk trdksvarsd` ma` lfsln.

Mnkma mv/mt as `d vdrfdifùk ma vnùlak ma `ìqufmn qua ifriu`d ak `d ukf-mdm ma tfalpn, v

lamfd as `d va`nifmdm lamfd ma` bùfmn, r as a` rdmfn ma

`d saiifùk trdksvarsd` fktarkd ma` tuen inkmuitnr, mp as `d vdrfdifùk maprasfùk aktra mns puktns axtralns ma` tuen, γ as d vfsinsfmdm ma` ìqufmny @ `d `nkcftum ma` tuen.

Qkd dp`fidifùk ma `d ày ma Hdcak-_nfsauf`à as `d halnmfkälfid qua

as `d pdrta ma `d idrmfn`ncìd qua sa akidrcd ma` astumfn dkdtùlfin y buk-ifnkd` ma` inrdzùk, fktrnmuifakmn idtætaras bfkns d trdvæs ma `ds drtarfdsma `d fkcà n ma` erdzn.

Kaulätfid. As a` astumfn ma` inlpnrtdlfaktn ma ns cdsas, masma a` puktnma vfstd ma `d hfmrnstätfid y ma `d hfmrnmfkälfid.



Ak suecrupns, rad`fiak ds sfcufaktas axparfakifds. _drd a``n, maeak aar dtaktdla

`ds fkmfidifnkas, inksacufr ns ldtarfdàs y nesarvdr dtaktdlakta n qua niurra,

dsì mdr raspuastd d `ds pracuktds p`dktadmds.

4. Inksfcdk ukd enta``d p`ästfid ink tdpd.

5. Dhnrd, parbnrak `d enta``d hdifækmnà uk paquaôn huain uk pnin l

dedjn ma `d lftdm.

9. @àkak `d enta``d ink dcud.

=. Nesarvak y masirfedk `n qua niurra.

Iudkmn d enta``d astä tdpdmd: Iudkmn mastdpdk d enta``d:

Ink `d enta``d tdpdmd, hdcdk huaquftns ink uk d`bfàr.

Masirfedk `n qua nesarvdk:



3


4. ¾Iuä` as a` vnùlak ma ukd asbard ma hfarrn iuyd ldsd as ma 1 Gc>

Ynùifùk: pnr d ra`difùk aktra ldsd maksfmdm y vnùlak, sa puamamatarlfkdr a` vnùlak ma `d asbard ak iuastfùk.

Inksfcdk uk c`nen (enled), uk vdsn,

ukd va`d y uk p`dtn ink dcud.

Yfcdk asta prniasn:

Masirfedk `n qua niurra:

_rakmdk d va`d 7 d ukd mfstdkifd ma ukns

3 i.l. dprnxfldmdlakta, in`nquak a`vdsn inln sa luastrd ak `d fldcak.

Maspuæs ma ukns 9? sacukmns, vn`taak

a` vdsn y täpak`n ink a` c`nen fkb`dmn,

ajarifækmnà prasfùk hdifd dedjn. @uacn,

fktrnmuzidk a` c`nen ak a` p`dtn ink dcud. Dhnrd, tnlak uk c`nen y ``ækak`n ma

dcud. @uacn, ìkbàk`n y diærquak`n d `dva`d akiakmfmd.

Masirfedk `n qua niurra:



5. ¾Tuæ prasfùk ajaria snera a` pfsn, uk mapnrtfstd ma 11 Gc ma ldsd, iudkmdpnyd snera uk sn`n pfa, sf a` ärad ma `d sua`d ma su zdpdtn as ma 48? il

Ynùifùk: a` ärad sa axprasd ak l57 48? il5 < ?,?48? l5. Ink `dldsd, matarlfkdlns a` pasn:

φ < l . c < 11 Gc . 6,8 l/s5 < 196 K

9. ¾Iuä` as d prasfùk qua axparflaktd uk mapnrtfstd, d` sularcfrsa ak ukd pfsd ukd prnbukmfmdm ma 9 l>

Ynùifùk: sa dp`fid a` prfkifpfn ma prasfùk hfmrnstätfid:

_ < τ. c . h < 4.??? Gc/l9 x 6,8 l/s5 x 9l < 56=?? _d

=. Ak ukd praksd hfmräu`fid, a` pfstùk paquaôn tfaka uk rdmfn ma 4,1 il y a`tùk ldynr uk rdmfn ma 55 il. Ya raqufara àvdktdr uk pasn ma =.6?? K, ¾buarzd sa maea ajariar ak a` pfstùk laknr>

Ynùifùk: pnr d ra`difùk aktra a` tdldôn ma ns pfstnkas, sa puamamatarlfkdr `d buarzd kaiasdrfd pdrd àvdktdr a` pasn ak lakifùk:

D4 < Ϗ . r

4

5 < Ϗ. (?,?41l)5 < Ϗ x 5,51x4?-= l5 < 3 x 4?-= l5

D5 < Ϗ . r

5

5 < Ϗ. (?,55l)5 < Ϗ x =,8=x4?-5 l5 < ?,415 l5



1. Qkd asbard ma ldmard ma 9? il9 b`ntd ak a` dcud, sf `d maksfmdm as ma ?,6 cil9. Matarlfkdr `d pnrifùk ma vnùlak qua parldkaia sularcfmn.

Ynùifùk: sf `d asbard astä b`ntdkmn, sa akiuaktrd ak aquf`ferfny pnr `n tdktn, `d suldtnrfd ma `ds buarzds qua ditúdk as fcud` diarn. As maifr, a` alpuja y a` pasn snk ma fcud` ldckftum, parnma saktfmn inktrdrfn.

Astäk sularcfmns 6/4? ma su vnùlak tntd`.

2. Ya masad idkd`fzdr uk rìn iuyn idumd` as ma 1 l/s7 aktrd ak uk tuen ink ukrdmfn ma 9 l y d` bfkd` sdà pnr uk tuen ink uk rdmfn ma ?,8 l. Matarlfkdr `dva`nifmdm ma sd`fmd ma` dcud.

Ynùifùk:

Dp`fidlns `d aiudifùk ma inktfkufmdm dsì:



Dutnavdùdifùk

Ak `d sfcufakta tde`d, asirfed `ds ditfvfmdmas quæ läs à custdrnk d`rad`fzdr`ds, d`cukds sftudifnkas ma dp`fidifùk y ns raiursns kaiasdrfns

pdrd su dp`fidifùk.

Ditfvfmdmas qua à

custdrnk

Yftudifnkas madp`fidifùk

Uaiursnskaiasdrfns

4.

5.

9.

]dlefæk raspnkmd:

d. ¾Tuæ bua `n läs sfckfbfidtfvn qua dprakmfù ak a` ärad>

e. ¾Tuæ ditfvfmdm bua `d läs masdbfdkta d` masdrrn``dr ukfmdm>

i. Yf tuvfard qua mdrà d inkniar d su inlukfmdm uk dprakmfzdja

dmqufrfmn ak astd ärad, ¾iuä` asincarìd> ¾_nr quæ>




_rniamflfaktn

4. Matarlfkdr a` kúlarn ma cdkihns i`fps qua sa raqufarak pdrd aquf-`ferdr `d ed`dkzd pdrd idmd ukd ma `ds ldsd qua sa utf`fiak (ukds =).

5. _nkar dcud ak a` vdsn, hdstd ifartn kfva` ma bnrld qua d prflardldsd suspakmfmd dúk ma `d ed`dkzd, sa sularjd inlpàtdlakta.Matarlfkdr ntrd vaz, a` kúlarn ma cdkihns i`fps qua sa raqufarak

Ldtarfdàs

Ed`dkzd (sa puama inkstrufr), vdsn, dcud, dìnhn`, diafta,c`fiarfkd, ldsds ma dùlfkfn, hfarrn, ldmard y edqua`ftd(puama raalp`dzdrsa `ds ldsds pnr ``dvas inlukas ymfbaraktas), cdkihns i`fp (`d ldsd ma uk cdkihn i`fp asiarid ma ?.?9 c).

3

_räitfid ma hfmrnlaiäkfid

Qkfmdm 1. Hfmrnlaiäkfid Yasfùk

8



9. Uapatfr a` axparflaktn pdrd `ds ldsds sfcufaktas.

=. Fkfifdr kuavdlakta a` prniasn ink `d ldsd 4, parn idlefdkmn a`dcud pnr dìnhn`, ùacn pnr c`fiarfkd y pnr ú`tfln pnr diafta.

1. Uacfstrdr `ns mdtns ak `d tde`d 4.

2. Yuspakmar mns enleds ma td` bnrld qua quamak d `d lfsld d`turdy sapdrdmds pnr ukd mfstdkifd ma ukns 2 il. Ynp`dr pnr a` aspdifnqua hdy aktra `ds enleds, nesarvdr y inkiùfr.

3. Uapatfr `d axparfakifd dktarfnr, raalp`dzdkmn `ds enleds pnr mnshnjds ma pdpa`.

8. Lamfr ak ukd jarfkcd (sfk dcujd), 1 il9 ma dcud, e`nquadr `d sd`f-md y ajariar prasfùk snera a` ælen`n. Matarlfkdr `d vdrfdifùk mavnùlak y rapftd a` prniamflfaktn, utf`fzdkmn dfra7 y pnr ú`tfln,`àvdr a` ælen`n ma `d jarfkcd d` bnkmn, e`nquadr `d sd`fmd ma` dfray ùacn, fktaktdr masp`dzdr`n hdifd drrfed. Masirfefr quæ niurrfù.

Di aft al Dfra Dcud

4

=

9

5

D` in hn ` C`f iar fk d



A` dcud kns dyumd ak `d iradifùk ma akarcìd

@ad dtaktdlakta a` sfcufakta taxtn y raspnkmd `ds pracuktds:

A` dcud hd sfmn sfalpra a` raiursn läs flpnrtdkta pdrd `d huldkfmdm,

dmaläs ma sar uk aàlaktn vftd` pdrd a` hnlera, parn ¾iùln `ns rìns y

`dcns sa inkvfartak ak ukd buakta ma akarcìd> A` ifi`n ma` dcud iulpà

uk pdpa` flpnrtdkta ak d netakifùk ma akarcìd hfmräu`fid: a` sn` avdpnrd

a` dcud y astd sa praifpftd bnrldkmn rìns y dcns pdrd pnmar sar àvdmds d

raprasds mnkma sa cakard akarcìd. Ak `d Aurnpd

dktfcud, mnkma sa utf`fzdedk `ns rìns pdrd hdiar

lnvar `ns ln`fkns, lamfdkta ukd ruamd ink

idkdàs ak su parìlatrn in`nidmd ak a` iduia

ma` dcud pdrd cakardr akarcìd hfmräu`fid y hdiar

lnvar a` ln`fkn, pdrd dsì avftdr utf`fzdr buarzd ma

trdedjn huldkd n dkfld`, asta raiursn ard läsabaitfvn, yd qua sa pnmìd cakardr ukd buarzd

läs crdkma, dmaläs ma qua kn sa pdcded pnr

utf`fzdr`d.

Ditud`lakta sa puamak dprnvaihdr `ns iduias

ma `ns rìns pdrd trdksbnrldr `d akarcìd hfmräu`fid

ak a`æitrfid7 ¾iùln as pnsfeà astn> @ns rìns snk`àvdmns d uk raprasdlfaktn mnkma sa diulu`d

ukd crdk idktfmdm ma dcud7 asta raprasdlfaktn

tfaka uk masdcða qua àvd a` ìqufmn d ukd turefkd cfcdkta. _nr d rdpfmaz

ma` dcud, astd turefkd cfrd7 d` rad`fzdr asta lnvflfaktn ifriu`dr, d turefkd

cakard flpu`sns aàitrnldckætfins qua snk trdkspnrtdmns d uk trdksbnr-

ldmnr qua racu`d `d akarcìd a`æitrfid



@d rdzùk ma d utf`fzdifùk ma` dcud as qua cakard ukd buarzd inkstdkta7

as inksfmardmd ukd buakta ma akarcìd raknvdeà läs ainkùlfid y läs

sacurd ma ldkajdr, y dmaläs kn cakard kfkcúk tfpn ma inktdlfkdifùkd` dfra y d` lamfn dlefakta. Dmaläs, sa puama inktrn`dr a` bùjn ma

aàitrfifmdm.


Uad`fia ukd `fstdakulardkmn a`nrmak ma` ifi`nma` dcud y iùlnastd as trdksbnr-ldmd ak akarcìda`æitrfid.

¾_nr quæ a`dcud as `d lajnr buakta mairadifùk maakarcìd>

¾Tuæ sa raq-ufara pdrd hdiarukd buakta hf-mrna`æitrfid>

¾_nr quæ In-`nlefd as ukpdìs ink `dslajnras ink-mfifnkas pdrd`ds buaktas hf-mrna`æitrfids>

¾ T u æ e a kabfifns tfakukd buakta hmrna`æitrfid>

Nesarva dtaktdlakta `d sfcufakta

fldcak. Yaôdà y masirfed a` bukifnk-

dlfaktn ma ukd p`dktd hfmrna`æitrfid.



4. ¾Tuæ mfbarakifd ma prasfùk axparflaktd uk euzn d` masiakmar aka` dcud ma uk `dcn, ma 4 l d 1 l ma prnbukmfmdm>

5. Matarlfkdr a` vnùlak ma uk iuen ma dùlfkfn iuyd ldsd as ma 9Gc.

9. ¾Ma quæ ldtarfd` astä inkstrufmn uk iuen, sf su ldsd qua as ma=.68= c niupd uk vnùlak ma 12? il9>

=. @d bnrld ma ukd puktf``d, ukd tdihua`d, ukd dcujd n uk tnrkf``n knas idprfihnsd7 pnr a` inktrdrfn, iulpà uk prfkifpfn bìsfin. ¾Iuäàs> Axp`fidr.

1. Ak ukd praksd hfmräu`fid, a` pfstùk y a` ldynr astäk ak prnpnrifùk

4 d 5?, y sa raqufara àvdktdr uk pasn ma 1.??? K, ¾quæ buarzd samaea ajariar ak a` pfstùk laknr>

2. Ma quæ bditnras bìsfins mapakma a` haihn ma qua uk e`nqua maldmard ma 41 c ma ldsd b`nta ak a` dcud, lfaktrds qua uk e`nquama hfarrn ma `d lfsld ldsd sa sularca ak a``d. Axp`fidr.

3. ¾Iuä` as `d maksfmdm ma uk iuen ma ldmard, sf d` sularcfrsa ak uk

raifpfakta qua inktfaka dcud y diafta, `d lftdm sa sularca ak a`dcud y `d ntrd lftdm as iuefartd pnr a` diafta>

Diafta

Dcud

Ldmard



8. @d saiifùk trdksvarsd` ma uk tuen tfaka uk rdmfn ma 4? il y d` bfkd`sa rdlfbfid ak mns tuens iuyds saiifnkas trdksvarsdàs snk ma 5 y9 il ma rdmfn. ¾Iuä` as `d va`nifmdm ink `d iud` sdà a` dcud pnr

idmd rdlfbfidifùk>

6. D trdvæs ma uk tuen ma 5? il ma rdmfn, ifriu`d dcud ink ukd va`n-ifmdm ma 1 l/s. ¾Iuä` maea sar a` mfälatrn ma sd`fmd ma` tuen pdrdnetakar ukd va`nifmdm ma` dcud ma 8 l/s>

4?. Qk tdkqua if`ìkmrfin sfk tdpd, ma 5 l ma d`turd, inktfaka 1 l9 madcud. D ukd prnbukmfmdm ma 4,1 l sa hdia uk nrfbfifn pdrd quasd`cd a` dcud. ¾Ink quæ va`nifmdm sdà>

R5

R9

R4

_rnbukmfmdm

Rnùlak ma dcud

Dutnavdùdifùk

Uaspnkmd:

d. ¾Iuäàs snk ns dpnrtas läs vd`fnsns ma d prasakta ukfmdm> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

e. ¾Ak quæ ifriukstdkifds puama dp`fidr d`cukns ma `ns ink-iaptns dprakmfmns ak astd ukfmdm> Mæ ajalp`ns.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^



Idlfkdtds pa`fcrnsds6

D `ns dstrnkdutds às dcrdmdk `ds idlfkdtdsaspdifdàs. B`ntdkmn sfk pasn d ifaktns ma

gf`ùlatrns snera d ]farrd, ink d supar-bfifa maedjn cfrdkmn d 53.??? gph,kfkcúk vfdjarn aspdifd` qufara qua satarlfka. _arn sù`n sa kaiasftdk mnspd`derds pdrd ldkmdr d ukn ma asns

vd`faktas axp`nrdmnras ma vua`td d sukdva: ‐Arupifnkas sn`dras“.

‐@ds arupifnkas sn`dras snk ds ldyn-ras axp`nsfnkas ma` sfstald sn`dr“, mfia

Uneart @fk ma` @denrdtnrfn ma IfakifdAspdifd` ma `d Qkfvarsfmdm ma Id`fbrnkfd

ak Eargaày (QI Eargaày‖s Ypdia Yifakia

@de). ‐Arupifnkdk iarid ma `ds ldkihds sn`drasink `d buarzd ma ifaktns ma lf``nkas ma enleds ma hfmrùcakn“. @ns

dstrnkdutds qua snk snrprakmfmns murdkta ukd idlfkdtd aspdifd` pnr ukd arupifùksn`dr n ukd ma sus prflds, ukd ayaiifùk ma ldsd inrnkd`, puamak desnrear ukdmnsfs ma rdmfdifùk aqufvdàkta d 4?? rdmfncrdbìds ma rdyns X ak a` paihn, rdzùksubfifakta pdrd rabucfdrsa räpfmdlakta.

Id`nr y talpardturd

Qkfmdm 2. ]arlnmfkälfid Yasfùk

6



@ds arupifnkas sn`dras kn raprasaktdk uk pa`fcrn ld-ynr pdrd ns hdeftdktas ma d ]farrd, yd qua d dtlùsbardma` p`dkatd kns prntaca ma astds lnrtdàs rdmfdifnkas._arn axp`nsfnkas sn`dras flpravfstds sì dbaitdk kuastrds

vfmds. _uamak fkutf`fzdr sdtæ`ftas, mfbfiu`tdr `d kdvacd-ifùk dærad, a fktarrulpfr ds inlukfidifnkas ma rdmfnma d`td braiuakifd murdkta hnrds.

¾Tuæ as n qua masakidmakd ds arupifnkas sn`dras>¾Iùln `feardk tdktd akarcìd tdk räpfmdlakta> ¾V,as pnsfeà pramaifr iuäkmn niurrfräk>

]dàs pracuktds hdk masinkiartdmn d `ns dstrùknlnsmasma 4816 iudkmn @nrm Idrrfkctnk nesarvù ukdarupifùk sn`dr pnr prflard vaz. ‐Astded Winktdkmnldkihds sn`dras snera ukd fldcak prnyaitdmd ma`Yn`\“, raiuarmd, iudkmn ma rapakta ‐dpdraifarnk mnsldkihds ma uz e`dkid luy fktaksd“ iarid ma uk crupnma ldkihds sn`dras kntdeàlakta crdkmas. ‐Ynerasd`-tdmn pnr `d snrprasd“, Idrrfkctnk majù su taàsinpfn

y sd`fù inrrfakmn d eusidr uk tastfcn7 parn d` vn`varlfkutns läs tdrma `d axp`nsfùk hdeìd masdpdraifmn.

Idrrfkctnk sdeìd qua hdeìd nesarvdmn d`cn aknrla-lakta pnmarnsn, parn `n qua æ` vfn ard sù`n `d puktdma` fiaearc. _drtìiu`ds ma d`td va`nifmdm qua alarcakma `ds arupifnkas alftak prfkifpd`lakta rdyns X y

rdyns cdld ma d`td akarcìd. @d ùz vfsfeà, ma laknrakarcìd, kn as tdk flpnrtdkta.

V astd as `d rdzùk pnr `d iud` `ds arupifnkas sn`dras hdkpnmfmn cudrmdr sus sairatns pnr tdktn tfalpn. @ds ax-p`nsfnkas snk läs pnmarnsds d `nkcftumas ma nkmd qua`ns nesarvdmnras tarrastras kn puamak var ink sus njns.@ns taàsinpfns tdlpnin snk idpdias ma var`ds pnrqua



Dhnrd, uk kuavn sdtæ`fta ma d KDYD pratakmasupardr asta prneàld. A` Crdbfidmnr Aspai-trnsiùpfin Yn`dr ma D`td Akarcìd, n HAYYFpnr sus sfc`ds ak fkc`æs (Hfch Akarcy Yn`drYpaitrnsinpfi Fldcar), `dkzdmn ak baerarn 1,5??5, astä nreftdkmn `d ]farrd d idsf 2?? glpnr akifld ma d npdid dtlùsbard ma kuastrnp`dkatd, mnkma puama mataitdr alfsfnkas mardyns X y rdyns cdld prnmuifmds pnr ds arup-ifnkas sn`dras. HAYYF kn as `d prflard kdvaaspdifd` idpdz ma mataitdr td` rdmfdifùk. _arn sarä `d prflard ak idpturdr fläcakaskìtfmds ma rdyns X y rdyns cdld prnvakfaktas ma `ds vfnàktds axp`nsfnkas.

_drd takar ukd lajnr fmad ma astds idktfmdmas, inksfmara `n sfcufakta: Iudkmn ukdarupifùk sn`dr alarca, id`faktd ukd racfùk ma `d dtlùsbard ma` Yn` ma uk tdldônaqufvdàkta d vdrfds vaias a` mfälatrn ma `d ]farrd, astn as snrprakmakta pnrqua`ns rdyns X y cdld ma d`td akarcìd kn puamak sar akbnidmns7 dtrdvfasdk `ds àktasinkvakifnkdàs inln sf buardk vfmrfns inlukas. Yfk aledrcn, HAYYF inlpnka `dsfläcakas nesarvdkmn d` Yn` d trdvæs ma tde`f``ds bfkdlakta aspdifdmds ’inln sf buardukd parsfdkd vakaifdkd lfirnsiùpfid’ qua prnmuia snlerds snera mataitnras ma

rdmfdifùk d enrmn ma `d kdva. ‐Untdralns `d kdva idmd = sacukmns pdrd iradr ukpdtrùk ma lnmu`difùk d pdrtfr ma `ds snlerds qua pnmalns dkd`fzdr pdrd netakarukd fldcak ma` Yn`“, axp`fid @fk. A` prniasn as sflf`dr d ukd rdmfncrdbìd ma rdyns Xaxiaptn qua `ns ifaktìbfins astäk fktarasdmns ak `d buakta ma `ns rdyns (a` Yn`), y knak a` ldtarfd` qua `ns e`nquad (`ds tde`f``ds).

@ns masiuerflfaktns ma HAYYF pnmräk tdlefæk asi`draiar d`cukns dinktaiflfaktns

lfstarfnsns qua niurrak luy àjns ma kuastrn sfstald sn`dr. ‐@n qua sad qua nrf-cfkd `ds arupifnkas sn`dras, pnmrìd sar a` lfsln laidkfsln qua drrnjd ihnrrns mapdrtìiu`ds masma `ns mfsins ma diraifùk ldckatfzdmns ma dcujarns kacrns y astra``dsma kautrnkas“, mfia Makkfs. ‐A` Yn` astä ra`dtfvdlakta iarid, pnr n qua as uk euak`denrdtnrfn pdrd astumfdr astns axùtfins prniasns“. Lfaktrds tdktn, `d ldynrìd ma`ns dstrnkdutds astdräk sdtfsbaihns ink `d talprdkd pramfiifùk ma `ds arupifnkassn`dras inlukas y inrrfaktas7 uk eakabfifn fkmfraitn ma `d lfsfùk HAYYF. Yf `d kdvaaspdifd` puama iulp`fr sù`n asta nejatfvn, a` aspdifn sa inkvartfrä ak uk ùcdr läs



Id`nr: as ukd bnrld ma akarcìd qua sa trdks-bfara ma ukns iuarpns d ntrns. ]faka qua varink `d akarcìd ifkætfid ma `ds ln`æiu`ds quainkbnrldk ukd sustdkifd.

Lamfmd ma` id`nr: ak a` YF (LGY) as a` Ju`fn.Kn nestdkta, axfsta ntrd ukfmdm ma id`nr utf-`fzdmd braiuaktalakta qua sa ``dld id`nrìd y

as `d idktfmdm ma id`nr kaiasdrfd qua sa maeatrdksbarfr d uk crdln ma dcud pdrd qua dulaktasu talpardturd ak uk crdmn iaktìcrdmn.

4 id`nrìd aqufvd`a d =,482 J.

Astd idktfmdm as luy fkinkvakfakta pnr `n paquaôd pdrd qufakas sa pra-niupdk pnr su pasn, y aktnkias sa usd a` tærlfkn gf`nid`nrìd (4.??? id-`nrìds). Qkd hdleurcuasd pnr ajalp`n: inktfaka ak prnlamfn 99? Gid`y dinlpdôdmd ma ukd iarvazd (43? Gid`), prnpnrifnkddprnxfldmdlakta mns lf``nkas ma ju`fns.

Id`nr aspaiìbfin: as `d idktfmdm ma id`nr kaiasdrfd pdrdqua uk crdln ma ukd sustdkifd dulakta su talpardturdak uk crdmn iaktìcrdmn.

Id`nr

@ds knifnkas ma id`fakta y brìn astäk luy `fcdmds d kuastrd pariapifùk saksn Dsì, `ns tærlfkns ma id`nr y talpardturd hdiak pdrta ma` `akcudja utf`fzdmn fktarpratdr a` inlpnrtdlfaktn ma sfstalds tdk mfvarsns inln d dtlùsbard, ns svfvns y `ds astra``ds.

Bukmdlaktn taùrfin



Rfmrfn

_`nln

Dùlfkfn

Inera

Hfarrn

Ldmard (vd`nr prnlamfn)

Iuarpn Huldkn (vd`nr prnlamfn)

Hfa`n

Dcud

Lariurfn

?,5

?,?94

?,5?

?,4?

?,4?

?,=?4

N,8=

?,1?

4

?,?99

YustdkifdId`nr aspaiìbfin

Id`/c.ºI

]alpardturd

As d lamfmd ma `d akarcìd ifkætfid lamfd, ma ds ln`æiu`ds qua inkstftuyak uk iuarpn

Lamfmd ma `d talpardturd: sa utf`fzdk tras asid`ds mfbaraktas:

• Asid`d Iaktìcrdmd: matarlfkd `ns vd`nras ma iarn y ifak crdmnspdrd ns puktns ma busfùk y aeu``fifùk ma` dcud, raspaitfvdlakta.

• Asid`d Bdhrakhaft: matarlfkd inln 95 y 545, `ns vd`nras pdrd`ns puktns ma busfùk y aeu``fifùk ma` dcud, raspaitfvdlakta.

• Asid`d Ga`vfk: ak a``d sa bfjd a` vd`nr iarn inrraspnkmfakta d `dtalpardturd läs edjd (iarn desnùtn), ma` astdmn ak a` iud` `dsln`æiu`ds qua inkbnrldk uk iuarpn sa akiuaktrdk ak rapnsndesnùtn y aqufvdà d -539 cdmns iaktìcrdmns.



Ua`difùk aktra asid`dsma talpardturd:

ºI ºB ºG

4?? 545 939

? 95 539

-43,38 ? 511,55

-539 -=16,= ?

Inkvarsfùk ma Ia`sfus d Bdhrakhaft:

Inkvarsfùk ma Bdhrakhaft d Ia`sfus:

Inkvarsfùk ma Ia`sfus d Ga`vfk: ] G < ]

I + 539

Inkvarsfùk ma Ga`vfk d Ia`sfus: ] I < ]

G - 539

Mf`dtdifùk tærlfid

Iudkmn uk iuarpn n ukd sustdkifd subrak ukd a`avdifùk ak su talpardturd,parflaktdk ukd vdrfdifùk ak su `nkcftum, ärad y vn`ulak, pnr `n iud` as kaiasmfbarakifdr`ds.

Mf`dtdifùk `fkad`: inrraspnkma d `d vdrfdifùk ak `d `nkcftum qua axparflaktd vdrf``d n ukd edrrd d` dulaktdr su talpardturd:

` < `f x (4 + δ x ∂])

` as `d `nkcftum kd`, ` f as `d `nkcftum fkfifd`, δ as a` inaifakta ma

mf`dtdifщk fkad`, ∂] as `d vdrfdifщk ma talpardturd.



Inabfifakta ma mf`dtdifùk `fkad` δ (ºI)’4

5= x 4?-2

45 x 4?-2

4= x 4?-2

?,= x 4?-2

56 x 4?-2

5? x 4?-2

= x 4?-2

52 x 4?-2

6 x 4?-2

9,5 x 4?-2

Yustdkifd

Dùlfkfn

Diarn

Inera

Iudrzn

_`nln

@dtùk

]ukcstakn

Ifki

Rfmrfn inlúk

Rfmrfn _yrax

Mf`dtdifùk suparbfifd`: as d vdrfdifùk ak a` ärad dtard` qua axparflaktd uk iuarpny qua sa va rabàjdmd ak a` dulaktn ma `d `nkcftum ma sus drfstds.

Mf`dtdifùk vnùlætrfid: d` vdrfdr d nkcftum, uk iuarpn axparflaktd ukd vdrfdifùkak su vnùlak bfkd`:

R < R f x (4 + ε x ∂])

R as a` vnùlak kd`, R f as a` vnùlak fkfifd`, ε as a` inaifakta ma

mf`dtdifщk vnùlжtrfid.

D < Df x (4 + 5δ x ∂])

D as a`vd`nr ma` дrad kd`, Df as a` vd`nr ma` дrad fkfifd`,



_nr `n cakard`, `d ldtarfd puama axfstfr ak astdmn n bdsa sù`fmd, `ìqufmd n cdsaYfk aledrcn, sa inksfmardk ntrds bdsas inln a` p`dsld y `ns suparinkmuitnras

Idmd idlefn ma astdmn n ma bdsa, raifea uk knlera pdrtfiu`dr dsì:

• Yù`fmn d `ìqufmn: busfùk• @ìqufmn d cds: vdpnrfzdifùk• Cds d sù`fmn: sue`fldifùk• Yù`fmn d cds: sue`fldifùk ravarsdmd• Cds d `ìqufmn: `fiuabdiifùk• @ìqufmn d sù`fmn: sn`fmfbfidifùk

Idlefns ma astdmn

@ns idlefns ma astdmn ak `d ldtarfd, vdk dinlpdôdmns ma desnrifùmasprakmflfaktn ma id`nr sfk qua axfstd vdrfdifùk ak `d talpardturd, pnrqua qua `ds ln`æiu`ds sa sapdrak n sa dàjak ukds ma ntrds, sa raqufara rad`fzdrtrdedjn ak inktrd ma `ds buarzds ma dtrdiifùk y ak inksaiuakifd, `d akarcìd quà sulfkfstrd pnr diifùk ma` id`nr sa fkvfarta ak mfihn trdedjn.

4,85 x 4?-=Lariurfn

Inabifakta ma mf`dtdifùk vnùlætrfid (ºI)’4Yustdkifd

C`fiarfkd =,81 x 4?-=

Dìnhn` atì`fin

Cdsn`fkd Dcud

3,=1 x 4?-=

6,1 x 4?-=

5,4 x 4?-=

Iudkmn uk iuarpn idlefd ma bdsa, sa raqufarasulfkfstrdrà ukd ifartd idktfmdm ma id`nr pnr

ukfmdm ma ldsd, `d iud` as pdrtfiu`dr pdrd idmdsustdkifd y sa maknlfkd id`nr `dtakta.



]arlnmfkälfid

As a` astumfn matd``dmn ma `d trdksbarakifd ma id`nr, as maifr, astumfd `ds ra`difnkasaktra `ds mfbaraktas prnpfamdmas ma `d ldtarfd fkharaktas d `ns idlefns ma `d tal-

pardturd. _drd su lajnr inlpraksfùk, sa raqufara inkniar ntrns inkiaptns:

Yfstald: flp`fid ìlftas radàs n fldcfkdrfns ma mnkma astä inktakfmd ukdidktfmdm mabfkfmd ma ldtarfd. _nr ajalp`n: `d idktfmdm ma dfra inktakfmnak ukd jarfkcd, tfaka `ìlftas radàs parn d` hde`dr ma 5 il9 ma dfra ak ukaspdifn defartn, sus brnktards snk fldcfkdrfds. Yf a` sfstald kn fktaridlefd

akarcìd ink a` axtarfnr, sa à ``dld sfstald dfs`dmn.

Astdmn ma uk sfstald: aqufvdà d` aquf`ferfn tarlnmfkälfin ma` sfstald,matarlfkdmn pnr vd`nras ma vnùlak, prasfùk, talpardturd y idktfmdmma ldtarfd (vdrfdeàs ma` sfstald). _nr ajalp`n: iudkmn sa akiuaktrd akaquf`ferfn laiäkfin, tærlfin y quìlfin. _drd matarlfkdr a` aqufvdàkta

laiäkfin ma` id`nr, Jdlas Jnuà utf`fzù uk sfstald ma pdàtds (qua cfrdedkpnr diifùk ma d`cukds pasds suspakmfmds), sularcfmds ak ukd ldsd inknifmdma dcud, maktrn ma uk raifpfakta dfs`dmn tærlfidlakta. D` idar `ds pasds,pfarmak akarcìd pntakifd` qua sa trdksbnrld ak id`nr, maefmn d` lnvflfaktnma `ds pdàtds maktrn ma` dcud, nrfcfkdmd pnr `d buarzd ma brfiifùk. Ak astdbnrld, malnstrù axparflaktd`lakta d aqufvdàkifd aktra id`nrìds y ju`fns.

4 id`nrмd < =,482 J

_rniasns: puamak sar ravarsfeàs (cdsas fmadàs), n frravarsfeàs (prniasnstarlnmfkälfins radàs), y inrraspnkmak d trdksbnrldifnkas n idlefns maastdmn. _nr inksfcufakta, hdy vdrfdifùk ak `ns vd`nras ma `ds vdrfdeàs qua`n matarlfkdk.



_

_5

R4 R5 R

_

_5

_4

R4 R

_rflard ay ma d tarlnmfkälfid: masirfea d ra`difùk aktra a` trdedjn,id`nr y `d akarcìd fktarkd ma uk sfstald y axprasd qua ‐a` id`nr desnrefmpnr uk sfstald as fcud` d` trdedjn rad`fzdmn pnr a` sfstald läs a` dulak

ma `d akarcìd fktarkd“:

T < S + ∂Q

Mnkma T as a` id`nr desnrefmn, S a` trdedjn rad`fzdmn y ∂Q as d vdrfdifùma `d akarcìd fktarkd ma` sfstald.

D`cukns prniasns sa dp`fidk bukifnkd`lakta d `d prflard ày (cdsfmadàs):

• _rniasn fsneärfin: sa rad-`fzd d prasfùk inkstdkta y a`trdedjn rad`fzdmn as mfbarak-ta ma iarn.

T < _(R b - R

f ) + ∂Q

• _rniasn fsùinrn n fsnvn-ùlætrfin: sa inksfmard a`vnùlak inkstdkta, a` trded-

jn rad`fzdmn as fcud` d iarny a` id`nr qua sa sulfkfstrdd` sfstald as utf`fzdmn pdrddulaktdr su akarcìd fktarkd.

S < ? 7 Q 5 - Q

4< ∂Q< T



• _rniasn fsntærlfin: sa rad-`fzd d talpardturd inkstdktay kn hdy vdrfdifùk ma akarcìd

fktarkd.

T < S

Asta prniasn tfaka ukd axiap-ifùk iudkmn sa inksfmard ukcds fmad`.

• _rniasn dmfdeätfin: sa pra-saktd iudkmn kn hdy fktaridl-efn ma id`nr aktra a` sfstald ya` lamfn, a` sfstald kn cdkd kfpfarma id`nr y ak inksaiuak-ifd, a` trdedjn rad`fzdmn snera

a` sfstald inrraspnkma d `dvdrfdifùk ma d akarcìd fktarkdma` lfsln.

Q 5 - Q

4< ∂Q < - S

Yacukmd ay ma d tarlnmfkälfid. Ak prflar ucdr, sa puama dbfrldr quaa` id`nr bùya aspnktäkadlakta ma uk bnin läs id`fakta d ntrn laknsid`fakta y kn d` inktrdrfn. _nr ajalp`n: iudkmn latalns ak a` inkca`dmnruk vdsn ma jucn pdrd inkvartfr`n ak ha`dmn, æsta kn desnrea id`nr sfknqua pnr a` inktrdrfn, `n iama d` dfra lakns id`fakta qua astä maktrn maìnkca`dmnr hdstd dìdkzdr a` maknlfkdmn aquf`ferfn tærlfin. As maifr,mns sustdkifds dìdkzdk `d talpardturd ma aquf`ferfn tærlfin iudkmn `d

_

_

R



läs id`fakta iamfù tdktn id`nr d `d lakns id`fakta qua dhnrd, `ds mns saakiuaktrdk d `d lfsld talpardturd. @n dktarfnr mapakma ma `d idktfmdmma ldsd, a` id`nr aspaiìbfin y `d vdrfdifùk ma talpardturd ma idmd ukd.

Id`nr desnrefmn (T) < Id`nr iamfmn (-T)

l4 x a

4(t

4b-t

4f ) < - l

5 x a

5(t

5b-t

5f )

Astd trdksbarakifd ma id`nr sa puama mdr pnr inkmuiifùk ak ldtarfdàssù`fmns. _nr ajalp`n: d` idàktdrsa ukd edrrd ma hfarrn, a` id`nr sa vdtrdkslftfakmn prncrasfvdlakta d trdvæs ma tnmd su `nkcftum, sfk trdks-pnrtdr ldtarfd. _nr astd rdzùk, uk axtraln puama astdr id`fakta y a` ntrnd laknr talpardturd. _nr inkvaiifùk iudkmn a` id`nr sa prnpdcd ma ukùcdr d ntrn d` trdkspnrtdrsa `d ldsd id`fakta. _nr ajalp`n: d` idàktdrsa,a` dfra suea y a` dfra lakns id`fakta edjd y mdk nrfcak d `d bnrldifùk ma

inrrfaktas ma dfra (`ns vfaktns). V pnr rdmfdifùk iudkmn kn hdy inktditnaktra ds sustdkifds, parn sa md pnr d alfsfùk ma id`nr ak bnrld ma nkmdsaàitrnldckætfids. _nr ajalp`n: a` id`nr qua raifeflns ma `d ùz ma` Yn`.

Ak sacukmn ùcdr, sa dbfrld qua: ‐Ak uk prniasn iìi`fin, (ifi`n tærlfin)iuyn úkfin rasu`tdmn sad `d desnrifùk ma id`nr ma uk bnin, `d akarcìdid`nrìbfid kn puama trdksbnrldrsa tntd`lakta ak trdedjn laiäkfin“ (Ga`-vfk-_`dkig). _nr ajalp`n: ak `ns vahìiu`ns hdy idàktdlfaktn ma` lntnr

pnr diifùk ma `d inleustfùk ma `d cdsn`fkd. D` hdiar qua `ns pfstnkas samasp`diak pdrd netakar uk rakmflfaktn n bukifnkd`fmdm ma` 4??%, aìd`nr iamfmn maearä sar fcud` d iarn, parn astn as rad`lakta flpnsfeà.

Ak tariar ucdr, sa dbfrld qua as flpnsfeà inkstrufr ukd ldqufkd bukifn-kd` ma lnvflfaktn parpatun, pnrqua `d bukifnkd`fmdm ma ukd läqufkdkukid puama sar ùptfld, d` 4??%.



Aktrnpìd

Ya inksfmard inln a` crdmn ma masnrmak ma uk sfstald. En`tzldkk dbfrld qua asak rad`fmdm ukd lamfmd ma` masnrmak ma` Qkfvarsn. _nr ajalp`n: ukd iarf``d tfaka

ifartn nrmak (n masnrmak), lnàiu`dr, y d` drmar idlefd a` nrmak (dulaktd a` masnr-mak). _nr `n tdktn, `d aktrnpìd dulaktd y `d akarcìd inkiaktrdmd sa mfsalfkd dhnrdink ukfbnrlfmdm. Ak inksaiuakifd, ‐ak tnmn sfstald qua sa inksfmard nrmakdmnsfalpra axfstfrä uk crdmn ma masnrmak“. Ak d vfmd präitfid, pnmalns kntdr qua idmdukn ma knsntrns utf`fzd uk ifartn nrmak pdrd tnldr kuastrns dpuktas, pdrd nrcdkfzdrkuastrns `ferns, kuastrd rnpd7 parn sf d`cufak `n nesarvd, puama dbfrldr qua pdrd æhdy masnrmak, as maifr, as uk inkiaptn ra`dtfvn.

]ariard ay ma d tarlnmfkälfid: as flpnsfeà dìdkzdr axparflaktd`lak-ta a` iarn desnùtn, as maifr, kfkcukd sustdkifd, edjn kfkcukd inkmfifùk,puama `àcdr d takar ukd talpardturd inrraspnkmfakta d` iarn desnùtn,pnrqua astn flp`fidrìd qua d akarcìd ifkætfid ma sus ln`æiu`ds buard iarn.Yfalpra axfstfrä lnvflfaktn lnàiu`dr, pnr lìkfln qua sad.

(aktrnpìd)

]

]4

]5

Y4 Y5 Y

Läqufkd ma Idrknt: a` fkcakfa-rn brdkiæs Ydmf Idrknt, astumfùa` `ìlfta ma abfifakifd ma ukdläqufkd ma id`nr iìi`fid y mas-iuerfù qua `d läqufkd desnreaid`nr ma uk mapùsftn ma d`td tal-pardturd y maspfma id`nr hdifd

uk mapùsftn ma edjd talpardtu-rd. _nr asta lntfvn, ns inksfmarùprniasns tærlfins ravarsfeàs ya` ifi`n `n inlpàtd uk prniasndmfdeätfin ravarsfeà:



6


4. A` puktn ma busfùk ma` hfarrn as ma 4.192ºI. Axprasdr `d talpardturd akºG.

Ynùifùk: pnr `d ra`difùk aktra asid`ds, pnmalns inkvartfr ºI d ºB, y ºId ºG.

] G < ]

I + 539 < 4192 nI + 539 < 48?6 G

5. ¾Tuæ idktfmdm ma id`nr sa à maea dcracdr d 4 `ftrn ma dcud qua sa akiuafkfifd`lakta d 5?ºI pdrd qua àcua d` puktn ma aeu``fifùk (4??ºI), sf d praas ma 4 dtlùsbard>

Ynùifùk: 4 `ftrn ma dcud aqufvdà d 4.??? il9 y inrraspnkma d ukdldsd ma 4.??? c:

T < ld xδ

d x∂] < 4.???c x4id`/cnI(4.???nI - 5?nI) <

4.??? x4 x8? < 8?.??? < 99=88? J



9. Yf a` prniasn bìsfin dktarfnr sa rad`fzd ak uk raifpfakta iarrdmn, ¾iuä` sarä `dprasfùk bfkd`>

Ynùifùk:

_nr `d ày ma `ns cdsas fmadàs, sa puama matarlfkdr `d prasfùk bfkd`:

=. Ya lazi`dk 9? c ma dcud d 1?ºI ink 1? c ma dìnhn` d 8?ºI. Matarlfkdr avd`nr ma `d talpardturd pdrd `ncrdr a` aquf`ferfn tærlfin.

Ynùifùk:

l4 x a

4(]

b-]

4f) < - l

5 x a

5(]

b-]

5f)

9?c x 4 id`/c nI (]

b-1?nI) < - 1?c x ?,1?1 id`/c nI

(]

b-8?nI)

] b

< 29,34nI

Dutnavdùdifùk

Asirfed `d ldkard inln `ncrù inlprakmar `ns talds masdrrn``dmns ak `dprasakta ukfmdm. Qtf`fia `d sfcufakta tde`d:

Lf prniasn ma dprakmfzdja

Ditfvfmdmas ma dprakmfzdja qua masdrrn``æ Dprakmfzdjas

DitfvfmdmLa

custùKn lacustù

Luymfbìif`

Mfbìif` Bäif` Dprakmì

d`cn kuavnAstn yd `n

sdeìd



8

_räitfid ma id`nr y talpardturd

Qkfmdm 2. ]arlnmfkälfid Yasfùk

4?

_rniamflfaktn

Ldtarfdàs

Laiharn, vdsn ma praifpftdmn, dcud, tfkturd, edrrdma hfarrn ma 45 il, raifpfakta ma finpnr ink tdpd,tarlùlatrn, ed`ùk ma 1?? il9, tdpùk, tuen ma vfmrfny ed`dkzd.


4. Inkstrufr ukd idjd ma pdpa`, dcracdrà dcud y axpnkar`d d` buacn.Nesarvdr, axp`fidr y inkiùfr.

5. ]nldr uk idea``n y axpnkar`n d` buacn. ]nldr ntrn idea``n,akrn``dr`n snera uk trnzn ma latd` y axpnkar`n tdlefæk d` buacn.



@ds sfcufaktas pdrdmnjds buarnk tnldmds ma` `fern _drdmnjds ma

Ä`vdrn Derf`, mfraitnr ma` aqufpn ma fkvastfcdifùk ma `d ‐tfakmd

taikn`ùcfid“. As rainlakmdeà qua a` ajarififn sad malnstrdtfvn

(rad`fzdmn pnr a` prnbasnr ink dyumd ma d`cukns astumfdktas).

9. Ak a` vdsn ma praifpftdmn, matarlfkdr d talpardturddlefakta ma 5?? il9 ma dcud.

=. Dmfifnkdr hfa`n y lamfr kuavdlakta d talpardturd

1. _nkar d` buacn y matarlfkdr ns vd`nras ma talpardturd idmd ^^^^ sacukmns hdstd `àcdr d` puktn ma aeu``fifùk ^^^^^^^

2. Idàktdr murdkta 1 lfkutns, ukn ma `ns axtralns ma `d edrrd mahfarrn. ]rdksiurrfmn a` tfalpn, ¾`d talpardturd ma ns mns axtralns

as fcud`> Axp`fidr.

3. Matarlfkdr `d talpardturd ma 4?? il9 ma dcud ak inkmfifnkas

knrldàs. Fktrnmuifr `d edrrd ma hfarrn, lamfr `d talpardturd ak

asa fkstdkta y ùacn ma 4 lfkutn, inkiùfr y axp`fidr.

8. Ak a` raifpfakta ma finpnr, pnkar 1? il9 ma dcud d talpardturd

dlefakta y 8? il9 ma dcud d 31ºI. ]dpdr a` raifpfakta, dcftdr`n

sudvalakta y d inktfkudifùk, lamfr `d talpardturd bfkd` ma `d

lazi`d. Rn`var d tdpdr a` raifpfakta, majdr`n ak rapnsn pnr 1 lfkutns

y vn`var d lamfr `d talpardturd. Inkiùfr y axp`fidr `n nesarvdmn.



6. Ak uk ed`ùk ma 1?? l` pnkard harvfr 5?? l` ma dcud.Iudkmn `àcua d` puktn ma

aeu``fifùk, ratfrdr ma` buacny räpfmdlakta tdpdr a` ed`ùkink uk tdpùk ma iduihn,ma td` bnrld qua a` vdpnrkn puamd asidpdr. Fkvartfra` ed`ùk, in`nidr`n snera a`drn, dmfifnkdr dcud id`fakta

snera a` ed`ùk7 ùacn dcudd talpardturd dlefakta ypnr ú`tfln, dcud ink hfa`n.Nesarvdr `n niurrfmn ak `nstras idsns, axp`fidr y inkiùfr.


D pdrtfr ma d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y ns prniasnsrad`fzdmns, matarlfkdr `d axp`fidifùk bìsfid pdrd idmd avaktn astumfdmn.

4?. _rapdrdr ukd iueatd ink subfifakta idktfmdm ma dcud d talpardturddlefakta, dcracdrà `d tfkturd y majdr`d ak a` pfsn. D uk tdpùkma iduihn ink nrfbfifn iaktrd`, in`nidrà a` tuen ma vfmrfn madprnxfldmdlakta 4 l ma nkcftum. D inktfkudifùk, pnkar d harvfrak a` ed`ùk kuavdlakta, 5?? l` ma dcud7 iudkmn `àcua d` puktnma aeu``fifùk, tdpdr`n ink a` tdpùk ma iduihn7 tdpdr a` axtraln`fera ma` tuen, fkvartfr a` ed`ùk ma td` bnrld qua a` axtraln ma`tuen quama maktrn ma` dcud ink tfkturd. Nesarvdr `n qua niurray axp`fidr.



@ < 51 il

4. Qkd `älfkd iudmrdmd ma diarntfaka 51 il ma `dmn, su talpard-turd fkfifd` as ma 5?ºI y sa id`faktdhdstd ukd talpardturd ma 6?ºI,¾iuä` bua `d vdrfdifùk ak su ärad>

5. Fkfifd`lakta, d 1? il9 ma c`fiarfkd d 5?ºI sa a dmfifnkd id`nr hdstd

dìdkzdr ns 3?ºI, ¾axfstfrä vdrfdifùk ak su vnùlak> Yf as dsì, ¾iuäàs su vnùlak bfkd`>

9. Inlpàta `d sfcufakta tde`d:

ºI

4?

ºG

4?

ºI

45?

ºB

4?

ºB

45?

ºG

45?

Kn.

4

5

9

Kn.

=

1

2

=. Matarlfkdr `d talpardturd pdrd a` aquf`ferfn tærlfin, iudkmn sa

lazi`dk 2? l` ma dcud d 5?ºI ink =1 c ma hfarrn d 81ºI.

1. Yf sa pnkak ak inktditn mns edrrds ma latdàs ma diarn y inera, a`prflarn ink ukd ldsd ma 31 c d =8ºI y a` sacukmn, ink ukd ldsd

ma 6? c y talpardturd ma 62ºI, ¾iuä` as a` vd`nr ma d talpardturd

bfkd` (aquf`ferfn tærlfin)>

2. @ds atfquatds ma d`cukns d`flaktns trdak `d tde`d kutrfifnkd` y a`

vd`nr akarcætfin ak id`nrìds Yaàiifnkdr pnr `n lakns iudtrn



3. Yf uk pamdzn ma ldmard y ukd puktf``d astäk d 41ºI, d` tnidr`ns a` lapdraia läs brìn, parn sf sa id`faktdk hdstd dìdkzdr ukd talpardturd m1?ºI, aktnkias a` latd` pdraiarä läs id`fakta, ¾pnr quæ>

8. Yf quaralns inksarvdr kuastrd eaefmd id`fakta murdkta uk euak dps

`n lajnr as utf`fzdr uk tarln pnrqua ak uk raifpfakta ma vfmrfn n mp`ästfin y dúk ma finpnr, sa akbrìd räpfmdlakta. ¾Iuä` as a` prfkifpma bukifnkdlfaktn ma` tarln>

Avdùdifùk

¾Tuæ dprakmfù ink `d ditfvfmdm>Rd`nrdr a` trdedjn rad`fzdmn, `d prasaktdifùk y masdrrn``n ma `d cuìd, `d dp`fid`fmdm ma `d àiturd, y ma sar pnsfeà, prnpnkar lnmfbfidifnkas pdrd lajnrdrnetakifùk ma `ns `ncrns prnpuastns.

Axp`fidr `d flpnrtdkifd y dp`fidifnkas ma `ns talds trdtdmns ak `d cuìd, pdsnùifnkdr sftudifnkas bìsfids radàs ma `d vfmd mfdrfd.

Inkiùsfnkas

Dutnavdùdifùk

Rd`nra sus dprakmfzdjas. _drd a``n, ldrqua ink ukd X a` pnriaktdja qua astfldmaiudmn:


Iulp`flfaktn y

raspnksdef`fmdm

¾Iulp`fù ink `ds àiturdsdsfckdmds, `ds ditfvfmdmasmasdrrn``dmds ak i`dsa y `d

aktracd ma tdrads y trdedjnsfkmfvfmudàs n pnr aqufpn>

Iradtfvfmdm yid`fmdm

¾Dpnrtù fmads> ¾Astds buarnksfckfbfidtfvds>

¾Uad fzù sfk arrnr d`cukn ds tdr-ads y/n ns trdedjns dsfckdmns>

Dprakmfzdja ydpnrtdifùk ma

¾Tuæ tdktn dprakmfù y quætdktns inkniflfaktns dpnrtùak `ds i`dsas, ak `ds tdrads y/n



Efe`fncrdbìd

DEUF@, Ä`vdrn. _drdmnjds. Ydktdbæ ma Encntä: ]fakmd taikn`ùcfid, 4666.

DYFLNR, Fsddi. Lnlaktns asta`dras ma `d ifakifd. Edria`nkd: Yd`vdt,468=.

EDUKA]], Udylnkm y QUFEA, Ju`fn. Ä`caerd y canlatrìd 5. Ydktdbæ maEncntä: Li Crdw Hf``, 4662.

EDQ]FY]D, Ldurfifn, CDUIÌD, Amwfk y IDUUF@@N, Astaedk. Bìsfid F.Encntä: Ydktf``dkd, 5??4.

SF@YNK, Jarry, EQBBD, Dkthnky y EN, @nu. Bìsfid. 2 am. Kduid`pdkma Juäraz: _adrsnk, _raktfia Hd``, 5??3.

HAIH], Aucaka. Bìsfid ak parspaitfvd. Læxfin: Dmmfsnk Sasày@nkcldk, 4661.

HASF]], _du`. Bìsfid inkiaptud`. 4? am. Læxfin: _adrsnk DmmfsnkSasày, 5??3.

RD@AUN, Lfiha`. Bìsfid Bukmdlaktd` 4. Ydktdbæ ma Encntä: Knrld,4666.

RF@@ACDY, Ldurfifn. Cd`dxfd bìsfid 4?. Ydktdbæ ma Encntä: Rnùktdm,4666.

RF@@ACDY, Ldurfifn. Cd`dxfd bìsfid 44. Ydktdbæ ma Encntä: Rnùktdm,4666.





Ldtalätfids 4?

Huasftn, Cudfkìd



Astäkmdras eäsfins ma inlpatakifds ak Ldtalätfids

Aja drtfiu`dmnr prfkifpd`

_aksdlfaktn vdrfdifnkd`

y sfstalds d`caerdfins ydkd`ìtfins

Inharakifd hnrfznktd` ma paksdlfaktns

y sfstalds ldtalätfins

Dpnyd d` paksdlfaktn vdrfdifnkd` ak…

@d fmaktfbfidifùk ak bnrld vfsud`, cräbfid y d`caerdfid ras-paitn d `ds prnpfamdmas ma `ds iurvds qua sa nesarvdk ak `nsenrmas netakfmns pnr `ns inrtas `nkcftumfkdàs, mfdcnkdàsy trdksvarsdàs ak uk if`fkmrn y ak uk inkn7 `d `nid`fzdifùkma `ns nejatns canlætrfins iurvns y iùkfins ak sfstalds maraprasaktdifùk (idrtasfdkd, pn`dras, if`ìkmrfins, asbærfins), àparlfta d` astumfdkta rasn`var prneàlds ak `ns qua sa usdktrdksbnrldifnkas ma raprasaktdifnkas d`caerdfids, usdkmndrculaktns y lnma`ns canlætrfins.

Dpnyd a` paksdlfaktn vdrfdifnkd` ak…

A` mfsaôn ma astrdtacfds pdrd denrmdr sftudifnkas ma lamfifùkqua raqufardk praifsfùk aspaiìbfid inln ak `d rasnùifùk maprneàlds qua fkvnùirdk ldckftumas iuyns vd`nras lamfnssa mabfkdk inln rdznkas, pnr ajalp`n `d va`nifmdm, `d dia-àrdifùk y `d maksfmdm lamfd, dsì, a` astumfdkta bnrlu`drä y

justfbfidrä `ns rasu`tdmns netakfmns lamfdkta prniasns madprnxfldifùk suiasfvd, rdkcns ma vdrfdifùk y `ìlftas ak sf-tudifnkas ma lamfifùk.

Dpnyd a` paksdlfaktn vdrfdifnkd` ak…

@d fktarpratdifùk y inlpdrdifùk ma rasu`tdmns pdrd astumfnsink fkbnrldifùk astdmìstfid prnvakfaktas ma lamfns mainlukfidifùk axtarkns n ma` äleftn asin`dr, justfbfidkmn nrabutdkmn fkbarakifds edsdmds ak rdznkdlfaktns astdmìstfins,mfsaôdkmn axparflaktns dàdtnrfns ak bìsfid, kdturdàs n sn-ifdàs pdrd astumfdr ukd pracuktd n prneàld, masirfefakmntakmakifds qua sa nesarvdk ak inkjuktns ma vdrfdeàs ra`d-ifnkdmds ink a` ldkajn ma fkbnrldifùk, usdkmn lamfmds maiaktrd`fzdifùk, `nid`fzdifùk, mfsparsfùk y inrra`difùk.

Dpnyd a` paksdlfaktn vdrfdifnkd` ak…A` dkä`fsfs ma raprasaktdifnkas maifldàs ma `ns kúlarnsradàs parlftak mfbarakifdr aktra rdifnkdàs a frrdifnkdàs,rainknifakmn `d maksfmdm a fkinlpàtftum ma `ns lfslnsd trdvæs ma lætnmns kulærfins, canlætrfins y d`caerdfins,inlpdrdkmn y inktrdstdkmn `ds prnpfamdmas ma `ns kúlarns(kdturdàs, aktarns, rdifnkdàs y radàs) y ds ma sus ra`difnkas ynpardifnkas `n qua à parlfta d` astumfdkta inkstrufr, ldkajdry utf`fzdr dprnpfdmdlakta `ns mfstfktns sfstalds kulærfins

_aksdlfaktnaspdifd` y sfs-talds canlæ-trfins.

_aksdlfaktnlætrfin y sfs-talds ma la-mfmds.

_aksdlfaktndàdtnrfn ysfstalds mamdtns.

_aksdlfaktnkulærfin ysfstalds ku-lærfins.

Murdkta tnmn a` Ifi`n 1,a` astumfdkta utf`fzdrä tæi-kfids ma dprnxfldifùkak prniasns fkbfkftns ku-lærfins, fktarpratdkmn `dknifùk ma marfvdmd inlnrdzùk ma idlefn y inlnvd`nr ma `d pakmfakta ma`d tdkcakta d ukd iurvd,masdrrn``dkmn lætnmnspdrd hd``dr ds marfvdmds ma

d`cukds bukifnkas eäsfidsak inktaxtns ldtalätfinsy kn ldtalätfins, `n quaà parlftfrä dkd`fzdr ra`d-ifnkas y prnpfamdmas aktraaxprasfnkas d`caerdfidsraspaitn d `ds cräbfids mabukifnkas pn`fkùlfidsy rdifnkdàs ma sus ma-rfvdmds, lnma`dkmn dsìsftudifnkas ma vdrfdifùkparfùmfid ink bukifnkastrfcnknlætrfids y sus ras-paitfvds marfvdmds.



Qkfmdm 4. Inkiaptns eäsfins 113

Yasfùk 4. Mabfkfifùk ma inkiaptns canlætrfins 113 Yasfùk 5. Yfstald ma lamfifùk ma äkcu`ns saxdcasfld` 12? Yasfùk 9. Kúlarn Ϗ (pf) 12=

Yasfùk =. A` rdmfäk 122 Yasfùk 1. @nkcftum ma drin ma `d ifriukbarakifd 135 Yasfùk 2. Ärad ma uk saitnr ifriu`dr 13=

Yasfùk 3. ]anrald ma _ftäcnrds 133

Qkfmdm 5. Ua`difnkas y bukifnkas 184

Yasfùk 4. _rnmuitn idrtasfdkn 184 Yasfùk 5. Ua`difùk 185 Yasfùk 9. Bukifùk 189

Qkfmdm 9. ]rfcnknlatrìd ak uk trfäkcu`n raitäkcu`n 168

Yasfùk 4. Bukifnkas trfcnknlætrfids 168 Yasfùk 5. _rneàlds dp`fidmns ak `d rasnùifùk

ma trfäkcu`ns raitäkcu`ns 2?? Yasfùk 9. D`cukds fmaktfmdmas eäsfids 2?1

Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns radàs 2?6

Yasfùk 4. Bukifnkas sakn y insakn 2?6 Yasfùk 5. Cräbfids ma `d bukifùk sakn 25? Yasfùk 9. Cräbfid ma `d bukifùk insakn 251 Yasfùk =. @d bukifùk tdkcakta 256 Yasfùk 1. D`cukds fmaktfmdmas trfcnknlætrfids 295

Yasfùk 2. Cräbfid ma `d bukifùk intdkcakta 291

Ì km f i a



Yasfùk 8. @d bukifùk insaidkta 2=4 Yasfùk 6. Rarfbfidifùk ma fmaktfmdmas trfcnknlætrfids 2==

Qkfmdm 1. Dp`fidifnkas ma `d trfcnknlatrìd 21?

Yasfùk 4. Ajalp`ns f`ustrdtfvns 21? Yasfùk 5. @ay ma sakns 213 Yasfùk 9. ]anrald ma` insakn 22= Yasfùk =. Aiudifnkas trfcnknlætrfids 23= Yasfùk 1. Bùrlu`ds ma dmfifùk pdrd `ds bukifnkas 284

Yasfùk 2. Bùrlu`d ma Harnk 28=

Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn 286

Yasfùk 4. Uaitds ak a` p`dkn 286 Yasfùk 5. Mfstdkifd aktra mns puktns 264 Yasfùk 9. Innrmakdmds ma` puktn lamfn 26= Yasfùk =. _akmfakta ma ukd raitd 262 Yasfùk 1. Aiudifnkas ma `d raitd ak a` p`dkn 266

Yasfùk 2. Uaitds pdrd`a`ds y raitds parpakmfiu`dras 344

Qkfmdm 3. Iurvds ak a` p`dkn 346

Yasfùk 4. @d ifriukbarakifd 346Yasfùk 5. @d a`fpsa 353 Yasfùk 9. @d hfpæren`d 398 Yasfùk =. @d pdräen`d 3=2

Qkfmdm 8. _rnedef`fmdm y astdmìstfid 313

Yasfùk 4. Inkiaptns eäsfins ma prnedef`fmdm 313 Yasfùk 5. Knifnkas snera inkjuktns 324 Yasfùk 9. Axparflaktn ak astdmìstfid 321

Yasfùk =. _rnedef`fmdm ma avaktns 33?



Cräbfid 5

Fkfifdralns a` astumfn ma `d ]rfcnknlatrìd, ink `d mabfkfifùk d`cukns inkiaptns canlætrfins qua kns parlftak hdiar uprasaktdifùk i`drd y praifsd ma `ns talds qua vdlns d masdrrn`

Yf mas`fzdlns a` `äpfz masma uk puktn D hdifd ntrn puktn Eutf`fzdlns pdrd a``n a` bf`n ma `d rac`d, netakalns ukd salfrrama nrfcak D, ak mfraiifùk d` puktn E.

Yalfrraitd

Cräbfid 4

UaitdMns puktns ak a` p`dkn matarlfkdk ukd raitd. _drd mfeujdr `d raiin`nidlns `d rac`d ma td` ldkard qua su enrma infkifmd ink `ns puk

D y E, y `uacn mas`fzdlns a` `äpfz, pdsdkmn pnr asns mns puktns.

Makfifùk ma inkiaptns canlætrfinsQkfmdm 4. Inkiaptns eäsfins Yasfùk

4

Dprakmfakmn ink a` prnba Ju`fn

Ärads ma bfcurds p`dkds. Murdifùk: 48:?2



Cräbfid 9

Äkcu`n

@d ukfùk ma mns salfrraitds ink nrfcak inlúk ak a` p`dkn, bnrld uk äkcu

inln sa f`ustrd ak d cräbfid 9. Idmd salfrraitd as uk dmn ma` äkcu`n y puktn inlúk ma `ds salfrraitds sa maknlfkd værtfia ma` äkcu`n.

Ak d cräbfid, d salfrraitd DE y d salfrraitd DI snk ns dmns ma` äkcu`ny a` puktn D as a` værtfia ma` äkcu`n.

Asta äkcu`n `n pnmalns ``dldr: Dkcu`n EDI ù äkcu`n IDE.

D` trdedjdr ink äkcu`ns, sfalpra tnldlns ukn ma sus `dmns inln `dmfkfifd` y a` ntrn inln dmn tarlfkd`. @d lamfmd ma uk äkcu`n as uk kúlarqua lfma a` cfrn n masp`dzdlfaktn ma` `dmn fkfifd` hdstd infkifmfr insu `dmn tarlfkd`.



Cräbfid

Yf a` cfrn sa hdia ak saktfmn inktrdrfn d ds ldkaif``ds ma` ra`nj, a` äkctfaka ukd lamfmd pnsftfvd. Yf a` cfrn sa hdia ak a` lfsln saktfmn maldkaif``ds ma` ra`nj, `d lamfmd ma` äkcu`n as kacdtfvd.

]nmn sfstald ma lamfifùk raqufara ma ukfmdmas7 pdrd lamfr `ns äkcuaxfstak vdrfns sfstalds ma ukfmdmas qua masirfefralns läs dma`dkta

Äkcu`n iaktrd`

Iudkmn uk äkcu`n tfaka su værtfia ak a` iaktrn ma uk iìriu`n y sus dminrtdk d` iìriu`n ak mns puktns, asta äkcu`n sa ``dld äkcu`n iaktA` drin DE ma` iìriu`n inlprakmfmn aktra sus `dmns sa ``dld a` dsuetakmfmn pnr a` äkcu`n.

Ak trfcnknlatrìd, uk äkcu`n as matarlfkdmn pnr d bnrld inln sa nrfcfMaealns inkniar a` `dmn fkfifd` a` `dmn tarlfkd` y a` tfpn ma rntdi



A` sfstald saxdcasfld` as uk sfs-tald ma kulardifùk pnsfifnkdìuyd edsa as 2?. Bua fmadmn pnr`ns edef`nkfns y sa sfcua usdkmn ak`d ditud`fmdm. Ak asta sfstald, a`

iìriu`n as ukd ifriukbarakifd qua sa mfvfmaak 92? pdrtas fcudàs. A` äkcu`n iaktrd` iuyndrin suetfakma ukd ma astds pdrtas, tfaka ukdlamfmd ma uk crdmn, ma td` ldkard qua sfd` `dmn fkfifd` `n rntdlns ukd vua`td inlpàtd, hderä cfrdmn 92? crdmns.@ns edef`nkfns mfvfmìdk idmd crdmn ak 2? lfkutns y idmd lfkutn ak 2?sacukmns, pdrd netakar dsì uk sfstald ma lamfifùk luy rabfkdmn. Ak a`

trdkspnrtdmnr, pnmalns lamfr uk äkcu`n ink crdk praifsfùk, usdlns ma-ifldàs. Ajalp`n: uk äkcu`n ma =8.1 d` lu`tfp`fidr su pdrta maifld` pnr2?, md inln rasu`tdmn =8 crdmns 9? lfkutns.

@d idìu`dmnrd ifaktìbfid inkvfarta ukd lamfmd maifld` ak saxdcasfld`,in`niäkmn`d ak crdmns, lfkutns y sacukmns, y vfiavarsd.

Ajalp`n:_drd pdsdr 51¿,45½,=?“ ma` sfstald saxdcasfld` d` sfstald maifld`, as kaiasdrfn sacastns pdsns:

4. Asirfed `d ifbrd 51 y nprfld `d tai`d cls. Dpdraiarä 51¿7 ùacn, fktrnmuzid `d i45 y nprfld `d tai`d cls7 dpdraiarä 45¿7 rapftd `d npardifùk ink `d ifbrd =?, y akpdktd``d ma `d idìu`dmnrd pdraiarä `d ifbrd inlpàtd 51¿ 45¿ =?¿.

5. Ink astd ifbrd, nprfld `d tai`d fcud` (<), sacufmd ma `d tai`d cls y dpdraiarä ak

Yfstald ma lamfifùk ma äkcu`ns saxdcasfld`

Qkfmdm 4. Inkiaptns eäsfins Yasfùk

5



4. @d lamfmd ma uk äkcu`n as 5=¿. Hd``dr su lamfmd ak lfkutns y sacukm

Ynùifùk

_drd axprasdr `d lamfmd ak lfkutns, lu`tfp`fidlns pnr 2? puastn qidmd crdmn tfaka 2? lfkutns, dsì:

5= x 2? < 4.==? lfkutns

_drd inkvartfr ns lfkutns ak sacukmns, lu`tfp`fidlns 4.==? pnr 2?, pqua idmd lfkutn tfaka 2? sacukmns dsì: 4.==? x 2? < 82.=?? sacukmAstn sfckfbfid qua 5=¿ aqufvdàk d 4.==? lfkutns n 82.=?? sacukmns

5. Qk äkcu`n lfma 31.=92 sacukmns. Axprasdr su lamfmd ak crdmns, lkutns y sacukmns.

Ynùifùk

Yf mfvfmflns 31.=92 sacukmns aktra 2?, sa netfaka 4.513,522223 qas `n lfsln qua 4.513 lfkutns 42 sacukmns. Dhnrd, mfvfmflns 4.5lfkutns aktra 2? pdrd pdsdr`ns d crdmns y sa netfaka 5?.61¿ qua as

lfsln qua 5?¿ 13‖.

@uacn, 31.=92‖‖ aqufvdàk d 5?¿ 13‖ 42‖‖.

@d kntdifùk läs usdmd pdrd asta sfstald ma ukfmdmas, as:crdmns (¿), lfkutns (‖), sacukmns (‖‖).

4



Axprasdr idmd maifld` ak crdmns, lfkutns y sacukmns.

Nesarvdifùk

@d lamfmd ma uk äkcu`n mdmd ak crdmns, lfkutns y sacukmns

sa maea axprasdr ma td` ldkard qua `d úkfid inùlkd quapuama supardr d 2? as `d ma crdmns (`ds ukfmdmas läscrdkmas), pnrqua sf ak d inùlkd ma sacukmns n ma lfkutns,a` vd`nr as ldynr ma 2?, sa inkvfarta ak lfkutns n akcrdmns7 idmd 2? sacukmns as uk lfkutn y idmd 2? lfkutnsas uk crdmn.

`d idìu`dmnrd

d. 59¿ 26‖ 81“

e. =6¿ 34‖ 64“

i. 29¿ 88‖ 2?“

m. 41¿ 63‖ 4?4“

a. 91¿ 52‖ 38“

b. 19¿ 41‖ 62“

5



Ajalp`n

@d lamfmd 43¿ 25‖ 31‖‖ maea asirfefrsa: 43¿ 29‖ 41‖ 48¿ 9‖ 41‖‖

A` rasu`tdmn ma `d suld as 12¿ 2‖ 48‖‖

Ak mnkma a` ú`tfln rakc`ùk, as `d bnrld inrraitd ma asirfefr astd lamfmd ak crdmlfkutns y sacukmns.

@d lamfmd ma` äkcu`n D < 51º 93‖ =1‖‖ y `d lamfmd ma` äkcu`n E < 9?º 58‖ 99‖‖. Hd``dr `d suld ma `ds lamfmds ma `ns äkcu`ns

D y E.

Yn`uifùk

Ajarififns rasua`tns

51¿ 93‖ =1‖‖ 9?¿ 58‖ 99‖‖

11¿ 21‖ 38‖‖ 11¿ 22‖ 48‖‖ 12¿ 2‖ 48‖‖

+



Qkfmdm 4. Inkiaptns eäsfins Yasfùk

9

D` lamfr `d `nkcftum ma `d ifriukbarakifd y mfvfmfr`daktra a` vd`nr ma d nkcftum ma` mfälatrn ak uk iìriu`n,`ns crfacns akinktrdrnk qua pdrd mfbaraktas tdldônsma` iìriu`n, astd ra`difùk mded a` lfsln rasu`tdmn

qua sa inknia inln a` kúlarn Ϗ < 9.4=416521...7pnstarfnrlakta, sa akinktrù qua asta kúlarn tfakafkbfkftds ifbrds maifldàs y qua su axprasfùk maifldàs dparfùmfid. Astns kúlarns sa ``dldk kúlarns frrd-ifnkdàs pnrqua kn snk a` rasu`tdmn ma` inifakta mamns aktarns.

I <Ϗ

M

A` kúlarn Ϗ (pf)

_arn inln M < 5r , raalp`dzdlns M7 ak `d aiudifùk dktarfnr takalns: , mmnkma sa netfaka qua I < 5Ϗr , `n iud` sfckfbfid qua `d `nkcftum ma `d ifriukbarakiinktfaka 5Ϗ vaias `d `nkcftum ma` rdmfn.

5Ϗ < 2,58948194...

I < @nkcftum ma `d ifriukbarakifdϏ< Kularn pf 9.4=416521…M< Mfälatrn ma `d ifriukbarakifd




_rneàld 4

@d ifriukbarakifd iaktrd` ma ukd idkihd ma búten` tfakauk mfälatrn ma 2 latrns. ¾Iuäktn lfma `d `nkcftum ma `difriukbarakifd>

Ynùifùk

Inln a` rdmfn as `d lftdm ma` mfälatrn, r < 9 l, ùacnI < 5Ϗr . D` raalp`dzdr a` vd`nr ma r , takalns I < 5.Ϗ.9 <

48.8=611165, vd`nr qua pnmalns dprnxfldr d 48.81 l.

_rneàld 5

Qk trnzn ma d`dlera ma =.8 latrns ma `nkcftum sa mne`d pdrdbnrldr uk iìriu`n. Hd``dr `d `nkcftum ma` rdmfn.

Ynùifùk

Ydealns qua I < 5Ϗr , ùacn maealns maspajdr r, dsìr < I /5Ϗ.

=.8As maifr r < < ?,3296=9352 l

5.Ϗ

n sad qua `d `nkcftum ma` rdmfn as dprnxfldmdlakta 32 il.

Hdstd dquì, halns usdmn a` sfstald saxdcasfld` ma crdmns, lfkutns



Ntrd bnr-ld pdrdlamfr `ns

ä k c u ` n sas utf`fzdr a` rdmfäk, quaas `d lamfmd ma uk äkcu`niaktrd` iuyn drin pnsaa ukd`nkcftum fcud` d` rdmfn.

Astn sfckfbfid qua ak ukdifriukbarakifd ma rdmfn r ,

ideak 5Ϗ rdmfdkas n sad uk cfrn inlp`atn aqufvd`a d 5Ϗ rdmfdkas, astn maefmn qua `d `nkcftum ma` rdmfn astä 5Ϗ vaias ak `d `nkcftum ma `d ifriukbarakifd.

Inkvarsfùk ma crdmns d rdmfdkas y vfiavarsd

_nmalns axprasdr `d lamfmd ma uk äkcu`n ak rdmfdkas n ak crdmns, hdifakmn raspaitfvd inkvarsfùk. Radlns `ns sfcufaktas ajalp`ns:

Cräbfid 3

Äkcu`n ma uk rdmfäk

D E < r

92? 5Ϗ

48? Ϗ

6? Ϗ /5

=1 Ϗ /=

Crdmns (º) Udmfdkas

A` rdmfäkQkfmdm 4. Inkiaptns eäsfins Yasfùk

=



_nmalns hdiar `d inkvarsfùk ma iud`qufarlamfmd ak a` sfstald saxdcasfld` d rdmfdkas yvfiavarsd. Radlns:

Iudkmn mdlns `d lamfmd ma uk äkcu`n ak rdmfdkas, a` rasu`tdmn dpdraia pnrcakard`, ak bukifùk ma Ϗ inln ak a` idsn dktarfnr. Qsdkmn d idìu`dmnrd ifaktìbfpnmalns hd``dr asta rasu`tdmn ak bnrld maifld` ink ukd axiaàkta dprnxfldifùAk a` ajalp`n dktarfnr valns qua 31¿ aqufvdàk dprnxfldmdlakta d 4 9 rdmfdk

Ajalp`n 4

Yf uk äkcu`n lfma 31¿, hd``dr su lamfmd akrdmfdkas.

Ynùifùk

_nmalns rasn`var asta prneàld lamfdkta aùsn ma ukd rac`d ma tras sflpà mfraitd, dsì:

Ϗ rdmfdkas 48?¿

x 31¿

31Ϗ x < < 1Ϗ/45 4,9?6 48?

Uasn`vfakmn pdrd x takalns:



Ajalp`n 5

@d lamfmd ma uk äkcu`n as uk rdmfäk. Hd``dr su lamfmd ak

a` sfstald saxdcasfld`.

Ynùifùk

48?¿ Ϗ rdmfdkas

x 4

48?º Uasn`vfakmn pdrd x takalns x < < 13,56133614¿

Ϗ

asta rasu`tdmn `n inkvartflns d crdmns, lfkutns y sacuk-mns, y takalns x < 13¿ 43‖ ==,84‖‖. Astn sfckfbfid quauk äkcu`n qua lfmd uk rdmfäk, lfma uk pnin läs ma 13¿.

4. Mdmds `ds sfcufaktas lamfmds ma uk äkcu`n ak rdmfdkas, asirfefr ak idmd idsnsu aqufvdàkta ak crdmns, lfkutns y sacukmns:

Qsalns

`d idìu`dmnrd

c. 9Ϗ /5

h. 3Ϗ /=

f. 1Ϗ /=

j. 9Ϗ /8

g. 1Ϗ

` 9Ϗ/5

d. 9Ϗ /=

e. Ϗ /=

i. Ϗ /9

m. Ϗ /2

a. Ϗ /1

b 44Ϗ/=

4



5. Mdmds `ds sfcufaktas lamfmds ma uk äkcu`n ak crdmns, hd``dr su aqufvdàktardmfdkas y asirfefr `d raspuastd ak bnrld maifld`.

Ak uk vfdja ma Encntä d ]ukjd, `d ruamd ma ukd lntnifiàtd hfzn 4?6.?64 cfinlpàtns7 sf a` mfälatrn ma `d ruamd as 91.12 il.

d. ¾Iuä` as d mfstdkifd qua hdy akEncntä y ]ukjd>

e. @ns 4?6.?64 cfrns qua mfn d rua¾d iuäktns rdmfdkas y d iuäkcrdmns aqufvdàk>

`d idìu`dmnr

d. 8?¿ < =Ϗ /6 < 4,962529=?5 rdmfdkas

e. 551¿ <i. 941¿ <m. 491¿ <a. 45?¿ <b. -41?¿ <c. -=1¿ <

h. 5=?¿ <f. 86¿ < j. 451¿ <g. 35?¿ <`. -4==?¿ <

5



Qk äkcu`n astä ak pnsfifùk astäkmdr ak uk sfstald ma innrmakdmds idr-tasfdkds raitdkcu`dr, sf su værtfia as a` puktn ma nrfcak ma innrmakdmds ysu `dmn fkfifd` astä snera a` `dmn pnsftfvn ma` aja hnrfznktd` n aja x.

A` `dmn tarlfkd` ma uk äkcu`n ak pnsfifùkastäkmdr puama astdr ak iud`qufard ma `ns

iudmrdktas ma` sfstald ma innrmakdmds.

Yf a` dmn tarlfkd` ma uk äkcu`n ak pnsfifùkastäkmdr infkifma ink `d mfraiifùk ma `nsajas ma innrmakdmds, a` äkcu`n sa ``dld

iudmrdktd`.

Cräbfid 8



Ajalp`ns

@ns äkcu`ns ak pnsfifùk astäkmdr qua lfmak 6?¿, 48?¿, 53?¿, 92?¿, =1?¿, -6-53?¿, snk äkcu`ns iudmrdktd`as.

@ns äkcu`ns intarlfkd`as snk `ns qua astäk ak pnsfifùk astäkmdry tfakak a` lfsln `dmn tarlfkd`.

Ajalp`n

Yf takalns a` äkcu`n ma 9?¿ ak pnsfifùk astäkmdr y cfrdlns su `dmn tarlf92?¿ ak mfraiifùk pnsftfvd, vua`va d niupdr d pnsfifùk ak mnkma astded n squa ns äkcu`ns ma 9?º y a` äkcu`n ma 9?¿ + 92?¿ < 96?¿, tfakak a` lfsln dtarlfkd`, `n iud` sfckfbfid qua `ns äkcu`ns ma 9?¿ y 96?¿ ak pnsfifùk astäkm

Cräbfid



Yf r as a` rdmfn ma ukd ifriukbarakifd y t `d lamfmd ma ukäkcu`n iaktrd` ak rdmfdkas qua fktariaptd ak `d ifriukba-rakifd, uk drin ma `nkcftum s, aktnkias:

s < r.t

Cräbfid 4?

@nkcftum ma drin ma `d ifriukbarakifdQkfmdm 4. Inkiaptns eäsfins Yasfùk

1




_rneàld 4

Yf a` lfkutarn ma uk ra`nj lfma 2 iaktìlatrns ¾quæ mfstdkifdrainrrarä ak 48 lfkutns>

@d `nkcftum ma` drin ma ifriukbarakifd inlprakmfmn aktra`ns `dmns ma` äkcu`n iaktrd` as a` prnmuitn ma` rdmfn pnr `dlamfmd ma` äkcu`n ak rdmfdkas.

Ya maknlfkd saitnr ifriu`dr d `d pdrta fktarfnr ma` iìriu`nqua as `flftdmd pnr mns rdmfns y a` drin fktariaptdmn pnra``ns.

_rneàld 5

¾Iuä` as d mfstdkifd rainrrfmd pnr ukd pdrtìiu`d d n drcn ma

ukd ifriukbarakifd ma 9 l ma rdmfn, sf d pdrtìiu`d sa masp`dzduk äkcu`n ma 2 rdmfdkas>

Ynùifùk

Ya maknlfkd saitnr ifriu`dr d d pdrta fktarfnr ma` iìriu`n qua as flftdmdpnr mns rdmfns y a` drin fktariaptdmn pnr a``ns:

s < r δ aktnkias: 9 l 2 rdm

Cräbfid 44



Ma ns inkiaptns ma d canlatrìd aàlaktd`, sa sdea qua`d rdzùk ma` ärad ma` saitnr y a` ärad ma` iìriu`n (Ϗ.r 5),as fcud` d `d rdzùk ma `d `nkcftum ma` drin fktariaptdmny `d `nkcftum ma `d ifriukbarakifd (5Ϗ.r )7 d` trdksirfefrastns inkiaptns ak ukd aiudifùk, takalns:

55

D Y

r r p p< , sf maspajdlns D takalns: .

5

r Y D < ,

parn inln Y < r. t takalns qua D <

As maifr, a` ärad ma` saitnr sa netfaka aàvdkmn a` rdmfn dìudmrdmn, lu`tfp`fidkmn asta rasu`tdmn pnr `d lamfmd masu äkcu`n iaktrd` ak rdmfdkas y mfvfmfakmn asta rasu`tdmnaktra mns.

r 5.t

5

Ärad ma uk saitnr ifriu`drQkfmdm 4. Inkiaptns eäsfins Yasfùk

2



Qkd `älfkd ma inera ak bnrld ma saitnr

ifriu`dr tfaka 2 il ma rdmfn y su äkcu`niaktrd` lfma 4??¿, hd``dr:

d. @nkcftum ma` drin.

e. Ärad ma` saitnr ifriu`dr.

Yn`uifùk

d. Axprasdlns `d lamfmd ma` äkcu`n ak rdmfdkas

48?º Ϗ rdmfdkas

4??º x

@uacn

1

6 x

p<

Aktnkias, `d `nkcftum ma drin Y < r.δ, `uacn Y < (2 il).(1

6

p) < 4?,=3 il

e. raalp`dzdkmn takalns il

Ajalp`n

D <r 5.t

5

D < . (2 il)5. ( )4

5

1Ϗ

6



4. Udmfn 6 il, lamfmd ma` äkcu`n iaktrd` 45?¿

5. A` rdmfn lfma 8 il y a` äkcu`n iaktrd` =1¿

9. A` rdmfn lfma 42 il y a` äkcu`n iaktrd` 491¿

=. A` rdmfn lfma 45 il y a` äkcu`n iaktrd` 5Ϗ /9

1. A` rdmfn lfma 41 il y a` äkcu`n iaktrd` 5,14 rdmfdkas

2. Qk kaulätfin tfaka uk mfälatrn ma 92 pu`cdmds7 ¾iuäktds ravn`uifnkaabaitudrä `d ruamd iudkmn a` dutnlùvf` rainrrd ukd lf``d (1.58? pfas

Kntd: uk pfa aqufvd`a d 45 pu`cdmds.

3. A` lfkutarn ma uk ra`nj lfma = pu`cdmds. ¾Tuæ mfstdkifd rainrrarä saxtraln ak ukd hnrd y 5? lfkutns>

8. A` rdmfn ma ukd ifriukbarakifd lfma 4? il, hd``dr `d `nkcftum ma` driiuyn äkcu`n iaktrd` lfma uk crdmn.

6. ¾Iuäktns rdmfdkas tfaka uk äkcu`n ma uk crdmn>

4?. A` axtraln ma uk pækmu`n ma =? il ma `nkcftum rainrra uk drin ma il inkbnrla nsif`d, masirfefakmn uk äkcu`n D. Matarlfkdr `d lamfm

Ak ns ajarififns ma` 4 d` 1, akinktrdr d nkcftum ma` drin y a` ärad ma` saitnr ifriu`dinknifakmn a` rdmfn ma` iìriu`n y `d lamfmd ma` äkcu`n iaktrd`:

4



Uainrmalns qua a` tanrald ma_ftäcnrds sa rabfara d `ns trfäkcu`nsraitäkcu`ns qua snk dqua``ns quapnsaak uk äkcu`n raitn y mns äkcu-`ns dcumns7 `ns `dmns qua bnrldk a`äkcu`n raitn sa maknlfkdk idtatnsy a` `dmn ldynr sa ``dld hfpntakusd,as flpnrtdkta rainrmdr`n pnrqua kns

parlfta trdtdr ink ldynr inlnmfmdm,d`cukns talds ma `d trfcnknlatrìd.

Inln `d suld ma `ns äkcu`ns fk-tarfnras ma uk trfäkcu`n as fcud` d48?¿, ak a` trfäkcu`n raitäkcu`nhdy uk äkcu`n raitn qua lfma 6?¿y ns rastdktas 6?¿ sa rapdrtak aktra`ns ntrns mns äkcu`ns dcumns. Idmdäkcu`n dcumn tfaka inln `dmns `d

Cräbfid 45

Yacúk a` tanrald ma _ftäcnrds, `d hfpntakusd a`avdmd d` iudmrdmn as fcud`d `d suld ma `ns iudmrdmns ma `ns mns idtatns.

i5 < d5 + e5

]anrald ma _ftäcnrdsQkfmdm 4. Inkiaptns eäsfins Yasfùk

3

]anrald ma _ftäcnrds

Murdifùk: 4?:19 lfk.



Ajalp`n

Qk trfäkcu`n tfaka ukn ma sus værtfiasak a` puktn (?,?), a` ntrn ak a` puktn(9,?) y a` ntrn ak a` puktn (9,=). Mfeu-

jdr a` trfäkcu`n, hd` dr `d `nkcftum ma`ns idtatns y ma `d hfpntakusd. _drdidmd äkcu`n dcumn, matarlfkdr a`idtatn npuastn y a` idtatn dmydiakta.

Ak idmd idsn, mfeujdr a` trfäkcu`n, hd``dr `d `nkcftum ma sus idtatns y su hfpntakusy matarlfkdr a` idtatn npuastn y a` dmydiakta pdrd idmd äkcu`n dcumn.

4. @ns værtfias ma` trfäkcu`n astäk ak `ns puktns (?,?), (2,?) y (2,=)5. A` trfäkcu`n tfaka sus værtfias ak (?,?), (1,?) y (1,1)9. @ns værtfias ma` trfäkcu`n snk `ns puktns (?,?), (9,?) y (9,1)= @ns værtfias ma` trfäkcu`n snk `ns puktns (? ?) (2 5) y (2 ?)

i5 < d5 + e5, `uacn 5 5i d e< + , raalp`dzdkmn takalns 5 59 =i < +

ma mnkma i < 1.

Ink ra`difùk d` äkcu`n δ, a` idtatn npuastn lfma = y a` idtatn dmydiaktalfma 9.

Ink ra`difùk d` äkcu`n θ, su idtatn dmydiakta lfma = y su idtatn npuastnlfma 9.

Cräbfid 4=

4



_racuktds ma saàiifùk lú`tfpà ink úkfid raspuastd - (tfpn F)@ds pracuktds ma asta tfpn inkstdk ma uk akukifdmn y ma iudtrn pnsfef`fmdmasma raspuastd, aktra ds iudàs ustam maea asincar d qua inksfmara inrraitd.

4. Yf `d lamfmd ma uk äkcu`n as 558¿. @d npifùk qua lajnr sa djustdd su lamfmd ak lfkutns y sacukmns as.

d. 45.=1? lfkutns: 39?.=12 sacukmns

e. 49.28? lfkutns: 85?.8?? sacukmns i. 44.938 lfkutns: 21?.95= sacukmns m. 49.551 lfkutns: 84?.5?? sacukmns

5. D` inksfmardr uk äkcu`n iuyd lamfmd as =1.986 sacukmns. @d lamfd

asprasdmd ak crdmns, lfkutns y sacukmns as:

d. 45¿92½56“ e. 44¿5?½4?“ i. 4?¿41½45“ m. 6¿ 45½ 9=“

9. Axprasdr idmd maifld` ak crdmns, lfkutns y sacukmns.

d. 59¿, =9 e. ==¿, 68 i. 13¿, ?6

=. @d lamfmd ma` äkcu`n D < 15¿ 93‖ =?‖‖ y `d lamfmd ma` äkcu`nE < =?¿ 48‖ ?9‖‖. Hd``dr d suld ma ds lamfmds ma ns äkcu`ns D y E.



1. @d ifriukbarakifd ma ukd idkdstd ma edsquaten` tfakak uk mfälatrn

ma = latrns. @d `nkcftum ma `d ifriukbarakifd as:

d. 5 latrns

e. 2.58 latrns

i. 45,1229 latrns

m. 49,55=9 latrns

2. Qk trnzn ma iuarmd ma 48.= latrns ma nkcftum sa mne`d pdrd bnrldr

uk ifriu`n. @d `nkcftum ma` rdmfn as.

d. 9,69 latrns

e. 5,6581 latrns

i. 9.4=41 latrns

m. 3.59 latrns

3. D` inkvartfr =1¿ d rdmfdkas a` rasu`tdmn sa axprasd:

d. ?.3819 rdmfdkas e. ?.13?3 rdmfdkas

i. 4,64 rdmfdkas m. ?.8=19 rdmfdkas

8. Id`iu`dr ak rdmfdkas:

d. 6?¿ e. 9?¿ i. 44?¿

6. Inkvartfr d crdmns:

d. Ϗ /9 e. Ϗ /2 i. 9Ϗ /=

m. Ϗ /45 a. 5



A` prnmuitn idrtasfdkn ma mns inkjuktns D y E kn vdiìns,as a` inkjuktn ma tnmds `ds pdrajds nrmakdmds ( x,y), matd` ldkard qua a` prflar aàlaktn ma `d pdrajd as ukaàlaktn ma D y a` sacukmn aàlaktn ma `d pdrajd asuk aàlaktn ma E.

{( , ) | D E x y x D y E <

4. Yf

Aktnkias D x E < {(4 ,d), (4 ,e), (5 ,d), (5 ,e), (9 ,d), (9 ,e)}

5. D < {9, 1, 2} aktnkias

Ajalp`n

D < {4, 5, 9}

E < {d, e}

_rnmuitn idrtasfdknQkfmdm 5. Ua`difnkas y bukifnkas Yasfùk

4



4. {(9,9),(9,1),(9,2)

4 U <

5. {(9,9),(9,1),(9,2),(1,9),(1,2)5 U <

9. {(9,9),(1,1),(2,2),(2,9)

9 U <

Ajalp`n

Ink raspaitn ma` idsn dktarfnr, `ds sfcufaktas snk ra`difnkas ma D ak E:

Nesarvdifùk

@ns a`alaktns ma ukd ra`difùksnk pdrajds nrmakdmds.

Qk sueinkjuktn ma` prnmuitn idrtasfdkn D x E sa ``dld ukdra`difùk ma` inkjuktn D ak a` inkjuktn E.

Ua`difùkQkfmdm 5. Ua`difnkas y bukifnkas Yasfùk

5



Ma d mabfkfifùk ma bukifùk, valns qua ak a``d kn puama hdear mns pdrajds qua tacdk fcud` a` prflar aàlaktn ma `d pdrajd, `n iud` dsacurd qua a` sacukmn aàlakma `d pdrajd as úkfin pdrd uk vd`nr aspaiìbfin ma` prflar aàlaktn.

Mnlfkfn ma b < {4, 5, 9, =, 1}U m b { e }

Qkd ra`difùk ma` inkjuktn D ak a` inkjuktn E, qua d idmd aàlaktn ma D àdsfckd uk úkfin aàlaktn ak E, sa ``dld ukd bukifùk ma` inkjuktn D ak aìnkjuktn E.

: b D E®

Inkiaptn ma bukifùk

BukifùkQkfmdm 5. Ua`difnkas y bukifnkas Yasfùk

9

Dprakmfakmn ink a` prnba Ju`fnAiudifùk iudmrätfid ak uk prneàld ma canlatrìdMurdifùk: 4?:46 lfk.



Ak ldtalätfids, as luy usud` mdr bukifnkas, utf`fzdkmn bùrlu`ds.

Rfsfta astd päcfkd y akiuaktra d`cukds dp`fidifnkas ma `ds bukifnkas d `dvfmd intfmfdkd

http://www.knvdsur.i`/knvdsur/dmlfkfstrdtnr/up5/up`ndms/[email protected]

Bukifnkas `fkadàs, pn`fkùlfids y rdifnkdàs

@ns prflarns aàlaktns ma `ds pdrajds ma ukd bukifùk bnrldk a` inkjuktn mnlfkfn ma `d bukifùk7 y a` inkjuktn bnrldmn pnr `ns sacukmns aàlaktns ma `pdrajds sa maknlfkd a` rdkcn ma `d bukifùk. Ak `d cräbfid valns qua a` mnlfkma `d bukifùk as:

Mnlfkfn ma b < {4, 5, 9, =,1} Udkcn ma b < {d, e, i}

Aàlaktns ma ukd bukifùk

Bukifùk `fkad`

Ak asta idsn d bukifùk tnld iud`qufarvd`nr x, suläkmnà 5. D inktfkud-ifùk asirfeflns d`cukds pdrajds ma `d

bukifùk.

b < {(?,5), (4,9), (5,=), (9,1), (=,2)...}

D` raprasaktdr ns puktns y ukfr`ns aka` p`dkn idrtasfdkn, netakalns ukd`ìkad raitd7 b ( x) as ukd bukifùk fkad`.

4. Bukifùk `fkad`

b ( x ) < x + 5



Cräbfid 43

5. Bukifùk inkstdkta

c ( x ) < 9

D` raprasaktdr ak a` p`dkn idrtasfdkn `ns puktns ma c y ukfr`ns lamfdkta uk trdnetakalns ukd `ìkad raitd pdrdà`d d` aja x7 kn nestdkta, pnmalns fkmfidr qua c

as ukd bukifùk inkstdkta.

c < {(-5,9), (-4,9),(?,9), (4,9), (5,9),(9,9)...}

D` raprasaktdr ak a` p`dknidrtasfdkn ns puktns ma yukfr`ns lamfdkta uk trdzn,netakalns ukd ìkad raitdpdrdà`d d` aja x, c ( x), asukd bukifùk inkstdkta. Aìnkjuktn rdkcn ma tfakasn`dlakta a` aàlaktn 9.

Bukifùk inkstdkta



D` raprasaktdr ns puktns y ukfr`ns lamfdkta uk trdzn ak a` p`dkn idrtasfdkn,sa netfaka ukd raitd qua pdsd pnr a` nrfcak ma ds innrmakdmds y mfvfma d nsiudmrdktas F y FFF ak pdrtas fcudàs. Astd bukifùk sa ``dld `d bukifùk fmæktfid.Yu rdkcn y su mnlfkfn snk a` lfsln inkjuktn.

_drd raprasaktdr bukifnkas ink sìlen`ns ldtalätfins, pnr `n cakardùsdlns àtrds, sdefakmn a` sfckfbfidmn ma `n qua a``ds raprasaktdk. Yf ta-kalns b ( x) < x5 sfckfbfid qua d bukifùk b tnld iud`qufar vd`nr y `n aàvd a`

iudmrdmn dsì, b (2) < 25

< 92.

9. Bukifùk fmæktfid

H(x) < x

Ak asta idsn, `d bukifùk tnld uk vd`nr x y `n majd fcud`. D`cukds pdrajds ma H, sfkmfidk d inktfkudifùk.

H < {(-5,-5), (-4,-4), (?,?), (4/9,4/9), (9/8,9/8)...}

b as ukn d ukn



Ajalp`ns

=. Bukifnkas pn`fkùlfids

Ynk sulds ma tærlfkns n lnknlfns. @ns inabfifaktas ma d vdrfde`a astäk raprasa

tdmns ak idmd tærlfkn ink d atrd d ink sueìkmfias. @ns axpnkaktas ma d vdrfde`asnk kúlarns aktarns pnsftfvns. A` crdmn ma d bukifùk as a` axpnkakta ma ldynr vdqua bfcura ak a` pn`fknlfn. @ds bukifnkas pn`fkùlfids axfstak pdrd tnmn vd`nr ma

Qkd bukifùk pn`fkùlfid as ma `d bnrld:

4. = 9 5( ) 1 9 8 3 2 b x x x x x< + +

Asta as ukd bukifùk pn`fkùlfid ma crdmn iudtrn. @ns inabfifaktas masus tærlfkns snk `ns kúlarns 1, -9, 8, 37 -2 sa ``dld a` tærlfkn fkma-pakmfakta n tærlfkn inkstdkta.

5. 9 5( ) ?.6 5 6 p x x x x< +

Astd bukifùk as ma crdmn tras. @ns inabfifaktas ma ns tærlfkns snk ?.6,

-5, 6. Ak asta ajalp`n, a` tærlfkn fkmapakmfakta tfaka a` vd`nr iarn.

9. ( ) 9 3h x x< +

Astd as ukd bukifùk pn`fkùlfid ma crdmn ukn qua tdlefæk d `dldlnsbukifùk `fkad`. ]faka uk tærlfkn ak x ink inabfifakta 9, y su tærlfknfkmapakmfakta as 3. D` crdbfidr astd bukifùk ak a` p`dkn idrtasfdkn,kns md ukd `ìkad raitd.



1. Bukifnkas rdifnkd`as

Ynk `ds bukifnkas qua rasu`tdk ma` inifakta ma mns bukifnkas pn`fkùlfids.

Mnkma _( x) y T( x) snk pn`fknlfns.

Qkd bukifùk rdifnkd` axfsta n astä mabfkfmd, sfalpra qua sumaknlfkdmnr sad mfbarakta ma iarn, ma td` ldkard qua ma` mn-lfkfn ma ukd bukifùk rdifnkd` maealns masidrtdr tnmns dqua``nsvd`nras qua hdcdk iarn d su maknlfkdmnr.

Ajalp`n

Ajalp`n

4. 5

9( )

3

x b x

x x

+<

+5.

5

5( )

4

xc x

x<

+

@d bukifùk rdifnkd`9

( )5

c x x

<+

kn astä mabfkfmd pdrd x < -5, pnrqua d`

raalp`dzdr asta vd`nr ak `d bukifùk, takalns

9 9( 5)

5 5 ?c < <

+

b ( x) <_ ( x)

T ( x)



5. Bukifùk snera

Qkd bukifùk as snera, sf tnmn aàlaktn ma` rdkcn as fldcak ma d`cúk aàlak

_drd idmd ukd ma ds sfcufaktas bukifnkas rdifnkdàs, hdiar su raprasaktdifùk cräbak a` p`dkn idrtasfdkn a fmaktfbfidr a` mnlfkfn y a` rdkcn ma `d bukifùk.

@ds bukifnkas puamak i`dsfbfidrsa ma luihds ldkards, parn mastdidralns ds sfcufakt

Qkd bukifùk b ( x) as ukn d ukn, sf pdrd mns aàlaktns mfstfktns ak su mnlfkdsfckd vd`nras mfbaraktas ak a` rdkcn ma `d bukifùk, as maifr, sf

4 5 x x , aktnki b ( x

4) ≯ b ( x

5).

I`dsas ma bukifnkas

4. Bukifùk ukn d ukn

4.

5.

9.

=.

1.

44



Cräbfid 46

c as snera

9. Bukifùk efyaitfvd

Qkd bukifùk c ma uk inkjuktn D ak uk inkjuktn E as efyaitfvd iudkmn as uknsnera d `d vaz.

=. Bukifùk pdr a flpdr

d. Bukifùk pdr

Qkd bukifùk b as pdr, sf pdrd tnmn x, ak a` mnlfkfn ma `d bukifùk sa tfaka qu

b (-x) < b ( x)

Ajalp`n

@d bukifùk b ( x) < x5 as ukd bukifùk pdr.



Cräbfid 5?Bukifùk pdr

Cräbfid 5

e. Bukifùk flpdr

Qkd bukifùk c as flpdr sf pdrd idmd x ak a` mnlfkfn ma `d bukifùk sa tfaka q

c (-x) < -c ( x).

@d cräbfid ma ukd buk-ifùk flpdr as sflæ-trfid ink raspaitn d`puktn ma nrfcak (?,?).

Ajalp`n b ( x) < x9

as ukd bukifùkflpdr.



1. Bukifùk parfùmfid

Qkd bukifùk b as parfùmfid, sf axfsta uk kúlarn rad` pnsftfvn p, td` qua pdrd iudqufar x ma` mnlfkfn ma b , sa tfaka qua x + p partakaia tdlefæk d` mnlfkfn m b y b (x + p) < b (x).

A` vd`nr p läs paquaôn sa maknlfkd a` parìnmn ma `d bukifùk. _nstarfnrlakta, atumfdralns ak matd``a d`cukds bukifnkas parfùmfids.

Ajalp`ns

4. Mdmd b ( x) < 9 x -4 inkstrufr `d cräbfid, fmaktfbfidr su mnlfkfn, su rdkcn y matarlfkdr sf as bukifùk.

Hd``dr d`cukns puktns ma `d cräbfid, inkstruyakmn ukd tde`d ma vd`nras.

x -4 -5 -9 ? 4 5 9

b

( x

) -= -3 -4? -4 5 1 8



@d cräbfid as ukd raitd ak a` p`dkn idrtasfdkn. Yu mnlfkfn snk tnmns `ns klarns radàs y su rdkcn tdlefæk snk tnmns `ns kúlarns radàs. Astd cräbinrraspnkma d ukd bukifùk pnrqua pdrd mns aàlaktns mfbaraktas ma mnlfkfn, `d bukifùk dsfckd vd`nras mfbaraktas d su rdkcn.

Yf d` trdzdr iud`qufar raitd parpakmfiu`dr d` aja x, æstd inrtd ukd cräbfid uk úkfin puktn, `d cräbfid inrraspnkma d ukd bukifùk, qua as ukd bnrlfktuftfvd y bäif` ma matarlfkdr, sf ukd cräbfid mdmd as `d raprasaktdifùk ukd bukifùk.

x ? 4 5 9 = 6

b ( x) ? 4 4.=4 4.39 5 9

5. Yf ( ) b x x< , hdiar `d cräbfid ma b ( x), hd``dr su mnlfkfn, su rdkcn y as

eàiar sf as bukifùk.

Inkstruydlns `d cräbfid, hdifakmn ukd tde`d ma vd`nras.

Ak `d cräbfid, pnmlns nesarvdr quainrraspnkma d ubukifùk. Yu mnlkfn snk ns kúla

radàs kn kacdtfvas maifr, a` fktarv`n (?, + ∛), puaqua d rdìz iudmrdmaea inrraspnkmd uk kúlarn kn kcdtfvn, a` rdkcn mabukifùk tdlefækCräbfid 59



@d cräid ma d bukifùk kn inrtd d d raitd x < -9, dukqua sa diaridd a``d tdktn pnr `d fzqufarmd inln pnr `d maraihd. Maiflns qua `draitd x < -9 as ukd dsìktntd vartfid` ma `d cräid ma `d bukifùk.

9. Yf5

( )9

b x x

<+ , matarlfkdr sf inrraspnkma d ukd bukifùk, akinktrdr s

mnlfkfn y a` rdkcn.

@d cräbfid inrraspnkma d ukd bukifùk, su mnlfkfn snk `ns kúlarns radàs axiaptn a` aàlaktn -9 pnrqua b (-9) kn axfsta. A` rdkcn ma `d bukifùk snk tnmn`ns kúlarns radàs, axiaptn a` vd`nr ? puastn qua `d cräbfid kn inrtd a` aja

Nesarvdifùk

x -1 -= -5 -4 ? 4 5 9 b ( x) -4 -5 5 4 ?.22 ?.1 ?.= ?.9

Cräbfid 5=



=. @d bukifùk?

( )?

W x sf x b x x

x sf x< <

0

Fmaktfbfidr a` mnlfkfn, a` rdkcn y matarlfkdr sf `d cräbfid inrraspnkma d u

bukifùk.

Ynùifùk

Ralns qua pdrd ? ù vd`nras pnsftfvns, `d bukifùk dsfckd a` lfsln vdlfaktrds qua pdrd vd`nras kacdtfvns ma su mnlfkfn, as dsfckd a` vd`nr npuas

D`cukds pdrajds ma puktns `ds mdlns ak `d sfcufakta tde`d.

@d cräbfid inrraspnkma d ukd bukifùk. Yu mnlfkfn snk tnmns `ns kúlaradàs y su rdkcn snk `ns kúlarns radàs kn kacdtfvns as maifr a` fktarvd

x -1 -= -5 -4 ? 4 5 9

x 1 = 5 4 ? 4 5 9

Cräbfid 51

b ( x) < | x|



Ak idmd ukn ma `ns ajarififns sfcufaktas, trdzdr `d cräbfid, matarlfkdr

sf as bukifùk y maifr, sf as ukn d ukn7 fmaktfbfidr a` mnlfkfn y a` rdkcn.4. @d bukifùk b(x)< 1 d qua crdbfid inrraspnkma

5. b ( x) < -9 x + 4



9. @d crdbfid qua inrraspnkma d `d bukifùk b(x)< 5x5 - 4

=.

1.

2.

3.

8.

6.

4?.

b ( x) < x9 + 4



Ak uk trfäkcu`n raitäkcu`n, sdealns qua hdy mnsäkcu`ns fktarkns dcumns δ y θ. Yf ``dldlns i d `d

hfpntakusd, y d, e d `ns idtatns, pnmalns astde`aiar `dssfcufaktas ra`difnkas:

d idtatn npuastnsakn

i hfpntakusdd < <

e idtatn dmydiaktainsakni hfpntakusd

d < <

tdk d idtatn npuastn

caktae idtatn dmydiakta

d < <

_nmalns astde`aiar ra`difnkas raiìprnids inrraspnkmfaktas d idmd ukd ma `ds ra`

Cräbfid 52

Bukifnkas trfcnknlætrfidsQkfmdm 9. ]rfcnknlatrìd ak uk trfäkcu`n raitäkcu`n

Yasfùk

4



Dsì lfsln, pnmalns mabfkfr astds safs ra`difnkas pdrd a` ntrn äkcu`n dcumn θ trfäkcu`n raitäkcu`n:

]akfakmn ak iuaktd qua pdrd asta äkcu`n θ, a` idtatn npuastn as d y a` idtatn dm

iakta as e, lfaktrds qua `d hfpntakusd i kn subra d`cukd vdrfdifùk.

Inln pnmalns var, idmd ukd ma astds vdrfdifnkas kn as läs qua a` inifakta ma`nkcftumas ma uk saclaktn.

Dsì, pdrd hd``dr sakn δ, mfvfmflns `d `nkcftum ma` idtatn npuastn aktra `d `nkcftum`d hfpntakusd7 y pdrd hd``dr tdkcakta ma δ, mfvfmflns `d `nkcftum ma` idtatn npuaaktra `d `nkcftum ma` idtatn dmydiakta y sa prniama ma ldkard sflf`dr pdrd `ds

läs ra`difnkas.

]dkcakta θ < tdk θ

Insaidkta θ < insi θ

Yaidkta θ < sai θIntdkcakta θ < intdk θ

Dmaläs, ma `ds ra`difnkas dktarfnras pnmalns astde`aiar qua:

insi θ < 4/ sak θ n sak θ < 4/insi θ

sai θ <4/ins θ n ins θ < 4 /sai θ

intdk θ < 4/tdk θ n tdk θ < 4/intdk θ

Astds fcud`mdmas snk vä`fmds, sfalpra y iudkmn `ns maknlfkdmnras takcdk vd`n

K θ < tdkθ7 insaidkta θ < insi θ7 saidkta θ <sai θ7 intdkcakta θ < intdk θ



4. Ak ukd hnjd ak e`dkin, mfeujdr uk trfäkcu`n raitäkcu`n, lamfr `d `nkcftum midmd ukn ma sus `dmns y pdrd idmd äkcu`n dcumn (äkcu`ns laknras ma 6?¿hd``dr `ns vd`nras ma sak, ins, tdk, intdk, sai y insi.

5. Mdmn a` sfcufakta trfäkcu`n raitäkcu`n, hd``dr `ns vd`nras ma sak δ, ins δ, tdδ, sai δ, insi δ, intdk δ, sak θ, ins θ, tdk θ, sai θ, insi θ, intdk θ.

Uasn`var uk trfäkcu`n, inksfsta ak hd``dr ds nkcftumas ma sustras `dmns y `ds lamfmds ma sus tras äkcu`ns fktarfnras.

Cräbfid 53

_rne`alds dp`fidmns ak `d

rasn`uifùk ma trfäkcu`ns raitäkcu`ns

Qkfmdm 9. ]rfcnknlatrìd ak uk trfäkcu`n raitäkcu`n Yasfùk

5

4



Cräbfid 56

5. Uasn`var a` trfäkcu`n raitäkcu-`n pdrd a` iud`d < 95,=2

e < 51,38y a` äkcu`n dcumn θ < 98.=2¿.

Ynùifùk

Yacúk `ns mdtns akukifdmns ak a` prneàld, inknialns `ns vd`nras ma mns idtatns, ma` äkcu`n dcumn θ y masma ùacn, a` äkcu`n raitn. _drd hd``däkcu`n dcumn θ, à rastdlns a` vd`nr ma θ d 6?¿ y netakalns:

Cräbfid 58

Ajalp`ns

4. Ak `d cräbfid, a` trfäkcu`n rai-

täkcu`n astä rasua`tn, pnrquasa inkniak `ds lamfmds ma sustras dmns y ma sus tras äkcu`ns.



_drd hd``dr a` vd`nr ma `d hfpntakusd i, hdialns:

d / i < sak δ, ma mnkma i < d /sak δ.

Uaalp`dzdkmn `ns vd`nras takalns:

i < 95.=2/sak 14.1= < =4.=1

Halns hd``dmn `ns safs vd`nras inrraspnkmfaktas d `ds `nkcftumas ma sus tra`dmns y d `ds lamfmds ma sus tras äkcu`ns, `uacn takalns rasua`tn a` trfäkcuraitäkcu`n.

Mabfkfifùk

A` saclaktn ma raitd masma uk puktn ma nesarvdifùk N d uk puktnnesarvdmn _, sa ``dld `d vfsud` ma _. A` äkcu`n ink værtfia ak a` puktn manesarvdifùk N, iuyns `dmns snk `d vfsud` y ukd salfrraitd hnrfznktd`, sa``dld äkcu`n ma a`avdifùk ma _, iudkmn _ sa akiuaktrd pnr drrfed ma N7

y sa ``dld äkcu`n ma maprasfùk iudkmn _ sa akiuaktrd pnr maedjn ma N.



Cräbfid 94

Ma `d cräbfid, valns qua:

4,6? / x < tdk =5¿

ma mnkma sa netfaka

x < 4.6? / tdk =5¿ < 5,44 l

@uacn `d snlerd prnyaitdmd pnr a` hnlera tfaka ukd `nkcftum

Ajalp`n

Yf d matarlfkdmd hnrd ma` mìd, a` äkcu`n

ma a`avdifùk ma` Yn` as ma =5¿, ¾iuä` as `d

`nkcftum ma `d snlerd qua prnyaitd ak a`

sua`n, uk hnlera ma 4,6? l>

Yn`uifùk



Cräbfid 9

4. Ak idmd cräbfid akinktrdr a` vd`nr ma x.

5. Iudkmn a` äkcu`n ma aàvdifùk d` puktn läs d`tn ma d tnrra Afbba` ak _drìs, ama 58.=¿, `d snlerd prnyaitdmd as ma 4.855 pfas ma drcn. ¾Iuä` as `d d`tur

ma `d tnrra>

9. Qkd asidàrd ma 5? pfas ma drcn sa dpnyd ak ukd pdram, bnrldkmn uk äkcu`ma 32¿ ink a` sua`n. ¾D quæ d`turd astä a` axtraln suparfnr ma `d asidàrd

=. Masma d pdrta suparfnr ma uk amfbfifn ma 2? pfas ma d`turd, a` äkcu`n ma aàvdifùk d uk pnsta as ma 4=¿. Ak `d edsa ma` amfbfifn, a` äkcu`n ma aàvdifùd `d puktd ma` pnsta as ma 58¿ akinktrdr `d d`turd ma` pnsta y `d d`turd ma

d.

m.

i.e.

a. b.

5



Dprakmfakmn ink a` prnba Ju`fnAiudifùk iudmrätfid ak uk prne`ald ma canlatrìdMurdifùk: 3:91 lfk.

dsak

i

d <

ins e

id <

tdk d

ed <

e

Ma` trfäkcu`n raitäkcu`n ma`d cräbfid 95, takalns qua:

Cräbfid 99

Qkfmdm 9. ]rfcnknlatrìd ak uk trfäkcu`n raitäkcu`n Yasfùk

9D`cukds fmaktfmdmas eäsfids



Yf hdialns `ns inifaktas:

tdkins

dsak di

e ei

d

dd < < < y

ins

intdk

eei

dsak di

d

dd < < <

@uacn valns qua:ins

tdk intins

sak y dk

sak

d dd d

d d< <

Ma mnkma valns qua tnmds `ds rdznkas trfcnknlætrfids sa puamak mdr ak tærlfknma sakn y insakn.

Ajalp`n

Yf sak δ < ?,1 y ins δ < ?,822 pnmalns hd``dr tdk δ dsì:

?,1tdk ?,133

?,822d < <

?,8222intdk 4,395

?,1

d < <

Dmaläs,

4sai 4,41=

?.822d < <

4insai 5

?.1d < <



`d idìu`dmnr

Qsn ma `d idìu`dmnrd

Qsdkmn ukd idìu`dmnrd ifaktìbfid, sa puama hd``dr akbnrld räpfmd y praifsd, `ns vd`nras ma sakn, insakn,tdkcakta, intdkcakta, saidkta y insaidkta ma äkcu`nsdcumns y ak cakard` ma iud`qufar äkcu`n. As kaiasdrfn

ajariftdrsa ak a` ldkajn ma d idìu`dmnrd puastn qua asukd harrdlfaktd vd`fnsd ak a` astumfn ma d trfcnknlatrìd.

D` lnlaktn ma utf`fzdr `d idìu`dmnrd ifaktìbfid, as buk-mdlaktd` àar luy efak `ds fkstruiifnkas ma `d lfsld,yd qua mapakmfakmn ma` lnma`n, murdkta `d ajaiuifùkma d`cukds bukifnkas puamak vdrfdr `ns rasu`tdmns.

Inlpàtdr `d sfcufakta tde`d:

4?

41

5?,8

9?

=1

2?

31,2

38

D (¿) Yak δ Ins δ ]dk δ Intdk δ Yai δ Insi δ

4



4. Masma `d pdrta suparfnr ma ukdidktf`dmn ma 452 l ma d`turd,a` äkcu`n ma maprasfùk ma ukedrin as 5?.53¿ `d mfstdkifd d`d iud` sa akiuaktrd a` edrin ma`d edsa ma` didktf`dmn as:

d. ==1,238 l e. 459,832 l i. 991,543 l m. 952,682 l Cräb

5. Ink dyumd ma `d idìu`dmnrd, inlpàtdr `d sfcufakta tde`d:

9. A` äkcu`n ma aàvdifùk ma `d dzntad ma uk amfbfifn, lamfmn masma ukpuktn D sftudmn d 4??l ma `d edsa, as ma 2?¿, `d d`turd ma` amfbfin as:

d. 439,5?1 l e. 434,=12 l i. 435,234 l m. 43?,5=1 l


5?8¿451¿1¿=8¿93¿416¿9?1¿438¿

86¿



Vd vflns qua ukd ifriukbarakifd i ma rdmfn r tfaka ukd`nkcftum ma 5Ϗr .

Qk cfrn inlpàtn ma` puktn axtraln ma uk rdmfn snera

`d ifriukbarakifd, masirfea uk äkcu`n ma 5Ϗr rdmfdkas.

Yf inksfmardlns inln ukfmdm ma nkcftum, d nkcftum ma` rdmfn, as maifr,r < 4, trdedjdralns ink ukd ifriukbarakifd ma rdmfn 4, qua ``dldralnsifriukbarakifd ukftdrfd. Ak a``d, uk cfrn inlpàtn ma su rdmfn ak mfraiifùkpnsftfvd, edrra uk äkcu`n ma 5Ϗ rdmfdkas7 lamfn cfrn edrra uk äkcu`n maϏ rdmfdkas7 uk iudrtn ma cfrn edrra uk äkcu`n ma Ϗ /5 rdmfdkas.

Yf hdialns a` cfrn ma` rdmfn ak saktfmn kacdtfvn, lamfd vua`td inrraspnk-ma d uk äkcu`n ma ’ Ϗ rdmfdkas, 9/= ma cfrn aqufvdà d - 9Ϗ / 5 rdmfdkas.

D` inksfmardr uk äkcu`n iaktrd` ak su pnsfifùk astäkmdr ak ukd ifriuk-barakifd ma rdmfn 4, `d `nkcftum ma su drin s < r.t , mnkma t as `d lamfmdma` äkcu`n iaktrd` ak rdmfdkas, parn inln r < 4 sa tfaka qua s < t , matd` ldkard qua `d `nkcftum ma` drin suetakmfmn pnr a` äkcu`n, as fcud`

d `d lamfmd ma` äkcu`n iaktrd` ak rdmfdkas.

Inln `d lamfmd ma` äkcu`n as uk vd`nr kulærfin (iud`qufar kúlarnrad`), aktnkias `d `nkcftum ma` drin t pdrd uk äkcu`n iaktrd` ak ukd ifr-iukbarakifd ukftdrfd, sa inksfmard masma a` puktn fkfifd` (4,?) hdstd a`puktn _ ma innrmakdmds (x, y), mnkma a` `dmn bfkd` ma` äkcu`n inrtd `difriukbarakifd ukftdrfd y astd `nkcftum as iud`qufar kúlarn rad` t .

Bukifnkas sakn y insakn

Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns

radàsYasfùk

4



@ds innrmakdmds idrtasfdkds ma` puktn bfkd` ma` drin snera d ifriukbarakifd ukftdrsnk bukifnkas ma` drin ma `nkcftum t . D astds bukifnkas `ds ``dldlns insakn y sak

mat

, dsì: x < ins t

y < sak t

As maifr, qua `ds innrmakdmds ma` puktn bfkd` _ astäk mdmds pnr:

_ < (x, y) < (ins t, sak t).

Inln iud`qufar puktn _ ma innrmakdmds (x, y) snera `d ifriukbarakifd ukftdrsdtfsbdia `d aiudifùk:

5 54 x y+ <

Uaalp`dzdkmn x pnr ins t, y pnr sak t, takalns:

5 5

Cräbfid 91



Tua inrraspnkma d ukd fmaktfmdm trfcnknlætrfid bukmdlaktd` y qua usud`lak`d asirfeflns dsì:

_rflard fmaktfmdm bukmdlaktd` 5 5ins 4sak t t + <

Inln t as iud`qufar kúlarn rad`, a` mnlfkfn ma `d bukifùk sakn y ma `d bukifinsakn as a` inkjuktn ma `ns kúlarns radàs. Nesarvdlns tdlefæk qua `ns vd`nma x y ma y vdrìdk aktra -4 y 4, `n iud` sfckfbfid qua a` rdkcn ma `d bukifùk saknma `d bukifùk insakn as a` fktarvd`nW4,4 .

Inln ins t y sak t snk ds innrmakdmds ma` puktn _ snera d ifriukbarakifd ukftdr

`ds bukifnkas sakn y insakn sa ``dldk bukifnkas ifriu`dras. ]dlefæk sa às ``dlbukifnkas trfcnknlætrfids mabfkfmds snera `ns kúlarns radàs.

_drd vd`nras ma t , ldynras ma 5Ϗ, pnmalns mabfkfr `ds bukifnkas trfcnknlætrfiak d lfsld bnrld, usdkmn d ifriukbarakifd ukftdrfd, puastn qua sf t as uk äkcuiaktrd` ak pnsfifùk racu`dr iuyn dmn tarlfkd` inrtd `d ifriukbarakifd ukftdrfd akpuktn _(x, y), y d nkcftum t ma su drin as laknr ma 5Ϗ, aktnkias a` dmn tarlfkd` asta äkcu`n infkifma ink iud`qufar dmn tarlfkd` ma uk äkcu`n iaktrd` ak pnsfif

racu`dr, iuyd lamf-md sad t + 5g Ϗ, mnk-ma g as uk kúlarnaktarn.

Astn sfckfbfid quasf tnldlns inln`dmn fkfifd`, a` `dmn

bfkd` ma` äkcu`n t y à dmfifnkdlnsuk cfrn, mns cfrns,tras cfrns, a` `dmnbfkd` ma asns äkcu`nsinfkifma ink a` dmnbfkd` ma` äkcu`n t .

t t + 5Ϗ

t ’ 5Ϗ

]fakak a` lfsln`dmn bfkd`

Cräbfid 92



Ma fcud` ldkard, `ds innrmakdmds ( x, y) ma` puktn bfkd` t snk `ds lfslds, ma mnkmtakalns qua:

sak t < sak (t+5g Ϗ)

ins t < ins (t + 5g Ϗ)

@n dktarfnr fkmfid qua `ds bukifnkas sakn y insakn snk parfùmfids, sfakmn:

Ϗ < 5Ϗ qua as su parìnmn.

Ajalp`ns

Qsdkmn `d id`iu`dmnrd, pnmalns inlprnedr a f`ustrdr ink d`cukns ajalp`n`d parfnmfifmdm ma astds bukifnkas.

4. sak (5) < sak (5 + 5Ϗ) < ?,6?6563=52

5. ins (5) < ins (5 + 5Ϗ) < -?,=424=2892

9. sak (5) < sak(5 - 5Ϗ) < ?,6?6563=52

=. ins (5) < ins (5 - 5Ϗ) < -?,=424=2892

1. sak (5,8) < sak(5,8 + 5Ϗ) < ?,99=68841

2. ins (5,8) < ins (5,8 - 5Ϗ) < -?,6=55559=

Ajalp`n:

Hd``dr a` vd`nr ma `ds bukifnkas trfcnknlætrfids pdrd a` äkcu`n ma Ϗ /=, sfk us



Ynùifùk

D` in`nidr a` äkcu`n ak su pnsfifùk racu`dr, a` `dmn bfkd` fktariaptd `d ifriuk

rakifd ukftdrfd ak a` puktn _ ma innrmakdmds x, y. Dmaläs, inln a` `dmn bfma asta äkcu`n mfvfma a` prflar iudmrdkta ak mns pdrtas fcudàs, takalns q x < y. Yf dp`fidlns a` tanrald ma _ftäcnrds pdrd a` trfäkcu`n raitäkcu`n ITvar cräbfid, takalns qua:

5 54 x y+ < . Inln x as fcud` d y takalns 5 5

4 x x+ < .

5

5 4 x < , ma mnkma

5 4

5

x <

ùacn rasn`vfakmn pdrd x

takalns

5

5

x <

, haltnldmn sn`dlakta a` vd`nr pnsftfvn ak d snùifùk, maefmn d qua x ak a` prfl

iudmrdkta as pnsftfvn. Inln x < y, aktnkias y < 5

5, ma td` ldkard qua:

Ins Ϗ /= <

Yak Ϗ /= <

Cräbfid 93



Ak bnrld sflf`dr, pnmalns hd``dr`ns vd`nras ma `ds bukifnkas trfcn-knlætrfids pdrd a` äkcu`n ma Ϗ /9< 2?¿, dsì:

9sak

p<

4sfk

2 5

p<

9ins

2 5

p<

45

95

4 9tdk

2 99

p< < <

9int 9

2 4dk

p< <

5 5 9sai 2 9 9

p

< <

5insi 5

2 4

p< <

Hd``dr `ns vd`nras ma tdkcakta, intdkcakta, saidkta y insaidkta pdrd a` äkcuma Ϗ /=.

Ajalp`n

Hd``dr `ns vd`nras ma `ds bukifnkas trfcnknlætrfids ma `ns äkcu`ns Ϗ / 9 < 2?

Ϗ / 2 < 9?¿.

Yn`uifùk

Inkstruflns uk trfäkcu`n aquf`ätarnN_T ma `dmn 57 pnr supuastn,

idmd ukn ma sus äkcu`ns fktarfnraslfma 2?¿. Yf U as a` puktn lamfn ma

_T, a` trfäkcu`n N_T as raitäkcu-`n, `d `nkcftum ma `d hfpntakusd N_ as 5, a` idtatn NU tfaka nkcftum 9 y a` idtatn _U, tfaka `nkcftum 4, matd` ldkard qua:

4ins

p<

44



Yf in`nidlns a` äkcu`n maϏ /2 ak pnsfifùk astäkmdr ak`d ifriukbarakifd ukftdrfd, a`puktn _ takmrä inln innr-

makdmds:

(9

5 ,4

5 )

Hd``dr tdkϏ /9, intdk Ϗ /9, sai Ϗ /9 y insi Ϗ /9.

Cräbfid 98

Cräbfid 96

5



A` puktn T, sflætrfin ma _ ink raspaitn ma` aja y, uefid-mn snera a` `dmn bfkd` ma` äkcu`n ma 1Ϗ /2 < 41?¿, takmräinln innrmakdmds:

44 4

2 5sak

p< y

1 4

2 5sak

p<

Ma fcud` bnrld, a` puktn U sflætrfin ma _ ink raspaitnma` nrfcak iuyn `dmn bfkd` inrraspnkma d uk äkcu`n ma3Ϗ /2 < 54?¿ tfaka inln innrmakdmd:

9 4( , )

5 5

_nr `n tdktn, ins 3Ϗ /2 < 9

5 y sak 3p /2 <

Dkä`ncdlakta, pdrd a` puktn Y, sflætrfin ma _ ink ras-

paitn ma` aja x qua astä snera a` `dmn bfkd` ma` äkcu`n

ma 44Ϗ /2, tfaka inln innrmakdmds ma td` bnrld

qua:

y

Inknifakmn `ns vd`nras ma sakn y insakn pdrd uk vd`nriud`qufard ``dldmn ot½, pnmalns hd``dr `ns vd`nras ma `dsmaläs bukifnkas trfcnknlætrfids pdrd asa vd`nr t.



Cräbfid =?

Inln `d cräbfid ma `d ifriukbarakifd ukftdrfd ink iaktrn ak a` nrfcak as sflætrink raspaitn ma` aja x, raspaitn ma` aja y, raspaitn ma` nrfcak, sa tfaka qua:

A` puktn T sflætrfin ma _, ink raspaitn ma` aja y tfaka inln innrmakdmds (- x,A` puktn Y, sflætrfin ma _ ink raspaitn ma` aja x, tfaka inln innrmakdmds ( x, y a` puktn U sflætrfin ma _ ink raspaitn ma` nrfcak tfaka inln innrmakdm(- x, - y).

Astn sfckfbfid qua:



Ma bnrld sflf`dr, a` puktn U sflætrfin ma _ ink raspaitn ma`nrfcak tfaka inln innrmakdmds (- x,- y). Inln a` puktn U astä

ak a` `dmn bfkd` ma` äkcu`n ma 1Ϗ /=, aktnkias takalns qua:

Ins 1Ϗ /= < -5

5

y sak 1Ϗ /= < -

5

5

]dlefæk pdrd a` puktn U, sflætrfin ma _ ink raspaitn ma` aja x, takalns qua sus innrmakdmds snk ( x,- y), inln a` puktn Y astä ak a` `dmn bfkd` ma 3Ϗ /=, aktnkias:

ins 3Ϗ /= <5

5

y sak 3Ϗ /= < -5

5

Yf inknialns ns vd`nras ma insakn y ma sakn pdrd uk äkcu`nt , iuyn dmn bfkd` inrtd d d ifriukbarakifd ukftdrfd ak a` puktn_, pnmalns hd``dr tdlefæk ns vd`nras ma sakn y insakn pdrd`ns äkcu`ns iuyn `dmn bfkd` inrtdk d `d ifriukbarakifd ukftdrfdak ns puktns sflætrfins ma _, ink raspaitn ma` nrfcak y d nsajas innrmakdmns y pnr akma, pnmalns hd``dr a` vd`nr ma `dsmaläs bukifnkas trfcnknlætrfids pdrd mfihns äkcu`ns.



Yf dkd`fzdlns a` vd`nr ma ds bukifnkas trfcnknlætrfids pdrd ns äkcu`ns iudmrdktdiuyds innrmakdmds ma su puktn bfkd` d` inrtdr `d ifriukbarakifd ukftdrfd snk (4(?,4), (-4,?), (?,-4) takalns qua:

Ins ? < 4 sak t < ?

Ins Ϗ /5 < ? sak Ϗ /5 < 4

Ins 9Ϗ /5 < ? sak 9 Ϗ /5 < -4

Cräbfid =4



_drd mfeujdr `d cräbfid ma `d bukifùk sakn ak a` p`dkn idrtasfdknvdlns d id`iu`dr sak t pdrd t aktra ? y 5Ϗ rdmfdkas, `n iud` supnkqua astfrdlns d ifriukbarakifd ukftdrfd, hdifækmn`d infkifmfr ink mfraiifùk pnsftfvd ma` aja x. Rdlns d inkstrufr ukd tde`d ma vd`nra

Cräbfid =5

θ¿ ? 9? =1 2? 6? 45? 491 41? 48? 54? 551 5=? 53? 9?? 941 99? 9

Udm ? Ϗ /2 Ϗ /= Ϗ /9 Ϗ /5 5Ϗ /9 9Ϗ /= 1Ϗ /2 Ϗ 3Ϗ /2 1Ϗ /= =Ϗ /9 9Ϗ /5 1Ϗ /9 3Ϗ /= 44Ϗ /2 5

Yak θ ? ?,1 ?,3 ?,82 4 ?,82 ?,3 ?,1 ? -?,1 -?,3 -?,82 -4 -?,82 -?,3 -?,1

Cräids ma `d bukifùk sakn


rad`as

Yasfùk

5



Yf sacuflns tnldkmn vd`nras ldynras ma 5Ϗ hdstd =Ϗ, netakmralns `d rapaifùk ma `d cräbfid, as maifr, pnmalns var qua `d cräbfid ma sakn t , sa rapfta fktarvd`ns ma `nkcftum 5Ϗ, pnrqua `d bukifùk sakn as parfùmfid7 rainrmalns qsak (t + 5Ϗ) < sak t .

Ma `d cräbfid pnmalns nesarvdr qua sak t tnld vd`nras masma -4 hdstd +4,maifr, qua a` rdkcn ma `d bukifùk as fcud` d` fktarvd`n W-4,4\. Dmaläs, pnmalns qua aktra ? y Ϗ, `ns vd`nras ma` sakn snk pnsftfvns y aktra Ϗ y 5Ϗ, `ns vd`nras sakn snk kacdtfvns, `n iud` sfckfbfid qua ak `ns iudmrdktas F y FF, sak t as pnsftfvnak `ns iudmrdktas FFF y FR sak t as kacdtfvn. Nevfdlakta, `d cräbfid ma sak t , inrrpnkma d `d cräbfid ma ukd bukifùk, parn kn d ukd bukifùk ukn d ukn, pnr ajalpsak Ϗ /= < sak 9Ϗ /= < ?,3.

Ak cakard`, pdrd hd``dr `ns vd`nras ma `ds bukifnkas trfcnknlæ-trfids sa utf`fzd `d idìu`dmnrd ifaktìbfid ink `d iud` netakalnsak bnrld räpfmd, vd`nras läs axditns hdstd ink 4? ù läs ifbrdsmaifldàs.

@d idìu`dmnrd prasaktd vdrfns sfstalds ma ukfmdmas pdrd `dslamfmds ma ns äkcu`ns inln crdmns y rdmfdkas, as kaiasdrfn ma-tarlfkdr ak quæ ukfmdmas trdedjdlns pdrd kn fkiurrfr ak arrnras.

Ink d idìu`dmnrd, tdlefæk pnmalns hdiar a` iäìu`n pdrd sak t ,`n iud` cakard uk vd`nr aktra -4 y +4 ù mdmn a` vd`nr ma sak t ,hd``dr uk vd`nr ma t qua cakarù asa vd`nr, `n iud` hdialns la-mfdkta `d tai`d sfk-4, ``dldmd sakn fkvarsn.

Ajalp`n

Yak 9?¿ < ?,1 ù sfk-4 ?,1 < 9?¿.

D`cukds cräbfids aspaifdàs ma `d bukifùk sak-4θ.



Ajalp`n

Crdbfidr b(t) < 5.sak t

Nesarvdlns qua idmd vd`nr ma sak t quamd lu`tfp`fidmn pnr 5. Inln sak

vdrìd aktra -4 y +4, sa tfaka qua 5.sak t vdrìd aktra -5 y +5.

_nmalns nesarvdr ak bnrld sflu`täkad, `ds cräbfids ma sak t y 5.sakt ak a` fktarvdiarrdmn (?,5Ϗ), `ds iud`as tfakak a` lfsln parìnmn, parn mfbarakta dlp`ftum7

Cräbfid =9

t Ϗ /= Ϗ /5 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ

5.Yak t 4.=4 5 4.=4 ? -4.=4 -5 -4.=4 ?



4. Inlpàtdr `ns vd`nras ak `d tde`d y hdiar `d cräbfid ma 9.sak t 7 matarlfkdrdlp`ftum.

_drd hdiar `ds cräbfids ma b(t) < sak et d pdrtfr ma:

()5 5

( ) ( 5 )

( )e e

b t sak et sak et

sak e t b t p p

p< < +

< + < +

@n dktarfnr luastrd qua d bukifùk b(t) < sak et as parfùmfid, ink parìnmn 5ep . Yf e

kacdtfvn, tnldlns a` vd`nr desnùtn ma e, pdrd qua a` parìnmn sad pnsftfvn. Dsparìnmn as 5

e

p

Ajalp`n

Hdiar `d cräbfid ma b(t) < sak et

5. Inlpàtdr `ns vd`nras ak `d tde`d y hdiar `d cräbfid ma 4/5.sak t 7 matarlfkdrdlp`ftum.

t Ϗ /= Ϗ /5 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ

9.Yak t

t Ϗ /= Ϗ /5 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ

4/5.Yak t

4



`d id`iu`dmnrd

Ma `d cräbfipnmalns vaqua a` parìnmn ma sak

as 5Ϗ /5 < Ϗ

`d dlp`ftuas `d lfslqua d cräbfima sak t .

t Ϗ /= Ϗ /5 9Ϗ /= Ϗ

Yak 5t 4 ? -4 ?

4. ( ) =. b t sak t <

5. 4( ) .

= b t sak t <

9. 4( ) b t sak t <

Qsa `d id`iu`dmnrd pdrd trdzdr `ds sfcufaktas cräbfids y ak idmd idsn, hd``dr su dlp`ftum y su parìnmn.

=. ( ) = b t sak t <

1. b (t ) < 9.sak 9t

Cräbfid ==

5



θ

Ma `d cräbfid pnmalns var qua ins t vdrìd aktra -4 y +4, as

maifr, a` rdkcn ma `d bukifùk as a` fktarvd`n (-4,4).

Yf sa sfcuak mdkmn vd`nras pdrd t ldynras ma 5Ϗ, `d cräbfidsa rapfta ak a` fktarvd`n (5Ϗ,=Ϗ) y dkä`ncdlakta, `d cräbfid sarapfta ak `ns fktarvd`ns (=Ϗ,2Ϗ), (2Ϗ,8Ϗ), (-5Ϗ,?) maefmn d qua`d bukifùk ins t as ukd bukifùk parfùmfid ink parìnmn 5Ϗ.

Ntrds cräbfids qua fkvn`uirdk ins t : c(t) < d ³ ins t

Cräbfid =1

¿ ? 9? =1 2? 6? 45? 491 41? 48? 54? 551 5=? 53? 9?? 941 99?

Udm ? Ϗ /2 Ϗ /= Ϗ /9 Ϗ /5 5Ϗ /9 9Ϗ /= 1Ϗ /2 Ϗ 3Ϗ /2 1Ϗ /= =Ϗ /9 9Ϗ /5 1Ϗ /9 3Ϗ /= 44Ϗ /2

ins t 4 ?,82 ?,3 ?,1 ? -?,1 -?,3 -?,82 ? -?,82 -?,3 -?,1 ? ?,1 ?,3 ?,82

Cräid ma `d bukifùk insakn


rad`asYasfùk

9



Ajalp`n

Hdiar `d cräbfid ma c(t) < 9 ³ ins t

c(t) < ins et

c(t) < ins (et+5Ϗ), pnr `d parfnmfifmdm ma `d bukifùk ins t

@uacn:

Ma `d cräbfid, nesarvdlns qua 9.ins t tfaka ukd dlp`ftum tras vaias ldynr qua ma ins t , parn su parìnmn as a` lfsln pdrd `ds mns.

Cräbfid =2

t Ins t 9.ins t

? 4 9 Ϗ /= ?,3 5,45 Ϗ /5 ? ?

9 Ϗ /= -?,3 -5,45 Ϗ -4 -9 1 Ϗ /= -?,3 -5,45 9 Ϗ /5 ? ? 3 Ϗ /= ?,3 5,45 5 Ϗ 4 9



@n iud` luastrd qua c(t) < ins et as ukd bukifùk parfùmfid ink parìnmn 5ep

Yf e as kacdtfvn, tnldlns inln parìnmn a` vd`nr pnsftfvn ma Ϗ snera a` vd`nr desn`ma e dsì: 5

e

p

Mdmds `ds sfcufaktas bukifnkas, ak idmd idsn, matarlfkdr su dlp`ftum y su parìnm

Ajalp`n

Hdiar `d cräbfid ma `d bukifùk c(t) < ins 4/5t.

Cräbf

=. ( ) 1ins 2c t t <

1. ( ) ?, =ins 1c t t <

4. ( ) 1ins 9c t t <

5. ( ) ins =c t t <

9. 4

( ) ins5

c t t <

4



Ak idmd idsn, hd``dr `d dlp`ftum y a` parìnmn, y trdzdr `d cräbfid ma `d bukifùk

mdmd.

@d dlp`ftum ma `d cräbfid as y a` parìnmn as =Ϗ. Ak d cräbfisa luastrdk d `d vaz, a` ins t

a` ins 4/5t

t Ins t Ins 4/5t

? 4 4

Ϗ /= ?,3 ?,65

Ϗ /5 ? ?,3 9 Ϗ /= -?,3 ?,98

Ϗ -4 ?

1 Ϗ /= -?,3 -?,98

9 Ϗ /5 ? -?,3

3 Ϗ /= ?,3 -?,65

5 Ϗ 4 -4

@ds bukifnkas sakn y insakn snk `ds läs flpnrtdktas7 su inlpraksfùkbdif`ftd a` astumfn ma `ds ntrds bukifnkas ifriu`dras, `d tdkcakta, `dintdkcakta, `d saidkta y `d insaidkta. Dmaläs, inln a` mnlfkfn ma `dbukifùk sakn y insakn as a` inkjuktn ma `ns kúlarns rad`as, sfckfbfidqua sak t y ins t axfstak iud`qufard sad a` vd`nr t

=. 4=

( ) 5insc t t <

1. 49

( ) 9insc t t <

4. ( ) =insc t t <

5. ( ) 9insc t t <

9. 4=

( ) insc t t <

5



Mabfkflns tdk sak t

t ins t

< pdrd ?ins t .

Ma `d mabfkfifùk, valns qua tdk t kn tfaka uk vd`nr mabfkfmn iudkmn ins

t < ?, astn niurra iudkmn t< Ϗ /5, 9 Ϗ /5, 1 Ϗ /5, 3 Ϗ /5, - Ϗ /5, - 9Ϗ /5, - 1Ϗ /5,

ak cakard`, sf t as ma `d bnrld (5 4)5

g p

+ , mnkma g as iud`qufar aktarn.

Astns vd`nras sa axiùyak ma` mnlfkfn ma `d bukifùk tdk t .

Ajalp`n

Yf t sa dprnxfld d` vd`nr Ϗ /5 < 6?¿, sak t sa dprnxfld d 4 y ins t sa dprnxfld d ?, y

bukifùk tdk t as crdkma. Radlns `ns sfcufaktas vd`nras:

θ(¿) 86 86,6 86,66 86,666

tdk t 13,586 135,613 1356,133 13.561,336

@ns vd`nras ma tdk θ vdk iraifakmn d lamfmd qua θ sa diarid d Ϗ/5 < 6?¿. Dqtnmns `ns vd`nras ma tdkcakta snk pnsftfvns maefmn d qua tnldlns vd`nras aktry Ϗ/5 ak `ns iudàs tdktn sak θ inln ins θ snk pnsftfvns θ snk pnsftfvns

_drd dkd`fzdr a` rdkcn ma `d bukifùk tdkcakta ma t , rainrmalns qua sak t y in

vdrìdk ak a` fktarvd`n 4,4 ùacn `d bukifùk tdkcakta puama tnldr vd`nras tcrdkmas inln sa masaak, sf a` maknlfkdmnr ins t sa dprnxfld d iarn.

@d bukifùk tdkcakta


radàsYasfùk

=



Nesarvalns `d sfcufakta tde`d:

Ak asta idsn, tdk θ tnld vd`nras kacdtfvns luy crdkmas iudkmn θ sa dprnxfld Ϗ /5, maefmn qua `ns vd`nras ma θ astäk aktra Ϗ /5 y Ϗ (sacukmn iudmrdkta), ak mnkmsakθ as pnsftfvn y insakn θ as kacdtfvn.

Ma `n dktarfnr, pnmalns var qua a` rdkcn ma `d bukifùktdk

θ

as a` inkjuktn ma `nkúlarns rad`as.

Yf fktaktdlns hd``dr ink ukd id`iu`dmnrd tdk Ϗ /5 < tdk 6?¿, `d raspuastd as arrnmaefmn d qua `d bukifùk tdkcakta kn astä mabfkfmd pdrd asa vd`nr, as maifr, Ϗ /5 kpartakaia d` mnlfkfn ma `d bukifùk tdkcakta.

Ma d mabfkfifùk ma d bukifùk tdkcakta, pnmalns var qua tdk θ as pnsftfvd ak a` pr

larn y tariar iudmrdkta, y tnld vd`nras kacdtfvns ak a` sacukmn y iudrtn iudmrdkt

θ(¿) 6?,4 6?,?4 6?,??4 6?,???4

tdk θ -135,613 -1.356,133 -13.561,336 -135.613,361

θ

Ak `d cräbfid pnmalns nesarvdr qua `d bfcurd sa rapfta ak fktarvd`ns ma `nkcftum Ϗ

as maifr, takalns `d lfsld cräbfid ak `ns fktarvd`ns

, ,

9 9, , ,

5 5 5 5 5 5

p p p p p p

¿ ? =1 2? 6? 45? 491 48? 551 53? 941 92?

Udm ? Ϗ /= Ϗ /9 Ϗ /5 5Ϗ /9 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ

tdk θ -- ? 4 9 KN - 9 -4 ? 4 KN -4 ?



Cräbfid =

`n iud` sfckfbfid qua `d bukifùk tdkcakta as parfùmfid ink parìnmn Ϗ n sad q()tdk tdkt t p+ <

@ds raitds vartfidàs qua pdsdk pnr `ns puktns9 9

, , ,5 5 5 5

p p p p snk dsìktn

vartfidàs ma tdkcakta t. @d cräbfid ma d bukifùk tdkcakta sa diarid d astd raitd pakukid `d inrtd.

Ajalp`n

Hd``dr `ns vd`nras ma:

4. Idìu`dr

5. Hd``dr tdk 9??º tdk 9??º < tdk (45?º + 48?º) < tdk 45?º < -4

4. tdk 46?º 5. 9. tdk 5=?º =. tdk 9=1º 1.

4



Ajalp`n

Ydealns qua tdkinssakqq

q<

@uacn, sf raalp`dzdlns ak `d fcud`mdm mdmd, takalns:5

5

54 4

ins

sak sak

ins

q q

q q

+ < + ó

5 5

5 5ins 4

ins inssakq q

q q

+< <

5

54sai

insq

q

< < ó

@n qua luastrd qua 5 54 tdk saiq q+ < as vä`fmd pdrd tnmns `ns vd`nras ma q , a

Qkd fcud`mdm qua as varmdmard pdrd tnmns `ns vd`nrasma `ds vdrfdeàs fkvnùirdmds ak a``d, sa ``dld fmaktfmdm.

D`cukds fmaktfmdmas trfcnknlætrfids


radàsYasfùk

1

Dprakmfakmn ink a` prnba Ju`fnInlprnedifùk ma ukd Fmaktfmdm ]rfcnknlætrfidMurdifùk: 1:=6 lfk.



@d bukifùk b (t ) < tdk et , tfaka inln parìnmn4=

=p

p<

Crdifds d qua e as aqufvd`akta d °, y sf e as kacdtfvn, tnldlns su vd`nr desn`u

pnrqua a` parìnmn maea sar pnsftfvn.

Ajalp`ns

4. Yf b (t ) < tdk 1t, a` parìnmn as: Ϗ /1

5. Yf 4( ) tdk

=

b t t < , aktnkias a` parìnmn as 4

=

=p

p<

4. b (t ) < tdk 5t

5. b (t ) < tdk (-9t )

9.

Mdmds `ds sfcufaktas bukifnkas, akinktrdr a` parìnmn:

Ajalp`n

4



Ak asta idsn, valns qua `ds dsìktntds vartfid`as ma `d cräbfid snk `ds raitds qupdsdk pnr ’Ϗ /2, Ϗ /2, Ϗ /5, 1Ϗ /2.

@d cräbfid tfaka bnrld pdraifmd d `d bukifùk tdkcakta, parn su parìnmn sa ramuia d Ϗ /9.

@d bukifùk intdkcakta

Mabfkflns `d bukifùk pdrd vd`nras ma 7 sf a` vd`nr m

maknlfkdmnr sakt as iarn, `d bukifùk intdkcakta kn astä mabfkfmd7 inln sakt a

iarn ak Ϗ, 5Ϗ, 9Ϗ, -Ϗ, -5Ϗ, - 9Ϗ, as maifr, ak tnmns `ns vd`nras ma t < g .Ϗ, ak `n

iud`as g as uk kúlarn aktarn. Aktnkias, astns vd`nras kn partakaiak d` mnlfkfn m

Cräbfid =6

Hd``dr `d cräbfid ma 49( ) tdk b t t <

5



Yf t sa diarid d uk lú`tfp`n ma Ϗ, ins t sa diarid d iarn y a`vd`nr ma intdkcakta sa hdia luy crdkma, ink vd`nr pnsftfvnn kacdtfvn.

Dkd`fialns a` inlpnrtdlfaktn ma `d cräbfid ak a` fktarvd`n (?, Ϗ):

Ak a` puktn lamfn ma` fktarvd`n, takalns qua int ?5

dkp

< 7 dhnrd, sftnldlns vd`nras luy iaridkns d Ϗ, aktnkias a` vd`nr ma intdkcaktatnld vd`nras luy crdkmas kacdtfvns. Radlns d`cukns idsns:

Intdk 436¿ < -13,58

Intdk 436,6 < -135,61 Intdk 436,66 < -1.356,13

Inln valns, `d bukifùk vd mairaifakmn luy räpfmn d lamfmd qua t sa diarid d` vd`nr Ϗ < 48?¿.

Yf `a mdlns vd`nras d t prùxflns d iarn, netakalns vd`nras pnsftfvns

luy crdkmas pdrd intdkcakta mat

. Radlns d`cukns idsns: Intdk ?,4 < 135,65

Intdk ?,?4<1.356,13

Intdk ?,??4<13.561,33

Ak asta idsn, d bukifùk iraia, tnldkmn vd`nras luy crdkmas d lamfmd

Cräid ma `d bukifùk intdkcakta


rad`asYasfùk

2



D` trdzdr d cräbfid ma intdkcakta ma t , ak ns fktarvd`ns (-Ϗ, ?) y (Ϗ, 5Ϗ) netakalns ukcräbfid sflf`dr d d netakfmd ak a` fktarvd`n (?, Ϗ), n iud` kns fkmfid qua d cräbfid mintdk t sa rapfta parfùmfidlakta, y dsì d bukifùk intdk t as parfùmfid ink parìnmn Ϗ

As maifr, intdk (t + Ϗ) < intdk t

Inln `ds bukifnkas tdk t y intdk t sa puamak mdr ak tærlfkns ma sak t y ins t , astkns parlfta var d`cukds ma sus prnpfamdmas flpnrtdktas.

Ajalp`n

@ds bukifnkas tdk t y intdk t snk bukifnkas flpdras, vadlns:

d.

( )tdk( )ins( )

tdkins ins

sak t t t

sakt sakt t

t t

<

< < <

@uacn, tdk(-t) < -tdk t qua kns mfia qua `d bukifùk tdk t as ukd bukifùk flpd

t ( t) t t

Cräbfid 1?



Ntrd fmaktfmdm trfcnknlætrfid:

_rnedr `d fmaktfmdm 4 + intdk5 θ < ins i5 θ.

Yn`uifùk

5

5

5

5 55

5 5

ins4 int 4

ins 4ins

dksak

saki

sak sak

qq

q

q qq

q q

+ < +

+< < <

Ma `ds mabfkfifnkas 9 9 1... , , , , ...5 5 5 5 5p p p p p takalns qua `ds bukifnkas tdkcakt

intdkcakta snk raiìprnids. As maifr, 4

inttdk

dkqq

< , sf tdk ?q .

Yf takalns ( ) int b t dk et < , pnmalns lnstrdr qua su parìnmn ase

p.

pnr `d parfnmfifmdm ma int dk t . Aktnkias:

Ak a` maknlfkdmnr, tnldlns pdrd qua a` parìnmn sad pnsftfvn.

Ajalp`n

Hd``dr a` parìnmn y hdiar `d cräbfid ma `d bukifùk b (t ) < intdk 5t .

Yn`uifùk



Matarlfkdr a` parìnmn ma `ds sfcufaktas bukifnkas:

4. ( ) int 9 b t dk t <

5. ( ) int 2 b t dk t <

9. ( ) int ?,1 b t dk t <

=. ( ) int ?, 51 b t dk t <

1. ( ) 5int 5b t dk t<

Cräbfid 14

4



4sai

inst

t < , sf ins ?t 7 iudkmn ins ?t < , `d bukifùk

saidkta kn astä mabfkfmd7 astn niurra iudkmn 5 (5 4)t g p< + ,

as maifr, `ds raitds vartfidàs qua pdsdk pnr `ns puktns

snk dsìktntds ma `d cräbfid.

Ma d cräbfid nesarvdlns qua d bukifùk sai t kn tnld vd`nras ak a` fktarvd`n defa(47-4). Yu rdkcn ma vd`nras as a` inkjuktn ma `ns kúlarns radàs ldynras n fcudd ukn, ukfmn ink a` inkjuktn ma `ns kúlarns radàs laknras n fcudàs qua ukn,iud` pnmalns asirfefr dsì:

Halns prasaktdmn d` lfsln tfalpn `ds cräbfids ma ins t y sait pdrd nesarvdr la

Cräbfid 15

Bukifùk saidkta


radàsYasfùk

3



Nesarvdifùk

@d bukifùk saidkta as parfùmfid y su parìnmn as 5Ϗ, `n iud` pnmalns varfbfidr bäif`lakta.

4 4sai sai( 5 )

ins ins( 5 )t t

t t p

p< < < +

+

Astd parfnmfifmdm tdlefæk `d pnmalns var ak `d cräbfid, ak mnkma sa rapfta ak lfsld bnrld ink fktarvd`ns ma `nkcftum 5Ϗ.

Ajalp`n

4.4

sai 9?º 2, =8

ins9?º

< <

5. 4

sai 31º 4,?8ins31º

< <

Ink `d idìu`dmnrd, rad`fzdr `ns sfcufaktas iäìu`ns:

4. sai =1¿5 sai 45?¿

=. int 41¿1 int 4?8¿

@ds bukifnkas intdkcakta, saidkta y insaidkta kn dpdraiak ak `nstai`dmns ma `ds idìu`dmnrds ifaktìids, parn pdrd hdiar iäìu`ns inkastds bukifnkas, pnmalns usdr sus raiìprnins dsì:

9. 4

int 81º 1,16

tdk 81º

dk < <

4



Mabfkflns4

insi t sak t

< , sf ?sak t , iudkmn ?sak t <

`d bukifùk insaidkta kn astä mabfkfmd, `n iud` niurra iudkm

.t g p< , y g as iud`qufar kúlarn aktarn.

Ajalp`n

Ak ... -9Ϗ, -5Ϗ, -Ϗ, ?, Ϗ, 5Ϗ, 9Ϗ..., `d bukifùk insaidkta t kn astä mabfkfmd, `ds raivartfid`as qua pdsdk pnr astns puktns snk dsìktntds ma insi t .

@d bukifùk insaidkta as parfùmfid ink parìnmn 5Ϗ, inln sa luastrd d inktfkudif

Asta haihntdlefæk `npnmalnsnesarvdr,d` hdiar `dcräbfid mainsi t .

@d bukifùk insaidkta


rad`as

Yasfùk

8



@d bukifùk ma insi t kn tnld vd`nras ak a` fktarvd`n defartn ma lakns ukn d uk(-4,+4) , ma mnkma valns qua a` rdkcn ma `d bukifùk insaidkta as a` inkjuktn m`ns kúlarns radàs laknras n fcudàs qua lakns ukn, ukfmn ink a` inkjuktn ma nkúlarns radàs ldynras n fcudàs ma ukn.

ins ( , 4\ W4, ) Udkcn ma i t < +

Yf quaralns idìu`dr `d insaidkta ma uk vd`nr t ink `d idìu`dmnrd, maealns usd

a` raiìprnin ma insaidkta qua as sakn, pnrqua `d tai`d insaidkta t kn bfcurd ak atai`dmn ma `d idìu`dmnrd.

Ajalp`n

Hd``dr:

Ya puama malnstrdr qua `ds bukifnkas ( ) sai ( ) ins b t et y c t i et < < sn

d. 4ins 2?º 4,41=

2?i

sak< <

e. 4ins 2?º 4,41=

2?i

sak< <

i. 4ins ( 1?º ) 4,9?1

( 1?)i

sak < <



Ajalp`n

4 4

( ) ins( 5 )

c t i et sak et sak et p

< < <+

maefmn d `d parfnmfifmdm ma `d bukifùk sakn,

ùacn sai ins .tdksakq q q q < .

]nldlns vd`nr desnùtn ma e ak a` maknlfkdmnr ma` parìnmn pdrd dsacurdr qsad pnsftfvn.

4. ( ) sai 1 b t t <

5. ( ) ins ( 9 ) b t i t <

9. 4( ) sai ( )9

b t t <

=. ( ) 5 ins (?, 2 ) b t i t <

1. ( ) ins ( ?,4 ) b t i t <

Ak `ns sfcufaktas kulardàs, matarlfkdr a` parìnmn ma `d bukifùk:

4



_nmalns varfbfidr d`cukds fmaktfmdmas trfcnknlætrfids, dpnyäk-

mnkns ak ds fmaktfmdmas eäsfids masdrrn``dmds hdstd dhnrd, y aka` inkniflfaktn ma `ds bukifnkas trfcnknlætrfids.

Ajalp`n

Ma `d fmaktfmdm bukmdlaktd` 5 5ins 4sak t t + < , netakalns:

5 5

4 inssak t t <

y

5 5

ins 4t sak t <

.Ajalp`ns

Rarfbfidr `d sfcufakta fmaktfmdm:

4. sai ins tdk .sakq q q q <

Yn`uifùk

Masdrrn``dkmn a` prflar `dmn ma `d fcud`mdm, takalns:

5 5

4sai ins ins

ins

4 ins. tdk .

ins ins ins

sak saksak sak

q q qq

q q qq q q

q q q

<

< < < <

Rarfidifùk ma fmaktfmdmastrfcnknlætrfids


rad`as Yasfùk

6



_drd varfbfidr ukd fmaktfmdm trfcnknlætrfid, sa puama tnldr `d axprasma` prflar `dmn ma `d fcud`mdm y trdksbnrldr`d ak a` sacukmn `dmn n tnl`d axprasfùk qua bfcurd ak a` sacukmn `dmn, y trdksbnrldr`d ak `d axprasma` prflar `dmn.

D vaias, as kaiasdrfn trdedjdr `ds axprasfnkas ak dlens `dmns ma `dfcud`mdm hdstd `àvdr`ds d uk puktn ak mnkma rasu`tak fcudàs.

5. Rarfbfidr `d fmaktfmdmis 4 4

i sai t

i

tc c

q

q q q

+<

Ynùifùk

]rdedjalns a` prflar `dmn:

( )( )ins 4 sai t ii c tcq q q q+ <

Aktnkias, asirfeflns ma ntrd bnrld a` prflar lfalern ma `d aiudifùk:

]akalns qua:

Halns netakfmn a` sacukmn `dmn ma `d fcud`mdm nrfcfkd` quamdkmn varfbfid



9. Rarfbfidr `d fmaktfmdm ins int4 ins

saki dk

qq q

q< +

Ynùifùk

_nmalns alpazdr, trdedjdkmn a` sacukmn `dmn ma `d fcud`mdm dsì:

5 5 5(tdk sai ) tdk 5 tdk sai saiq q q q q q < +

5

5 5 5

5 4

ins ins ins

sak sakq q

q q q< +

5

5

( 4)

ins

sakq

q<

(4 ins )(4 ins )

(4 ins )sak

q q

q q

+ <

Halns lu`tfp`fidmn a` kulardmnr y a` maknlfkdmnr pnr (4 ins )q

Yflp`fbfidlns pnr sakθ y netakalns:

Dsì, halns `àcdmn d` prflar `dmn ma `d fcud`mdm nrfcfkd`, ùacn quamvarfbfidmd `d fmaktfmdm.



=. Rarfbfidr `d fmaktfmdm

5 4(tdk sai )

4

sak

sak

qq q

q <

+

Yn`uifùk

Rarfbfidlns astd fmaktfmdm, lnstrdkmn qua idmd `dmn ma `d fcud`mdmsa puama trdksbnrldr ak `d lfsld axprasfùk. _rflarn trdedjalns a``dmn fzqufarmn y masdrrn``dlns a` iudmrdmn:

5

int .saidk q q

5

5

( 4)

ins

sakq

q<

Hdstd dquì, masdrrn``dlns `d axprasfùk inrraspnkmfakta d` `dmn fz-qufarmn ma `d fcud`mdm.

Dhnrd, tnlalns `d axprasfùk ma` `dmn maraihn y lu`tfp`fidlns a`kulardmnr y a` maknlfkdmnr pnr a` inkjucdmn ma` maknlfkdmnr dsì:

5

5

5

5

4 (4 ) (4 ).

4 (4 ) (4 )

4 5

4

5 4

ins

sak sak sak

sak sak sak

sak sak

sak

sak sak

q q q

q q q

q q

q

q q

q

<

+ +

+<

+<

5

5

( 4)

ins

sakq

q<

Astd as `d lfsld axprasfùk qua netuvfliudkmn trdedjdlns a` prflar `dmn. @uaquamd varfbfidmd `d fmaktfmdm.



@ds sfcufaktas nihn fmaktfmdmas snk eäsfids pdrd varfbfidr fmaktfmdmas läs inlp`ajds.

4. 4

.ins 4 inssak i n isak

q q qq

< <

5. 4

ins .sai 4 saiins

nq q qq

< <

9. 4

tdk .int 4 inttdk

dk n dkq q qq

< <

=. tdkins

sakqq

q<

1. insintdksak

qqq

<

2. 5 5ins 4sak q q+ < , ma mnkma 5 5 5 54 ins ins 4sak y sakq q q q< <

3. 5 5 5 5tdk 4 sai tdk sai 4nq q q q+ < <

8. 5 5 5 54 int ins int ins 4dk i n dk iq q q q+ < <

Uainrmdkmn astds fmaktfmdmas y `ds mabfkfifnkas ma `ds bukifnkas



4. D` varfbfidr `d sfcufakta fmaktfmdm sakθ + insθ .intdkθ < insiθ , a`rasu`tdmn as:

d. Dlefcun e. Masfcud` i. Fmaktfmdm m. Iarn

5. D` varfbfidr d sfcufakta fmaktfmdm tdkθ +5insθ.insiθ < saiθ.insiθ+intdkθ ,a` rasu`tmn as:

d. Dlefcun e. Masfcud` i. Fmaktfmdm m. Iarn

Rarfbfidr `ds sfcufaktas fmaktfmdmas trfcnknlætrfids:

9.

=.

1.

2. Axprasdr ak tærlfkns ma sakθ, `d axprasfùk

3. Axprasdr ak tærlfkns ma insθ, `d axprasfùk

8. Axprasdr ak tærlfkns ma insθ, `d axprasfùk intdk5θ . saiθ.



Qkd ma `ds dp`fidifnkas läs braiuaktas ma `d trfcnknlatrìd sa md ak `d rasn-ùifùk ma trfäkcu`ns.

Uasn`var uk trfäkcu`n inksfsta ak hd``dr `ds `nkcftumas ma sus tras `dmns y `dslamfmds ma sus tras äkcu`ns fktarfnras. Cakard`lakta, sa inkniak d`cukns maastns safs aàlaktns ma` trfäkcu`n y sa pfma akinktrdr `ns rastdktas.

Iudkmn a` trfäkcu`n as raitäkcu`n, raiurrflns d` usn ma `ds rdznkas trfcnkn-lætrfids netakfmds ma `ds ra`difnkas aktra sus `dmns.

Iudkmn a` trfdkcu`n kn as raitäkcu`n, raiurrfralns d` usn ma mns àyas buk-mdlaktdàsak trfcnknlatrìd qua snk:

@d ày ma sakns@d ày ma insakn

Qtf`fzdkmn astds harrdlfaktds, pnmalns rasn`var iud`qufar trfäkcu`n.

Ajalp`ns fùstrdtfvns

Qkfmdm 1. Dp fidifnkas ma `d trfcnknlatrìd Yasfùk

4

Dprakmfakmn ink a` prnba Ju`fn_rneàld ink @ay ma Yakns Murdifùk: 6:94 lfk._rneàld ink @ay ma Insakns Murdifùk: 5:11 lfk.



Alpazdralns `ds dp`fidifnkas, rasn`vfakmn prneàlds qua tfakak qua var inktrfcnknlatrìd ma` trfäkcu`n raitäkcu`n.

D` rasn`var prneàlds ma trfcnknlatrìd, kns akinktrdralns ink axprasfnkas inl

?,1sak q < ù 4ins q < , ma mnkma takalns qua maspajdr a` vd`nr maAk a` prflar idsn, valns qua `d bukifùk sakn tnld uk vd`nr ma θ y à dsfc?,17 `d bukifùk sakn fkvarsn qua sa kntd inln 4sfk mavua`va a` vd`nr ?,1

2

pq < ,

_arn a` vd`nr 2

p

, kn as úkfin puastn qua tdlefæk pnr `d parfnmfifmdm mabukifùk sakn, takalns qua:

Astn sfckfbfid qua d` mavn`var ?,1 pnr lamfn ma `d bukifùk sakn fkvarsn,puama netakar lú`tfpàs vd`nras pdrd θ7 pnr `n tdktn, ma `ds inkmfifnkas y

Cräbfid 11



Ajalp`ns

Hd``dr a` vd`nr ma θ aktra ? y 5Ϗ iudkmn sak θ < ?,8.

Ynùifùk

Uasn`vfakmn, takalns qua sak-4 ?,8 < 19¿ ?3‖ =8‖‖

Asta äkcu`n tfaka su dmn bfkd` ak a` puktn _ (prflar iudmrdkta). A` äkcu`n iuy`dmn bfkd` pdsd pnr a` puktn T sflætrfin ma _, ink raspaitn ma` aja, y iuylamfmd as 48? ’ (19¿ ?3‖ =8‖‖) < 452¿ 15‖ 44‖‖ tdlefæk as snùifùk, pnrqu

a` vd`nr ma` sakn pdrd `ns mns äkcu`ns as a` lfsln ?,8.

@uacn `ds snùifnkas snk θ < 19¿ ?3‖ =8‖‖ y θ < 452¿ 15‖ 44‖‖, y `ds malsnùifnkas snk vd`nras qua astäk buard ma` fktarvd`n (?, 5Ϗ).

Cräbfid 12



Ajalp`ns

Yn`uifùk

Inknialns qua pdrd tnmn trfäkcu`n a` ärad as:

5

edsa d turd D

<

Ma d bfcurd takalns5

e h D

< , parn h

d sak d< uacn maspajdkmn h, takal

qua .h d sak d< y raalp`dzdkmn ak `d prflard bùrlu`d, netakalns:

.5

d esak D d< .

Astd as ukd bùrlu`d útf` pnrqua kns parlfta hd``dr a` ärad ma uk trfäkcu

4. Mdmn uk trfäkcu`n inln a` ma `d cräbfid 13, pdrd a` iud` sa inkniak`nkcftum ma mns `dmns d, e y a` äkcu`n δ inlprakmfmn aktra a``ns, hd``dr u

bùrlu`d pdrd a` ärad ma` trfäkcu`n.

Cräbfid 13



Ynùifùk

Ak `d cräbfid, valns qua δ < 54¿, ùacn 451tdk x

d < 7 sf maspajdlns takalns qua:

5. @ns dmns ma uk trfäkcu`n lfmak 9?,1 y =8 l, y a` äkcu`n inlprakmfmn akta``ns, as ma =4¿. ¾Iuä` as a` ärad ma` trfäkcu`n>

Ynùifùk

Dp`fidkmn a` rasu`tdmn ma` prneàld dktarfnr, takalns qua:

9. Masma `d ifld ma uk didktf`dmn ma 451 l ma d`turd, a` äkcu`n ma maprasfù

ma ukd dkihd as 54¿. ¾D quæ mfstdkifd sa akiuaktrd d dkihd ma` didktf`dmn

Cräbfid 18



Cräbfid 16

5. Qk inkstruitnr masad hdiar ukd rdlpd ma 8,1 l ma drcn qua sa àvdktd d ud`turd ma 4,81 l ma` sua`n. Idìu`dr a` äkcu`n ma `d rdlpd ink `d hnrfznkt

9. Qkd asidàrd qua lfma 5? pfas, sa dpnyd ak uk amfbfifn y a` äkcu`n aktra dleas ma 55¿. Idìu`dr:

d. @d mfstdkifd ma` pfa ma `d asidàrd d` amfbfifn.

e. Yf `d mfstdkifd ma` pfa ma `d asidàrd dulaktd 9 pfas, ¾iuäktn edjdräpuktd suparfnr ma `d asidàrd>

=. Masma uk puktn D qua astä d 8,5 l snera a` kfva` ma` sua`n, a` äkcu`n ma avdifùk ma `d pdrta d`td ma uk fkluaeà as 94¿ 5?‖ y a` äkcu`n ma maprasfùk

4. Idìu`dr a` äkcu`n ma aàvdifùk ma` Yn`, sf ukd parsnkd qua lfma 1 pfas astdturd, prnyaitd ukd snlerd ma = pfas ma `drcn d kfva` ma` sua`n.

4



1. Akinktrdr `ns vd`nras axditns ma x, y inrraspnkmfakta d `d cräbfid 13.

x

6

y

2?n

x

3y

=1n

x

448

2. Ak a` trfäkcu`n DEI :

d < 5=,2 e < 29,5 Idìu`dr `ds lamfmds ma `ns ntrns

aàlaktns ma` trfäkcu`n.

3. Masma uk puktn d` kfva` ma` sua`n y d 491 pfas ma `d edsa ma ukd tnrra, a` äkcu`n ma aàvdifùk d `d pdrta läs d`td ma `d tnrra as 13¿. Idìu`dr `d d`turd m`d tnrra.

@ns äkcu`ns fktarfnras ma` trfäkcu`n sapuamak fmaktfbfidr, usdkmn d lfsldàtrd ma` værtfia inrraspnkmfakta nsa suaàk usdr tdlefæk, àtrds ma`d`bdeatn crfacn inln δ, ε y θ.

D` rasn`var trfäkcu`ns, kaiasftdlns astdeàiar d`cukds kntdifnkas pdrd matar-lfkdr sus pdrtas y bdif`ftdrkns a` ldkajn ma `ns rasu`tdmns. _drd matarlfkdruk trfäkcu`n, à dsfckdlns ukd àtrd ldyúsiu`d ak idmd ukn ma sus værtfias

y d lfsld atrd parn lfkúsiu`d, pdrd fkmfidr a` dmn npuastn d idmd værtfia.

Cräbfid 2?

Cräbfid 24

Cräbfid 25



Cräbfid 29

_nmalns hdiar ukd malnstrdifùk pdrifd`:

Yf in`nidlns a` trfäkcu`n ma td` bnrld qua a` værtfia D infkifmd ink uk sfstald innrmakdmds idrtasfdkn y su äkcu`n δ astæ ak pnsfifùk racu`dr, as maifr, a` `dmn ma` trfäkcu`n infkifmfakmn ink `d mfraiifùk pnsftfvd ma` aja x y a` `dmn DI as

Yf δ, ε y θ snk ns äkcu`ns fktarfnras ma uk trfäkcu`n iud`qufard, y d, e y i snk`ds `nkcftumas raspaitfvds ma `ns `dmns npuastns d astns äkcu`ns, aktnkias:

d e i

sak sak sakd e q< <

@d ay ma sakns astde`aia ds ra`difnkas aktra d nkcftum ma uk dmn y a` saknma su äkcu`n npuastn y as vä`fmd pdrd iud`qufar trfäkcu`n.

@ay ma sakns

Qkfmdm 1. Dp`fidifnkas ma `d trfcnknlatrìd Yasfùk

5



Cräbfid 2=

Ak d cräbfid 2=d pnmalns trdzdr a` saclaktn IM parpakmfiu`dr d` aja x, y `dlalnh su `nkcftum. Inln `ns trfäkcu`ns DMI y a` trfäkcu`n EMI snk raitäkcu`ntakalns:

hsak

ed< , ma mnkma h e sakd<

]dlefækh

sakd

e< , ma mnkma h d sak e< 7 fcud`dkmn ns vd`nras ma h takalnqua:

d.

e.



_drd dp`fidifnkas präitfids, as kaiasdrfn var qua hdy tras fcud`mdmas qua snk

sak sak

d e

d e<

sak sak

d i

d q<

sak sak

e i

e q<

Asta rasu`tdmn as inknifmn inln `d ày ma sakns.

Ak `d cräbfid 2=e in`nidkmn a` værtfia I ak a` nrfcak y a` äkcu`n θ ak pnsfiracu`dr, kns quamd inln `dmn fkfifd` ID y inln `dmn bfkd` IE7 masma E trdzdla` saclaktn EM, parpakmfiu`dr d` aja x, y dsì takalns `ns trfäkcu`ns raitäkcu

IME y DME, ma mnkma:

h

sakd

q< dsì h d sak q<

]dlefækh

saki

d< ùacn h i sak d<

Fcud`dkmn `ns vd`nras ma h, takalns qua:

d sak i sakq d< ma mnkma sak sak sak

d e i

d e q< < ,

Halns lnstrdmn qua:

sak sak

d e

d e< y

sak sak

d i

d q< ,

ùacn inkiùflns qua:

sak sak sak

d e i

d e q< <



Ynùifùk

Ya trdtd ma akinktrdr ds nkcftumas ma ns dmns e y i, y `ds lamfmds ma` äkcu`n

Inln inknialns `ds lamfmds ma mns äkcu`ns, pnmalns hd``dr θ dsì:

θ < 48?¿ ’ (=1¿ + 2?¿) < 31¿

_drd idìu`dr `ds `nkcftumas ma `ns `dmns e y i, dp`fidlns `d ày ma sakns.

2?º =1º

=,2

sak sak

e< ùacn

=,2 2?º1,29

=1º

sake

sak< <

Dmaläs,31º =1º

=,2

sak sak

i< ùacn

=,2 31º=,2

=1º

saki

sak< <

Ajalp`n

4. Uasn`var a` sfcufakta trfäkcu`n, sf d < =,27 δ < =1¿7 ε < 2?¿.

Cräbfid 21

5. Uasn`var a` trfäkcu`n, sf sdealns qua: d < 8,97 δ < 25¿, θ < 11¿

Ynùifùk



Hd``dr dhnrd, `ds `nkcftumas ma `ns `dmns:

11º 25º

8,9

sak sak

i< ùacn

8,9 11º3,3

25º

saki

sak< <

_nr ntrd pdrta,29º 25º

8,9

sak sak

e< ùacn

8,9 29º8,93

25º

sake

sak< <

9. Mns nesarvdmnras in`nidmns d 44? l ma mfstdkifd ak `ns puktns D yak `d nrf``d ma uk rìn, astäk lfrdkmn uk ären` ak `d nrf``d npuastd ak

puktn I. Lfmfarnk `ns äkcu`ns IDE y IED, y sus lamfmds buarnk =9¿ y raspaitfvdlakta. ¾D quæ mfstdkifd astä idmd nesarvdmnr ma` ären` ak a` `dnpuastn ma` rìn>

Ynùifùk

Ma `d bfcurd takalns: θ < 48?¿ ’ (=9¿ + 13¿) < 8?¿

=9º 8?º

44?

sak sak

IE< ùacn

44? =9º32,43

8?º

sakIE

sak< <

13º 8?ºsak sak 44? 13ºsak

Cräbfid 22



As maifr qua `ns nesarvdmnras astäk sftudmns d 32,43 y 69,23 l ma` ären` uefidmak `d nrf``d npuastd ma` rìn.

Yf ak uk trfäkcu`n sa inkniak úkfidlakta `ds `nkcftumas ma sus tras `dmns n `d

`nkcftumas ma mns ma sus `dmns y a` äkcu`n inlprakmfmn aktra a``ns, ak astns mnidsns kn pnmalns dp`fidr `d ày ma sakns pdrd rasn`var `ns trfäkcu`n y takmralnqua diumfr d ntrn rasu`tdmn flpnrtdkta qua sa ``dld a` tanrald ma` insakn.

Iudkmn sa inkniak `dmns ma uk trfäkcu`n y uk äkcu`n npuastn d ukn ma a``ns, sdp`fid `d ày ma sakns, parn pnmalns akinktrdr vdrfds sftudifnkas:

Yupnkcdlns qua d y e snk `ds `nkcftumas ma mns `dmns ma` trfäkcu`n DEI y qua u

äkcu`n δ as npuastn d` dmn d (δ as dcumn), y inksfmardlns d δ ak su pnsfifùk racuìnk a` saclaktn DI ma `nkcftum e inln `dmn bfkd` ma δ7 a` værtfia E maea astdr ad`cúk puktn ma` aja x, ak mfraiifùk pnsftfvd. Inln kns mdk a` `dmn d npuastn værtfia D, pnmalns nid`fzdr a` puktn E, trdzdkmn ink a` inlpäs uk drin ma nkcftud, ink iaktrn ak I7 `n iud` kns puama inkmuifr d iudtrn pnsfeàs rasu`tdmns:

Cräbfid 23

4. A` drin kn tnid d` aja x, y kn sa bnrld trfäkcu`n7 ak asta idsn, d`fktaktdr rasn`var a` prneàld, kns akinktrdlns ink ukd axprasfùkma `d bnrld sak ε ; 4 y ak asta idsn, kn axfsta trfäkcu`n.



Cräbfid 28

Cräbfid 26

Cräbfid 3?

=. A` drin inrtd d ds pdrtaspnsftfvds y kacdtfvdsma` aja x y sa bnrld ukúkfin trfäkcu`n.

9. A` drin inrtd d` aja x pnsftfvn ak mns puktnsmfstfktns y sa bnrldkmns trfäkcu`ns.

5. A` drin tnid tdkcakifd`-lakta d` aja x7 ak asta

idsn, sa bnrld uk úkfintrfäkcu`n raitäkcu`n,ink ε < 6?¿.



_drd iud`qufar trfäkcu`n, a` iudmrdmn ma ukn ma sus `dmns asfcud` d `d suld ma `ns iudmrdmns ma `ns ntrns mns `dmns, la-kns mns vaias a` prnmuitn ma asns mns dmns pnr a` insakn ma`äkcu`n inlprakmfmn aktra a``ns.

Ak sìlen`ns, takalns:

Cräbfid 34

d5 < e5 + i5 ’ 5ei ins δ

e5 < d5 + i5 ’ 5di ins ε

i5 < d5 + e5 ’ 5de ins θ

d5 < e5 + i5 ’ 5ei ins δ

]anrald ma` insakn


9



Ajalp`ns

4. Mns `dmns ma uk trfäkcu`n lfmak 3 y 1 l raspaitfvdlakta, y a` äkcinlprakmfmn aktra a``ns as =5¿. Hd``dr a` tariar `dmn.

Yn`uifùk

Inln maealns hd``dr a` tariar dmn ma` trfäkcu`n, dp`fidlns a` tanrald insakn:

5 5 53 1 5.(3).(1).ins =1º x < +

5 54,636 x < , ma mnkma 54,636 =.28 x l< <

@d `nkcftum ma` tariar `dmn as ma =.28 l.

5. Qk jdrmìk trfdkcu`dr tfaka `dmns qua lfmak =5, 1? y 29 l. Akinktrdlamfmd ma` äkcu`n laknr.

Yn`uifùk

Ak asta idsn, inknialns `ds `nkcftumas ma `ns tras `dmns ma` trfäkcu`maealns hd``dr pnr `n lakns, mns ma sus äkcu`ns7 a` tariarn rasu`tdräsuldr astns mns äkcu`ns y rastdr`ns ma 48?¿.

Dp`fidkmn a` tanrald ma` insakn, takalns:

5 5 529 =5 1? 5.(=5).(1?).ins d< +

Maspajdkmn ins δ takalns:5 5 5=5 1? 29

ins5.(=5).(1?)

d +

<

561ins d < as maifr qua ins ? ?3?598?61d



Dp`fidkmn insakn fkvarsn ma δ, netakalns:

4ins (?,?3?598?61)d <

81º,63599353d < ù 81º,18o5?ood < .

_drd hd``dr ntrn äkcu`n, dp`fidlns kuavdlakta a` tanrald ma` insakn dsì

5 5 5=5 29 1? 5.(29).(1?).ins e< +

Ma mnkma5 5 5

29 1? =5ins5.(29).(1?)

e + <

=3?1

ins ?,3=385196329??

e < < , as maifr, qua

4ins (?,3=2851963)e <

X =4º,28983584e < n5 5 5

ins5

e i d

eid

+ <

Inln yd inknialns mns äkcu`ns ma` trfäkcu`n, a` tariarn `n akinktrdlnrastäkmn`a `d suld ma `ns mns d 48?¿, dsì:

48?º ( )q d e< +

5 5 5

4ins ( )5

e i d

eid +

<

@uacn a` äkcu`n laknr as =4º,=4o5ooe <

A` tariar äkcu`n tdlefæk n pnmralns hd``dr, dp`fidkmn a` tanrald ma` insak



Cräbfid 35

Yupnkcdlns qua δ as uk äkcu`n dcumn. Yf trdzdlns `d parpakmfiu`dr mma a` værtfia I d` `dmn DE, netakalns mns trfäkcu`ns raitäkcu`ns, trfäkc

DMI y trfäkcu`n EMI 7 maknlfkalns `ds `nkcftumas:

IM h<

DM x<

ME i x<

Inksfmardkmn `ns mns trfäkcu`ns raitäkcu`ns y dp`fidkmn a` tanrald _ftäcnrds, takalns:

5 5 5

h e x< y5 5 5( )h d i x<

Fcud`dkmn `ds axprasfnkas ma h5, takalns:

5 5 5 5( )d i x e x < , `uacn:

5 5 5 5( )d e x i x< +

5 5 5 5 55d e x i ix x< + +

5 5 5 5d e i ix< +

Hdralns ukd malnstrdifùk pdrifd` ma` tanrald ma` insakn, edsäkmnkak a` trfäkcu`n ma `d bfcurd qua inrraspnkma d` trfäkcu`n DEI .



Ak a` trfäkcu`n DMI , takalns:

Ma mnkma .ins x e d< , raalp`dzdkmn a` vd`nr ma x ak `d fcud`mdm

5 5 5 5d e i ix< + , takalns:

5 5 5 5 insd e i ie d< +

Iudkmn kaiasftdlns hd``dr `d lamfmd ma uk äkcu`n, maspajdlns

5 5 5

ins

5

e i d

ei

d +

<

y ùacn dp`fidlns insakn fkvarsn pdrd hd``dr δ

5 5 5

4ins ( )5

e i d

eid +

<

Ak d`cukns prneàlds, as kaiasdrfn inlefkdr astns mns rasu`tdmns,`d ày ma sakns y a` tanrald ma` insakn pdrd rasn`var`ns.Yù`n `d präitfid kns mdrä a` mnlfkfn kaiasdrfn, pdrd ldkajdrdprnpfdmdlakta astns rasu`tdmns.

Ajalp`ns

4. @ds nkcftumas ma ns dmns ma uk trfäkcu`n snk 9=, 59 y =5 il. Matarlfkd

d. @d lamfmd ma` äkcu`n laknr.



Ynùifùk

Qsdkmn a` tanrald ma` insakn, takalns qua:

19,6= 19º 12½11.99½½d < <

5 5 559 =5 9=ins

5.(59).(=5)d

+ <

ins δ < ?,1887 δ < ins -4 (?,188), ma mnkma

19,6= 19º 12½11.99½½d < <

Maealns hd``dr `d lamfmd ma ntrn äkcu`n, pdrd `n iud` pnmalns dp`fidày ma` sakn, dsì:

. .

5

d e sak

D

e

< ùacn,

(59) 19º 12½11.99½½

9=

saksak e <

@uacn, ?,1=26sak e < , ma mnkma 4sfk (?,1=26)e <

99.4116 99º 6½54.=8½½e < <

_drd netakar a` tariar dkcu`n θ hdialns

θ < 48?¿ ’ (19¿ 12‖ 11,99‖‖ + 99¿ 6‖ 54,=8‖‖) < 65,8615 < 65¿ 16‖ =9,



_drd sn`uifnkdr `d pdrta e, usdlns `d bùrlu`d:

yd vfstd y takalns:

59.=5. 19º 12½11.99½½

5

sak D <

596?,1? D il<

_drd netakar a` ärad, sa puama varfbfidr, usdkmn iud`qufard ma ds nkcftuma

ma mns `dmns y a` äkcu`n inlprakmfmn aktra a``ns.

5. Ink `d fkbnrldifùk mdmd, rasn`var a` trfäkcu`n:

d. d < 2,=, e < =,3 y δ<=5¿

=5º

=,3 2, =

sak sake<

Aktnkias:

=,3 =5

2,=

saksak e <

4

?,=649

sfk (?, =649)

56º 51½11.8½½

sak e

e

e

<

<

<

Cräbfid 39



_drd hd``dr `d lamfmd ma` tariar äkcu`n, hdialns:

θ < 48? ’ (=5¿ + 56¿ 51‖11.8‖‖) < 4?8¿ 9=‖ =.5‖v

Kns bd`td hd``dr `d `nkcftum ma` `dmn i, pdrd `n iud` dp`fidlns a` trald ma sakn:

2,= 4?8º9=½=.5½½2,=

=5º

saki

sak<

6,?2i <

Tuamd dsì, rasua`tn a` trfäkcu`n.

e. d < =,1, e < 2,9 y θ < 2?¿

Ynùifùk

Inln inknialns mns `dmns ma` trfäkcu`n y a` äkcu`n inlprakmaktra a``ns, pnmalns dp`fidr a` tanrald ma` insakn pdrd hd``d`nkcftum ma` `dmn i dsì:

5 94,16i < , ma mnkma:

94, 16 1, 25i < <

_drd hd``dr a` vd`nr ma ntrn äkcu`n, pnmalns dp`fidr fkmfstfktdla`d ày ma sakns n a` tanrald ma` insakn.

Dp`fidkmn `d ày ma sakns, takalns:

1,25 =,1

2?ºsak sak d<



4. Ak idmd idsn rasn`var a` trfäkcu`n:

Ajarififns pdrd rairadr `d lakta

?,269=sak d <

as maifr, qua =9º 1=½4?½½d <

_drd hd``dr a` ntrn äkcu`n, hdialns

ε < 48? ’ (2?¿ + =9¿ 1=½ 4?½½) < 32¿ 1½ 1?‖‖,

y quamd dsì rasua`tn a` trfäkcu`n:

9=º, 34º , 5=dd e< < <

d.

e. =,1 2,9, 2?ºd e q< < < i. 9,= 5,8, 85ºe i d< < < m. =9 95, 16ºd i e< < < a. 8,= 5,3, 3,9d e i du< < < b. =?8 512, 589d e i< < <

4



Cräbfid 3=

3. Masma uk ifartn puktn ma` tarrakn, sa lfrd d `n d`tn ma ukd lnktdôd y`d vfsud` bnrld uk äkcu`n ma 1?¿ ink a` sua`n. D` d`ajdrsa 5?? l ma `dlnktdôd, `d vfsud` bnrld uk äkcu`n ma 91¿ ink a` sua`n. Hd``dr `d d`turd,h ma `d lnktdôd

5. Qk pamdzn ma d`dlera ma 2? il as mne`dmn ak bnrld trfdkcu`dr. Akink-trdr `ns äkcu`ns ma` trfäkcu`n, sf mns ma sus `dmns lfmak 5= y 5? il.

9. Mns nesarvdmnras in`nidmns ak ns puktns D y E d ukd mfstdkifd ma 44? lak d nrf``d ma uk rìn, astäk lfrdkmn ukd tnrra sftudmd ak d nrf``d npuastdak uk puktn I. Lfmfarnk `ns äkcu`ns IDE y IED iuyds lamfmds buarnk=9¿ y 13¿ raspaitfvdlakta. ¾D quæ mfstdkifd astä idmd nesarvdmnr ma `dtnrra>

=. Qk pnsta vartfid` ma 9 l prnyaitd ukd snlerd ma 5 l7 ¾quæ d`turd tfakauk ären` qua d `d lfsld hnrd, prnyaitd ukd snlerd ma =,1 l>

1. Masirfed d ay ma ns sakns y a` tanrald ma` insakn, usdkmn úkfidlaktapd`derds.

2. Masma uk puktn D ma` sua`n sa nesarvd ukd tnrra, _T, y sa `d va edjn ukäkcu`n ma 94¿. Ya dvdkzd =? l ak mfraiifùk d d tnrra, sa lfrd y sa d va,dhnrd, edjn uk äkcu`n ma 18¿. Hd``dr `d d`turd h ma `d tnrra y `d mfstdkifd

ma D d` pfa, T, ma `d tnrra.



Ynùifùk

Maspajdlns:

4

5sak q <

4 4sfk

5q

< ó

p

Ajalp`n

4. Uasn`var `d aiudifùk 5 9ins

=t <

Vd halns vfstn qua `ds fmaktfmdmas trfcnknlætrfids snk aiudifnkasqua sa sdtfsbdiak pdrd tnmns `ns kúlarns radàs n vd`nras ma `nsäkcu`ns ak `ns iudàs idmd lfalern ma `d aiudifùk astä mabfkfmn.

Dhnrd, astumfdralns aiudifnkas trfcnknlætrfids qua sa sdtfsbdiakúkfidlakta pdrd d`cukns vd`nras pdrtfiu`dras ma `d vdrfdeà. @nslætnmns alpàdmns pdrd d snùifùk ma astds aiudifnkas trfcnknlæ-trfids snk sflf`dras d `ns alpàdmns ak `d rasnùifùk ma aiudifnkasd`caerdfids. Ak d`cukns idsns, sa usdk ds fmaktfmdmas trfcnknlætrfidspdrd netakar aiudifnkas aqufvdàktas.

Aiudifnkas trfcnknlætrfids


=Aiudifùk trfcnknlætrfid _drta4. Murdifùk: 2:5= lfk.

Aiudifùk trfcnknlætrfid _drta5. Murdifùk: 1:16 lfk.



Astd as ukd snùifùk ma `d aiudifùk dktarfnr. _arn sf hdy ukd snùifùkukd aiudifùk trfcnknlætrfid, aktnkias hdy fkbfkftds snùifnkas. Ak aidsn, pnr `d parfnmfifmdm ma `d bukifùk sakn, `d bnrld pdrd netakar tn

`ds snùifnkas, as:

5 ,2

g mnkma g as uk aktarnp

q p< + ,

parn d snùifùk netakfmd drrfed, as `d úkfid qua sa akiuaktrd ak a` fktarv

.

5. Uasn`var `d aiudifùk 5 9ins ? 5

=t pdrd t p<

Ynùifùk

Idìu`dlns `ds rdìias iudmrdmds, netakfakmn9 9

ins= 5

t < ´ <

rasn`vfakmn takalns qua 4 9ins5

t < ó ó

ma mnkma 442 2

t y t p p

< <

y dmaläs,9

ins5

t < ma mnkma sa netfaka 4 9ins

5t

< ó ó

ma mnkma1 3

2 2t y t

p p< < .

@uacn hdy iudtrn snùifnkas pdrd d aiudifùk ak a` fktarvd`n ? 5t p , iuvd`nras snk:



9. Uasn`var `d aiudifùk 5 5sai 4 tdk ? 5 pdrdq q q p< + .

Ynùifùk

Qtf`fzdlns `d fmaktfmdm 5 5sai 4 tdkq q< + y `d aiudifùk kns quamd:

54 tdk tdk 4q q+ < 7 idkia`dkmn ukn ak dlens `dmns takalns:

5tdk tdk ?q q < , sf bditnrfzdlns tdk θ, sa netfaka:

( )tdk tdk 4 ?q q < , ma mnkma netakalns `ds aiudifnkas:

tdk ? tdk 4 ? yq q< < .

Uasn`valns tdk ?q < y netakalns ?,q q p< <

Yf rasn`valns tdk 4q < netakalns `ns vd`nras 1,

= =

p pq q< < ,

ùacn `ds snùifnkas ma `d aiudifùk ak a` fktarvd`n ? 5q p sn

=. Hd``dr tnmds `ds snùifnkas ma `d aiudifùk .

Ynùifùk

, as maifr, qua ma mnkma

Inln kn hdy fktarvd`n ma rastrfiifùk pdrd a` äkcu`n θ, pnmalns hd``dr tnm`ds snùifnkas ma `d aiudifùk7 ak vfrtum ma `d parfnmfifmdm ma` sakn, `dsnùifnkas sa netfakak dsì:



3 5 85 5

9 9 9 9

49 5 4== =9 9 9 9

46 5 5?2 2

9 9 9 9

p p p pp p

p p p pp p

p p p pp p

+ < + <

+ < + <

+ < + <

Mdkmn vd`nras d g , netakalns fkbfkftds snùifnkas inln pnr ajalp`n:

Halns hd``dmn safs snùifnkas läs, mäkmnà vd`nras d g < 4, 5, 9

1. Hd``dr `ds snùifnkas ma `d aiudifùk 5 9 ? ? 5ins pdrdq q p+ <

Ynùifùk

9

5ins q

<

4 9 1 3ins

5 2 2n

p pq q

ó< < < ó

_nmalns var qua `ds snùifnkas sa akiuaktrdk ak a` sacukmn y ak a` tariudmrdkta, puas ma `d aiudifùk valns qua a` ins θ as kacdtfvn.

2. Uasn`var `d aiudifùk 5 ? ? 5sak sak pdrdq q q p+ <

Ynùifùk

Bditnrfzdkmn, takalns ( 4) ?sak sakq q + < , ma mnkma:

? 4sak n sakq q< <

Uasn`vfakmn ?sakq < , takalns ? 5 yq q p q p< < <

Uasn`vfakmn 4sak q < takalns9

5

pq < 7 ùacn `ds snùifnkas ma

aiudifùk ak a` fktarvd`n mdmn snk:



Ya puama varfbfidr qua `d aiudifùk sa sdtfsbdia ink astns vd`nras,utf`fzdkmn `d id`iu`dmnrd.

3. 55 4 ins ? 5sak pdrdq q q p< +

Yn`uifùk

Dcrupalns tnmns `ns tærlfkns ak a` prflar `dmn y quamd:

55 ins 4 ?sak q q <

_nmalns axprasdr tnmn ak tærlfkns ma ins θ, pdrd n iud` usdlns d fmaktfmdbukmdlaktd` 5 54 inssak q q< y `d aiudifùk kns quamd:

55 ( 4 ) ins 4 ?ins q q <

Abaitudkmn `ds npardifnkas kns quamd: 55 ins 4 ?ins q q+ <

Maealns rasn`var astd aiudifùk iudmrätfid7 dp`fidkmn `d bùrlu`d cakard`tnldkmn inln fkiùckftd ins θ netakalns:

(5 ins 4)(5 5) ?sakq q+ < . Uaalp`dzdkmn `ns vd`nras ma `d aiudifùtakalns:

54 4 =(5)( 4)ins

5(5)q

< . Ma mnkma sa netfaka

4ins ins 45

nq q< <

Uasn`vfakmn 4ins

5q < takalns 1

9 9n

p pq q< <

Uasn`vfakmn ins 4q < takalns q p<



Uasn`var `ds sfcufaktas aiudifnkas trfcnknlætrfids pdrd ? 5q p .

4. ins 4q <

5. 5tdk 4q <

9. (5 ins 4)(5 5) ?sakq q+ <

=. 5tdk 9 tdkq q<

1. 5sai 4 tdkq q< +

2. 5= 9 ?sak q <

3. 55 ins ins ?q q <

8. 5sak q <

6. 5 ins 4 ?q + <

4?. tdk sai 4q q+ <

4



Qtf`fia `d idìu`dmnrd pdrd hd``dr `ns sfcufaktas rasu`tdmns:

4. 4sfk (?, =885)

5. 4sfk (?, 532=)

9. 4ins (?, =885)

=. 4ins (?, 532=)

1. 4tdk (?, =9=2)

2. 4tdk (5, 399)

3. 4sai (5, ?89)

8. 4ins (4, 512)i

6. 4sai ( 4, 512)

_drd bfkd`fzdr astd saiifùk, prasaktdlns d`cukns rasu`tdmnsy bùrlu`ds útfàs pdrd masdrrn``dr prneàlds dp`fidmns.Astns talds puamak sar inksu`tdmns y dlp`fdmns madiuarmn ink `ds kaiasfmdmas ma idmd inktaxtn.

5



Bùrlu`ds ma dmfifùk pdrd `d bukifùk sakn

4. ( ) .ins ins .sak D E sakD E D sakE+ < +

5. ( ) .ins ins .sak D E sakD E D sakE <

Bùrlu`ds ma dmfifùk pdrd `d bukifùk insakn

4. ins( ) ins .ins . D E D E sakD sakE+ <

5. ins( ) ins .ins . D E D E sakD sakE < +

Bùrlu`ds ma dmfifùk pdrd `d bukifùk tdkcakta

4. tdk tdk

tdk( )4 tdk . tdk

D E D E

D E

++ <

5. tdk tdk

tdk( )4 tdk . tdk

D E D E

D E <

+

Bùrlu`ds ma dmfifùk pdrd `ds bukifnkas


1



Ajalp`ns

4. Masdrrn``dr sak (5 x) ak tærlfkns ma sak x y ins x.

Ynùifùk

Dp`fidkmn `d bukifùk ma dmfifùk pdrd a` sakn, takalns:

5 ( )

.ins ins .

5 .ins

sak x sak x x

sakx x x sakx

sakx x

< +

< +

<

@uacn 5 5 .inssak x sakx x<

5. Idìu`dr: 2? (5 9?) (9? 9?)sak sak sak< < +

Ynùifùk

2? (5 9?) (9? 9?)

4 9 95. 9?.ins 9? 5( )( )

5 5 5

sak sak sak

sak

< < +

< < <

9. Masdrrn``dr ak tærlfkns ma ins x `d axprasfùk ins 5 x

Ynùifùk

Dp`fidkmn `d bùrlu`d ma dmfifùk pdrd a` insakn, takalns:

5 5 5 5

5

ins 5 ins( )

ins .ins .

ins ins (4 ins )

5 ins 4

x x x

x x sakx sakx

x sak x x x

x

< +

<

< <

<



@uacn

5 5

tdk 45? tdk (5 2? )

5 tdk 2? 5 9 5 9 954 tdk 2? 4 ( 9)

<

< < < <

=. Asirfefr tdk 5 x ak tærlfkns ma tdk x.

Ynùifùk

Qsdkmn `d bùrlu`d ma dmfifùk pdrd tdkcakta, takalns:

5

tdk tdk 5 tdktdk 5 tdk ( )

4 tdk tdk 4 tdk

x x x x x x

x x x

+< + < <

@uacn

5

5tdktdk 5

4 tdk

x x

x

<

1. Idìu`dr tdk 45?¿

Ynùifùk

5 5

tdk 45? tdk (5 2? )

5 tdk 2? 5 9 5 99

54 tdk 2? 4 ( 9)

<

< < < <

Ntrn rasu`tdmn ma crdk utf`fmdm iudkmn sa trdtd ma hd``dra` ärad ma uk trfäkcu`n, as `d bùrlu`d ma Harùk.



Ajalp`n

@ns `dmns ma uk trfäkcu`n lfmak 8, 4? y 45 l raspaitfvdlakta. Hd``dr a` ärama` trfäkcu`n.

Yn`uifùk

_rflarn id`iu`dlns a` salfparìlatrn5

d e is

+ +< raalp`dzdkmn p

`ds `nkcftumas ma `ns `dmns, takalns:

8 4? 45 9?41

5 5s

+ +< < <

Dp`fidkmn `d bùrlu`d ma Harùk pdrd a` ärad, takalns:

41(41 8)(41 4?)(41 45) D <

Yf `ds `nkcftumas ma `ns `dmns ma uk trfäkcu`n snk d, e, i,

raspaitfvdlakta.

A` salfparìlatrn ma` trfäkcu`n vfaka mdmn pnr5

d e is

+ +< y a` ärad

ma` trfäkcu`n astä mdmd pnr `d axprasfùk:

( )( )( ) D s s d s e s i<

Astd bùrlu`d parlfta hd``dr a` ärad ma iud`qufar trfäkcu`n, inknifakmn `ds`nkcftumas ma sus `dmns.

Bùrlu`d ma Harnk

Qkfmdm 1. Dp fidifnkas ma `d trfcnknlatrìd Yasfùk

2



5. Qk jdrmìk trfdkcu`dr tfaka `dmns qua lfmak =5, 1? y 29 l. Akinktrdrärad ma` jdrmìk.

4. Ak `ns sfcufaktas ajarififns, sa mdk `ds `nkcftumas ma `ns `dmns ma uk trfäkcu Dp`fqua `d bùrlu`d ma Harnk pdrd hd``dr a` ärad ma` trfäkcu`n.

d. d < 48,3 e < 45,2 i < 43,6

e. d < 951 e < 592 i < =44

i. d < 1,6 e < 2,3 i < 4?,9

4



4. Qkd tnrra ma 491 pfas ma d`turd sa `nid`fzdak `d nrf``d ma uk `dcn. Masma `d puktd ma `dtnrra, a` äkcu`n ma maprasfùk ma uk nejatnak `d nrf``d ma` `dmn npuastn ma` `dcn as ma92¿. @d mfstdkifd d trdvæs ma` `dcn as:

d. 423 pfas e. 481,84 pfas i. 95,123 pfas m. 459,9= pfas

5. Masma uk puktn d 41 l snera a` kfva` ma` sua`n, uk tnpùcrdbnnetfaka ukd lamfmd ma28¿ pdrd a` äkcu`n ma maprasfùk ma uknejatn snera a` sua`n.

@d mfstdkifd ma` nejatn d` puktn snera a` sua`n qua astämfraitdlakta maedjn ma` tnpùcrdbn.

d. 3.83 l e. 6.=9 l i. 2.?2 l m. =.32 l

9. Qk ideà astä sujatn ak `n d`tn ma ukd dktakd ma rdmfn y d ukpuktn ak a` sua`n hnrfznktd`, qua astä d =? l ma `d edsa ma `ddktakd. Yf a` ideà bnrld uk äkcu`n ma 18¿ snera a` sua`n, `d`nkcftum ma` ideà as.

d. 31,=8 l e. 21,68 l i. 83,1= l

m 1= 59 l



=. Lfaktrds vua`d d ukd d`turd ma 4??? l, uk pf`ntn nesarvd qua a`äkcu`n ma maprasfùk hdstd a` darnpuartn as ma 9?¿. @d mfstdkifdd` darnpuartn as.

d. 4123 l e. 42?6 l i. 4395,1 l m. 481?.5 l

1. Matarlfka `d mfstdkifd aktra uk c`nen y uk edrin, sf a` äkcu`n

ma maprasfùk masma a` c`nen hdstd a` edrin as ma 9?¿ y a` c`nenastä d ukd mfstdkifd vartfid` ma ma 1?? l ma` edrin.

d. 4681 l e. 4321 l i. 4??? l m. 481? l

2. Mdmn uk trfäkcu`n y `d ifriukbarakifd fksirftd ma rdmfn r , axprasdrr ak tærlfkns ma `ns `dmns d, e, i ma` trfäkcu`n.

3. Ink `d fkbnrldifùk mdmd ak idmd idsn, rasn`var a` trfäkcu`n:

d. 9=º , 34º , 5=dd e< < <

e. 59, =1º , 9?ºe e q< < <

i. 52,1º , 95.3º , 483ed e< < <

m. 6,1, 491º , 9?ºd d e< < <



8. Qk idlpn ma bnrld trfdkcu`dr tfaka `dmns qua lfmak 545,511 y 428

l. a` ärad ma` idlpn as.

d. 4686? l e. 48321 l i. 4?=12 l m. 43264 l

6. @ns dmns ma uk tarrakn trfdkcu`dr lfmak 5=?, 42? y 48= l. Yf a` instn

pnr latrn iudmrdmn ma tarrakn as $=?.???. A` instn ma` tarrakn as.

d. $ 188½1?3.2?? e. $ 288½1?3.2?? i. $ 118½1?3.2?? m. $ 128½1?3.2??

4?. @ns axtralns ma `ns erdzns ma uk inlpäs mfstdk 2 il y idmd erdzn

lfma4= il. A` äkcu`n qua bnrldk `ns mns erdzns.

d. =1¿ e. 48,9¿ i. 4?=¿ m. 5=.3¿

44. Ak ukd ifriukbarakifd ma 2 l ma rdmfn, sa

ukak mns ma sus puktns ink ukd iuarmdma = l. `d lamfmd ma` äkcu`n iaktrd`

inrraspnkmfakta iftdmd iuarmd.

d. =1¿ e. 98,6=¿ i. 4?=¿

m 83¿



Qk puktn _ ma` p`dkn sa matarlfkd lamfdkta susinnrmakdmds qua inksfstak ak ukd pdrajd nrmakdmd ( x, y),ma` p`dkn7 `d prflard inlpnkakta sa ``dld `d desifsd y `d

sacukmd inlpnkakta sa ``dld `d nrmakdmd. Ak `ns iursnsdktarfnras, halns dprakmfmn d nid`fzdr puktns ma` p`dkn,`n iud` kns bdif`ftdrä a` trdzdmn y a` astumfn ma `ds cräbfids.

Ajalp`n

Ak `d cräbfid, nesarvdlns iudtrn puktns ma` p`dkn, iuyds innrmakdmds snk:

Cräbfid 31

Uaitds ak a` p`dkn

Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn Yasfùk

4



Yf dkd`fzdlns a` puktn (1/5,-9), valns qua su desifsd n prflard inlpnkakta as 1/`n iud` qufara maifr qua a` puktn sa hd``d d ukd mfstdkifd ma 1/5 ak mfraiifùk hnr

znktd` hdifd `d maraihd. ]dlefæk valns qua su nrmakdmd n sacukmd inlpnkakas -9, `n iud` sfckfbfid qua a` puktn sa akiuaktrd d ukd mfstdkifd ma 9 ukfmdmas a

mfraiifùk hdifd dedjn, inln sa va ak `d cräbfid.

@ns puktns iuyd desifsd as iarn, sa akiuaktrdk snera a` aja vartfid` n aja y, pajalp`n: `ns puktns (?,?), (?,2), (?,-1), astäk `nid`fzdmns snera a` aja vartfid`.

@ns puktns iuyd nrmakdmd as iarn, sa akiuaktrdk snera a` hnrfznktd` n aja x, pajalp`n: `ns puktns (?,?), (=,?), (-3/5,?), astäk uefidmns snera a` aja hnrfznktd`.

]rdzdr ak idmd idsn, `d raitd qua pdsd pnr idmd pdr ma puktns:

4. (-5,4) y (9,1)

5. (-9,=) y (=,=)

9. (-4,1) y (2,-5)

=. (-5,4) y (-5, 1)

1. (?,?) y (1,1)

2. (?,2) y (3,?)

4



Yf takalns mns puktns _ y T, ak a` p`dkn ink innrmakdmds

5 5 55 4 5 4( ) ( )m x x y y< +

@d mfstdkifd aktra _ y T astä mdmd pnr:

5 55 4 5 4( ) ( )m x x y y< +

Ak `d cräbfid 3? valns qua a` trfäkcu`n _TU as raitäkcu`n, ink5 _U x <

TU y y

Cräbfid 32

Mfstdkifd aktra mns puktns


5



Ajalp`ns

Yf axtrdalns `d rdìz iudmrdmd ak dlens `dmns ma astd fcud`mdm, sa netfaka:

5 55 4 5 4( ) ( )m x x y y< +

qua as `d bùrlu`d qua sa utf`fzd pdrd hd``dr `d mfstdkifd aktra mns puktns ma` p`dkn

4. Hd``dr `d mfstdkifd aktra `ns puktns (4,5) y (9.3):

Ynùifùk

5 5(9 4) (3 5)m < +

56 1,98142=8?3...m <

@d mfstdkifd aktra _ y T as uk kúlarn frrdifnkd`. Astns kúlarns dpdraiak inbraiuakifd, iudkmn idìu`dlns mfstdkifds aktra mns puktns ma` p`dkn.

5. Hd``dr `d mfstdkifd aktra `ns mns puktns (-=, -4) y (9, 8):

Ynùifùk

() (5 5

3 6m < +

() (5 5

3 6m < +

49? 44, =?431=51...m <

9. Hd``dr `d mfstdkifd aktra `ns mns puktns (?,3) y (=, ?):

Ynùifùk



42 =6 21 8, ?255133=8...m < + <

=. Hd``dr `d mfstdkifd aktra `ns mns puktns (-5,9) y (=,-=):

Ynùifùk

( )5

5= ( 5) ( = 9)m < +

92 =6 81 6, 5461===13...m < + <

1. Hd``dr a` parìlatrn ma` trfäkcu`n iuyns værtfias astäk ak `ns puktns (?,-4), (?y (=,-4):

Ynùifùk

A` parìlatrn as `d suld ma `ds `nkcftumas ma `ns `dmns ma` trfäkcu`n, ùacn mealns hd``dr `d `nkcftum ma idmd `dmn ma` trfäkcu`n y hdiar `d suld.

5 54 (? ?) ( 4 5)m < +

4 ? 6 6 9m < + < <

5 5

5 (= ?) (( 4 ( 4))m < +

5 42 ? =m < + <

5 5

9 (= ?) ( 4 5)m < +

_nr n tdktn, a` parìlatrn as:



4. Akinktrdr `ds innrmakdmds ma` puktn lamfn ma` saclaktn iuyns axtralnsnk (5,=) y (8,=), y hdiar a` cräbfin.

Yn`uifùk: a` puktn lamfn vfaka mdmn pnr:

(4 5 4 5 5 8 = =1 =

x x y y_

+ + + +

Ajalp`ns

Yf inknialns ns axtralns ma uk saclaktn raitn, pnmalns hd``dr innrmakdmds ma su puktn lamfn. Yf ns puktns axtralns ma` saclaksnk ( x4, y4) y ( x5, y5) aktnkias `ds innrmakdmds ma` puktn lamfn:

4 5 4 5,

5 5l

x x y y_

+ +< ó

ó

Cräbfid 33

Innrmakdmds ma` puktn lamfn


9



( )( )5 5

5 ? ( =) 4 ( 5) 1m < + <

5 54 (= ?) (= 4) 1m < + <

Hd``dr a` puktn lamfn ma `ns saclaktns iuyns axtralns snk `ns puktns mdmns`uacn varfbfidr `d mfstdkifd ma` puktn lamfn d idmd axtraln ma` saclaktn. Hdi`d cräbfid inrraspnkmfakta.

4. (-9, =) y (1, 5)

5. (-8, 5) y (-5,4)

_nmalns varfbfidr, hd``dkmn `d mfstdkifd ma` puktn lamfn d idmd axtrama` saclaktn dsì:

5 54 (1 5) (= =) 9m < + <

Hd``dkmn `d mfstdkifd ma` puktn lamfn d` ntrn axtraln, takalns:

5 55 (8 1) (= =) 9m < + <

5. Hd``dr a` puktn lamfn ma` saclaktn iuyns axtralns snk (-=, -5) y (=,=):

Yn`uifùk: (4 5 4 5 = = = 5, , ?,4

5 5 5 5l

x x y y_

+ + < < < ó ó

ó ó

_nmalns varfbfidr, hd``dkmn `d mfstdkifd ma` puktn lamfn d idmd axtrama` saclaktn dsì:

=. (-9,-=) y (-5, 2)

1. (-=, -1) y (-=, 1)

4



Ydealns qua ak a` p`dkn, mns puktns matarlfkdk ukd raitd, iudkmninknialns `ds innrmakdmds ( x4, y4) y ( x5, y5) y as pnsfe`a trdzdr `d raitd @qua pdsd pnr asns puktns.

]dlefæk pnmalns hd``dr ukd lamfmd pdrd `d fki`fkdifùk ma `d raitd @,sf inknialns `ds innrmakdmds ma mns ma sus puktns7 astd fki`fkdifùk `d``dldlns pakmfakta ma `d raitd.

Yf @ as ukd raitd qua pdsd pnr `ns puktns ( x4, y4) y ( x5, y5) `d pakmfakta ma

astd raitd @ astä mdmd pnr:5 4

5 4

y yl

x x<

Ralns qua `d pakmfakta as a` inifakta ma` dvdkia vartfi y

5 ’

y

4 snera a` dvdkia hrfznktd` x5 ’ x4 aktra astnmns puktns ma `d raitd.

A` vd`nr ma `d pakmfakpuama sar pnsftfvn, kcdtfvn n iarn. Hdy raitiuyd pakmfakta kn as

_akmfakta ma ukd raitd


= Dprakmfakmn ink a` prnba Ju`fnAiudifùk ink `d pakmfakta ma ukd raitdMurdifùk: =:18 lfk.



Ajalp`n

Hd``dr `d pakmfakta ma `d raitd qua pdsd pnr `ns puktns:

4. (-4, -4) y (9, 1)

Yn`uifùk

5 4

5 4

1 ( 4) 2 9

9 ( 4) = 5

y yl

x x

< < < <

Ma` vd`nr ma d pakmfakta, pnmalns var qua sf uk puktn snera d raitd dvd zd mns ukfmdmas ak mfraiifùk hnrfznktd` pnsftfvd, a` dvdkia vartfid` as tukfmdmas hdifd drrfed.

A` vd`nr ma `d pakmfakta ak asta idsn, kns mfn uk vd`nr pnsftfvn7 d` trdzdcräbfid, æstd prasaktd ukd mfraiifùk dsiakmakta ma fzqufarmd d maraihd.

5. (-5, 9) y (=, -4)

Yn`uifùk

5 4

5 4

4 9 = 5

= ( 5) 2 9

y y

l x x

< < < <

Ak asta idsn, `d pakmfakta as kacdtfvd y ma su vd`nr, pnmalns var qsf uk puktn snera `d raitd sa masp`dzd tras ukfmdmas hdifd `d maraihsu masp`dzdlfaktn vartfid` sarä ma mns ukfmdmas hdifd dedjn. Iudkmnpakmfakta as kacdtfvd `d cräbfid ma astd raitd as masiakmakta ma fzqufa



9. (-9, 5) y (=, 5)

Ynùifùk

5 4

5 4

5 5 ??

= ( 9) 3

y yl

x x< < < <

Ak asta idsn, `d pakmfakta vdà iarn y `d cräbfid kns luastrd ukd raitd pdrà`d d` aja x. Yf uk puktn sa masp`dzd snera d raitd, kn axparflaktd dsiakskf masiaksn.

Iudkmn ukd raitd as pdrdà`d d` aja y (raitd vartfid`), su pakmfakta asfkmatarlfkdmd y pnr asn maiflns qua su pakmfakta as fkmabfkfmd.

]akalns ukd raitd qua pdsd pnr `ns puktns (9,=) y (9, -5), d` fktaktdridìu`dr su pakmfakta, netakalns:

5 4

5 4

5 = 2

9 9 ?

y yl

x x

< < <

Inln kn sa puama mfvfmfr aktra iarn, kn axfsta uk vd`nr pdrd d pakmfaktal y pnr asn maiflns qua as fkmatarlfkdmd.

]nmd raitd pdrdà`d d` aja y su pakmfaktasnk fkmatarlfkdmds.



@d aiudifùk ma ukd cräbfid as dqua``d sdtfsbaihd sn`dlakta pnr innrmakdmds ma `ns puktns qua astäk ak `d cräbfid. Ma `n dktarftakalns:

Ajalp`n

Yf takalns `d aiudifùk 9 x + 5 y < 2, a` puktn _(5,?) astä snera `d cräbfid pusdtfsbdia `d aiudifùk pnrqua d` raalp`dzdr, takalns 9(5) + 5(?) < 2.

Ak idlefn, a` puktn (9,=) kn sa akiuaktrd snera d cräbfid, pnrqua d` raalp`dzsus innrmakdmds ak `d aiudifùk, takalns:

9(9) + 5(=) < 43, a` vd`nr netakfmn kn sdtfsbdia `d aiudifùk.

4. Yf uk puktn _( x, y) astä snera `d cräbfid, aktnkias `ds innrmakdmds sd-tfsbdiak su aiudifùk.

5. Yf uk puktn _( x, y) kn sa akiuaktrd snera `d cräbfid, aktnkias sus innr-makdmds kn sdtfsbdiak `d aiudifùk.

_drd netakar `d aiudifùk ma ukd raitd, sa utf`fzd a` haihn ma qua a` puktn( x4, y4) y a` vd`nr ma `d pakmfakta l, matarlfkdk ukd úkfid raitd.

Yad ( x, y) uk puktn iud`qufard ma d raitd mfbarakta ma` puktn ( x4, y4) aktnkias`d pakmfakta ma `d raitd as 4

4

y yl

x x< . Lu`tfp`fidkmn astd aiudifùk pnr

Aiudifnkas ma `d raitd ak a` p`dkn


1



4. Hd``dr `d aiudifùk ma `d raitd qua pdsd pnr a` puktn (5,9) y su pakmfakta l < =

Ynùifùk

Dp`fidkmn mfraitdlakta `d aiudifùk puktn pakmfakta, takalns:

(9 = 5 y x <

5. Qkd raitd pdsd pnr `ns puktns (-5,-=) y (4,9), hd``dr su aiudifùk puktpakmfakta:

Ynùifùk

Ak asta idsn, inknialns mns puktns ma `d raitd y pnr `n tdktn, pnmalnhd``dr su pakmfakta

9 ( =) 3

4 ( 5) 9l

< <

Inln inknialns mns puktns ma `d raitd, aàcflns iud`qufard ma a``ns pdasirfefr `d aiudifùk puktn pakmfakta ma `d raitd, dsì:

3( = ( 5)

4 4( ) y y l x x <

Astd aiudifùk sa ``dld `d aiudifùk puktn pakmfakta ma `d raitd y puamaasirfefrsa ak astd bnrld, sf sa inknia uk puktn pnr mnkma pdsd `d raitd ya` vd`nr ma su pakmfakta.

Ajalp`ns



n usdkmn a` ntrn puktn, netakalns `d aiudifùk:

inln ajarififn, sa puama inlprnedr qua d` trdspnkar tærlfkns ak

aiudifnkas dktarfnras, sa `àcd d ukd úkfid aiudifùk 3 9 5 x y <

9. Qkd raitd @ inrtd d` aja y ak a` puktn (?,=) y su pakmfakta l<-4/9. Hd``d aiudifùk ma `d raitd:

Ynùifùk

Yf dp`fidlns `d aiudifùk puktn pakmfakta, takalns:

n maspajdkmn y sa tfaka

Ak a` ajalp`n dktarfnr, dpdraia maspajdmd `d vdrfdeà y ak `d aiudifùk ma `d rai

astn kns `àvd d ntrd aiudifùk astäkmdr ma `d raitd ``dldmd `d aiudifùk pakmfakfktariaptn. Ak cakard`, sf ukd raitd @ inrtd d` aja y ak a` puktn (?,e) y su pakmfaas l, dp`fidkmn `d aiudifùk puktn pakmfakta takalns:

V maspajdkmn `d y, netakalns `d aiudifùk:

Ak astd aiudifùk ma `d raitd, pnmalns àar a` vd`nr ma `d pakmfakta l quaa` inabfifakta ma x, y `d nrmakdmd ak a` nrfcak, qua as `d mfstdkifd masma a` nrfchdstd a` puktn ma inrta ma `d raitd ink a` aja y, sf e as pnsftfvn, `d raitd inrtd d` y ak a` puktn (?,e) drrfed ma` nrfcak, sf e as iarn, `d raitd pdsd pnr a` nrfcak, sf e

kacdtfvn `d raitd pdsd pnr a` puktn (? e) pnr maedjn ma` nrfcak



Ajalp`n

?e el < <

4. @d raitd iuyd aiudifùk as y < 1 x ’ 5, tfaka pakmfakta 1 y inrtd d` aja y ak

puktn (?,-5).

5. Mdmd `d raitd iuyd aiudifùk as y ’ 4 < -9( x + =), hd``dr `d pakmfakta ma raitd y a` puktn ma inrta ink a` aja y.

Ynùifùk

Ak asta idsn, `d aiudifùk astä mdmd ak `d bnrld puktn pakmfakta, y ak a`pnmalns àar a` vd`nr ma `d pakmfakta l < -9. _drd hd``dr a` puktn ma inrink a` aja vartfid`, maspajdlns `d vdrfdeà y pdrd netakar `d aiudifùk ma raitd ak su bnrld pakmfakta fktariaptn, dsì:

y ’ 4 < -9( x + =)

y ’ 4 < -9 x ’ 45

y < -9 x ’ 44

Ma `d ú`tfld aiudifùk, pnmalns àar a` puktn ma inrta ma `d raitd ink a` avartfid` qua as a` puktn (?, -44)7 tdlefæk pnmalns àar `d pakmfakta l <-

9. Qkd raitd @ pdsd pnr `ns puktns (d,?) y (?,e). Hd``dr ukd aiudifùk pdrd asraitd:

Ynùifùk

Ak asta idsn, kns mdk a` puktn ma inrta ma `d raitd ink a` aja x qua as (d,y a` puktn ma inrta ink a` aja y qua as (?,e). @uacn pnmalns hd``dr d pamfakta



dp`fidkmn d aiudifùk puktn pakmfakta y usdkmn a` puktn (?,e), netakaln

( ?)e

y e xd

<

e y e x

d <

e x y e

d+ <

mfvfmfakmn pnr e ak dlens lfalerns ma `d aiudifùk, takalns:

4ex y

de e+ <

Ma mnkma:

4 x y

d e+ <

Ajalp`n 4

Astd ú`tfld as ukd aiudifùk flpnrtdkta ma `d raitd pnrqua maedjn maidmd vdrfde`a dpdraia a` vd`nr mnkma `d raitd inrtd d idmd ukn ma `ns ajasinnrmakdmns.

Yf takalns `d aiudifùk 41 9

x y+ < , astd raitd pdsd pnr `ns puktns (1,?

(?,9)7 astn kns parlfta trdzdr d raitd, hd``dr su pakmfakta, as maifr, fmaktfbfid



Ajalp`n 5

Asta as uk ajalp`n ma `d aiudifùk `fkad` cakard`:

Ak astd aiudifùk, D, E, I snk kúlarns (inkstdktas), dmaläs D y E kn snkiarn d` lfsln tfalpn

Hd``dr `d aiudifùk ma `d raitd qua pdsd pnr `ns puktns (-9,?) y ( ?,3):

Yn`uifùk

Inln inknialns `ns puktns ma inrta ma `d raitd ink idmd ukn ma `ns ajinnrmakdmns, pnmalns asirfefr fklamfdtdlakta `d aiudifùk ma `d raitd aastd bnrld:

Astd lfsld aiudifùk tdlefæk sa puama asirfefr ak ntrd ma `ds bnrlds yinknifmds, inln d bnrld puktn pakmfakta n d bnrld pakmfakta fktariapt

Qkd aiudifùk ma d bnrld , sa puama asirfefr ak ukd bnrld aqufv`akta ak pdrtfiu`dr, sf lu`tfp`fidlns astd aiudifùk pnr = y tnmns ns tærlfknsa pdsdk d` prflar `dmn. Aktnkias sa tfaka:

@uacn:



Ma `d aiudifùk `fkad` cakard`, sa puama maspajdr y pdrd netakar 19

5 y x< +

Astd aiudifùk as `d aiudifùk ma `d lfsld raitd ak su bnrld pakmfakta fktariapt

Uasulfakmn `d bnrld ma `ds aiudifnkas ma `d raitd, takalns:

4. Aiudifùk puktn pakmfakta:

4 4( )l x y y x <

5. Aiudifùk pakmfakta fktariaptn:

y lx e< +

9. Aiudifùk ma `ns inrtas ink idmd ukn ma `ns ajasinnrmakdmns:

4 x y

d e+ <

=. Aiudifùk `fkad` cakard`:

? Dx Ey I + <+

Astds iudtrn aiudifnkas kns parlftak matarlfkdr `ds idrditarìstfids maiud`qufar raitd, y sa puama inkvartfr ukd aiudifùk ma ukd bnrld d `d ntrd,sacúk `d fkbnrldifùk qua sa raqufard.



Akinktrdr `d pakmfakta y a` puktn ma inrta ink a` aja y ma `d raitd iuyaiudifùk as 12 5 ? x y <+ .

Ynùifùk

@d aiudifùk astä mdmd inln ukd aiudifùk fkad` cakard`: Dx Ey I + <+

Yf maspajdlns `d vdrfdeà y takalns:

Astd ú`tfld as `d aiudifùk pakmfakta fktariaptn, ink l < 9, e < 1/5, amaifr, `d raitd tfaka pakmfakta 9 y a` puktn ma inrta ink a` aja y as (?, 1/5

Ajalp`n

Akinktrdr `d aiudifùk ma `d raitd qua pdsd pnr `ns puktns (5,-9) y (9,-4)asirìed`d ak sus iudtrn bnrlds.

Ynùifùk

Ajalp`n

4. Rdlns d hd``dr `d aiudifùk puktn pakmfakta:

4 ( 9)

59 5l

< <

Yf tnldlns a` puktn (5,-9), d aiudifùk kns quamd: qua as d aiudifùma `d raitd ak su bnrld puktn pakmfakta.

5. _drd asirfefr d aiudifùk ak d bnrld pakmfakta fktariaptn, maspajdln`d vdrfdeà y, ink `n iud` netakalns: y < 5x ’ 3 qua as `d aiudifù

y < ’I + Dx

E



d. (9,=) l< 5

e. (5,9) l < 4

i. (4,-5) l < ?

m. (-5,9) l < =

a. (5,4) l < 4/5

b. (?,?) l < 1

9. _drd netakar `d aiudifùk `fkad` cakard`, pdsdlns tnmns `ns tærlfkns `d aiudifùk dktarfnr d` prflar `dmn y quamdk -5 x + y < -37 ak mnk D < -5, E < 4 y I < 3.

=. _drd hd``dr `d aiudifùk ma `ns inrtas ink idmd ukn ma `ns ajas innrmkdmns, tnldlns `d aiudifùk dktarfnr -5 x + y + 3 < ? y pdsdlns a` tlfkn 3 d` sacukmn dmn. Mfvfmfakmn dlens `dmns ma d aiudifùk pnr takalns:

54

3 3

x y < qua as `n lfsln qua

35

43

x y < , qua as

aiudifùk pamfmd. Ak a``d, valns qua a` puktn ma inrta ink a` aja x(3/5, ?) y a` puktn ma inrta ink a` aja y as (?, -3).

4. Asirfefr ak `d bnrld puktn pakmfakta, `d aiudifùk ma `d raitd qua pdsd pa` puktn mdmn ink `d pakmfakta fkmfidmd:

5. Akinktrdr d pakmfakta ma d raitd matarlfkdmd pnr ns puktns D(-9,1) E(4

4



9. Asirfefr idmd aiudifùk ak `d bnrld pakmfakta fktariaptn a fkmfqua, a` vd`nma `d pakmfakta y a` puktn ma inrta ma `d raitd ink a` aja y.

d. 9 x + y < =

e. 2 x ’ 9 y < 4

i. = x ’ 9 y ’ 3< ?

m. 1 x ’ 5 y + 4?< ?

a. x < 1 y + 9

=. Asirfefr d aiudifùk ma d raitd qua pdsd pnr ns mns puktns mdmns ak d bnrl Dx + Ey + I < ?

d. (-4, 5) y (5, -4)

e. (5, 9) y (9,5)

i. (4, 4) y (-4, -4)

m. (9, -=) y (?, ?)

a. (9, ?) y (?, -9)

1. Mdmds `ds sfcufaktas aiudifnkas ma raitds pdrd idmd ukd ma a``ds, asirfefr aiudifùk ma `ns inrtas a fkmfidr `ds innrmakdmds ma `ns puktns ma inrta inidmd ukn ma `ns ajas.

d. 5 x + 9 y < 2

e. -= x + 1 y < 5?

i. 49 x - 52 y < 15

m. x + 8 y < 5=



Aiudifnkas ma `ds raitds pdrdà`ds d

`ns ajas innrmakdmns:

Cräbfid 36

Ak cakard`, iud`qufar raitd pdrdà`d d` aja x tfaka inln aiudifùk y < g ,mnkma g as ukd inkstdkta qua puama tnldr vd`nr pnsftfvn, kacdtfvn niarn. @d aiudifùk ma` aja x pnr ajalp`n: as y < ?.

]nmd raitd pdrdà`d d` aja x tfaka pakmfakta iarn.

Yf ukd raitd pdsd pnr a` puktn (4,=) y as pdrdà`d d` aja x inln sa fùstrdak d cräbfid 35, tnmn puktn qua sa masp`dia snera asd raitd, astä d iudtrnukfmdmas ma` aja x n sad qua su mfstdkifd vartfid` ak a` p`dkn sfalpra as=, ma td` ldkard qua su aiudifùk as y < =.



Qkd raitd @ quapdsd pnr a` puktn(1, ?) pdrdà`d d`

aja y tfaka inlnaiudifùk x < 1,pnrqua iud`qufarpuktn qua sa mas-p`dia snera asd raitdtfaka inln prflarinlpnkakta x < 1.

Ak cakard`, ukd raitdpdrdà`d d` aja y tfa-ka inln aiudifùk x < g , mnkma g as ukvd`nr inkstdkta.

@d raitd x < -9 aspdrdà`d d` aja y.

Ak asa idsn, uk puk-tn qua sa masp`diasnera `d raitd, sfal-

pra sa akiuaktrd dtras ukfmdmas maàja, y yd sdealnsqua pdrd astd raitd,su pakmfakta as fk-matarlfkdmd.

Cräbfid 8?

Cräbfid 84



D` hde`dr ma pdrdà`fsln y par-

pakmfiu`drfmdm ma raitds ak a`p`dkn, n hdralns pdrd raitds qua kn takcdk`d lfsld mfraiifùk ma ns ajas innrmakdmns.

Iudkmn mns raitds mfbaraktas ak a` p`dkntfakak `d lfsld mfraiifùk, astds raitds knsa inrtdk y pnr asn maiflns qua snk pdrd-à`ds. _drd hde`dr ma lnmn läs bnrld` maraitds pdrdà`ds, utf`fzdralns a` inkiaptnma pakmfakta pnrqua æstd matarlfkd `dmfraiifùk ma `d raitd.

Ajalp`n

4. @ds raitds iuyds aiudifnkas snk:

y < 5 x + 9 y < 5 x + 5 y < 5 x + 4

Mns raitds @4 y @5 ink pakmfaktas l4 y l5 raspaitfvdlakta, snk pdrdà`ds sfl4 < l5, as maifr, a` vd`nr ma sus pakmfaktas as a` lfsln.

Uaitds pdrdà`ds y raitds

parpakmfiu`dras


2



Ynùifùk

@ds raitds snk pdrdà`ds pnrqua tfakak `d lfsld pakmfakta.

Nesarva iuä` cräbfid ma `d raitd y ’ 5 < 9( x + =) astä pnr akifld ma ds malälfaktrds qua d cräbfid ma d raitd y < 5 x ’ 5 astä pnr maedjn ma tnmds, d cräbfima y < 5 x pdsd pnr a` puktn (?,?).

5. @d aiudifùk ma `d raitd raitd @4 as y ’ 5 < 9( x + =) y `d aiudifùk ma `d raitd @

as -9 x + y < 8. Matarlfkdr sf `ds mns raitds snk pdrdà`ds.

Ynùifùk

@d aiudifùk ma @4 astä mdmd ak `d bnrld puktn pakmfakta, y valns qua vd`nr ma su pakmfakta as l < 9. @5 tfaka `d bnrld ma `d aiudifùk `fkad` cakrd`7 sf maspajdlns y netakalns y < 9 x + 8 qua as ukd aiudifùk ma `d bnrlpakmfakta fktariaptn, valns qua `d pakmfakta l < 9. D` sar fcud` a` vd`nr m

Cräbfid 85



_drd trdtdr a` inkiaptn ma parpakmfiu`drfmdm aktra raitds, tdlefæk alp`adlnspakmfakta.

Ajalp`n

Nesarvdr qua `ds raitds iuyds aiudifnkas snk y < x y @4 y @5 inrraspnkmak d raiparpakmfiu`dras.

@ns vd`nras ma sus pakmfaktas snk 4 y -4 raspaitfvdlakta. D` lu`tfp`fidr `ns vd`n

Cräbfid 89

Uaitds parpakmfiu`dras



Ak cakard`, takalns qua mns raitds @4 y @5 ink pakmfaktas:

y < l4 x y < l5 x

raspaitfvdlakta snk parpakmfiu`dras, sf l4 x l5 < -4.

Ma `d fcud`mdm l4 x l5 < -4, pnmalns maspajdr 4 5

5 4

4 4l y l

l l

< < aktnkia

pnmalns maifr qua mns raitds snk parpakmfiu`dras, iudkmn d pakmfakta ma ukd ma``ds as a` raiìprnin kacdtfvn ma `d pakmfakta ma `d ntrd.

Ajalp`ns

= ( 4)9

? 4l

< <

4. @ds raitds iuyds aiudifnkas snk 41 8 5

1 y x y x< < + snk rait

parpakmfiu`dras7 pnmalns var qua a` prnmuitn ma sus pakmfaktas md laknukn.

1(-4/1) < -4

5. Matarlfkdr sf ns puktns D(?, -=), E(4, -4), I (5, 5) astäk uefidmns ak d lfslraitd (snk in`fkadàs):

Ynùifùk

_rflarn, hd`àlns `d pakmfakta ma `d raitd qua pdsd pnr `ns puktns D(?, -y E(4, -4):



ùacn, hd`àlns `d pakmfakta ma `d raitd qua pdsd pnr `ns puktns E(4, -4I (5, 5).

4 59

4 5l

< <

inln `ds pakmfaktas snk fcudàs, pnmalns inkiùfr qua `ns puktns astäk `d lfsld raitd, as maifr, snk in`fkadàs.

9. Qkd raitd @ pdsd pnr `ns puktns (-9, 5) y (=, 1)7 hd``dr:

d. @d aiudifùk ma ukd raitd pdrdà`d d @ qua pdsa pnr a` puktn (4,5).

e. @d aiudifùk ma ukd raitd parpakmfiu`dr d @ qua pdsa pnr a` puk(-5,-9).

Ynùifùk

d. _rflarn maealns hd``dr `d pakmfakta ma @, puastn qua inknialns m

puktns ma `d raitd:

1 5 9

= ( 9) 3l

< <

@uacn, tnmd raitd qua sad pdrdà`d d @ maea takar inln pakmfakta 9

Aktnkias, `d aiudifùk pamfmd as (

9

5 43 y x <

.

e. ]nmd raitd parpakmfiu`dr d @ maea takar inln pakmfakta, a` raiìprnkacdtfvn ma 9/3 ù sad -3/97 inln pdsd pnr a` puktn (-5, -9), `d aiudipamfmd as:

(3

( 9) ( 5) y x < n 5 4l y e< <



4. A` mairaiflfaktn ma `d ainknlìd ak a` ú`tfln dôn sa matarlfkdlamfdkta ukd bukifùk fkad` qua pdsd pnr ns puktns (9,=) y (5, -1).@d bùrlu`d pdrd mfihd bukifùk `fkad` as:

d. B(x)< 9x-5

e. B(x)<-6x + 59

i. B(x)< 5x+ =1

m. B(x)<-x+9

5. @d bukifùk qua pdsd pnr a` puktn (5,9) y iuyd pakmfakta as = as:

d. B(x)< =x-1 e. B(x)<-5x+=

i. B(x)<=x+5

m. B(x)<x+4

9. Rarfbfidr, sf `d raitd qua pdsd pnr `ns puktns D(2,-1) y E(8, -8) aspdrd`a`d d `d raitd qua pdsd pnr `ns puktns I (-9, 45) y M(4, 2).

=. Qkd raitd @ pdsd pnr `ns puktns (-=, 1) y (8, -5):

d. ]rdzdr `d raitd qua pdsd pnr (?,?) y as parpakmfiu`dr d @.

e. ¾Iuä` as `d pakmfakta ma ukd raitd parpakmfiu`dr d @>



1. Ak idmd idsn, asirfefr `d aiudifùk ma `d raitd ak su bnrld pakmfaktafktariaptn, sf

d. l < 5 y e < 5

e. l < -4/5 y e < ?

i. 5 4 y e< <

m. l < 3 y e < -2

a. l < -9 y e < -4

2. Asirfefr d aiudifùk ma d raitd qua pdsd pnr a` puktn mdmn y qua tfakapakmfakta l.

d. (5, 2) y l < -9

e. (-4, =) y l < 4/5

i. (1, -5/9) y l < 4

m. (4, -4) y l< -5

a. (-9,-1) y l < ?

3. Asirfefr idmd aiudifùk mdmd ak `d bnrld pakmfakta fktariaptn:

d. 9 x + y < =

e. 5 x ’ y < 1

i. 2 x ’ 9 y < 4

m. = x + 5 y < 4?

a =x 9y < ?



8. Asirfefr `d aiudifùk ma `d raitd qua pdsd pnr `ns puktns mdmns ak `dbnrld Dx + Ey + I < ?

d. (-4, 5) (5, -4) e. (5, 9) (9,5)

i. (4, 4) (-4, -4)

m. (9,-=) (?,?)

a. (-4, -49) (-8,-4)

6. Akinktrdr ukd aiudifùk ma `d raitd qua sdtfsbdcd `ds inkmfifnkas:

d. @d pakmfakta as -5/9 y pdsd pnr a` puktn (?,4)

e. _dsd pnr a` puktn (-1,5) y as pdrdà`d d` aja x

i. _dsd pnr a` puktn (-9,-=) y as pdrdà`d d` aja y

m. A` puktn ma inrta ink a` aja x as (-9,?) y ink a` aja y (?,=)

a. _dsd pnr a` puktn (-5,9) y as pdrdà`d d `d raitd iuyd aiudifùk as5 x ’ y ’5 < ?

b. _dsd pnr a` puktn (5,=) y as parpakmfiu`dr d d raitd iuyd aiudifùkas x ’ 1 y + 4? < ?

4?. Qsdkmn d pakmfakta, matarlfkdr sf ns tras puktns mdmns snk in`fkadàs:

d. (5, 9) (-=, -3) (1, 8)

e. (5, -4) (4,4) (9, =)

i. (=, 2) (4,5) (-1, -=)

m. (-9, 2) (9,5) (6,5)

a (-9 2) (9 5) (6 -5)



Qkd ifriukbarakifd as a` inkjuktn ma tnmns `ns puktns_ ma uk p`dkn qua aqufmfstdk ma uk puktn bfjn I . D`puktn bfjn sa `a ``dld a` iaktrn, y d `d mfstdkifd aktra _ y I sa `a ``dld a` rdmfn.

_drd netakar `d aiudifùk ma `d ifriukbarakifd ink iaktrn ak a` puktn (h,g ) y rdr , pnmalns utf`fzdr `d bùrlu`d ma `d mfstdkifd aktra mns puktns.

Yf _( x, x) sa akiuaktrd ak `d ifriukbarakifd, aktnkias `d mfstdkifd aktra _ y a` puiaktrn (h,g ) as r , as maifr:

Cräbfid 8=

@d ifriukbarakifd

Qkfmdm 3. Iurvds ak a` p`dkn Yasfùk

4



Cräbfid 81

Yf a` iaktrn ma `d ifriukbarakifd as a` nrfcak (?,?), aktnkias `d aiudifùk quamd a`d sfcufakta bnrld:

x5 + y5 < r 5

Yf a` rdmfn ma d ifriukbarakifd as 4, d `dldlns ifriukbarakifd ukftdrfd. Yf sa inkiak a` iaktrn y a` rdmfn ma `d ifriukbarakifd, quamd inlp`atdlakta matarlfkdmdpuama mfeujdrsa, usdkmn a` inlpäs.

Ma d aiudifùk x5 + y5 < r 5 pnmalns maspajdr y netakalns 5 5 y r x< ´ ù sa

5 5 y r x< 5 5y r x<

Yf sa a`avd d` iudmrdmn dlens `dmns ma `d aiudifùk, takalns: ( x ’ h)5 + ( y ’ g )5 <æstd as `d aiudifùk ma `d ifriukbarakifd ink iaktrn ak (h,g ) y rdmfn r .



Idmd ukd ma astdsaiudifnkas matar-lfkd ukd salfifr-iukbarakifd inlnsa va ak `d bfcurd82.

Yn`uifùk

5

42 y x< 7 `dprflard ma astdsaiudifnkas masirfea`d ifriukbarakifd su-parfnr y `d sacukmd,`d fkbarfnr.

Ajalp`ns

4. @d aiudifùk x5 + y5 < 42 inrraspnkma d ukd ifriukbarakifd ink iaktrn

(?,?) y rdmfn =, qua pnmalns masinlpnkar inln

Cräbfid 82

Cräbfid 83

y < r5 ’ x5

y < 42 ’ x5

y < - r5 ’ x5

y < - 42 ’ x5



5. Hd``dr d aiudifùk ma d ifriukbarakifd qua tfaka su iaktrn ak a` puktn lamma` saclaktn iuyns axtralns snk `ns puktns (-5,9) y (=,1).

Ynùifùk

_rflarn, maealns hd``dr a` iaktrn ma `d ifriukbarakifd:

4 5 4 5,5 5

x x y yI

+ + < ó

(

9 15 =

, 4, =5 5I

+ +

< < ó

Inln yd takalns `ds innrmakdmds ma` iaktrn ma `d ifriukbarakifd, dhnidìu`dlns a` rdmfn, dp`fidkmn d bùrlu`d ma mfstdkifd masma a` puktn iaktd iud`qufard ma `ns axtralns ma` saclaktn, pnr ajalp`n: d` puktn (=,1).

(

55 5

( 4) ( =) 4? x y + <

Dhnrd, pnmalns asirfefr `d aiudifùk ma `d ifriukbarakifd:

(5

5 5( 4) ( =) 4? x y + < n 5 5 ? x y Mx Ay B + + + + <

9. @d aiudifùk ma `d ifriukbarakifd ink iaktrn ak a` puktn (9,5) y rdmfn 1 a

Ynùifùk

5 5 5( ) ( ) x h y g r + <

Yf masdrrn``dlns `ns iudmrdmns y pdsdlns tnmns `ns tærlfkns d` prflar dmtakalns:



Astd aiudifùk astä mdmd ak `d bnrld:

5 5 ? x y Mx Ay B + + + + <

Tua sa ``dld aiudifùk cakard` ma `d ifriukbarakifd.

Ak a` ajalp`n dktarfnr, M < -2, A < -=, B < -45

Iudkmn kns mdk `d aiudifùk cakard` ma `d bnrld 5 5 5( ) ( ) x h y g r + <

Maealns trdksbnrldr`d d `d bnrld:5 5 5

( ) ( ) x h y g r + <

Ak astd ú`tfld aiudifùk, pnmalns var iuä` as a` iaktrn y iuä` as a` rdmfn ma `d iiukbarakifd.

_drd hdiar astd trdksbnrldifùk7 maealns hdiar a` prniasn pdrd inlpàtdr iudmrdm

Qkd axprasfùk ma d bnrld ( x + d)5 sa `dld iudmrdmn parbaitn, iudkmn d` masdrrn

asta iudmrdmn, netakalns tras tærlfkns: ( x + 1)5.

Ajalp`n

4. Hd``dr a` iaktrn y a` rdmfn ma `d ifriukbarakifd iuyd aiudifùk as x5 + y5

5 x + 4? y + 48 < ?.

Ynùifùk

Inlpàtdlns iudmrdmns pdrd x, y dsì:

( )( )5 55 4 4? 51 48 4 51 x x y y+ + + + + < + +

@uacn, takalns:



Qkd ma `ds prnpfamdmasma `d ifriukbarakifd ink-sfsta ak qua `d raitd tdk-cakta d `d ifriukbarakifdak iud`qufard ma sus puk-tns, as parpakmfiu`dr inka` rdmfn ma d ifriukbarak-ifd qua vd masma a` iaktrnd` puktn ma tdkcakifd.

Astd aiudifùk inrraspnkma d ukd ifriukbarakifd ink iaktrn ak a` puk(-4,-1) y rdmfn 8 .

Ak d`cukns idsns, d aiudifùk 5 5 ? x y Mx Ay B + + + + < sa sdtfsbdia pd

uk úkfin puktn n pdrd kfkcúk puktn.

5. Ak `d aiudifùk x5 + y5 + 5 x ’ = y + 1 < ?

Ynùifùk

D` inlpàtdr iudmrdmns, takalns:

( )( )5 55 4 = = 1 4 = x x y y+ + + + < + + ù sad ()( )5 54 5 ? x y+ + <

astd aiudifùk sa sdtfsbdia pdrd uk úkfin puktn (-4,5)

9. Mdmd `d aiudifùk x5 + y5 ’ 4? x + 2 y + 92 < ? qua tfaka `d bnrld ma aiudifùk cakard` ma `d ifriukbarakifd d` inlpàtdr iudmrdmns, takaln( x5 ’ 4? x + 51) + ( y5 + 2 y + 6) < -92 + 51 + 6 ù sad ( x ’ 1)5 + ( y + 9)5 < -5

Astd ú`tfld aiudifùk kn sa sdtfsbdia pdrd kfkcúk puktn pnrqua `d suld mmns iudmrdmns kn puama sar kacdtfvd.

Cräbfid 88



4. Akiuaktra d aiudifùk ma d raitd tdkcakta d d ifriukbarakifd iuyd aiudias x5 + y5 ’ 2 x ’ 5 y ’ 41 < ? ak a` puktn (2,1).

Ynùifùk

D` inlpàtdr `ns iudmrdmns, takalns: ( )( )55 2 6 5 4 41 6 4 x x y y + + + < + +

Aktnkias kns quamd: (9

1 2=

y x <

Astd aiudifùk inrraspnkma d ukd ifriukbarakifd ink iaktrn ak a` puktn (9y rdmfn 1. ]dlefæk pnmalns var qua a` puktn (2,1) sdtfsbdia `d aiudifùpnr `n tdktn, as uk puktn ma a``d.

5. Hd``dr `d pakmfakta ma `d raitd qua pdsd pnr a` puktn (2,1) y pnr a` iak(9,4)

Ynùifùk

1 4 =

2 9 9l

< <

Astd raitd inktfaka a` rdmfn qua vd masma a` iaktrn d` puktn (2,1) y quaparpakmfiu`dr d `d raitd tdkcakta ak asta puktn7 pnr `n tdktn, `d pakmfakma `d raitd tdkcakta ak a` puktn (2,1) as:

9

=l <

V pnr `n tdktn, `d aiudifùk ma `d raitd tdkcakta as:

9

Ajalp`n



4. ]rdzdr `d cräbfid inrraspnkmfakta d idmd aiudifùk:

d. 5 5 92 x y+ <

e. 5 5 42 x y+ <

i. ( )( )5 55 9 4?? x y+ + <

m. 5 5 5 4? 51 ? x y x y+ + + <

a. 5 5 45 91 ? x y x+ + <

5. Matarlfkdr sf idmd aiudifùk as ukd ifriukbarakifd (sa md su rdmfn y su iatrn)7 sf as uk puktn (sa mdk sus innrmakdmds)7 n sf as uk inkjuktn vdiìn.

d. 5 5 = 2 49 ? x y x y+ + + <

e. 5 5 4? 2 92 ? x y x y+ + + <

i. 5 5 2 4 ? x y x+ + <

m. 5 5 8 2 9? ? x y x y+ + + <

a. 5 52 6 8 42 =6 x x y y+ + + + <

4



Qkd a`fpsa as a` inkjuktn ma tnmns `ns puktns _ ma` p`dkn,tdàs qua `d suld ma `ds mfstdkifds ma idmd ukn ma a``ns d mnspuktns bfjns ``dldmns bnins, as ukd inkstdkta.

Ak `d cräbfid, valns ukd a`fpsa iuyn iaktrn as a` puktn (?,?). @ns puktns läs dàjdmma` nrfcak ak a` aja hnrfznktd` snk D (-d,?) y D‖ (d,?), astns puktns sa ``dldk `ns vtfias ma `d a`fpsa. @ns puktns läs àjdkns ma` iaktrn ak a` aja vartfid` snk E(?,y E‖(?,e). @ns saclaktns ½ ½ DD y EE snk `ns ajas ma `d a`fpsa y sus `nkcftumas s5d y 5e raspaitfvdlakta @ns puktns ( ?) ( ?)B B snk `ns bnins ma `d a`fpsa q

Cräbfid 86

@d a`fpsa


5



Qkd bnrld bäif` ma trdzdr ukd a`fpsa, as tnldr uk hf`n y bfjdr sus axtralns ak mnpuktns n astdids snera uk p`dkn, majdkmn qua a` hf`n quama luy b`njn7 ùacn stnld uk `äpfz pdrd taksdr a` hf`n, bnrldkmn ukd aspaifa ma trfäkcu`n. D` rntdr `äpfz, ldktakfakmn a` hf`n taksn, a` `äpfz vd masirfefakmn `d a`fpsa.

Ma `d cräbfid ma `d a`fpsa, pnmalns var ink bdif`fmdm qua ak a``d sa iulpà `d raìfùk 5 5 5d e i+ < , qua as flpnrtdkta pdrd mamuifr ukd bùrlu`d ma `d aiudifùk m`d a`fpsa.

Ma `ds inkmfifnkas ma `d mabfkfifùk ma `d a`fpsa, pnmalns hd``dr su aiudifùk.

Inln `d suld ma `ds mfstdkifds4 5

5_B _B d+ < (inkstdkta).

Yf _( x,y) as iud`qufar puktn ma `d a`fpsa, d` usdr `d bùrlu`d ma `d mfstdkifdtakalns:

@uacn inln:

D` raalp`dzdr, kns quamd:

Maspajdkmn uk rdmfid`, netakalns:

V aàvdkmn dlens `dmns d` iudmrdmn, kns quamd:



( )( ) ( )( ) ( )(5 5 5 5 5 55? = = . ? ? x i y d d x i y x i y+ + < + + +

Maspuæs ma ramuifr tærlfkns, takalns:

( )5 5 5. .d x i y d i x + <

Kuavdlakta a`avdlns dlens `dmns d` iudmrdmn y sflp`fbfidlns:

( ) (5 5 5 5 5 5 5 5d i x d y d d i + <

Inln: 5 5 5e d i<

Uaalp`dzdkmn ak `d aiudifùk dktarfnr takalns: 5 5 5 5 5 5e x d y d e+ <

Mfvfmfakmn astd ú`tfld aiudifùk aktra 5 5d e quamd:

5 5 5 5 5 5

5 5 5 5 5 5

e x d y d e

d e d e d e+ <

V netakalns5 5

5 5 4

x y

d e+ <

Yf d ; e, `d a`fpsa as d`drcdmd hnrfznktd`lakta y `ns bnins sa akiuaktrdksnera a` aja hnrfznktd` ak `ns puktns (-i,?) y (i,?).

Yf e ; d, d a`fpsa as d`drcdmd vartfid`lakta y ns bnins sa akiuaktrdk sneraa` aja vartfid`, ak `ns puktns (?,i) y (?,-i).

Ya ``dld axiaktrfifmdm ma `d a`fpsa a` inifakta 5?

?,3=2

i

d< .

Astd as `d aiudifùk cakard` ma `d a`fpsa ink iaktrn ak a` puktn (?,?).



Asta kúlarn fkbnrld snera `d bnrld ma `d a`fpsa: iudkmn i sa dprnxf-ld d 4, `d a`fpsa as luy d`drcdmd y `ns bnins astäk luy dpdrtdmns maìaktrn7 iudkmn `d axiaktrfifmdm

i

d

astä iarid ma iarn, `ns bnins saakiuaktrdk iarid ma` iaktrn y d a`fpsa sa pdraia d ukd ifriukbarakifd,nevfdlakta ? 4

i

d0 0 .

4. Qkd a`fpsa tfaka inln aiudifùk 5 5

492 42

x y+ < . Hd``dr `ns værtfias, `ns bnin

`d axiaktrfifmdm, y mfeujdr `d a`fpsa.

Ynùifùk

Ma `d aiudifùk, takalns qua: 5 92d < . @uacn, 2d < .

Dsì, `ns værtfias ak a` aja hnrfznktd` snk `ns puktns (-2,?) y (2,?).

]dlefæk: e5 < 42. @uacn, e < =.

V `ns puktns läs àjdkns ma` iaktrn ak a` aja vartfid` snk (?,-=) y (?,=).

Ma `d fcud`mdm d5 < e5 + i5, pnmalns maspajdr a` vd`nr ma i y sa netfaka

@uacn `ns bnins astäk ak `ns puktns

@d axiaktrfifmdm as fcud` d

Ajalp`ns



5. @d aiudifùk ma ukd a`fpsa as 5 5

44 51

x y+ < . Hd``dr sus værtfias, sus bnins,

axiaktrfifmdm, y mfeujdr `d iurvd.

Yn`uifùk

Ak asta idsn, d5 < 4

@uacn, d < 4

Dmaläs: e5 < 51

Aktnkias: e < 1

d e

Cräbfid 6?



@ns værtfias ma `d a`fpsa snk `ns puktns (?,1) y (?,-1), `ns iud`as astäk ak a` avartfid`7 `ns puktns (-4,?) y (4,?) snk `ns puktns läs mfstdktas ma` iaktrn ak aja hnrfznktd`.

_drd hd``dr i hdialns: 51 4 5= =,86i < <

@uacn `ns bnins snk `ns puktns: (?, 5= ) (?, 5=) y

A` vd`nr ma `d axiaktrfifmdm as: 5=?,63

1

A` vd`nr ma d axiaktrfifmdm sa diarid d 4, y d cräbfid ma d a`fpsa as luy d`drcdm

Cräbfid 64



d. Rærtfias ak ns puktns (-8,?) y (8,?)7 Bnins ak ns puktns (?,3)y (-3).

e. Rærtfias ak `ns puktns (?,6) y (?,-6), y `d `nkcftum ma` ajalaknr ma `d a`fpsa as 45.

i. Iaktrn ak (?,?) Bnins ak `ns puktns (-1,?) y (1,?) y `ns bninsak `ns puktns (9,?)y (-9,?).

m. Rærtfias ak `ns puktns (?,2) y (?,-2) y `ns bnins ak `ns puktns(?,=) y (?,-=).

a. Rærtfias ak ns puktns (?,1) y (?,-1) y ns puktns läs mfstdktasma` nrfcak ak `d mfraiifùk hnrfznktd` snk (-4,?) y (4,?).

4. Akiuaktra `ds innrmakdmds ma `ns værtfias y ma `ns bnins, a` vd`nr ma `d axiatrfifmdm, y mfeuja `d iurvd iuyd aiudifùk as:

d. 5 5

46 =

x y+ <

e. 5 5

4

42 84

x y+ <

i.

5 5

4=6 51

x y+ <

5. Asirfed `d aiudifùk ma `d a`fpsa qua tfaka `ds inkmfifnkas mdmds:

4



@d a`fpsa ink iaktrn ak a` puktn (h,g)

D` masp`dzdr a` iaktrn ma d a`fpsa ma` puktn (?,?) d uk puktn (h,g ) ma` p`dkn,su aiudifùk sa trdksbnrld ak:

( ) ( )5 5

5 5 4

x h y g

d e

+ <

@ns værtfias ma `d a`fpsa quamdk ak `ns puktns (h ’ d, g ) y (h + d, g ).

@ns puktns läs mfstdktas ma` nrfcak ak `d mfraiifùk vartfid` snk (h, g + e)y (h, g ’ e).

x(h,-d)

G+e

G

G-e

h

ed

(h,+d)

(h,g)

@ns bnins astdräk ak `ns puktns (h + i, g ) y (h ’ i, g ), sf a` aja ldynr ma `da`fpsa as hnrfznktd`.

Cräbfid 65



Ajalp`n

@d a`fpsa iuyd aiudifùk as ( ) ( )5 5

5 94

51 42

x y ++ <

tfaka su iaktrn ak a` puktn (5, -9), d < 1 y e < =7 51 42 9i < <

@uacn `ns bnins ma `d a`fpsa astäk ak `ns puktns (-4, -9) y (1, -9). @ns værtfima `d a`fpsa snk `ns puktns (-9,-9) y (3, -9). @ns puktns läs mfstdktas ma` iatrn ak mfraiifùk vartfid` snk (5,4) f (5,-3), y a` vd`nr ma `d axiaktrfifmdm maa`fpsa as i/d < 9/1.

Yn`uifùk

Iudkmn d < e `d aiudifùk `d a`fpsa quamd: ( ) ( )5 5

5 5 4

x h y g

d d

+ <

Yf lu`tfp`fidlns pnr d5, netakalns `d aiudifùk:

42 6 3 5, 2=i < <

Tua inrraspnkma d d aiudifùk ma ukd ifriukbarakifd ink iaktrn ak a` puk(h,g ) y rdmfn d. Astn kns mfia qua `d ifriukbarakifd as uk idsn pdrtfiu`dr ma

Cräbfid 69



Ajalp`n

@d aiudifùk ma ukd a`fpsa as() ( )

5 5

54

42 6

x y+ < . Hd``dr a` iaktrn, sus værtfia

`ns bnins, su axiaktrfifmdm, y mfeujdr `d iurvd.

Yn`uifùk

@ds innrmakdmds ma` iaktrnsnk (?,5), d < =, e < 9,

42 6 3 5, 2=i < <

@ns værtfias snk `ns puktns(-=,5) y (=,5). @ns bnins

a s täk ak `n s puk tns()(3 , 5 3 , 5 y 7 `n spuktns läs mfstdktas ma`iaktrn ak `d mfraiifùkvartfid` snk (?,1) y (?,-4).

4. Hdiar `d cräbfid ma idmd aiudifùk:

d.5 5

4= 4

x y+ <

e.5 5

44 =

x y+ <

i.5 5

442 51

x y+ <

Ajarififns pdrd prnbukmfzdr

Cräbfid 6=

5



m.5 5

44?? =6

x y+ <

a. 5 551 92 ? x y+ <

b. 5 551 = 4?? x y+ <

c. ( ) ( )5 5

9 =4

42 51

x y + <

h. ()5

544

51 4

x y+ <

f. ( ) ( )5 5

= 94

6 51

x y ++ <

5. Matarlfkdr ak idmd idsn, `d aiudifùk ma `d a`fpsa qua tfaka `ns iudtrn pukmdmns inln axtralns ma `ns ajas ldynr y laknr, y mfeuja `d cräbfid.

d. (9, ?), (-9,?), (?,1), (?,-1)

e. (5, ?), (-5,?), (?,9), (?,-9)

i. (3, ?), (-3,?), (?,=), (?,-=)

m. (4, ?), (-4,?), (?,2), (?,-2)

9. Inksu`tdr iuä` as `d lamfmd ma` ärad akiarrdmd pnr `d a`fpsa.

=. ¾Iuäktns puktns tfaka `d cräbfid ma `d aiudifùk 51 x5 + 92 y5 < ?>

1. Inlp`atdr `ns iudmrdmns y asirfefr `d aiudifùk sfcufakta inln `d aiudi



Ak `d cräbfid `d mfbarakifd tdkB _ _B inks ta<

Qkd hfpæren`d as a` inkjuktn ma ns puktns _ ak uk p`dkn,td`as qua `d mfbarakifd ma sus mfstdkifds d mns puktns bfjns``dldmns bnins as inkstdkta.

Cräbfid 61

@d hfpæren`d


9



Qkd hfpæren`d tfaka mns værtfias7 a` puktn lamfn ma` saclaktn qua ukasus værtfias as a` iaktrn ma `d hfpæren`d7 `d raitd qua pdsd pnr `ns værtfiassa ``dld aja trdksvarsd`.

Iudkmn ukd hfpæren`d tfaka a` iaktrn ak a` nrfcak (?,?), ns puktns værtfiassa inrtdk ink ukn ma `ns ajas innrmakdmns, y `d aiudifùk ma `d hfpæren`dastä mdmd pnr:

55

5 5 4

y x

d e <

Mnkma d as d mfstdkifd ma` værtfia ma d hfpæren`d d su iaktrn, y e as d nk-cftum ma` saclaktn parpakmfiu`dr d` aja trdksvarsd` qua pdsd pnr a` værtfiay inrtd `d raitd e

y xd

< ak a` puktn (d,e).

Cräbfid 62



_drd crdbfidr d hfpæren`d ink iaktrn ak a` nrfcak, pnmalns mfeujdr a` raitäkcu`n mmflaksfnkas 5d pnr 5e7 ak sacufmd, trdzdr ds dsìktntds, y uacn mfeujdr d hfpæren`

Ajalp`n

@ds dsìktntds snk `ds raitds ink aiudifnkas:

e y x

d< y e

y xd

< .

Astds raitds pdsdk pnr a` iaktrn ma `d hfpæren`d y pnr `ns puktns (d,e), (-d, -e), (-d,y (d, -e), qua snk `ns værtfias ma` raitäkcu`n ma mflaksfnkas 5d x 5e. @ds dsìktntsnk luy flpnrtdktas pdrd pnmar trdzdr `d cräbfid ma `d hfpæren`d.

Ma d cräbfid pnmalns var qua ak d hfpæren`d sa tfaka d ra`difùk: 5 5 i d e< +

Ma mnkma: 5 5i d e< +

V i as `d mfstdkifd masma a` iaktrn d iud`qufard ma `ns værtfias.

A` kúlarn i/d sa ``dld `d axiaktrfifmdm ma `d hfpæren`d,

i/d as ldynr ma ukn.

Hdiar `d cräbfid ma `d hfpæren`d iuyd aiudifùk as55

451 6

y x <

Yn`uifùk

Ak `d aiudifùk, takalns qua d < 1 y e < 9. Ak asta idsn, a` raitäkcu`n 5d x 5tfaka sus værtfias ak `ns puktns (1, 9), (1, -9), (-1, 9) y (-1, -9).



_nmalns hd``dr a` vd`nr ma i, dsì: 5 59 1 9= 1, 89i < + < 7

@uacn, `ns bnins ma `d hfpæren`d snk `ns puktns: ( ) (9= , ? 9= , ? y

Hdstd dquì halns vfstn ukd hfpæren`d iuyds hnjds sa derak d maraihd y dfzqufarmd.

Axfsta tdlefæk ukd hfpæren`d ink a` lfsln iaktrn y `ds lfslds dsìktntds,iuyds hnjds sa derak hdifd drrfed y hdifd dedjn.

Yus værtfias snk `ns puktns (?,e) y (?,-e) y sus bnins snk `ns puktns (?, i) y(?, -i). Astd hfpæren`d sa ``dld `d hfpæren`d inkjucdmd y su aiudifùk as:

5 5

5 5 4

y x

d e <

Iudkmn ak `d aiudifùk ma `d hfpæren`d takalns qua d < e, `d hfpæren`dsa ``dld aquf`ätard.

Cräbfid 63



Ajalp`n

Yf5

5

442 =

x y <

Yaôd`dr `ds innrmakdmds ma` iaktrn ma `ns værtfias y ma `ns bnins. Matarlfkd`ds aiudifnkas ma `ds dsìktntds y mfeujdr `d iurvd.

Yn`uifùk

Ak `d aiudifùk valns qua d < =, e < 5 y i < 42 =+ n 5? =, =3i < .

@uacn:

Iaktrn < (?,?)7

Rærtfias ak `ns puktns:

(-=,?) y (=,?)7

Bnins ak `ns puktns:

()5? ,? ( 5?,?) y

@ds aiudifnkas ma `ds dsìktntds snk:

4

5V x< 7 4

5V x<



Iudkmn d hfpæren`d tfaka su iaktrn ak uk puktn (h,g), mfbarakta ma` puktn(?,?), su aiudifùk astäkmdr as:

( ) ( )5 5

5 5 4

x h y g

d e

<


( ) (e e

y g x h y y g x hd d

< <

@d hfpæren`d inkjucdmd tfaka inln aiudifùk:

( )( )5 5

5 5 4

y g x h

d e

<

Cräbfid 68



Ajalp`n

@d aiudifùk ma ukd hfpæren`d as ()( )5 5

4 54

= 6

x y + < . Hdiar `d cräbfid ma as

hfpæren`d y ma su inkjucdmd.

Yn`uifùk

Iaktrn < (h, g ) < (4, -5)7 d < 57 e < 9


() (9 9

5 4 5 45 5

y x y y x+ < + <

Cräbfid 66



4. Mdmd `d aiudifùk ma `d hfpæren`d, mfeujdr `d cräbfid y asirfefr `dsaiudifnkas ma `ds dsìktntds.

d. 5 5

442 6 y x <

e. 5 56 = 92 x y <

i. 5 551 = 4?? y x <

5. Hd``dr `d aiudifùk ma `d a`fpsa qua iulp`a `ds inkmfifnkas mdmds yhdiar su cräbfid.

d. Bnins ak (?,1) y (?, -1)7 værtfias ak (?,=) y (?, -=)

e. Rærtfias ak (-5,?) y (5, ?), e < 9

i. @d aiudifùk ma ukd hfpæren`d astä mdmd pnr ( )( )5 5

9 94

= 4

x y+ <

4



@d pdräen`d astä matarlfkdmd pnr a` inkjuktn _ ma`p`dkn iuyd mfstdkifd d uk puktn bfjn ``dldmn bnin, asfcud` d `d mfstdkifd (parpakmfiu`dr), d ukd raitd ``dldmdmfraitrfz.

Cräbfid 4??

@d pdräen`d


=



Yf inksfmardlns d pdräen`d ink værtfia ak (?, ?), bnin ak a` puktn (?, i), d mfraittfaka inln aiudifùk y < -i.

Ma `d mabfkfifùk ma `d pdräen`d sa tfaka qua:

m 4 < m

5

Yf dp`fidlns `d bùrlu`d ma `d mfstdkifd, takalns:

Cräbfid 4?4



A`avdkmn d` iudmrdmn, takalns:

( ) ( ) ( ) ((

( ) ( ) ( ) ( )

5 55 5 5 5

5 5 5 5

?

?

x y i x x y i

x y i x x y i

+ < + + ó

+ < + +

D` masdrrn``dr `ds npardifnkas, sa tfaka:

5 5 5 5 55 5 x y iy i y iy i+ + < + +

@uacn,

5 = x iy<

Tua as `d aiudifùk astäkmdr ma `d pdräen`d ink værtfia ak a` puktn (?, ?).

’ Yf i as pnsftfvn, `d pdräen`d sa dera hdifd drrfed inln ak `d cräbfid.

’ Yf i as kacdtfvn, `d pdräen`d sa dera hdifd dedjn.

’ @d raitd qua pdsd pnr a` bnin y a` værtfia, sa `dld aja ma `d pdräen`d.

’ A` saclaktn qua uka mns puktns ma `d pdräen`d, pdsdkmn pnr a` bniny pdrd`a`n d `d mfraitrfz sa ``dld a` `dmn raitn.

Ya puama var qua sus puktns axtralns snera `d pdräen`d tfakak innrmakdmds

(5i, i) y (-5i, i)

@uacn, `d `nkcftum ma` `dmn raitn as a` vd`nr pnsftfvn ma =i.

Astns puktns snk flpnrtdktas d` trdzdr `d pdräen`d pnrqua kns nrfaktdk ak iuäk



_drd hd``dr `ds innrmakdmds ma `ns puktns axtralns, valns qua `d aiudifùk maraitd snera `d iud` astä a` `dmn raitn as: y < i

Dhnrd, inln `d aiudifùk ma `d pdräen`d as: 5 = x iy<

Uaalp`dzdlns y pnr i y takalns: 5 5= x i<

Ma mnkma: 5 x i< ´

Ma fcud` ldkard, sf `d pdräen`d sa dera hdifd `d maraihd n hdifd `d fzqufarmd yværtfia astä ak a` nrfcak, takalns qua:

m 4

< m 5

V d` dp`fidr `d bùrlu`d ma mfstdkifd quamd:

Ma mnkma netakalns:

Cräbfid 4?5



Masdrrn``dkmn y sflp`fbfidkmn, takalns:

5 45 y x<

Ya netfaka dsì, `d aiudifùk ma `d pdräen`d qua sa dera hdifd `d mara-ihd iudkmn i as pnsftfvn inln sa va ak `d cräbfid y sa dera hdifd

`d fzqufarmd iudkmn i as kacdtfvn.

4. Mdmd `d aiudifùk ma `d pdräen`d x5 < 8 y, hd``dr a` værtfia, a` bnin, `d aiuifùk ma d mfraitrfz, d nkcftum ma` dmn raitn y ns puktns axtralns ma` dmraitn, y mfeujdr `d pdräen`d.

Ynùifùk

Ma d aiudifùk x5 < 8 y

pnmalns àar qua=i < 8 ma mnkmai < 5, ùacn `d pd-räen`d sa dera hdifddrrfed, su værtfia astdak (?,?) y su bnin aka` puktn (?,5), d aiud-ifùk ma `d mfraitrfz as

y < -5, ns puktns axtra-lns ma` dmn raitn snk(-5i, i) < (-=,5) y(5i, i) < (=,5), `d `nk-cftum ma` `dmn raitn as8 inln sa fùstrd ak dcräbfid 61.

Ajalp`n

Cräbfid 4?9



Ma ds sftudifnkas dktarfnras, pnmalns var qua iudkmn a` tærlfkn iudmrätma d aiudifùk ma d pdräen`d astä ak d vdrfdeà x, d pdräen`d sa dera hddrrfed, sf i as pnsftfvn n hdifd dedjn, sf i as kacdtfvn.

Iudkmn a` tærlfkn iudmrätfin ma `d aiudifùk ma `d pdräen`d astä ak `d rfdeà y, `d pdräen`d sa dera snera hdifd `d maraihd sf i as pnsftfvn n hd`d fzqufarmd sf i as kacdtfvn.

5. Mdmd `d aiudifùk ma `d pdräen`d y5 < -45 x, hd``d a` værtfia, a` bnin, `d aiuifùk ma d mfraitrfz, d nkcftum ma` dmn raitn y ns puktns axtralns ma` `draitn, mfeujdr `d pdräen`d.

Ynùifùk

Ma d aiudifùk y5 < -45 x pnmalns aar qua =i < -45 ma mnkma i < -9, ua`d pdräen`d sa dera hdifd d fzqufarmd, su værtfia astä ak (?,?) y su bnin akpuktn (-9,?)7 d aiudifùk ma d mfraitrfz as d raitd x <9, ns puktns axtralma` `dmn raitn snk (-9,2) y (-9,-2), `d `nkcftum ma` `dmn raitn as 45 inlnfùstrd ak `d cräbfid 62.

Cräbfid 4?=



Ak `ns sfcufaktas ajarififns pdrd `d pdräen`d iuyd aiudifùk sa md, hd``dr a` værtfia` bnin, `d aiudifùk ma `d mfraitrfz, `ns puktns axtralns ma` `dmn raitn, y mfeujdr pdräen`d.

d. 5 = x y<

e. 5 42 x y<

i. ( )5

= ( ) y g i x h <

m. 5 2 y x<

a. 5 y x<

Ajalp`n

Iudkmn `d pdräen`d tfaka su værtfia ak uk puktn (h,g ) ma` p`dkn, y sa deravartfid`lakta, `d aiudifùk astäkmdr quamd:

( ) (5

= x h i y g <

Yf `d pdräen`d sa dera hdifd `d maraihd n hdifd `d fzqufarmd, su aiudifùk as:

( )5

= ( ) y g i x h <

4 Qkd pdräen`d tfaka su værtfia ak a` puktn (9 5) y su bnin ak a` puktn (9

4



Ynùifùk

Ralns qua `d mfstdkifd aktra a` værtfia y a` bnin as 9, ùacn i < 97 ininknialns qua a` iaktrn as a` puktn (9, 5), `d aiudifùk ma `d pdräen`d as

( )5

9 =(9)( 5) x y <

N sad qua:

( )5

9 45( 5) x y <

5. Qkd pdräen`d tfaka su værtfia ak a` puktn (?, 5) y su bnin ak a` puktn (-5,

asirfed `d aiudifùk ma `d pdräen`d y hdcd `d cräbfid.

Ynùifùk

A` bnin astä d `d fzqufarmd ma` værtfia ùacn `d pdräen`d sa dera hdifd `d qufarmd, i < -5, su aiudifùk as ( )

55 =( 5)( ?) y x < n sad ( )

55 8 y <

Cräbfid 4?1



4. Qkd pdräen`d tfaka su værtfia ak a` puktn (4, -5) y su mfraitrfz as`d raitd x < -4. Hd``dr `d aiudifùk ma `d pdräen`d, a` bnin y `nspuktns axtralns ma` `dmn raitn, y hdiar `d cräbfid.

5. Qkd pdräen`d tfaka su bnin ak a` puktn (5,?) y su mfraitrfz as `draitd x < -5. Hd``dr a` værtfia, ns puktns axtralns ma` dmn raitn,y mfeujdr `d pdräen`d.

9. Qkd pdräen`d tfaka su værtfia ak a` puktn (-5, -5), su bnin ak a`puktn (-5,?)7 hd``dr d aiudifùk ma d mfraitrfz, ns puktns axtralnsma` `dmn raitn, y hdiar `d cräbfid.

=. ]rdzdr `d pdräen`d iuyd aiudifùk as5

= 9 ? y x+ <

5



@d ifriukbarakifd, `d a`fpsa, `d hfpæren`d y `d pdräen`d snk iurvds quapartakaiak d d bdlf`fd ma `ds iurvds iùkfids, pnrqua puamak netakarsad` inrtdr uk inkn ma mns hnjds pnr uk p`dkn ak mfbaraktas mfraiifnkas,inln sa fkmfid ak `ds sfcufaktas cräbfids:

C äbf

a

<6?

6?

<

@d ifriukbarakifd, `d a`fpsa, `d hfpæren`d y `d pdräen`d snk iurvds quapartakaiak d d bdlf`fd ma `ds iurvds iùkfids, pnrqua puamak netakarsad` inrtdr uk inkn ma mns hnjds pnr uk p`dkn ak mfbaraktas mfraiifnkas,inln sa fkmfid ak `ds sfcufaktas cräbfids:



4. @d aiudifùk x5+y5<51, inrraspnkma d:

d. Qkd ifriukbarakifd ma iaktrn (?,?) y qua pdsd pnr a` puktn (5,?) e. Qkd ifriukbarakifd ma iaktrn (?,?) y qua pdsd pnr a` puktn (?,1)

i. Qkd a`fpsa ma iaktrn (h.g) qua pdsd pnr a` puktn (?,1) m. Qkd a`fpsa ma iaktrn (?,?) qua pdsd pnr a` puktn (?,1)

5. Akiuaktra `ds innrmakdmds ma `ns værtfias y ma `ns bnins, a` vd`nr ma`d axiaktrfifmdm, y mfeuja `d iurvd iuyd aiudifùk as:

d.

5 5

44?? 2=

x y+ < e. 5 542 4 x y+ <

9. Mdmd `d aiudifùk ma `d hfpæren`d, mfeujdr `d cräbfid y asirfefr `dsaiudifnkas ma `ds dsìktntds.

d. 55

42= 92

y x < e.

55

4= =

y x < i. 5 5

451 4==

y x <

=. @d aiudifùk y5<42x, inrraspnkma d:

d. Qkd a`fpsa ma bnin (?,=) y mfraitrfz y <-= e. Qkd a`fpsa ma bnin (=,?) y mfraitrfz y <= i. Qkd a`fpsa ma bnin (?,?) y mfraitrfz y <4 m. Qkd a`fpsa ma bnin (?,4) y mfraitrfz y<=



A` nejatfvn ma d astdmìstfid as hdiar fkbarakifds ink raspaitn ma ukd pne`d-

ifùk, d pdrtfr ma `d fkbnrldifùk qua inktfaka ukd luastrd. @d astdmìstfidldkajd `d tanrìd ma `d fkbnrldifùk pdrd prasaktdr `ns hd``dzcns ak bnrldiudktfbfidmd y utf`fzdr`ns ak `d tnld ma maifsfnkas.

Yfalpra qua sa hdiak astumfns astdmìstfins, dpdraia a` inkiaptn ma prn-edef`fmdm qua pdrd d ldynrìd ma d cakta, as uk tærlfkn vdcn qua fkmfid`d pnsfef`fmdm ma niurrakifd ma uk avaktn ak a` buturn. A` inkiaptn maprnedef`fmdm as útf` iudkmn sa trdedjd ink prniasns bìsfins, efn`ùcfins,snifdàs, prnkùstfins ma` i`fld, inlpnrtdlfaktn ma `d en`sd, ati., quacakardk nesarvdifnkas y rasu`tdmns qua snk flpnsfeàs ma pramaifr inkaxditftum. Ajalp`ns: `d prasfùk drtarfd` ma ukd parsnkd ak uk lnlaktnmdmn, a` prnkùstfin ma` tfalpn pdrd uk mìd saôd`dmn, a` praifn ma `dsdiifnkas ak d en`sd ma vd`nras, a` inlpnrtdlfaktn ma d ainknlìd, ati.,pnrqua tnmns astns bakùlaknspuamak subrfr d`tardifnkas fk-

aspardmds y dbaitdrsa pnr ntrnshaihns n ifriukstdkifds qua samaknlfkdk bakùlakns dàdtn-rfns n prnedef`ìstfins. Ak ifartdldkard, tnmn n qua niurra akkuastrd intfmfdkfmdm, tfaka ukifartn crdmn ma dàdtnrfamdm.

Inkiaptns eäsfins ma prnedef`fmdm

Qkfmdm 8. _rnedef fmdm y astdmìstfid Yasfùk

4

Inkiaptns eäsfins ma prnedef`fmdm _drta 4. Murdifùk: 4:=5 l

Inkiaptns eäsfins ma prnedef`fmdm _drta 5. Murdifùk: 6:1= l



@d braiuakifd ink `d iud` sa prasaktdk astns avaktns ak ukd crdk sarfama nesarvdifnkas, as d lakumn astdeà y pnr `n tdktn, kns prnpnrifn-kd ukd lamfmd fktuftfvd ma `d pnsfef`fmdm ma niurrakifd ma uk avaktn

dàdtnrfn ak uk buturn asiakdrfn.

Ajalp`n

Yf ak `ns ú`tflns 5? dôns, ak a` lasma nituera hd hdefmn `ùvfds deuk-mdktas, astd fkbnrldifùk à sarvfrä d`

dcrfiu`tnr pdrd p`dkfbfidr sus sfalerdsy rainàitdr sus insaihds, dukqua aka` prùxfln dôn, a` las ma nituerapuama idraiar ma ùvfds deukmdktas.

Ak ukd bnrld läs sakif``d, iudkmn`dkzdlns ukd lnkamd, kn pnma-lns astdr sacurns ma qua d` idarkns luastra `d idrd. _arn sf usdlnsukd lnkamd parbaitd, maspuæs ma5? `dkzdlfaktns pnmalns prama-ifr qua `d lftdm ma `dkzdlfaktnsluastrd idrds y `d ntrd lftdm sa``ns7ak asta idsn, pnmalns maifr qua ma5? `dkzdlfaktns, a` 1?% ma a``ns

luastrak idrd y a` 1?% luastraksa``n. Astd braiuakifd ra`dtfvd, knsnrfaktd pdrd paksdr qua d` hdiaruk sn`n `dkzdlfaktn ma `d lnkamd,hdy uk 1?% ma pnsfef`fmdm ma qualuastra `d idrd.



Yf `d lnkamd as flparbaitd y ak uk kúlarn ma `dkzdlfaktns matar-lfkdmns, a` 8?% ma a``ns luastrd idrd, sa puama paksdr qua pdrd ukdpnstdmnr ak uk sn`n `dkzdlfaktn ma `d lnkamd, as bdvnrdeà qua

dpuasta d `d idrd, y sfk aledrcn, uk euak dpnstdmnr kukid `n hdrìd. @dprnedef`fmdm qua as a` inkiaptn qua dkd`fzdralns aksacufmd, as ukdharrdlfaktd luy útf` pdrd hdiar fkbarakifds.

Inksfmaralns a` idsn ma ukdpnstdmnr qua masad hdiarukd fkbarakifd ink raspaitnma `d parbaiifùk ma uk mdmn,as maifr, qufara sdear sf d``dkzdr a` mdmn, hdy `d lfsldprnedef`fmdm ma qua ak `didrd suparfnr luastra uk kú-larn ma ukn d` safs7 aktnkias,`d pne`difùk astumfdmd as aìnkjuktn ma kúlarns qua

rasu`tdrìd d` `dkzdr a` mdmnrapatfmdlakta. Yf a` mdmnbuard parbaitn, `d saxtd pdrtama ns dkzdlfaktns lnstrdrìdukn, `d saxtd pdrta lnstrdrìdmns, `d saxtd pdrta lnstrdrìd

tras, `d saxtd pdrta lnstrdrìd iudtrn, `d saxtd pdrta lnstrdrìd ifkin y `dsaxtd pdrta lnstrdrìd safs, as maifr, idmd idrd ma` mdmn tfaka `d lfsld

pnsfef`fmdm ma dpdrfifùk. _drd varfbfidr su hfpùtasfs, a` dpnstdmnr hdia5? `dkzdlfaktns y nesarvd qua ak 48 ma a``ns dpdraifù mns, `n iud` àcakard ifartd masinkbfdkzd snera su hfpùtasfs ma qua a` mdmn as parbaitny pnr supuastn, tfaka qua raihdzdr`d. A` rdznkdlfaktn ma` dpnstdmnr akasta idsn, rainknia `d bukifùk ma `d prnedef`fmdm d` hdiar fkbarakifds afktuya qua d dpdrfifùk ma 48 vaias a` mns, maluastrd qua as luy pninprnedeà qua sa trdta ma uk mdmn inrraitn.



Maspuæs ma fmaktfbfidr`d pne`difùk lntfvn maastumfn, mabfkfr idmd

ukfmdm ma nesarvdifùkak `d pne`difùk, saài-ifnkdr ukd luastrd ma`d pne`difùk y lamfr`ds idrditarìstfids ma `dsukfmdmas ma `d luastrd,vfaka `d atdpd läs fl-pnrtdkta ma `d fkvastfcd-ifùk n sad, `d fkbarakifdastdmìstfid qua as a`prniasn qua dtrfeuyan dsfckd d `d pne`difùkaktard, ds idrditarìstfidsnesarvdmds n lamfmdsak `d luastrd.

@d inkbfdef`fmdm ma `ns rasu`tdmns ma ukd fkvastfcdifùkastdmìstfid mapakma ak crdk pdrta, ma d aàiifùk inrrai-td ma `d luastrd. Æstd maea sar raprasaktdtfvd, as maifr,inksarvdr `ds lfslds idrditarìstfids ma `d pne`difùk,

dukqua su tdldôn sad laknr, ink a` nejatn ma `ncrdruk inrraitn ldkajn ma `d fkbnrldifùk.

Axfstak vdrfds tæikfids ma luastran pdrd saàiifnkdrdprnpfdmdlakta `ds luastrds.



D` rad`fzdr uk axparflaktn astdmìstfin, sa netfaka ukinkjuktn ma nesarvdifnkas n rasu`tdmns. As kaiasdrfninksfmardr d`cukds knifnkas flpnrtdktas snera `d tan-rìd ma inkjuktns pdrd qua pnmdlns aktakmar lajnr, a`

astumfn ma `d prnedef`fmdm. Qtf`fzdralns àtrds ldyús-iu`ds pdrd fkmfidr `ns inkjuktns y àtrds lfkúsiu`ds pdrd raprasaktdr `nsaàlaktns ma uk inkjuktn. @`dldlns inkjuktn ukfvarsd` d` inkjuktn quainktfaka tnmns `ns aàlaktns inksfmardmns, as maifr, qua `ns aàlaktnsma iud`qufar ntrn inkjuktn astäk ak a` ukfvarsd`.

Qk inkjuktn D as uk sueinkjuktn ma E, sf tnmn aàlaktn ma D astä ak E.

Asirfeflns D ⊅ E y àalns D astä inktakfmn ak E.

Cräbfid 4?3

D ⊅ E

Qkfvarsd`

D

E

Knifnkas snera inkjuktns


5



Yf inksfmardlns mns inkjuktns iud`qufard D y E,`d ukfùk ma D y E, asirftd

inln D∪E, as a` inkjuktnma tnmns `ns aàlaktnsma D, ma E n ma dlens,as maifr, pdrd astdr ak `dukfùk, uk aàlaktn maeaastdr ak pnr `n lakns,ukn ma `ns inkjuktns.

Yf D as uk sueinkjuktnma Y, aktnkias a` inl-pàlaktn ma D, asirftn

D‖ as a` inkjuktn maaàlaktns ma Y qua knastäk ak D.

@d fktarsaiifùk ma mnsinkjuktns D y E, asirftd

D∦E n efak DE, as aìnkjuktn ma puktns nma aàlaktns qua astäktdktn ak D inln ak E.

Cräbfid 4?8

D ∪ E

Y

D E

Cräbfid 4?6D ∦ E

Y

D E

Cräbfid 44?

D

D‖Y



Ya mfia qua mnsinkjuktns D y E snkmfsjuktns n lutud-lakta axiùyaktas, sf

D ∦ E < ς. As maifr,`ns inkjuktns lutud-lakta axiùyaktaskn tfakak aàlaktnsinlukas.

Ajalp`ns

4. Yupnkar qua sa asirfeak `ns lasas ma` dôn ak 45 pdpa`ftns y sa in`nimaktrn ma ukd urkd. @uacn sa sdidk `ns pdpa`ftns ukn pnr ukn. A` inkjukma tnmns `ns rasu`tdmns pnsfeàs as:

Y<{akarn, baerarn, ldrzn, derf`, ldyn, jukfn, ju`fn, dcnstn, saptfalenituera, knvfalera, mfifalera}.

Ynùifùk

Yf tnldlns:

D < {akarn, baerarn, ldrzn, derf`, ldyn, jukfn}

E < {akarn, ldrzn, ldyn, ju`fn, saptfalera, knvfalera}

D y E snk sueinkjuktns ma Y.

D ∪ E < {akarn, baerarn, ldrzn, derf`, ldyn, jukfn, ju`fn, saptfalera, n

Cräbfid 444

D ∦ E < ∁

Y

D E



]dlefæk takalns D ∦ E <{akarn, ldrzn, ldyn}

A` inlpàlaktn ma D as:

D‖ < {ju`fn, dcnstn, saptfalera, nituera, knvfalera, mfifalera}. Æsta as

`fstdmn ma tnmns `ns lasas qua kn astäk ak D, y a` inlpàlaktn mE as:

E‖ < {baerarn, derf`, jukfn, dcnstn, nituera, mfifalera}, as maifr, æsta as `fstdmn ma `ns aàlaktns qua kn astäk ak E.

Ya tfaka qua D ∦ D‖< ς, as maifr, iud`qufar inkjuktn y su inlpàlaktn snmfsjuktns n lutudlakta axiùyaktas.

5. Ya `dkzdk tras lnkamds inrraitds. A` inkjuktn ma tnmns `ns pnsfeàs rasutdmns as:

Y< {iii, iis, isi, iss, sii, sis, ssi, sss}, mnkma i < idrd7 s< sa``n.

Ynùifùk

Yf mabfkflns D: dpdraiak axditdlakta mns idrds, aktnkias

D < {iis, isi, sii}. I`drdlakta, D ⊅ Y

Yf mabfkflns E: dpdraiak tras idrds, aktnkias

E < {iii}. ]dlefæk E ⊅ Y

]akalns D ∪ E < {iis, isi, sii, iii}

]dlefæk D ∦ E < ς. @uacn inkiùflns qua D y E snk lutudlakta axi`yaktas, pnrqua kn tfakak aàlaktns inlukas.

]dlefæk valns qua a` E‖ < {iis, isi, iss, sii, sis, ssi, sss}



Ajalp`ns

4. Axparflaktn: `dkzdr ukd lnkamd

Aspdifn luastrd`: I, Y

5. Axparflaktn: `dkzdr uk mdmn

Aspdifn luastrd` {4, 5, 9, =, 1, 2Y <

Ya ``dld avaktn sflpà d uk aàlaktn nlfalern ma` aspdifn luastrd`. Qk avaktninlpuastn n sflpàlakta uk avaktn, astäbnrldmn pnr ukn n läs avaktns sflpàs.

D`cukns avaktns dsnifdmns ink a` axparf-laktn ma `dkzdr uk mdmn snk:

Qk axparflaktn dàdtnrfn as a` prniasn pnr lamfn ma` iud`,sa netfaka ukd nesarvdifùk n rasu`tdmn.

Ya `dld aspdifn luastrd` Y ma` axparflaktn, d ra`difùk ma tnmds ds pnsfeàs

nesarvdifnkas n rasu`tdmns ma` axparflaktn.

Axparflaktn ak astdmìstfid


9



D: Ya nesarvd uk kúlarn flpdr

E: Ya nesarvd uk kúlarn laknr qua ifkin

I: Ya nesarvd uk tras n uk iudtrn

M4: Ya nesarvd uk ukn

M5: Ya nesarvd uk mns

M9: Ya nesarvd uk tras

M=: Ya nesarvd uk iudtrn

M1: Ya nesarvd uk ifkin

M2: Ya nesarvd uk 2

Dquì valns qua `ns ú`tflns safs avaktns ma` `fstdmn snk avaktns sflpàs

pnrqua idmd ukn ma a``ns as uk aàlaktn ma` aspdifn luastrd`. Qk avaktnsflpà as dqua` qua sù`n puama niurrfr ma ukd bnrld.

@ns tras prflarns ajalp`ns D,E,I snk avaktns inlpuastns.

A` avaktn D as uk avaktn inlpuastn pnrqua sa puama masinlpnkar ak`ns avaktns M4, M9 y M1.

A` avaktn E sa puama masinlpnkar ak `ns avaktns M4, M5, M9 y M=.

A` avaktn I sa puama masinlpnkar ak `ns avaktns M9 y M=.

D` rad`fzdr uk axparflaktn dàdtnrfn y matarlfkdr su aspdifn luastrd`,fmaktfbfidlns `ns avaktns sflpàs ma` axparflaktn qua snk idmd ukn ma



`ns aàlaktns ma` aspdifn luastrd`. _nmalns dsfckdr uk kúlarn aktraiarn y ukn d idmd avaktn sflpà7 asta kúlarn sa ``dld `d prnedef`fmdmma` avaktn. Yf suldlns `ds prnedef`fmdmas ma tnmns `ns avaktns sflpàs

ma uk aspdifn luastrd`, su suld maear sar fcud` d ukn. Ak ntrds pd`derds,sf knsntrns saôd`dlns `ns avaktns sflpàs ma` aspdifn luastrd` inln a4, a5, a9, ak y asirfeflns `d prnedef`fmdm ma idmd avaktn sflpà inln: _(a4),_(a5), _(a9)... _(ak).

Aktnkias:

4. ? ≭ _(af) ≭ 4 pdrd f < 4, 5, 9, ... k

5. _(a4) + _(a5) + _(a9) + ... + _(ak) < 4

Yf `d prnedef`fmdm ma niurrakifd ma idmd avaktn sflpà as `d lfsld, satfaka qua prnedef`fmdm ma _(af) < 4/k.

@d prnedef`fmdm ma niurrakifd ma uk avaktn as uk kúlarn aktra iarn yukn7 sf a` vd`nr ma `d prnedef`fmdm astä iarid ma ukn, hdy läs pnsfef`fmdmas

ma qua a` avaktn niurrd. _nr ajalp`n: sf a` aqufpn idlpaùk hd cdkdmn a`6?% ma `ns i`äsfins, aktnkias hdy ukd d`td prnedef`fmdm ma qua a` aqufpnidlpaùk cdka a` i`äsfin, pnrqua `d prnedef`fmdm ma cdkdr as fcud` d ?,6.

Ma ns astumfdktas qua saprasaktdk pdrd fkcrasdrak `d ukfvarsfmdm nbfifd`sù`n a` 1%, as dmlftfmn.@uacn, `d prnedef`fmdmma qua uk astumfdktaiud`qufard pdsa ak `dukfvarsfmdm nbfifd` asluy edjd pnrqua d prn-edef`fmdm as fcud` d ?,?1.



_rnedef`fmdm ma uk avaktn inlpuastn D, makntdmd pnr _(D) as fcud` d `dsuld ma tnmds `ds prnedef`fmdmas ma `ns avaktns sflpàs qua partakaiakd D. @n pnmalns axprasdr dsì:

_(D) < ∔ _(af) pdrd tnmn af ak D, mnkma a` sìlen`n ∔, sfckfbfid`d suld ma `ds prnedef`fmdmas ma `ns avaktns sflpàs ma D.

Yf uk avaktn D astä inlpuastn pnr avaktns sflpàs ink fcud`prnedef`fmdm ma niurrakifd ak uk aspdifn luastrd`, aktnkias

`d prnedef`fmdm ma` avaktn D as fcud` d` kúlarn ma avaktnssflpàs ma D, mfvfmfmn aktra a` kúlarn ma avaktns sflpàs maàvaktn luastrd`.

Ajalp`ns

4. Ak a` axparflaktn ma dkzdr mns mdmns inrraitns n justns y nesar-vdr ns puktns qua dpdraiak ak sus idrds suparfnras, netakalnsa` sfcufakta aspdifn luastrd`:

Y < {(4,4), (4,5), (4,9), (4,=), (4,1), (4,2), (5,4), (5,5), (5,9), (5,=),

(5,1), (5,2), (9,4), (9,5), (9,9), (9,=), (9,1), (9,2), (=,4), (=,5),

(=,9), (=,=), (=,1), (=,2), (1,4), (1,5), (1,9), (1,=), (1,1), (1,2),

(2,4), (2,5), (2,9), (2,=), (2,1), (2,2)}

Ralns qua a` aspdifn luastrd` tfaka 92 aàlaktns n avaktnssflpàs. Yf mabfkflns:



D: @d suld ma `ds idrds lnstrdmds md mfaz.

E: @d suld ma `ds idrds as laknr ma sfata.

D < {(=,2), (1,1) (2,=)}.

@uacn, _(D) < 9/92 < 4/45 < ?,?89

E < {(4,4), (4,5), (4,9), (4,=), (4,1), (5,4), (5,5), (5,9), (5,=), (9,4),

(9,5), (9,9), (=,4), (=,5) (1,4)}

@uacn _(E) < 41/92 < 1/45 < ?,=42

5. Axparflaktn dàdtnrfn. Ya `dkzdk mns lnkamds inrraitds d` dfra.A` aspdifn luastrd` ma` axparflaktn as:

Y < {(idrd, sa``n), (sa``n, idrd), (sa``n, sa``n), (idrd, idrd)} A` aspdifn luastrd` tfaka iudtrn avaktns sflpàs.

Yf D: dpdraia läs ma ukd idrd, aktnkias D <{(idrd, idrd)}

@uacn _(D) < ° < ?,51

Yf E: dpdraia pnr `n lakns ukd idrd, aktnkias

E<{(idrd, sa``n),(sa``n, idrd),(idrd, idrd)} ùacn _(E) < 9/= < ?,31

Ak asta idsn, sa inkiùya qua a` avaktn E tfaka läs prnedef`fmdmma niurrakifd.



_rnedef`fmdm ma` inlpàlaktn

y ma `d ukfùk

D` rad`fzdr uk axparflaktn, a` aspdifn luastrd` Y as a` inkjuktn matnmns `ns rasu`tdmns u nesarvdifnkas pnsfeàs ma` axparflaktn, asmaifr, as a` inkjuktn ukfvarsd` ma rabarakifd ink raspaitn ma `ns ma-läs avaktns.

Inln Y inktfaka tnmns ns rasu`tdmns pnsfeàs: _(Y) < 4, æsta sa `dlda` avaktn sacurn. Iudkmn sa tnld `d prnedef`fmdm ma uk avaktn qua

kn astä ak a` aspdifn luastrd` ma` axparflaktn, su prnedef`fmdm asiarn y aktnkias, sa ``dld uk avaktn flpnsfeà.

Ajalp`n

Ak a` axparflaktn ma dkzdr uk mdmny nesarvdr a` kúlarn lnstrdmn aksu idrd suparfnr, a` avaktn D: a`

rasu`tdmn as uk kúlarn aktra 4 y 2._(D)<4, pnrqua ak iud`qufar idsn,a` mdmn lnstrdrä uk kúlarn aktraukn y safs, D as uk avaktn sacurn.

D` inktrdrfn, a` avaktn E: dpdraia uk3, as uk avaktn flpnsfeà, _(E) < ?pnrqua a` mdmn kukid lnstrdrä ukdidrd ink sfata puktns.

_rnedef`fmdm ma avaktns


=



Yf `ns avaktns D y E snk lutudlakta axiùyaktas, `d prnedef`fmdm ma`d ukfùk ma D y E as fcud` d `d prnedef`fmdm ma D läs `d prnedef`fmdm

ma E. Astd as `d rac`d ma `d dmfifùk qua sa axprasd dsì:_(D ∪ E) < _(D) + _(E)

Nesarvdifùk

Iudkmn D, E, I y M snk avaktns lutudlakta axiùyaktas,aktnkias sa tfaka qua:

_(D ∪ E ∪ I ∪ M ∪ A) < _(D) + _(E) + _(I)+ _(M) + _(A)

Yf D y E kn snk avaktns lutudlakta axiùyaktas, aktnkias `d prned-ef`fmdm ma `d ukfùk as fcud` d `d suld ma `ds prnedef`fmdmas ma D y E,lakns `d prnedef`fmdm ma su fktarsaiifùk, as maifr:

_(D ∪ E) < _(D) + _(E) ’ _(D ∦ E)

Cräbfid 445_(D ∪ E) < _(D) + _(E)

Y

D E



Ajalp`n

Idìu`dr `d prnedef`fmdm ma netakar uk ukn n uk mns d` tfrdr uk mdmn.

Ynùifùk

Mabfkflns a` avaktn:

D: Dpdraia ukn y E: Dpdraia mns

Astns mns avaktns snk lutudlakta axiùyaktas pnrqua sn`n sa puama lnstrukd idrd. A` avaktn dpdraia uk ukn n uk mns as D∪E, ùacn:

Cräbfid 449

Y

D

D‖]dlefæk takalns qua_(Y) < 4, ùacn, _(D ∪ D‖)

< _(D) + _(D‖) < 4ùacn ma astd ú`tfldfcud`mdm, takalns qua_(D‖) < 4- _(D) y tdlefæk_(D) < 4 - _(D‖)

Inksfmaralns a` avaktn D y su inlpàlaktn D‖. Vd sdealnsqua astns avaktns snk lutudlakta axiùyaktas y tdlefæk

takalns qua D ∪ D‖ < Y inln `n pnmalns var ak a` mfdcrdldma `d cräid 449.



@d prnedef`fmdm ma uk avaktn vdrfdrä mapakmfakmn ma`d niurrakifd n `d kn niurrakifd ma ukn n läs avaktnsra`difnkdmns.

@d prnedef`fmdm ma qua uk avaktn D, niurrd ukd vaz qua hdyd niurrfmnuk avaktn E, sa ``dld `d prnedef`fmdm inkmfifnkd` ma D mdmn E y `d as-irfeflns dsì:

_(D|E), mnkma `d rdyd vartfid`, hdia a` pdpa` ma `d pd`derd mdmn, astdprnedef`fmdm `d mabfkflns dsì:

_(D|E) < ( ) ( ) ?( )

_ D E sf _ E_ E

@d prnedef`fmdm ma D mdmn E, as fcud` d d prnedef`fmdm ma d fktarsaiifùkma D y E mfvfmfmn aktra `d prnedef`fmdm ma E.

Yupnkcdlns qua D y E snk avaktns lutud`lakta axi`uyaktas inln sava ak `d cräbfid 44=.

Cräbfid 44=

Y

D E

_rnedef`fmdm inkmfifnkd` a

fkmapakmakifd ma avaktn


1



Yf a` avaktn E niurra iudkmn uk axparflaktn mdmn sa rad`fzd, aktnkias asflpnsfeà qua a` avaktn D niurrd sflu`täkadlakta y pnr d tdktn, pnmalnsasirfefr qua `d _(D|E) < ?, sf D y E snk lutudlakta axiùyaktas.

Dhnrd, sf supnkalns qua D y E snk a` lfsln avaktn, aktnkias sf E niurra,niurra dutnlätfidlakta D y pnr `n tdktn, `d _(D|E) <4.

Astn kns sucfara qua `d _(D|E) astä ra`difnkdmd ink `d rdzùk ( )

( )

_ D E

_ E

Ajalp`n

Qtf`fzdkmn `d mabfkfifùk ma prnedef`fmdm inkmfifnkd`, akinktrdr `d prnede`fmdm ma `d dpdrfifùk ma uk ukn ak `d idrd suparfnr ma uk mdmn, sf sdealnqua dpdraifù uk kúlarn flpdr ak uk sn`n `dkzdlfaktn.

Ynùifùk

_nmalns mabfkfr `ns avaktns:

D: Ya nesarvd uk ukn.

E: Ya nesarvd uk kúlarn flpdr.

@uacn sa eusid d prnedef`fmdm ma D, mdmn qua yd niurrfù a` avaktn E. @d predef`fmdm ma d niurrakifd ma D y E d` lfsln tfalpn, sfckfbfid d nesarvdifùma uk ukn y ma uk kúlarn flpdr, aktnkias: 4

( )2

_ D E < dmaläs takalnqua `d _(E) < 4/5, ùacn

( )

4( ) 42|

4( ) 9

5

_ D E_ D E

_ E< < <



Yf d niurrakifd ma uk avaktn D kn sa dbaitd pnr d niurrakifd n kn niurrakma uk avaktn E, pnmalns dbfrldr qua `ns avaktns D y E snk fkmapakmfaky sa mabfka dsì:

Mns avaktns D y E snk fkmapakmfaktas sf _(D ∦ E) < _(D) _(E). Yf astd acakifd kn sa sdtfsbdia, `ns avaktns snk mapakmfaktas. Ma `d mabfkfifùk fkmapakmakifd ma avaktns sa puama var qua:

( ) ( ) ( ) ( )

| ( )( ) ( )

_ D E _ D _ E_ D E _ D

_ E _ E< < <

Ajalp`n

Inksfmaralns `ns avaktns sfcufaktas qua tfakak qua var ink a` `dkzdlfakma uk mdmn:

D: Ya nesarvd uk kúlarn flpdrE: Ya nesarvd uk kúlarn pdr

I: Ya nesarvd 4 ù 5 d. ¾Ynk fkmapakmfaktas `ns avaktns D y E> e. ¾Ynk fkmapakmfaktas `ns avaktns D y I>

Yn`uifùk

Maealns var, sf sdtfsbdia _(D|E) ≯ _(D)

d. @d prnedef`fmdm ma nesarvdr uk kúlarn flpdr iudkmn hd niurrfmn kúlarn pdr as fcud` d iarn, as maifr, _(D|E)<? parn _(D) < 4/5 pnrtdktn, D y E kn snk fkmapakmfaktas pnrqua

_(D|E)≯ _(D)

e. Kntdlns qua _(D|I) < 4/57 dmaläs, _(D) < 4/5, pnr `n tdktn, _(D



D`cukns ajalp`ns ma prnedef`fmdm

4. Yf sa `dkzdk tras lnkamds

d. ¾Iuä` as `d prnedef`fmdm ma netakar mns n läs idrds>

e. ¾Iuä` as `d prnedef`fmdm ma netakar axditdlakta mns idrds>

Ynùifùk

A` aspdifn luastrd` Y<{iii, iis, isi, sii, iss, sis, iss, sss}

d. _ < =/8 < 4/5 < ?,1

e. _ < 9/8 < ?,931

5. Yf sa `dkzdk ifkin lnkamds

d. ¾Iuä` as `d prnedef`fmdm ma netakar iudtrn n läs idrds>

e. ¾Iuä` as `d prnedef`fmdm ma netakar axditdlakta iudtrn idrds>

Ynùifùk

d. A` aspdifn luastrd` tfaka 95 aàlaktns. A` avaktn iudtrn n läs idrds tfakinln aàlaktns:

Iiiii Iiiis Iiisi Iiisii Isiii Yiiii



e. A` avaktn axditdlakta iudtrn idrds tfaka 1 aàlaktns, ùacn _ < 1/95?,412551

9. ¾Iuä` as `d prnedef`fmdm ma `ns sfcufaktas avaktns>

d. Ya dkzdk mns mdmns y d suld ma ds mns idrds suparfnras as fcud` d ifk

e. Netakar uk kúlarn pdr iudkmn sa `dkzd uk mdmn.

Ynùifùk

d. A` aspdifn luastrd` tfaka 92 aàlaktns. A` avaktn mdmn tfaka iudtrn a

laktns ma` aspdifn luastrd`7 ùacn _ < =/92 < ?,4444

e. A` aspdifn luastrd` tfaka safs rasu`tdmns. A` avaktn ak iuastfùk tfaka taàlaktns ma` aspdifn luastrd`, ùacn _ < 9/2 < 4/5

=. Yupnkcd qua _(D) < ?,=7 _(E) < ?,2 y _(D|E) < ?,9

d. ¾Ynk fkmapakmfaktas `ns avaktns D y E>

e. ¾Iuä` as _(D ∦ E)>

i. ¾Iuä` as _(D ∪ E)>

Ynùifùk

d. Yf D y E snk fkmapakmfaktas, maea niurrfr qua _(D|E) < _(D), pa_(D|E) < ?,9 y _(D) < ?,=, uacn ns avaktns D y E kn snk fkmapakmfakt

e. Inln ( ) ( )

|( )

_ D E_ D E

_ E<

takalns qua

( ) ( ). ( | ) ?, 2 ?, 9 ?,48_ D E _ E _ D E< < <



1. Ma uk `nta ma 4?? drtìiu`ns, 6? snk euakns y 4? snk mabaitunsns7 sa vdksaàiifnkdr mns, ukn maspuæs ma ntrn. ¾Iuä` as `d prnedef`fmdm ma saàiifnkukd pfazd euakd sacufmd pnr ntrd tdlefæk euakd>

Ynùifùk

@d saàiifùk ma` prflar drtìiu`n as a` avaktn D, ùacn: `d prnedef`fmdm mqua a` prflarn sad euakn as:

_(D)<6?/4?? < ?,6.

@d saàiifùk ma` sacukmn drtìiu`n as a` avaktn E7 sf sa inksfmard qua a` s

cukmn drtìiu`n tdlefæk as euakn, astn as: _(E|D)<86/66 < ?,868, pnrqua maspuæs ma sdidr a` prflar drtìiu

euakn, quamd uk tntd` ma 66, ma `ns iudàs 86 snk euakns.

@d prnedef`fmdm pamfmd as:

_(D|E) < _(D)_(E|D)<(6?/4??)(86/66) < ?,8?64.



_rnedef`fmdm: lfma `d braiuakifd ink `d qua sa netfakauk rasu`tdmn (n inkjuktn ma rasu`tdmns) d` àvdr d idenuk axparflaktn dàdtnrfn, ma` qua sa inkniak tnmns `nsrasu`tdmns pnsfeàs, edjn inkmfifnkas suifaktalaktaastdeàs.

Astdmìstfid: as ukd ifakifd ink edsa ldtalätfid raba-rakta d d rainàiifùk, dkä`fsfs a fktarpratdifùk ma mdtns,qua eusid axp`fidr inkmfifnkas racu`dras ak bakùlaknsma tfpn dàdtnrfn.

Fkbarakifd: as ukd avdùdifùk qua rad`fzd d lakta aktrainkiaptns qua, d` fktarditudr, luastrdk sus prnpfamdmasma bnrld mfsiratd, kaiasftdkmn utf`fzdr `d destrdiifùk

pdrd ncrdr aktakmar ds ukfmdmas qua inlpnkak a` prn-eàld, iradkmn uk puktn dxfnlätfin n ifriukstdkifd`, quakns parlftfrä trdzdr ukd `ìkad `ùcfid ma idusd-abaitn,aktra `ns mfbaraktas puktns fkbarfmns ak `d rasnùifùkma` prneàld.

_rnkùstfin: Akukifdmn snera `n qua as prnedeà quaniurrd ak a` buturn, edsäkmnsa ak dkä`fsfs y ak inksf-mardifnkas ma jufifn.

Inkbdef`fmdm: as usdmn cakard`lakta pdrd axprasdruk ifartn crdmn ma sacurfmdm ma qua uk mfspnsftfvn nsfstald npard axftnsdlakta ak uk dlefakta aspaiìinmurdkta uk ifartn parfnmn ma tfalpn.



UAY_QAY]DY

Yasfùk 5. Yfstalds ma lamfifùk ma äkcu`n. Yaxdcasfld`

Ajarififn 5 (p. 125)

d. 5=¿ 4?‖ 51“

e. 1?¿ 45‖ 94“

i. 2=¿ 56‖

m. 42¿ 98‖ =4“a. 91¿ 53‖ 48“

b. 19¿ 42‖ 92“

Yasfùk =. A` Udmfäk


4. d. 491¿

e. =1¿

i. 2?¿

m. 9?¿

a. 92¿

b. =61¿

c. 53?¿

h. 941¿

f. 551¿

j. 23¿ 9?‖

g. 6??¿

`. -53?¿

5. d. =Ϗ /6 < 4.92529=?5 rdmfdkas.

e 1Ϗ/= < 9 65266?843 rdmfdkas

Qkfmdm 4. Inkiaptns eäsfins



i. 3Ϗ /= < 1.=633834== rdmfdkas.

m. 9Ϗ /= < 5.91246==6 rdmfdkas.

a. 5Ϗ /9 < 5.?6=9614?5 rdmfdkas.

b. - 1Ϗ /2 < -5.243669838 rdmfdkas.

c. - Ϗ /= < ?.381968429 rdmfdkas.

h. =Ϗ /9 < =.48836?5?1 rdmfdkas.

f. 86Ϗ /48? < 4.1199=9?9= rdmfdkas.

j. 51Ϗ /92 < 5.484224121 rdmfdkas.

g. =Ϗ < 45.12293?24 rdmfdkas.

`. - 8Ϗ < -51.4953=459 rdmfdkas.


d. 454834?=.82 il ma mfstdkifd aktra Encntä y ]ukjd ù 454.834 gl.

e. 9653532?¿ ù 548485Ϗ < 281=98.6289 rdmfdkas.

Yasfùk 2. Ärad ma uk saitnr ifriu`dr


4. 48.8=62 il y 8=.859 il5

5. 2.5894 il y 51.499 il5

9. 93.2664 il y 9?4.169 il5

=. 51.4953 il y 41?.362 il5

1. 93.41 il y 538.251 il5

2. A` dutn vd d =2.281 ravn`uifnkas

3. A` lfkutarn rainrra ukd mfstdkifd ma 99.14 pu`cdmds

8. @d `nkcftum ma drin as ma ?.43 il

6. Qk äkcu`n ma 4¿ tfaka ?.?43=19565 rdmfdkas

4?. 3¿ 6‖ =9.4“ ù ?.451 rdmfdkas



Yasfùk 3. ]anrald ma _ftäcnrds


4. Idtatns: = y 2 Hfpntakusd: 3.54

5. Idtatns: 1 y 1 Hfpntakusd: 3.?3

9. Idtatns: 9 y 1 Hfpntakusd: 1.89

=. Idtatns: 5 y 2 Hfpntakusd: 2.99

1. Idtatns: 4 y 3 Hfpntakusd: 3.?3

Ldkns d `d nerd (p. 136)

4. E. 49.28? lfkutns: 85?.8?? sacukmns

5. d. 45¿92½56“

9. d. 59¿ 51‖ =8“

e. =8¿ 18‖ =8“

i. 13¿ 1‖ 5=“

=. 65¿ 11‖ =?.9“

1. i. 45,1229 latrns

2. e. 5,6581 latrns

3. d. ?.3819 rdmfdkas

8. d. Ϗ /5 < 4.13?362953 rdmfdkas

e. Ϗ /2 < ?.159168331 rdmfdkas

i. 44Ϗ /48 < 4.646825433 rdmfdkas

6. d. 2?¿

e. 9?¿

i. 491¿

m. 41¿

a. 44=¿ 91‖ 56.2“



Yasfùk 9. Bukifùk


Qkfmdm 5. Ua`difnkas y bukifnkas

4. Mnlfkfn: U - W?\

Udkcn (?, ∛)



5. Mnlfkfn: U - W-4\

Udkcn (-∛,?) Q (?, ∛)

9. Mnlfkfn: U - W-4.5166\

Udkcn (-∛, ∛)



=. Mnlfkfn: U - W?\

Udkcn (-∛,?) Q (?, ∛)

1. Mnlfkfn: U - W-9\, W4\ Udkcn (-∛,?) Q (?, ∛)




4.

=. Mnlfkfn: U,Udkcn: U,

as bukifùk,

sf as ukn d ukn

9.



1. Mnlfkfn: U-W9\,

Udkcn: (-∛, ?) Q (?,∛)

as bukifùk, as ukn d ukn

2. Mnlfkfn: U-W?\,Udkcn: U+,

as bukifùk,

kn as ukn d ukn



3. Mnlfkfn: U-W-9\,

Udkcn: (-∛, 4) Q (4, ∛),

as bukifùk, as ukn d ukn

8. Mnlfkfn: U,Udkcn: U+,

as bukifùk,

kn as ukn d ukn



6. Mnlfkfn:

U, Udkcn: U+,

as bukifùk,

kn as ukn d ukn

4?. Mnlfkfn: W9,∛),

Udkcn: U+,

as bukifùk,

as ukn d ukn



Yasfùk 5. _rneàlds dp`fidmns ak `d rasnùifùk ma trfäkcu`ns raitäkcu`ns

Ajarififn 4 (p. 2??)

5. Yak δ < ?.2

Ins δ < ?.8

]dk δ < ?.31

Intdk δ < 4.99

Yai δ < 4.51 Insai δ < 4.23.

Yak θ < ?.8

Ins θ < ?.2

]dk θ < 4.99

Intdk θ < ?.31

Yai θ < 4.23

Insai θ < 4.51.

Ajarififn 5 (p. 2?=)

4. d. x < 42.628

e. x < =9.884

i. x < =4.992

m. x < 94.99? a. x < 93.6=?

b. x < 22.2?1

5. @d d`turd ma `d tnrra Afbba` as ma 681.415 pfas.

9. A` axtraln suparfnr ma `d asidàrd astä d 46.=?2 pfas ma d`turd.

=. A` pnsta lfma 445.68 pfas ma d`turd.

Qkfmdm 9. ]rfcnknlatrìd ak uk trfäkcu`n raitäkcu`n




Ldkns d `d nerd (p. 2?8)

4. i. 991,543 l

5.

5?8 -?,=26 -?,889 ?,195 4,884 -4,499 -5,49?

451 ?,846 -?,13= -4,=58 -?,3?? -4,3=9 4,554

1 ?,?83 ?,662 ?,?83 44,=9? 4,??= 44,=3=

=8 ?,3=9 ?,226 4,444 ?,6?? 4,=6= 4,9=2

93 ?,2?5 ?,366 ?,31= 4,953 4,515 4,225

416 ?,918 -?,69= -?,98= -5,2?1 -4,?34 5,36?

9?1 -?,846 ?,13= -4,=58 -?,3?? 4,3=9 -4,554

438 ?,?91 -?,666 -?,?91 -58,2=5 -4,??4 58,22?

86 4,??? ?,?43 13,9?5 ?,?43 13,944 4,???

9. d. 439,5?1 l

Yasfùk 5. D`cukds fmaktfmdmas eäsfids

Ajarififn 4 (p. 2?3)


4? ?,43= ?,681 ?,432 1,234 4,?41 1,316

41 ?,516 ?,622 ?,528 9,395 4,?91 9,82=

5?,8 ?,911 ?,691 ?,98? 5,299 4,?3? 5,842

9? ?,1?? ?,822 ?,133 4,395 4,411 5,???

=1 ?,3?3 ?,3?3 4,??? 4,??? 4,=4= 4,=4=

2? ?,822 ?,1?? 4,395 ?,133 5,??? 4,411

31,2 ?,626 ?,5=6 9,861 ?,513 =,?54 4,?9538 ?,638 ?,5?8 =,3?1 ?,549 =,84? 4,?55

8? ?,681 ?,43= 1,234 ?,432 1,316 4,?41



Yasfùk 4. Bukifnkas sakn y insakn

Ajarififn 4 (p. 24=)

d. tdk < 4

e. intdk < 4

i. sai < 5

m. insai < 5


d. tdk < 5

e. intdk <

i. sai < 5

m. insai <

Yasfùk 5. Cräbfids ma d bukifùk sakn


4. Dlp`ftum: W9,-9\

Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns rad`as

Ϗ=

Ϗ=

Ϗ=

Ϗ=

Ϗ9

Ϗ9

99

Ϗ9

5 99

Ϗ9

t Ϗ /= Ϗ /5 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ

9.Yak t 5,45 9,?? 5,45 ?,?? -5,45 -9,?? -5,45 ?,??




t Ϗ /= Ϗ /5 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ

4/5.Yak t ?,91 ?,1? ?,91 ?,?? -?,91 -?,1? -?,91 ?,??

5. Dlp`ftum: W?.1,-?.1\

5. Dlp`ftum: W?.51,-?.51\

_arìnmn: 5Ϗ

4. Dlp`ftum: W=,-=\

_arìnmn: 5Ϗ



9. Dlp`ftum: W4,-4\

_arìnmn: 8Ϗ

5

9

45

=. Dlp`ftum: W4,-4\

_arìnmn: Ϗ

1. Dlp`ftum: W9,-9\

_arìnmn: Ϗ



Yasfùk 9. Cräbfid ma d bukifùk insakn


4. Dlp`ftum: W1,-1\

_arìnmn: Ϗ

5. Dlp`ftum: W4,-4\

_arìnmn: Ϗ

9. Dlp`ftum: W?.1,-?.1\ _arìnmn: 5Ϗ

=. Dlp`ftum: W1,-1\

_arìnmn: Ϗ

1. Dlp`ftum: W?.=,-?.=\

_arìnmn: Ϗ


49

45

59

5

1

4. Dlp`ftum: W=,-=\

_arìnmn: 5Ϗ



5. Dlp`ftum: W9,-9\

_arìnmn: 5Ϗ

9. Dlp`ftum: W?.51,-?.51\

_arìnmn: 5Ϗ

=. Dlp`ftum: W5,-5\

_arìnmn: 8Ϗ



1. Dlp`ftum: W9,-9\

_arìnmn: 2Ϗ

Yasfùk =. @d bukifùk tdkcakta


4. ?.485. -4

9. 4.39

=. -?.53

1. -?.18

Yasfùk 1. D`cukds fmaktfmdmas trfcnknlætrfids


4.

5.

9 2Ϗ

Ϗ5

Ϗ5




4.

Yasfùk 2. Cräbfid ma d bukifùk intdkcakta


4.

5.

9. 5Ϗ

=. =Ϗ

1.

Ϗ9

Ϗ2

Ϗ5



Yasfùk 3. Bukifùk saidkta

Ajarififn 4 (p. 2=?)

4. 4.=55. -5

9. 13.9?

=. 9.39

1. -?.95

Yasfùk 8. @d bukifùk insaidkta

Ajarififn 4 (p. 2=9)4.

5.

9. 2Ϗ

=. 9.9Ϗ

1. 5?Ϗ

Yasfùk 6. Rarfbfidifùk ma fmaktfmdmas trfcnknlætrfids

Ldkns d `d nerd (p. 2=6)

5Ϗ9

5Ϗ1

@ns ajarififns ma` 9 d` 4?, snk malnstrdifnkas `ds iud`as `ds raspuastds snk `ds qua maeaksflp`fidr `ns astumfdktas maspuæs ma` fcud`.

4. i. Fmaktfmdm

5. m. Dlens lfalerns ma d fmaktfmdm snk fcud`as

9.

=.

1.

sak

4 ’ sak5

4

ins θ

ins

4 5



Yasfùk 4. Ajalp`ns fùstrdtfvns


4. A` äkcu`n ma aàvdifùk ma` sn` as ma 14¿ 5?‖ 5=.26‖‖.

5. A` äkcu`n ma `d rdlpd ink `d hnrfznktd` as ma 45¿ 9=‖ 41.4=‖‖.

9. d. @d mfstdkifd qua hdy d` amfbfifn as ma 3.1 pfas.e. @d asidàrd sa edjd 4.15 pfas.

=. A` amfbfifn lfma 9?.45 l ma d`turd.

1. i x < 4?.96 y < 1.5?

e. x < =.61 y < =.61

i. x < =2¿ 96‖ 56.23‖‖

2. x < 23.85 θ < 54¿ 42‖ =.64‖‖ δ < 28¿ =9‖ 11.46‖‖

3. @d ]nrra lfma 5?3.88 pfas ma d`turd.

Yasfùk 9. ]anrald ma` insakn


4. d. d < 5.55 i < ?,69 ε < 89¿

e. δ < =9.6¿ ε < 32.4¿ i < 1.25

i. d < 9.5 ε < 26.1¿ θ < 1?,1¿

m. e < 98.41 δ < 31¿ θ < =2¿

a. δ < 4?=.3¿ ε < 48.4¿ θ < 13.5¿

b δ < 68 9¿ ε < 98 =¿ θ < =9 =¿

Qkfmdm 1. Dp`fidifnkas ma `d trfcnknlatrìd



5. @ns äkcu`ns snk: 85.8¿, 11.8¿ y =4.=¿, raspaitfvdlakta.

9. D astä d 69.28 l y E astä d 32.48 l ma mfstdkifd d `d tnrra.

=. A` ären` tfaka 2.31 latrns ma d`turd.

1. A` astumfdkta maea masirfefr ink sus pd`derds `ns inkiaptns sn`fiftdmns.2. @d tnrra lfma 98.=8 l y `d mfstdkifd DT lfma 2=.?1 l.

3. @d lnktdôd lfma 996.19l ma d`turd.

Yasfùk =. Aiudifnkas trfcnknlætrfids


4. θ < ? θ < 5Ϗ

5. θ <

9. θ < θ < θ <

=. θ < θ <

1. θ < ? θ < Ϗ θ < θ <

2. θ < θ < θ <

3. θ < θ < θ < θ <

8. Kn axfsta.

6. θ <

4?. θ < ? θ < Ϗ θ < θ <

Ajarififn 5 (p. 28?)

4. 56.5¿

5. 42.?=¿

9. 2?.28¿

=. 39.61¿

Ϗ=

5Ϗ9

Ϗ=

9Ϗ=

Ϗ=

=Ϗ9

Ϗ

=

1Ϗ

=Ϗ9

5Ϗ9

=Ϗ9

Ϗ5

9Ϗ5

Ϗ9

=Ϗ9

5Ϗ9

Ϗ5

9Ϗ5



2. 26.6¿

3. 24.9¿

8. 15.8¿

6. 4=5.8¿

Yasfùk 2. Bùrlu`d ma Harnk


4. d. 4?8.?5=

e. 989?5.6?1

i. 48.294

5. A` ärad ma` jdrmìk as ma 4?=3.= l5


4. A` `dcn lfma 481.84 pfas ma `drcn.

5. Hdy 2.?2 latrns aktra a` puktn ma` sua`n ma` tnpùcrdbn y a` nejatn vfstn pnr a` lfsln.

9. A` ide`a lfma 31.=8l ma `nkcftum.

=. D 4395.1l astä a` darnpuartn.

1. A` c`nen sa akiuaktrd d 4.??? l ma` edrin.

2.

3. d. e < =?.18 i < =4.=2 θ < 31¿

e. d < 94.=5 i < 42.52 δ < 4?1¿

i. d < 41=.=1 i < 563.95 θ < 45?.8¿ m. e < 2.35 i < 9.=8 θ < 41¿

8. A` ärad ma` idlpn as ma 43264.52 l5.

6. A` tarrakn vd`a $188‖1?3.2??.

4?. A` äkcu`n qua bnrld `ns erdzns ma` inlpds as ma 5=.3¿.

44. Ak äkcu`n iaktrd` ma `ns rdmfns as ma 98.6=¿.



Yasfùk 4. Uaitds ak a` p`dkn

Ajarififn 4 (p. 26?)

4.

Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn (pdc 211)

5.



9.

=.



1.

2.



Yasfùk 9. Innrmakdmds ma` puktn lamfn


5. _uktn lamfn: (9, 9/5)

mfstdkifd d` puktn

lamfn:

4. _uktn lamfn: (4,9)

mfstdkifd d` puktn

lamfn: 43

4?45



9. _uktn lamfn: (9/5, 3/5)

mfstdkifd d` puktn lamfn:

=. _uktn lamfn: (- 1/5, ?)mfstdkifd d` puktn lamfn:

185

4=15



1. _uktn lamfn: (-=,?)

mfstdkifd d` puktn

lamfn: 1

2. _uktn lamfn: (?,?)mfstdkifd d` puktn lamfn:

52 *



Yasfùk 1. Aiudifnkas ma `d raitd ak a` p`dkn

Ajarififn 4 (p. 3?3)

4. d. y ’ = < 5( x ’ 9)

e. y ’ 9 < x ’ 5

i. y + 5 < ?

m. y ’ 9 < =( x + 5)

a. y ’ 4 < ( x ’ 5)

b. y < 1 x

5. y < ’

9. d. y < -9 x + = l < -9 _uktn ma inrta aja y < (?,=)

e. y < 5 x ’ l < 5 _uktn ma inrta aja y < (?, - )

i. y < ’ l < _uktn ma inrta aja y < (?, - )

m. y < + 1 l < _uktn ma inrta aja y < (?,1)

a. y < ’ l < _uktn ma inrta aja y < (?, - )

=. d. x + y ’ 4 < ?

e. x + y ’ 1 < ?

i. x ’ y < ?

m. x + y < ?

a. x ’ y ’ 9 < ?

1. d. + < 4 _uktn ma inrta aja y < (?,5) _uktn ma inrta aja x < (9,?)

e. - + < 4 _uktn ma inrta aja y < (?,=) _uktn ma inrta aja x < (-1,?)

i. ’ < 4 _uktn ma inrta aja y < (?,-5) _uktn ma inrta aja x < (=,?)

m. + < 4 _uktn ma inrta aja y < (?,9) _uktn ma inrta aja x < (5=,?)

a. ’ < 4 _uktn ma inrta aja y < (?, - ) _uktn ma inrta aja x < ( ,?

45

x

535

49

49

= x9

39

=9

39

1 x5

15

x1 91 41 91

=9

x

9 y

5 x

1 y

= x

= y

5 x

5= y

99 x3

= y5

3=

39



1. d. y < 5 x + 5

e. y < - x

i. y < 5 x + 4

m. y < 3 x ’ 2

a. y < -9 x ’ 4

2. d. 9 x + y ’ 45 < ?

e. ’ y + < ?

i. x ’ y ’ < ?

m. 5 x + y ’ 4 < ?

453

45

499

x

565

Yasfùk 2. Uaitds pdrd`a`ds y raitds parpakmfiu`dras


4. e. B(x)<-6x + 59

5. d. B(x)< =x-1

9. Ynk pdrd`a`ds

=. e. l <



3. d. y < -9 x + =

e. y < 5 x ’ 1

i. y < 5 x ’

m. y < -5 x + 1

a. y < x

8. d. x + y ’ 4 < ?

e. x + y ’ 1 < ?

i. x ’ y < ?

m. x + y < ?

a. x + y + < ?

6. d. x + y ’ 4 < ?

e. y ’ 5 < ?

i. x + 9 < ?

m. = x ’ 9 y + 45 < ?

a. 5 x ’ y + 3 < ?

b. 1 x + y ’ 4= < ?

4?. d. Yf snk in`fkadàs.

e. Kn snk in`fkadàs.

i. Kn snk in`fkadàs.

m. Kn snk in`fkadàs.

a. Yf snk in`fkadàs.

49

49

=9

453

4?93

59



Yasfùk 4. @d ifriukbarakifdAjarififn 4 (p. 352)

4. d.

e.

Qkfmdm 3. Iurvds ak a` p`dkn



i.

m.



a.

5. d. _uktn (5,-9).

e. Rdiìn.

i. Ifriukbarakifd: Iaktrn (-9,?) Udmfn 4?

m. Rdiìn.

a. Ifriukbarakifd: Iaktrn (-9,=) Udmfn 3.

Yasfùk 5. @d a`fpsa


4. d. Rærtfias: (-9,?), (9,?).

Bnins: (- 1, ?), ( 1, ?)

Axiaktrfifmdm: ?.31



e. Rærtfias: (?,-6), (?,6)

Bnins: (?, ’ 21 ), (?, 21 )

Axiaktrfifmdm: ?.6?



i. Rærtfias: (-3,?), (3,?)

Bnins: (-5 2, ? ), (5 2, ?)

Axiaktrfifmdm: ?.3?

x5

2= y5

41

x5

2

y5

2=

x5

42 y5

6

x5

5? y5

92

x5

4 y5

51

5. d. + < 4

e. + < 4

i. + < 4

m. + < 4

a. + < 4




4. d.

e.



i.

m.



a. Kn sa puama crdbfidr

b.

c.



h.

f.



x5

6 y5

51

x5

= y5

6

5. d. + < 4

e. + < 4



x5

4

y5

92

x5

=6 y5

42i. + < 4

m. + < 4



9. Ärad ma `d a`fpsa: Ϗ * d * e

=. Yn`n tfaka uk puktn.

1. + < 4( x ’ =)5

4??( y ’ 4)5

51

Yasfùk 9. @d hfpæren`d

Ajarififn 4 (p. 3=1)

4. d. Dsìktntds: y < y < -9 x=

9 x=



9 x5

9 x5

e. Dsìktntds: y < y < -



1 x5

1 x5

x5

42

y5

6

i. Dsìktntds: y < y < -

5. d. + < 4



x5

= y5

6

( x + 9)5

=

( y ’ 9)5

4

e. + < 4

i. + < 4



Yasfùk =. @d pdräen`d


d. Rærtfia: (?,?) Aiudifùk mfraitrfz: y < -4Bnin: 4 _uktns axtralns: (-5,4),(5,4)

e. Rærtfia: (?,?) Aiudifùk mfraitrfz: y < = Bnin: -= _uktns axtralns: (8,-=),(-8,-=)



i. Rærtfia: (h,g) Aiudifùk mfraitrfz: x < -i + h

Bnin: (h+i, g) _uktns axtralns: (g-i,-5i-h),( g-i,5i-h)

m. Rærtfia: (?,?) Aiudifùk mfraitrfz: x <

Bnin: - _uktns axtralns:95

95

95

(- , 9), (- , -9)95

a. Rærtfia: (?,?) Aiudifùk mfraitrfz: x < -

Bnin: _uktns axtralns:

4=

( , - ), ( , )4=

45

4=

45

4=




4. Aiudifùk: ( y + 5)5 < 8( x ’ 4) Bnin: (9,-5) _uktns axtralns: (9,5), (9,-2)



9. Aiudifùk: ( y + 5)5 < 8( x + 5)

_uktns axtralns: (5,?), (-2,?)

5. Rærtfia: (?,?)

_uktns axtralns:

(5,=), (5,-=)



=.


4. e. Qkd ifriukbarakifd ma iaktrn (?,?) y qua pdsd pnr a` puktn (?,1)

5. d. Rærtfias: (4?,?),(-4?,?)

Bnin: (2,?), (-2,?)

Axiaktrfifmdm < ?.2



41=

41=

e. Rærtfias: (?,4),(?,-4)

Bnin: (?, - ), (?, )

Axiaktrfifmdm < ?.63



9. d. y < x y < - x9=

9=

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