Parallelogrammum Prosopographicum Sive Modus Novus Delineandi per Radios Parallelos adAequalitatem Orthogrophicam, Gestus, Situs, Habitusque Quoscunque Humani Corporis, ServataSymmetria,& Proportione Partium. Autore Ioanne de Sancto-Claro Scoto-LothianoAuthor(s): Ioanne de Sancto-Claro Scoto-LothianoSource: Philosophical Transactions (1665-1678), Vol. 8 (1673), pp. 6079-6085Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/101365 .

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Philosophical Transactions

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( 60?9 )

PARAL LELO G RAMMUM

PROSOPOGR APHICUM

SIVE

Modus novus delineandi per radios paral- lelos ad IEqualitatem Orthogrophicam, geftus, fitus, habitufque quofcunque hu- mani corporis, fervata Symmetria,& pro- portione partium.

Autore IO ANNE de San5o- Claro Scoto-Lothiano.

Vt varias ufus meditando extunderet artes.

Virg. Georg. i.

Ovum mnodm delineandi per radios parallelos defcriptirus, de Cl-. ri7mi Scheineri arte delineandi, per eonum radiofum, quam bre.

vimffm potero paucis ab/olvam. Conficiendum mihi curavi Parallelogram mum lineare , cujt u/f non contemnendam progreffum in piturafect , prcs- tertim in Profopographice,qae ab hoc mirabili ilftrumento (Mt ait Inven- tor) injupremo quafi eruditionis vertice collocatur , cujs ope nuper vultus hominsm naturalesf(cuindum omniafaciei lineamenta etiam ad capileum CA- pitis in dato itu expreff, corporis hsmanige/fl ad vivum di&fo citits, /dque non foltm arte infallibili, fcientifica, fed etiam modo cito, fectro, fubtili, abfquefatigatione mentis,imitatus fum.

Expertt fam tamen(licetlob hoc non eft quod fejqu;s de hbjHs infirumen- ti

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f 6c8x ) t prfltntia; ab Art'fic fljatnatur) neqgaquam ;nter partes Emypi in pla- o, earn effe fymmetriam, qua inter partes Prototypi dif/it;.

Cum enim delinearem nuper circino graphico Efjgiem viri fintis , Vul- tuffqe ereFlos adfudum colnum tollenfti , Cujus manus dextera propinquior catheira innixa eft, altera remotior demiffa animadverti, Prototypon lor.ge diveryfam formam naEtam efe in plano, qua}m in fe babebat. Partes enim Autcgra?hi aquales , tranfcripta funt in planum prorfus inMquales. Nulla quidem fuit difcrepantia fenfibilis inter apparentem magnit. dinem manus dexterp Prototypi, licet oculo propinquioris , C finiftra remotio- ris ; Etypi tamen in plano delineati manus dextera, finiftra major fit , quia nSeEio communis pIani , & radio coni ad manum dexteram tendentis, major ftit fecione commumi plani, ef pyramidis optica ad manum finifiram protenfe.

Statui prcterea magnuim librum Fig. . Tab.ll./fuper menfar, ad an. gulos axi optico obliquos , cuj in eo Jit-u apparent magnitudo h,,d magno- pere differebat ab ejufdem apparente magmnitdine in fitt perpendiculari. In

terpojito autem piano delineatorio in quod projec7us eft liver , hanc formrm, Fig.II Tab. I.exrefam, acqmfijvit priori prorfus difJImilem,cujus par- tes profit ab oculo (omnium radiorum, qui ab objecis protenduntur, principio & origine communi) remotiores, in planopaulatim dimiuMt, funt , ut pater in libro, Fig. I . Tab. II, ob rationemfnpra memoratam. Ex quo lu,-len . tercernere eft dijFerentiam , inter rei Apparentim , ejuffjue Projectio- nem. Nam manente oculo (ut ait Aquilonius) ac rei ftu, quamtumvis planum in omnem partem mutetur, eodem tamen femper modo res apparet: At fecxndum planlfitumrn alia & alia erit rei Proje&tio. Apparentia ex dH- orum duntaxat habitudine pendet, rei nempeobjeca, e& intuentis oculi Pro jedtio vero infuper (qu eft rei fo/ide in planum tranfcriptio), planum deof- sit , in qtod prof4ji radii vMr:e incidtaNt. Obverfetur enim Circulus af- petsi direc! e apparebit ut Circulus, fi vero imterponatur pl/num obliqCuum neuti iuam in Cirt Klnm pri jiciet ur, Jfd genuinam famJimilit/ dinem exfet,

forma vel Ellipfsos, Iy perbolaes, el P3rabola, pro variafWe.iine Py- ramidis optic:, cujUs vertex Gculus. bags autem res vifia

Eft quidem inter re; pro;etlas a Parallelogrammo, ecrumqye proje.t#lur, Opticafimilitudo ~ a. l/itas. I ,tia, ctm projeTturx iftjfint optice fimi- les &e aq.uales u ni fmir,ii & e qualium , nim. Speciei interfe/io?ni , cst, ebjec'fm quo, & picitura objeci rationalis, e aerea dicitur, erunt etiam

cptice fimin/es - qcuales alte i qxoque fimilium & aualium, nim. obiecto quod, fiet rei proje6e. Sed ut adpropojrtum revertar, Excperentia didici qudodjamprilem rebar fu

turum. AMemini enim,: n efflEiem cujufdam in hortofedentis, cuj w imaoo per lentema convexam ii cbhartam tranfmrifafuit, ducerem, crura pedes mMnl turn ultra reliutl corporis proportionem, utpote proxiores, crefcere. Neqve efAl quod hoc novum aut iifJlitum videatHurjficut enimf e habet Pantogarphices planum ad imaginem corporis propinqi, qu abip;fo intercipitur ;, fc

" char - talenti convex. pratentt ad imaginem, qu4 ab ifa excipitur, qxaque cor-

pore:

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( 6082 ) pere non admodum diffito per fenefram tranfmittitur. Planum drtem Pan- togr3phices dico uperficiem illam imaginariam in aere, 'quam Index Ste-

reographicms percnrrit, qcuaque produE?a cum tabl lafperficie, in qua fit de- lineatio, coincidit.

Sed &' aperti.rs hoc fiet in umbra hhmaxi corporis qtio piroriores enim unot nou candelg, manus ant pedes a!:t cetera membra eo majorem in pa-

r e em oppofltum umbram eftzndnat i qod cuivis obvium eft. Exten'is e- aim bra hiis, qz.e manus pariti proxima cfi minorem , qje remotior ejft '

candcl-propior , majorem uimbram redait; non fecus ac qua ma nas oculo aclineantzM propior eft, ampliori imginc, q.ce vero remctisr, inoAor d;:citr. S icut enimfe habet Pera!lelogrammi planum ad imaginem cerpora defcriben- ai, firc paries aci firYamkiq Y, dn .

HmIi a Me a mal/o qugod b ingeiofijmf alioquin Pantographices Inven- tore nencqayam n.tat,tm eft , rit rcmeai:tm aliquod reptrirem, r,:t/ra nt iro zv,leam. Sebilbat iraterdum, num qcun ratione ad diftantiam partium Pro. t ovoi, ant/orfurbm retrorJum Paral!/e!ogrammum movendo, debita pro- pfrti5N;'s in cffl7ie retine,i po5ent. Se d,trn nec in hoc exi:um ulltum mens re,r'ret, da imagine, qua a plano Parallelogrammi intercepta, effigiem Pro' Iot ;o 0,-tho7raVhbce eq4alem redderet, cogitare copi. Hoc invento, coetera oi;4;ia pona . proclivi fore. In mentem igitur venit Problematis illiu , qc,od o'irm aptd Keplerur in Dioptricis legere memini : Lumen, fcil. Cindcla2 notu quam longirfime ejjcul'rl, odf pijfime me, & frd' t,-e, 's io frqe qui nobt;tc'm literis operam dabant , crebri experiments p4- irem meum aocti!e recordor. IJiberhisl e,n:m no0tibus per tenebra den- iffi'm.u tr.jeclo ad /ongiffimam dis7antiam lufmine, quaf minutijffimis typis im?rej fafere, facra bibl ia non mirsJ faJci/e, quam in meridiana luce lege- re erat,Cum enim , ut docIiffimm ille Keplerus docet , eadem ft refractio r;~dio m,] Jve illi natur tfua e iM;rediantur, five egzediantur , ckm z flamma lamiadis aut candela in pundo, ubi radii f,la es concurrere foent, pone len- tem co'iocatur, lumen tranfmif um radi'is Jf non Parallelts, quaf itamen Pa- rallellM,ad lo,giffmam dftantiam transfunditur ; fit que ut qe, ratione inter- a.ram lmnen foils fuperficiem lentis aver fam irgreditur, no/r,t lumen candelx a,;t ncerna ab eadem dizreaiatnr. Siccqxe fi (quod docent, nec fine ratione nonn/li) lumen fit corpora lucidi pecies vifibi/ts, imago Parallela zndique tr.ebrzs conftricia habetur. Nec ejt quod cuiquam di/pliceat, quod voce hac in r[er;f abfolto utar, cum fJri'te loguendo in Categoria Relatorumfit. Omne enim parallelum cu-m alicni parailelum fit, j- eelatum ejf, cHin delta f i'nt qua id quod fuint aliorum eJe acicunttr.

Sed cam /n4rfonomi dicant S ph.ram P'arallelam, cur non & mihi ima- eircem Parallelam, dicere liceat ?

S'e qjuandoquidem mentioumbre pa 'all'et incidit, ecce tibi aliud imagi$ ris aralle,x exemplum in umbris , qua oriente vel occidente Sole in parie- tibus radiis folarItbs ad angulos rectos oppofitis confpiciuntur, qucj ue licet tenebrofe , multurm tamen lcis in prafenti negotio a,ferunt , c(m Geome. rice corplrib,s, Ntuefinunnt, a,tuales Jiat. Dent venimm optici, qui fa.

cite

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( 608 ) ile demonYirAbunt, fne r4diosfolares qui mwbrt illt parallel chlaudunt,in

rigore mathematico parallel fcjfe cuem non ad demotltrationem, fed ad tiU-

flrationem hoc exempo Wtar.

-ifce pramifJis,fingawtu ab omnibu Prototypi Punis radioo p ,ralle. los pratendi, adanrglos qua fieri poteft reEtiEffios in planvm Panto. graphices incidere qma ratione fiat, t Index Stereographicus Gmn.4A illapunta faltem precipflapercurrat , nunc inquirendam re/lat.

PoJf#lat Scheinerus inter deli4eandum , ocu/um prorf; fi rvm. Sed, (fi hac nova methodo delineandi utarir,) fit oculus in Pro f'pogra-

phia liber & foltzts, nejee ulli certo anto affixm , Proq'e 1 dicv 3 tere. ographicoftt Tigillurn, feuregula oblega, piano Paralle.'grammi ad an- gglos retos aptaita. Tigillo deinde hbic injfiganmur d da optrx.per 5ua4 ocu- lM qUaifi collimare in omnia corporis defcribendi pn;la, faltem pracipwa, ec ratione pofit , tft radius vifwalis,per dioptras admiJftw, piano infirumen- tifmper firt perpndiclariir, excipiatsqe Pantographices planum em ?gi. rem aeream ad angelos reEos, Et dam oculi acies anicuilqe obje&ti depingena di punsofuccef/ive applicatur, ftylus, debito preeunte apparatu, i:n charta

fubjec7al, figuram objeii, fecundtur naturalerm ipJfiu fSmmetriam , da.a proportione, exa4-e defcribet.

In hoc cafu dico , dimmodo tantum 4 centre inftrumenti di[/et fy/tls frcriptorius,quantum ab eodem,radii ab objeito ad oculum per dioptra porter. fm,imaginem in Charta dauHam Ortbographice Prototypo aqualemfore. ,Qod fait quftitam. Idqe fic colligitur.

u, 9funt Orthographice equatla uni tertio,inter fcfunt qualia. SedEffiges defcripta, Protetypen,funt Orthographice q4ualiA unm tertto,

xim, interceptton irmaginis parallele, quam excipit Paralle/tgrammiplanum ad angtlos reFlo. E. e '

inter fe fnt aqualia; Major eY certa , utpote principium Geometricum. Minorex hypothef patet. Si qwiu autem Effi giemfervatis propertionibai & fymmetria diminui cupidt, hoc ficillime affe- quetur, ltylum Scriptorium inter indicem centrumrqe infirumenti collocan. do.

Sed oejicientforfan quidam, in obj¢etis longe diJJitzi aiioptrarum nullum

fore ffum. juid vere illudnofrx intereft, cam ad toltends tartX m in Profopographia diffictltates , quibs hatenus Scheineri Para f'/es ram. mum laboravit hbc nofra A4Methodus comparata fit ? Eft eni, zU om1C d- us fixo, eJfl;bi commodius foluto culo d.lineatio t, an/ligtur, ,y,aNat: autem folutO , e quando fixo oculo delineanax'im fit, altiorio eft a/i / .i. t

tionit. Occupatior fim imprefentiarum, quArm ut hnic indag..tioni va. cem. Hac , brevitati fldens , moaQojujcere arbitror. Reliqaa inge. niofo tyroni data opera -refervo.

Londini pri- dS. Kal,Maii MUCLXXII.

N nn nnn Birevit

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( 6084 )

Brevis & dilucida Parallelogrammi Profopographici defcrip. tio, quo delineantur modo novo, per radios Parallelos ad aqualitatem Orthographicam, geftus, (itus, habitufque quicun- que humani corporis , fervataSymmetria & proportione Par- tium.

N Schemate Fig. 3. Tab. II. Parallelgrammum rrofopographicmr eft ABCD , flylu centralis HF, calamw defignator LC, Index K

A, ive regula oblonga plano Parallelogrammi, ope clavi ftriati ex aere, fecundunm fpecimen E, adangulos reftos aptata. aHic regaul infiguntur dua Dioptrx PR, SV ; in medio PR pertufum efforamen 0, in medio S V

erigitur filim perpendiculare regla R A, in cs)jz medio ejt globulus qcui dam parvzu, per qzem, & foramen 0, radius ad oculum (qcem inter deline andum non oportet efe fixum, fed liberum a folutum) ab objecto protendi tur.

I. Animadvertendum ,radium per foramen 0 r globulum protenf#m,fem. per fore perpendicularem plano Prallelograwmi, five ejxs Diametro , quc eft recda linea extenfa per flylum defignatorixm LC, & centrkm fixum H F, d diEtum globulum parvum, in qua linea (emper verfatur ifte globules, qualifcunqae fit Parallelogramm motus.

2. Not. Planum delineatorimrmfenfibile , frer quod voltatur pex L,

flyli picoriiLC,adamuffim decribentis imaginem ad motumlndicis KA ,- in quod infix.u e ftylus centralis HF ,efe QYXT;pianm vera mere rati-

onale, five mathematicum , priori continuum, effe s JI y. 3. Not, Omnes radios ab objeao per glbulum & foramen 0 protenfos (ad

oculum , in tot meidii diaphani ptunis, dce Indice KA. collocatum, qact funt puncdta infuperficie Viibili objeCi defcribendi, qua fnt infinita,) femper fo. re fibi invicem Parallelos.

uoedfic probatur; ,^a eidem rera line funt Paralle/l, fed non in eodem caW illa plano,h4

quoque inter ft fint Parallele; per Prop. io. lib. i. Eucli-

dis. Sed omnes radii ob objeao per Dioptr.u ad ocClMm protenfT, eidem rel7e Ii.

nex, viz. radio ab objeclo per globuxlm foramen 0 protenfo, fnt Parallc- li.

Ergo fibi invice funt Paralleli.

Prob. Minor. Si dut rete linex eidem plano ad refos 7t angulos, Paral-

lela earut illx reda tinen, per Prop. 6. lib. 1. Eucl. Sed Primarius radius ab ebjeato per Dioptras ad oculum protefus,& om-

ncs reliqui radiifecundarii, plano mere rationali, mathematicos viz,i ¢Cy, ad rel2oJ funt angulos i ex hypothefi.

Ergo

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¢ 6085 ) Ergo emnes radii ab objec7o per dioptrae ad oculum protenfi eidem rec74

linea,viz. radio ab objecto per glObXulm & foramen 0 protenfo, funt paral- lli, qod eratprobandum.

Now,to the end that the Reader may the more readily fee the dif- ference between this Infirument, and that of the Learned Scheiner, our Author thought fit, here to fubjoyn a fhort de cription of that ofScheiner's, wlich perforni the work by Conical, as the Author's doth by Parallel, fpccies,

Defcriptio parailelogrammi Stereograp!ici a ClariffimoMathemati. co Chriflophoro Scheinero excogitati, quo per conum radio.umm, omv nia quaecunque fub afpetCumcadunt (tit pluribus apud authorem le- gere eft) arte infallibili, dieto citius, in planum projici poflunt, eodem fitu, ordine, figura, magnitudine apparente quo oculus illa haufic.)

N figurl Tab. I I. fuper menram A , C D bene planatamr, horihontiqec parallelam, erige adperpendiculum duu trabes LS, Fl,conjunUaa liz- no tranfverfo 0 E ab anteriore, & alio fimili a pofteriore parte, is

imponatur lignum oblongum L F, it ut ad arbitrium erigi ac deprim?poft, in cujns vertice infigatur dioptra K, ad/pecierum vifbilium receptionem col. ligendam.

Pofiea ad diflantiam H) tantam, quantam maXns Artificis, ex K ex- tenta, vetr(s parallelogrammum regen4tm poftulat, excita adperpendiculum fuper tabulam DH aferem planum H M N Z, qui & parallelogrammum pendulum P QJR T fuflentet, e piSuram depingendam recipiat. Ad puntum foraminis K cerradiant fingula punta objeCii oppofiti YEd, lineis YK, OK, EK, K, & aliis infinitis,qu intelligi, non exprimi,fo4 lent. Per ha ergo lineas, fpecies vifibiles obje&lum in foramen, & trans forAmen in oculum defert, qui fi in objeElumfertnr, & Jingulos ejus radios Indicis apice P abfcindit, calamo T, imaginem depinget in fperficie ta6laI H M N Z, fimilem illi imagini,eamplanum V X M H, fpeciem vi/ibiem fecans, in aere comprehendit.

Afer dellneatorius H M N Z mobilis efl faEus in extremitatibus bene- ficio cardinit H, & arcus quadrantalis Z h, t pofjit attolli &

deprimi, in. clinari & erigi, fecuned&m arbitrium Artiicis, & rei exigentiam.

Nnn nnn z Ar.

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I,iI ~~~~~~~~~ K.~~~~~~~~~~~~~~~~~~~~i~

I' i! .. ~i ;I:iii i ' ,l

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