MATH 5400, History of MathematicsLecture 3: Archimedes of Syracuse
Professor: Peter Gibson
http://people.math.yorku.ca/pcgibson/math5400
September 25, 2012
Historical context
Archimedes lived from 287-212 BC, during the Hellenistic period.
The age in which he lived was marked by the rise of Rome as a regionalpower, and by the first and second Punic Wars.
P. Gibson (YorkU) Math 5400 25.9.2012 2 / 10
Historical context
Archimedes lived from 287-212 BC, during the Hellenistic period.
The age in which he lived was marked by the rise of Rome as a regionalpower, and by the first and second Punic Wars.
P. Gibson (YorkU) Math 5400 25.9.2012 2 / 10
The punic wars (264-146 BC) pitted Rome against Carthage.
P. Gibson (YorkU) Math 5400 25.9.2012 3 / 10
The punic wars (264-146 BC) pitted Rome against Carthage.
P. Gibson (YorkU) Math 5400 25.9.2012 3 / 10
During the Second Punic War Carthage was led by Hannibal.
P. Gibson (YorkU) Math 5400 25.9.2012 4 / 10
During the Second Punic War Carthage was led by Hannibal.
P. Gibson (YorkU) Math 5400 25.9.2012 4 / 10
Archimedes himself was killed by a Roman soldier during the seige ofSyracuse.
He left behind numerous works, including
On the Equilibrium of Planes
On the Measurement of a Circle
On Spirals
On Floating Bodies
The Method of Mechanical Theorems
He is also credited with numerous mechanical inventions.
P. Gibson (YorkU) Math 5400 25.9.2012 5 / 10
Archimedes himself was killed by a Roman soldier during the seige ofSyracuse.
He left behind numerous works, including
On the Equilibrium of Planes
On the Measurement of a Circle
On Spirals
On Floating Bodies
The Method of Mechanical Theorems
He is also credited with numerous mechanical inventions.
P. Gibson (YorkU) Math 5400 25.9.2012 5 / 10
Archimedes himself was killed by a Roman soldier during the seige ofSyracuse.
He left behind numerous works, including
On the Equilibrium of Planes
On the Measurement of a Circle
On Spirals
On Floating Bodies
The Method of Mechanical Theorems
He is also credited with numerous mechanical inventions.
P. Gibson (YorkU) Math 5400 25.9.2012 5 / 10
The screw of Archimedes:
P. Gibson (YorkU) Math 5400 25.9.2012 6 / 10
Transmission of Archimedes worksSome of Archimedes works have been rediscovered relatively recently.
P. Gibson (YorkU) Math 5400 25.9.2012 7 / 10
Transmission of Archimedes worksSome of Archimedes works have been rediscovered relatively recently.
P. Gibson (YorkU) Math 5400 25.9.2012 7 / 10
The Archimedes Palimpsest contains the only known version of his Methodof Mechanical Theorems, along with other previously known works.
The former is a letter, written to Erastosthenes of Alexandria, a famouscontemporary of Archimedes.
Translations of all Archimedes known works are freely available.
P. Gibson (YorkU) Math 5400 25.9.2012 8 / 10
The Archimedes Palimpsest contains the only known version of his Methodof Mechanical Theorems, along with other previously known works.
The former is a letter, written to Erastosthenes of Alexandria, a famouscontemporary of Archimedes.
Translations of all Archimedes known works are freely available.
P. Gibson (YorkU) Math 5400 25.9.2012 8 / 10
The Archimedes Palimpsest contains the only known version of his Methodof Mechanical Theorems, along with other previously known works.
The former is a letter, written to Erastosthenes of Alexandria, a famouscontemporary of Archimedes.
Translations of all Archimedes known works are freely available.
P. Gibson (YorkU) Math 5400 25.9.2012 8 / 10
ON THE EQUILIBKIUM OF PLANES
OR
THE CENTKES OF GEAVITY OF PLANES.
BOOK I.
"I POSTULATE the following:
1. Equal weights at equal distances are in equilibrium,and equal weights at unequal distances are not in equilibriumbut incline towards the weight which is at the greater distance.
2. If, when weights at certain distances are in equilibrium,
something be added to one of the weights, they are not in
equilibrium but incline towards that weight to which the
addition was made.
3. Similarly, if anything be taken away from one of the
weights, they are not in equilibrium but incline towards the
weight from which nothing was taken.
4. When equal and similar plane figures coincide if appliedto one another, their centres of gravity similarly coincide.
5. In figures which are unequal but similar the centres of
gravity will be similarly situated. By points similarly situated
in relation to similar figures I mean points such that, if straightlines be drawn from them to the equal angles, they make equal
angles with the corresponding sides.
P. Gibson (YorkU) Math 5400 25.9.2012 9 / 10
We have reached the point of Exhaustion; on to the blackboard...
P. Gibson (YorkU) Math 5400 25.9.2012 10 / 10
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