math 5400, history of mathematicspcgibson/math5400/math5400files/lecture3-2… · the archimedes...

MATH 5400, History of MathematicsLecture 3: Archimedes of Syracuse

Professor: Peter Gibson

pcgibson@yorku.ca

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.

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During the Second Punic War Carthage was led by Hannibal.

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During the Second Punic War Carthage was led by Hannibal.

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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:

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Transmission of Archimedes worksSome of Archimedes works have been rediscovered relatively recently.

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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.

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We have reached the point of Exhaustion; on to the blackboard...

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