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MATH 4400, History of Mathematics Lecture 2: The Greek era (con’t) Professor: Peter Gibson [email protected] http://people.math.yorku.ca/pcgibson/math4400 September 27, 2016
MATH 4400, History of MathematicsLecture 2: The Greek era (con’t)
Professor: Peter Gibson
http://people.math.yorku.ca/pcgibson/math4400
September 27, 2016
Recall from last lecture...
The political authority of the Golden Age was fragile, however, and in338BC Philip of Macedon conquered much of Greece.
His son, Alexander, succeeded him in 336BC.
P. Gibson (YorkU) Math 5400 27.9.2016 2 / 15
Recall from last lecture...
The political authority of the Golden Age was fragile, however, and in338BC Philip of Macedon conquered much of Greece.
His son, Alexander, succeeded him in 336BC.
P. Gibson (YorkU) Math 5400 27.9.2016 2 / 15
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals,
leading to the Hellenistic period.
Some mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
Appolonius of Perga (262-190BC)
P. Gibson (YorkU) Math 5400 27.9.2016 3 / 15
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals, leading to the Hellenistic period.
Some mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
Appolonius of Perga (262-190BC)
P. Gibson (YorkU) Math 5400 27.9.2016 3 / 15
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals, leading to the Hellenistic period.
Some mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
Appolonius of Perga (262-190BC)
P. Gibson (YorkU) Math 5400 27.9.2016 3 / 15
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals, leading to the Hellenistic period.
Some mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
Appolonius of Perga (262-190BC)
P. Gibson (YorkU) Math 5400 27.9.2016 3 / 15
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals, leading to the Hellenistic period.
Some mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
Appolonius of Perga (262-190BC)
P. Gibson (YorkU) Math 5400 27.9.2016 3 / 15
Upon Alexander’s death in 323BC, his empire was divided amongst hisgenerals, leading to the Hellenistic period.
Some mathematicians from the period after Alexander:
Euclid of Alexandria (323-285BC)
Archimedes of Syracuse (287-212BC)
Appolonius of Perga (262-190BC)
P. Gibson (YorkU) Math 5400 27.9.2016 3 / 15
Archimedes
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 27.9.2016 4 / 15
Archimedes
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 27.9.2016 4 / 15
The punic wars (264-146 BC) pitted Rome against Carthage.
P. Gibson (YorkU) Math 5400 27.9.2016 5 / 15
The punic wars (264-146 BC) pitted Rome against Carthage.
P. Gibson (YorkU) Math 5400 27.9.2016 5 / 15
During the Second Punic War Carthage was led by Hannibal.
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During the Second Punic War Carthage was led by Hannibal.
P. Gibson (YorkU) Math 5400 27.9.2016 6 / 15
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 27.9.2016 7 / 15
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 27.9.2016 7 / 15
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 27.9.2016 7 / 15
The screw of Archimedes:
P. Gibson (YorkU) Math 5400 27.9.2016 8 / 15
Transmission of Archimedes worksSome of Archimedes works have been rediscovered relatively recently.
P. Gibson (YorkU) Math 5400 27.9.2016 9 / 15
Transmission of Archimedes worksSome of Archimedes works have been rediscovered relatively recently.
P. Gibson (YorkU) Math 5400 27.9.2016 9 / 15
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 27.9.2016 10 / 15
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 27.9.2016 10 / 15
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 27.9.2016 10 / 15
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 27.9.2016 11 / 15
Both Euclid of Alexandria and Appolonius of Perga are known for havingeach authored a compilation of mathematics.
Euclid wrote the Elements, consisting of thirteen volumes mainlyconcerning geometry (but also other mathematics)
Appolonius is famous for the eight volumes entitled Conics
These works were highly influential in later eras.
P. Gibson (YorkU) Math 5400 27.9.2016 12 / 15
Ptolemy
After Euclid’s Elements the next important compilation of Greekmathematics from antiquity is Ptolemy’s Almagest.
Ptolemy of Alexandria (85-165AD) was known for
the Almagest, consisting of 13 books, coveringI geometrical theorems, trigonometric tablesI the motion of the sunI the moonI eclipsesI the fixed starsI the motion of the planets
Geography
P. Gibson (YorkU) Math 5400 27.9.2016 13 / 15
Ptolemy
After Euclid’s Elements the next important compilation of Greekmathematics from antiquity is Ptolemy’s Almagest.Ptolemy of Alexandria (85-165AD) was known for
the Almagest, consisting of 13 books, coveringI geometrical theorems, trigonometric tablesI the motion of the sunI the moonI eclipsesI the fixed starsI the motion of the planets
Geography
P. Gibson (YorkU) Math 5400 27.9.2016 13 / 15
The geocentric theory of Ptolemy held sway for 14 centuries, until thetime of Copernicus, who in 1543 proposed a heliocentric theory.(By contrast, Euclid’s Elements endure.)
P. Gibson (YorkU) Math 5400 27.9.2016 14 / 15
DiophantusDiophantus of Alexandria (c. 3rd century AD) is known for is compilation,entitled the Arithmetica, of 130 algebraic problems.
P. Gibson (YorkU) Math 5400 27.9.2016 15 / 15
