MATH 4400, History of Mathematics

MATH 4400, History of Mathematics Lecture 2: The Greek era (con t) Professor: Peter Gibson pcgibson@yorku.ca 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 in 338BC Philip of Macedon conquered much of Greece. 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 in 338BC 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 his generals, P. Gibson (YorkU) Math 5400 27.9.2016 3 / 15

Upon Alexander s death in 323BC, his empire was divided amongst his generals, leading to the Hellenistic period. P. Gibson (YorkU) Math 5400 27.9.2016 3 / 15

Upon Alexander s death in 323BC, his empire was divided amongst his generals, leading to the Hellenistic period. Some mathematicians from the period after Alexander: P. Gibson (YorkU) Math 5400 27.9.2016 3 / 15

Upon Alexander s death in 323BC, his empire was divided amongst his generals, leading to the Hellenistic period. Some mathematicians from the period after Alexander: Euclid of Alexandria (323-285BC) P. Gibson (YorkU) Math 5400 27.9.2016 3 / 15

Archimedes Archimedes lived from 287-212 BC, during the Hellenistic period. 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 regional power, 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

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 of Syracuse. P. Gibson (YorkU) Math 5400 27.9.2016 7 / 15

Archimedes himself was killed by a Roman soldier during the seige of Syracuse. 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 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 works Some 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 Method of Mechanical Theorems, along with other previously known works. P. Gibson (YorkU) Math 5400 27.9.2016 10 / 15

The Archimedes Palimpsest contains the only known version of his Method of Mechanical Theorems, along with other previously known works. The former is a letter, written to Erastosthenes of Alexandria, a famous contemporary of Archimedes. 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 equilibrium but 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 applied to 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 straight lines 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 having each authored a compilation of mathematics. Euclid wrote the Elements, consisting of thirteen volumes mainly concerning 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 Greek mathematics from antiquity is Ptolemy s Almagest. P. Gibson (YorkU) Math 5400 27.9.2016 13 / 15

Ptolemy After Euclid s Elements the next important compilation of Greek mathematics from antiquity is Ptolemy s Almagest. Ptolemy of Alexandria (85-165AD) was known for the Almagest, consisting of 13 books, covering geometrical theorems, trigonometric tables the motion of the sun the moon eclipses the fixed stars 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 the time 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

Diophantus Diophantus 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