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ARCHIMEDES OF SYRACUSE
Life Archimedes, the greatest mathematician of the ancient world and the greatest mathematical genius in Europe until Newton, was born, lived and died in the Greek city-state of Syracuse, in Sicily. He was the son of an astronomer called Phidias, and was closely associated with (and possibly related to) the city's ruler, Hieron II. He studied at Alexandria, in Egypt, where he met Euclid's successors Eratosthenes and Dositheus; he was also a friend and associate of Conon of Samos. His output was prodigious, both in quantity and in quality; and his enquiring mind explored many different fields: geometry, mirrors and lenses, hydraulics, mechanics, architecture, siege craft. His name is inextricably associated with the genesis of engineering in ancient Greece, and with the resolution of many famous mathematical problems. He is perhaps most celebrated, however, for his part in the defence of Syracuse against a besieging Roman fleet. Legend has it that when an act of treachery finally delivered the city to the enemy, a Roman soldier came upon Archimedes working out the answer to a problem in mathematics and killed him on the spot. His burial site was discovered by Cicero in 75 BC.

A commentary on Archimedes is found in the work of 6th century writer Eutocius of Ascalon, who also mentions a biography (now lost) of the celebrated mathematician written by Heraclides.


Work
The principal extant works are:

"On the Sphere and Cylinder": books I and II. Book I: Quadrature of the parabola, 6 definitions, 5 propositions (the 5th is the axiom of continuity), 44 theorems.

"Measurement of the Circle": 3 theorems are preserved.

"On Conoids and Spheroids": The book contains 32 theorems and 1 corollary following the 6th theorem. Some of the theorems use trigonometric functions and integral calculus.

"On Spirals": The book contains 28 theorems and 6...