Ancient Science · Part 9 · Alexandria · B2–C1
Archimedes: The Lever, the Sphere and “Eureka” as a Later Story
Part 9 of Ancient Science: Archimedes of Syracuse wrote some of the greatest works of ancient mathematics and built the machines that held off a Roman army, but the stories everyone knows about him, from the bath to the burning mirrors, were written down centuries later. Sophia separates the man from the legends. It was Vitruvius who… and What he actually wrote was…, with Philo, Sophia, Marcos and Demetria.
Tonight: Archimedes of Syracuse, perhaps the greatest mathematician of the ancient world, and certainly the one with the most stories told about him.
The man in the bath! He ran through the streets with no clothes on, shouting “Eureka!”
That is the story everyone knows, Marcos. It was written two hundred years after his death, by a Roman architect. Shall we look at what Archimedes wrote himself?
Enough to keep mathematicians busy for two thousand years. Let me show you.
Archimedes lived in Syracuse, a Greek city in Sicily, and was a friend, perhaps a relative, of its king, Hiero. He may have studied in Alexandria as a young man, and all his life he sent his discoveries in letters to mathematicians here, among them Eratosthenes, the librarian.
About a dozen of his works survive. In them he finds the area of a circle and shows that pi lies between 3 10/71 and 3 1/7; he proves that a sphere has two thirds of the volume of the cylinder around it; he explains the lever and the centre of gravity; and in On Floating Bodies he shows that a body in water is pushed up by a force equal to the weight of the water it pushes aside.…
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