Archimedes

Archimedes lives in Syracuse and corresponds with the scholars of Alexandria. He finds the ratio of the volume of a sphere to that of its circumscribed cylinder and asks that the figure be carved on his tombstone; he computes the areas of curved figures by a method close to later integration; and he explains why a body in water loses exactly as much weight as the water it displaces. He also builds compound pulleys, the water-screw, and the engines with which Syracuse holds off the Roman siege for two years. When the city falls at last, he is killed by a soldier — as the story goes, bent over a diagram in the sand.