Archimedes (Syracuse, 287-212 B.C.). Greek mathematician and engineer which is included among the top ranking mathematicians in history. Also a natural philosopher. He demonstrated that all numbers can be written down, by writing down the number of grains of sand needed to fill the entire universe. He expertly used the method of exhaustion developed by Eudoxus. He found ratios of the volumes of various figures, such as that of a sphere and a cylinder with a height equal to the diameter of the sphere which is equal to two thirds. He was the first to apply mathematical laws to levers. He is also known for his discovery that a body immersed in fluid displaces an amount of fluid equal to its own mass. Legend has it that he discovered this while in the bath and later ran naked around the streets of Syracuse shouting Eureka (I have found it). He used levers to pull a fully loaded ship on shore, thus supporting his statement: "give me a lever long enough and a place to stand and I can move the Earth". According to legend he was killed by a soldier while contemplating geometric figures drawn in the sand, even though the soldier's commander had ordered Archimedes' life spared.
I also found a bit about a Greek who though the Earth was a cylinder! He must already have been confined to General Ledge as I can't remember his name.
Archytas of Tarentum (420-350 B.C.). Greek mathematician. Built a series of toys, among them a mechanical pigeon
Poseidonius (Apamea, 140-50 B.C.). Incorrectly calculated the Earth's circumference, which 1500 year later, led Columbus to believe that Asia was only about 3000 miles west of Europe. (Just shows you shouldn't rely on someone else's workings!)
