Archimedes (Ca 287-212 BC) was an inventor, an engineer, an astronomer and possibly the first mathematical physicist. He revolutionized important parts of geometry. Plutarch is the source of most of what we know about Archimedes but it is sometimes hard to separate fact from myth concerning aspects of his life.
Archimedes invented various war machines, including the catapult and cranes used to capsize Roman ships. He also invented the Archimedes screw, used to drain swamps and ships. He postulated the Law of Levers, discovered how to determine the volume of a sphere and anticipated parts of integral calculus almost two thousand years before Newton and Leibniz.
King Hiero asked Archimedes to determine whether a laurel crown he had commissioned was truly made of gold, as ordered. The King suspected that it was diluted with silver.
While entering a bathtub, Archimedes observed that the water overflowed and realized that an object is buoyed up by a force equal to the weight of the water displaced. This enabled him to determine that the jewelers tried to cheat the King by mixing silver in the crown.
It is said he ran through the streets of Syracuse shouting "Eureka!" after comprehending the Law of Buoyancy.
