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Archimedes studied astronomy, engineering, mathematics, and war tactics.
"Eureka!" (I have found it!) - his shout after discovering of so called Archimedes' Principle.
Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cyclinder. He is known for his formulation of a hydrostatic principle (known as Archimedes' principle) and a device for raising water, still used in developing countries, known as the Archimedes screw.
Archimedes principle - weight of the liquid displaced by the object= buoyant force weight=mass x acceleration due to gravity =volume x density x acceleration due to gravity
There isn't anywhere that lists an exact date for the discovery of the Archimedes Principle. The closest that could be found was that the special event occurred some time 2200 years ago somewhere between 287 BC and 212 BC.