early 17th century: from Greek heurēka 'I have found it' (from heuriskein 'find'), said to have been uttered by Archimedes when he hit upon a method of determining the purity of gold. The noun dates from the early 20th century.
In the 3rd century bc the Greek mathematician and inventor Archimedes of Syracuse in Sicily, was asked by the king Hiero to test his new crown to find out whether it was really solid gold as the maker claimed, or was an alloy made up to be the same weight. The story goes that the solution eluded Archimedes until he overfilled his bath, which overflowed as he got in. Suddenly the solution to the problem hit him. He realized that he could test whether or not the crown was pure gold by putting it in water and seeing whether it made the water overflow as much as a similar volume of genuine gold did. He is said then to have run through the streets shouting ‘Eureka!’, or rather heurēka, which means ‘I have found it’ in Greek. The name Archimedes' principle is given to the law stating that a body immersed in a liquid is subject to an upward force equal to the weight of liquid it displaces.