This exclamation is from the Greek heureka, meaning I have found it.
Legend has it that Archimedes uttered this exclamation when he realized that objects placed in water displace an amount of water equal to their own volume. Hiero II, tyrant of Syracuse, had supplied a goldsmith with gold to make a crown. But Hiero was not certain that the smith had used all the gold and so he asked Archimedes to test the crown. How to measure the volume of such an irregularly shaped object stumped Archimedes until one day, when climbing into his bath, he noticed the water displacement and realized that he could measure the volume of the crown through displacement.
From John Dee’s 1570 Preface to H. Billingsley’s Euclid:
For this, may I (with ioy) say ΕΥΡΗΚΑ.
By the mid-18th century, the word was Anglicized and being used outside of direct references to Archimedes. From Henry Fielding’s 1742 The History of the Adventures of Joseph Andrews:
Adams...returned overjoyed...crying out “Eureka.”
(Source: Oxford English Dictionary, 2nd Edition)
Copyright 1997-2016, by David Wilton