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From Ancient Greekεὕρηκα(heúrēka, “I have found”), perfect active indicative first singular of εὑρίσκω(heurískō, “to find”). Archimedes supposedly exclaimed this when he figured out how to determine the density of an object. First use appears c. 1603 in a text by Philemon Holland.
Eureka! I have found it! What I mean / To say is, not that love is idleness, / But that in love such idleness has been / An accessory, as I have cause to guess.
"Eureka!" he cried, his teeth shining through his beard. "Gentlemen, you may congratulate me and we may congratulate each other. The problem is solved."
1970, Peter Porter, The Sanitized Sonnets, The Last of England:
A page is turned - eureka, a snatch of tune / is playing itself, the piss-proud syllables / are unveiling a difficult prosody.