A king's fake crown led Archimedes to discover buoyancy

King Hiero suspected his goldsmith had swapped silver into a golden crown and asked Archimedes to prove it without melting it down. Soaking in a bath, Archimedes realized a submerged object displaces its own volume of water, letting him compare the crown's density to pure gold. He supposedly ran through the streets shouting 'Eureka.'

— Vitruvius, De Architectura, Book IX (Introduction) — c. 1st century BCE