A quiz question · easy
Where did Archimedes work out the principle of displacement, according to Vitruvius?
Vitruvius's De architectura IX, preface — written about 25 BCE — records that Archimedes saw water rise as he entered a bath, realised volume could be measured by displacement, and ran home shouting 'Eureka!' without dressing.
Read the full story →From the story
The Syracusan Mathematician Who Ran Naked Through the Streets in About 250 BCE Shouting Eureka After Working Out the Principle of Displacement in His Bath Archimedes was asked by King Hiero II of Syracuse to determine whether a goldsmith had fraudulently substituted silver for some of the gold in a royal crown. The principle of displacement — that a submerged body displaces a volume of water equal to its own volume — occurred to Archimedes in the public bath. He reportedly ran home shouting "Eureka!" without dressing. The first surviving record of the story is Vitruvius, two centuries later.
Related questions
- Archimedes is supposed to have run naked through Syracuse shouting *Eureka!* — 'I have found it!' — after a sudden insight came to him while bathing. What had he figured out?
- What technique in Archimedes's *Method of Mechanical Theorems* anticipated what later mathematics?
- Which Greek astronomer proposed that the Earth orbits the Sun — eighteen centuries before Copernicus?
- The Archimedes Palimpsest is a 13th-century Greek prayer book whose vellum pages were originally scraped Archimedes manuscripts. Some of the works it preserves — including the *Method of Mechanical Theorems* — exist nowhere else. Who identified the underlying Archimedes text, and when?