On Floating Bodies
Peri Ochoumenon
A solid body immersed in a fluid displaces a volume of fluid equal to its own submerged volume and is buoyed up by a force equal to the weight of that displaced fluid, a single principle that determines whether any given shape will float, sink, or rest at any particular depth.
- Archimedes's Principle of buoyancy
- geometric rigor applied to fluid statics
- the floating paraboloid problem
- the (likely embellished) 'Eureka' story
- founding text of hydrostatics
On Floating Bodies establishes what is now called Archimedes's Principle, that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces, and uses this principle to work out, with full geometric rigor, the conditions under which various solid shapes float or sink. Heath's reconstruction of Archimedes's own cross-references places it among his later treatises, after On the Sphere and the Cylinder, On Spirals, and On Conoids and Spheroids. Its second book applies the analysis to a floating paraboloid, a level of sophistication in fluid statics not matched again until the early modern period. According to a story told by Vitruvius, Archimedes discovered the principle while checking a goldsmith's alloy for King Hiero II, supposedly running through the streets shouting 'Eureka.'
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