Buoyancy

Archimedes' principle: a body fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. Derivation: the hydrostatic pressure at the bottom of the body exceeds that at the top by ρ·g·h, where h is the vertical extent; integrated over the body's horizontal cross-section, this gives ρ_fluid·g·V_submerged, which is exactly the weight of displaced fluid.

Whether an object floats, sinks, or hovers depends on the ratio of its density to the fluid's. Ice floats on water because it's 9% less dense; steel sinks because it's eight times denser; a helium balloon rises because helium is one-seventh the density of air.

Stated by Archimedes of Syracuse around 250 BCE, according to Vitruvius's anecdote about the crown of King Hiero and the famous naked run through Syracuse shouting 'Eureka!'