On Floating BodiesArchimedes
About On Floating Bodies
Archimedes' , in two books, is the first systematic hydrostatics. Book I derives the principle that a solid immersed in a fluid is buoyed up by a force equal to the weight of the fluid it displaces. From that ground he proves that a floating segment of a homogeneous sphere finds stable equilibrium when its base lies parallel to the fluid surface.
Book II extends the analysis to right paraboloids of varying shape and density. Archimedes determines the positions of stable equilibrium when the base of the solid lies entirely above or entirely below the water line. The geometric argument is dense and exact. Later hydrostatics, from Stevin through Galileo and beyond, builds on this foundation.