Archimedes studies floating bodies

Archimedes lived in Syracuse during the third century BCE and studied geometry, mechanics, and equilibrium in liquids. Floating ships and the apparent lightness of an immersed object were familiar observations. On Floating Bodies brought them into mathematical argument. It begins with conditions for the equilibrium of an ideal fluid and then examines bodies of different shapes and densities. The surviving text builds conclusions from stated assumptions in a sequence of demonstrations.

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The action of a liquid on an immersed body is related to the liquid displaced. A body less dense than the liquid floats, and equilibrium connects its weight with the weight of displaced liquid. For a submerged body, buoyancy accounts for a reduction in apparent weight. The second book also investigates the stability of floating paraboloids, comparing inclined positions through geometry and the distribution of weight. These are substantial problems of equilibrium.

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This approach made floating and sinking calculable. Later hydrostatics developed its results, while ship design drew on displacement and stability and material testing used density comparisons. Archimedes’ writings survived through Greek, Arabic, and Latin traditions. The sequence of propositions in On Floating Bodies allows readers to compare how different cases satisfy conditions of equilibrium, tracing results through geometry and density. It preserves detailed mathematical reasoning about a physical process.

References: [1]