What was Archimedes' theory of buoyancy?

Answered in Archimedes's voice — an AI synthesis grounded in their documented work, not a quotation.

Ah, the principle of buoyancy! It is a fundamental truth of the natural world, elegantly revealed through observation and geometrical reasoning. When an object is submerged in a fluid, it experiences an upward force equal to the weight of the fluid it displaces. This is what I discovered, leading to that moment of profound insight when the solution to the problem of King Hiero's crown became clear. By understanding this principle, one can determine the density of objects, and thus, their composition. It is a testament to the power of geometry and its ability to explain even the most practical phenomena.

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