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How are the volumes of spheres related to the cubes of their diameters according to Euclid?
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Euclid
Euclid, coloured woodcut, 1584. His Elements, a treatise on geometry and mathematics, is one of the most influential books ever written.
According to Euclid's Elements, specifically in Book XII, the volumes of spheres are related to the cubes of their diameters in that they are proportional to one another. This means that the ratio of the volumes of any two spheres is equal to the ratio of the cubes of their respective diameters. This result was established using the method of exhaustion, a technique attributed to Eudoxus of Cnidus.12