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How are the areas of circles related to the squares 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, in his work Elements (Book XII, proposition 2), circles are related to the squares of their diameters in that they are proportional to them. This means that the ratio of the areas of any two circles is equal to the ratio of the squares of their respective diameters.1