Abstract: The concepts of ratio, equal ratio, proportion played an important role in ancient Greek mathematics. The Book V of Euclid's Elements contains a proportion theory of (geometrical) magnitudes based on the equal ratio definition of Eudoxus (Definition V.5). In this paper we study both the pre-Eudoxian theory of proportion, and the genesis of Eudoxus's definition.
Keywords: Proportion theory, same ratio definition, Eudoxus, incommensurability.
Classification (MSC2000): 01A20
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