Abstract

Euclid's definition of proportional magnitudes in the Fifth Book of the Elements gave rise to many commentaries. We examine closely two of these commentaries, one by al-Jayy and the other by Saunderson. Both al-Jayy and Saunderson attempted to defend Euclid's definition by making explicit what Euclid had only implied. We show that the two authors explain Euclid's position in a virtually identical manner