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.

Written by the 11th-century Spanish Arab, Abh Muhammad ibn MucnOn Twilight and the Rising of Cloudsdh's value of around 52 miles remained standard until the 17th century, when it was revised sharply downward in consideration of atmospheric refraction and barometric studies. The treatise itself survives in a single Hebrew exemplar, 25 Latin exemplars, and an Italian exemplar derived from the Latin. At the heart of this present study is a critical text based on a fullscale comparative transcription of 22 of (...) the Latin manuscripts, ranging in date from the 13th to the 17th century. (shrink)