Al-mahani's commentary on the concept of ratio

Arabic Sciences and Philosophy 12 (1):9-52 (2002)
Abstract
The mathematician al-Mahani (9th century AD) is the author of one of the first commentaries on the fifth Book of Euclid's Elements which have been handed down to us. In this commentary, al-Mahani intends to justify Definitions V. 5 and V. 7 of the Elements, which deal with the identity of ratios and with greater ratio, by starting from an anthyphairetic conception of ratio, and by proving the equivalence of the Euclidean and the anthyphairetic points of view. We will try in this paper to describe in detail the content of al-Mahani's commentary, basing ourselves on a thorough examination of most of the extant manuscripts of the Arabic text. The reader will also find in the appendices a mathematical commentary, an English translation, and a critical edition of al-Mahani's commentary.
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DOI 10.1017/S0957423902002023
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