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Two Commentaries on Euclid's Definition of Proportional Magnitudes*

Published online by Cambridge University Press:  24 October 2008

Bijan Vahabzadeh
Affiliation:
Centre d'histoire des sciences et des philosophies arabes et médiévales, 27 rue Damesme, C.N.R.S., 75013 Paris, France

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-Jayyānī (11th century) and the other by Saunderson (18th century). Both al-Jayyānī 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.

La définition qu'Euclide a donnée, dans son cinquième livre des Éléments, de la proportionnalité de quatre grandeurs a donné lieu à de nombreux commentaires. Parmi ces commentaires, nous en avons choisi deux, qui eurent pour but non de critiquer le point de vue qu'Euclide a adopté, mais au contraire de le justifier en tentant d'expliciter ce qu'Euclide avait sous-entendu. Le premier est dû à al-Jayyānī (XIe siècle), et le second à Saunderson (XVIIIe siècle). Nous montrons, après avoir décrit leur contenu respectif, que ces deux commentaires expliquent le point de vue euclidien en adoptant une démarche essentiellement similaire.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1994

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