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SUR UN THÉORÈME DE GÉOMÉTRIE SPHÉRIQUE: THÉODOSE, MÉNÉLAÜS, IBN ʿIRĀQ ET IBN HŪD

Published online by Cambridge University Press:  26 August 2010

ROSHDI RASHED
Affiliation:
Centre d’histoire des sciences et des philosophies arabes et médiévales, CNRS – Université Paris-Diderot, UMR 7219,5 rue Thomas Mann, Bâtiment Condorcet, Case 7093, 75205 Paris Cedex 13 Email: rashed@paris7.jussieu.fr
MOHAMAD AL-HOUJAIRI
Affiliation:
Université libanaise, Faculté de Génie, CNRS-Liban, rue al-Arz, al-Koubbé, Tripoli, Liban Email: houjairi@hotmail.com

Abstract

In his encyclopedic book (al-Istikmāl), the mathematician of Saragossa, Ibn Hūd (d. 1085/478 H.), established by an intrinsic demonstration of spherical geometry, a remarkable theorem which generalizes the proposition III.11 from Theodosius’s Spherics and integrates the propositions III.23-25 from Menelaus’s Spherics. In this paper, we study this theorem and the demonstration of Ibn Hūd. The reader will find also some established and translated texts (Ibn Hūd, Ibn ʿIrāq, al-Ṭūsī) addressing the same theme.

Résumé

Dans son livre encyclopédique (al-Istikmāl), le mathématicien de Saragosse, Ibn Hūd (mort en 1085/478 H.), établit par une démonstration intrinsèque de la géométrie sphérique un théorème remarquable qui généralise la proposition III.11 des Sphériques de Théodose et intègre les propositions III.23-25 des Sphériques de Ménélaüs. Dans cet article, on étudie ce théorème ainsi que la démonstration d’Ibn Hūd. Le lecteur trouvera aussi établis et traduits quelques textes (Ibn Hūd, Ibn ʿIrāq, al-Ṭūsī) qui portent sur le même thème.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2010

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SUR UN THÉORÈME DE GÉOMÉTRIE SPHÉRIQUE: THÉODOSE, MÉNÉLAÜS, IBN ʿIRĀQ ET IBN HŪD
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SUR UN THÉORÈME DE GÉOMÉTRIE SPHÉRIQUE: THÉODOSE, MÉNÉLAÜS, IBN ʿIRĀQ ET IBN HŪD
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