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LES CONSTRUCTIONS GÉOMÉTRIQUES ENTRE GÉOMÉTRIE ET ALGÈBRE: L'ÉPÎTRE D'AB AL-JD À AL-BRN

Published online by Cambridge University Press:  05 March 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

Abstract

Abū al-Jūd Muḥammad ibn al-Layth is one of the mathematicians of the 10th century who contributed most to the novel chapter on the geometric construction of the problems of solids and super-solids, and also to another chapter on solving cubic and bi-quadratic equations with the aid of conics. His works, which were significant in terms of the results they contained, are moreover important with regard to the new relations they established between algebra and geometry. Good fortune transmitted to us his correspondences with the mathematician and astronomer al-Bīrūnī. The questions they debated, and the answers they yielded, all offer us multiple in vivo perspectives on the research that was undertaken in that period. The reader would find in this article a critical edition and French translation of this correspondence, with historical and mathematical commentaries.

Résumé

Abū al-Jūd Muḥammad ibn al-Layth est l’un des mathématiciens du xe siècle qui ont le plus contribué au nouveau chapitre sur les constructions géométriques des problèmes solides et sur-solides, ainsi qu’à un autre chapitre, sur la solution des équations cubiques et biquadratiques à l’aide des coniques. Ses travaux, importants pour les résultats qu’ils renferment, le sont aussi par les nouveaux rapports qu’ils instaurent entre l’algèbre et la géométrie. La bonne fortune nous a transmis sa correspondance avec le mathématicien et astronome al-Bīrūnī. Les questions qui y sont débattues, les réponses apportées, nous offrent, in vivo, plusieurs perspectives sur la recherche qui était alors menée. Le lecteur trouve dans cet article l’édition critique de cette correspondance, sa traduction française ainsi qu’un commentaire historique et mathématique.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2010

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