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L'histoire des nombres amiables: le témoignage des textes hébreux médiévaux

Published online by Cambridge University Press:  24 October 2008

Tony Lévy
Affiliation:
Centre d'histoire des sciences et des philosophies arabes et médiévales, C.N.R.S., 7 rue Guy Môquet, B.P. n° 8, 94801 Villejuif Cédex, France

Abstract

This article analyzes new material on the history of the amicable numbers. It discusses Hebrew texts which throw new light on the diffusion in Medieval Europe of Ṯābit ibn Qurra's (9th century) work. We find Ṯābit's theorem on amicable numbers in a Hebrew translation, made in Saragossa in 1395, of an arithmetical commentary written by Abū al-Ṣalt al-Andalusī (ca. 1068–1134), and also in an original Hebrew text probably written by the Jewish Provençal scholar Qalonymos ben Qalonymos (1287 – after 1329). These texts lend strong support to the surmise that the Arabic tradition concerning amicable numbers could not have remained unknown to European mathematicians before the work of Descartes and Fermat in the 17th century.

Dans cet article, on analyse des données nouvelles concernant l'histoire des nombres amiables. Les textes hébreux qui sont cités permettent d'éclairer la diffusion, dans l'Europe médiévale, des résultats établis par Tābit ibn Qurra au IXe siècle: en effet, le théorème sur les nombres amiables auquel est attaché son nom apparaît aussi bien dans une traduction effectuée à Saragosse, en 1395, d'un commentaire arithmétique d'Abū al-Ṣalt al-Andalusī (ca. 1068–1134), que dans une composition originale attribuée au savant juif provençal Qalonymos ben Qalonymos d'Arles (1287 – ap. 1329). Ces témoignages renforcent l'hypothèse selon laquelle la tradition arabe dans ce domaine n'a pas pu être ignorée des mathématiciens européens, avant les résultats énoncés par Descartes et Fermat au XVIIe siècle.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1996

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