Euclid's Elements were translated into Hebrew from Arabic in the 13th century; but precious few of the Arabic commentaries have come down to us in a Hebrew version. Nonetheless, a study of several texts dealing with the Fifth Postulate of Book I reveals that the Hebrew authors are greatly indebted to Arabic sources.

The ArgumentThe major part of the mathematical “classics” in Hebrew were translated from Arabic between the second third of the thirteenth century and the first third of the fourteenth century, within the northern littoral of the western Mediterranean. This movement occurred after the original works by Abraham bar Hiyya and Abraham ibn Ezra became available to a wide readership. The translations were intended for a restricted audience — the scholarly readership involved in and dealing with the theoretical sciences. In some (...) cases the translators themselves were professional scientists (e.g., Jacob ben Makhir); in other cases they were, so to speak, professional translators, dealing as well with philosophy, medicine, and other works in Arabic.In aketshing this portrait of the beginning of Herbrew scholarly mathematics, my aim has been to contribute to a better understanding of mathematical activity as such among Jewish communities during this period. (shrink)

It has long been considered that Arabic algebra scarcely left any traces in mathematical literature of Hebrew expression. Thanks to the unpublished sources we have discovered, and to an attentive examination of already-known texts, one can no longer subscribe to such a judgement. The evidence we examine in this first article sheds light on the circulation, in erudite Jewish circles, of Arabic algebraic knowledge in Spain, Italy, Provence, and Sicily, between the 12th and the 14th centuries. The Epistle on number (...) by the Castillian astronomer Isaac ben Salomon al-A[hudot]dab was written in Sicily at the end of the 14th century, and based on the Talkhi[sudot] a'mal al-[hudot]isab of Ibn al-Banna' (1256-1321). That part of the Epistle that is devoted to algebra follows the tradition of al-Karaji. It offers, for the first time in Hebrew, a rational presentation of arithmetical operations extended to algebraic expressions. (shrink)

Maimonide, philosophe dans la mouvance d'al-Farabi, etait medecin, informe des mathematiques et maitre de la litterature talmudique. Ce livre a pour ambition d'examiner les liens entre philosophie et science dans l'oeuvre de Maimonide, et aussi de placer celle-ci dans son veritable contexte historique entre Cordoue et Le Caire au XIIe siecle. Les etudes rassemblees ici explorent plusieurs facettes de cette oeuvre: logique, savoir et philosophie mathematiques, ecrits medicaux, conception du libre-arbitre ou des rapports entre nature et loi... Elles examinent aussi (...) l'impact qu'a eu l'oeuvre de Maimonide en arabe, en hebreu et en latin. Maimonides, a philosopher in the tradition of d'al-Farabi, was a physician, well-informed in mathematics, and a master of Talmudic literature. The goal of this book is to examine the links between philosophy and science in Maimonides' work, and also to situate it within its genuine historical context, between Cordoba and Cairo in the 12th century. The studies collected here explore several facets of this work: logic, mathematical knowledge and philosophy, medical writings, conception of free will and of the relations between nature and law, etc. They also examine the impact of Maimonides' work on Arabic, Hebrew, and Latin scientific and philosophical literature. (shrink)

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 IXesiècle: 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 XVIIesiècle. (shrink)

Until the end of the 14th century, the sources of Hebrew mathematical writings were almost exclusively in Arabic. This was particularly true of texts that contained elements of algebra or algebraic developments. The testimonies we present and analyze here are due to Jewish authors living in Italy, primarily in the 15th century, who made use of the most varied sources, in addition to Arabic: in Castilian, in Italian, and perhaps in Latin. These testimonies constitute both an indication, and a product, (...) of the circulation of Arab algebraic traditions in Renaissance Italy. Simon Mo&tdotu;o&tdotu;’s book on The Calculation of Algebra stems from the Italian tradition of ‘‘treatises on the abacus’’. Mordekhay Finzi of Mantua is the author of a Hebrew version of the great work on algebra by Abū Kāmil, as well as of a version, distinct from the preceding, of the Arabic scholar’s introductory exposition. Beginning in 1473, Finzi also translated from Italian to Hebrew the important treatise on algebra by Maestro Dardi of Pisa. We also indicate some 16th century continuations of Hebrew mathematical production, which contain algebraic developments. (shrink)