Le modèle de la sphère transparente et l'explication de l'arc-en-ciel : Ibn al-Haytham, al-Farisi.

Rashed Roshdi. Le modèle de la sphère transparente et l'explication de l'arc-en-ciel : Ibn al-Haytham, al-Farisi.. In: Revue d'histoire des sciences et de leurs applications, tome 23, n°2, 1970. pp. 109-140

Abu Kamil: algèbre et analyse diophantienne

The mathematical wrks of Abu Kamil (floruit circa 880) were produced two generations after the works of Al-Khwarizmi, the founder of algebra. They opened up fields of research that proved fertile up until the seventeenth century, and were soon to become both a reference and a model. Their influence was decisive on the development of algebra in Arabic no less than in Latin and Hebrew. There will be found in the present publication the first rigorously critical edition of Abu Kamil s works, as well as the first ever translation into a modern language.Text and translation are preceded by an exha

Fuat Sezgin, Geschichte des arabischen Schrifttums. Band V : Mathematik, bis ca. 430 H.

Rashed Roshdi. Fuat Sezgin, Geschichte des arabischen Schrifttums. Band V : Mathematik, bis ca. 430 H.. In: Revue d'histoire des sciences, tome 29, n°2, 1976. pp. 183-184

Apollonius de Perge, Coniques

Book VI of the Konika is essentially devoted to the question of the identity and similarity of two conic sections, or two parts of conic sections. In Book VII Apollonius deals with the various relationships between the lengths of diameters and conjugate diameters. The results are applied to the exposition of a number of problems, as well as to some problems which Apollonius indicates will be demonstrated and solved in Book VIII, which was lost in Antiquity. Books VI and VII have only survived in an Arabic translation, and are presented here in a critical edition, together with a faithful tran

L'analyse diophantienne au Xe siècle : l'exemple d'al-Khäzin.

SUMMARY. — First introduced in the 10th century, the Arithmetica of Diophantus contributed much to the development of mathematics in the Middle Ages. Most notably it permitted the extension of classical Diophantine analysis, which existed already, independently of the Arab translation of Diophantus, among the Arab algebrists. Less known but more original, is the contribution of the Arithmetica to the development of new research on modern Diophantine analysis, as that term was understood by Bachet de Méziriac and Fermat. The examination of two unpublished documents in this article demonstrates this fact more clearly than before. The author shows that this research, inspired by a reading of Diophantus, was however the work of mathematicians who deliberately placed themselves outside the algebraic tradition and chose a style intentionally different from that of the Arithmetica.RÉSUMÉ. — Introduites au Xe siècle, les Arithmétiques ont diversement contribué au développement des mathématiques de l'époque. Elles ont tout d'abord permis l'extension de ce qui existait déjà chez les algébristes arabes, indépendamment de la traduction arabe de Diophante : l'analyse diophantienne ancienne. Beaucoup moins connue que la précédente, la deuxième contribution est plus originale : il s'agit de l'essor de nouvelles recherches sur l'analyse diophantienne moderne, au sens où l'entendent Bachet de Méziriac et Fermat. L'analyse de deux inédits permet d'établir plus formellement ce fait. On montre ici que ces recherches, suscitées par la lecture de Diophante, sont cependant l'œuvre de mathématiciens qui se situaient délibérément hors de l'algèbre et optaient pour un style autre que celui des Arithmétiques de Diophante.Rashed Roshdi. L'analyse diophantienne au Xe siècle : l'exemple d'al-Khäzin.. In: Revue d'histoire des sciences, tome 32, n°3, 1979. pp. 193-222

Fuat Sezgin, Geschichte des arabischen Schrifttums. Band V : Mathematik, bis ca. 430 H.

Rashed Roshdi. Fuat Sezgin, Geschichte des arabischen Schrifttums. Band V : Mathematik, bis ca. 430 H.. In: Revue d'histoire des sciences, tome 29, n°2, 1976. pp. 183-184

Les travaux perdus de Diophante (I)

Rashed Roshdi. Les travaux perdus de Diophante (I). In: Revue d'histoire des sciences, tome 27, n°2, 1974. pp. 97-122

Les travaux perdus de Diophante (II)

SUMMARY. — In a previous article, the author presented the first of Diophantus' four Books in Arithmetics, of which no Greek copy survives and rediscovered in an Arabic translation. In this article, he will present the three following Books. But if in the first article he intended principally to show how this discovery brought a new light on the question of the order of Diophantus' Books, here he will insist on the extent of his arithmetical contribution. A particular attention should be given to the content of Book V, beginning with the seventh problem.RÉSUMÉ. — Dans un premier article, l'auteur présentait le premier de quatre des Livres arithmétiques de Diophante, tous perdus en grec et retrouvés dans une traduction arabe. Il présente ici les trois Livres qui achèvent l'ouvrage. Ayant déjà montré comment la découverte de la traduction arabe renouvelle la question de l'ordre des Livres de Diophante, il insiste sur l'extension de son œuvre arithmétique et attire l'attention sur le contenu du Livre V, à partir du septième problème.Rashed Roshdi. Les travaux perdus de Diophante (II). In: Revue d'histoire des sciences, tome 28, n°1, 1975. pp. 3-30