The role of algebraic inferences in Na‘im ibn Musa's Collection of geometrical propositions
Résumé
Na‘im ibn Musa's lived in Baghdad in the second half of
the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions---recently edited and translated in French by Roshdi Rashed and Christian Houzel---reflects quite well the mathematical practice that was common in Thabit ibn Qurra's school. A relevant characteristic of Na‘im's treatise is its large use of a form of inferences that can be said ‘algebric' in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic analyses that are mainly used to reduce the geometrical problems they are concerned with to al-Khwarizmi 's equations.
the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions---recently edited and translated in French by Roshdi Rashed and Christian Houzel---reflects quite well the mathematical practice that was common in Thabit ibn Qurra's school. A relevant characteristic of Na‘im's treatise is its large use of a form of inferences that can be said ‘algebric' in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic analyses that are mainly used to reduce the geometrical problems they are concerned with to al-Khwarizmi 's equations.
Na‘im ibn Musa a vécu à Bagdad pendant la seconde moitié du IXème siècle. Il n'a pas été probablement un mathématicien majeur. Néanmoins, sa Collection de proposition géométriques}---qui a été récemment éditée en traduite en français par Roshdi Rashed and Christian Houzel---reflet assez bien la pratique mathématique qui était commune à l'école de Thabit ibn Qurra. Une caractéristique relevante du traité de Na‘im est son large usage d'une forme d'inférences qui peut être dite `algébrique' en un sens qui sera expliqué. Celles-ci interviennent autant dans la preuve de théorèmes que dans la solution de problèmes. En ce dernier cas, elles participent de différentes sortes d'analyses qui sont surtout employées pour réduire les problèmes géométriques auxquelles elles s'appliquent à des équations au sens d'al-Khwarizmi.
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