Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 1
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Berggren, J.Lennart 1997. Mathematics and Her Sisters in Medieval Islam: A Selective Review of Work Done from 1985 to 1995. Historia Mathematica, Vol. 24, Issue. 4, p. 407.


    ×

Sharaf al-Dīn al-Ṭūsī et le polygone de Newton

  • Christian Houzel (a1)
  • DOI: http://dx.doi.org/10.1017/S0957423900002046
  • Published online: 24 October 2008
Abstract

The Treatise on Equations of Sharaf al-Dīn al-Ṭūsī (2nd half of the 12th century) is in the tradition of ‛Umar al-Khayyām (d. 1131). However, it has two special features. First, it contains a full discussion of the existence of a solution for third-degree equations, which al-Ṭūsī establishes by proving that the conic curves that represent this solution effectively intersect – a proof based on an intuitive notion of connexity. Secondly, al-Ṭūsī develops algorithms for the numerical resolution of these third-degree equations. The first stage of one of these algorithms follows a procedure which is akin to the so-called method of Newton's polygon.

Le Traité des équations de Sharaf al-Dīn al-Ṭūsī (2e moitié du XIIe siècle) se situe dans le prolongement de l'œuvre de ‛Umar al-Khayyām (m. 1131). Il s'en distingue toutefois par deux traits. 1) II contient une discussion complète de I'existence de la solution d'une équation du 3e degré, existence qu'al-Ṭūsī établit en démontrant que les deux courbes coniques destinées à construire cette solution se rencontrent effectivement. Cette démonstration se fonde sur une idée intuitive de la connexité. 2) Il présente des algorithmes pour la résolution numérique des mêmes équations. La première étape de l'un de ces algorithmes suit une procédure qui s'apparente à la méthode dite du polygone de Newton.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J.P. Hogendijk [“Sharaf al-Dīn al-Ṭūsī on the number of positive roots of cubic equations,” Historia Mathematica, 16 (1989): 6985] sur la base du livre II des Éléments d'Euclide nous paraît assez forcée.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Arabic Sciences and Philosophy
  • ISSN: 0957-4239
  • EISSN: 1474-0524
  • URL: /core/journals/arabic-sciences-and-philosophy
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×