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ON MENELAUS' SPHERICS III.5 IN ARABIC MATHEMATICS, II: NAṢĪR AL-DĪN AL-ṬŪSĪ AND IBN ABĪ JARRĀDA

  • Roshdi Rashed (a1) and Athanase Papadopoulos (a2)
Abstract
Abstract

In his Sphaerica, Menelaus did not prove Proposition III.5 which is particularly important. He only gave an outline of a proof. Once the Sphaerica were translated into Arabic, mathematicians, starting from the end of the 9th century on, took up this proof. That was made possible to Ibn ʿIrāq thanks to the development of spherical geometry. A first paper contained the history of his contribution. Two other mathematicians, from the 13th century – Naṣīr al-Dīn al-Ṭūsī and Ibn Abī Jarrāda – worked out again the proof of the proposition with the help of Menelaus' book and of the new acquisitions of Ibn ʿIrāq. This is the subject of this second paper.

Résumé

Dans les Sphériques, Ménélaüs ne démontre pas l'importante proposition III.5, mais propose seulement une esquisse de démonstration. Une fois le livre des Sphériques traduit en arabe, les mathématiciens, à partir de la fin du IXe siècle, ont voulu en donner une démonstration complète. Le développement de la géométrie sphérique a permis à Ibn ʿIrāq de parvenir au but. Un premier article a été consacré à sa contribution. Deux mathématiciens du XIIIe siècle – Naṣīr al-Dīn al-Ṭūsī et Ibn Abī Jarrāda – ont repris la démonstration de cette même proposition, à partir de Ménélaüs et des acquis d'Ibn ʿIrāq. C'est le sujet du présent article.

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Corresponding author
Email: rashed@univ-paris-diderot.fr
Email: athanase.papadopoulos@math.unistra.fr
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Arabic Sciences and Philosophy
  • ISSN: 0957-4239
  • EISSN: 1474-0524
  • URL: /core/journals/arabic-sciences-and-philosophy
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