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Article ID: CBB001551207

On Menelaus' Spherics III.5 in Arabic Mathematics, II: Naṣīr al-Dīn al-Ṭūsī and Ibn Abī Jarrāda (2015)

Rashed, Roshdi (Author)
Papadopoulo, Athanase (Author)

Arabic Sciences and Philosophy
Volume: 25, no. 1
Issue: 1
Pages: 1-32

DOI: 10.1017/S0957423914000083

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Mathematics Arab/Islamic world, civilization and culture Translations 9th century al-Ṭūsī, Abū Jaʿfar Muḥammad Naṣīr al-Dīn Menelaus of Alexandria

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 Ir q thanks to the development of spherical geometry. A first paper contained the history of his contribution. Two other mathematicians, from the 13th century -- Na r al-D n al- s and Ibn Ab Jarr da -- worked out again the proof of the proposition with the help of Menelaus' book and of the new acquisitions of Ibn Ir q. This is the subject of this second paper.

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