ESHS/HSS Annual Meeting

The Taḥrīr of Euclid’s Elements by Muḥyi al-Dīn al-Maghrabī – Its Sources

• In Event: Euclid and Geometry Across Traditions

English Abstract

The Taḥrīr of Euclid’s Elements by Muḥyi al-Dīn al-Maghrabī (died about 1290) has not been subjected to a full and careful analysis, apart from the study of its demonstration of the parallel lines postulate (Sabra 1969, 14-18; Jaouiche 1974, 250-251) and of the section on regular polyhedra (Hogendijk 1994). Scholars believe that al-Maghribī composed his treatise some time before 1260, the date that he moved to Marāghā to work with Naṣīr al-Dīn al-Ṭūsī. Current research suggests that al-Maghribī relied heavily on an earlier Taḥrīr of the Elements by Abū al-Qāsim `Alī ibn Ismā`īl al-Naysābūrī (active during 10th-11th centuries), although not mentioning his source apart from criticizing its techniques for condensing Euclid’s text. As part of his edition of the Elements, al-Naysābūrī had revised the labeling of the diagram points and al-Maghribī used the same labeling conventions rather than following the traditional pattern of labelling found in the Arabic translation versions of Euclid. These competing labelling conventions suggest that there were alternative assumptions about the nature of mathematical entities circulating in the medieval mathematical community.

Author

• Gregg De Young, The American University in Cairo