MATHEMATICS IN ANTIQUITY AND MIDDLE AGES

The first results of the study of al-Abhari's treatise “Emendation of Euclid's ‘`Elements” ’'.

I. O. Lyuter

Moscow

Abstract: The investigation of al-Abhari's “Emendation of Euclid's ‘`Elements” ’' was carried out according to its Chester Beatty Library manuscript copy (CBL Ar 3424) studied in the beginning of the article. The main part of the work is a critical survey of the peculiarities of the definitions of the straight line, plane surface and parallels typical for medieval Arabic commentaries and editions of Euclid's “Elements”. This research was conditioned by al-Abhari's enunciations of these definitions different from the ones given in the works of his Arabic predecessors and contemporaries and, as has been shown, had been borrowed from Ibn al-Haytham's commentary on the “Elements”. The article contains also a commented Russian translation of al-Abhari's proof of the Vth postulate known before only through the commentary of al-Rumi on the treatise “Propositions of substantiation” by al-Samarqandi.