Al-Sijzī and the \textit{Elements} of Euclid: Commentaries and other demonstrations of the propositions (Q2717221)

This article is devoted to the development of Euclidian studies in Arabic, by focusing in particular on two main works of a tenth century mathematician by the name of Sijzi: One is a treatise written by this mathematician to criticize one of his contemporaries for producing a faulty method to divide a straight line, and the other he called `Demonstrations of the Elements of Euclid by Way of Elucidation and Exercise'. NEWLINENEWLINENEWLINEAfter taking specific examples from the tenth century mathematician, the author concludes by emphasizing that Euclid's \textit{Elements} occupied a very special and paradoxical position in tenth century Arabic mathematics. On the one hand it was considered to be an exemplary reference text, and yet was itself the object of several treatises all explicating alternative ways of demonstrating its theorems and more elegant ways to elaborate on its methods of construction. But none of the authors seems to have claimed that his resulting work was in any way superior to that of Euclid. The driving force seems to have been that which is enunciated in the title of Sijzi's work, namely, by way of ``Exercise'', for young aspiring engineers and geometricians. One additional result that is made obvious in this article is the extent to which such vigorous geometrical ``Exercises'' were pursued during the tenth century.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00025].