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The treatise of Ab\=u Ja'far al-Kh\=azin (Xth century), entitled "Commentaryon the introduction of the tenth book of the treatise of Euclid" ("tafs\={i}rsadr al-maq\={a}la al-'\={a}shira min kit\={a}b Uql\={i}dis") exists in eightmanuscripts. In this paper we present a study of this treatise, based on afirst edition we have made, according to the copies of the manuscripts ofParis, Leiden and Tunis, Ahmadiya. A reading of this treatise of al-Kh\={a}zinproves that this mathematician did a profound study of the Xth book of EuclidElements, in order to gain a global comprehension. In effect, he presented acondensed commentary, the originality of which can be felt both on the formaland the contents levels. The aim of our study is to try, as much as possible,to show this originality, referring specially to Pappus commentary of the "Xthbook", the works of R. Rashed on the history of algebra and a recent work of M.Ben Miled on the Arabic commentaries of the Xth book. It appears to us that thework of al-Kh\={a}zin concerning the Xth book, is situated in the current of anArabic tradition identified, mainly due to the works of R. Rashed, by: - analgebraic representation of the geometrical work of Euclid, - a numericalinterpretation of the Euclidian notions, rendered possible by the introductionof a unity for every kind of magnitude.

La Notion D'irrationalit\'E Selon Un Math\'Ematicien Du Xe Si\`Ecle: Ab\=u Ja'far Al-Kh\={a}zin