Commentaries of Ibn al-Haytham on Euclid's definition of ratio

The research deals with the problems called forth by the commentaries of Ibn al-Haytham on Euclid's definition of ratio. In particular: a connection between the definition of ratio of the "ancients" given by al-Haytham and the anthyphairetic ratio theory, which preceded Eudoxus-Euclid theory of ratios, is surmised and substantiated; the tradition according to which the genus of a ratio relates to the category of quantity (according to Euclid, it relates to the category of relation) is traced mainly through the 13th century Arabic editions of Euclid's "Elements"; it is noted that the interpretation of ratio as quantity allowed medieval Arabic mathematicians to extend the concept of number to ratios of continuous quantities.