Abstract

This article presents the Arabic text of al-Q's short geometric treatise, The Book of the centres of the tangent circles on lines, by the method of analysis, with translation and a mathematical commentary. In this treatise al-Q solves by analysis an ordered set of eight problems where the goal is to locate, on a given line, the centre of a circle which is tangent to two given elements, which may be points, straight lines or circles. For example, in the first problem he wanted to find the centre of a circle which contains two given points. In fact, al-Q establishes the locus of the solutions, and this locus can be a straight line or a conic. The treatise is reminiscent of one of the purposes of al-Q's work on the perfect compass, namely to assign to the conics the status of regular lines