ABSTRACT
Like many of his contemporaries, Ibn al-Haytham was concerned with the extraction of square and cube roots. It is clear that he encountered the familiar problem of approximation; but this time, in contrast to other areas where the author deals with infinitesimal determinations, he refers neither to what is known as Archimedes’ axiom nor to the exhaustion method: the two concepts which go some way to unify the diverse works of research on the infinitesimal are absent here. The approximation of roots would therefore seem to constitute a separate area, which would only later be included in this research. It will be shown in my third volume that algebra is instrumental in introducing this work, firstly in the twelfth century with alSamaw’al and Sharaf al-Dîn al-™ºsî, then five centuries later, in quite a distinct branch of study, where it developed in a completely different direction. This is what led us to take up Ibn al-Haytham’s texts herein, but in an appendix in order to highlight the differences in their status: the two texts which have come down to us and which have only recently been found, are devoted to the square and the cube root respectively. If the evidence of ancient biobibliographers is to be accepted, then these are the only texts which Ibn al-Haytham wrote on this theme.
