Mathematical Summary

Abstract

The following mathematical summary renders the more important constructions in the Completion in modernized language, by means of analytic geometry, equations, and a few mappings of the Euclidean plane. Thus the essential relations can be stated and derived more easily than in Ibn al-Haytham’s text, and complicated arguments involving similar triangles and proportions can be avoided. The reader should realize that this procedure distorts Ibn al-Haytham’s reasoning to some extent. Ibn al-Haytham’s arguments will be summarized and commented upon in the footnotes to the text (Chapter 14) and in Chapter 7 in a way which is more adapted to his own reasoning. In the present summary I render the equations of the conics in such a way that the correspondence with the text is obvious. Points in the geometrical figures will almost always be denoted by the same letters as in the translation (Chapter 13). The summary includes some comments of my own in italics.