Infinitesimal mathematics from the IXth to the XIth century. Vol. III. Ibn al-Haytham. Theory of conics, geometric constructions and practical geometry (Q2723383)

The third volume of Rashed's well-known and ambitious research and publication project regarding Arabic mathematics consists of four chapters, two appendices and addenda to the second volume (1993; Zbl 0970.01002). All four chapters have the same clear structure: an introduction is followed by a subtle mathematical commentary, a critical edition of the Arabic text and its French translation. Nearly always Rashed provides the first critical edition. NEWLINENEWLINENEWLINEThe first chapter deals with Ibn al-Haytham's `Completion of Apollonius's Conics'. The last, that is the eighth book of the Conics was lost at least since Pappus. Ibn al-Haytham tried to complete the work so that first of all Rashed discusses the question: What did al-Haytham mean by `completing Apollonius'? He added a double mathematical commentary. The first is geometrical and follows al-Haytham's thought. The second is analytical and helps to discuss the necessary completion. The second chapter is dedicated to al-Haytham's correction of the last lemma of the treatise by the Banū Mūsā. They elaborated a treatise which should serve as an introduction to Apollonius. The third chapter concerns problems of geometrical construction (regular heptagon, division of a straight line, numerical problem). The last chapter concerns `practical geometry' or `the art of measuring'. Ibn al-Haytham wrote a treatise `On the principles of measure' and two on the measuring of heights.NEWLINENEWLINENEWLINEThe first appendix comprehends nineteen texts of Archimedes, Abū al-Jūd, al-Sijzī, al-Qūhī, al-Ṣāghānī, al-Shannī, Naṣr ibn `Abd Allāh, Anonymous, Ibn Yūnus dealing with the regular heptagon. The second appendix deals with Sinān ibn al-Fatḥ's `optical measurements'.NEWLINENEWLINENEWLINEThis impressive volume ends with an Arabic-French glossary (58 pages) and indices of names, subjects, cited treatises, manuscripts, cited works.