Book VI of the Konika is essentially devoted to the question of the identity and similarity of two conic sections, or two parts of conic sections. In Book VII Apollonius deals with the various relationships between the lengths of diameters and conjugate diameters. The results are applied to the exposition of a number of problems, as well as to some problems which Apollonius indicates will be demonstrated and solved in Book VIII, which was lost in Antiquity. Books VI and VII have only survived in an Arabic translation, and are presented here in a critical edition, together with a faithful translation and a historical-mathematical commentary.

Le livre VI des Coniques est consacré essentiellement à l'étude de l'égalité et de la similitude de deux sections coniques, ou de deux parties de sections coniques. Au livre VII, Apollonius établit de nombreuses relations entre longueurs des diamètres, de leurs diamètres conjugués et des côtés droits qui leur sont associés, ainsi que de nombreuses relations métriques, toutes utiles aux diorismes multiples et en particulier aux problèmes «résolus et démontrés» au livre VIII, perdu dès l'Antiquité. Ces deux livres n'ont survécu que dans la traduction arabe. On en trouvera ici une édition véritablement critique, une traduction rigoureuse ainsi qu'un commentaire historique et mathématique.

Autorentext

Roshdi Rashed, Centre National de la Recherche Scientifique und Université de Paris VII, Paris, Frankreich.

Klappentext

Book VI of the Konika is essentially devoted to the question of the identity and similarity of two conic sections, or two parts of conic sections. In Book VII Apollonius deals with the various relationships between the lengths of diameters and conjugate diameters. The results are applied to the exposition of a number of problems, as well as to some problems which Apollonius indicates will be demonstrated and solved in Book VIII, which was lost in Antiquity. Books VI and VII have only survived in an Arabic translation, and are presented here in a critical edition, together with a faithful translation and a historical-mathematical commentary.