On a theorem of spherical geometry: Theodosius, Menelaus, Ibn Iraq and Ibn Hud

In his encyclopedic book (al-Istikmāl), the mathematician of Saragossa, Ibn Hūd (d. 1085/478 H.), established by an intrinsic demonstration of spherical geometry, a remarkable theorem which generalizes the proposition III.11 from Theodosius's Spherics and integrates the propositions III.23-25 from Menelaus's Spherics. In this paper, we study this theorem and the demonstration of Ibn Hūd. The reader will find also some established and translated texts (Ibn Hūd, Ibn 'Irāq, al-Tcombining dot belowūsī) addressing the same theme. Copyright © Cambridge University Press 2010.