Many studies on the astrolabe were written during the period from the ninth to the eleventh century, but very few of them related to projection, i.e., to the geometrical transformation underlying the design of the instrument. Among those that did, the treatise entitled The Art of the Astrolabe, written in the tenth century by Abū Sahl al-Qūhī, represents a particulary important phase in the history of geometry. This work recently appeared in a critical edition with translation and commentary by Roshdi Rashed. It contains the earliest known theory of the projection of the sphere, a theory developed in a commentary written by a contemporary mathematician, Ibn Sahl. Following R. Rashed, the present article offers here a thorough mathematical analysis of al-Qūhī's treatise and of the commentary by Ibn Sahl. It also presents, with commentary, an account of a contemporary treatise on the projection of the sphere, written by al-[Sdotu]āġānī. The latter work is concerned with the conical projection of a sphere on a plane, from a point on an axis of the sphere, other than its pole. The author consciously avoids the case of stereographic projection, but he studies all the other cases of conical projection which, if we employ the terms of al-Qūhī's theory, are compatible with the movement of the instrument (i.e. the rotation of the sphere around its axis). These three texts provide clear evidence of the emergence, during the second half of the tenth century, of a new field of study, that of projective geometry.

This article continues and improves the research already accomplished in Géométrie et dioptrique au Xesiècle (1993). It presents two fragments and an additional treatise which enlarge our understanding of the work of Ibn Sahl on the geometrical constructions and projections. All the necessary corrections are included.

The question of which areas of the earth are fit for human habitation and which ones are not is dealt with in several Hebrew scientific texts of the twelfth and thirteenth century. Medieval Jewish scholars such as Abraham bar [Hdotu]iyya, Samuel ibn Tibbon, and the three thirteenth-century Hebrew encyclopedists were familiar with theories of the oikoumene and its boundaries through Arabic sources. These Hebrew texts display a variety of views on the earth's habitability, all of which ultimately go back to antiquity. Whereas some texts adopted a division of the inhabited portion of the earth into seven climes, others divided the earth into five zones of temperature, of which two were habitable and three were not owing to extreme temperatures. Some of these Jewish authors also pay attention to the question of how climatological or astrological conditions in a given region influence the mental constitution of its inhabitants.

The Hippocratic Aphorisms is a well-known treatise which was very popular throughout the ages. This paper studies the Arabic translation of [Hdotu]unayn ibn Ishaq, the renowned Arab translator, of the first book of the Aphorisms as well as the commentary of Ibn al-Nafīs, the thirteenth-century Arab doctor, on the same book. This study highlights the difficulties that occasionally confronted the Arab commentator while commenting. The obscurity of a few Hippocratic sentences as well as [Hdotu]unayn's interpretation and alteration in meaning were probable sources for those difficulties. Ibn al-Nafīs, however, was unaware of the role played by [Hdotu]unayn in shaping the Arabic text. Ibn al-Nafīs reflected a deep trust in the Arabic text to the degree of commenting on every single word. He used both his intellect and his knowledge of other commentaries to solve those problematic phrases. He did not exhibit an interest in philological matters to help explain the text. His commentaries reflect his respect and appreciation for both Hippocrates and Galen, the latter of whom exercised some influence on [Hdotu]unayn and Ibn al-Nafīs in their understanding of the work. Nonetheless both [Hdotu]unayn and Ibn al-Nafīs showed traces of independence from Galen's influence.