We study to what extent the Milky Way was used as an orientation tool at the beginning of the Islamic period covering the 8th to the 15th century, with a focus on the first half of that era. We compare the texts of three authors from three different periods and give detailed comments on their astronomical and traditional content. The text of al-Marzūqī summarises the information on the Milky Way put forward by the astronomer and geographer ʾAbū Ḥanīfa al-Dīnawarī. The text makes it clear that in some areas the Milky Way could be used as a geographical guide to determine the approximate direction toward a region on Earth or the direction of prayer. In the 15th century, the famous navigator Aḥmad b. Māǧid describes the Milky Way in his nautical instructions. He frequently demonstrates that the Milky Way serves as a guidance aid to find constellations and stars that are useful for precise navigation on land and at sea. On the other hand, Ibn Qutayba quotes in his description of the Milky Way a saying from the famous Bedouin poet Ḏū al-Rumma, which is also mentioned by al-Marzūqī. In this saying the Milky Way is used to indicate the hot summer times in which travelling the desert was particularly difficult. Hence, the Milky Way was useful for orientation in space and time and was used for agricultural and navigational purposes.

ʾAbū Saʿīd al-Siǧzī was a prominent fourth/tenth century astronomer and mathematician who was one of the first contributors to the new genre of ʿilm al-hayʾa (science of the configuration). However, little is known about the initial steps taken in the formation of the discipline, or its independence from other astronomical writings and practices. In this paper, I will discuss new findings about Siǧzī’s life to determine details of his biography and a more precise time period for his scientific activities. I then describe, for the first time, a composition in theoretical astronomy from the fourth/tenth century, the “Structure of the orbs” (Tarkīb al-aflāk) by Siǧzī to show its place in the formation of the discipline of ʿilm al-hayʾa, comparing Siǧzī’s book to the earlier work of al-Farġānī on the size of the earth and the number of celestial spheres. I conclude that Siǧzī’s Tarkīb al-aflāk is the earliest known example of a book that contains only topics found in later hayʾa and may be the first appearance of the ninth celestial orb that became standard in the later genre.

According to Avicenna, some of the objects of mathematics exist and some do not. Every existing mathematical object is a non-sensible connotational attribute of a physical object and can be perceived by the faculty of estimation. Non-existing mathematical objects can be represented and perceived by the faculty of imagination through separating and combining parts of the images of existing mathematical objects that are previously perceived by estimation. In any case, even non-existing mathematical objects should be considered as properties of material entities. They can never be grasped as fully immaterial entities. Avicenna believes that we cannot grasp any mathematical concepts unless we first have some specific perceptual experiences. It is only through the ineliminable and irreplaceable operation of the faculties of estimation and imagination upon some sensible data that we can grasp mathematical concepts. This shows that Avicenna endorses some sort of concept empiricism about mathematics.

L'article propose une première approche systématique de la tradition manuscrite du Liber de causis, en étudiant à la fois les variantes manuscrites et les difficultés doctrinales suscitées par la translittération de l'arabe al-ʿaql conservée dans la traduction latine. Certains médiévaux (tel Albert le Grand) l'entendent comme un concept sans équivalent en latin, forgé par des philosophes arabes dont on ignore tout. D'autres médiévaux (tels Thomas d'Aquin et Gilles de Rome), qui ont probablement connu une branche différente de la tradition manuscrite du Liber de causis, n'en font aucune mention. En examinant cent dix manuscrits latins du Liber de causis (sur deux cent soixantecinq actuellement connus), on constate de nombreuses variations tant pour la présence de cette translittération dans les propositions du texte que pour les formes et les graphies (alatyr, alachili, adlahic, etc.). Cette analyse permet de comprendre tant la position d'Albert que la grande diversité, jusqu’à présent insoupçonnée, de la transmission du Liber de causis dans le monde latin.

Dans le cadre des algorithmes numériques introduits et élaborés par les mathématiciens arabes, à partir du ixe siècle, figure l'algorithme de l'extraction de la racine carrée d'un entier naturel. Cet algorithme a été étudié chez plusieurs d'entre eux et surtout bien expliqué par alBaġdādī (mort vers 1037) dans le chapitre « Comment extraire la racine des nombres entiers » de son livre « La complétion du calcul », Al-takmila fī al-ḥisāb 1. Dans ce chapitre, al-Baġdādī expose son travail pédagogiquement en six sections traitant de plusieurs manières différentes le problème de l'extraction de la racine carrée d'un entier 2. À la même époque, dans un texte isolé intitulé « Sur la cause de la racine, de son doublement et de son déplacement 3 », Ibn al-Hayṯam (mort vers 1040) donne une justification géométrique de l'algorithme en se basant sur des notions algébriques précises.