From the second half of the 10th century, mathematicians developed a new chapter in the geometry of conic sections, dealing with the theory and practice of their continuous drawing. In this article, we propose to sketch the history of this chapter in the writings of al-Qūhī and al-Sijzī. A hitherto unknown treatise by al-Sijzī - established, translated, and commented - has enabled us better to situate and understand the themes of this new research, and how it eventually approached the problem of the classification of curves in previously unknown terms.

The classic Arabic bibliographies ascribe to al-Fārābī a treatise entitled Fī māhiyyat al-nafs (“On the Essence of the Soul”), of which no Arabic manuscript is known to exist. There is however a Hebrew text, translated from the Arabic by Zeraḥiah ben She'altiel Ḥen of Rome in 1284, which is ascribed to al-Fārābī in all the manuscripts and which carries the title Ma'amar be-mahut ha-nefesh (“Treatise on the Essence of the Soul”). Since Steinschneider, this text is taken to be the translation of al-Fārābī's treatise lost in the original. In this paper I argue that the Ma'amar be-mahut ha-nefesh is not by al-Fārābī: it is in vain that one looks in it for ideas characteristic to the Second Master, while the ideas expressed therein are incompatible with those of al-Fārābī. I offer a study of Ma'amar be-mahut ha-nefesh, followed by an annotated translation into French. This is a “popular” Neoplatonic text, whose ideas are mostly very ordinary, but in part uncommon. It notably explains the emergence of forms in matter by positing the existence of a pneuma that by circulating around the body “brings forth” the vegetative and animal souls. The author also draws on an unusual notion called hemshel in Hebrew (a term probably translating the Arabic mithāl, rendered as exemplum in Latin): the exemplum is said to become visible as a result of the pneuma's circular motion. The paper is followed by a short Note by Rémi Brague looking into the sources of the treatise. Brague concludes that the text cannot be assigned to any specific tradition.

The paper discusses al-Kindī's response to doctrines held by contemporary theologians of the Mu‘tazilite school: divine attributes, creation, and freedom. In the first section it is argued that, despite his broadly negative theology, al-Kindī recognizes a special kind of “essential” positive attribute belonging to God. The second section argues that al-Kindī agreed with the Mu‘tazila in holding that something may not yet exist but still be an object of God's knowledge and power (as the Mu‘tazila put it, that “non-being” is a “thing”). Also it presents a new parallel between al-Kindī and John Philoponus. The third section gives an interpretation of al-Kindī as a compatibilist, in other words as holding that humans may be free even though their actions are necessitated. In all three cases, it is argued, al-Kindī is close to the Mu‘tazilite point of view, though he departs from them in the arguments he gives for that point of view.

Il est bien difficile de situer notre traité dans le temps et l'espace, ou même de le rattacher à une école déterminée. Aucune allusion ne permet de se faire une idée de l'appartenance religieuse de son auteur. Bénédiction initiale et eulogie finale sont des rites obligé (§ 60). La référence au “Créateur béni soit-il” (§17) ou à la sagesse divine (§ 31) est présente chez tout le monde. Aucun penseur n'est cité par son nom propre.

This paper sets out to chart the fortunes of one of the most significant moral propositions in Mu'tazilite moral theory — namely, that it is evil to lie, and it is evil irrespective of the consequences of so doing. The reasons which promote this principle to significance relate to the broader context of Mu'tazilite theological orientation, which aims to vindicate God's justice through demonstrating that moral value does not derive from revelation. Yet this principle suffers the difficulties which commonly afflict deontological precepts, particularly the challenges posed by their conflict with teleological moral demands in certain situations, as well as the difficulty of empirically ascertaining that a moral principle has in fact given the agent his reason for action, as the Mu'tazilites attempt to do. These were difficulties which Aš'arite critics of Mu'tazilite moral claims were quick to pick up on, and it is in the light of such hostile fire that the coherence of the Mu'tazilite position on the evilness of lies is examined. This is the principal focus of this essay, and it is complemented by an examination of how the principle carries over to the realm of divine morality: can God tell a lie? If not, why not? And what does this reveal about the ordering of moral values in Mu'tazilite thought?

The modern physiological optics introduces the notions related to the conditions of fusion of binocular images by the concept of correspondence, due to Christiaan Huygens (1704), and by an experiment attributed to Christoph Scheiner (1619). The conceptualization of this experiment dates, in fact, back to Ptolemy (90-168) and Ibn al-Haytham (d. after 1040). The present paper surveys Ibn al-Haytham's knowledge about the mechanisms of binocular vision. The article subsequently explains why Ibn al-Haytham, a mathematician, but here an experimenter, did not give the circular figure of the theoretical horopter, construction due to Gerhard Vieth (1818) and Johannes Müller (1826). But, on the other hand, it is clear that Ibn al-Haytham's experimental study puts in place the notion of corresponding points, the cases of homonymous and cross diplopia, and even prepares the discovery of Panum area.

It has long been considered that Arabic algebra scarcely left any traces in mathematical literature of Hebrew expression. Thanks to the unpublished sources we have discovered, and to an attentive examination of already-known texts, one can no longer subscribe to such a judgement. The evidence we examine in this first article sheds light on the circulation, in erudite Jewish circles, of Arabic algebraic knowledge in Spain, Italy, Provence, and Sicily, between the 12th and the 14th centuries. The Epistle on number by the Castillian astronomer Isaac ben Salomon al-Aḥdab was written in Sicily at the end of the 14th century, and based on the Talkhīṣ a'māl al-ḥisāb of Ibn al-Bannā' (1256-1321). That part of the Epistle that is devoted to algebra follows the tradition of al-Karajī. It offers, for the first time in Hebrew, a rational presentation of arithmetical operations extended to algebraic expressions.

After his refutation of the doubts concerning Proposition I.7 (in the Book of solving doubts), Ibn al-Haytham mentions three possible ways in which circles may intersect, submitting them to the following “intuitive” argument: one part of one of the two circles is situated inside of the other circle, and its other part is situated outside of it. One is therefore tempted to believe that the commentator accepts the principle of continuity in the case of circles, since his argument has the following meaning: if a circle is divisible into two parts (or, again, passes through two points), one of which (or one of the two points) is situated inside the other circle, and the other outside of it, then the two circles cut one another. The author of this article proposes to establish the limits of this belief, on the basis of the following reflections: 1). It will be noted first of all that what could be called the ‘principle of the intersection of circles’ does not constitute ipso facto a principle in the mind of Ibn al-Haytham: no allusion is made to it in the commentary on Proposition I.1, among others. 2) It will be established later on that if one accepts (according to the explanation of Ibn al-Haytham in his Commentary on the premisses) that a line is the result of the movement of a point, the principle of continuity should be considered by him as something which is obvious by itself, without being stated. This conclusion will be based on an analysis of the notion of continuity in its classical meaning, and on Ibn al-Haytham’s commentary on Proposition X.1. 3) On the other hand, we should note the presence of a ‘sketch’ of topological language, which Ibn al-Haytham develops for the notion of a circle (particularly in the Commentary): one could say in this context that his reflection constitutes an important, if not principal, stage in the process which was to lead to the explicit formulation of the principle of continuity.

The production of manuscripts can be an indication for the scientific, linguistic or medical interests of a community. In this paper the author argues that Parisinus Graecus 2293, a bilingual Greek-Arabic manuscript, containing parts of the first three books of Paul of Aegina's medical encyclopaedia, was produced in Sicily or Southern Italy, probably in Palermo during the reign of the Hohenstaufen. It is thus a testimony to the fervent scientific and medical interest of the Swabian court which promoted cultural exchange between the East and the West. The purpose of the manuscript was not so much to help medical practice but rather to further bilingualism by giving the reader a tool with which he could improve his knowledge of either language.

John Walbridge, The Leaven of the Ancients. Suhrawardī and the Heritage of the Greeks (Albany, State University of New York Press, 2000), xviii + 305 pp.

R. Rashed, Les mathématiques infinitésimales du IXe au XIe siècles, vol. IV: Méthodes géométriques, transformations ponctuelles et philosophie des mathématiques, London, al-Furqān Islamic Heritage Foundation, 2002, XIII-1064-VII p.

Né le 4 février 1917 dans un village des environs de Damiette, ‘Abd al-Rahmān Badaī s'est éteint au Caire, où il avait étudié puis enseigné – à l'Universitél – avant de joindre l'Université d'Héliopoplis. ‘A. Badawī nous laisse une oeuvre monumentale, plus de cent-vingt livres en arabe et cinq autres en français. Mondialement connu, son impact sur l'histoire de la philosophie grecque, sur l'histoire de la philosophie islamique et sur la pensée arabe au cours de la seconde moitié du XXe siècle, est immense et incontestable. Travailleur solitaire et acharné, il n'a jamais été égalé pour ses connaissances tant linguistiques que philosophiques et historiques, et surtout pour l'étendue des champs du savoir qu'il a pu couvrir.