Abū al-Wafā’ al-Būzjānī proposed, in a fragment established and translated herein, two methods to build a parabolic mirror. The lack of demonstration, particularly for the first method, raises a difficult question of interpretation. To understand this method, O. Neugebauer used, in an unpublished article translated herein, concepts of descriptive geometry. He then eliminated the space construction used, to keep only simple geometrical considerations known by the Greeks. The second interpretation, given by R. Rashed, is based on the geometrical practices of al-Būzjānī's contemporaries, like al-Qūhī and Ibn Sahl, i.e. on the methods of conical projections. The second method borrowed by al-Būzjānī from Ibn Sinān seems to support this last interpretation.

This study, limited to Kitāb Taḥṣīl al-sa'āda, examines two points: the first point concerns the place of political science in the hierarchy of the sciences and its dependence on Metaphysics. This dependence gives it a theoretical status and a proper subject, namely voluntary intelligibles which appear as objective entities and stable essences. The second point to be examined concerns these intelligibles, considered in their relationship to deliberation. From this viewpoint, they appear as formal invariants open to different formulations which correspond to different modes of existence. These formulations are also formal rules to the realisation of intelligibles, and though they are more or less general, they are not universal. They are objects for deliberative discovery and the model of deliberative operations seems similar to the model of ingeniosity present in Algebra and the arts of ingenious devices.

Abū Bakr al-Rāzī (d. 925) and al-Fārābī (d. 950) both adopt the classical ideal of a philosophical way of life in the sense that being a philosopher implies certain ethical guidelines to which the philosopher should adhere. In both cases, moreover, their ethical writings appear to reflect a certain tension with respect to what the ethical goal of the philosopher consists of. In this study, I will argue that this apparent tension is relieved when their ethics is understood as a progression in a double sense. In the first sense, both authors adopt the Neoplatonic distinction between pre-philosophical and philosophical ethics. The second aspect of the progression takes place within the degree of virtue required of the philosopher, which for al-Rāzī and al-Fārābī proceeds in contrary directions. For al-Rāzī, the philosopher progresses from the moderately ascetic requirements of Spiritual Medicine to the higher license present in Philosophical Life, following the stages of the life of Socrates. In contrast, for al-Fārābī the progression follows roughly along the Neoplatonic grades of virtue from Aristotelian moderation, which in Exhortation to the Way to Happiness is connected with character training in a pre-philosophical sense, towards purely contemplative existence.

Euclid's definition of proportional magnitudes in the Fifth Book of the Elements gave rise to many commentaries. We examine closely two of these commentaries, one by al-Jayyānī (11th century) and the other by Saunderson (18th century). Both al-Jayyānī and Saunderson attempted to defend Euclid's definition by making explicit what Euclid had only implied. We show that the two authors explain Euclid's position in a virtually identical manner.

N. Oresme passe pour l'un des rares (sinon le seul) grand universitaire médiéval mathématicien. C'est ainsi que son grand traité De Configurationibus qualitatum et motuum est vu traditionnellement comme un traité de mathématiques et analysé comme tel. En fait, l'examen de ses Questiones super Physicam montre qu'Oresme est un philosophe de la nature original. Ses thèses sont souvent en opposition avec celles de Buridan et saméthode est différente: ses arguments empruntent fort peu à la logique et presque exclusivement à la philosophie naturelle.

As is well known, taṣawwur and taṣdīq, conceptualization and assent, are essential notions in the epistemology of Arabo-Islamic philosophy. Conceptualization amounts to the definition of an object of knowledge, and assent to the recognition, via some kind of reasoning, that this definition is true. One of the authors who dealt with both topics in greatest depth was al-Fārābī, whose oeuvre exerted a profound influence on Ibn Bājja. This article analyzes the materials on taṣawwur and taṣdīq found in Ibn Bājja's notes regarding al-Fārābī's writings on logic and scientific method, namely the glosses to Kitāb al-Burhān. The analysis shows, on the one hand, that he understood perfectly the importance of both terms in al-Fārābī's construal of Aristotle's scientific method; and on the other, that he used them to deal with human thought processes. Indeed, conceptualization and assent were essential notions for Ibn Bājja, and underlie some of his best-known works.

We here present the Arabic text, with an English translation, of certain pages dedicated by al-Khayyām to the mathematical theory of music. Our edition is based on a manuscript extant in a library in Manisa (Turkey), and corrects the mistakes found in another transcription. Lastly, we compare the theory of al-Khayyām with other Arabic theories of Music, and with those coming from other traditions.

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.

The mathematician al-Māhānī (9th century AD) is the author of one of the first commentaries on the fifth Book of Euclid's Elements which have been handed down to us. In this commentary, al-Māhānī intends to justify Definitions V. 5 and V. 7 of the Elements, which deal with the identity of ratios and with greater ratio, by starting from an anthyphairetic conception of ratio, and by proving the equivalence of the Euclidean and the anthyphairetic points of view. We will try in this paper to describe in detail the content of al-Māhānī's commentary, basing ourselves on a thorough examination of most of the extant manuscripts of the Arabic text. The reader will also find in the appendices a mathematical commentary, an English translation, and a critical edition of al-Māhānī's commentary.

The twelfth century philosopher-theologian Fakhr al-Dīn al-Rāzī is well known for his critique of Avicennan metaphysics. In this paper, I examine his critique of Avicenna's physics, and in particular his rejection of the Avicennan and Aristotelian theory of place as the inner boundary of a containing body. Instead, Fakhr al-Dīn defends a definition of place as self-subsisting extension, an idea explicitly rejected by Aristotle and Avicenna after him. Especially in his late work, the Maṭālib, Fakhr al-Dīn explores a number of important philosophical issues with reference to this theory of place, including the principle that two indiscernible things (in this case two overlapping extensions) must be identical and the idea that motion and rest are always relative.

The focus of this study is the definitions of substance and accident as expressed and outlined in Ibn Daud's book The Exalted Faith. The original Arabic text of Ibn Daud's book, completed in 1160, is lost. However the work survives through two Hebrew translations (both date from the late 14th century). In this study I suggest a hypothetical reconstruction of the Arabic text based on a wide comparison with Ibn Daud's Muslim predecessors, such as Alfarabi, Avicenna and Alghazali, on the one hand, and the Hebrew translations on the other. By returning to Ibn Daud's direct sources, I hope to shed more light on two subjects: (1) Ibn Daud's dependance on non-Jewish sources in his attempt to establish a philosophical synthesis between Aristotelism and traditional faith; and (2) to clarify the true philosophical meaning embodied in professional terminology, such as the definitions of substance and accident.

The extant texts of the Arabic Plotinus contain material from Enneads IV-VI without, however, covering the Plotinian treatises in their entirety, nor preserving their traditional order – a circumstance which raises questions about scope and structure of the original Arabic Plotinus source. This article aims to contribute to the discussion by presenting newly discovered fragments of an Arabic translation of Ennead IV.6 (On sense-perception and memory), one of the ten treatises that are not represented in the Arabic Plotinus corpus as it is currently known. Section I of the article introduces the text within which the new fragments are found: Maqāla I of Kitāb al-Ḥiss wa-al-maḥsūs, the Arabic adaptation of Aristotle's Parva Naturalia. In Section II the Arabic fragments are presented in comparison with their Greek counterparts. Section III addresses the question whether these new fragments stem from the same original translation as the other fragments of the Arabic Plotinus. Section IV discusses the implications which the appearance of the new fragments may have for our views on the Arabic Plotinus as well as on the genesis of Kitāb al-Ḥiss wa-al-maḥsūs.

This article aims to reconstruct part of Book IV of Galen's lost treatise On Demonstration. This reconstruction is based on testimonies transmitted by Abū Bakr al-Rāzī (d. 925) in the Doubts About Galen, as well as on a source that until now has never been studied, namely the Solution to the Doubts About Galen of Abū al-ʿAlāʾ ibn Zuhr (d. 1131). This paper argues that, in Book IV, Galen maintains that no one can reach any certain conclusion regarding the eternity of the world, and that he consequently criticizes Aristotle's treatment of the subject in On the Heavens. Galen approves only of one of the arguments used by Aristotle in On the Heavens I, 3 (270b12–17), because it is based on empirical evidence. Al-Rāzī focuses on Galen's commentary on this passage. Our hypothesized reconstruction resolves some of the contradictions between the fragments of Book IV that are transmitted in al-Rāzī's report and Philoponus’ Against Proclus On the Eternity of the World. Finally, this article shows that al-Rāzī's interest in this passage from On Demonstration can be explained with reference to his own philosophical-theological goals. As my examination will make clear, al-Rāzī objects to Galen's arguments because he considers that Galen's teleology is based on a framework where the world is eternal (although Galen does not state this view explicitly), and that this framework does not allow Galen to understand that theodicy is prior to both cosmology and biology.

The author investigates the different readings of Ibn ṬufayPs epistle, Ḥayy b. Yaqẓan. Following a suggestion by L. Gauthier, who simply asked that the epistle should be read as a whole, the author adds Ṣalāḥ ‘Abd al- ḥabūr's reworking of the tale as a children's story to L. Gauthier's list of partial readings. The author juxtaposes Ṣalāḥ ‘Abd al- ḥabūr's reading, which does justice only to what Asāl taught Ḥayy, to G. Hourani's reading, which succeeds in reflecting only what Ḥayy taught Asāl. This impasse in the readings of Ḥayy b. Yaqẓān reveals what is missing, namely an understanding of the tale which fundamentally conforms to several of Alfarabi's teachings, though not to L. Gauthier's interpretation.

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 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.

Before Ṯābit b. Qurra's translation, there was a first Arabic version of Nicomachus’ Introduction to arithmetic. Full of mistakes, it was revised by an anonymous student of al-Kindī. Thanks to the part that Freudenthal and Levy have edited and translated, we are now able to identify this reviser as Aḥmad b. al-Ṭayyib al-Saraḫsī, who we also identified as the author of the Rasā᾿il Iḫwān al-Ṣafā᾿. The comparison of the gloss written by this reviser with a new fragment of Saraḫsī on one part, and with the “ Epistles of the Brethren in Purity ” on the other, corroborate Saraḫsī’s authorship of the epistles. Furthermore, studying the misunderstandings on Nicomachus’ text in this kindianised version gives a new light on al-Kindī’s attempt to unify philosophy and on the specific ontology of the Brethren in Purity.

The article considers a brief catechistic presentation of a Galenic medical doctrine, the critical days, by the 9th century translator and thinker, Qusṭā ibn Lūqā (d. 912/3), found in a manuscript in Iran. The piece is first shown to have been derived from Galen's treatise on the critical days. Then, it is discussed section by section, in commentary form, to elucidate the medical doctrines Qusṭā propounds. Lastly, the piece is compared with an earlier attempt, by al-Kindī (d. c. 870), to describe the critical days mathematically. The various medical doctrines behind the treatise are discussed, as are the varying approaches to scientific method. The article concludes with contrasting the a priori mathematical scientific method of al-Kindī with the a posteriori empirical method of Galen/Qusṭā, and offers suggestions about the chronologies of the appearances of these doctrines and texts in Arabic. A transcription of the Arabic text is appended.

The editing of three anonymous Greek texts preserved in the Parisinus Suppl. gr. 643 allows us to clarify certain ideas on the transmission of knowledge in the Mediterranean during the second half of the 13th century. These texts – an introduction to the Physics of Aristotle, one to De generatione et corruptione and a page of Medical Problems – are in fact translations from Latin probably made at Salerno at the end of the Norman period or at the beginning of the Angevin dynasty. They allow us to establish the influence of the Parisian Faculty of Arts on the Sicilian intellectual milieu of the period and to illustrate how, whilst remaining true to its medical vocation, the University of Salerno evolved nonetheless towards a model of general education in the Arts. Finally these texts reveal the considerable influence – both philological and doctrinal – of Arabic learning on the Aristotelian teaching of their author. This very fact, combined with the presence of the Parisinus in Byzantium, in an environment of advanced philological learning, a few decades after its composition, leads us to question our understanding of the Palaeologan Renaissance as well as its independence with regard to the Arabo-latin scholarly tradition of the 13th century.