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.

This article claims that Averroes wrote his Middle Commentary on the De anima after he composed both his Short and Long commentaries. A close comparison of the two texts proves that he had the Long commentary before him when composing the Middle. This has implications both for the development of Averroes' doctrine of the intellect, and for understanding Averroes' style of composing commentaries.

Ṯābit b. Qurra is especially known as a mathematician, but his work in astronomy is also important. This article reviews his eight surviving astronomical treatises, as well as relevant fragments of his lost works cited by later authors in Arabic and Latin. We conclude that, as an active participant in the scientific movement of 9th-century Baghdad, Ṯābit played a crucial role in the establishment of astronomy as an exact science. The argument is based on an assessment of his contribution in three areas: the relationship between observation and theory, the “mathematization” of astronomy, and the relationship between “mathematical” astronomy and “physical” astronomy.

Aristotle’s Topics, and especially, as far as the subject of this study is concerned, their central books (II-VII), played a role of central importance both in the medieval Latin and in the Arabic logical tradition. This did not occur without transformations, which affected the nature and the function of the loci of which these books set forth the theory. One of the most visible signposts of this tradition of re-elaboration of the Topics is represented by Themistius (ob. c. 388), to whom both Boethius and Averroes refer. Yet no work by Themistius on the Topics has come down to us in Greek. With a view to reconstructing the work(s) of this author, we have here collected and translated the passages that are attributed to him explicitly (with the exception of one of them) in Averroes’ Middle Commentary on the Topics, comparing them, where necessary, to the testimonies collected by Boethius in his De topicis differentiis. In addition – and this is a new element added to the file – we show that the Themistian classification of loci was taken up by Abū al-Barakāt al-Baġādī (ob. after 1164), author of a philosophical summa entitled al-Kitāb al-mu‘tabar (The meditated book). These three testimonies are all the more precious in that they are independent of one another. The study of the chapter in the logical part of al-Kitāb al-mu‘tabar, containing the Themistian classification of loci, of which a corrected text with translation is offered, shows that one finds in it some of the most singular aspects of this classification, as it appears in Boethius. Abū al-Barakāt al-Baġādī thus reveals himself to be closer than Averroes to the testimony of Boethius. This suggests the idea of a double redaction by Themistius of the classification of loci: one, more concentrated, comes from an introduction to the paraphrase of the central books of the Topics, which may have inspired Averroes; the other, more extensive, which will have been part of an original work, and inspired the classifications of Boethius and of Abū al-Barakāt al-Baġādī.

Kalām atomism stood in opposition to the Aristotelian natural philosophy of the falāsifa. In the Physics of the Shifā', Ibn Sīnā undertook a detailed refutation of kalām atomism through several arguments. These arguments elicited a muted response from al-Ghazālī, whose commitment to kalām was minimal at best. A more forceful response seems to have been offered by al-Shahrastānī but its details remain sketchy due to the lack of surviving sources. Fakhr al-Dīn al-Rāzī, whose intellectual development went through a phase of commitment to Avicennism and thereby a vigorous endorsement of Ibn Sīnā's anti-atomist arguments followed by a phase of a critical engagement with Avicennism, provides a detailed rebuttal to Ibn Sīnā's arguments in addition to constructing novel arguments in defense of kalām atomism.

The purpose of this paper is to present a comprehensive and systematic study of Avicenna's account of animal self-awareness and cognition. In the first part, I explain how, for Avicenna, in contrast to human self-awareness, animal self-awareness is taken to be indirect, mixed-up (makhlūṭ), and an intermittent awareness. In his view, animal self-awareness is provided by the faculty of estimation (wahm); hence, in the second part, I explore the cognitive role of the faculty of estimation in animals, and how that relates to self-awareness. The faculty of estimation, according to Avicenna, serves to distinguish one's body and its parts from external objects, and plays a role in connecting the self to its perceptual activities. It follows that animal self-awareness, unlike human self-awareness, is essentially connected to the body. In the third part of the paper, I show that, while Avicenna denies animals awareness of their self-awareness, he explicitly affirms that animals can grasp their individual identity, but, unlike humans, do so incidentally, as part of their perceptual awareness.

Avicenna's discussion of space is found in his comments on Aristotle's account of place. Aristotle identified four candidates for place: a body's matter, form, the occupied space, or the limits of the containing body, and opted for the last. Neoplatonic commentators argued contra Aristotle that a thing's place is the space it occupied. Space for these Neoplatonists is something possessing dimensions and distinct from any body that occupies it, even if never devoid of body. Avicenna argues that this Neoplatonic notion of space is untenable on the basis of three arguments. In general he maintains that bodies' impenetrability is explained by reference to dimensionality. Consequently, if it is dimensionality that explains impenetrability, and yet as the Neoplatonists hold space inherently possesses dimensions, material bodies could never interpenetrate space and so occupy it and thus bodies could never have a place. The conclusion is patently false. In additions Avicenna argues that the method used to arrive at the possibility of space is illicit, and so Neoplatonist cannot show that space is even possible. Thus, concludes Avicenna, Aristotle's initial account must be correct. The paper outlines the historical context of this debate and then treats Avicenna's arguments against space in detail.

The Compendium of the Almagest of Averroes, extant only in Hebrew translation, remains unpublished and hardly studied. The present article aims to make it known. It provides a history of the Compendium: its date of writing, translation into Hebrew, and the transmission, reception, and audience of the Hebrew translation, as well as a preliminary study of the text. This includes an annotated outline of its contents, and a discussion of its sources and their critical use by Averroes. The article also contains a translation of significant extracts from the Prologue, with a brief analysis. The Compendium provides direct and relatively early evidence from a leading protagonist of the 12th-century movement by Andalusian thinkers – mostly Aristotelian philosophers – to criticize and reform Ptolemean astronomy.

In his commentary on the first Aphorism of Hippocrates Maimonides lists the seven parts of medicine. Scholars have studied the relation of this text to the work of al-Fārābī. In particular, they have focused on the Iḥṣāʼ al-ʼulῡm, which in its present form does not contain a discussion of medicine, and on al-Fārābīʼs Risāla fi al-ţibb. The article examines the medieval Hebrew versions of the Iḥṣāʼ al-ʽūlum (versions made by Falaqera, Qalonimos and Rieti). On the basis of these versions, it is argued that there existed a version of the Ihşāʼ al-ʽulūm which did contain a section on medicine; that the Risala fi al-ţibb could have originated in such a fuller version of the Ihsa' al-'ulum; and that Maimonides's ultimate source for his classification of medicine was probably the Iḥṣāʼ al-ʽulūm. An appendix to the paper examines Maimonides's references to Galen and to Abū Bakr al- Rāzī. These references show Maimonides's perception of al-Fārābīʼs view of physicians who claim to be philosophers.

Man's individual responsibility is a very central notion in Muslim theology. Rational foundations for moral responsibility presuppose, however, that man has in some way control over his actions. It was therefore of central concern to theologians to formulate theories of action that were coherent enough to account for human self-determination. This article examines al-Bāqillānī's reflections on human acts and attempts to contextualise his thought within the discussions of his time. I will briefly review the Muʿtazilites’ theory of freedom of action, against which the Ašʿarite school developed its own position. I will then outline the fundamentals of the opposing standpoint adopted by Abū al-Ḥasan al-Ašʿarī, who proposed to base human self-determination on voluntariness. Finally, I will discuss how al-Bāqillānī drew on and further developed al-Ašʿarī's ideas. Based on the extant volumes of al-Bāqillānī's Hidāyat al-mustaršidīn, I argue that he attempts to coherently organise the school's understanding of the famous theory of “acquisition” (kasb) by affirming two fundamental principles: a) that human acts are created by God and b) that there is nevertheless a real correlation between man and his “acquired” acts.

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.

R. Rashed, Géométrie et dioptrique au Xesiècle, Ibn Sahl, al-Qūhī et Ibn al-Haytham (Paris, Les Belles Lettres, 1993); OEuvres philosophiques et scientifiques d'al Kindī, vol. I: L'Optique et la catoptrique (Leiden, E.J. Brill, 1997); Les Catoptriciens grecs (Paris, Les Belles Lettres, 2000).

In the thirteenth century, the influential logician Afḍal al-Dīn al-Khūnajī (d. 1248) departed from the Avicennan view that the subject matter of logic is “second intentions”. For al-Khūnajī, the subject matter of logic is “the objects of conception and assent”. His departure elicited intense and sometimes abstruse discussions in the course of subsequent centuries. Prominent supporters of Khūnajī's view on the subject matter of logic included Kātibī (d. 1277), Ibn Wāṣil (d. 1298) and Taftāzānī (d. 1390). Defenders of Avicenna's view included Ṭūsī (d. 1274), Samarqandī (d. 1303) and Quṭb al-Dīn al-Rāzī (d. 1365). This article presents the outline of the development of this discussion down to the end of the fourteenth century and attempts to reconstruct the major arguments of both sides.

This paper provides an analysis and translation of a previously edited, but otherwise unstudied work by Miskawayh (d. 1030) entitled On Pleasures and Pains (Fī al-Laḏḏāt wa-al-ālām). After a brief orientation regarding the Aristotelian account of pleasure in the Nicomachean Ethics, which is Miskawayh's main source, the theory of pleasure set out in On Pleasures and Pains is compared to the discussion of pleasure in Miskawayh's better known Refinement of Character (Tahḏīb al-aḫlāq). Despite considerable harmony between the two texts, their treatments of pleasure differ in that the Refinement accepts, whereas On Pleasures and Pains rejects, the “restoration” theory of pleasure of Plato's Timaeus.

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.

Al-Kindī's views concerning time are dispersed in different places in his works, but they are to be found principally in his On First Philosophy and De quinque essentiis (Sermo de tempore). Yes, he does follow Aristotle, but he insists on the homogeneity of the instant and of time; he also distances himself from the Philosopher by denying the eternity of the world a parte ante as well as a parte post. On the other hand, in his accounts of the realization of possible things and of the organization of the cosmos, he presents certain views that sometimes tend toward the principle of plenitude, and sometimes toward the doctrine of the best possible world, and here one can discern a principle that is distinctly theological.

Where Averroes' commentaries on Aristotle can be dated, the Middle Commentary on a given work can be seen to predate the Long Commentary. As an accompaniment to his fine edition of Averroes' Middle Commentary on the De anima, A. Ivry has maintained that in this instance matters are reversed and the Middle Commentary on the De anima is “an abridged and revised version” of the Long Commentary on the same work. Ivry develops his thesis most fully in Arabic Sciences and Philosophy 5. There he argues that two passages in the Middle Commentary on the De anima refer to the Long Commentary by name, that a third passage alludes to the Long Commentary, and that in other passages the Middle and Long Commentaries use similar phraseology and the former can be seen to have abridged the latter. The present article replies as follows: The pair of passages in the Middle Commentary which Ivry reads as referring explicitly to the Long Commentary can plausibly be read as cross-references within the Middle Commentary itself. The passage that he takes as alluding to the Long Commentary does not in fact allude to that work, but is an unambiguous reference to a later section of the Middle Commentary. And there is no justification for regarding the passages in the Middle Commentary cited by Ivry which use phraseology similar to that of the Long Commentary as borrowings from the latter. In the course of his arguments, Ivry refers to Averroes' position on the nature of the human material intellect, the issue that gave Averroes the most trouble in his commentaries on Aristotle's De anima and that has most intrigued students of Averroes ever since. The present article points out that on the subject of the human material intellect, neither the Middle nor the Long Commentary on the De anima borrows from the other, for the conceptions of the material intellect which they espouse are different and incompatible.

Avicenna refers on a number of occasions in his Book of the Syllogism to “the eminent later scholar” (al-fā[ddotu]il min al-muta'a[hbrevu][hbrevu]irī). At least three recent studies have argued or assumed that this eminent later scholar is Alexander of Aphrodisias. It is argued in this article that Avicenna is in fact referring to Alfarabi. This has consequences for reconstructing the lost first part of Alfarabi's Great Commentary on the Prior Analytics, for highlighting certain aspects of Alfarabi's logical doctrines, and for understanding more about the relation between Avicenna and Alfarabi in matters logical.

Though much has been written of late about Averroes and his philosophy, little attention has been paid to his political teaching. Generally speaking, his works can be divided into two categories: (a) commentaries on Aristotle and other important thinkers and (b) occasional treatises written to resolve particular questions. The subject of this essay, his political teaching, is stated most directly in the first classification of writings – especially in his commentaries on Aristotle's Rhetoric and Plato's Republic. Even though the second kind of writings helps to nuance some of his broader themes — especially the two treatises having to do with the relationship between philosophy anddivine law, namely, the Decisive Treatise and its sequel Kashf an manāhij al-adilla — considerations of space preclude an analysis of them here. Our examination of the first two writings will focus primarily on what Averroes has to say about the different kinds of political regimes and, above all, the best regime, for his discussion of it leads him to reflect more generally on other major political questions.

The Liber de compositione alchemiae or the The Book of the Composition of Alchemy is believed to have been the first book on alchemy that was translated from Arabic into Latin. The translator was the Englishman Robert of Chester who was one of the earliest translators to flock to Spain to learn Arabic and to translate some of the Arabic works. He completed his translation on 11 February, 1144.