Although the existence of an Arabic translation of a section of Proclus' commentary on Plato's Timaeus lost in the Greek has been known since long, this text has not yet enjoyed a modern edition. The present article aims to consummate this desideratum by offering a critical edition of the Arabic fragment accompanied by an annotated English translation. The attached study of the contents and structure of the extant fragment shows that it displays all typical formal elements of Proclus' commentaries, whereas its conciseness and shortcomings raise certain doubts about its completeness. As a parergon, the article includes an analysis of a hitherto neglected letter by Ḥunayn ibn Isḥāq, which is attached to the fragment in the manuscript transmission. In addition to providing some insight into the origins of the Proclian fragment, this letter sheds some light on the Syriac and Arabic reception of some works by Hippocrates and Galen, especially Hippocrates' On Regimen in Acute Diseases and the history of its Arabic translation.

This article analyzes new material on the history of the amicable numbers. It discusses Hebrew texts which throw new light on the diffusion in Medieval Europe of Ṯābit ibn Qurra's (9th century) work. We find Ṯābit's theorem on amicable numbers in a Hebrew translation, made in Saragossa in 1395, of an arithmetical commentary written by Abū al-Ṣalt al-Andalusī (ca. 1068–1134), and also in an original Hebrew text probably written by the Jewish Provençal scholar Qalonymos ben Qalonymos (1287 – after 1329). These texts lend strong support to the surmise that the Arabic tradition concerning amicable numbers could not have remained unknown to European mathematicians before the work of Descartes and Fermat in the 17th century.

This article presents the Arabic text of al-Qūhī's short geometric treatise, The Book of the centres of the tangent circles on lines, by the method of analysis (Xe century), with translation and a mathematical commentary. In this treatise al-Qūhī solves by analysis an ordered set of eight problems where the goal is to locate, on a given line, the centre of a circle which is tangent to two given elements, which may be points, straight lines or circles. For example, in the first problem he wanted to find the centre of a circle which contains two given points. In fact, al-Qūhī establishes the locus of the solutions, and this locus can be a straight line or a conic. The treatise is reminiscent of one of the purposes of al-Qūhī's work on the perfect compass (an instrument to draw conics by moving continuously), namely to assign to the conics the status of regular lines.

In his Sphaerica, Menelaus did not prove Proposition III.5 which is particularly important. He only gave an outline of a proof. Once the Sphaerica were translated into Arabic, mathematicians, starting from the end of the 9th century on, took up this proof. That was made possible to Ibn ʿIrāq thanks to the development of spherical geometry. A first paper contained the history of his contribution. Two other mathematicians, from the 13th century – Naṣīr al-Dīn al-Ṭūsī and Ibn Abī Jarrāda – worked out again the proof of the proposition with the help of Menelaus' book and of the new acquisitions of Ibn ʿIrāq. This is the subject of this second paper.

The Persian philosopher Atīr al-Dīn al-Abharī (d. 1265), in his Revealing Thoughts, sketches out several different logics of propositions containing complex terms such as ‘writing man’. I will outline his results and the criticisms of them made by Naṣīr al-Dīn al-Ṭūsī (d. 1274) in his Setting the Scale for an Evaluation of “Revealing Thoughts”, and I will compare Abharī’s various logics of complex terms with modern treatments.

This article aims at presenting for the first time a central concept in al-Fārābī’s work that constitutes a keystone in understanding his thought, be it in its logical or political aspects. This concept is that of naqla, which, in terms of transmission and translation, its generic transcription can be rendered as ‘transfer’. The naqla is a notion that pertains to rupture in linguistic, logical or temporal continuities, and hints at confusing contiguities in the use of words, in demonstrations and in historical processes. This notion of naqla is at the centre of the preoccupations of al-Fārābī in his various domains of thinking. First of all, in terms of his linguistic reflection that consists of thinking about the transfer (naqla) of a given word in between its notions of first and second imposition. Then, in logic, the integration of the modes of reasoning of the theologians in Aristotelian syllogism, which passes by way of a mechanism of logical transference in the case of induction and the shift in paradigm. Finally, the Fārābian conception of intellectual history, as a transmission of knowledge, cannot be grasped in its fullest scope except through an understanding, not only of the common notion of naqla, but rather in terms of its particular Fārābian sense; namely as a concept that entirely renews the question of transmission and translation.

A part of chapter 1, Book II of the Physics of the šif¯' is dedicated to the aristotelian definition of motion (Physics III, 1, 201a10-11). The developments to which the treatment of this question gives rise are distinctive of the Avicennian style in his Physics. By assuming the notion of double entelechy, Avicenna is following the most classical exegetical tradition. However, by setting a correspondence between the double entelechy and the double notion of motion: 1) motion as an intermediary state, which can be ascribed to a moving object at any instant of its trajectory, and 2) motion as a traversal of a given distance, which cannot be ascribed to the moving object, but at the end-point of its trajectory, Avicenna gives a new content to a lieu commun of the exegetical tradition.

In his Short Treatise and his Commentary on the Peri hermeneias, al-Fārābī offers two different but related accounts of indefinite terms and the propositions that contain them. In both works he presents a series of different senses that an indefinite term may have, commencing with a sense in which such a term would be equivalent to a privative term, and concluding with a sense in which it would determine the logical complement of the corresponding definite term. I offer an interpretation of this series according to which they reveal the workings of a fine analytical mind and a subtle teacher.

From the late thirteenth to the early seventeenth century, the process of visual imaging was understood in the Latin West as an essentially subjective act initiated by the eye and completed by the brain. The crystalline lens took center stage in this act, its role determined by its peculiar physical and sensitive capacities. As a physical body, on the one hand, it was disposed to accept the physical impressions of light and color radiating to it from external objects. As a sensitive body, on the other hand, it was enabled by the visual spirit flowing to it from the brain to feel those impressions visually. Acting as a sentient selector of visual information, the lens transformed the brute physical impressions of light and color into visual impressions. These, in turn, gave rise to perceptual “depictions” that were passed back along the stream of visual spirits to the brain. Known in Scholastic parlance as “intentional species,” these depictions served as virtual representations of their generating objects. As such, they provided the wherewithal not only for perception, but also for conception and cognition.

Among the extensive correspondence of Timothy I, Catholicos of the Church of the East, are two letters which refer to his collobaration in a translation of Aristotle's Topics into Syriac and Arabic, commissioned by the Caliph al-Mahdī. An annotated English translation of both letters is provided.

The essence of the theory of minima naturalia is the contention that a physical body is not infinitely divisible qua that specific body. A drop of water cannot be divided again and again and still maintain its “wateriness”. There are several statements in Aristotle's Physics which suggest such an interpretation, and the theory of minima naturalia is commonly considered to have originated in the thirteenth century as an interpretation of these statements. The present paper is a preliminary presentation of the role of Ibn Rushd in the evolution of the theory, hitherto neglected. His theory developed not only as an elaboration on the “suitable” statements of Aristotle, but mainly as an attempt to solve the difficulties raised by Aristotle's thesis (developed in Physics VI and VII) that body and motion are continuous, infinitely divisible entities and are associated qua such. According to Ibn Rushd's interpretation, body and motion are associated not qua being continuous but qua having indivisible minimal parts. It seems that Epicurus' and Ibn Rushd's theories of minima developed as responses to Physics VI and offer modifications of classical atomism and of classical Aristotelianism (respectively), which to a certain extent reduce the gap between these two systems.

In Avicenna's expositions of his theory of the temporal origination of the human rational soul, its ḥudūth, one meets difficulties in understanding of what he actually means. Some of the expressions used are left unexplained and one has to extract their meaning from discussions given in a different context. There are also ambiguities in his use of such terms as al-‘aql al-kulliyy (the universal intellect) and al-nafs al-kulliyya (the universal soul). Although in one place he makes it clear that these expressions refer to concepts that exist only in the mind, distinguishing them from ‘aql al-kull (the intellect of ‘the whole [universal]') and nafs al-kull (the soul of ‘the whole [universel]'), the distinction is not uniformly observed. In a number of his works the term ‘‘universal'' is used to refer to both the celestial intellect and the celestial soul. There is also an ambiguity in his statements about the role the celestial soul plays in the emanation of the human rational soul. In some discussions he seems to hold that the rational human soul emanates from both the celestial intellect and the celestial soul. The Metaphysics of al-Shifā' (The Healing) suggests a resolution of this ambiguity. At the same time, there are statements in this work that are left unexplained and one has to look for their explanation in other books of The Healing. Thus questions do arise regarding the details of Avicenna's theory of the temporal origination of the human rational soul. His general exposition of his theory, however, remains comprehensible, its pivotal position within his entire philosophical system clear.

Avicenna's logic is presented in many treatises, of which the most important is Al-Qiyās (Prior analytics), which is included in his encyclopaedic book Al-Šifā’. But the treatise entitled Manṭiq al-mašriqiyyīn is said to express Avicenna's own logic by some commentators. One can thus ask: is this treatise in conflict with Al-Qiyās and the other logical writings? In this paper, we will answer this question by comparing Avicenna's analyses of the absolute – i. e. non modal – propositions. We will show that there is no radical difference between both treatises in this respect, since most conditions added to the absolute propositions in Al-Qiyās can be found in Manṭiq al-mašriqiyyīn. These conditions are: (1) “as long as S exists”, (2) “as long as it is S”, (3) “as long as it is P”, (4) “at some times”, (5) “at one determined time”, (6) “sometimes but not permanently”. In Manṭiq al-mašriqiyyīn, the ḍarūrīya contains (1), the lāzima contains (2), the muntašira contains (4), the mafrūḍa contains (5), the wujūdiyya contains (6), but (3) is abandoned. The waqtiyya was evoked in Al-Qiyās, although not classified. So the temporal analysis initiated in Al-Qiyās is pursued and developed in Manṭiq al-mašriqiyyīn, even if in the latter it is sometimes confused.

In Avicenna's Nafs there are two investigations that run in parallel from its very beginning: (a) the investigation of the soul as a relational entity, always considered in connection with the body, and (b) that of the human soul in itself. Both investigations aim at ascertaining the existence and the essence of the soul, in relation to the body, of which it is the soul, and in itself respectively. The aim of this contribution is to reconstruct the phases of these investigations, in order to single out the way in which they are mutually related to each other, and to detect what acts as an indicator of the transition from the first, more general investigation to the second, more specific one. In my reconstruction, this role is assigned to the Flying Man experiment. In order to corroborate this interpretation, passages from three other Avicennian works (Ḥikma mašriqiyya or al-Mašriqiyyūn, Kitāb al-Išārāt wa-l-Tanbīhāt, and Risāla Aḍḥawiyya fī l-ma‘ād) are taken into account, since they contain the three other attested formulations of the Flying Man experiment, and an argumentative move similar to the one detectable in the Nafs.

Ibn Sarābiyūn is one of the last exponents of classical Syriac medical writing, and one of the most influential authors for the development of medical theory and practice in late ninth-century Baghdad in particular, and for the Arabic medical tradition in general. During the last thirty years, three important studies have been published regarding the life and work of Ibn Sarābiyūn, each of which dealing with a different aspect of the transmission of this important author’s œuvre. Likewise, during the last twenty-five years, a number of texts associated with Ibn Sarābiyūn's works have been edited, allowing us today to shed new light on the relation between the original Syriac and the numerous translations into Arabic, Latin and Hebrew. Furthermore, through analysing and comparing a number of manuscripts containing different parts of Ibn Sarābiyūn's work which have not hitherto been considered together, progress can be made towards answering the question how Ibn Sarābiyūn was translated and used during the medieval period.

Averroes wrote three kinds of commentaries on the books of Aristotle - epitomes, middle commentaries, and long commentaries - and each kind had its own purposes. His aims may have also differed from text to text. That is, it seems reasonable to assume that he would stick closer to Aristotle in the logical works than, for example, in the metaphysical works. The present study investigates what may be called the “theological aspects” of Averroes' commentaries, and explores the commentary of Averroes that appears least likely to contain such elements, the Middle Commentary on the Prior Analytics. The Prior Analytics is perhaps the most straightforward, even pedantic, of all of Aristotle's writings, and of Averroes' three kinds of commentaries, it is the middle commentaries which are least likely to diverge or digress from the text of Aristotle. The only trace of a religious hand in the commentary is Averroes' use of examples, and, in particular, examples that conclude that “the world is created” and the like. It is argued that Averroes chose these examples to show the traditionalist reading public the falsity of the theologians claims against the logic of the philosophers. The Appendix to the article shows that medieval commentators on Averroes' commentaries were also struck by his “creation of the world” examples.

The thirteenth-century Hebrew texts that discuss salinity all ultimately go back to Aristotle's treatment of the subject in the Meteorology. However, in these Hebrew texts the question of what exactly makes the sea salty is answered in diverging ways. The oldest of them, the Otot ha-Shamayim (1210), being the Hebrew translation of the Arabic paraphrase of the Meteorology, proposes various causes of the sea's salinity, to wit, the dry exhalation, the action of heat, and the admixture of an earthy substance. This is due partly to Aristotle's own ambiguity, and partly to the fact that his Greek commentators interpreted his words in different ways. Two later encyclopedias, the Midrash ha-Hokhma (c. 1245) and the De'ot ha-Philosofim (c. 1275?) base their expositions of salinity on Ibn Rushd, whose two commentaries on the Meteorology contain various theories. The first encyclopedia opts for the action of heat as the major cause in producing saltiness, whereas the second attempts to explain in which way the various causes are interrelated by advisedly combining Ibn Rushd's accounts.

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.

This article aims to present a summary account of the role of Syriac in the transmission of Aristotle's Organon from Greek to Arabic. The main sources for that purpose lie in the Syriac and Arabic translations of Aristotle's works, that were achieved during the period from the 7th to the 9th centuries. Some problems related to these translations are discussed, with more attention paid to the emergence of a technical language of logic.

This paper presents the first edition, translation and analyse of al-Māhānī’s commentary of the Book X of Euclid’s Elements (9th century, the most ancient to have reached us) and of an anonymous’ one (prior to 968, among the first algebraic commentaries). For the first time, irrational numbers are defined and classified. The algebraisation of Elements’ X-91 to 102, on the basis of al-Khwārizmī’s Algebra, shows irrational numbers as solution to algebraic quadratic equations. The algebraic calculus makes here the first steps. On this occasion, negative numbers and their calculation rules appears. Simplifications imposed by the algebraic writings are sometimes in opposition with the conclusions of propositions conceived in a purely geometrical framework, revealing a contradiction between geometrical and algebraic goals. It will be resolved by the independant way algebra will take with mathematicians belonging to the tradition of al-Karajī and al-Samaw’al from the 11th-12th centuries on.