The autobiography witnesses a significant evolution in Avicenna's approach to Aristotle's Metaphysics during the years of his education. It clearly shows that, at a certain point of his philosophical training, Avicenna faced the entire text of the Metaphysics, was puzzled by its extent and complexity, and found in a treatise by al-Fārābī a guide for its understanding. But, albeit less perspicuously, the autobiography also suggests that this was not Avicenna's first encounter with the Metaphysics. Avicenna dealt with Aristotle's work in a previous stage of his studies as well. Then, however, he did not read the Metaphysics in its entirety, but, rather, focused only on its essential parts and some commentaries thereupon. The parts of the Metaphysics that Avicenna read in this earlier stage were books Alpha Elatton and Lambda, as constituting the natural theology of Aristotle's work. He neglected, on the contrary, the books corresponding to its ontological part. The special attention to Alpha Elatton and Lambda and the close connection between these two books in a theological context were peculiar traits of al-Kindī's approach to Aristotle's Metaphysics. Therefore, the evolving approach to Aristotle's Metaphysics that Avicenna's autobiography witnesses can properly be described as a passage from the Kindian to the Farabian way of interpretation.

The Treatise on Equations of Sharaf al-Dīn al-Ṭūsī (2nd half of the 12th century) is in the tradition of ‛Umar al-Khayyām (d. 1131). However, it has two special features. First, it contains a full discussion of the existence of a solution for third-degree equations, which al-Ṭūsī establishes by proving that the conic curves that represent this solution effectively intersect – a proof based on an intuitive notion of connexity. Secondly, al-Ṭūsī develops algorithms for the numerical resolution of these third-degree equations. The first stage of one of these algorithms follows a procedure which is akin to the so-called method of Newton's polygon.

Ibn al-Faḍl al-Anṭākī's Kitāb Bahjat al-muʾmin, the Book of the Delight of the Believer preserves, in the first part, in at least three of its 100 philosophical and theological problems, passages from the hitherto lost Arabic version of Philoponus' De Aeternitate mundi contra Proclum. All quotations are taken from the refutation of the first proof, one of them from the beginning which is also lost in Greek. For this latter passage a parallel is found in al-Isfizārī who draws on the same Philoponus source in his Kitāb fī Masāʾil al-umūr al-ilāhiyya (Book on Metaphysical Questions). A comparison of the other passages to the extant Greek text suggests that al-Anṭākī quotes Philoponus faithfully, but with some omissions and occasional re-arrangement of his source. Additional evidence for al-Anṭākī's overall accurate use of sources can be gained from his quotations of the extant Arabic versions of the De Anima-paraphrase, Nemesius' De Natura hominis and ʿAlī b. Rabban al-Ṭabarī's Firdaws al-ḥikma (Paradise of Wisdom).

From Euclid to the second half of the 17th century, mathematicians as well as philosophers continued to raise the question of the angle of contact and, generally, of the concept of angle. This article is the first essay devoted to this subject in Arabic mathematics. It deals with Greek writings translated into Arabic on the one hand, and contributions of Arabic mathematicians on the other hand: al-Nayrīzī, Ibn al-Haytham, al-Samawʾal, al-Shīrāzī, al-Fārisī, al-Qūshjī, among others. Most of these contributions are hitherto unknown.

Mainly based on the study of a hitherto neglected epigraphic document from Antinoë, the present article aims at showing that the geometer Serenus – the author of two treatises On the Section of a Cylinder and On the Section of a Cone – lived at the beginning of the 3rdcentury AD. On the ground of a renewed study of various elements taken both from the treatises and the indirect tradition, it also suggests that Serenus must be placed among a scientific tradition closely linking geometry of conics and catoptrics that can be traced back to the works of Conon of Samos and Pythion of Thasos. This hypothesis raises the problem of the nature of his alleged Platonism, which is examined in relation to Menaechmus' heterodox constructivism. Finally, the study of an element in the Arabic transmission of the treatise on Conics by Apollonius enables us to clarify some point regarding the textual tradition of the treatises On the Section of a Cylinder and On the Section of a Cone.

In order to get rid of the contradictions he had identified in Ptolemy’s Astronomy, Ibn al-Haytham abandons cosmology and develops a purely kinematic description of the movement of the wandering stars. This description culminates with the proof that such a star, during its daily movement, reaches exactly one time a maximum height above the horizon and that any inferior height is reached exactly twice. The proofs of these facts necessitates new mathematical tools and Ibn al-Haytham is led to establish very sophisticated statements concerning the variation of certain ratios of arcs of circles on the sphere. He also introduces the fruitful idea of assimilating a very small spherical triangle to a plane triangle.

On some of the end-leaves of a Bible manuscript someone has copied out a passage from the Theology of Aristotle in Hebrew translation. The passage deals with the immunity of person of intellect from magical manipulation. No other copies of this passage in Hebrew are known to exist. The dependence of the translator upon the so-called “long version” of the Theology, specifically the copy in St Petersburg, is demonstrated, and it is suggested that the translator may be Shem Tov ibn Falaquera. The passage differs significantly from other versions of the Theology, and from Plotinus, in placing intellectual achievement ahead of ethical perfection in the scale of values.

In diesem Aufsatz möchte ich einen Überblick über unser heutiges Wissen bezüglich der Übersetzung der Elemente Euklids ins Lateinische geben. Cicero hat als Quästor in Sizilien (im Jahre 75 v. Chr.) das Grab des Archimedes aufgesucht und instandsetzen lassen, er nennt gelegentlich Euklid und Archimedes (De oratore III, 33, 132) und er zitiert in Academica I, Buch II, § 116, die Definitionen von Punkt und Linie. Vor dem 6.

Ptolemy presents only one argument for the eccentricity in his models of the superior planets, while each one of them has two eccentricities: one for center of the uniform motion, the other for the center of the constant distance. To take into account the first eccentricity, he introduces the equant point, but he provides no argument for the eccentricity of the center of the deferent. Why is the second eccentricity different from the first one? The 13th century astronomer Quṭb al-Dīn al-Shīrāzī, a member of the famous school of Marāgha, who was interested in this problem, suggests the “retrograde arcs” as the empirical origin of the second eccentricity and develops an argument to justify this conjecture. Although his argument is not without difficulty, his suggestion is in line with the suggestions made by some historians of astronomy in recent decades.

Since the beginning of mankind, man has been concerned with the conservation of food in order to prolong its edibility. Over time, different food preservation methods have been discovered and improved, and there are many works that describe these techniques. This work will describe the knowledge and the development of preservation techniques of inhabitants of the Iberian Peninsula. The work focuses on the various achievements from the first to the sixteenth centuries, allowing us to appreciate the different historic contributions. The selected and consulted works are: L.J.M. Columela, Los doce libros de Agricultura (The Twelve Books of Agriculture), Abū al-Jayr, Kitāb al-Filāḥa. Tratado de agricultura (Book of Agriculture), Ibn Baṣṣāl, Kitāb al-Filāḥa. Libro de agricultura (Book of Agriculture), Ibn al-ʿAwwām, Kitāb al-Filāḥa. Libro de Agricultura (Book of Agriculture), Ibn Luyūn, Kitāb al-Filāḥa. Tratado de Agricultura (Book of Agriculture), Alonso de Herrera, Agricultura general (General Agriculture).

Ever since the rediscovery of Ibn Khaldūn's Muqaddima in modern times, debates have been ongoing regarding his identity as a scholar: was he a revolutionary thinker in the modern sense of the word, breaking away from classical and medieval modes of thinking, or was he in fact a conservative Muslim scholar who did not venture far from his traditional Muslim horizons? Through a careful examination of the preface to the Muqaddima, this article shows what he thought about the nature of his project and why he thought it necessary. Accordingly, it builds the case that Ibn Khaldūn is indeed a revolutionary – but not in the modern sense of the word – who did not shy away from challenging tradition in order to reform society's moral and political horizons. An examination of the preface alone will not provide a definitive answer to the question of Ibn Khaldūn's radical vs. conservative thought, but it does put his conservatism (apparent and real) in context.

Galen's On the Elements according to Hippocrates is an important source for physical doctrines circulating in late antiquity. The variety of atomistic doctrines that Galen brings into the discussion, as well as his arguments aimed at refuting them, were closely studied by the early kalām atomists. Of particular interest are the summaries of this text, which seem to have been written many centuries after Galen; some of them are products of early Islamicate culture. In this paper, we present an edition, translation, and study of a hitherto unknown summary, extent in a unique manuscript where it is attributed to Ḥunayn ibn Isḥāq. Like the other summaries, it presents a doxography of physical doctrines, not always repeating precisely what Galen says, but rather reflecting the discourse of its period.

This essay is concerned with the complex relationships between falsafa and kalām. As regards the history of the latter, it has been generally agreed that al-Juwaynī played a decisive role at a moment when Avicennism became intrusive. It is mainly in his al-ʿAqīda al-niẓāmiyya that al-Juwaynī initiated a doctrinal and methodic evolution of Ashʿarism. One necessarily invokes here Ibn Rushd, who, by exposing the dogmas in their literal manifestation in his al-Kashf ʿan manāhij al-adilla fī ʿaqāʾid al-milla, actually sought to operate a systematic refutation of the Ashʿarites' theses. It should be noted, however, that, despite his critical distance, Ibn Rushd nonetheless remained attentive to al-Juwaynī's evolutionary study. In this contribution, some aspects of the major issues in kalām will be examined: the existence of God and the argument of takhṣīṣ (particularization), His unicity (waḥdāniyya) and the argument of mumānaʿa (mutual hindering), as well as human agency with the acknowledgement of man's capacity (qudra) and its role. Albeit limited in scope, the essay attempts to make a more profound evaluation of al-Juwaynī's role at a crucial moment of the history of kalām in its specific development during which the Great Masters have not always been faithful to the classical tenets of their school, but also in its relations with falsafa and its influence on al-Juwaynī, and then and mainly on his disciple al-Ghazālī's theological thought.

The aim of this article is to present a new witness of Averroes' reception in the Muslim world, in the years that immediately followed his death. Indeed Abū al-Ḥağğāğ al-Miklātī (d. 1237) is an Ašʿarite theologian, who was born in Fez. He is the author of a Quintessence of the Intellects in Response to Philosophers on the Science of Principles in which he aims at refuting the Peripatetic philosophers in their own field, using their own weapons. This article will first attempt to draw the portrait of this atypical theologian. It will then focus on showing that al-Miklātī – although he never mentions his name – is a reader of Averroes and in particular, of his Tahāfut al-Tahāfut, of which he makes various and unexpected uses. A close look at these uses will enable us to better define the nature of al-Miklātī's work. More importantly, this article will try to prove that al-Miklātī provides us with a key passage of Averroes' lost treatise On the Prime Mover. At the heart of the Rushdian criticism of Avicenna's “metaphysical” proof, this passage should throw new light on Averroes' precise understanding of this proof.

The spirits (arwāḥ) found in Arabic alchemical texts, namely zi'baq, kibrīt, nūshādir and zarnīkh are identified with their modern counterparts, which are mercury, sulfur, ammonium chloride (carbonate) and arsenic (arsenous) sulfide, respectively. Jābir's conception of spirits has been shown to be related to his practice. The puzzling experiments of Jābir on ‘mineral and organic’ spirits are compared as far as possible with modern knowledge of chemistry. These comparisons lead to an understanding of Jābir's sequence of manipulations within the logic of his alchemy. In treatment of naturally occuring spirits, Jābir aimed at removing the combustibility of spirits and so improving their effect on fusible bodies. Jābir's notion of transmutation (iqlāb) of fusible bodies is shown to be a flexible term that is equivalent to purification (tanẓīf) or reformation (iṣlāḥ).

Dans l'introduction à un texte majeur consacré à la composition des rapports et dans lequel on s'accorde à voir un pas important dans l'élaboration de la notion de nombre irrationnel, al-Khayyām remarque:

After he wrote his well-known De aspectus, al-Kindī wrote a substantial critical commentary on Euclid's Optics: the “Rectification of error and difficulties due to Euclid's book: the Optics.” This previously ignored work enriches our knowledge of the optics not only of the geometers of the mid-9th century, but also of late antiquity. This is the first known commentary on Euclid's treatise, and it raises again the questions of its textual traditions, their multiplicity, and the role of Theon of Alexandria; it also poses the problem of the survival of al-Kindī's thought through his successors, such as Ahmad b. 'Īsā. The article examines these and related issues.

Euclid discusses the ex aequali relationship twice in the Elements. The first is in Book V (based on definitions 17 and 18, propositions 22 and 23), during his discussion of arithmetical relations between mathematical magnitudes in general. The second is in Books VII–IX (developed using proposition VII,14), where he focuses on arithmetical relations in the case of numbers only. Although the distinction between mathematical magnitudes in general and numbers in particular often seems somewhat forced to contemporary philosophers, it was apparently very real to Euclid. Because Euclid seemed so conscious of the differences between the subject matter of Book V (magnitudes) and Books VII–IX (numbers), he was not much troubled by the differences between his treatment of ex aequali ratios in these two contexts. Later generations of mathematicians, however, found these differences less acceptable and tried to minimize them in various ways. This paper summarizes Euclid's use of the ex aequali relation in developing his mathematics. The paper then outlines the fate of the post-Theonine Greek attempts to “improve” the Euclidean discussion when the Elements entered the Arabic/Islamic intellectual tradition. The study concludes with the attempts by Ibn al-Hayṯam and Ibn al-Sarī to improve the parallelism between the discussions of ex aequali ratios in Book V and Book VII.

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.

Alongside his much-discussed theory that humans are permanently, if only tacitly, self-aware, Avicenna proposed that in actively conscious self-knowers the subject and object of thought are identical. He applies to both humans and God the slogan that the self-knower is “intellect, intellecting, and object of intellection (‘aql, ‘āqil, ma‘qūl)”. This paper examines reactions to this idea in the Islamic East from the 12th-13th centuries. A wide range of philosophers such as Abū l-Barakāt al-Baghdādī, Faḫr al-Dīn al-Rāzī, al-Šahrastānī, Šaraf al-Dīn al-Mas‘ūdī, al-Abharī, al-Āmidī, and Naṣīr al-Dīn al-Ṭūsī raised and countered objections to Avicenna's position. One central problem was that on widely accepted definitions of knowledge – according to which knowledge is representational or consists in a relation – it seems impossible for the subject and object of knowledge to be the same. Responses to this difficulty included the idea that a self-knower is “present” to itself, or that here subject and object are different only in “aspect (i‘tibār)”.