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.

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 To understand this method, O. Neugebauer used, in an unpublished article translated herein, concepts of descriptive geometry.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.

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.

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.

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.

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.

Having constituted a new epoch in human history and a new religiouspolitical order, the revealed religions challenged the tradition of Greek philosophy to adjust to, investigate, and make intelligible a religiouspolitical order based on prophecy, revelation, and the divine law. The challenge led certain Arab and Muslim philosophers to reassess the relative distance between the thought of the Greek masters, (Plato, Aristotle, Plotinus, in particular) and the doctrines propagated by the revealed religions, and to make use of such works as Plato's Republic and Laws, rather than Aristotle's Politics, when offering a philosophic account of the new religious–political phenomenon and of such new disciplines as the science of the divine law and the science of revealed theology.

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 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.

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.

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 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.

In the Greek/Indian period, it is noticeable that different radii were used in connection with the chord. This manner continued in the Indian period with the sine, i.e. different sine tables existed. But throughout the Arabic-Islamic period, there was stability in the radius (for the sine). At the time of al-Battānī new terms were introduced, not as functions of angles but as lengths, and again different tables for the same term. Here these terms were not bounded to the circle, and the term miqyās r (measure), which was variable, was used to express “the radius” related to these terms. The trigonometric “functions” at that time were treated as if they were two different groups. While at Abū al-Wafā’’s time, there was an advancement by introducing the new terms as functions of angles, and they were immediately bounded to the circle, and instead of having two circles in the same figure, a kind of unity appeared, and again there was stability in the value of r, and therefore only one table for each function, and thus the new functions started to appear more abstract than practical as the sine did before, and this unity remained fixed in the modern times.

The aim of this work is to end the debate about the widespread acceptance among specialists, that the 6th century Byzantium treatise by Cassianus reached Muslim scholars by means of two routes: a “direct” translation from Greek into Arabic (Filā[hdotu]a rūmiyya attributed to Qus[tdotu]ūs) and the other “indirect” translation by means of a Persian translation (Filā[hdotu]a fārisiyya attributed to either Kasīnūs or Qus[tdotu]ūs). Thanks to a comparison of the texts, one can prove beyond all doubt that there was only a secondary translation route into Arabic from the Persian version. Additionally, this work highlights the significant influence of the Filā[hdotu]a rūmiyya on the Andalusian agronomy. The most influenced subjects are pointed out and those agronomic sources derived from this treatise and the 10th century Greek Geoponica (based on Cassianus) are studied. This study allows us to conclude that the later work was never translated into Arabic, therefore, the Andalusian agronomists only had access to the Arabic versions of Anatolius and Cassianus to which the Pseudo-Qus[tdotu]ūs' work was later added.

That the medieval Latin version of Ibn al-Haytham's Kitāb al-Manā[zdotu]ir was translated into Italian in the fourteenth century has been known for well over a century. Recent studies have shown that this translation, which is contained in Vat. Lat. 4595, was instrumental in the composition of Lorenzo Ghiberti's Commentario terzo on art. Some eight years ago, the author of the present article tentatively identified the actual manuscript-source of that translation as MS Royal 12.G.7, which is currently held in the British Library. This study establishes beyond reasonable doubt that his tentative identification was correct: MS Royal 12.G.7 is indeed the Latin source for the Italian translation in Vat. Lat. 4595.

Metaphor was based on similarity. During their history the Arabs adopted different logical systems in their scientific investigations. They shifted from Aristotle's logic accepted by the philosophers to that of the theologians and jurisconsults, and later again back to Aristotle's logic. In all these logical systems the definition of metaphor was dependent on the ever changing meaning of “similarity”. The seemingly unchanging definition of metaphor implies different interpretations in different ages parallel to the changing logical background.

The article aims at demonstrating that in attributing the creatio ex nihilo to both Plato and Aristotle as their unanimous philosophical conviction the Treatise on the Harmony between the Two Sages deeply depends upon the Neoplatonic reading of those two philosophers. The main obstacles for such a view in the works of the two sages are Plato's assumption of a precosmic chaos in the Timaeus and Aristotle's denial of any efficient causality to the unmoved mover in the Metaphysics. Both of these points had been, however, done away with by the Neoplatonist commentators already, especially by Ammonius in his lost treatise on efficient and final causality in Aristotle the use of which in the Harmony is shown by a comparison with Simplicius. Christian and Muslim readers just had to transfer those arguments and hermeneutical techniques into an anti-eternalist context in order to make the two philosophers agree with one of the basic tenents of their face, a hermeneutical technique considerably different from the one employed by al-Fārābī in his exposition of Plato's and Aristotle's philosophy which is compared to the Harmony in a briefly sketched concluding section.