The thesis presented in the present article is not the widely-accepted one according to which Mu‘tazilite thought indirectly influenced the birth and development of Arab rhetoric (balāġa ) as an intellectual trend at the time that witnessed the constitution of this discipline of Arab language sciences, but the more specific thesis that it was primarily in Mu‘tazilite thought that the foundations of balāġa as a technical discipline were truly elaborated. To argue this thesis, we shall proceed in two stages. In the first, we shall try to identify the indirect Mu‘tazilite sources of balāġa; that is, the theses and overall positions of this movement, an echo of which may be found in constitutive elements of the discipline. In the second, we will try to identify some of the direct Mu‘tazilite sources of balāġa on the basis of Mu‘tazilite studies directly devoted to the status of the Koranic text, and the concepts elaborated to account for it.

The classical theory of errors can be divided into stochastic and determinate parts, or branches. The birth of the first of therse became inevitable after Bradley's idea of cultivating astronomy and natural science in general by “regular series of observations and experiments” became universally accepted. Such scholars as Lambert, Simpson, Lagrange, Daniel Bernoulli and Euler were responsible for the development of the stochastic theory of errors while Laplace and Gauss completed its construction. About fifty or sixty years ago it was included into mathematical statistics.

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.

This paper presents the Arabic text, the French translation and an analysis of al-Sijzīʼs treatise (second half of the tenth century), the Book of Measurement of Spheres by Spheres. In this text, al-Sijzī divides the cube into several sub-cubes and parallelopipedes, thus offering us a stereometric interpretation of algebraic identities of the third degree usually credited to mathematicians of the sixteenth and seventeenth centuries. However, this was not al-Sijzīʼs motivation for writing this treatise; rather it was his theoretical interest in the Euclidian concept of the “power” of a segment, an interest which is clearly geometric rather than algebraic. This has led al-Sijzī to the notion of dimension, at least in outline.

This article explores the reception of Avicenna's theories of motion in the sixth/twelfth century. Avicenna had devised innovative ways of understanding motion in response to various challenges and conditions that the preceding philosophical tradition and his own internal critique had posed. Motion for him was either the state of being between two termini or the traversal of an interval, where the former of these was the extramentally real type and the latter a product of the imagination. In the sixth/twelfth century, the implicit critique of some leading scholars led to the adoption of the thesis in some circles that motion by traversal is extramentally real. This position was accepted as viable both by those who endorsed the atomic and the continuous theory of bodies.

Suscités par la reprise massive de la recherche en astronomie au IXe siècle dans le monde islamique et essentiellement à Bagdad, laquelle nécessite des outils mathématiques nouveaux, une floraison de traités, tant astronomiques que mathématiques, voit le jour à cette époque. D'entre les traités mathématiques, un certain nombre est consacré à la ‘‘figure secteur” (al-shakl al-qattā‘), c’est-à-dire au théorème dit ‘‘de Ménélaüs” sur la sphère, lequel généralise le théorème dit ‘‘de Ménélaüs” dans le plan. Ce théorème de Ménélaüs sur la sphère, ou règle des six quantités, est, en l’absence du théorème des sinus sur la sphère, lequel ne date que de la deuxième moitié du Xe siècle, le principal outil de l'astronomie sphérique. Le traité de Thābit ibn Qurra (mort en 901) sur La figure secteur est le premier de ces traités consacrés au théorème de Ménélaüs, tant dans le plan que sur la sphère, à nous être parvenu; point de départ de tout un courant, il influencera profondément le développement ultérieur de la géométrie sphérique. Ce traité, qui est en fait une épître adressée à un correspondant malheureusement anonyme, présente en outre l'intérêt de montrer que, dans le milieu scientifique de cette époque à Bagdad, beaucoup s'intéressaient à ce théorème, essayaient d'en énoncer d'autres cas de figure et de compléter la démonstration qu'en donne Ptolémée dans l'Almageste.

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.

Coinciding with the scientific flourishing of the 5th / 11th century, which was favoured by the cultural policy of the Andalusī kingdoms ( mulūk al-tawā'if ), Abū ‘ Umar ibn ‘ Abd al-Barr, Ibn Hazm and Sā‘ id al-Andalusī all dealt with the classification of the sciences in many works that are already known. Ibn Bājja began his career at the end of this period. In his glosses to al-Fārābī’s commentary to the Isagoge he wrote a text on this subject that has not yet been analysed. The present paper studies Ibn Bājja's classification in connection with his predecessors and with the scientific and philosophical background of Andalusī culture. In their classifications of the sciences, all these authors express and stress important factors of the evolution of Andalusī science and thought, such as the dialectic between religious and rational sciences and the importance of the scientific method derived from Aristotle's logic. Sā‘ id al-Andalusī and Ibn Bājja ( and, to a lesser extent, Ibn Hazm ) show the profound influence exerted by al-Fārābī’s works, particularly the Ihsā' al-‘ ulūm. Thus, Ibn Bājja foreshadows the evolution of sciences in the next century and the movement headed by Ibn Rushd, Ibn Tufayl and others, characterized by the search for concordance with the postulates set forth by philosophical disciplines.

The article deals with the Arabic sources of Chr. Clavius in Rome and the six different ways they were used by him in mathematics and astronomy. It inquires especially into his attitude towards al-Farghānī, Thābit ibn Qurra, al-Bi[tdotu]rūjī, Ibn Rushd, Mu[hdotu]ammad al-Baghdādī, Pseudo-Ibn al-Haytham, Jābir ibn Afla[hdotu], and Pseudo-al-[Tuotu]ūsī.

The production of manuscripts can be an indication for the scientific, linguistic or medical interests of a community. In this paper the author argues that Parisinus Graecus 2293, a bilingual Greek-Arabic manuscript, containing parts of the first three books of Paul of Aegina's medical encyclopaedia, was produced in Sicily or Southern Italy, probably in Palermo during the reign of the Hohenstaufen. It is thus a testimony to the fervent scientific and medical interest of the Swabian court which promoted cultural exchange between the East and the West. The purpose of the manuscript was not so much to help medical practice but rather to further bilingualism by giving the reader a tool with which he could improve his knowledge of either language.

What is the function of logic in al-Kindī's corpus? What kind of relation does it have with mathematics? This article tackles these questions by examining al-Kindī's theory of categories as it was presented in his epistle On the Number of Aristotle's Books (Fī Kammiyyat kutub Arisṭū), from which we can learn about his special attitude towards Aristotle theory of categories and his interpretation, as well. Al-Kindī treats the Categories as a logical book, but in a manner different from that of the classical Aristotelian tradition. He ascribes a special status to the categories Quantity (kammiyya) and Quality (kayfiyya), whereas the rest of the categories are thought to be no more than different combinations of these two categories with the category Substance. The discussion will pay special attention to the function of the categories of Quantity and Quality as mediators between logic and mathematics.

Deux opuscules nous sont parvenus de Thābit ibn Qurra sur la théorie des parallèles. Ces deux traités sont bien connus et ont fait déjà l'objet de plusieurs commentaires et traductions. Nous pensons reprendre ici aussi bien l'édition que la traduction et le commentaire pour mieux situer la contribution de Thābit ibn Qurra après la publication récente de ses œuvres en astronomie et en mathématiques.

Starting from the Greek definition of philosophy as the love of wisdom, and from the semantic richness of the Arabic word ḥikma, several fourth- and fifth-century writers tried to establish the position of philosophy in the Islamic cultural system by identifying it with wisdom. For them this wisdom is tantamount to the ‘eternal wisdom’ recorded in the ancient books and taught by the prophets. Philosophers are described as the prophets' disciples or witnesses. However, depicting philosophy as eternal wisdom only gives the discipline an illusory advantage. Ultimately it reduces it to pure repetition and therefore precludes any change.

In a manuscript which is being studied here for the first time, al-Samaw'al (12th century) quotes a paragraph from al-Bīrūnī (11th century) which shows that the latter knew not only of Brahmagupta's method of quadratic interpolation, but also of another Indian method (called sankalt). Al-Samaw'al examines these methods, as well as linear interpolation, compares them, and evaluates their respective results. He also tries to improve them. In this article the author shows that al-Bīrūnī had used four methods of interpolation, two of which were of Indian origin; and that al-Samaw'al explicitly introduced a new way of evaluating these different methods. He also throws light on the active movement of research on numerical methods that constitutes the background to al-Bīrūmī's and al-Samaw'al's work, and uses modern means to evaluate the different methods and to justify the mathematicians' choices. The author has edited and translated al-Samaw'al's text in order to make it available to historians of Arabic and Indian mathematics. This allows them to follow the history and the mathematical arguments, and deepens our understanding of the importance to the development of mathematics of certain astronomical work. It also highlights the contribution of Indian mathematicians to the development of Arabic mathematics.

The first and more important section of this article lists all the known treatises in Arabic on Fine Technology – water-clocks, automata, pumps, trick vessels, fountains, etc. The ideas, techniques and components in these treatises are of great importance in the history of machine technology. For each treatise information is given on the provenance of MSS, editions in Arabic and translations, paraphrases or commentaries in modern European languages. In addition to treatises by Arabic writers, similar information is also given on Greek mechanical treatises if these have survived only in Arabic versions.

The second section deals with utilitarian machines such as mills and water-raising machines. The various sources of information about these machines is discussed, including Arabic works on geography and travel, iconography and archaeology.

In his encyclopedic book (al-Istikmāl), the mathematician of Saragossa, Ibn Hūd (d. 1085/478 H.), established by an intrinsic demonstration of spherical geometry, a remarkable theorem which generalizes the proposition III.11 from Theodosius’s Spherics and integrates the propositions III.23-25 from Menelaus’s Spherics. In this paper, we study this theorem and the demonstration of Ibn Hūd. The reader will find also some established and translated texts (Ibn Hūd, Ibn ʿIrāq, al-Ṭūsī) addressing the same theme.

The aim of this paper is to present the modes of action of venom as construed by Abū 'Uthmān 'Amr ibn Ba[hdotu]r al-Jā[hdotu]i[zdotu] (780-868) in his Kitāb al-[Hdotu]ayawān (The Book of Animals). The toxicological information presented by Jā[hdotu]i[zdotu] is a synthesis of data available in his time, but Jā[hdotu]i[zdotu] complemented these early conceptions by his personal theoretical views. Jā[hdotu]i[zdotu]'s fundamental idea is that venoms act through their specific natures; this idea in a way is reminiscent of present-day theory of enzymes.

In his analysis of the hypothetical (šarṭīyya) connected (muttaṣila) and disjunctive (munfaṣila) propositions (Al-qiyās, section V), Ibn Sīnā suggests that they can be quantified and presents in section VI a hypothetical system containing the conditional ones, which is exactly parallel to categorical syllogistic and makes use of the same conversion rules and the same proofs. In section VII, he provides four lists of hypothetical quantified propositions whose clauses are themselves quantified and says that the relations of the Aristotelian square of opposition hold for them. In addition, he says that some conditional universal affirmative propositions are equivalent to some universal negative ones with opposed consequents, and to some quantified disjunctive ones. The problem is that these claims are incompatible with each other, since they require two different readings of the universal affirmative conditional proposition, which Ibn Sīnā does not distinguish clearly. In this paper we solve the problem by distinguishing explicitly between these two readings and showing that the first one satisfies the conversion rule of the universal affirmative and the relations of the logical square, and validates all the admitted moods, while the second one satisfies the contraposition rule and the equivalences stated by Ibn Sīnā. This accounts for all Ibn Sīnā’s claims and makes the system coherent.

In the fifth book of his De aspectibus, the medieval Latin version of Ibn al-Haytham’s Kitāb al-Manāẓir, Alhacen undertakes to determine precisely where a given ray of light will reflect to a given center of sight from a variety of convex and concave mirrors based on circular sections. As applied specifically to convex and concave spherical mirrors, this problem exercised several seventeenth-century thinkers, Christiaan Huygens foremost among them, and in that context it soon became known as ‘‘Alhazen’s Problem.’’ By current standards, Alhacen’s solution (or solutions) of this problem is deficient in comparison to that of Huygens and later mathematicians. It is my purpose in this paper to show by reconstruction that in fact, far from deficient in any absolute sense, Alhacen’s approach to this problem was remarkably ingenious and elegant in its conceptual simplicity.

Until the end of the 14th century, the sources of Hebrew mathematical writings were almost exclusively in Arabic. This was particularly true of texts that contained elements of algebra or algebraic developments. The testimonies we present and analyze here are due to Jewish authors living in Italy, primarily in the 15th century, who made use of the most varied sources, in addition to Arabic: in Castilian, in Italian, and perhaps in Latin. These testimonies constitute both an indication, and a product, of the circulation of Arab algebraic traditions in Renaissance Italy. Simon Moṭoṭ’s book on The Calculation of Algebra stems from the Italian tradition of ‘‘treatises on the abacus’’. Mordekhay Finzi of Mantua is the author of a Hebrew version of the great work on algebra by Abū Kāmil (9th century), as well as of a version, distinct from the preceding, of the Arabic scholar’s introductory exposition. Beginning in 1473, Finzi also translated from Italian to Hebrew the important treatise on algebra by Maestro Dardi of Pisa (1344). We also indicate some 16th century continuations of Hebrew mathematical production, which contain algebraic developments.