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.

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Turkey, Afghanistan, Israel, Pakistan, and the countries of the Arab World from the 7di century to modern times. Spain, Southeastern Europe,

Ibn Rušd devoted a certain number of works to Aristotle'sPrior Analytics. In a series ofopusculeswritten over a period of twenty years and following upon hisMiddle Commentary on Aristotle's Prior Analytics, he faced a problem particular to the modal syllogism – that of the mood of the conclusion in mixed syllogisms.The problem can be stated as follows: At the beginning of thePrior Analytics, Aristotle established a formal deductive principle – that of universal attribution (Pr. An.I.1.24b26–30). Applied to the modal syllogism, this principle is inadequate as stated. It is too general to be applied in a univocal manner in all modal syllogisms. To preserve a sense of coherence in Aristotle's declarations, the commentators had to interpret it. Presenting the interpretations of the commentators, primarily al-Fārābī and Alexander, on the basis of al-Fārābī'sLarge Commentary on Aristotle's Prior Analytics, Averroes criticizes them. Applied according to Alexander's interpretation, the principle of universal attribution is valid only for modal syllogisms one of whose premises is necessary and the other assertoric; according to al-Fārābī's interpretation, it is verified only when the minor premise is possible. Averroes proposes two preliminary solutions. Either this formal deductive principle must be applied differently according to the modal differences of the minor premises in mixed syllogisms (first solution) or would be used in two ways, generally or in keeping with each mood (second solution). These solutions are not satisfactory, for they call into question the unity and universality of the principle of universal attribution as established by Aristotle. What is the utility, Averroes asks, of a principle which does not hold for all modalities or does not apply to all the premises when thePr. An.ought to furnish formal and universal principles of deduction? And why did Aristotle define the principle of universal attribution without distinguishing its application according to each of the three modal premises? Returning at the end of his career to a literal exegesis of Aristotle's propositions and without harkening back to the earlier solutions, he proposes a theory of making the terms modal (fourth solution) in order to save Aristotle's declarations with respect to the principle of universal attribution and the mood of the conclusion of mixed syllogisms (Pr. An.I. 9.30al5–20). Though formally inadequate, this solution, which had a continued history, proposes a new way of looking at the classification of modal propositions.

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First century Chinese, fifth century Indian, and Arabic documents from the 9th century onwards, contain similar tabular procedures to extract square and cube roots on place-value numeration systems. Moreover, an 11th century Chinese astronomer, Jia Xian, as well as al-Samaw'al, a 12th century Arab mathematician, extracted roots of higher order with the so-called Ruffini-Horner procedure. This article attempts to define a textual method to organize this corpus, by distinguishing relevant criteria for identifying similarities and differences from a historical as well as conceptual point of view. The first part analyses three different states of the descriptions of algorithms in China between the 1st and the 11th centuries, all of which exhibit a definite historical stability. The rewriting which allows one to proceed progressively from one state to the next shows a uniformity in the components of the algorithm, which culminates in procedures of the type Ruffini-Horner. Textual criteria demonstrate a greater affinity of certain algorithms, such as those described by Kūshyār ibn Labbān (ca1000) with Chinese rather than with Indian texts, which are in turn closer to algorithms described by al-Khwārizmī. Criteria of the same kind link the algorithms of Jia Xian and al-Samaw'al on the one hand, and those of Kūshyār and al-Samaw'al on the other.

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The article describes several representations of Alexander the Great which were current in medieval Arabic learned circles and proposes some ideas on the genesis of these representations in the Greek and Syriac civilizations: 1) Alexander as moralist; 2) Alexander as a mystical philosopher who knew the mysterious links governing the cosmos; 3) Alexander as a monotheist philosopher who was charged with responsibility for the Ğihād; 4) Alexander as a cunning politician.

The author examines the relationship between mathematics and philosophy in the works of al-Kindī, and suggests that the real character of his contribution will become clear only when we restore to mathematics their proper role in his philosophy. The recently discovered treatise of al-Kindī on the approximation of π, of which the author gives the editio princeps here, throws important new light on al-Kindī's knowledge of mathematics, and on the history of the transmission of The Measurement of the Circle of Archimedes. The author shows that al-Kindī's commentary on the third proposition of the Measurement of the Circle was written before 857, at the same time if not before that of the Banū Mūsā, and that it was one of the sources of the Florence Versions, the Latin commentary on the same proposition.

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