Our intention here is to present the essential character of classical, sunnī kalām within a strictly formal perspective and to set out its basic aspects. It was conceived by the mutakallimīn as a rational, conceptual, and critical science and, although kalām differed in a number of basic concepts and constructs and in its analytic system, the topical organisation of the major compendia parallels that of metaphysics as understood in the contemporary Aristotelian tradition. The debates between kalām and falsafa need to be examined within this context. Kalām, however, is theological in the strict sense of the term and it is as such that its problematic and its procedures are primarily to be understood. Thus seen, the object of kalām is to rationalise the cognitive content presented to Believers in the symbolic language of the koranic revelation. It has, then, four principal tasks, sc, to conceptualise, to order, to explain, and where possible to justify the primary doctrines of the community whose belief is held to be normative. Within this framework the differences that characterise the major schools as such and the various tendencies of individual masters within each school may readily be brought to light.

Euclid's Elements were translated into Hebrew from Arabic in the 13th century; but precious few of the Arabic commentaries have come down to us in a Hebrew version (al-Fārābī, Ibn al-Hayṯam). Nonetheless, a study of several texts dealing with the Fifth Postulate (the Parallel Postulate) of Book I reveals that the Hebrew authors are greatly indebted to Arabic sources.

We shall examine three attempted proofs of the Parallel Postulate. The two attempts by Moses ha-Levi of Seville (13th century) and Alfonso of Valladolid (14th century) are mathematically unconvincing. Nevertheless they are interesting historically: Moses ha-Levi exploits the movement of lines which are infinite in actu; and Alfonso, starting from a critique of Ibn al-Hayṯam and al-Nayrīzī, claims to innovate in the use of the method of superposition.

In contrast, Gersonides' attempt (14th century) is a well-articulated series of premises and proofs, including several arguments which we have traced back to the Taḥrīr Uṣūl Uqlīdis of Pseudo-Ṭūsī. We feel it is important to emphasize this relationship, even though it is impossible to establish the route by which these arguments found their way to Gersonides.

Though much has been written of late about Averroes and his philosophy, little attention has been paid to his political teaching. Generally speaking, his works can be divided into two categories: (a) commentaries on Aristotle and other important thinkers and (b) occasional treatises written to resolve particular questions. The subject of this essay, his political teaching, is stated most directly in the first classification of writings – especially in his commentaries on Aristotle's Rhetoric and Plato's Republic. Even though the second kind of writings helps to nuance some of his broader themes — especially the two treatises having to do with the relationship between philosophy anddivine law, namely, the Decisive Treatise and its sequel Kashf an manāhij al-adilla — considerations of space preclude an analysis of them here. Our examination of the first two writings will focus primarily on what Averroes has to say about the different kinds of political regimes and, above all, the best regime, for his discussion of it leads him to reflect more generally on other major political questions.

Written by the 11th-century Spanish Arab, Abū ʿAbd Allāh Muhammad ibn Mucādh al-Jayyānī, “On Twilight and the Rising of Clouds” represents a unique attempt to determine the height of the atmosphere on the basis of the first tinging of its upper reaches by dawn light. In fact, Ibn Mucādh's value of around 52 miles remained standard until the 17th century, when it was revised sharply downward in consideration of atmospheric refraction and barometric studies. The treatise itself survives in a single Hebrew exemplar, 25 Latin exemplars, and an Italian exemplar derived from the Latin. At the heart of this present study is a critical text based on a fullscale comparative transcription of 22 of the Latin manuscripts, ranging in date from the 13th to the 17th century.

Quand on compare l'Optique d'Ibn al-Haytham (Alhazen) à celle de Ptolémée, on rencontre des innovations à coup sûr capitales, et qui chacune mériterait une analyse particulière: étude expérimentale de la propagation rectiligne de la lumière, nouvelle théorie de la vision fondée sur la réception dans l'œil de rayons lumineux, recherche du lien entre l'anatomie de 1'œil et sa fonction optique, preuve expérimentale que la réfraction joue un rôle important dans la vision, et j'en passe: les dimensions d'un article de revue n'y suffiraient pas. Aussi bien mon but est-il plus global et plus synthétique. Il consiste à tenter de faire le point sur ce qu'est devenue, après Ibn al-Haytham, l'insertion de l'optique dans le système des savoirs qui lui sont connectès, en comparant cette insertion à ce qu'elle était au temps de Ptolémée, c'est-à-dire dans l'œuvre de référence (plus encore que celle d'Euclide et du pseudo-Euclide) reçae et travaillée par lui.

As early as the ninth century, Muslim astronomers started refining the Ptolemaic astronomy which, by this time, had been fully adopted as the framework of their research. Already, in the early part of this century, refinements were based on improved observational techniques, and included a variety of phenomena such as the length of the seasons, the solar equation, mean motion parameters, and many others.

The use of the immediate and common point of view (bādi' al-ra'y al-muštarak) is presented, in Arab philosophy, as characteristic of the rhetorical method. We will endeavour, in this article, to determine the importance, the significance and the origins of this concept in the works of Fārābī. The first part examines the concept's position in the structure of Kitāb where Fārābī, while following Rhet. I 2 (a veritable introduction to the discipline of oratory) tries to improve the structure of Aristotle's chapter around this concept, which is not in Aristotle. The concept is then defined in the second part. What is at issue is not the immediate point of view of an individual who might think of certain propositions as being universally accepted, when in fact they are not, but rather the point of view which is accepted without question by the majority. It relies on a kind of testimony (šahāda) rather than on the personal judgement of the auditor. It differs nevertheless from propositions which are really universally accepted because these can only be invalidated by an elite and not by any ordinary examination. In the third part, we will review those doctrines of Kitāb which depend on the concept of the immediate and common point of view, focusing in particular on the definition of enthymema. In the last part, we will investigate some philological and philosophical difficulties, such as the difference between rhetorical and dialectical premises, which constitute the background to the development of the concept.

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.