Roshdi Rashed

The Development of Arabic Mathematics: Between Arithmetic and Algebra

Preface. Introduction. I: The Beginnings of Algebra. II: Numerical Analysis. III: Numerical Equations. IV: Number Theory and Combinatorial Analysis. Appendix 1: The Notion of Western Science. Appendix 2: Periodization in Classical Mathematics. Bibliography. Index.

The celestial kinematics of Ibn al-Haytham

After having reformulated optics, Ibn al-Haytham conceived of an analogous project for astronomy. This has just been revealed by an important book by the mathematician which has never been studied until now. Ibn al-Haythams reform consists in excluding all cosmology, and in developing a systematic study of a celestial kinematics that has been completely geometrized. In turn, the realization of such a reform demanded innovative research in infinitesimal geometry. In this article, an attempt is made to present this new geometry, as well as the mathematical means invented to elaborate it.

Thabit ibn Qurra: Science and Philosophy in Ninth-Century Baghdad

The series Scientia Graeco-Arabicais devoted to the study of scientific and philosophical texts from the Classical and the Islamic world handed down in Arabic. Through critical text editions and monographs it provides access to the topics of inquiry in which ancient science presented itself and developed over time in a continuous tradition between Antiquity and the modern period. All editions are accompanied by translations and philological and explanatory notes. Languages of publication are English, German, French and Italian.

Ibn al-haytham et les nombres parfaits

Zusammenfassung De Aufsatz ist den Untersuchungen der arabischen Mathematiker zur Zahlentheorie gewidmet. Er zeigt, das Ibn al-Haytham die Umkehrung des Satzes IX, 36 uber vollkomene Zahlen der Elemente Euklids ausgesprochen und zu beweisen versucht hat. Der Aufsatz erortert die Berechnung einiger dieser Zahlen durch spate Mathematiker und beschreibt einige Ergebnisse von al-An t a k i (° 987). Bestimmte Fragmente von dessen arithmetischen Arbeiten wurden vor kurzem identifiziert.

Al-Quhi and al-Sijzi on the perfect compass and the continuous drawing of conic sections

From the second half of the 10th century, mathematicians developed a new chapter in the geometry of conic sections, dealing with the theory and practice of their continuous drawing. In this article, we propose to sketch the history of this chapter in the writings of al-Qūhī and al-Sijzī. A hitherto unknown treatise by al-Sijzī - established, translated, and commented - has enabled us better to situate and understand the themes of this new research, and how it eventually approached the problem of the classification of curves in previously unknown terms.

Al-Quhi: From Meteorology to Astronomy

Among the phenomena examined in the Meteorologica , some, although they are sublunar, are too distant to be accessible to direct study. To remedy this situation, it was necessary to develop procedures and methods which could allow observation, and above all the geometrical control of observations. The eventual result of this research was to detach the phenomenon under consideration from meteorology, and to insert it within optics or astronomy. Abū Sahl al-Qūhī (second half of the tenth century), composed a treatise on shooting stars in which he carries out such an insertion. In a second treatise, he deals with another type of observation, intended to measure maritime, terrestrial, and celestial surfaces. Here, the author studies al-Qūhīs contribution and gives the editio princeps of these two treatises, as well as their translation.

Indian Mathematics in Arabic

Although speculations abound concerning the transmission of Indian Mathematics into Arabic, there is little convincing evidence that many methods and results were known to Arab mathematicians. Many texts are either lost or not yet published, or carelessly edited and analyzed. No important work either, as far as I know, is devoted to the Indian legacy in Arabic, and to translation from Sanskrit to Arabic. Consequently, it is not yet possible to draw a synthetic picture of the transmission of Indian mathematics or grasp its general characteristics. The only conjecture that I dare suggest is that the Indian mathematics transmitted were mainly computational, dependent on Astronomy. My concern in this talk is rather modest: 1 should like to present a hitherto unknown source1 which provides further confirmation of the previous conjecture — partially at least — and which illustrates why and how a sector of Indian mathematics was transmitted and diffused among Arab mathematicians. It is necessary however to recall at first — very briefly — the mathematical context in which this Indian text took place.

Science classique et science moderne a l’époque de l’expansion de la science européenne

First, let me thank my colleagues of REHSEIS who organized this International Colloquium, Patrick Petitjean, Annick Horiuchi, Catherine Jami and Anne Marie Moulin, and the scientific committee which helped them. Second, I would like to thank UNESCO, and particularly Professor Badran for all their help and all their support for the organization of this colloquium.

Recommencements de L’Algèbre aux XIe et XIIe Siècles

Parfois encore l’histoire de l’algebre classique est relatee comme la succession de trois evenements separes: la constitution de la theorie des equations quadratiques, la resolution plus ou moins generale de l’equation cubique, l’introduction et le developpement du symbolisme algebrique. Au premier evenement on associe souvent le nom d’al-Khwarizmi, au second on rattache toujours ceux des mathematiciens de l’ecole italienne, et en particulier de Tartaglia et de Cardan, au troisieme enfin sont lies les noms de Viete et de Descartes.

L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUES

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.