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Les textes réunis dans ces quatre volumes portent sur l’histoire et la philosophie des mathématiques et de leurs applications. Les trois premiers tomes sont consacrés à l’histoire des mathématiques (arithmétique, algèbre, géométrie), de l’optique et de l’astronomie, de l’Antiquité à l’Âge classique. Les très nombreuses études qu’ils contiennent ont renouvelé, au cours des cinquante dernières années, l’étude des principaux mathématiciens grecs – Euclide, Archimède, Apollonius, Diophante, Ménélaüs – et ont montré quelle a été la nature et la...

Einem einzigartigen und schwierigen Problem gewidmet, ist die Abhandlung Uber den Verhaltnisschnitt von Apollonius aus Perge ein bemerkenswert komplexes Beispiel fur die Erforschung der notwendigen Voraussetzungen fur die Existenz einer Losung. Der vorliegende Band bietet die editio princeps des nur arabisch uberlieferten Textes. Erschlossen wird er durch eine franzosische Ubersetzung und einen Kommentar, der die Mechanismen des schwierigen Beweises durch Apollonius aufzeigt und dabei besonders auf deren konzeptionelle Innovationen hinweist.

Despite its importance in the history of Ancient science, Menelaus' Spherics is still by and large unknown. This treatise, which lies at the foundation of spherical geometry, is lost in Greek but has been preserved in its Arabic versions. The reader will find here, for the first time edited and translated into English, the essentials of this tradition, namely: a fragment of an early Arabic translation and the first Arabic redaction of the Spherics composed by al-Māhānī /al-Harawī, together with a historical and mathematical study of Menelaus' treatise....

This book follows the development of classical mathematics and the relation between work done in the Arab and Islamic worlds and that undertaken by the likes of Descartes and Fermat.

'Early modern, ' mathematics is a term widely used to refer to the mathematics which developed in the West during the sixteenth and seventeenth century. For many historians and philosophers this is the watershed which marks a radical departure from 'classical mathematics, ' to more modern mathematics; heralding the arrival of algebra, geometrical algebra, and the mathematics of the continuous. In this...

This is the first comprehensive treatment of the history of the angle from Euclid to classical Arabic mathematics. The volume presents critically edited texts, with translations and commentaries, of Greek and Arabic philosophers and mathematicians including Euclid, Simplicius, al-Nayrīzī, Avicenna, Ibn al-Haytham, al-Tūsī, al-Shīrāzī, and al-Fārisī.

Al-Khwarizmi's Algebra (Kitab al-Jabr wa-al-muqabala), written around 820, was the first scientific text in history to systematically present algebra as a mathematical discipline that is independent of geometry and arithmetic. Roshdi Rashed has produced the first Arabic critical edition of Al-Khwarizmi's work, containing an annotated translation into English, an introductory essay, and extensive commentaries on the text.

Roshdi Rashed is a leading authority in the history and philosophy of science and mathematics. He is senior director of research at the Centre...

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.

The first three books of the Conica deals with the basic elements of the theory of conical sections, before Apollonius turns to particular problems in the following books. Until recently these three books were only known from Eutocius' text. However, they were known to be part of an Arabic translation of a Greek version independent of Eutocius' text.

A close study of the Arabic texts of books 2 and 3 leads to the same conclusion as that which, as a result of the new edition, was reached for the first book: that the Greek version provides a better and sounder text. This...

This fifth volume of A History of Arabic Sciences and Mathematics is complemented by four preceding volumes which focused on the main chapters of classical mathematics: infinitesimal geometry, theory of conics and its applications, spherical geometry, mathematical astronomy, etc.

This book includes seven main works of Ibn al-Haytham (Alhazen) and of two of his predecessors, Thābit ibn Qurra and al-Sijzī

• The circle, its transformations and its properties;
• Analysis and synthesis: the founding of analytical art;

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