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Menelaus' ›Spherics‹

Menelaus' ›Spherics‹

Roshdi Rashed; Athanase Papadopoulos

De Gruyter
2017
sidottu
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-Mahani /al-Harawi, together with a historical and mathematical study of Menelaus’ treatise. With this book, a new and important part of the Greek and Arabic legacy to the history of mathematics comes to light. This book will be an indispensable acquisition for any reader interested in the history of Ancient geometry and science and, more generally, in Greek and Arabic science and culture.
L’hydrostatique de Ménélaüs

L’hydrostatique de Ménélaüs

Roshdi Rashed

De Gruyter
2020
sidottu
Menelaus of Alexandria (1st century CE) is the author of the treatise Sphaerica and as of a treatise on fluid statics. Both of these works only survive in Arabic translations. This book provides an editio princeps of Menelaus’s second text as well as the recently discovered commentary thereon, written by the philosopher and scholar Muhammad ibn al-Haytham (10th–11th century).
L'algèbre arithmétique au XIIe siècle: ›Al-Bahir‹ d'al-Samaw'al
Après qu'al-Khwarizmi eut rédigé son livre fondateur de l'algèbre au début du IXe siècle, les recherches algébriques se sont rapidement développées et enrichies, avant de se scinder et de se concentrer en deux principaux courants: l'algèbre arithmétique, l'analyse indéterminée et la théorie des nombres d'une part, la géométrie algébrique élémentaire d'autre part. C'est à partir des travaux du premier courant qu'al-Samaw'al (mort en 1175) rédige le premier traité en algèbre arithmétique: "Le Brillant en Algèbre", al-Bahir fi al-Jabr. On trouvera ici l'édition critique de cet ouvrage fondamental, sa traduction en français, ainsi que son commentaire mathématique et historique. Le présent livre est important non seulement pour comprendre l'histoire de l'algèbre en arabe, mais aussi celle de l'algèbre latine à partir de Leonardo Pisano et, plus généralement, l'histoire des mathématiques classiques .
Arithmétique, Algèbre et Théorie des Nombres
The texts in these four volumes deal with the history and philosophy of mathematics and its applications. The first three volumes are devoted to the history of mathematics (arithmetic, algebra, geometry), optics and astronomy, from Antiquity to the Classical Age. Over the last fifty years, the numerous studies contained in this volume have renewed the study of the main Greek mathematicians - Euclid, Archimedes, Apollonius, Diophantus, Menelaus - and have shown the nature and scope of their reception and transformations, both in classical Islam and in early European modernity. The fourth volume establishes and explores various fields of research between philosophy and mathematics, from the polymorphous interactions specific to Greek, Arab and Latin science to the mathematisation of the social sciences in the eighteenth century. Both in terms of the novelty of the material discovered and published for the first time and the power and finesse that continue to guide its epistemological analysis, the dozens of contributions collected here represent a major work that has changed the history of science in our time.
Géométries

Géométries

Roshdi Rashed

De Gruyter
2023
sidottu
The texts in these four volumes deal with the history and philosophy of mathematics and its applications. The first three volumes are devoted to the history of mathematics (arithmetic, algebra, geometry), optics and astronomy, from Antiquity to the Classical Age. Over the last fifty years, the numerous studies contained in this volume have renewed the study of the main Greek mathematicians - Euclid, Archimedes, Apollonius, Diophantus, Menelaus - and have shown the nature and scope of their reception and transformations, both in classical Islam and in early European modernity. The fourth volume establishes and explores various fields of research between philosophy and mathematics, from the polymorphous interactions specific to Greek, Arab and Latin science to the mathematisation of the social sciences in the eighteenth century. Both in terms of the novelty of the material discovered and published for the first time and the power and finesse that continue to guide its epistemological analysis, the dozens of contributions collected here represent a major work that has changed the history of science in our time.
Optique et Astronomie

Optique et Astronomie

Roshdi Rashed

De Gruyter
2023
sidottu
The texts in these four volumes deal with the history and philosophy of mathematics and its applications. The first three volumes are devoted to the history of mathematics (arithmetic, algebra, geometry), optics and astronomy, from Antiquity to the Classical Age. Over the last fifty years, the numerous studies contained in this volume have renewed the study of the main Greek mathematicians - Euclid, Archimedes, Apollonius, Diophantus, Menelaus - and have shown the nature and scope of their reception and transformations, both in classical Islam and in early European modernity. The fourth volume establishes and explores various fields of research between philosophy and mathematics, from the polymorphous interactions specific to Greek, Arab and Latin science to the mathematisation of the social sciences in the eighteenth century. Both in terms of the novelty of the material discovered and published for the first time and the power and finesse that continue to guide its epistemological analysis, the dozens of contributions collected here represent a major work that has changed the history of science in our time.
Mathématiques et Philosophie

Mathématiques et Philosophie

Roshdi Rashed

De Gruyter
2023
sidottu
The texts in these four volumes deal with the history and philosophy of mathematics and its applications. The first three volumes are devoted to the history of mathematics (arithmetic, algebra, geometry), optics and astronomy, from Antiquity to the Classical Age. Over the last fifty years, the numerous studies contained in this volume have renewed the study of the main Greek mathematicians - Euclid, Archimedes, Apollonius, Diophantus, Menelaus - and have shown the nature and scope of their reception and transformations, both in classical Islam and in early European modernity. The fourth volume establishes and explores various fields of research between philosophy and mathematics, from the polymorphous interactions specific to Greek, Arab and Latin science to the mathematisation of the social sciences in the eighteenth century. Both in terms of the novelty of the material discovered and published for the first time and the power and finesse that continue to guide its epistemological analysis, the dozens of contributions collected here represent a major work that has changed the history of science in our time.
L'Optique Dans l'Inde Islamique Au Xviie Siècle: Ibn Ṣāliḥ, >Sur Les Miroirs Ardents Paraboliques
Le trait d'Ibn Ṣāliḥ Sur les miroirs ardents paraboliques repr sente une contribution majeure l'histoire de l'optique g om trique. Le pr sent ouvrage contient la premi re dition de ce texte, accompagn e d'une traduction fran aise et d'un commentaire historique et math matique. L'int r t principal du texte d'Ibn Ṣāliḥ consiste dans la mani re originale dont il construit sa d marche catoptrique partir des oeuvres optiques et g om triques de la tradition. Partant des recherches d'Ibn al-Haytham (XIe si cle) sur les miroirs paraboliques, il infl chit le traitement de ces objets dans deux directions nouvelles: tout d'abord, Ibn Ṣāliḥ traduit dans les termes de la g om trie d'Euclide des propri t s des coniques trait es par ses pr d cesseurs arabes dans le style d'Apollonius; en second lieu, il montre un int r t technique pour la construction des miroirs, dont il fournit un v ritable manuel l'attention des architectes et des ing nieurs de l'entourage de Shāh Jahān. Le pr sent ouvrage contient en outre la premi re dition d'un trait catoptrique anonyme conserv en Inde. Ces nouveaux mat riaux permettent de documenter pour la premi re fois les d veloppements remarquables de la catoptrique arabe au XVIIe si cle, ainsi que les avanc es de la science islamique dans l'Inde moghole l' poque de Shāh Jahān.