"Thabit ibn Qurra est l'un des esprits les plus originaux de tous les temps. On lui doit le premier dépassement de Ptolémée en astronomie et la première critique radicale de l'ontologie aristotélicienne au nom de l'idéalisme mathématique. Au vu de son importance historique, il était urgent de publier ses œuvres encore inédites, ou non éditées de manière critique, et de les étudier de manière véritablement historique. On trouvera, dans cet ouvrage, l'édition, la traduction et le commentaire d'une douzaine de ses (...) opuscules mathématiques et philosophiques, éclairant différentes facettes de son génie universel."--. (shrink)

Al-Q, mathematician of the 10th century, examines critically two arguments in the 6th book of the Aristotelian Physics. This critic does not follow the method of the philosophers, with doctrinal amendments, but with a mathematical and experimental style. For understanding of this critical examination and its influence, it is necessary to situate it in the mathesis of al-Q and to produce its mechanical presuppositions. This is the purpose of the author of this paper.

The author examines the relationship between mathematics and philosophy in the works of al-Kind on the approximation of 's knowledge of mathematics, and on the history of the transmission of The Measurement of the Circle of Archimedes. The author shows that al-Kind M, and that it was one of the sources of the Florence Versions, the Latin commentary on the same proposition.

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. (shrink)

Al-Qūhī, mathematician of the 10th century, examines critically two arguments in the 6th book of the Aristotelian Physics. This critic does not follow the method of the philosophers, with doctrinal amendments, but with a mathematical and experimental style. For understanding of this critical examination and its influence, it is necessary to situate it in the mathesis of al-Qūhī and to produce its mechanical presuppositions. This is the purpose of the author of this paper. Le mathématicien du X e siècle al-Qūhī (...) critique deux theses du sixième livre de la Physique d’Aristote. Cette critique n’est pas à la manière des philosophes, par amendements doctrinaux, mais elle adopte un style mathématique et expérimental. Comprendre cette critique et son impact, c’est la placer dans la mathesis d’al-Qūhī et exhiber ses présupposés mécaniques. C’est à quoi s’emploie l’auteur de cet article. (shrink)

In a manuscript which is being studied here for the first time, al-Samaw'al quotes a paragraph from al-Bīrūnī which shows that the latter knew not only of Brahmagupta's method of quadratic interpolation, but also of another Indian method. Al-Samaw'al examines these methods, as well as linear interpolation, compares them, and evaluates their respective results. He also tries to improve them. In this article the author shows that al-Bīrūnī had used four methods of interpolation, two of which were of Indian origin; (...) and that al-Samaw'al explicitly introduced a new way of evaluating these different methods. He also throws light on the active movement of research on numerical methods that constitutes the background to al-Bīrūmī's and al-Samaw'al's work, and uses modern means to evaluate the different methods and to justify the mathematicians' choices. The author has edited and translated al-Samaw'al's text in order to make it available to historians of Arabic and Indian mathematics. This allows them to follow the history and the mathematical arguments, and deepens our understanding of the importance to the development of mathematics of certain astronomical work. It also highlights the contribution of Indian mathematicians to the development of Arabic mathematics. Dans un texte manuscrit jamais examiné auparavant, al-Samaw'al cite un paragraphe d'un écrit d'al-Bīrīnī qui montre bien que ce dernier connaissait non seulement la méthode d'interpolation quadratique de Brahmagupta, mais également une autre methode indienne. Al-Samaw'al éetudie ces méthodes ainsi que l'interpolation linéaire, les compare les unes aux autres et par conséquent s'interroge sur leurs performances respectives afin d'opter pour la meilleure, et tente de les perfectionner. Dans cet article, l'auteur montre qu'al-Bīrūnī disposait de quatre méthodes d'interpolation, dont deux sont d'origine indienne, et qu'al-Samaw'al a introduit explicitement une nouvelle interrogation pour juger de la performance des différentes méthodes; il restitue les études d'al- Bī;rūnī et d'al-Samaw'al dans le mouvement actif de recherche sur les méthodes numériques, et reprend avec des moyens modernes la comparaison entre les diverses méthodes pour comprendre les choix des différents mathématiciens. L'auteur établit et traduit le texte d'al-Samaw'al afin de le rendre accessible aux historiens des mathématiques arabes et indiennes, et pour permettre aux lecteurs de suivre l'exposé' historique et mathématique qui vise, au-delà de ces résultats, à mieux connaître l'apport de certaines recherches en astronomie au développement des mathématiques, et d'autre part, la contribution des mathématiciens de l'Inde à l'histoire des mathématiques arabes. (shrink)

In his encyclopedic book, the mathematician of Saragossa, Ibn Hūd, established by an intrinsic demonstration of spherical geometry, a remarkable theorem which generalizes the proposition III.11 from Theodosius’s Spherics and integrates the propositions III.23-25 from Menelaus’s Spherics. In this paper, we study this theorem and the demonstration of Ibn Hūd. The reader will find also some established and translated texts addressing the same theme. Résumé Dans son livre encyclopédique, le mathématicien de Saragosse, Ibn Hūd, établit par une démonstration intrinsèque de (...) la géométrie sphérique un théorème remarquable qui généralise la proposition III.11 des Sphériques de Théodose et intègre les propositions III.23-25 des Sphériques de Ménélaüs. Dans cet article, on étudie ce théorème ainsi que la démonstration d’Ibn Hūd. Le lecteur trouvera aussi établis et traduits quelques textes qui portent sur le même thème. (shrink)

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, 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-Qūhī's contribution and gives the editio princeps of these two treatises, as well as their translation. (shrink)

Abū al-Jūd Muḥammad ibn al-Layth is one of the mathematicians of the 10th century who contributed most to the novel chapter on the geometric construction of the problems of solids and super-solids, and also to another chapter on solving cubic and bi-quadratic equations with the aid of conics. His works, which were significant in terms of the results they contained, are moreover important with regard to the new relations they established between algebra and geometry. Good fortune transmitted to us his (...) correspondences with the mathematician and astronomer al-Bīrūnī. The questions they debated, and the answers they yielded, all offer us multiple in vivo perspectives on the research that was undertaken in that period. The reader would find in this article a critical edition and French translation of this correspondence, with historical and mathematical commentaries. Résumé Abū al-Jūd Muḥammad ibn al-Layth est l’un des mathématiciens du x e siècle qui ont le plus contribué au nouveau chapitre sur les constructions géométriques des problèmes solides et sur-solides, ainsi qu’à un autre chapitre, sur la solution des équations cubiques et biquadratiques à l’aide des coniques. Ses travaux, importants pour les résultats qu’ils renferment, le sont aussi par les nouveaux rapports qu’ils instaurent entre l’algèbre et la géométrie. La bonne fortune nous a transmis sa correspondance avec le mathématicien et astronome al-Bīrūnī. Les questions qui y sont débattues, les réponses apportées, nous offrent, in vivo, plusieurs perspectives sur la recherche qui était alors menée. Le lecteur trouve dans cet article l’édition critique de cette correspondance, sa traduction française ainsi qu’un commentaire historique et mathématique. (shrink)

Abzj proposed, in a fragment established and translated herein, two methods to build a parabolic mirror. The lack of demonstration, particularly for the first method, raises a difficult question of interpretation. To understand this method, O. Neugebauer used, in an unpublished article translated herein, concepts of descriptive geometry. He then eliminated the space construction used, to keep only simple geometrical considerations known by the Greeks. The second interpretation, given by R. Rashed, is based on the geometrical practices of al-Bnhzj (...) from Ibn Sinān seems to support this last interpretation. (shrink)

RésuméLes mathématiciens et les philosophes arabophones, comme leurs prédécesseurs grecs, ont soulevé plusieurs questions épistémologiques fondamentales. Parmi ces questions figure celle qui porte sur le concept d’égalité et sur celui de congruence des grandeurs géométriques. Mais qu'entendait-on par de tels concepts? quelle était leur relation à l'idée de mouvement? Comme les réponses à ces questions combinaient souvent des éléments métriques et d'autres, philosophiques, j'ai choisi d’étudier celles d'un mathématicien, d'un philosophe et d'un mathématicien-philosophe.

RésuméC'est le premier d'une série d'articles comportant quatre textes composés entre le XIeet le XIIIesiècle, qui traitent de la proposition 5 du livre III desSphériquesde Ménélaüs. Le premier article comprend des commentaires historiques et mathématiques de l'œuvre d'Ibn ʿIrāq en géométrie sphérique et une édition critique des deux textes qu'il a consacrés à la rectification de la proposition III.5, ainsi que la traduction de ces deux textes. Le second article propose une édition critique des textes de Naṣīr al-Dīn al-Ṭūsī et (...) d'Ibn Abī Jarrāda sur le même sujet, cette fois aussi avec une traduction et des commentaires historiques et mathématiques. (shrink)

Obituaries Roshdi Rashed, Arabic Sciences and Philosophy, FirstView Article.

This publication of al-Kindī's Optics and Catoptrics provides editio princeps and the first translation of three books including the Rectification of Euclid's Optics hitherto unknown. In this book, the reader will find genuine and new information about Greek and Arabic optics and catoptics.

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. (shrink)

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.Depuis Euclide jusque tard dans le xviie siècle, mathématiciens et philosophes n'ont cessé de s'interroger sur l'angle de contingence et, plus généralement, sur la notion d'angle. Cet article est le premier essai où sont examinés les écrits grecs portant sur ce thème et transmis en arabe, ainsi que les nombreux travaux, pour la plupart jusqu'ici inconnus, des mathématiciens arabes eux-mêmes: al-Nayrīzī, Ibn al-Haytham, al-Samawʾal, al-Shīrāzī, al-Fārisī, al-Qūshjī, entre autres.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

Né le 4 février 1917 dans un village des environs de Damiette, ‘Abd al-Rahmān Badaī s'est éteint au Caire, où il avait étudié puis enseigné – à l'Universitél – avant de joindre l'Université d'Héliopoplis. ‘A. Badawī nous laisse une oeuvre monumentale, plus de cent-vingt livres en arabe et cinq autres en français. Mondialement connu, son impact sur l'histoire de la philosophie grecque, sur l'histoire de la philosophie islamique et sur la pensée arabe au cours de la seconde moitié du XX (...) e siècle, est immense et incontestable. Travailleur solitaire et acharné, il n'a jamais été égalé pour ses connaissances tant linguistiques que philosophiques et historiques, et surtout pour l'étendue des champs du savoir qu'il a pu couvrir. (shrink)

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.Depuis Euclide jusque tard dans le xviie siècle, mathématiciens et philosophes n'ont cessé de s'interroger sur l'angle de contingence et, plus généralement, sur la notion d'angle. Cet article est le premier essai où sont examinés les écrits grecs portant sur ce thème et transmis en arabe, ainsi que les nombreux travaux, pour la plupart jusqu'ici inconnus, des mathématiciens arabes eux-mêmes: al-Nayrīzī, Ibn al-Haytham, al-Samawʾal, al-Shīrāzī, al-Fārisī, al-Qūshjī, entre autres.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

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 , 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-Qūhī's contribution and gives the editio princeps of these two treatises, as well as their translation. (shrink)

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 , 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-Qūhī's contribution and gives the editio princeps of these two treatises, as well as their translation. (shrink)

Like his Greek and Arab predecessors, Avicenna’s research in mathematics concerned the development of methods of exposition, proof procedures and analytical tools. But Avicenna belonged to a new era of mathematics, and the question that this paper seeks to examine is how Avicenna applied this new mathematical knowledge in his philosophy. A treatment of the subject of Avicenna and mathematics cannot, then, confine itself to generalities, important as these are, but must start from the degree of knowledge he had of (...) the various branches and the use he actually made of them. I shall restrict myself here to a number of examples which seem to me to possess evidential value and which all reveal a new conception of the connections between philosophy and mathematics. It will turn out that what Avicenna in fact did was to develop an analytical philosophy of mathematical concepts. (shrink)

RésuméDans son livre encyclopédique, le mathématicien de Saragosse, Ibn Hūd, établit par une démonstration intrinsèque de la géométrie sphérique un théorème remarquable qui généralise la proposition III.11 des Sphériques de Théodose et intègre les propositions III.23-25 des Sphériques de Ménélaüs. Dans cet article, on étudie ce théorème ainsi que la démonstration d’Ibn Hūd. Le lecteur trouvera aussi établis et traduits quelques textes qui portent sur le même thème.

RésuméCet article examine l'opposition entre preuve directe et preuve per impossibile, introduite en géométrie par al-Sijzī dans un mémoire intitulé Le côté n'est pas commensurable à la diagonale. À partir de cet exemple qu'il donne pour illustrer cette opposition, al-Sijzī défend en effet la supériorité de la preuve directe. L'article propose également l'editio princeps et la première traduction de ce mémoire.

RésuméAbū al-Jūd Muḥammad ibn al-Layth est l’un des mathématiciens du xe siècle qui ont le plus contribué au nouveau chapitre sur les constructions géométriques des problèmes solides et sur-solides, ainsi qu’à un autre chapitre, sur la solution des équations cubiques et biquadratiques à l’aide des coniques. Ses travaux, importants pour les résultats qu’ils renferment, le sont aussi par les nouveaux rapports qu’ils instaurent entre l’algèbre et la géométrie. La bonne fortune nous a transmis sa correspondance avec le mathématicien et astronome (...) al-Bīrūnī. Les questions qui y sont débattues, les réponses apportées, nous offrent, in vivo, plusieurs perspectives sur la recherche qui était alors menée. Le lecteur trouve dans cet article l’édition critique de cette correspondance, sa traduction française ainsi qu’un commentaire historique et mathématique. (shrink)

RésuméDans l’Almageste, Ptolémée a proposé le concept du mouvement d'enroulement pour expliquer notamment les latitudes planétaires. Ibn al-Haytham a rédigé un traité intitulé Fī ḥarakat al-iltifāf, « Surle mouvement d'enroulement ». Un anonyme a écrit une critique de ce traité. Les deux mémoires sont perdus; mais heureusement a survécu la réponse d'Ibn al-Haytham, intitulée Fī ḥall šukūk ḥarakat al-iltifāf, « La résolution des doutes sur le mouvement d'enroulement ». Il y rappelle le modèle élaboré et en détaille encore l'explication. Nous (...) donnons ici édition critique, traduction et commentaire de cette réponse, ainsi qu'une édition et traduction de passages apparentés des Hypothèses planétaires de Ptolémée et de la Nihāyat al-idrāk de Quṭb al-Dīn al-Shīrāzī. (shrink)

This article includes the editio princeps of Ibn al-Hayṯam’s treatise “On the Parabolic Burning Mirror,” Fī al-marāyā al-muḥriqa bi-al-quṭūʿ, as well as its first translation into French. We examine its place in the history of the parabolic mirror for more than a millennium and a half, in Greek as well as in Arabic and Latin.

This article continues and improves the research already accomplished in Géométrie et dioptrique au Xe siècle (1993). It presents two fragments and an additional treatise which enlarge our understanding of the work of Ibn Sahl on the geometrical constructions and projections. All the necessary corrections are included.