This paper is devoted to Ibn Sinn's text deals with two distinct, though closely related, subjects. First he considers the classification of problems, founded on the logical criteria which are the number and degree of indetermination of the solutions and the number of hypotheses and their possible independence. This classification does not replace the Hellenistic one, which remains relevant insofar as it purports to solve geometrical problems, but complements it and has a different frame of reference, applying principally to algebra, (...) that new born science. Ibn Sinn to bestow more importance on the role played by analysis in the course of the proof, the only role left to synthesis being to check that all implications involved in the course of analysis are in fact equivalences. This method will prove to be productive in algebra too, so much so that some algebraists will explicitly identify algebra with analysis. (shrink)

Suscités par la reprise massive de la recherche en astronomie au IXe siècle dans le monde islamique et essentiellement à Bagdad, laquelle nécessite des outils mathématiques nouveaux, une floraison de traités, tant astronomiques que mathématiques, voit le jour à cette époque. D'entre les traités mathématiques, un certain nombre est consacré à la ‘‘figure secteur”, c’est-à-dire au théorème dit ‘‘de Ménélaüs” sur la sphère, lequel généralise le théorème dit ‘‘de Ménélaüs” dans le plan. Ce théorème de Ménélaüs sur la sphère, ou (...) règle des six quantités, est, en l’absence du théorème des sinus sur la sphère, lequel ne date que de la deuxième moitié du Xe siècle, le principal outil de l'astronomie sphérique. Le traité de Thābit ibn Qurra sur La figure secteur est le premier de ces traités consacrés au théorème de Ménélaüs, tant dans le plan que sur la sphère, à nous être parvenu; point de départ de tout un courant, il influencera profondément le développement ultérieur de la géométrie sphérique. Ce traité, qui est en fait une épître adressée à un correspondant malheureusement anonyme, présente en outre l'intérêt de montrer que, dans le milieu scientifique de cette époque à Bagdad, beaucoup s'intéressaient à ce théorème, essayaient d'en énoncer d'autres cas de figure et de compléter la démonstration qu'en donne Ptolémée dans l'Almageste. (shrink)

Once Apollonius' Conics had been translated from Greek into Arabic, they became a main reference and the principal tool in studying solid problems, algebraic equations of 3rd and 4th degrees, infinitesimal mathematics, etc. Mathematicians of the 9th–10th centuries also studied the conic sections' constructions, as well as their continuous drawing and their drawing by points. Ibrāhīm ibn Sinān, as his grandfather Thābit ibn Qurra, was one of the most active and inventive mathematicians in these fields. Late Hélène Bellosta examined in (...) this article Ibn Sinān's contribution.Une fois les Coniques d'Apollonius traduits en arabe, ces livres sont devenus la référence indispensable et le principal instrument dans l'étude des problèmes solides, des équations algébriques des 3e et 4e degrés, des problèmes des mathématiques infinitésimales, etc. Les mathématiciens des ixe-xe siècles ont également étudié les constructions des sections coniques ainsi que leur tracé par points et leur tracé continu. Ibrāhīm ibn Sinān, comme son grand-père Thābit ibn Qurra, était l'un des mathématiciens les plus actifs et les plus inventifs en ce domaine. Dans cet article, la regrettée Hélène Bellosta a examiné la contribution d'Ibn Sinān.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.DE L'USAGE DES CONIQUES CHEZ IBRĀHĪM IBN SINĀNVolume 22, Issue 1Hélène Bellosta DOI: https://doi.org/10.1017/S0957423911000129Your 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. DE L'USAGE DES CONIQUES CHEZ IBRĀHĪM IBN SINĀNVolume 22, Issue 1Hélène Bellosta DOI: https://doi.org/10.1017/S0957423911000129Available 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. DE L'USAGE DES CONIQUES CHEZ IBRĀHĪM IBN SINĀNVolume 22, Issue 1Hélène Bellosta DOI: https://doi.org/10.1017/S0957423911000129Available 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)

Ibrāhīm Ibn Sinān was one of the most famous scientists of the tenth century. His specialities were geometry, logic and philosophy of mathematics. In this volume, the works of this scientist are thoroughly researched, and three new hypotheses presented.