Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-zdfhw Total loading time: 0.385 Render date: 2022-08-18T19:48:18.090Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Les cercles tangents d'al-Qūhī

Published online by Cambridge University Press:  24 October 2008

Philippe Abgrall
Affiliation:
Centre d'histoire des sciences et des philosophies arabes et médiévales, C.N.R.S., 27 rue Damesme, 75013 Paris, France; Institut Français d'Études Arabes de Damas (I.F.E.A.D.), B.P. 344, Damas, Syrie

Abstract

This article presents the Arabic text of al-Qūhī's short geometric treatise, The Book of the centres of the tangent circles on lines, by the method of analysis (Xe century), with translation and a mathematical commentary. In this treatise al-Qūhī solves by analysis an ordered set of eight problems where the goal is to locate, on a given line, the centre of a circle which is tangent to two given elements, which may be points, straight lines or circles. For example, in the first problem he wanted to find the centre of a circle which contains two given points. In fact, al-Qūhī establishes the locus of the solutions, and this locus can be a straight line or a conic. The treatise is reminiscent of one of the purposes of al-Qūhī's work on the perfect compass (an instrument to draw conics by moving continuously), namely to assign to the conics the status of regular lines.

Nous présentons ici l'édition, la traduction et le commentaire mathématique d'un court traité de géométrie composé par al-Qūhī, et intitulé: Le livre des centres des cercles tangents situés sur des lignes, par la méthode de l'analyse. L'auteur y résout, par I'analyse, un ensemble ordonné de huit problèmes dont le but est de rechercher sur une ligne donnée, le centre d'un cercle tangent à deux éléments donnés, pris parmi des points, des droites ou des cercles. Par exemple, dans le premier problème, il cherche le centre d'un cercle passant par deux points donneés. En fait, al-ūuhī détermine des lieux de solutions, et ces lieux sont soit des droites, soit des coniques. Ce traité constitue un témoin de la recherche qui s'est faite au Xe siècle sur les coniques. II rappelle notamment un des buts poursuivis par al-Qūhī dans son étude sur le compas parfait, un instrument pour tracer les coniques d'un mouvement continu: assigner aux coniques le statut de lignes régulières.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
6
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org 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 saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved 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.

Les cercles tangents d'al-Qūhī
Available formats
×

Save article to Dropbox

To save 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 used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Les cercles tangents d'al-Qūhī
Available formats
×

Save article to Google Drive

To save 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 used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Les cercles tangents d'al-Qūhī
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *