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L'idée De Dimension Chez Al-Sijzī

Published online by Cambridge University Press:  24 October 2008

Pascal Crozet
Affiliation:
Centre d'Études et de Documentation Économique Juridique et Sociale (C.E.D.E.J), B.P. 494, Dokki, Cairo, Egypt

Extract

This paper presents the Arabic text, the French translation and an analysis of al-Sijzīʼs treatise (second half of the tenth century), the Book of Measurement of Spheres by Spheres. In this text, al-Sijzī divides the cube into several sub-cubes and parallelopipedes, thus offering us a stereometric interpretation of algebraic identities of the third degree usually credited to mathematicians of the sixteenth and seventeenth centuries. However, this was not al-Sijzīʼs motivation for writing this treatise; rather it was his theoretical interest in the Euclidian concept of the “power” of a segment, an interest which is clearly geometric rather than algebraic. This has led al-Sijzī to the notion of dimension, at least in outline.

Cet article contient l'édition du texte arabe, la traduction françhise et une analyse d'un traité d'al-Sijzī (deuxième moitié du Xe siécle), le Livre de la mesure des sphéres par les sphères. Dans ce texte, al-Syzī expose plusieurs décompositions du cube en réunions de cubes et de parallélépipédes, donnant ainsi une interprétation stéréométrique d'identités algébriques de degré 3 qu'on avait coutume d'attribuer à des mathématiciens des XVTe et XVIIe siècles. Pourtant, ce n'est pas cette interprétation qui, pour l'auteur, semble avoir motivé la rédaction du traité, mais bien une réflexion théorique sur le concept euclidien de “puissance” d'un segment, réflexion de nature clairement géométrique et non pas algébrique, et qui a conduit le mathématicien à dégager, au moins en filigrane, la notion de dimension.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1993

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