Les commentaires d'al-Māhānī et d'un anonyme du Livre X des Éléments d'Euclide

Bibliographic Data

ID20399997
AuthorsMAROUANE BEN MILED (Faculté des sciences, Département de mathématiques, B.P. 763, route Soukra, 3038 Sfax, Tunisie, corresponding author)
Year1999
Volume9
Issue1
Pages89-156
Publication date1999-03-01
Open AccessYes
TypeARTICLE
VenueArabic Sciences and Philosophy (JOURNAL)
Journal identifiersISSN: 0957-4239 • E-ISSN: 1474-0524
PublisherLiverpool University Press (PUBLISHER • GB)
DOI10.1017/s0957423900002617
OpenAlexW2019742592
LanguageFR
Citations received2
References cited2

This paper presents the first edition, translation and analyse of al-Māhānī’s commentary of the Book X of Euclid’s Elements (9th century, the most ancient to have reached us) and of an anonymous’ one (prior to 968, among the first algebraic commentaries). For the first time, irrational numbers are defined and classified. The algebraisation of Elements’ X-91 to 102, on the basis of al-Khwārizmī’s Algebra , shows irrational numbers as solution to algebraic quadratic equations. The algebraic calculus makes here the first steps. On this occasion, negative numbers and their calculation rules appears. Simplifications imposed by the algebraic writings are sometimes in opposition with the conclusions of propositions conceived in a purely geometrical framework, revealing a contradiction between geometrical and algebraic goals. It will be resolved by the independant way algebra will take with mathematicians belonging to the tradition of al-Karajī and al-Samaw’al from the 11th-12th centuries on

Abstract algebra · Algebra over a field · Algebraic number · Combinatorics · Contradiction · Epistemology · Geometry · Irrational number · Mathematical analysis · Pure mathematics · Historical Astronomy and Related Studies · History and Theory of Mathematics · Law · Mathematics · Medieval and Classical Philosophy · Philosophy

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