L'algèbre al-Badi d'al-Karagi
This work contains the study of the algebra called al-Badī‘ fī al-ḥisāb (literally : "the Wonderful on calculation"), written by the Persian mathematician Abu Bakr Muḥammad ibn al-Ḥusain al-Karaǧi (previously known as al-Karẖī, native from Karaǧ, Persia. Written c. 1010 in Bagdad, this work takes an important place in history of mathematics in general. Of particular interest are the first known appearance of a theory on root extracting of algebraic polynomials, and the beginning of a tendency to get rid of illustrating formulas and the resolutions of equations with help of geometric figures, which makes it a pure algebraic text. This work of high level adresses to a public with advanced mathematic knowledge. This algebra is, by will of the author, written in three main parts (books), containing part of Euclid's Elements (book I), a theory on root extracting of algebraic polynomials (book II), and a collection of problems on indeterminate analysis (book III). Some chapters are written hastily, while others go into the details. We provide a complete translation of the Badī‘, based on the transcription of the manuscript 36,1 of the Vatican library Barberini Orientale by Adel Anbouba (edited in Beyrouth in 1964), as well as a glossary. This translation comes with a mathematical commentary, and includes a list of significant words used by the author. We will also relate this algebra with other prior and later works containing the same problems.
Keywords: al-Badi' ; al-Karagi ; al-Karaji ; Anbouba ; algebra ; mathematics in islamic countries ; Euclid's Elements ; root extraction of algebraic polynomials ; indeterminate analysis ; Diophantine equations ; al-Badi' ; al-Karagi ; al-Karaji ; Anbouba ; algèbre ; mathématiques des pays de l'Islam ; Éléments d'Euclide ; extraction de racines de polynômes algébriques ; analyse indéterminée ; équations diophantiennesThèse École polytechnique fédérale de Lausanne EPFL, n° 4297 (2009)
Programme doctoral Mathématiques
Faculté des sciences de base
Institut de géométrie, algèbre et topologie
Chaire de géométrie
Record created on 2008-11-27, modified on 2016-08-08