Title: Algèbre et analyse diophantienne : édition, traduction et commentaire /
Authors: Abū Kāmil Shujāʻ ibn Aslam.; Abū Kāmil Shujāʻ ibn Aslam.; Abū Kāmil Shujāʻ ibn Aslam.; Rāshid, Rushdī.
Publisher: De Gruyter,
Year: 2012
Subjects: Abū Kāmil Shujāʻ ibn Aslam.; Algebra Early works to 1800; Mathematics, Arab Early works to 1800.; Diophantine analysis.
Abstract: "The mathematical works of Abū Kāmil (floruit circa 880) were produced two generations after the works of Al-Khwarizmī, the founder of algebra. They opened up fields of research that proved fertile up until the seventeenth century, and were soon to become both a reference and a model. Their influence was decisive on the development of algebra in Arabic no less than in Latin and Hebrew. There will be found in the present publication the first rigorously critical edition of Abu Kamil s works, as well as the first ever translation into a modern language. Text and translation are preceded by an exhaustive commentary, at once mathematical and historical."--
Contents: Abū Kāmil: algébriste et ingénieur -- Les écrits mathématiques d’Abū Kāmil -- La théorie des équations et la démonstration des algorithmes -- : Le calcul algébrique et ses applications -- L’application de l’algèbre à la géométrie plane: les pentagones et les décagones réguliers -- L’analyse indéterminée rationnelle -- Problèmes arithmétiques -- Analyse indéterminée entière du premier degré -- La démonstration aux commencements de l’algèbre -- Livre d’algèbre et d’al-muqābala -- Appendice: Extrait d’al-Bāhir en algèbre d’al-Samaw’al.