Abū Kāmil. Algèbre et analyse Diophantienne. Édition, traduction et commentaire

Abstract

After al-Khwārizmī, Abū Kāmil (late ninth century) is the next Arabic author whose book on algebra is extant in its entirety. Where al-Khwārizmī's book was deliberately brief, Abū Kāmil's Kitāb al-jabr wa'l-muqābala (Book of Algebra) occupies 111 folios in the only surviving manuscript. 1 That is long enough for Abū Kāmil to show features and techniques omitted by al-Khwārizmī and to exhibit his own originality with regard to proofs, irrational numbers, and the manipulation of algebraic expressions. Abū Kāmil's influence was deservedly almost as far-reaching as al-Khwārizmī's. The Book of Algebra became a major influence on such well-known figures as al-Karajī, al-Samawʾal, and Ibn al-Bannāʾ, as well as on lesser ones like ʿAlī al-Sulamī and Ibn Badr. Most of the book was translated into Latin in the 12th century and whole portions found their way into the Liber Mahameleth in the 12th century, into Fibonacci's Liber abaci and De practica geometrie in the 13th century, and into Jean de Murs' Liber quadripartitum in the 14th century. From there its influence spread through Italian abbacus texts to Luca Pacioli's Summa de arithmetica of 1494 and into 16th-century European algebra. We also possess several manuscripts of a Hebrew translation made before 1475, possibly in Spain. 2 Two other books of Abū Kāmil are extant. One is his brief Kitāb al-Ṭayr (Book of Birds), in which he uses algebra to solve problems with several ⋆ English translations are mine unless noted otherwise. In referring to Rashed's text,