Rasa’il Al-Khayyam Al-Jabriyya / L’oeuvre Algébrique d’Al-Khayyam

DESCRIPTION

192 pp. of French text + 112 pp. of Arabic text, profusely illustrated in figures, title in French and Arabic; edited and translated by Roshdi Rashed and Ahmad Djebbar; publisher's original wrappers; index; copy clean and in good condition. In the Algebra, al- Khayyam sets out to deal systematically with all fourteen types of cubic equations. He solves each one in sequence again through the use of intersecting conic sections. In an algebra where powers of x corresponded to geometrical dimensions, the solution of cubic equations was the apex of the discipline. Nevertheless, even here al- Khayyam was able to advance algebra by considering its unknowns as dimension-free abstractions of continuous quantities. 15 Khayyam also considers circumstances under which certain cubic equations have more than one solution. Although he does not handle this topic perfectly, his effort nevertheless stood out from previous efforts._x000d_ A geometric solution to a cubic equation may seem peculiar to modern eyes, but the study of cubic equations (and indeed much of medieval algebra) was motivated by geometric problems. Khayyam was nevertheless explicitly aware that the arithmetic problem of the cubic remained to be solved. He never produced such a solution; nor did anyone else until Gerolamo Cardano in the mid-16th century.