ABSTRACT
The successors of al-Khwārizmī not only set about the application of arithmetic to algebra, but they also applied algebra revived by al-Karajī to arithmetic, trigonometry and the Euclidean theory of numbers. These applications, like those of algebra to geometry and of geometry to algebra examined in the preceding chapter, always led to the founder acts of new mathematical disciplines, or at least, of new areas. Algebra, it cannot be emphasized enough, has in this way played a central role not only to restructure and organize the disciplines of Hellenistic heritage, in order to widen their domains and methods, but also and above all to create new ones. It is in this way that combinatorial analysis, numerical analysis, new elementary number theory, integer Diophantine analysis came about. It is the story of these areas, yesterday still for the most part unknown, that we are going briefly to recapture.1
