Abstract

In sixteenth century Paris a circle of mathematicians produced texts of the most advanced kind of algebra. This "French algebraic tradition" will be the context for Viete's symbolic algebra. Comparing French algebraic texts with Italian and German, and examining the publishing context , I establish a periodization in two phases. ;Jacques Peletier stands for the introduction of the abacus tradition and algebra at the court. Peletier's algebraic program is connected to his theory of rhetoric. He establishes a genre of texts devoted to algebra in vernacular, promoting French as a scientific language. Rhetorical criteria order L'Algebre, emphasizing structure and theory . He innovates on Cardano's and Stifel's treatments of equations in several unknowns. ;Phase two changes style and content; Guillaume Gosselin is representative. Manuals shift focus from problems and questions to equations and classification. Solution of equations becomes the purpose of algebra. Problems are no longer addressed as such, but conceived in their most general form as corresponding equations. Algebrists connect with a milieu of jurists important in politics and scholarship. This erudite milieu favored the recovery of Diophantus' Arithmetic, which provides a set of theoretical problems on numbers. Diophantus solved problems by transforming them into particular cases; Gosselin reaches a general solution by transforming them into equations. Gosselin's notation makes the difference. The algebrists create an illustrious genealogy for algebra, deriving it from Greece rather than abacus schools. ;Three features of this tradition can be traced back to Italian humanism: Cardano's and Tartaglia's algebra, imitatio , and the construction of a history for the discipline. The French algebrists radically transformed all three. Their translatio authorized them to abandon links to the medieval tradition and to build a new discipline that they could see as national. Preparing the adoption of this discipline by the legal elite was the rhetorical interpretation of logic developed in Paris at the time. This provided a theoretical frame in which generalized algebraic problems were seen as Cicero's quaestiones infinitae, i.e. scientific questions