La question de l'algèbre. Mathématiques et rhétorique des hommes de droit dans la France du XVIe siècle.

Résumé En

The Question of Algebra. Mathematics and Rhetoric of Jurists in Sixteenth-Century France. We have inherited from seventeenth-century philosophy of the new sciences negative view of sixteenth-century rhetoric and dialectic. However, a close study of the French algebraic tradition shows not only that sixteenth-century rhetoric and dialectic should be considered as the conceptual framework for scientific discourse later replaced by algebra but that, in turn, algebra itself was significantly modified within this framework. Combining cultural and social history with the history of the discipline, we can see that this transformation occurred when algebra moved from the Italian and German schools, closer to abacist mathematics and the commercial context to the French court and humanist milieu of the College Royal and related publishers. French dialectic, in particular, was the source of borrowings for algebraic notions. Not only was the presentation of the new discipline forged in the dialectical style, but the very idea of scientific question was explicitly associated to that of an algebraic problem. This transition allowed better known scientists such as Viète and Descartes to generalize the form of algebraic problems and eventually to conceive of applying it to sciences beyond mathematics. A. Koyré's view of rhetoric as opposed to science stems from the cartesian legacy.