Jean Prestet’s Éléments des Mathématiques: A Cartesian textbook by a Cartesian Author?

AlthoughGoldstein, Catherine the idea of ‘Elements of mathematics’ is usually closely linked to that of geometry, some early-modern authors also proposed alternatives. Jean PrestetPrestet, Jean, a protégé of the philosopher Nicolas Malebranche, developed an analytic basis for mathematicsMalebranche, Nicolas, which he presented as largely Cartesian. Prestet’s emphasis on arithmeticArithmetic and algebraAlgebra pushed him to subject to proof what had been hitherto seen as obvious facts, to treat symbolicAlgebra, symbolical expressions as integers, and to renew and extend Diophantine analysisDiophantine analysis as well as combinatorial questions. These features, in return, challenged both Prestet’s publisher and Descartes’ Descartes, Renè viewpoint. These interconnected aspects of Prestet’s treatise, several editions of which are kept in the Russell LibraryMaynooth, Russell Library, are discussed here.