Abstract: My method of drawing tangents, René Descartes told Marin Mersenne, “is the most noble way of demonstrating that can be, namely, that called a priori.” Descartes turned to scholastic terminology to describe his new mathematics; yet its practice involved compound compasses and scratched-out symbols, the former an emphatically banausic generalization of Euclidean practice, the latter an adaptation of merchant mathematics. Tools-based practice permeated the Essais that Descartes presented as instances of his general method. My focus here is not on Descartes’ use of artisanal techniques so much as on his efforts to naturalize these techniques within scholastic philosophy or scientia. Much has been written about the efforts of higher-status practitioners to occult the manual or intellectual contributions of technicians; I look at the ars-ification of scientia from a different perspective, focusing on Descartes’ efforts in the Discours and accompanying Essais to persuade both gentlemen and philosophers that they should care about craft. These efforts were themselves a kind of art: for example, Descartes referred to his suppressed physical treatise as a painting that represented his arguments “in a frieze.” Understanding the artistry of Descartes’ rhetoric, I argue, will require us to reconsider not just the relationship between ars and scientia, but also our own prejudices about the putatively doctrinal aspirations of the new science.
