Abstract

In this article, I examine the respective role of equations and construction in geometrical problem solving according to Descartes and Pascal. I argue that whereas Descartes claims that an equation provides a solution to a geometrical problem even if it leads to an entangled construction, Pascal dismisses this claim and gives priority to construction. To this end, I deal with prototypical problems like Apollonius' problem of the three cir cles or Pappus' problem, both of which were tackled by Descartes and Pascal in their work or correspondence. I also pay close attention to the cor respondence between Pascal and Sluse of October-December 1657 and compare Sluse's conception of algebraic analysis in geometrical problem solving with Descartes'. These letters, not thoroughly studied until now, supply an interesting discussion about what it is to provide a solution to a geometrical problem. Finally, I consider Descartes' algebraization of geometry as a kind of mathematization