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Pascal versus Descartes on Solution of Geometrical Problems and the Sluse-Pascal Correspondence

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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 let ters, not thoroughly studied until now, supply an interesting discussion about what it is to provide a solution to a geomet rical problem. Finally, I consider Descartes’ algebraization of geometry as a kind of mathematization.


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1. Archive for History of Exact Sci- ences 00039519 1984; Vol 30: 331
2. REVUE D HISTOIRE DES MATHEMATIQUES 1262022x 2006; Vol 12: 199

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