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date: 21 January 2021

Abstract and Keywords

This chapter points out some issues about Cartesian geometry and Descartes’s program of solving geometrical problems by means of algebraic analysis. With this aim, it extends the corpus to Descartes’s mathematical correspondence and takes into account recent interpretations. The chapter first concentrates on Descartes’s methodological reflections on the algebraic resolution of geometrical problems like Pappus’s problem or Apollonius’s problem of the three circles, and compares Descartes’s classifications of mathematical problems of 1619 and 1637. It then addresses problems tackled by Descartes in his mathematical Correspondence that question the boundaries set in the Géométrie for the application of method. Finally, the method of indeterminate coefficients and its use in Descartes’s method of normals are briefly studied in order to underscore an Ariadne’s thread in Cartesian geometry: the elimination of equations. In conclusion, it is claimed that Cartesian geometry is neither the single Géométrie of 1637, nor a mere anticipation or deduction of this classic by Descartes, but the collection of somewhat different geometries, which are to be found in the mathematical Correspondence or the Latin editions of 1649 and 1659–61.

Keywords: Cartesian geometry, Descartes’s mathematical Correspondence, resolution of geometrical problems, algebraic analysis, method of indeterminate coefficients

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