Cartesian Coordinates

  • Alexander Ostermann
  • Gerhard Wanner
Part of the Undergraduate Texts in Mathematics book series (UTM)


The so-called Cartesian coordinates,1 used to determine the position of a point in the plane (see Fig. 7.1, left), first appeared (in a somewhat hidden form) in Descartes’ solution of a problem of Pappus (see below). They came into general use only a few decades later. We owe important simplifications to Newton (1668), who freely used negative values for coefficients and coordinates. A clear exposition is given in Euler’s Introductio (1748), vol. II, §1–4.


Fermat Point Angle Bisector Maximal Surface Area Euler Line Orthogonal Angle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of InnsbruckInnsbruckAustria
  2. 2.Section de mathématiquesUniversité de GenèveGenève 24Switzerland

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