• Albert W. Grootendorst †
  • Jan Aarts
  • Miente Bakker
  • Reinie Erné
Part of the Sources and Studies in the History of Mathematics and Physical Sciences book series (SHMP)


The first mention of the problem that would later become known as Pappus’s problem can be found in the introduction to the Conica (I, 1) by Apollonius. There he writes that Euclid had insufficiently worked out the problem of the locus in the case of three or four lines and that the results of Euclid were not even that good. Apollonius refers to the work of Euclid on conics, which is now lost. He attributes the shortcomings of Euclid to the unavailability of two relevant fundamental theorems that Apollonius himself found and proved. We will see further on which theorems these are.


Line Segment Continuous Movement Geometric Algebra Plane Curf Admissible Curf 
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  1. [43]
    Knorr, W.R., The Ancient Tradition of Geometric Problems. New York, Dover Publications Inc., 1993.Google Scholar
  2. [26]
    Grootendorst, A.W., Grepen uit de Geschiedenis van de Wiskunde. Delft, D.U.P., 1988.Google Scholar
  3. [6]
    Bos, H.J.M., The Structure of Descartes's Géométrie. Lectures in the History of Mathematics 7, pp. 37–57. Providence, Rhode Island, American Mathematical Society, 1997.MathSciNetGoogle Scholar
  4. [70]
    Wickefoort crommelin, H.S.M. van, Johan de Witt en zijn Tijd. Amsterdam, Nederlandse Algemene Maatschappij van Levensverzekering “Conservatrix,” 1913.Google Scholar
  5. [53]
    Scott, J.F., The Scientific Work of René Descartes. London, Taylor and Francis, 1976.MATHGoogle Scholar
  6. [71]
    Zeuthen, H.G., Geschichte der Mathematik im Altertum und Mittelalter. Kopenhagen, A.F. Host, 1896.MATHGoogle Scholar
  7. [30]
    Heath, sir thomas L., Apollonius of Perga, Treatise on Conic Sections. Cambridge, Barnes and Noble (reprint), 1961.Google Scholar
  8. [5]
    Bos, H.J.M., Descartes, Pappus’s Problem and the Cartesian Parabola, a Conjecture, Festschrift for D.T. Whiteside, ed. P. Harman and A. Shapiro. Cambridge, C.U.P.,1992Google Scholar
  9. [16]
    Descartes, rené, The Geometry of René Descartes, translated from the French and Latin by David Eugene Smith and Maria L. Latham. New York, Dover Publications, 1954.Google Scholar
  10. [18]
    Dijksterhuis, E.J., De Elementen van Euclides I&II.Groningen, Noordhoff, 1930.Google Scholar
  11. [45]
    Maanen, J.A. van, Facets of Seventeenth Century Mathematics in the Netherlands. Utrecht, Elinkwijk, 1987.Google Scholar

Copyright information

© Springer London 2011

Authors and Affiliations

  • Albert W. Grootendorst †
    • 1
  • Jan Aarts
    • 1
  • Miente Bakker
    • 2
  • Reinie Erné
    • 3
  1. 1.Delft University of TechnologyDelftThe Netherlands
  2. 2.Centrum Wiskunde & InformaticaAmsterdamThe Netherlands
  3. 3.LeidenThe Netherlands

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