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One-Dimensional Projectivities

In: The Real Projective Plane

Author

Listed:
  • H. S. M. Coxeter

    (University of Toronto, Department of Mathematics)

  • George Beck

Abstract

The present chapter is concerned with the most important kind of ordered correspondence: the projectivity, which may be defined either as the product of several perspectivities or as a correspondence that preserves harmonic sets. The first definition, due to Poncelet, has been adopted by Veblen, Baker, and other authors; it has the advantage of remaining valid in complex geometry. This book, however, follows Enriques in using the second definition, due to von Staudt, which generalizes more readily to two (or more) dimensions. It is an immediate consequence of 2·82 that every Poncelet projectivity is a von Staudt projectivity, and we shall prove in §4·2 that every von Staudt projectivity (in real geometry) is a Poncelet projectivity. Thus from that point on the two treatments coincide.

Suggested Citation

  • H. S. M. Coxeter & George Beck, 1993. "One-Dimensional Projectivities," Springer Books, in: The Real Projective Plane, edition 0, chapter 0, pages 39-54, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2734-2_4
    DOI: 10.1007/978-1-4612-2734-2_4
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