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Euclidean Geometry

In: The Real Projective Plane

Author

Listed:
  • H. S. M. Coxeter

    (University of Toronto, Department of Mathematics)

  • George Beck

Abstract

The time has come for us to fulfil the promise of §1·8, that we should return to ordinary geometry from a new point of view. We shall see how von Staudt’s idea of choosing an elliptic involution on the line at infinity of the affine plane enables us to define perpendicularity and congruence, so that distances can be compared in any direction. Many problems of Euclidean geometry are most easily solved by the projective approach, but at this stage we are free to use either the new method or the old, whichever is found more convenient at the moment.

Suggested Citation

  • H. S. M. Coxeter & George Beck, 1993. "Euclidean Geometry," Springer Books, in: The Real Projective Plane, edition 0, chapter 0, pages 126-146, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2734-2_9
    DOI: 10.1007/978-1-4612-2734-2_9
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