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Projectivities on a Conic

In: The Real Projective Plane

Author

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  • H. S. M. Coxeter

    (University of Toronto, Department of Mathematics)

  • George Beck

Abstract

This chapter deals with those properties of a non-degenerate conic which may be most readily derived by means of the notion that the points on the conic form a range, resembling in many ways the points on a line. Pascal’s theorem is the most famous instance; but its original proof must have been different. The idea of projectivity on a conic is due to Bellavitis (1838). We shall see that the construction for such a projectivity is simpler than for a projectivity on a line. In fact, some authors, such as Holgate, rearrange the material so as to treat ranges on a conic before ranges on a line. Involutions are especially easy to deal with, for the joins of pairs of corresponding points are concurrent, as we shall see in § 7.5.

Suggested Citation

  • H. S. M. Coxeter & George Beck, 1993. "Projectivities on a Conic," Springer Books, in: The Real Projective Plane, edition 0, chapter 0, pages 92-104, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2734-2_7
    DOI: 10.1007/978-1-4612-2734-2_7
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