Projectivities on a Conic

H. S. M. Coxeter and George Beck
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H. S. M. Coxeter: University of Toronto, Department of Mathematics

Chapter Chapter 7 in The Real Projective Plane, 1993, pp 92-104 from Springer

Abstract: 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.

Keywords: Conjugate Point; Invariant Point; Real Projective Plane; Concurrent Line; Exterior Line (search for similar items in EconPapers)
Date: 1993
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DOI: 10.1007/978-1-4612-2734-2_7

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