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Poncelet’s Poristic Polygons

Published online by Cambridge University Press:  03 November 2016

J. A. Todd
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Extract

1. Poncelet’s well-known theorem states that if two conies S and S′ in a plane are such that an n-gon exists whose vertices lie on S′ and whose sides touch S, then an infinite number of such polygons exist. When this is the case, a relation holds between the invariants of the two conies. The explicit determination of this relation is due to Cayley, whose result is quoted by Salmon in a footnote on p. 342 of his Conic Sections (reprint of 1929). With a slight change of notation, Cayley’s result takes the following form.

Type
Research Article
Information
The Mathematical Gazette , Volume 32 , Issue 302 , December 1948 , pp. 274 - 280
Copyright
Copyright © Mathematical Association 1948 

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References

page 274 note* Cayley, Phil. Mag. (4), 6 (1853), 99; Collected Papers, II, 87.

page 274 note† Lebesgue, Ann. Fac. Sci. Toulouse (3), 13 (1922), 61.

page 274 note‡ cf. Salmon, loc. cit., p. 343.