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Some chains of theorems derived by successive projection

Published online by Cambridge University Press:  24 October 2008

H. Lob
H. Lob
Affiliation:
King's College
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Extract

1. In a paper read to this Society Mr F. P. White has derived a remarkable chain of theorems in [n] which, for n = 2, becomes Clifford's chain. White's method is so elegant that, as he has restricted himself to curves going through two given points, it may be permissible to shew that his line of argument applies equally to curves going through three or more given points, thus producing other chains of theorems analogous to Clifford's. For this purpose it is necessary to consider the successive projections, not of a simplex, but of a figure of n, n − 1, n − 2,…vertices in [n].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 29 , Issue 1 , January 1933 , pp. 45 - 51
Copyright
Copyright © Cambridge Philosophical Society 1933

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References

* White, , “An extension of Wallace's, Miquel's and Clifford's theorems on circles”, Proc. Camb. Phil. Soc. 22 (1925), 684–687.CrossRefGoogle Scholar

† Encyk. Math. Wiss. III C 7, p. 894, footnote 368 (quoted by Mr White).

* II 1I 2 … I n−2 projects into the osculating [n − 2] at I to the C n−1 considered, and JJ 1 … J n−2 into the osculating [n − 2] at J. IZ and JZ′ are the intersections of π2 with these [n − 2]'s.