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A Proof of Miquel's Theorem by Involutions in the Argand Diagram

Published online by Cambridge University Press:  24 October 2008

R. A. Frazer
R. A. Frazer
Affiliation:
Pembroke College
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Extract

Miquel's Theorem, as generalised by Clifford, states that the four circles through the intersections of four straight lines, taken in triads, meet in a point; that the five such points derived from five lines, taken in sets of four, lie on a circle; that the six such circles, determined by six lines, meet in a point……. The process continues indefinitely.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 3 , July 1929 , pp. 285 - 288
Copyright
Copyright © Cambridge Philosophical Society 1929

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References

* I.e. a linear ∞1 class system. For the adoption of the Italian word fascio, see Dr Baker, : “On some Recent Advances in the Theory of Algebraic Surfaces” Proc. London Math. Soc. (2), 12 (1913), 33.Google Scholar

* For some general remarks on Z-involutions of order 2, see Frazer, : “On the Invariant Geometry of Binary Forms in the Complex Variable” Quarterly Journal of Mathematics, 44 (1913), pp. 311–321.Google Scholar