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Desargues configurations and their collineation groups

Published online by Cambridge University Press:  24 October 2008

H. S. M. Coxeter
H. S. M. Coxeter
Affiliation:
University of Toronto
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Extract

When two triangles, ABC and A′B′C′, are perspective from a point 0, their pairs of corresponding sides meet on a line 0, the axis of perspective. The line OA passes through A′ and some point on 0. These four points have a certain cross ratio which is the same if B or C is used instead of A. The reciprocal cross ratio arises if A′B′C′ is regarded as the first triangle and ABC the second. The complete figure contains ten pairs of perspective triangles, yielding twenty cross ratios. In section 6 a technique, suggested by D. W. Babbage and John Rigby, is used to express these cross ratios in the form

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 2 , September 1975 , pp. 227 - 246
Copyright
Copyright © Cambridge Philosophical Society 1975

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