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A Note on Affine Pappus Conditions

Published online by Cambridge University Press:  20 November 2018

N. D. Lane
N. D. Lane*
Affiliation:
McMaster University and University of California, Los Angeles
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Let ℓ, m, n be three mutually distinct lines in the projective plane. The (ℓ, m, n)-Pappus condition can be described as follows.

Let A, B, C, A', B', C' be any six mutually distinct points such that A, B, C lie on ℓ; A', B', C' lie on m; and none of these points lies on ℓ∩m, m∩n, or n∩ℓ. If the points AB'∩BA' and BC'∩CB' both lie on n, then the point AC'∩CA' also lies on n.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 3 , August 1967 , pp. 453 - 457
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Artin, E., Geometric Algebra. Interscience (1955).Google Scholar
2. Blumenthal, L. M., A Modern View of Geometry. Freeman (1966).Google Scholar
3. Coxeter, H. S. M., Introduction to Geometry. Wiley (1966).Google Scholar
4. Pickert, G., Projektiven Ebenen. Springer (1955).Google Scholar
5. Pickert, G., Der Satz von Papposmit Festelementen. Arch. Math. Vol. X, 1959, pp. 56-61.Google Scholar