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A Note on Affine Pappus Conditions

Published online by Cambridge University Press:  20 November 2018

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
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
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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