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The Petersen-Morley theorem, I

Published online by Cambridge University Press:  24 October 2008

R. J. Lyons  and
R. Frith
R. J. Lyons
Affiliation:
St John's College
R. Frith
Affiliation:
Trinity College
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Extract

Two perpendicular intersecting straight lines will be said to be normal to each other. Then the Petersen-Morley theorem is: Given arbitrarily three lines a, b, c, let a′ be the unique normal to b and c, b′ that to c and a, and c′ that to a and b; then the lines x, y, z, normal respectively to the pairs of lines a and a′, b and b′, c and c′, have a common normal.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 30 , Issue 2 , 30 April 1934 , pp. 192 - 196
Copyright
Copyright © Cambridge Philosophical Society 1934

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References

* Morley, F., Proc. London Math. Soc. (1), 29 (1898), 670–673.Google Scholar

† Petersen, J., Oversigt over d. k. danske Vidensk. Selskabs Forhand. (1898), 283–344 (293).Google Scholar

‡ Study, E., Geometrie der Dynamen (1903), 107, 237.Google Scholar

§ Bennett, G. T., Proc. London Math. Soc. (2), 9 (1911), 273–285.CrossRefGoogle Scholar