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A theorem of M. L. Urquhart's and some consequences

Published online by Cambridge University Press:  01 August 2016

R. T. Leslie
R. T. Leslie*
Affiliation:
25A Newark Drive, Pollokshields, Glasgow G41 4QA
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Extract

In an obituary of M. L. Urquhart in [1], David Elliott quotes him as claiming that Urquhart's theorem (below) is the most elementary theorem of Euclidean Geometry ‘since it involves only the concepts of straight line and distance’.

Urquhart's theorem

Let AC and AE be two straight lines.

Let B be a point on AC, D a point on AE, and suppose that BE and CD intersect at F.

If AB + BF = AD + DF then AC + CF = AE + EF. (1)

Type
Articles
Information
The Mathematical Gazette , Volume 91 , Issue 520 , March 2007 , pp. 39 - 50
Copyright
Copyright © The Mathematical Association 2007

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References

1. Elliot, D., Urquhait, M. L., Australian Journal of Mathematics 8 (1967) pp. 129–133.Google Scholar
2. Pedoe, D., The most ‘elementary’ theorem of Euclidean geometry, Mathematics Magazine 49 (1976) pp. 40–42.Google Scholar