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289. [K. 1.] Note on Euclid I. 16, 27

Published online by Cambridge University Press:  03 November 2016

E.J. Nanson
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Type
Mathematical Notes
Information
The Mathematical Gazette , Volume 5 , Issue 79 , April 1909 , pp. 88
Copyright
Copyright © The Mathematical Association 1909

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References

* “This proposition is not universally true under the Riemann hypothesis of a space endless in extent but not infinite in size.” v. The Thirteen Books of Euclid’s Elements. Heath, T.L. Vol. I. p. 280.Google Scholar And again, p. 309. “De Morgan observes that 1. 27 is a logical equivalent to 1. 16. Thus if A means ‘straight lines forming a triangle with a transversal,’ B, ‘straight lines making angles with a transversal on the same side which are together less than two right angles,’ we have:—all A is B, and it follows logically that all not – B is not – A.” [Ed.]