Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-14T07:22:13.478Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on the Parallel-Postulate

Published online by Cambridge University Press:  03 November 2016

A. A. Krishnaswami Ayyangar
Get access Rights & Permissions [Opens in a new window]

Extract

Some teachers may not have noticed that there is a real connection between the parallel postulate and another and more fundamental property of space which it is also more natural to assume, viz. that stated by John Wallis in the seventeenth century:

Type
Research Article
Information
The Mathematical Gazette , Volume 12 , Issue 172 , October 1924 , pp. 191 - 194
Copyright
Copyright © Mathematical Association 1924

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

page 191 note * In a footnote on p. 167, vol. xii., Mathematical Gazette, July 1924, Prof. 31. J. M. Hill remarks that either his proof or Prof. Nunn’s or some equivalent proof should find a place in every textbook of elementary geometry in place of Euclid’s Postulate of Parallels. I have been therefore tempted to sketch here an equivalent proof, which, I believe, will be at least as commendable as the others. On p. 413, vol. xi., Prof. Hill mentions that he has received a full statement of Prof. Nunn’s Arguments which, so far as I know, has not been published anywhere, in extenso and I do not know therefore how far I may have been anticipated by him.

page 192 note * Vide ii. (3) infra where we set off AM=BE in AB and in order that M may fall between A and B, AB should be greater than BE and this will be secured if AB ≥ BC, BCbeing obviously greater than BE.