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What's wrong with Euclid Book V

What's wrong with Euclid Book V Not having the real numbers, Euclid defined ratios abstractly in Book V for use in geometric theorems, but failed to define ratios of ratios, in effect blocking certain further developments of Greek mathematics. We introduce a new axiom that can be used instead of subtraction, not only to prove the propositions of Book V but also to define ratios of ratios. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

What's wrong with Euclid Book V

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References (4)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/bdm104
Publisher site
See Article on Publisher Site

Abstract

Not having the real numbers, Euclid defined ratios abstractly in Book V for use in geometric theorems, but failed to define ratios of ratios, in effect blocking certain further developments of Greek mathematics. We introduce a new axiom that can be used instead of subtraction, not only to prove the propositions of Book V but also to define ratios of ratios.

Journal

Bulletin of the London Mathematical Society – Wiley

Published: Feb 1, 2008

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