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The Teaching of Euclid

Published online by Cambridge University Press:  03 November 2016

Bertrand Russell
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Extract

It has been customary when Euclid, considered as a text-book, is attacked for his verbosity or his obscurity or his pedantry, to defend him on the ground that his logical excellence is transcendent, and affords an invaluable training to the youthful powers of reasoning. This claim, however, vanishes on a close inspection. His definitions do not alwaysdefine, his axioms are not always indemonstrable, his demonstrations require many axioms of which he is quite unconscious. A valid proof retains its demonstrative force when no figure is drawn, but very many of Euclid’s earlier proofs fail before this test.

Type
2. Highlights
Information
The Mathematical Gazette , Volume 55 , Issue 392 , March 1971 , pp. 143 - 145
Copyright
Copyright © Mathematical Association 1971

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References

* Cf. Pasoh, Vorlesungen über neuere Geometrie Leipzig, 1882; Peano, I Principii di Geometria, Turin, 1889.

† Cf. Hilbert, Grundfagen der Geometrie, Leipzig, 1899, p. 16.