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On the Use of Symmetry in Geometry
Published online by Cambridge University Press: 20 January 2009
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Two features characterise the treatment of Geometry as presented in Euclid's “Elements”: (1) the propositions are arranged in a definite sequence which cannot be greatly altered without invalidating the proofs; (2) there are no methods of proof applicable to a large number of propositions. If we except the method of reductio ad absurdum, it is scarcely an exaggeration to say, for example, that in Book I no three propositions are proved by the same method.
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- Copyright © Edinburgh Mathematical Society 1903
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