If from an odd number an odd number be subtracted, the remainder will be even.
For from the odd number AB let the odd number BC be subtracted; I say that the remainder CA is even.
For, since AB is odd, let the unit BD be subtracted; therefore the remainder AD is even. [VII. Def. 7]
For the same reason CD is also even; [VII. Def. 7] so that the remainder CA is also even. [IX. 24] Q. E. D.
Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.
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