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