If from an even number an odd number be subtracted, the remainder will be odd.
For from the even number AB let the odd number BC be subtracted; I say that the remainder CA is odd.
For let the unit CD be subtracted from BC; therefore DB is even. [VII. Def. 7]
But AB is also even; therefore the remainder AD is also even. [IX. 24]
And CD is an unit; 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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