If an odd number by multiplying an odd number make some number, the product will be odd.
For let the odd number A by multiplying the odd number B make C; I say that C is odd.
For, since A by multiplying B has made C, therefore C is made up of as many numbers equal to B as there are units in A. [VII. Def. 15]
And each of the numbers A, B is odd; therefore C is made up of odd numbers the multitude of which is odd.
Thus C is odd. [IX. 23] Q. E. D.
Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.
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