PROPOSITION 28.

If an odd number by multiplying an even number make some number, the product will be even.

For let the odd number A by multiplying the even number B make C ;

I say that C is even.

A B C
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 B is even ;
therefore C is made up of even numbers.
But, if as many even numbers as we please be added together, the whole is even. [IX. 21]
Therefore C is even.
Q. E. D.

Dependency Graph

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