Let the odd number A multiplied by the even number B make C.
I say that C is even.
Since A multiplied by B makes C, therefore C is made up of as many numbers equal to B as there are units in A. 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. Therefore C is even.
Therefore, if an odd number is multiplied by an even number, then the product is even.
Note that the proof for this theorem makes no use of the assumption that A is an odd number. The statement of this theorem might just as well be “if any number is multiplied by an even number, then the product is even.”