|If an odd number is multiplied by an even number, then the product is even.|
|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.||VII.Def.15|
|But, if as many even numbers as we please be added together, the whole is even. Therefore C is even.||IX.21|
|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."
Next proposition: IX.29
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