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Proposition 28

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.
Q.E.D.

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(Forthcoming)

Book IX Introduction - Proposition IX.27 - Proposition IX.29.

© 1996
D.E.Joyce
Clark University