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Proposition 29

If an odd number is multiplied by an odd number, then the product is odd.
Let the odd number A multiplied by the odd number B make C. I say that C is odd.
| 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 each of the numbers A and B is odd, therefore C is made up of odd numbers the multitude of which is odd. Thus C is odd. | VII.Def.15 IX.23
Therefore, if an odd number is multiplied by an odd number, then the product is odd.
Q.E.D.

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(Forthcoming)

Book IX Introduction - Proposition IX.28 - Proposition IX.30.

© 1996
D.E.Joyce
Clark University