## 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.
With the completion of this proposition, the study of addition, subtraction, and multiplication of even and odd numbers is also completed. There remain a few more propositions about even and odd numbers.

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