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Euclid: Elementa
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PROPOSITION 28. 
 
 
If an odd number by multiplying an even number make some number, the product will be even. 
 
 
For let the odd number A by multiplying the even number B make C;  I say that C is even. 
   
   
For, since A by multiplying B has made C,  therefore C is made up of as many numbers equal to B as there are units in A. [VII. Def. 15]  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. [IX. 21]  Therefore C is even.  Q. E. D. 
             
             
 
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