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Euclid: Elementa
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PROPOSITION 27. 
 
 
If from an odd number an even number be subtracted, the remainder will be odd. 
 
 
For from the odd number AB let the even number BC be subtracted;  I say that the remainder CA is odd. 
   
   
Let the unit AD be subtracted;  therefore DB is even. [VII. Def. 7]  But BC is also even;  therefore the remainder CD is even. [ IX. 24 ]  Therefore CA is odd. [VII. Def. 7]  Q. E. D. 
           
           
 
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