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Euclid: Elementa
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PROPOSITION 25. 
 
 
If from an even number an odd number be subtracted, the remainder will be odd. 
 
 
For from the even number AB let the odd number BC be subtracted;  I say that the remainder CA is odd. 
   
   
For let the unit CD be subtracted from BC;  therefore DB is even. [VII. Def. 7]  But AB is also even;  therefore the remainder AD is also even. [IX. 24]  And CD is an unit;  therefore CA is odd. [VII. Def. 7]  Q. E. D. 
             
             
 
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