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Euclid: Elementa

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Euclid: Elementa
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PROPOSITION 17. 
 
 
If a cube number do not measure a cube number, neither will the side measure the side; and, if the side do not measure the side, neither will the cube measure the cube. 
 
 
For let the cube number A not measure the cube number B, and let C be the side of A, and D of B;  I say that C will not measure D. 
   
   
For if C measures D, A will also measure B. [VIII. 15]  But A does not measure B; therefore neither does C measure D.  Again, let C not measure D;  I say that neither will A measure B. 
       
       
For, if A measures B, C will also measure D. [VIII. 15]  But C does not measure D; therefore neither will A measure B.  Q. E. D. 
     
     
 
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