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Euclid: Elementa
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PROPOSITION 16. 
 
 
If a square number do not measure a square number, neither will the side measure the side; and, if the side do not measure the side, neither will the square measure the square. 
 
 
Let A, B be square numbers, and let C, D be their sides; and let A not measure B;  I say that neither does C measure D. 
   
   
For, if C measures D, A will also measure B. [VIII. 14]  But A does not measure B; therefore neither will 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. 14]  But C does not measure D;  therefore neither will A measure B.  Q. E. D. 
       
       
 
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