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Euclid: Elementa
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PROPOSITION 24. 
 
 
If two numbers have to one another the ratio which a square number has to a square number, and the first be square, the second will also be square. 
 
 
For let the two numbers A, B have to one another the ratio which the square number C has to the square number D, and let A be square;  I say that B is also square. 
   
   
For, since C, D are square, C, D are similar plane numbers.  Therefore one mean proportional number falls between C, D. [VIII. 18]  And, as C is to D, so is A to B;  therefore one mean proportional number falls between A, B also. [VIII. 8]  And A is square;  therefore B is also square. [VIII. 22]  Q. E. D. 
             
             
 
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