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Euclid: Elementa

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Euclid: Elementa
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PROPOSITION 22. 
 
 
If three numbers be in continued proportion, and the first be square, the third will also be square. 
 
 
Let A, B, C be three numbers in continued proportion, and let A the first be square;  I say that C the third is also square. 
   
   
For, since between A, C there is one mean proportional number, B,  therefore A, C are similar plane numbers. [VIII. 20]  But A is square;  therefore C is also square.  Q. E. D. 
         
         
 
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