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Euclid: Elementa

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Euclid: Elementa
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PROPOSITION 23. 
 
 
If four numbers be in continued proportion, and the first be cube, the fourth will also be cube. 
 
 
Let A, B, C, D be four numbers in continued proportion, and let A be cube;  I say that D is also cube. 
   
   
For, since between A, D there are two mean proportional numbers B, C, therefore A, D are similar solid numbers. [VIII. 21]  But A is cube;  therefore D is also cube.  Q. E. D. 
       
       
 
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