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.