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.