If three numbers are in continued proportion, and the first is square, then the third is also square.

Let *A, B,* and *C* be three numbers in continued proportion, and let *A* the first be square.

I say that *C* the third is also square.

Since between *A* and *C* there is one mean proportional number, *B,* therefore *A* and *C* are similar plane numbers. But *A* is square, therefore *C* is also square.

Therefore, *if three numbers are in continued proportion, and the first is square, then the third is also square.*

Q.E.D.