Let A and B be square numbers, and let C and D be their sides, and let A not measure B.
I say that neither does C measure D.
If C measures D, A also measures B. But A does not measure B, therefore neither does C measure D.
Next, let C not measure D.
I say that neither does A measure B.
If A measures B, then C also measures D. But C does not measure D, therefore neither does A measure B.
Therefore, if a square does not measure a square, then neither does the side measure the side; and, if the side does not measure the side, then neither does the square measure the square.