If a square number does not measure a(nother) square number then the side (of the former) will not measure the side (of the latter) either. And if the side (of a square number) does not measure the side (of another square number) then the (former) square (number) will not measure the (latter) square (number) either. * Let $A$ and $B$ be square numbers, and let $C$ and $D$ be their sides (respectively). * And let $A$ not measure $B$. * I say that $C$ does not measure $D$ either. * So, again, let $C$ not measure $D$. * I say that $A$ will not measure $B$ either.
(not yet contributed)
Proofs: 1