Proposition 7
Incommensurable magnitudes do not have to one another the ratio which a number has to a number.
Let A and B be incommensurable magnitudes.
I say that A does not have to B the ratio which a number has to a number.
If A does have to B the ratio which a number has to a number, then A is commensurable with B.
But it is not, therefore A does not have to B the ratio which a number has to a number.
Therefore, incommensurable magnitudes do not have to one another the ratio which a number has to a number.
Q.E.D.