| 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. | X.6 | |
| 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. | ||
