For, if possible, let it be so.
Then, since A measures B according to C,
therefore A by multiplying C has made B.
Therefore B is made up of odd numbers the multitude of which is odd.
Therefore B is odd: [IX. 23] which is absurd, for by hypothesis it is even.
Therefore C is not odd; therefore C is even.
Thus A measures B an even number of times.
For this reason then it also measures the half of it.
Q. E. D.