For, if not, there will be some number less than G which will have the parts A, B, C.
Let it be H.
Since H has the parts A, B, C, therefore H will be measured by numbers called by the same name as the parts A, B, C. [VII. 38]
But D, E, F are numbers called by the same name as the parts A, B, C; therefore H is measured by D, E, F.
And it is less than G: which is impossible.
Therefore there will be no number less than G that will have the parts A, B, C.
Q. E. D.