For, as many times as B measures A, so many units let there be in C.
Since B measures A according to the units in C,
and the unit D also measures the number C according to the units in it,
therefore the unit D measures the number C the same number of times as B measures A.
Therefore, alternately, the unit D measures the number B the same number of times as C measures A; [VII. 15]
therefore, whatever part the unit D is of the number B, the same part is C of A also.
But the unit D is a part of the number B called by the same name as it;
therefore C is also a part of A called by the same name as B,
so that A has a part C which is called by the same name as B.
Q. E. D.
Complete text
Book I