If a first magnitude have to a second the same ratio as a third to a fourth, and the third have to the fourth a greater ratio than a fifth has to a sixth, the first will also have to the second a greater ratio than the fifth to the sixth.
Proof
Combine V.11 (sameness transitivity) with Definition V.7 (greater
ratio): the witness equimultiples for c:d>e:f work for a:b via
the V.5 sameness of a:b and c:d.