If a first magnitude have to a second the same ratio as a third to a fourth, any equimultiples whatever of the first and third will also have the same ratio to any equimultiples whatever of the second and fourth respectively, taken in corresponding order.
Proof
By definition V.5, the original proportion gives an equimultiple
relation across all multipliers. Substituting ma for a and mc
for c throughout simply rescales the test multipliers; the test
itself still passes for the rescaled magnitudes.