2. We suppose A:B is not proportional to C:D and we will find a contradiction
of the hypothesis a/b=c/d.
Assume A:B is not proportional to C:D, so we can assume there are numbers k and p so that kA > pB but it is not the case that kC > pD.
We'll suppose kC < pD. [We leave the case that kC = pD as an exercise for the reader.]
Using the corresponding measurements we have: ka > pb but kc < pd.
Since these are all positive numbers we have by multiplication that kp ad > kp bc which contradicts ad=bc, an immmediate consequence of the hypothesis that a/b=c/d.