If there are three magnitudes, and others equal to them in multitude, which taken two and two together are in the same ratio, and the proportion of them be perturbed, then they are also in the same ratio ex aequali.
The proof for this is at: http://aleph0.clarku.edu/~djoyce/java/elements/bookV/propV23.html
there are 22 other axioms at: http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html
if you are interested i have the formula that combines the "best" transcendental numbers... pi and e and also tau(the golden ratio), it also has i so it must be imaginary... it is directly related to the 5 pointed star... i derived it from e^pi = -1.0... write to firstname.lastname@example.org in the subject line leave name and the discordian date...
i am not logged in - please do not frag me or poke in my machine ;)