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Also known as the continuity axiom, this Lemma survives in the writings of Eudoxus 
(Boyer 1968).
It states that, given two magnitudes having a ratio, one can find a multiple of either which will exceed the other. This
principle was the basis for the Exhaustion Method which Archimedes invented to solve problems of
Area and Volume.
See also Continuity Axioms
References
Boyer, C. B. A History of Mathematics. New York: Wiley, p. 100, 1968.