info prev up next book cdrom email home

Archimedes' Lemma

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


Boyer, C. B. A History of Mathematics. New York: Wiley, p. 100, 1968.

© 1996-9 Eric W. Weisstein