Doubling the cube: A new interpretation of its significance for early greek geometry

Abstract

It is widely known that Hippocrates of Chios reduced the problem of doubling the cube to the problem of finding two mean proportionals between two given lines. Nothing, however, is known about how this reduction was justified. To answer this question, propositions and patterns of arguments in Books VI, XI, and XII of the Elements are examined. A reconstruction modelled after Archimedes' On Sphere and Cylinder, Proposition II-1, is proposed, and its plausibility is discussed. © 1995 Academic Press, Inc.