Descartes implicitly assumed a complete correspondence existed between the real numbers and the points of a fixed axis. ...tacitly, because it seemed so natural as to go without saying, he accepted it as axiomatic that between the points of a plane and the aggregate of all pairs of real numbers there can be established a perfect correspondence. Thus the Dedekind-Cantor axiom, extended to two dimensions, was tacitly incorporated in a discipline which was created two hundred years before Dedekind and Cantor saw the day. This discipline became the [tool and] proving-grounds for all achievements of the following two centuries: the calculus, the theory of functions, mechanics, and physics. Nowhere did this discipline, analytic geometry, strike any contradictions; and such was its power to suggest new problems and forecast the results that wherever applied it would soon become the indispensable tool of investigation.