"Up to this point mathematics alone appeared to Descartes worthy of being called a science. ...in order to establish the science or philosophy sought by Descartes, it was sufficient to find a method that should be to philosophy what the method of mathematical deduction is to arithmetic, algebra and geometry. ...How could one pass from these processes, which are especially adapted to particular sciences, to the general method required by general science or philosophy? Descartes would undoubtedly never have conceived such an audacious hope, had not a great discovery of his set him on this track. He had invented analytical geometry... In this way, Descartes substituted for the old methods, which were especially adapted to algebra and geometry as distinct branches, a general method, applicable to what he called the "universal mathematical science," viz., to the study of "the various ratios or proportions to be found between the objects of the mathematical sciences, hitherto regarded as distinct." Not only did this discovery mark a decisive epoch in the history of mathematics, which it provided with an instrument of incomparable simplicity and power, but it furthermore gave Descartes a right to hope for the philosophical method he was seeking. Ought not a last generalization to be possible, by means of which the method he had so happily discovered should become applicable, not only to the "universal mathematical science," but also to the systematic combination of all the truths which our finite minds may permit us to attain?"