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508 BEUCE MCEWEN : science. Indeed so commonplace is this observation, that in consequence the historian is usually led to neglect the vast difference which distinguishes Kant's first appearance from that of the many other " mathematical philosophers ". The followers of Descartes, especially on the continent of Europe, had pinned their faith in mathematical matters to the analytical method introduced into geometry by their great master. The comparatively modern science of Algebra was applied to the problems of Space and Motion, and in the hands of such colossal geniuses as the Bernouillis, Leibniz and Euler problems, which had long been the despair of the Euclideans, now found a simple and accurate solution. For the time there appeared to be no limit to the powers of the new mathematical analysis. In Geometry, in Dynamics, even in the mixed sciences, Astronomy and Physics, it ab- sorbed, transformed and reproduced all previous results with such startling rapidity that the credit of discovery has often been wholly filched away from the original author by those who merely borrowed his thoughts. 1 But alongside of this rapidly advancing Cartesian system the old conservative methods, which had come down from the days of Pytha- goras and Plato, always retained many illustrious intellects in their service. The English school of Scientists, repre- sented by Boyle, Hooke, Newton, and the other founders of the Royal Society, continued to give ample proof of the vitality of pure geometry and experimental investigation in science. Still, as we have said, their discoveries were no sooner proclaimed than appropriated by the analytical method, all signs of the source from which they came being thereby obliterated. Accordingly it must have been with feelings of surprise that Kant's contemporaries beheld one who was born into and educated under the new analytical school throwing off the traditions of his time, and returning to the methods they were wont to consider superseded. From the outset Kant attached himself unreservedly to the " Natural Philosophy " of Newton, adopting at the same time the peculiarly New- tonian preference for pure geometrical methods. Kant, it must never be forgotten, was a mathematician of no mean order; even if we disregard his professedly mathematical writings, we have sufficient indication of this fact in the many references to Mathematics in his philosophical works, 1 A most striking instance of this tendency may be noticed in the case of the invention of the Differential Calculus originally discovered by Newton, but afterwards almost universally ascribed to Leibniz, who gave it the convenient algebraical form in which it now appears. .