The most general fundamental principle of the philosophical system of D., is the essential difference of spirit and matter—the thinking and the extended substances— a difference so great, according to D., that they can exert no influence upon each other. Hence, in order to account for the correspondence betwixt the material and spiritual phenomena, he was obliged to have recourse to a constant co operation (concurs-us) ou the part of God; a doctrine which gave rise subsequently to the system called Occa sionalism (q.v.). the principle of which was, that body and mind do not really affect each other, God being always the true cause of the apparent or occasional influence of one on the other. This doctrine received its complete development in the pre-established harmony of Leibnitz. See LEIBNITZ.
D. did not confine his attention to mental philosophy, but devoted himself systemati cally,to the explanation of the properties of the bodies composing the material universe. In this department, his reforms amounted to a revolution, though many of his explana tions of physical phenomena are purely a priori, and certainly sufficiently absurd. His corpuscular philosophy—in which he endeavored to explain all the appearances of the material world simply by the motion of the ultimate particles of bodies—was a great advance on the system held up to that time, according to which, special qualities and powers were assumed to account for every phenomenon. It was in mathematics, how ever, that D. achieved the greatest and most lasting results; and, indeed, his mathemati cal discoveries procured among his contemporaries, for his, in many cases, wild philo sophical views, a greater importance than they in themselves are entitled to. It was D.
who first recognized the true meaning of the negative roots of equations; and we owe to him the theorem, which is called by his name, that an equation may have as many posi tive roots as there arc changes of sign in passing from term to term, and as many nega tive roots as there are continuations of sign, and not more of either kind. He gave a new and ingenious solution of equations of the fourth degree; and first introduced exponents, and thereby laid the foundation for calculating with powers. lie showed, more over, how to draw tangents and normals at every point of a geometrical curve, with the exception of mechanical or transcendental curves; and, what perhaps was his highest merit, he showed how to express the nature and the properties of every curve, by an equation between two variable co-ordinates; thus, in fact, originating analytical geometry, which has led to the brightest discoveries. D. was less happy in his cosmological exer citations, in which he attempted to explain the movements of the heavenly bodies by vortices (tourbillons), consisting in the currents of the ether which he supposed to fill the universe; a theory which not only then, but even after the discoveries of Newton, made a great noise, and found many adherents, but which has long ago been consigned to oblivion. The philosophical and mathematical works of D., which are composed in Latin, were published at Amsterdam (9 vols. 4to, 1692-1701, also in 1713), and at Paris (1724-1720. in 13 vols. 12mo). More recently, an edition of his whole works has been published by M. Cousin (11 vols., Paris, 1824-20).
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