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THREE:Under such guidance as this. Platonism had made but little way. We saw, in the concluding sections of the last chapter and in the opening section of the present chapter, that it profited by the religious and literary revival of the second century, just as it was to profit long afterwards by the greater revival of the fifteenth century, so much so as to become the fashionable philosophy of the age. Yet, even in that period of its renewed splendour, the noblest of contemporary thinkers was not a Platonist but a Stoic; and although it would be unfair to measure the moral distance between the Porch and the Academy by the interval which separates an Aurelius from an Apuleius, still it would seem as if naturalism continued to be the chosen creed of strenuous and dutiful endeavour, while spiritualism was drifting into an alliance with hysterical and sensuous superstition. If we may judge by the points which Sextus Empiricus selects for controversial treatment, Stoicism was still the reigning system in his time, that is to say, about the beginning of the third century; and if, a generation later, it had sunk into neglect, every rival school, except that of Epicurus, was in exactly the same condition. Thus the only advance made was to substitute one form of materialism for another, until Neo-Platonism came and put an end to their disputes by destroying the common foundation on which they stood; while, at the same time, it supplied a completely organised doctrine round which the nobler elements of the Hellenic revival could rally for a last stand against the foes that were threatening it from every side.Meanwhile Atomism continued to exercise a powerful influence on the method even more than on the doctrines of science. The analytical mode of treatment, applied by Galileo to dynamics, was applied, with equal success, by other mathematicians, to the study of discrete and continuous quantity. It is to the division of numbers and figures into infinitesimal parts��a direct contravention of Aristotle��s teaching��that we owe logarithms, algebraic geometry, and the differential calculus. Thus was established a connexion between spiritualism and materialism, the philosophy of Plato and the philosophy of Democritus. Out of these elements, together with what still survived of Aristotelianism, was constructed the system of Descartes.

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