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ONE: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. THREE:Meanwhile, Charles, compelled to wait the course of events in Edinburgh, endeavoured to render himself popular by his moderation and magnanimity. Volunteers began to flock to his standard, the chief cause, however, being, no doubt, the prestige of his victory. Fresh reinforcements poured down from the Highlands. Altogether, Charles's army now amounted to nearly six thousand men. It would have amounted to ten thousand had the Macdonalds and Macleods of Skye and Lord Lovat joined him. But though Charles sent a Macleod of Skye over to the island chiefs, urging them now to join his standard as certain of victory, they refused to move. He then went over from Skye to Castle Dounie to stimulate Lord Lovat, but that deceitful old miscreant was playing the double game, and waiting to see which side would be the stronger. At length his army had received the last reinforcements that he expected, by the arrival of Menzies of Sheen with a considerable body of men, and he was impatient to march southwards. He was the more ready to quit Scotland because Lord Lovat had now sent him word that though he could not, from the state of his health, join the march into England, both he and the Macdonalds and the Macleods of the Isles were prepared to defend his interests in the Highlands. The greater part of this intelligence was false, entirely so as regarded the Islesmen, and it was now well known that the English Government had got together twelve thousand veteran troops, besides thirteen regiments of infantry and two of cavalry newly raised. The Highland chiefs, therefore, strenuously opposed the march till they should receive the reinforcements which he had promised them from France, as well as more money. Others contended that he ought not to invade England at all, but to remain in Scotland, make himself master of it, and reign there as his ancestors had done. But it was not merely to secure the Crown of Scotland that he had come; it was to recover the whole grand heritage of his race, and he determined to march into England without further delay. The Highland chiefs, however, resolutely resisted the proposal, and at three successive councils he strove with them in vain to induce them to cross the Border and fight the army of Marshal Wade, which lay at Newcastle, consisting of Dutch and English troops. At length Charles said indignantly, "Gentlemen, I see you are determined to stay in Scotland; I am resolved to try my fate in England, and I go, if I go alone."
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