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THREE:Meanwhile a new and powerful agency was about to interpose with decisive effect in the doubtful struggle. This was the study of mathematics. Revived by the Arabians and never wholly neglected during the Middle Ages, it had profited by the general movement of the Renaissance, and was finally applied to the cosmical problem by Galileo. In this connexion, two points of profound philosophical interest must be noted. The first is that, even in its fall, the Aristotelian influence survived, to some extent, both for good and for evil. To Aristotle belongs the merit of having been the first to base astronomy on physics. He maintains the earth��s immobility on experimental no less than on speculative grounds. A stone thrown straight up in the air returns to its starting-point instead of falling to the west of it; and the absence of stellar385 parallax seems to show that there is no change in our position relatively to the heavenly bodies. After satisfying himself, on empirical considerations, that the popular astronomy is true, he proceeds to show that it must be true, by considerations on the nature of matter and motion, which, although mistaken, are conceived in a genuinely scientific spirit. Now Galileo saw that, to establish the Copernican system, he must first grapple with the Peripatetic physics, and replace it by a new dynamical theory. This, which he could hardly have effected by the ordinary mathematical methods, he did by borrowing the analytical method of Atomism and applying it to the measurement of motion. The law of falling bodies was ascertained by resolving their descent into a series of moments, and determining its rate of velocity at successive intervals; and curvilinear motions were similarly resolved into the combination of an impulsive with an accelerating force, a method diametrically opposed to that of Bacon, who would not even accept the rough analysis of the apparent celestial motions proposed by Greek astronomers.Prince Ferdinand this summer had to contend with numerous armies of the French. De Broglie marched from Frankfort into Hesse with a hundred thousand men. On the 10th of July they met the hereditary Prince of Brunswick at Corbach, and defeated him, though he gained a decided advantage over them a few days after at Emsdorf, taking the commander of the division and five battalions prisoners. This was followed by Ferdinand himself, who was at Warburg, where he took ten pieces of artillery, killed one thousand five hundred of the French, and drove them into the Dimel, where many were drowned. The British cavalry had the greatest share in this victory. In fact, the Marquis of Granby led them on all occasions with such spirit and bravery, that Ferdinand placed them continually in the post of danger, where of course they suffered more severely than the other troops.