THREE:221II.
THREE:By placing the axes of tangent gearing so that the threads or teeth of the pinions are parallel to the face of the driven teeth, [53] as in the planing machines of Messrs Wm. Sellers & Co., the conditions of operation are changed, and an interesting problem arises. The progressive or forward movement of the pinion teeth may be equal to the sliding movement between the surfaces; and an equally novel result is, that the sliding action is distributed over the whole breadth of the driven teeth.To get rid of superstitious beliefs was, no doubt, a highly meritorious achievement, but it had been far more effectually57 performed by the great pre-Socratic thinkers, Heracleitus, Empedocles, Anaxagoras, and Democritus. These men or their followers had, besides, got hold of a most important principlethe vital principle of all sciencewhich was the reign of law, the universality and indefeasibility of physical causation. Now, Epicurus expressly refused to accept such a doctrine, declaring that it was even worse than believing in the gods, since they could be propitiated, whereas fate could not.119 Again, Greek physical philosophy, under the guidance of Plato, had been tending more and more to seek for its foundation in mathematics. Mathematical reasoning was seen to be the type of all demonstration; and the best hopes of progress were staked on the extension of mathematical methods to every field of enquiry in turn. How much might be done by following up this clue was quickly seen not only in the triumphs of geometry, but in the brilliant astronomical discoveries by which the shape of the earth, the phases of the moon, and the cause of eclipses were finally cleared up and placed altogether outside the sphere of conjecture. Nor was a knowledge of these truths confined to specialists: they were familiar alike to the older Academy, to the Peripatetic, and to the Stoic schools; so that, with the exception of those who doubted every proposition, we may assume them to have been then, as now, the common property of all educated men. Epicurus, on the other hand, seems to have known nothing of mathematics, or only enough to dispute their validity, for we are told that his disciple Polyaenus, who had previously been eminent in that department, was persuaded, on joining the school, to reject the whole of geometry as untrue;120 while, in astronomy, he pronounced the heavenly bodies to be no larger than they appear to our senses, denied the existence of Antipodes, and put the crudest guesses of early philosophy on the same footing with the best-authenticated results of later observation. It is no wonder, then, that during the whole58 continuance of his school no man of science ever accepted its teaching, with the single exception of Asclepiades, who was perhaps a Democritean rather than a disciple of the Garden, and who, at any rate, as a physiologist, would not be brought into contact with its more flagrant absurdities.
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