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THREE:With these conclusions in his mind, but little progress will be made, and hence the reason for introducing the subject here.

THREE:A true movement of carriages is dependent upon the amount or wearing power of their bearing surface, how this surface is disposed in reference to the strain to be resisted, and the conditions under which the sliding surfaces move; that is, how kept in contact. The cutting strain which is to be mainly considered, falls usually at an angle of thirty to forty degrees downward toward the front, from the centre of the lathe. To resist such strain a flat top shear presents no surface at right angles to the strain; the bearings are all oblique, and not only this, but all horizontal strain falls on one side of the shear only; for this reason, flat top shears have to be made much heavier than would be required if the sum of their cross section could be employed to resist transverse strain. This difficulty can, however, be mainly obviated by numerous cross girts, which will be found in most lathe frames having flat tops.

THREE:So matters stood when the introduction of Aristotle��s entire system into western Europe brought about a revolution comparable to that effected two centuries later by the complete recovery of ancient literature. It was through Latin translations from the Arabic, accompanied by Arabic commentaries, that the Peripatetic philosophy was first revealed in its entirety; and even Albertus Magnus, living in the thirteenth century, seems to have derived his knowledge of the subject from these exclusively. But a few years after the capture of Constantinople by the Crusaders in 1204, the Greek manuscripts of Aristotle were brought to Paris; and, towards the middle of the century, a new Latin version was made from these under the supervision of St. Thomas Aquinas.536 The triumph of Aristotle was now, at least for a time, secured. For, while in the first period of the Middle Ages we find only a single great name, that of Ab��lard, among the Nominalists, against a strong array of Realists, in the second period the proportions are reversed, and Realism has only a single worthy champion, Duns Scotus, to pit against Albertus, Aquinas, and William of Ockham, each of them representing one of the principal European nations.537 The human intellect, hitherto confined within the narrow bounds of logic, now ranged over physics, metaphysics, psychology, and ethics; and although all these subjects were368 studied only at second-hand, and with very limited opportunities for criticism, still the benefit received must have been immense. The priceless service of the later Schoolmen is to have appropriated and successfully upheld, against Platonism on the one hand and theological mysticism on the other, a philosophy which, however superficial, took in the whole range of natural phenomena, derived all knowledge from external observation, and set an example of admirable precision in the systematic exposition of its results. If no positive addition was made to that vast storehouse of facts and ideas, the blame does not lie with Aristotle��s method, but with the forcible suppression of free mental activity by the Church, or its diversion to more profitable fields by the study of Roman jurisprudence. Even as it was, Aristotle contributed largely to the downfall of ecclesiastical authority in two ways: directly by accustoming men to use their reason, and indirectly by throwing back mysticism on its proper office��the restoration of a purely personal religion.To understand Descartes aright, we must provisionally disregard the account given in his work on Method of the process by which he arrived at a new theory of the world; for, in truth, there was nothing new about it except the pro388portion in which fragments taken from older systems were selected and recombined. As we have already noticed, there is no such thing as spinning philosophies out of one��s own head; and, in the case of Descartes, even the belief that he was so doing came to him from Plato; for, along with Aristotle��s dogmatic errors, his sound teaching with regard to the derivation of knowledge had fallen into oblivion. The initial doubt of the Discourse on Method and the Meditations is also Platonic; only it is manifested under an individual and subjective, instead of a universal and objective form. But to find the real starting-point of Descartes�� enquiries we must look for it in his mathematical studies. A geometrician naturally conceives the visible world under the aspect of figured extension; and if he thinks the figures away, nothing will remain but extension as the ultimate material out of which all determinate bodies are shaped. Such was the result reached by Plato in his Timaeus. He identified matter with space, viewing this as the receptacle for his eternal and self-existent Ideas, or rather the plastic medium on which their images are impressed. The simplest spatial elements are triangles; accordingly it is with these that he constructs his solid bodies. The theory of triangular elements was probably suggested by Atomism; it is, in fact, a compromise between the purely mathematical and the materialistic methods. Like all Plato��s fancies, this theory of matter was attacked with such convincing arguments by Aristotle that, so long as his physics remained in the ascendent, it did not find a single supporter; although, as we saw in the last chapter, Plotinus very nearly worked his way back to it from the Peripatetic definition. Even now, at the moment of Aristotle��s fall, it might have failed to attract attention, had not the conditions under which it first arose been almost exactly repeated. Geometrical demonstration had again become the type of all reasoning; there was again a sceptical spirit abroad, forcing men to fall back on the most elementary and universal con389ceptions; an atomistic materialism again threatened to claim at least the whole field of physical enquiry for its own. That Descartes followed the Timaeus in identifying matter with extension cannot be doubted; especially when we see that he adopts Plato��s analysis of body into elementary triangles; but the theory agreed so well with his intellectual predispositions that he may easily have imagined it to be a necessary deduction from his own �� priori ideas. Moreover, after the first two steps, he parts company with Plato, and gives himself up, so far as his rejection of a vacuum will permit, to the mechanical physics of Democritus. Much praise has recently been bestowed on his attempt to interpret all physical phenomena in terms of matter and motion, and to deduce them from the unaided operation of natural causes; but this is no more than had been done by the early Greek thinkers, from whom, we may observe, his hypothesis of an initial vortex was also derived. His cosmogony is better than theirs, only in so far as it is adapted to scientific discoveries in astronomy and physiology not made by Descartes himself; for where his conjectures go beyond these they are entirely at fault.