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Returning to our more immediate subject, we must observe that the Pythagoreans did not maintain, in anticipation of modern quantitative science, that all things are determined by number, but that all things are numbers, or are made out of numbers, two propositions not easily distinguished by unpractised thinkers. Numbers, in a word, were to them precisely what water had been to Thales, what air was to Anaximenes, the absolute principle of existence; only with them the idea of a limit, the leading inspiration of Greek thought, had reached a higher degree of abstraction. Number was, as it were, the exterior limit of the finite, and the interior limit of the infinite. Add to this that mathematical studies, cultivated in Egypt and Phoenicia for their practical utility alone, were being pursued in Hellas with ever-increasing ardour for the sake of their own delightfulness, for the intellectual discipline that they supplieda discipline even12 more valuable then than now, and for the insight which they bestowed, or were believed to bestow, into the secret constitution of Nature; and that the more complicated arithmetical operations were habitually conducted with the aid of geometrical diagrams, thus suggesting the possibility of applying a similar treatment to every order of relations. Consider the lively emotions excited among an intelligent people at a time when multiplication and division, squaring and cubing, the rule of three, the construction and equivalence of figures, with all their manifold applications to industry, commerce, fine art, and tactics, were just as strange and wonderful as electrical phenomena are to us; consider also the magical influence still commonly attributed to particular numbers, and the intense eagerness to obtain exact numerical statements, even when they are of no practical value, exhibited by all who are thrown back on primitive ways of living, as, for example, in Alpine travelling, or on board an Atlantic steamer, and we shall cease to wonder that a mere form of thought, a lifeless abstraction, should once have been regarded as the solution of every problem, the cause of all existence; or that these speculations were more than once revived in after ages, and perished only with Greek philosophy itself.There is nothing more interesting, or at the same time more useful, in the study of mechanics, than to analyse the action of cutting machines or other machinery of application, and to ascertain in examples that come under notice whether the main object of a machine is increased force, more accurate guidance, or greater speed than is attainable by hand operations. Cutting machines as explained may be directed to either of these objects singly, or to all of them together, or these objects may vary in their relative importance in different operations; but in all cases where machines are profitably employed, their action can be traced to one or more of the functions named.<024> このページの先頭です
ONE:I informed a few priests of the Pope's death, which had been known in The Netherlands for several days. They knew nothing about it, and asked whether I had any proof by me. I gave them De Tijd printed with a black border, and armed with this document they went to communicate the sad news to the Right Reverend Rutten, bishop of Lige.
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TWO:Five minutes later the smoke had disappeared almost, and I was able to see what had happened on the field in front of me. Terrible! On all sides lay scattered the lads, who but a short time ago started with so much enthusiasm, and here and there a gun knocked over, five, six corpses lying around it.The rules which Aristotle gives us for the conversion of propositions are no doubt highly instructive, and throw great light on their meaning; but one cannot help observing that such a process as conversion ought, on his own principles, to have been inadmissible. With Plato, the copulation of subject and predicate corresponded to an almost mechanical juxtaposition of two self-existent ideas. It was, therefore, a matter of indifference in what order they were placed. Aristotle, on the other hand, after insisting on the restoration of the concrete object, and reducing general notions to an analysis of its particular aspects, could not but make the predicate subordinate to, and dependent on, the subjecta relation which altogether excludes the logical possibility of making them interchangeable with one another.275
TWO:Rhetoric conferred even greater power in old Athens than in modern England. Not only did mastery of expression lead to public employment; but also, as every citizen was permitted by law to address his assembled fellow-countrymen and propose measures for their acceptance, it became a direct passport to supreme political authority. Nor was this all. At Athens the employment of professional advocates was not98 allowed, and it was easy to prosecute an enemy on the most frivolous pretexts. If the defendant happened to be wealthy, and if condemnation involved a loss of property, there was a prejudice against him in the minds of the jury, confiscation being regarded as a convenient resource for replenishing the national exchequer. Thus the possession of rhetorical ability became a formidable weapon in the hands of unscrupulous citizens, who were enabled to extort large sums by the mere threat of putting rich men on their trial for some real or pretended offence. This systematic employment of rhetoric for purposes of self-aggrandisement bore much the same relation to the teaching of Protagoras and Gorgias as the open and violent seizure of supreme power on the plea of natural superiority bore to the theories of their rivals, being the way in which practical men applied the principle that truth is determined by persuasion. It was also attended by considerably less danger than a frank appeal to the right of the stronger, so far at least as the aristocratic party were concerned. For they had been taught a lesson not easily forgotten by the downfall of the oligarchies established in 411 and 404; and the second catastrophe especially proved that nothing but a popular government was possible in Athens. Accordingly, the nobles set themselves to study new methods for obtaining their ultimate end, which was always the possession of uncontrolled power over the lives and fortunes of their fellow-citizens. With wealth to purchase instruction from the Sophists, with leisure to practise oratory, and with the ability often accompanying high birth, there was no reason why the successors of Charmides and Critias should not enjoy all the pleasures of tyranny unaccompanied by any of its drawbacks. Here, again, a parallel suggests itself between ancient Greece and modern Europe. On the Continent, where theories of natural law are far more prevalent than with us, it is by brute force that justice is trampled down: the one great object of every ambitious99 intriguer is to possess himself of the military machine, his one great terror, that a stronger man may succeed in wresting it from him; in England the political adventurer looks to rhetoric as his only resource, and at the pinnacle of power has to dread the hailstorm of epigrammatic invective directed against him by abler or younger rivals.74III.
TWO:"That's it. For the present we have to sit here in the passage with the kitchen door open and watch for the faint gleam of light in the courtyard. It is safe to have a light there because there are blank walls on either side. I think, I rather think, that I am going to astonish you presently.""Good!" Lalage went on. "That letter was written in gaol. It looked so innocent that the people there passed it. They did not know that every letter had a meaning. It seemed all about my defence. You acted on that letter?"
THREE:They stormed the Belgian lines with lowered bayonets. The Belgians quietly allowed them to come near, but as soon as they were at a certain distance from the trenches they wished to take, I heard the rattle of the mitrailleuses, and the thunder of the guns. The storming soldiers then disappeared in a fog of smoke and dust, in which I saw their shadows fall and stagger. This went on for about ten minutes, and then they came back in complete disorder, still followed by the hostile bullets and shrapnel."Because there was one who hated him. I cannot and will not say any more than that. He stood in the way of somebody. So long as he kept away it was all right. But Leon was not one of that sort. He was as brave as a lion. Had he not been so fond of the drink he might have done anything. But there was something in the blood of both of us that took us into evil ways. Thank God our mother is dead, the flower farm gone, and the secret of the wonderful perfume that made the name of Lalage famous for two centuries is buried in my mother's grave."
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THREE:By examining automatic hammers it will be found that their valves are connected to the drop by means of links, producing [162] coincident movement of the piston and valve, and that the movement of one is contingent upon and governed by the other. It will also be found that these connections or links are capable of extension, so as to alter the relative position of the piston and valve, thereby regulating the range of the blow, but that the movement of the two is reciprocal or in unison. Reasoning inductively, not discovering or inventing, it may be determined that to secure a stamp blow of a hammer-head, the valve must not open or admit steam beneath the piston until a blow is completed and the hammer has stopped.