The science of mechanics: a critical and historical account of its development, by Ernst Mach: supplement to the 3rd English ed. containing the author's additions to the 7th German ed

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The Open Court Publishing Co., 1911 - Science - 106 pages
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Page 79 - had Newton proved this superb theorem — and we know from his own words that he had no expectation of so beautiful a result till it emerged from his mathematical investigation — than all the mechanism of the universe at once lay spread before him.
Page 34 - The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forwards in a right line without any circular motion.
Page 33 - This appeared to him to cause the difficulty of distinguishing between true (absolute) and apparent (relative) motion. By this he was also impelled to set up the conception of absolute space. By further investigations in this direction— the discussion of the experiment of the rotating spheres which are connected together by a cord and that of the rotating waterbucket (pp.
Page 33 - ... as valid, they could not, and were not, admitted without previously being subjected to experimental tests. No one is warranted in extending these principles beyond the boundaries of experience. In fact, such an extension is meaningless, as no one possesses the requisite knowledge to make use of it. We must suppose that the change in the point of view from which the system of the world is regarded, which was initiated by Copernicus, left deep traces in the thought of Galileo and Newton. But while...
Page 34 - But how we are to collect the true motions from their causes, effects, and apparent differences; and, vice versa, how from the motions, either true or apparent, we may come to the knowledge of their causes and effects, shall be explained more at large in the following tract. For to this end it was that I composed it.
Page 35 - ... only lies before us, and our business is, to bring it into accord with the other facts known to us, and not with the arbitrary fictions of our imagination. 6. When Newton examined the principles of mechanics discovered by Galileo, the great value of the simple and precise law of inertia for deductive derivations could not possibly escape him. He could not think of renouncing its help. But the law of inertia, referred in such a naive way to the earth supposed to be at rest, could not be accepted...
Page 34 - But how we are to collect," says Newton in the Scholium at the end of the Definitions, "the true motions from their causes, effects, and apparent differences, and vice versa; how from the motions, either true or apparent, we may come to the knowledge of their causes and effects, shall be explained more at large in the following Tract.
Page 36 - Newtonian laws of force are not altered thereby; only the initial positions and initial velocities — the constants of integration — may alter. By this view Newton gave the exact meaning of his hypothetical extension of Galileo's law of inertia. We see that the reduction to absolute space was by no means necessary, for the system of reference is just as relatively determined as in every other case. In spite of his metaphysical liking for the absolute, Newton was correctly led by the tact of the...
Page 33 - Try to fix Newton's bucket and rotate the heaven of fixed stars and then prove the absence of centrifugal forces. 4. It is scarcely necessary to remark that in the reflections here presented Newton has again acted contrary to his expressed intention only to investigate actual facts. No one is competent to predicate things about absolute space and absolute motion; they are pure things of thought, pure mental constructs...

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