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absolute space Adolf Mayer ancient Archimedes Aristotle Benedetti body calculus of variations Cardano Chicago and London conception of mass Conservation of Energy convenient German Daniel Bernoulli Descartes Dictionnaire Philosophique Discorsi discovery Duhem dynamical Encykl equations equilibrium Euler experience exposition fifth corollary fixed stars Galileo Gauss Gauss's principle German translation gravity historical Huygens inclined plane investigations Jacobi Jellett Jordanus Joseph Bertrand Lagrange Lagrange's Lange last line law of inertia Least Action Leipsic Leonardo lever line 13 line 9 Mach's Mechanics math Maupertuis Maupertuis's Mechanik memoir Monist for April Monist for July motion of falling motu Newton Newtonian notes Oettingen Ostwald's Klassiker paper Paris Philip E. B. Jourdain Principia principle of least principle of virtual recognised remarks Roberval rotation seqq seventh German edition Stevinus supposition system of co-ordinates system of reference theorems theory tion Uber Vailati velocity virtual displace Voss weight Wiss Wohlwill xxii
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 80 - ... radius — but now they were mathematically true, excepting only for the slight deviation from a perfectly spherical form of the sun, earth and planets. We can imagine the effect of this sudden transition from approximation to exactitude in stimulating Newton's mind to still greater efforts. It was now in his power to apply mathematical analysis with absolute precision to the actual problems of astronomy.
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 water-bucket (pp.
Page 35 - Galileo's happy discovery could only hold approximately for small times and spaces, during which the rotation did not come into question. Instead of that, Newton's conclusions about planetary motion, referred as they were to the fixed stars, appeared to conform to the law of inertia. Now, in order to have a generally valid system of reference, Newton ventured the fifth corollary of the Principia (p. 19 of the first edition). He imagined a momentary terrestrial system of coordinates, for which the...
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 53 - Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre und ihre Aufnahme durch die Zeitgenossen " (Scientia : Rivista di Scienza, vol.
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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 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...