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" Quantities, and the ratios of quantities, which in any finite time converge continually to equality, and before the end of that time approach nearer to each other than by any given difference, become ultimately equal. "
Proceedings of the Edinburgh Mathematical Society - Page 13
by Edinburgh Mathematical Society - 1920
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Institutes of Natural Philosophy: Theoretical and Practical

William Enfield - Astronomy - 1811 - 476 pages
...another. LEMMA I. Quantities and the ratios of quantities, which, in any finite time, tend continually to equality, and, before the end of that time, approach...by any given difference, become ultimately equal. If you deny it, let them be ultimately unequal ; and let their ultimate difference be D. Therefore...
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The First Three Sections of Newton's Principia: With Copious Notes and ...

Isaac Newton - Curves, Plane - 1826 - 208 pages
...DEMONSTRATED. LEMMA I. Quantities, and tfte ratios of quantities, which, in any finite time, tend continually to equality ; and, before the end of that time, approach...by any given difference, become ultimately equal. JF you deny it, let them be ultimately unequal ; and let their ultimate difference be D. Therefore...
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The Three First Sections and Part of the Seventh Section of Newton's ...

Isaac Newton - Curves, Plane - 1850 - 184 pages
...DEMONSTRATED. LEMMA I. Quantities, and the ratios of quantities, which, in any finite time, tend continually to equality; and, before the end of that time, approach...by any given difference, become ultimately equal. IF you deny it, let them be ultimately unequal; and let their ultimate difference be D. Therefore they...
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Newton's Principia: Sections I. II. III.

Sir Isaac Newton - Curves, Plane - 1863 - 316 pages
...Quantities, and the ratios of quantities, which, in any finite time, tend constantly to equality, and which, before the end of that time, approach nearer to each other than by any assigned difference, become ultimately equal. If not, let them become ultimately unequal, and let their...
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Hints from the Dawning; Or, The Creation Story Considered Under the Laws of ...

Edward Dingle - Creation - 1868 - 350 pages
...Newton's first lesson, " Quantities, and ratios of quantities, which in any finite time, tend continually to equality; and before the end of that time, approach...by any given difference, become ultimately equal." They should have seen that the first law nature required as in interior command is inertia, as a resister...
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The True Doctrine of Orbits: An Original Treatise on Central Forces

H. G. Rush - Orbits - 1887 - 156 pages
..."Quantities, and the ratios of quantities, which, in any finite time, tend constantly to equality, and 'which, before the end of that time, approach nearer to each other than by any assigned difference, become ultimately equal. The quantities of which Newton asserts equality are not...
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Principia: First Book. sections I, II, III

Isaac Newton - Curves, Plane - 1900 - 320 pages
...Quantities, and the ratio of quantities, which, in any finite time, tend constantly to equality, and ivhich, before the end of that time, approach nearer to each other than by any assigned difference, become ultimately equal. If not, let them become ultimately unequal, and let their...
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A History of the Conceptions of Limits and Fluxions in Great Britain, from ...

Florian Cajori - Mathematics - 1919 - 320 pages
...Translated into English, and illustrated with a Commentary, by ROBERT THORP, MA, vol. i, London, 1777. before the end of that time, approach nearer to each...by any given difference, become ultimately equal. " If you deny it, let them be ultimately unequal ; and let their ultimate difference be D. Therefore,...
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The Historical Development of the Calculus

C.H.Jr. Edwards - Mathematics - 1994 - 368 pages
...limit concept: "Quantities, and the ratios of quantities, which in any finite time converge continually to equality, and before the end of that time approach...by any given difference, become ultimately equal." In modern notation, we would say that if, given e > 0, it follows that/(f) and g(t) differ by less...
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Never at Rest: A Biography of Isaac Newton

Richard S. Westfall - Biography & Autobiography - 1983 - 934 pages
...infinite series. Quantities, and the ratios of quantities, which in any finite time converge continually to equality, and before the end of that time approach...other than by any given difference, become ultimately equal.65 Three further lemmas compared the areas of sets of parallelograms inscribed in and around...
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