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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. "
The Three First Sections and Part of the Seventh Section of Newton's ... - עמוד 33
מאת Sir Isaac Newton - 1850 - 163 דפים
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The Mathematical Principles of Natural Philosophy, כרך 1

Isaac Newton - 1729 - 320 דפים
...that follow. LEMMA I. Quantities, and the rations of quantities, which in any finite time converge continually to equality, and before the end of that time approach nearer the one to the other than by any given difference, become ultima-til? equal. If you deny it ; fuppofe...
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The Analogy of Divine Wisdom: In the Material, Sensitive, Moral, Civil and ...

Richard Barton - 1750 - 234 דפים
...natural philofophy is : Quantities, and the ratio of quantities, which in any finite time converge continually to equality, and before the end of that time, approach nearer the one to the other, than by any given difference, become ultimately equal. This is plainly the fame,...
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Mathematical Tracts of the Late Benjamin Robins ...: Discourse on the ...

Benjamin Robins, James Wilson (M.D., of London.) - 1761
...lemma all ultimate difference is excluded, the confequences drawn of thefe two lines, let us fay thus. If you deny it, let them be ultimately unequal, and let their difference be D ; therefore they cannot approach to equality nearer than by the given difference D,...
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The Doctrine of Fluxions: Not Only Explaining the Elements Thereof, But Also ...

William Emerson - 1768 - 432 דפים
...general Proportion is to be underftood. AXIOM. Quantities, which in any finite Time continually converge to Equality, and before the End of that Time, approach nearer to one another than by any given Difference, do at Jaft become equal. If any ihould think this not clear...
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The mathematical principles of natural philosophy, כרך 1

Sir Isaac Newton, William Davis, William Emerson, John Machin - 1803
...time converge continually to equality, and before the end of that time approach nearer the one to the other than by any given difference, become ultimately equal. If you deny it, fuppofe them to be ultimately unequal, and let 1) be their ultimate difference. Therefore they cannot...
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The Mathematical Principles of Natural Philosophy, כרך 1,מהדורה 1

Isaac Newton - 1803
...converge continually t& equality, and before the end of that time approach nearer the one to the otlter than by any given difference, become ultimately equal. If you deny it, fuppofe them to be ultimately unequal, and let D be their ultimate difference. Therefore they cannot...
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A Dissertation on the Philosophy of Aristotle: In Four Books ...

Thomas Taylor - 1812 - 577 דפים
...any finite time converge continually to equality, and before that time approach nearer the one to the other than by any given difference, become ultimately equal. If you deny it ; suppose them to be unequal, and let D be their ultimate difference. Therefore they cannot approach...
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A Philosophical and Mathematical Dictionary: Containing an ..., כרך 2

Charles Hutton - 1815
...ultimate ratios. — LEM. 1. Quantities, and the ratios of quantities, which in any finite time converge continually to equality, and before the end of that time approach nearer the one to the other than by any given difference, become ultimately equal. — LEM. 2 shows, that...
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Encyclopaedia Perthensis, Or Universal Dictionary of the Arts ..., כרך 16

1816
...any finite time converge continually to equality, and before that time approach nearer the one to the other than by any given difference, become ultimately equal. If you deny it ; fuppo4e them to be ultimately unequal, and let D be their ultimate difference. Therefore they, cannot...
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The First Three Sections of Newton's Principia: With Copious Notes and ...

Isaac Newton - 1826 - 183 דפים
...RATIOS, BY THE HELP OF WHICH THE FOLLOWING PROPOSITIONS ARE DEMONSTRATED. LEMMA I. Quantities, and tfte ratios of quantities, which, in any finite time, tend...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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