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Books Books 1 - 10 of 62 on QUANTITIES, AND THE RATIOS OF QUANTITIES, WHICH IN ANY FINITE TIME CONVERGE CONTINUALLY....  
" 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. "
The Mathematical Principles of Natural Philosophy - Page 41
by Sir Isaac Newton, John Machin - 1729
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The Analogy of Divine Wisdom: In the Material, Sensitive, Moral, Civil and ...

Richard Barton - Analogy (Religion) - 1750 - 234 pages
...Lemma of his book of mathema-> tical principles of natural philofophy is : Quantities, and the ratio of quantities, which in any finite time converge continually...to the other, than by any given difference, become ultimately equal. This is plainly the fame, tho' in other words, with the principles of the .antient...
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Institutes of Natural Philosophy: Theoretical and Practical

William Enfield, Alexander Ewing - Astronomy - 1811 - 428 pages
...equal to one 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 nearer to each other than by any given difference, become ultimately equal. If you deny it, let them be ultimately...
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A Dissertation on the Philosophy of Aristotle: In Four Books ...

Thomas Taylor - Philosophy - 1812 - 577 pages
...the mathematical part of the Newtonian philosophy depends is this : " That quantities and the ratios of quantities, which in 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....
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A philosophical and mathematical dictionary: containing an ..., Volume 2

Charles Hutton - Science - 1815
...first; containing the doctrine of prime and ultimate ratios. LEM. 1. Quantities, and the ratios of quantities, which in any finite time converge continually...to the other than by any given difference, become ultimately equal. LEM. 2 shows, that in a space bounded by two right lines and a curve, if an infinite...
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Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volume 16

Encyclopedias and dictionaries - 1816
...depends on the following lemmas ; of which the firlt is the principal. LEM. I. Quantities, and tbe ratios of quantities, which in 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....
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The first three sections of Newton's Principia: with copious notes and ...

Sir Isaac Newton - Curves, Plane - 1826 - 183 pages
...ARE 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 nearer to each other than by any given difference, become ultimately equal. JF you deny it, let them be ultimately...
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The London encyclopaedia, or, Universal dictionary of science, art ...

Thomas Curtis (of Grove house sch, Islington)
...depends on the following lemmas; of which ihe first is the principal. Lem. I. Quantities, and the ratios of quantities, which in any finite t'ime converge continually to equality, and before that time approach nearer the one to the other than by any given difference, become ultimately equal....
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The Treasury of Knowledge and Library of Reference: A million of facts [The ...

Reference - 1850
...Limma 1. Quantities, and thera- '! tios of quantities, which, in any finite I term, convei ty, and befc approach nearer the one to the other than by any given difference, become ultimately equal. Lemma 2. Snows, that, in a space bounded by two right lines and a curve, if an infinite...
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The Three First Sections and Part of the Seventh Section of Newton's ...

Sir Isaac Newton - Dynamics of a particle - 1850 - 163 pages
...ARE 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 nearer to each other than by any given difference, become ultimately equal. IF you deny it, let them be ultimately...
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Treasury of Knowledge and Library of Reference, Volume 3

Samuel Maunder - 1855
...quantities, which, in any finite term, converge continually to equalir ty, and before the end ot thai time approach nearer the one to the other; than by any given dilTcrence, become uftimatelv equal. Lemma 2. Shows, that, in a space bounded by two right lines and...
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