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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 Analogy of Divine Wisdom: In the Material, Sensitive, Moral, Civil and ... - Sivu 6
tekijä(t) Richard Barton - 1750 - 234 sivua
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The Mathematical Principles of Natural Philosophy, Nide 1,Numero 1

Isaac Newton - 1803
...LEMMA I. Quantities, and the ratios of quantities, which in any finite time 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...

Institutes of Natural Philosophy: Theoretical and Practical

William Enfield - 1811 - 428 sivua
...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...

A Dissertation on the Philosophy of Aristotle: In Four Books ...

Thomas Taylor - 1812 - 577 sivua
...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....

Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Nide 16

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....

The First Three Sections of Newton's Principia: With Copious Notes and ...

Isaac Newton - 1826 - 183 sivua
...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...

The London encyclopaedia, or, Universal dictionary of science ..., Osa 2,Nide 15

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....

The Three First Sections and Part of the Seventh Section of Newton's ...

Sir Isaac Newton - 1850 - 163 sivua
...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...

Hints from the Dawning; Or, The Creation Story Considered Under the Laws of ...

Edward Dingle - 1868
...grace. of 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 nearer to each other than by any given difference, become ultimately equal." They should have seen that the...

Key to the Hebrew-Egyptian Mystery in the Source of Measures Originating the ...

James Ralston Skinner - 1875 - 324 sivua
...geometrically false statement, as regards exactitude of definition — palpably so. His " Lemma I " states : "Quantities and the ratio of quantities, which in...time converge continually to equality, and, before that lime, approach nearer the one to the other, than by any given difference, ultimately become equal."...

Elements of the Differential and Integral Calculus: By a New Method, Founded ...

Catherinus Putnam Buckingham - 1875 - 343 sivua
...Quantities and ratios of quantities, which in any finite time converge continually to equality, aml before the end of that time approach nearer the one to the other than by any gircn difference, become ultimately equal." The principle here stated would be applied to the solution...




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