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ספרים ספרים 11 - 20 מתוך 23 עבור 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 to each other than by any given difference, become ultimately equal. "
The Analogy of Divine Wisdom: In the Material, Sensitive, Moral, Civil and ... - עמוד 22
מאת Richard Barton - 1750 - 234 דפים
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Transactions of the Kansas Academy of Science, כרך 12

Kansas Academy of Science - 1890
..."-Method of Limits," as enunciated by one of the discoverers of the Calculus, that "quantities, and ratios of quantities, which in any finite time converge continually...time approach nearer the one to the other than by any difference, become ultimately equal,'1 we know that dropping the higher orders will give beyond a peradventure...
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Transactions of the ... Annual Meetings of the Kansas Academy of Science, כרך 12

Kansas Academy of Science. Meeting - 1890
..."Method of Limits," as enunciated by one of the discoverers of the Calculus, that "quantities, and ratios of quantities, which in any finite time converge continually...time approach nearer the one to the other than by any difference, become ultimately equal,'' we know that dropping the higher orders will give beyond a peradventure...
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The Great Pyramid Jeezeh

Louis Phillipe McCarty - 1907 - 586 דפים
...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 time, approach nearer the one to the other, than by any given difference, ultimately become equal."...
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The Historical Development of the Calculus

C.H.Jr. Edwards - 1994 - 368 דפים
...Principia is, in effect, Newton's attempted definition of the limit concept: "Quantities, and the ratios of quantities, which in any finite time converge continually...equality, and before the end of that time approach nearer to each other than by any given difference, become ultimately equal." In modern notation, we would...
תצוגה מקדימה מוגבלת - מידע על ספר זה

Never at Rest: A Biography of Isaac Newton

Richard S. Westfall - 1983 - 908 דפים
...a definition of equality which drew upon his work with infinite series. Quantities, and the ratios of quantities, which in any finite time converge continually...equality, and before the end of that time approach nearer to each other than by any given difference, become ultimately equal.65 Three further lemmas compared...
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The Nature of Mathematical Knowledge

San Diego Philip Kitcher Professor of Philosophy University of California - 1983 - 300 דפים
...announces an important new concept: "Quan10. See ibid., volume 3.1, pp. 180ff. titles and the ratios of quantities, which in any finite time converge continually...equality, and, before the end of that time approach nearer to one another by any given difference become ultimately equal." Here Newton comes close to advancing...
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Berkeley's Philosophy of Mathematics

Douglas M. Jesseph - 1993 - 322 דפים
...introduction of the doctrine of prime and ultimate ratios in the Principia: Quantities, and the ratios of quantities, which in any finite time converge continually...equality, and before the end of that time approach nearer to each other than by any given difference, become ultimately equal. (Principia I, 1, 1) Newton's proof...
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Lectures on the Hyperreals: An Introduction to Nonstandard Analysis

Robert Goldblatt - 1998 - 293 דפים
...Fluents. His conception of limits is conveyed by the following passages: Quantities, and the ratios of quantities, which in any finite time converge continually to equality, and before the end of time approach nearer to each other than by any given difference, become ultimately equal . . . Those...
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Numbers and Functions: Steps Into Analysis

R. P. Burn, Robert P. Burn - 2000 - 356 דפים
...continuity'. The E in our definition of limit is foreshadowed in Euclid XI, and also by Newton who wrote 'Quantities, and the ratio of quantities, which in...equality, and before the end of that time approach nearer to each other than by any aiven difference, become ultimately equal.' (Principia, Book 1, Lemma 1,...
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Philosophy of Nature

Georg Wilhelm Friedrich Hegel - 2002 - 392 דפים
...factor. See op. cit. bk. I lemma i, 'Quantities, and the ratios of quantities, which, in any finite tune converge 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, suppose them to...
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