 | Georg Wilhelm Friedrich Hegel - 2002 - 400 pagine
...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... | |
 | I. Grattan-Guinness - 2003 - 872 pagine
...Newton (7657: Book I, Section 1, Lemma 1) stated: 'Quantities and the ratios of quantities; which in any 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.' In his first published work on... | |
 | Laurence Richardson - 2007 - 232 pagine
...Newton, Philosophiae naturalis principia matematica, book 1 , lemma I: '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.' Quotation is taken from Sir Isaac... | |
 | John Lane Bell - 2005 - 354 pagine
...demonstrate the propositions that follow"; its first Lemma reads: Chapter 2 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;1 its third: ...the ultimate ratio... | |
 | Giovanni Ferraro - 2007 - 392 pagine
...the first of the 11 mathematical lemmas of Book 1 of Principia: Lemma 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. (Newton [PN, 73]) This lemma contains the following explicit hypotheses: (H1) two... | |
 | 1810 - 516 pagine
...that Newton meant in his first lemma in the Principia, where he says that " quantities, and the ratios of quantities, which in any finite time converge continually...to the other than by any given difference, become ultimately equal." It was the calling those results true which are only approximations indefinitely... | |
 | 1915 - 390 pagine
...reach their limits appears even more clearly in the following passage : "Quantities, and the ratios of quantities, which in any finite time converge continually...to the other than by any given difference, become ultimately equal."2 Other passages in the first book of the Principia allow variables to reach their... | |
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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 THE ONE TO THE OTHER THAN BY ANY GIVEN DIFFERENCE, BECOME ULTIMATELY EQUAL. 
