 | Colin Macfarquhar, George Gleig - 1797 - 450 דפים
...the Newtonian philofophy depends on the following lemmas ; of which the firil is the principal. LEM. I. Quantities, and the ratios of quantities, which in any finite time converge continually to cqua- Nrwtonhn lily, and before that time approach nearer the one to l'1-il..UT.hy.... | |
 | Isaac Newton - 1803 - 310 דפים
...offirft and laft ratios of quantities, by the help whereof we demonjirate the propofitioits that follow. 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... | |
 | Isaac Newton - 1826 - 208 דפים
...throughout unreservedly borrowed from every valuable source within his reach. MATHEMATICAL PRINCIPLES SECTION I. OF THE METHOD OF PRIME AND ULTIMATE RATIOS,...PROPOSITIONS ARE DEMONSTRATED. LEMMA I. Quantities, and tfte ratios of quantities, which, in any finite time, tend continually to equality ; and, before the... | |
 | Thomas Curtis (of Grove house sch, Islington) - 438 דפים
...the Newtonian philosophy 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... | |
 | Benjamin Theophilus Moore - 1863 - 320 דפים
...This line FT, which is the limiting position of PQ, is the tangent to the curve at the point P. 55. Lemma I. Quantities, and the ratios of quantities,...any finite time, tend continually to equality, and which, before the end of that time, approach nearer to each otli-er than by any assigned difference,... | |
 | Sir Isaac Newton - 1863 - 316 דפים
...FIRST BOOK CONCERNING THE MOTION OF BODIES. SECTION I. ON THE METHOD OF PRIME AND ULTIMATE RATIOS. LEMMA I. Quantities, and the ratios of quantities, which, in any finite time, tend constantly to equality, and which, before the end of that time, approach nearer to each other than... | |
 | Isaac Newton, Percival Frost - 1863 - 312 דפים
...FIRST BOOK CONCERNING THE MOTION OF BODIES. SECTION I. ON THE METHOD OF PRIME AND ULTIMATE RATIOS. LEMMA I. Quantities, and the ratios of quantities, which, in any finite time, tend constantly to equality, and which, before the end of that time, approach nearer to each other than... | |
 | H. G. Rush - 1887 - 156 דפים
...consult lemma 1 of the Principia and find that the equality of Q x and Q v is not warranted. He says: — "Quantities, and the ratios of quantities, which, in any finite time, tend constantly to equality, and 'which, before the end of that time, approach nearer to each other than... | |
 | Florian Cajori - 1919 - 320 דפים
...fiant ultimo inaequales, & sit earum, etc." [As in the first edition.] Translation by Robert Thorp:1 8. "Quantities, and the ratios of quantities, which,...any finite time, tend continually to equality; and 1 Mathematical Principles of Natural Philosophy, by Sir Isaac Newton, Knight. Translated into English,... | |
 | Michel Blay - 1998 - 230 דפים
...fixed, and serve for their limit.51 Newton's statement of the first lemma is particularly illuminating: Lemma I Quantities, and the ratios of quantities, which in any finite time converge to equality, and before the end of that time approach nearer to each other than by any given... | |
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LEMMA I 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. 
