 | Richard Barton - Analogy (Religion) - 1750 - 278 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... | |
 | William Enfield - Astronomy - 1811 - 476 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... | |
 | Thomas Taylor - Philosophy, Ancient - 1812 - 622 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.... | |
 | Charles Hutton - Astronomy - 1815 - 686 pages
...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... | |
 | Encyclopedias and dictionaries - 1816 - 778 pages
...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.... | |
 | Isaac Newton - Curves, Plane - 1826 - 208 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... | |
 | Thomas Curtis (of Grove house sch, Islington) - 438 pages
...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.... | |
 | 1850 - 766 pages
...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... | |
 | Isaac Newton - Curves, Plane - 1850 - 184 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... | |
 | Samuel Maunder - 1855 - 766 pages
...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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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. 
