 | Isaac Newton - Celestial mechanics - 1803 - 310 pages
...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... | |
 | 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.... | |
 | 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.... | |
 | 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... | |
 | Edward Dingle - Creation - 1868 - 350 pages
...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... | |
 | James Ralston Skinner - Pyramids - 1875 - 354 pages
...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."... | |
 | Catherinus Putnam Buckingham - Calculus - 1875 - 362 pages
...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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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. 
