| Richard Barton - Analogy (Religion) - 1750 - 234 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, Alexander Ewing - Astronomy - 1811 - 428 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 - 1812 - 577 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 - Science - 1815
...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
...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.... | |
| Sir Isaac Newton - Curves, Plane - 1826 - 183 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)
...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
...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... | |
| Sir Isaac Newton - Dynamics of a particle - 1850 - 163 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
...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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