| Isaac Newton - 1803
...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 - 1811 - 428 sivua
...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 sivua
...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.... | |
| 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.... | |
| Isaac Newton - 1826 - 183 sivua
...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.... | |
| Sir Isaac Newton - 1850 - 163 sivua
...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 - 1868
...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 - 1875 - 324 sivua
...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 - 1875 - 343 sivua
...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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