 | John Clarke - Celestial mechanics - 1730 - 382 pages
...them at the end of this Time to be unequal, and let the laft difference of them be called D : Then they cannot approach nearer to Equality than by the given Difference D, which is contrary to the Hypothefis. It is fuppofed in this Lemma, that the Time in which the Quantities... | |
 | William Enfield - Astronomy - 1811 - 476 pages
...nearer to each other than by any given difference, become ultimately equal. If you deny it, let them be ultimately unequal ; and let their ultimate difference...Therefore they cannot approach nearer to equality than by that given difference D 5 whichis contrary to the supposition. If a straight and a curve line, continually... | |
 | Rev. John Allen - Astronomy - 1822 - 508 pages
...differ from each other less, than by any given difference, are ultimately equal. If not, let them be ultimately unequal, and let their ultimate difference...equality, than by the given difference D ; contrary to the supposition. LEMMA II. If in any fgnre AacE bounded by two right lines Aa and AE at right dltgles 1o... | |
 | Rev. John Allen - Astronomy - 1822 - 516 pages
...differ from each other less, than by any given difference, are ultimately equal. If not, let them be ultimately unequal, and let their ultimate difference be D. Therefore they cannot approach nearerto equality, than by the given difference D ; contrary to the supposition. LEMMA II. If in any... | |
 | Isaac Newton, George Leigh Cooke - Curves, Plane - 1850 - 176 pages
...nearer to each other than by any given difference, become ultimately equal. IF you deny it, let them be ultimately unequal ; and let their ultimate difference...Therefore they cannot approach nearer to equality than by that given difference D. Which is against the supposition. Of any two quantities or two ratios coming... | |
 | Benjamin Theophilus Moore - Measurement - 1863 - 320 pages
...that time, approach nearer to each otli-er than by any assigned difference, became -ultimately equal. If not, let them become ultimately unequal, and let their ultimate difference be D. Therefore, (since they tend continually to equality), they cannot approach nearer to each other than by the difference... | |
 | Sir Isaac Newton - Curves, Plane - 1863 - 316 pages
...that time, approach nearer to each other than by any assigned difference, become ultimately equal. If not, let them become ultimately unequal, and let their ultimate difference be D. Hence, [since, throughout the time, they tend constantly to equality,] they cannot approach nearer... | |
 | Isaac Newton - Curves, Plane - 1900 - 320 pages
...that time, approach nearer to each other than by any assigned difference, become ultimately equal. If not, let them become ultimately unequal, and let their ultimate difference be D. Hence [since, throughout the time, they tend constantly to equality], they cannot approach nearer to... | |
 | Florian Cajori - Mathematics - 1919 - 294 pages
...to each other than by any given difference, become ultimately equal. " If you deny it, let them be ultimately unequal ; and let their ultimate difference...Therefore, they cannot approach nearer to equality than by that given difference D. Which is against the supposition. " Principia, Book /, Section /, Lemma II... | |
 | Niccol- Guicciardini - Mathematics - 2003 - 296 pages
...quantity, become ultimately equal.ยง Newton's ad absurdum proof runs as follows: If you deny this, *let them become ultimately unequal, and* let their ultimate difference be D. Then they cannot approach so close to equality that their difference is less than the given difference... | |
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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 by any assigned difference, become ultimately equal. 
