 | Isaac Newton - Celestial mechanics - 1803 - 344 pages
...objection is founded on a falfe fuppofition. For thofe ultimate ratios with which quantities vanifh are not truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreafmg without limit do always converge ; and to which they approach nearer than by any given difference,... | |
 | John Mason Good - 1819 - 788 pages
...in the lOtli book of his Elements. But this objection is founded on a False supposition. For those ultimate ratios with which quantities vanish are not...towards which the ratios of quantities decreasing continually approach." Lm. II. If in any figure A ac E (PI. 129, fig. 1.) terminated by the r'ght line... | |
 | Encyclopedias and dictionaries - 1816 - 778 pages
...objection is founded on a falfc fuppofition. For thofe ultimate ratios with which quantities vanifh are not truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreafing continually approach." I,EM. IF. If in any figure A ac E (PI. CCXLVI. N° i.) terminated... | |
 | Thomas Curtis (of Grove house sch, Islington) - 438 pages
...in the tenth book of his elements. But this objection is founded on a false supposition. For those ultimate ratios with which quantities vanish are not...towards which the ratios of quantities decreasing continually approach.' 641 » C FB em. II. If in the figure AocE, terminated >e right line A a, A nd... | |
 | Robert Potts - Algebra - 1879 - 672 pages
...in the tenth book of his Elements. But this objection is founded on a falso supposition. For those ultimate ratios with which quantities vanish are not...ratios of ultimate quantities, but limits towards which tho ratios of quantities decreasing without limit do always converge, and to which they approach nearer... | |
 | Florian Cajori - Mathematics - 1919 - 294 pages
...in the tenth book of his Elements. But this objection is founded on a false supposition, for those ultimate ratios with which quantities vanish are not truly the ratios of ultimate quantities, but the limits to which the ratios of quantities, decreasing without end, always converge ; and to which... | |
 | Salomon Bochner - Mathematics - 1992 - 480 pages
...derivative of a function. He termed it an "ultimate ratio" and phrased its description thus: For those ultimate ratios with which quantities vanish are not truly the ratios of ultimate quantities, hut limits towards which the ratios of quantities, decreasing without a limit, do always converge:... | |
 | William Bragg Ewald - Mathematics - 2005 - 696 pages
...a false hypothesis. Those last ratios with which quantities vanish are not truly the ratios of last quantities, but limits towards which the ratios of quantities decreasing without limit always approach |appropinquant|; and to which they approach nearer than by any given difference, but... | |
 | Gert Schubring - Mathematics - 2005 - 700 pages
...“ultimate ratios” indeed meant limits that are more and more approximated by the ratios: For those ultimate ratios with which quantities vanish are not...truly the ratios of ultimate quantities, but limits toward which the ratios of quantities approach nearer than by any given difference (ibid., 39; orig.... | |
 | Mathematicians - 1915 - 390 pages
...issue in the "Achilles." For that reason Newton's statements on this point are of interest: "... those ultimate ratios with which quantities vanish are not...truly the ratios of ultimate quantities, but limits toward which the ratios of quantities decreasing without limit do always converge; and to which they... | |
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... ratios of quantities decreasing without limit do always converge, and to which they approach nearer than by any given difference, but never go beyond, nor in effect attain to, till the quantities are diminished in infinitum. 