 | Isaac Newton - Celestial mechanics - 1803 - 310 pages
...tlie ratios of ultimate quantities, but limits towards which 'he ratios of quantities . decreafing without limit do always converge ; and to which they...any given difference, but never go beyond, nor in eflècì; attain to, 'ill the quantities are diminiilied in irifiiiitum. This thing will appear more... | |
 | John Mason Good - 1813 - 830 pages
...incommensurables, in the 10th book of his Elements. But this objection is founded ou a false (apposition. For those ultimate ratios with which quantities vanish...truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing continually approach." LRM. II. If in any figure... | |
 | Thomas Luby - Astronomy - 1828 - 368 pages
...incommensurables, in the 10th book of his Elements. But this objection is founded on a false supposition. For those ultimate ratios with which quantities vanish...truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing without limit do always converge; and to which they... | |
 | Science - 1828 - 456 pages
...his Scholium to the XL Lemma of his Principia. Speaking of the nature of ultimate ratios, he says: " Those ultimate ratios with which quantities vanish,...truly the ratios of ultimate quantities, but limits, towards which the ratios of quantities decreasing without limit do always converge; and to which they... | |
 | Thomas Curtis (of Grove house sch, Islington) - 438 pages
...incommensurables, in the tenth book of his elements. But this objection is founded on a false supposition. For those ultimate ratios with which quantities vanish...truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing continually approach.' Lem. II. If in the figure... | |
 | Isaac Newton - Celestial mechanics - 1848 - 606 pages
...incommensurables, in the 10th Book of his Elements. But this objection is founded on a false supposition. For those ultimate ratios with which quantities vanish...truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing without limit do always converge ; and to which they... | |
 | Robert Potts - Algebra - 1879 - 672 pages
...incommensurables in the tenth book of his Elements. But this objection is founded on a falso supposition. For those ultimate ratios with which quantities vanish...truly the ratios of ultimate quantities, but limits towards which tho ratios of quantities decreasing without limit do always converge, and to which they... | |
 | Robert Potts - 1879 - 668 pages
...incommouaurables in tho tenth book of his Elements. But this objection is founded on a false supposition. For those ultimate ratios with which quantities vanish...truly the ratios of ultimate quantities, but limits towards which tho ratios of quantities decreasing without limit do always converge, and to which they... | |
 | Albert Taylor Bledsoe - Mathematics - 1886 - 253 pages
...all. Mr. Robins has suppressed an important clause in the definition of Newton. Newton says: " These ultimate ratios with which quantities vanish are not...truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing without limit do always converge, and to which they... | |
 | Bertrand Russell - Mathematics - 1903 - 565 pages
...other hand, definitely asserts that his fluxion is not a fraction. "Those ultimate ratios, 1 'he says, "with which quantities vanish are not truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing without limit do always converge, and to which they... | |
| |
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 approach nearer than by any given difference,... 
