 | Isaac Newton - Celestial mechanics - 1729 - 444 pages
...truly the ratio's of u'timate quantities, but limits towards which the ratio's of quantities decreafing without limit, do always converge ; and to which they...approach nearer than by any given difference, but n.ver go beyond, nor in effed attain to, till the quantities are dim:nilhed in wfiaitttm. This thing... | |
 | Isaac Newton - Celestial mechanics - 1803 - 344 pages
...truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreafmg without limit do always converge ; and to which they...beyond, nor in effect attain to, till the quantities are diminifhed in injinitum. This thing will appear more evident in quantities infinitely great. If two... | |
 | John Mason Good - 1819 - 788 pages
...nsurable!!, in the lOtli 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." Lm. II. If in any figure A... | |
 | 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.' 641 » C FB em. II. If in... | |
 | 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
...incommensurables in tha 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 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 - 576 pages
...in his article "On the Relations of the Philosophy of Spinoza and that of Leibniz," Mind, NS No 31 . 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... | |
 | Florian Cajori - Mathematics - 1919 - 294 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...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... | |
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For those 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 approach nearer than by any given... 
