 | 1876 - 1088 pages
...its last place and the motion ceases, nor after, but at the very instant it arrives ; that is, the velocity with which the body arrives at its last place,...the ratio of the quantities, not before they vanish, not afterwards, but with which they vanish. In like manner, the first ratio of nascent quantities is... | |
 | Albert Taylor Bledsoe - Mathematics - 1886 - 253 pages
...neither before it arrives at its last place and the motion ceases, nor after, but at the very instant it arrives ; that is, that velocity with which the...quantities not before they vanish, nor afterwards, but with which they vanish. In like manner the first ratio of nascent quantities is that with which they... | |
 | Isaac Newton - Curves, Plane - 1900 - 320 pages
...last position and with which the motion ceases. And, similarly, by the ultimate ratio of vanishing quantities is to be understood the ratio of the quantities, not before they vanish nor after, but with which they vanish. Likewise, also, the prime ratio of nascent quantities is the ratio... | |
 | Florian Cajori - Mathematics - 1919 - 294 pages
...instant when it arrives ; that is, that very velocity with which the body arrives at its last place, when the motion ceases. And, in like manner, by the ultimate...ratio of the quantities, not before they vanish, nor after, but that with which they vanish./ In like manner, the first ratio of nascent quantities is that... | |
 | Robert S. Cohen, J.J. Stachel, Marx W. Wartofsky - Biography & Autobiography - 1974 - 702 pages
...proportion, before the quantities have vanished is not the ultimate and when they are vanished, is none.... And in like manner, by the ultimate ratio of evanescent...quantities not before they vanish, nor afterwards, but with which they vanish. (Struik, 1969, pp. 299-300) To which Bishop Berkeley in 1734 retorted: And... | |
 | C.H.Jr. Edwards - Mathematics - 1994 - 368 pages
...specifies that By the ultimate ratio of evanescent quantities (ie, ones that are approaching zero) is to be understood the ratio of the quantities not before they vanish, nor afterwards, but with which they vanish. . . . Those ultimate ratios with which quantities vanish are not truly the... | |
 | Morris Kline - Mathematics - 1982 - 380 pages
...at its last place and the motion ceases, nor after, but at the very instant it arrives; that is, the velocity with which the body arrives at its last place, and with which the motion ceases. And, in hke manner, by the ultimate ratio of evanescent quantities is to be understood the ratio of the quantities... | |
 | Morris Kline - Mathematics - 1990 - 434 pages
...at its last place, when the motion ceases, nor after; but at the very instant when it arrives. . . . And, in like manner, by the ultimate ratio of evanescent quantities is to be understood the ratio of quantities, not before they vanish, nor after, but that with which they vanish." In the Principia Newton... | |
 | Douglas M. Jesseph - Mathematics - 1993 - 344 pages
...neither before it arrives at its last place and the motion ceases, nor after, but at the very instant it arrives; that is, that velocity with which the...quantities not before they vanish, nor afterwards, but with which they vanish. In like manner the first ratio of nascent quantities is that with which they... | |
 | Philip J. Davis, Reuben Hersh, Elena Anne Marchisotto - Mathematics - 1995 - 520 pages
...its last place, when the motion ceases, nor after; but at the very instafit when it arrives. . . . And, in like manner, by the ultimate ratio of evanescent...ratio of the quantities, not before they vanish, nor after, but that with which they vanish." When he proceeded to compute, however, he still had to justify... | |
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But the answer is easy; for by the ultimate velocity is meant that with which the body is moved, neither before it arrives at its last place and the motion ceases, nor after, but at the very instant it arrives; that is, that velocity with which the body... 
