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" ... quantities is that with which they begin to be. And the first or last sum is that with which they begin and cease to be (or to be augmented or diminished). There is a limit which the velocity at the end of the motion may attain, but not exceed. This... "
A History of the Conceptions of Limits and Fluxions in Great Britain, from ... - Page 10
by Florian Cajori - 1919 - 299 pages
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 8

John Mason Good - 1819 - 788 pages
...end of the motion may attain, but not exceed ; and this is the ultimate velocity. And there is the like limit in all quantities and proportions that...geometrical. But whatever is geometrical we may be allowed to make use of in determining and demonstrating any other thing that is likewise fometrical. MIS C EJLJLAXIE...
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The London encyclopaedia, or, Universal dictionary of ..., Part 2, Volume 15

Thomas Curtis (of Grove house sch, Islington) - 438 pages
...end of the motion may attain, but not exceed ; and this is the ultimate velocity. And there is the like limit in all quantities and proportions that...geometrical. But whatever is geometrical we may be allowed to make use of in determining and demonstrating any other thing that is likewise geometrical. 'It may...
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Elementary algebra, with brief notices of its history

Robert Potts - 1879 - 668 pages
...at the end of the motion may attain, but not exceed. This is the ultimate velocity. And there is the like limit in all quantities and proportions that...be allowed to use in determining and demonstrating every other thing that is likewise geometrical. "It may also be objected that if the ultimate ratios...
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Elementary algebra: with brief notices of its history

Robert Potts - Algebra - 1879 - 672 pages
...at the end of the motion may attain, but not exceed. This ie the ultimate velocity. And there is the like limit in all quantities and proportions that...geometrical. But whatever is geometrical we may be allowed to nee in determining and demonstrating every other thing that is likewise geometrical. "It may also be...
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The Philosophy of Mathematics: With Special Reference to the Elements of ...

Albert Taylor Bledsoe - Mathematics - 1886 - 253 pages
...at the end of the motion may attain, but not exceed. This is the ultimate velocity. And there is the like limit in all quantities and proportions that begin and cease to be." * Thus, the ultimate ratio of quantities, as considered by Newton, is the ratio, not of quantities...
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Berkeley's Philosophy of Mathematics

Douglas M. Jesseph - Mathematics - 1993 - 344 pages
...at the end of the motion may attain, but not exceed. This is the ultimate velocity. And there is the like limit in all quantities and proportions that...strictly geometrical. But whatever is geometrical we may use in determining and demonstrating any other thing that is also geometrical" (Principia I, 1, Scholium)....
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The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise

Mary Tiles - Mathematics - 2004 - 276 pages
...at the end of the motion may obtain, but not exceed. This is the ultimate velocity. And there is the like limit in all quantities and proportions that...determine the same is a problem strictly geometrical, (Newton, 1934, pp. 38-9) In this context differentiation is (a) defined as an algebraic operation,...
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Conflicts Between Generalization, Rigor, and Intuition: Number Concepts ...

Gert Schubring - Mathematics - 2005 - 700 pages
...is a genuinely geometrical task to examine these values because the limit is fixed and determined: “And since such limits are certain and definite,...determine the same is a problem strictly geometrical” (ibid., 39; orig. 87 f.). Finally, Newton gives a hint at the conception of mathematizing limit processes...
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The Rise and Development of the Theory of Series up to the Early 1820s

Giovanni Ferraro - Mathematics - 2007 - 392 pages
...at the end of the motion may attain, but not exceed. This is the ultimate velocity. And there is the like limit in all quantities and proportions that begin and cease to be" (Newton [PN, 87]). 91For a more general discussion of the differences between the 17th- and 18th-century...
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