On Infinity; And on the Sign of Equality

On Infinity; And on the Sign of Equality

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1865 edition. Excerpt: ... form. Kepler, Cavalieri, Wallis, and Newton, distinctly recognize the moment; Leibnitz, and (I think) Barrow, make it of no account: though Leibnitz, as we have seen, uses it in illustration. Newton, who overtly employed infinitesimals in his early fluxions, in his private explanations to Locke, and in his communication upon quadratures to Wallis, introduces moments into the first edition of the Principia (Book n. Lemma 2) in a manner which can be only infinitesimal: in the second edition there is a change of phrase, which seems to have reference to the express renunciation of infinitesimals which had taken place a few years before. But in both they are principia jamjam nascentia finitarum magnitudinum. As late as 1714 Newton1 writes to Keill, 6 Moments are infinitely little parts.' It cannot therefore be shewn that Newton ever completely abandoned the notion of infinitesimals: but it is probable that he halted between this notion, and that of which Leibnitz makes use when he adds a point to a line in illustration of incomparably small augmentation. What I have to do is to prevent any reader of mine from carrying this ambiguity into his interpretation of my view of infinitesimals. The 0 must be the ultimate infinitesimal, the point, if we be speaking of length; the correlative of the ultimate infinite, the whole length which the parallel never does meet, as distinguished from the infinites at which lines meet under an infinitely small angle. Take a square, and let all the lines be drawn which are parallel to one pair of sides and bounded by the other. We cannot think of these lines as successively drawn, but we can take them as we take the individuals when we think of a species. This I say because there are those who will tell me that I cannot...
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Product details

  • Paperback | 28 pages
  • 189 x 246 x 2mm | 68g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236596056
  • 9781236596055