The First Three Sections of Newton's Principia; With Copious Notes and Illustrations, and a Great Variety of Deductions and Problems

The First Three Sections of Newton's Principia; With Copious Notes and Illustrations, and a Great Variety of Deductions and Problems

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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. 1821 edition. Excerpt: ... and while the point K describes K B, T K being greater than T Q, R T must be greater than M T, and the arc E M of the curve must pass without the O E R, betwixt it and the tangent E T: and since any O described through E, upon a chord less than E B touching E T, falls within the (c) E R B, it is manifest that no such 0 can pass betwixt the curve E M and (c) E R B. Nor can any (c) E r b described upon a chord E b greater than E B touching E T pass between E R and E M; for let T K meet this (c) in r and q, then rT X Tj-ET = MT X TK;.. MT: rT:: Tj: T K, and since FKB (by hypothesis) passes through $5 so that the part of it, that is next adjoining B, must be within the arc b q of the 0 b q E, it follows that while K describes this part of F K B, T q must be greater than T K; and.. M T greater than r T. Therefore the arc E r of the (c) E r h is without the CHrve EM, and passes betwixt it and the tangent E T. Hence no (c) whatever can pass betwixt E M and E R; and consequently the (c) E R B has the same curvature with E M at E. Suppose now that the part of the curve B K F, that is next adjoining to B, falls within BQ (Fig. SI); then while K describes this part of the curve FKB.TK being less than T Q, R T must be less than M T, and the arc E M must fall within E R; and since any (c) described through E, upon a chord greater than E B, falls without the 0 E R, it is manifest that no such (c) can pass betwixt E R and E M. Nor can any 0 Eri described upon a chord E b less than EB touching ET, pass between E R and E M; for let T K meet this (c) in r and q, and M T beiug: r T:: T q: T K, and T q being less than T K while K describes K B, M T must be less than r T; and consequently the arc E r must fall withishow more

Product details

  • Paperback | 36 pages
  • 189 x 246 x 2mm | 82g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236536150
  • 9781236536150