An Account of Sir Isaac Newton's Philosophical Discoveries. 2. Ed

An Account of Sir Isaac Newton's Philosophical Discoveries. 2. Ed

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1750 edition. Excerpt: ...' P z from a from the loss of velocity that happens by its impulfizs at n and 1-2, upon the contiguous planes. That multiplying the number of planes from c to a A, till the path of the body becomes curvilinear, the velocity at A will be accurately the same as in the perpendicular fall c B. or of any two homologous lines belonging to the _ Coral. 4. Let A 1) (Fig. 1V.) be the diameter ofa circle touching the horizontal line in A; CA, ca, any two chords drawn to A. Then, if bodies descend by the force of gravity along these chords, the times of descent will be equal; and the velocities will be proportional to the chords cA, c A. For, joining DC, 1) c, and making c B, ce, perpendiculars to the diameter; because the triangles DCA, E CA are fimilar, as also DCA, ecA; it is easily shewn, that: c A is to cA in the subdtlplicate ratio of the elevations AE, A e: and this compounded with the same ratio inverted, gives the ratio of equality 5 which, by Coral. 1. is that of the times. And, by Coral. 2. the velocities are in the subduplicate ratio of an to A e, or that of CA to c A. I. Of the mation of przgjectiles." PROPOSITION I. Fig. V. The line dr-zsbribed by a ben-ay body, thrown in any direction not perpendicular to t/ae horizon, is a parabola. Suppose a body projected in the direction A n, with the velocity it would have acquired by falling from B to A, the body, by that force alone acting upon it, would uniformly describe the'right line A D; and any part of the line of direction, as AH, reprez sents the time in which it would be described. Suppose that the force of gravity, acting alone, would have, in the same time, carried the body from A to P', compleat the parallelogram A PMH, and, at the end of the time represented by A H, the more

Product details

  • Paperback | 68 pages
  • 189 x 246 x 4mm | 141g
  • United States
  • English
  • black & white illustrations
  • 123684999X
  • 9781236849991