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Geometrical Conics; Including Anharmonic Ratio and Projection

Geometrical Conics; Including Anharmonic Ratio and Projection


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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. 1863 Excerpt: ...a hyperbola. Show that a pair of their common chords are parallel to PQ. One of these chords being R8, prove that if Pit touches the hyperbola at P, then QS touches it at 8. 33. Prove also that the straight line drawn from T to the intersection of PS, QR, bisects PQ. 34. A hyperbola, of given eccentricity, always passes through two given points; if one of its asymptotes always pass through a third given point in the same straight line with these, the locus of the centre of the hyperbola will be a circle. 35. If, from any point P in the hyperbola, BPQS be drawn meeting the hyperbola in P, Q, and the asymptotes in B, S, then PK, QL being drawn parallel to one asymptote to meet the other, LS=PK. 36. If a chord PQ intersect the asymptotes in R, S, and a tangent RE be drawn to the hyperbola; then, PM, QN, EL being drawn parallel to one asymptote and meeting the other, 2EL is equal to PM+ QN. 37. Tangents through V cut one asymptote in S, T and the other in 8 T; prove that VS: V8' = VT': VT. 38. The area of the sector of a hyperbola made by joining any two points of it to the centre is equal to the area of the segment made by drawing parallels from those points to the asymptotes. 39. Lines drawn parallel to an asymptote from the points P, Q, B, 8, on the curve, meet the other asymptote in K, L, M, N. Prove that the areas PQKL, BSMN, will be equal, if PK: QL = BM:8N. 40. The lines PK, QL, BM, drawn parallel to one asymptote, meet the other in K, L, M) P, Q, B are points on the curve. Prove that, if QL bisect the area PKMB, it will be a mean proportional between PK and BM. CHAPTER VIII. THE RECTANGULAR HYPERBOLA. In the Rectangular or Equilateral Hyperbola the asymptotes are at right angles and the axes equal. In the second proposition of the preceding chapter, if CB.


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Product Details
  • ISBN-13: 9781231131831
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 52
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1231131837
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 109 gr


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