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A Geometrical Treatise on Conic Sections with Examples

A Geometrical Treatise on Conic Sections with Examples


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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. 1864 edition. Excerpt: ... plane to the axis of the cone, and will be greatest when this plane passes through the axis, in which case it will be double the constant angle between the axis and the generating line. If the cutting plane pass through a generating line dod' and be perpendicular to the plane containing this line and the axis, it will simply touch the cone along this line. Should the cutting plane not pass through the vertex, and be at right angles to the axis of the cone, the section will evidently be a circle. In any other case the section will, as we proceed to show, be a Parabola, Ellipse, or Hyperbola. Whatever be the position of the cutting plane with respect to the cone, we can-always suppose a plane drawn through the axis of the cone at right angles to it; and it will be convenient to have this latter plane represented by the plane of the paper as D Od. The cutting plane will therefore always be taken at right angles to the plane DOd of the paper. Peop. I. 69. The curve formed by the intersection of the surface of a right cone with a plane (which neither passes through its vertex nor is at right angles to its axis) will be a Parabola, Ellipse, or Hyperbola, according as the inclination of the cutting plane to the axis of the cone is equal to, greater, or less than the constant angle which the generating line forms with the axis. Let the plane of the paper represent the plane drawn through the axis IOT of the cone at right angles to the cutting plane; and let it intersect the surface of the cone in the two generating lines OD, Od. Let the cutting plane intersect the surface of the cone in the curve PA, and the plane of the paper in the line ANH. The curve will evidently be symmetrical with respect to this line. On AH take any point N, and through...


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Product Details
  • ISBN-13: 9781234230135
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 34
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1234230135
  • Publisher Date: 15 Jan 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 82 gr


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