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Wentworth's Solid Geometry

Wentworth's Solid Geometry


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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. 1899 Excerpt: ...cone may be generated by the revolution of a right triangle about one of the sides of the right angle, it is called a cone of revolution. In this case the hypotenuse corresponds to an element of the surface and is called the slant height. 599. Conic Section. A section formed by the intersection of a plane and the conic surface of a cone of revolution is called a conic section. Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 In Fig. 1 the conic section is two intersecting straight lines, and this is discussed in 600. This is true for all kinds of cones. In Fig. 2 the conic section is a circle, and this is discussed in 601. In Fig. 3 the conic section is called an ellipse, the form a circle seems to take when looked at obliquely. The orbit of a planet is an ellipse. In Fig. 4 the conic section is a parabola, the path of a projectile (in a vacuum). Here the cutting plane is parallel to an element. In Fig. 5 the conic section is an hyperbola. The general study of conic sections is not a part of elementary geometry, but the names of the sections may profitably be known. Proposition XXV. Theorem 600. Every section of a cone made by a plane passing through its vertex is a triangle. Given a cone, with AVB a section made by a plane passing through the vertex V. To prove that A VB is a triangle. Proof. AB is a straight line. 429 Draw the straight lines VA and VB. The lines VA and VB are both elements of the surface of the given cone. 594 These lines lie in the cutting plane, since their extremities are in the plane. 422 Hence VA and VB are the intersections of the conic surface with the cutting plane. But VA and VB are straight lines. Const. Therefore the intersections of the conic surface and the plane are straight lines. Therefore the section ...



Product Details
  • ISBN-13: 9781151834607
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 44
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1151834602
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 95 gr


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