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Manual of Geometry and Conic Sections

Manual of Geometry and Conic Sections


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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. 1876 Excerpt: ...the surface are the bases of the zone. If one of the limiting planes is tangent to the surface, the zone has but one base. 122. A spherical segment is a portion of a sphere included between two parallel planes. The distance between the planes is the altitude of the segment, and the sections which the planes cut from the sphere are the bases of the segment. If one of the limiting planes is tangent to the surface of the sphere, the segment has but one base. 123. A spherical sector is a volume that may be generated by any sector of a semicircle when the semicircle is revolved about its diameter. The spherical sector is usually bounded by a zone and two conic surfaces; if the axis coincides with one of the extreme radii of the circular sector, the spherical sector is bounded by a z ine and one conical surface. One of the conic surfaces may reduce to a plane. Propos1t1on V. Theorem. Any plane section of a sphere is a circle. Let the sphere OQ be cut by any plane ACD; let OQ be a rad1us of the sphere /" perpendicular to the plane ACD, and / piercing it at P. f Let A, C, and D, be any three points / of the intersection of the plane with the / surface of the sphere, and draw OA, OC, and OD. Because OA, OC, and OD are radii of the sphere they are equal; consequently the points A, C, and D, are in the circumference of a circle whose centre is P, (P. 4, Cor., B. 6). But A, C, and D, are any points in the line of intersection; hence, the intersection is a circle, which was to be proved. Cor. 1. If the cutting plane passes through the centre of the sphere, the radius of the section is equal to the radius of the sphere; such a section is called a great circle. If the cutting plane does not pass through the centre of the sphere, the radius of the section is less than...


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Product Details
  • ISBN-13: 9781233672660
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 70
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1233672665
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 141 gr


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