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Solid Geometry Developed by the Syllabus Method

Solid Geometry Developed by the Syllabus Method


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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. 1918 Excerpt: ... the mean proportional between them. where h is the altitude, and rx and r2 are the radii of the bases. 153. A monument is in the form of a pillar of granite 1 ft. in diameter and 12 ft. high, surmounted by the frustum of a cone 1 ft. high with an upper base of radius 10 in., and a cone of height 6 in. How much does the stone weigh at 175 lb. to the cubic foot? 185. SUMMARY OF PROPOSITIONS I. The Straight Line: (1) Sects equal: The edges of a prism are equal (107). The elements of a cylinder are equal (107). (2) Sects proportional: The edges of a pyramidal space cut by parallel planes are proportional (149). II. Tangent Planes And Sections: (1) Tangent planes: The plane determined by an element and a tangent to the base of a cylinder (or a cone) is tangent to the cylinder (or the cone), and conversely (119, 120, 163, 164). (2) Sections: (a) of a prismatic space: Parallel sections are congruent polygons (108). Any pair of opposite faces of a parallelepiped may be considered its bases (126); its opposite faces are congruent (126). (6) of a cylindrical space: Parallel sections are congruent (109). A section through an element of a cylinder is a parallelogram (117). (c) of a pyramidal space: Parallel sections are similar polygons (150); their areas are proportional to the squares of their distances from the vertex (150). (d) of a cone: A section parallel to the base of a circular cone is a circle (161). A section through an element is a triangle (160). III. Limiting Cases: If the number of faces of a prism (or a pyramid) of regular base, inscribed in or circumscribed about a circular cylinder (or a cone), is increased indefinitely, the lateral area and the volume of the prism (or the pyramid) approaches as its limit the lateral area and the volume of the cylind...


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Product Details
  • ISBN-13: 9781152612440
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 54
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1152612441
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 113 gr


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