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The Normal Elementary Geometry; Embracing a Brief Treatise on Mensuration and Trigonometry: Designed for Academies, Seminaries, High Schools, Normal Schools, and Advanced Classes in Common Schools

The Normal Elementary Geometry; Embracing a Brief Treatise on Mensuration and Trigonometry: Designed for Academies, Seminaries, High Schools, Normal Schools, and Advanced Classes in Common Schools


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About the Book

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. 1865 Excerpt: ...two planes which cut each other are both perpendicular to a third plane, their intersection is perpendicular to that plane. 6. Prove that through a given line of a given plane, only one plane perpendicular to the given plane can be passed. 6. Prove that through a line parallel to a given plane, only one plane perpendicular to the given plane can be passed. 7. If two planes which intersect contain two lines parallel to each other, the intersection of the planes will be parallel to the lines. 8. If a line is parallel to one plane and perpendicular to another, these two planes are perpendicular. 9. Only one plane can be drawn through a given point parallel to a given plane. 10. If two planes are parallel to a third, they are parallel to each other. 11. If two lines are parallel in space, and planes be passed through them perpendicular to a third plane, the two planes will be parallel. PROBLEMS. The following problems are easily solved from the principles already presented. 1. To erect a perpendicular to a given plane at a given point of the plane. (See Prop. III.) 2. To construct a plane parallel to a given plane. 3. To construct a plane perpendicular to a given plane intersecting it in a given straight line. 4. To draw a line from a given point of a plane making any given angle with the plane. 5. To draw a plane intersecting a given plane and making any given angle with it. 10 BOOK VI. POLYEDRONS. DEFINITIONS. 1. A PoLYEDKONisa volume bounded by polygons. The bounding polygons are called the faces of the polye dron; the lines in which the faces meet are called edges; and the points in which the edges meet are called vertices of the polyedron. 2. A Pr1sm is a polyedron, two of whose faces are equal polygons, having their homologous sides parallel; the other fa...


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Product Details
  • ISBN-13: 9781232282457
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 48
  • Spine Width: 3 mm
  • Weight: 104 gr
  • ISBN-10: 1232282456
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Designed for Academies, Seminaries, High Schools, Normal Schools, and Advanced Classes in Common Schools
  • Width: 189 mm


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The Normal Elementary Geometry; Embracing a Brief Treatise on Mensuration and Trigonometry: Designed for Academies, Seminaries, High Schools, Normal Schools, and Advanced Classes in Common Schools
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