An Elementary Treaise on Plane and Solid Geometry.
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An Elementary Treaise on Plane and Solid Geometry.

An Elementary Treaise on Plane and Solid Geometry.


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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.1855 Excerpt: ... Intersection and Angle of two Planes. upon the extent, but merely upon the position of the planes. 315. Theorem. The angle of two planes, which cut each other, is measured by the angle of two lines drawn perpendicular to the common intersection of the two planes, at the same point, one in one of the planes, and one in the other. Proof. In order to show the legitimacy of this measure we have only to prove that the angle of the two lines is proportional to the angle of the two planes. Let AB (fig. 147) be the common intersection of the two planes; and let AC and AD be the two lines drawn in these planes perpendicular to the common intersection AB. Let a third plane be drawn having also the common intersection JIB with the two given planes, and let AE be drawn in this plane perpendicular to JIB. We are to prove that the angle of the planes DAB and CAB is to that of the two planes EAB and CAB as BAC is to EAC. For this purpose, suppose the angles of the planes to be to each other as any two whole numbers, and let the angle of the two planes CAB and a AB be their common divisor, A a being perpendicular to AB. The angle CA a must be a common divisor of the two angles CAE and CAD; and it is shown by precisely the reasoning so often adopted, that the angles of the planes are to each other as CAD to CAE. 316. Corollary. When the angle CAD is a right angle, the planes are perpendicular to each other. 317. Definitions. A straight line is perpendicular to a plane, when it is perpendicular to every straight line drawn through its foot in the plane. Line Perpendicular to a Plane. Reciprocally, the plane, in this case, is perpendicular to the line. The foot of the perpendicular is the point in which it meets the plane. 318. Theorem. When a straight line is perpendicular t...


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Product Details
  • ISBN-13: 9781151111135
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 36
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1151111139
  • Publisher Date: 01 Feb 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 82 gr


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