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An Elementary Course of Plane Geometry

An Elementary Course of Plane 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. 1868 Excerpt: ...through D' draw D' C parallel to D C: the point O where the two parallels intersect, being equidistant from the two sides of the angle, is in the bisecting line. Repeat the operation, making use as much as possible of the construction already made, so as to obtain a second point, O'. O O' will be the bisecting line. Two parallel secants intercept equal arcs. 203. This is another consequence of the symmetry of the circle with respect to the perpendicular let fall from the centre upon one of the secants or upon a line parallel to it. In turning the figure N A C M Fig. 176. (fig. 175) about this perpendicular, it will coincide with NBDM, and consequently the arc A 0 is equal to the arc B D. We are now enabled to solve the following problem: --Through a given point in a circumference, to draw a straight line parallel to a given secant to the circle. 204. Let A A' (fig. 176) be the secant, B the given point; take the length of the chord A B, and make A'B' equal to it; join B B' it will be the required parallel to the given secant. Suppose two pieces of a cornice or beading are to be fitted together (fig. 177), they must be cut so that the line of section makes with the edge an angle equal to half that which must be made by the two parts; that is to say, the joint bisects the angle which the parts make with each other. Hence the parts of a picture-frame and the side-posts of a door or window are cut at an angle of 450, in order that when they are fitted Fig. 177. together the angle made may be 900. The angle inscribed in a circle. 205. Any angle in a circle, having its apex on the ifc D Fig. 178. Fig. 179. circumference, is termed an inscribed angle; it is said to stand upon the arc intercepted by its sides. An inscribed angle is half the angle at the centre on t...


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Product Details
  • ISBN-13: 9781235288630
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 60
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1235288633
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 127 gr

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