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Elementary Course of Geometry

Elementary Course of 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. 1847 Excerpt: ...two sides forming a triangle; if these two sides be not equal, they may be replaced by two others which are equal, and which, by the last theorem, will inclose a greater triangle. This process may be repeated with all the sides of the polygon. THEOREM III. Of all triangles formed Kith two given sides, that is, a maximum in which the two given sides make a right angle. For with the same base it will have the greater altitude. These definitions are suited to our present purpose. THEOREM IV. Of all polygons formed with sides all given except one side, that is, a maximum, of which the given sides are inscribed in a semicircle, of which the side not given is the diameter. E Let ABCDEF be the maximum polygon formed with sides all given except AB. Join AD, BD; then ADB must be a right angle: otherwise, preserving the parts BCD and ADEF the same, the triangle ADB might be increased (th. 3); the point D must, therefore, be in the semicircumference described on AB as a diameter. In the same manner it may be proved that the points E, F, C, &c., must be in the semicircumference. Q. E. D. Schol. There is but one way of forming the polygon; for if, after having found a circle which satisfies the requisition, a larger circle be supposed, the chords which are the sides of the polygon correspond to smaller angles at the center, and the sum of these will be less than two right angles. THEOREM V. Of all polygons formed with given sides, that is, a maximum which can be inscribed in a circle. G Let ABCEFG be an inscribed polygon, abcefg one which is not capable of being inscribed, and of equal sides with the former; draw the diameter EM; join AM, MB; upon ab make the triangle abm--ABM, and join em. By th. 4, EFGAM efgam and ECBM ecbm... by addition, EFGAMBC minus AMB efgamb...


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Product Details
  • ISBN-13: 9781150343452
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 64
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1150343451
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 132 gr


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