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The Elements of Plane Geometry Volume 1-2

The Elements of Plane Geometry Volume 1-2


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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. 1884 Excerpt: ...Two triangles ABC, DBC are upon the same base BC, and AD is parallel to BC. If ABC is isosceles, shew that its perimeter is less than that of DBC. 68. The sum of the distances of any point in the base of an isosceles triangle from the two sides is constant. 69. If the base of an isosceles triangle be produced to any point, the difference of the distances of the point from the two sides is constant 70. Shew that the sum of the distances of any point within an equilateral triangle from the three sides is constant. 71. ABCD is a parallelogram, AD is bisected at E, and BC at F: shew that BE and DF trisect the diagonal AC. 72. In the triangle ABC, D and E are the middle points of BC and CA: shew that BE cuts off a third part from DA. 73-Shew that the three straight lines drawn from the vertices of a triangle to the middle points of the opposite sides meet in a point. SECTION IV. Problems., A Geometrical Problem is a proposition, of which the object is to effect some Geometrical construction. The solution of a Problem depends on the instruments, the use of which is allowed; and it will be readily understood that the more restricted the choice of instruments, the more limited will be the Problems which can be solved by their use, and the more difficult will the solution of many that are possible be found. Owing to the existence of this arbitrary element in the treatment of Problems, they are grouped together in a separate section. Though important as applications of Geometrical truths, it should be clearly, understood that Problems form no part of the chain of connected truths embodied in the Theorems of Geometry, so that, though they may advantageously be studied r in connection with the Theorems on which they directly depend, they are not a necessary part of the...


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Product Details
  • ISBN-13: 9781130749113
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 26
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 1130749118
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 68 gr


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