Plane Geometry Volume 1 by Thomas Hunter at Bookstore UAE
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Plane Geometry Volume 1

Plane Geometry Volume 1


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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. 1872 Excerpt: ...the equality of the triangles so formed. 11. Easily demonstrated by means of the propositions in the beginning of Book I. relating to the equality of triangles. 12. Through F, the middle point of AC, draw KE perpendicular to AB: produce CD to E, and draw CH perpendicular to FG. It is easy to prove that the sum of the angles HCD and A IK CHG is equal to two right angles, the theorem. Hence the truth of 13. Required to prove that DB2]AC2=AB2-f BC2+DC2+AD2-4FE2. See Props. XXL and XVI., Cor. The student commences DC2+CB2= 2DE2+2EC2; and, followk ing up this line of demonstration, the truth of the theorem is easily established. 14. It is required to prove that the triangles ABC, AEF, GBL, and CMN are all equal. A glance will show the equality ofABCandAEF. BH is made N equal to AB, and KC to AC. The student can now prove that the triangles LHB and KCM are each equal to ABC (Prop. IV., Bk. I.); and by Prop. IX. he can demonstrate that LBH and KCM are respectively equal to LBG and CMN. D 15. It is required to prove that the sum of the squares of AE and ED is equal the sum of the squares of CE and EB. Draw the diagonals CB and AD, and join the points E and F. See Props. IV. and XXI. 16. It is required to prove that AD2+BC2=AC2+DB2 +2(AB.CD). Erect the perpendiculars AE and BF, and produce CD to E andF. The students who can solve or demonstrate without the aid of the Key should be encouraged to do so; and if they can discover other and easier methods, so much the better. The teacher is recommended to make his reviews in Geometry by means of test examples. Indeed, two or three of these, carefully selected, compel a general review of the previous principles. BOOK IIL DEFINITIONS. 1. An Arc is any portion of the circumference of a circle. 2. A Chord is a line joining th..


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Product Details
  • ISBN-13: 9781235945960
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 30
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1235945960
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 73 gr


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