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Elements of the Geometry of Planes & Solids

Elements of the Geometry of Planes & Solids


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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. 1828 Excerpt: ...equal to the half of the same angle, therefore the sides CB, and CE, are equal also; because the CD, and EB, are parallel and cut the sides AB, and AE, about the angle A, these sides are cut proportional: that furnishes the proportion; AC: CE=AD: DB; and because CE=CB, AC: CB=AD: DB, that is: the segments of AB, made by the CD, bisecting the opposite angle are as the sides of the triangle adjacent to them; which was to be demonstrated. 66. Theorem. When in a right angled triangle a perpendicular is drawn from the right angle upon the hypothenuse, this perpendicular is a mean proportional between the two segments of the hypothenuse; and each side about the right angle is a mean proportional between the hypothenuse, and the segment of it adjacent to that side. Appjlic Let the triangle ABC, fig. 72, ) be right angled at A, and the perpendicular, AD, be drawn from the right angle upon the hypothenuse BC, then will the following proportions take place as enounced, viz: BD: AD=AD: DC. BC: AB=AB: BD BC: CA=CA: CD. Demonstr. Because the AD, is perpendicular upon BC, the triangle ABC, is divided by it into two right angled triangles; the triangle ABC, has with the triangle ABD, the angle B, common, and with the triangle ACD, the angle at C; the angles at D, being right angles as also the angle A, of the triangle ABC, these three triangles are all equiangular; therefore, their sides opposite to the equal angles, or their homologous sides, are proportional; which gives the proportions following: by the triangles ABB, and ADC; BD: AD=AD: CD ADB, and ABC; BC: AB=AB: BD ABC, and ADC; BC: AC=AC: DC; which was to be demonstrated. Scholium 1. By this Theorem, a mean proportional between two given lines is found by laying them in continuance of each other in one straig...


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Product Details
  • ISBN-13: 9781235929960
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 46
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1235929965
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 100 gr


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