New Elements of Geometry by Seba Smith at Bookstore UAE
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New Elements of Geometry

New Elements 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. 1850 edition. Excerpt: ...as DBCE; therefore it is equal to fifteen of the smaller rectangles. And the circumference of the pentagon is equal to five such rectangles as ABFG; therefore it is equal to twenty of the smaller rectangles. Fifteen is three-fourths of twenty, therefore the area of the pentagon, whose diameter is three, equals three-fourths of its circumference, agreeably to the proposition. PROPOSITION XV. In the regular pentagon, whose diameter is four, the area equals the circumference. In the present diagram, diameter being four, the radius, CD, is two. If CD be produced to H, making DH equal to one, the breadth of the line of circumference, it is manifest that the two rectangles drawn in DBCE are severally equal to the two rectangles drawn in ABFG, for they all have equal bases and equal heights by construction. But DBCE equals one-fifth of the area of the pentagon; therefore the area of the pentagon equals ten such rectangles as the two contained in DBCE. ABFG is one-fifth of the circumference of the pentagon, therefore the circumference equals ten such rectangles as the two contained in ABFG. Therefore the area of the pentagon, whose diameter is four, equals its circumference, agreeably to the proposition. PROPOSITION XVI. In the regular hexagon, whose diameter is one, the area equals one-fourth of the circumference. Let the diameter of the circle he unit, or one, one inch; then the diameter of the regular hexagon, circumscribed about it, is one; Def. 17. The sides of the hexagon being equal, Def. 68, lines drawn from the center to the six angles divide the area into six equal triangles, for they all have equal bases and equal heights. One triangle, as ABC, is equal to the rectangle, DBCE, Prop. 6. Therefore the area of the hexagon equals six such...


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Product Details
  • ISBN-13: 9781150275852
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 50
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1150275855
  • Publisher Date: 01 Jul 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 109 gr


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