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A Supplement to the Elements of Euclid

A Supplement to the Elements of Euclid


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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. 1819 Excerpt: ...no solution. 89. Cor. 2. In the same manner, the greater side of a given oblong may be divided into two parts, so that the rectangle contained by them shall be equal to the given oblong, a square having first (E. 14. 2.) been found that is equal to the oblong: But, in this case, the half the greater side of the oblong must exceed the double of the lesser side. 90. Cor. 3. In the same manner, also, a straight line may be divided into two parts, so that the rectangle contained by them, shall be equal to a given rectangle; if the side of a square which is equal to the given rectangle, do not exceed the half of the given straight line. 91. Cor. 4. If the measure of the surface of an oblong be given, and if its perimeter be also given, the rectangle itself may hence be constructed. ' Prop. LXXII. 92. Theorem. Iffrom a given point without a circle, two equal straight lines be drawn to the convex circumference, one of which touches the circle, tfie other shall also touch it. For, if not, draw (E. 17. 3.) from the given point a straight line to touch the circle, and (S. 19. 3. cor. 1.) it will be equal to the other tangent; and thus more than two equal straight lines can be drawn from a point, without a circle, to the circumference; which (E. 8. 3.) is absurd;.'. the straight line which is drawn from the same point, without the circle, as the tangent, and which is equal to the tangent, itself also touches the circle. Prop. LXXIII. 93. Problem. To produce a given straight line, so that the rectangle contained by the whole line thus produced, and the part of it produced, shall be equal to a given square. Let AB be a given straight line, and L the side so that the rectangle, contained under the whole line produced, and the part of it produced, may be equal to the squa...


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Product Details
  • ISBN-13: 9781130623796
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 62
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1130623793
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 127 gr


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