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Difficulties of Euclid Simplified

Difficulties of Euclid Simplified


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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. 1879. Excerpt: ... angled triangles form a right-angled triangle. Construct the figure, and prove that one of the given triangles is equal to the sum of the other two. 32. If A be the point of intersection of the diagonals of a parallelogram, then every straight line drawn through A will meet opposite sides of the parallelogram in points equidistant from A, and will divide the parallelogram into two equal parts. 33. A quadrilateral being formed by joining the middle points of the adjacent sides of a rectangle, investigate what kind of a quadrilateral it is. 34. Prove that a quadrilateral which has two opposite sides parallel, is equal in area to a rectangle between the same parallels on a base equal to half the sum of the parallel sides of the given quadrilateral. 35. From any point in one of the sides of a triangle draw a straight line which shall bisect the triangle. BOOK II. I. Class1f1ed Exerc1ses. 1. Let A, B, C, D be four points in a straight line taken in order. Show that the rectangle AC.BD is equal to the sum of the rectangles AB.CD and AD.BC (n. 1). 2. If a straight line be divided into two parts so that twice the rectangle contained by those parts is equal to the sum of the squares on those parts, show that the straight line is bisected (11. 4). 3. Show that any rectangle is the half of the rectangle contained by the diagonals of the squares on its two sides (11. 4). 4. In a right-angled triangle the square on the perpendicular from the right angle on the hypotenuse is equal to the rectangle contained by the segments of the hypotenuse (11. 4). 5. Prove that the rectangle on two parts of a line can never exceed the square of half the line (11. 4). 6. If a straight line be divided into any two parts, show that the rectangle under the parts will be the greatest poss...


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Product Details
  • ISBN-13: 9781235696718
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 18
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 1235696715
  • Publisher Date: 01 Feb 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 54 gr

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