The Synoptical Euclid
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The Synoptical Euclid

The Synoptical 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. 1853 Excerpt: ...of BC, CD, DA, and twice the rectangle BC, CD; but the square of BA is equal (I. 47.) to the squares of BD, DA, because the angle at D is a right angle; and the square of CA is equal (I. 47.) to the squares of CD, DA; therefore 3. The square of BA is equal to the squares of BC, CA, and twice the rectangle BC, CD; that is, the square of BA is greater than the squares of BC, CA, by twice the rectangle BC, CD. Therefore, in obtuse-angled triangles, &c. a.e.-. PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles; and upon BC, one of the sides containing it, let fall (I. 12.) the perpendicular AD from the opposite angle: the square of AC opposite to the angle B, is less than the squares of CB, BA, by twice the rectangle CB, BD. B D C First, let AD fall within the triangle ABC; and because the straight line CB is divided into two parts in the point D, (II. 7.) 1. The squares of CB, BD, are equal to twice the rectangle contained by CB, BD, and the square of DC; to each of these equals add the square of AD; therefore 2. The squares of CB, BD, DA, are equal to twice the rectangle CB, BD, and the squares of AD, DC; but the square of AB is equal (I. 47.) to the squares of BD, DA, because the angle BDA is a right angle; and the square of AC is equal to the squares of AD, DC; therefore 3. The squares of CB, BA, are equal to the square of AC, and twice the rectangle CB, BD; that is, the square of AC alone is le..


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Product Details
  • ISBN-13: 9781232243700
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 34
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1232243701
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 82 gr


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