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Notes on Descriptive Geometry

Notes on Descriptive 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. 1908 Excerpt: ...moving in a plane so that its distance from a given point is constant. 82. An ellipse is the path of a point moving in a plane so that the sum of its distances from two fixed points is constant. Construction. Let F and Fi, Fig. 47, be the two fixed points and let the sum of the distances from these points to any point on the curve be equal to the line AB. Select any point, as O, on the line AB. With F as center and AO as radius, strike an arc; also with Fi as center and BO as radius, strike an arc cutting the first arc in the points P and Q. These are points on the curve since FP + FiP=AB and FQ + FiQ=AB. Selecting any other point on AB, as Oi, and going through the construction as before, two other points Pi and Qi are located. By continuing this process enough points can be located so that the curve can be drawn. The points F and Fs are the foci of the ellipse. AB is the major axis. The minor axis CD is perpendicular to the major axis at its middle point. The intersection of the axes is the center of the ellipse. Lines drawn from any point on the curve, as P, to the foci F and Fi are called focal radii. If the axes of an ellipse are given, the foci can be found by taking one-half the major axis as a radius and with the end of the minor axis as a center, cut the major axis in two points which are the focii. To draw a tangent to the ellipse at a point on the curve. Let P, Fig. 47, be the point on the curve. Draw the focal radii PF and PFi. The line PT which bisects the angle FtPE is the required tangent. (Wood's Co-ordinate Geometry, Art. 108A. This method applies to all conies.) To draw a tangent to the ellipse from a point without the curve. Let S, Fig. 47, be the point without the curve. With Fi as center and AB as radius, strike an arc. With S as center...


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Product Details
  • ISBN-13: 9781130977516
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 26
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 113097751X
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 68 gr


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