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First Course in Projective Geometry

First Course in Projective Geometry


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About the Book

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 edition. Excerpt: ... the horizon, so that the section may be a parabola, and draw the section in this case. Ex. 2. Construct the section when the angle the plane makes with the horizon is 15. 20. Having given the positions of the axis of projection, vanishing line and vertex of projection, when rabatted into the plane of the figure, we might employ the construction of 13 to obtain the axes. This furnishes an independent check upon the accuracy of the previous work, as of course they must bisect the angles between the asymptotes (when such exist). In the accompanying figures (59, 60, 61) both axes and asymptotes are shown. In each of these 0 is the centre of the circle whose projection is drawn. V is the rabatted vertex. K its inverse with respect to this circle. a: the axis of projection. l the vanishing line in the plane of the circle. a, b the axes of the conic. k, k the asymptotes of the conic. C the centre of the conic. For convenience we repeat the construction of 13 for the axes. Take the inverse of V with respect to the circle, centre 0. Through V and this point describe a circle having its centre on the vanishing line. (This cuts the circle, centre 0, orthogonally.) Join O to the points R, R, where this circle cuts the vanishing line. Join R and R to the points where these lines cut the circle again, and let the joining lines meet in T. Then TR, TR are a pair of conjugate lines with respect to the circle, centre 0, such that the intercept RR on the vanishing line between them subtends a right angle at V. They therefore project into conjugate lines for the conic at right angles, which, as proved in 13, are the axes. We get the axes then by joining to C the points where TR, TR meet the...


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Product Details
  • ISBN-13: 9781234087579
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 58
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 123408757X
  • Publisher Date: 14 Jan 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 122 gr


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