The Elements of Descriptive Geometry, Shadows and Perspective; With a Brief Treatment of Trihedrals, Transversals, and Spherical, Axonometric and Oblique Projections for Colleges and Scientific Schools

The Elements of Descriptive Geometry, Shadows and Perspective; With a Brief Treatment of Trihedrals, Transversals, and Spherical, Axonometric and Oblique Projections for Colleges and Scientific Schools

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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. 1888 edition. Excerpt: ...and the construction is evidently the same as that for finding where a given line pierces a plane which is given by a point and a line. In Projection.--PI. XIII., Fig. 101. Considering the construction from the point of view last named, we will examine the peculiar case in which the two traces of the given plane coincide, as at PQP, and in which also the two projections of the given line coincide in the line OB. Then applying (Prob. XI., a) this line pierces that plane at a point whose two projections coincide in m. A line whose projections thus coincide is in the bisecting plane of the second and fourth angles, hence m is also in that plane. Therefore if a series of such lines as those whose projections coincide in OC, OD, etc., be passed through O where the given line OB meets the ground line, they, and consequently their intersections with PQP, all found by Prob. XL, will be in the same bisecting plane. But these points are also in the plane PQP, hence in the intersection of these two planes. That is, they are all in the same straight line. 92. The last problem, looking upon its construction, Fig. 101, as a plane figure, gives the following: THEOREM VI.--Of transversals.--If two lines, GA and DA, intersect at a point A, and if from a point O on GA a series of lines, OB, OC, OD, be drawn, cutting the other line, DA, as at B, C, D, and if from the latter points perpendiculars, BE, CP, etc., be drawn to GA, and if Oo be drawn, also perpendicular to GA, the lines oE, oF, oG will cut OB, OC, OD in points m, n, p, which, with A, are on the same straight line. The perpendiculars to GA at E, F, O, G may have any other direction if only they remain parallel. CHAPTER II. DEVELOPABLE SURFACES. Definitions, etc. 93. There are two kinds of developable...show more

Product details

  • Paperback | 90 pages
  • 189 x 246 x 5mm | 177g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236584163
  • 9781236584168