The Elements of Descriptive Geometry Shadows And Perspective With a Brief Trea
The Elements of Descriptive Geometry Shadows And Perspective With a Brief Trea
S Edward Samuel Edward Warren
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XL, b y i) of the point, which determines the given projection, and find the intersection of this plane with the surface. The intersection of this line with the given pro- jecting line will be the point whose required projection will thence be known. In Projection. ?\. XIV. , Fig. 113. Let / be the given projection of a point on the paraboloid. A line pk in any convenient direction will then be the horizontal trace of a vertical plane containing the projecting line whose projec- tion is /. This... plane intersects the elements of the para- boloid, giving the curve knr k'n'r', on which / is vertically projected at/', the point required. EXAMPLE. Let p' be given, and find /. DESCRIPTIVE GEOMETRY. 159 131. Four straight lines intersecting at four points, not in the same plane, form a warped quadrilateral. The opposite sides of this quadrilateral, as A'B' and C'D f, PL XIV. , Fig 114 (the vertical projection), are pairs of ele- ments, one pair of the first, and the other of the second generation of a hyperbolic paraboloid, for through A'B', for example, a plane can be passed parallel to CD', which will be the plane director of these elements.
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