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. 1868 Excerpt: ... are found by using as auxiliary planes the two planes whose traces are si and sn. To drav) a tangent to the curve at any point, as X, pass a plane tangent to the cone at X. ic is its horizontal trace, Art. (129). It intersects tTt' in cX, which is therefore the required tangent, Art. (157). The part of the curve which ...
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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. 1868 Excerpt: ... are found by using as auxiliary planes the two planes whose traces are si and sn. To drav) a tangent to the curve at any point, as X, pass a plane tangent to the cone at X. ic is its horizontal trace, Art. (129). It intersects tTt' in cX, which is therefore the required tangent, Art. (157). The part of the curve which lies above the two extreme elements SL and SN, is seen, and therefore its projection, wyzq, is full. For a similar reason the projection, z'c/x'u', of that part of the curve which lies in front of the two extreme elements, SM and SO, is full. To show the curve in its true dimensions, revolve the plane about tT until it coincides with H, and determine each point, as Q at ql as in Art. (17). Or the position of (svr) may be found at v." Then if the points c, a, b, p, &c, be each joined with this point by right lines, we have the revolved positions of the lines cut from the given plane by the auxiliary planes, and the points y' z' r," x' in which these lines are intersected by the perpendiculars to the axis, yy," zz," &c, are points of the revolved position of the curve. x"c is the revolved position of the tangent. 168. The intersection of the single curved surface, with a helical directrix, by a plane, may be found by intersecting by a system of auxiliary planes tangent to the projecting cylinder of the helical directrix. These intersect the surface in rectilinear elements, and the plane in right lines, the intersection of which will be points of the required curve. 169. Problem 43. To find the intersection of any surface of revolution by a plane. Let the surface be a hyperboloid of revolution of one nappe, _ given as in Fig. 70, and let f tf be the cutting plane. Analysis. If a meridian plane be passed perp...
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All Editions of Elements of Descriptive Geometry, with Its Applications to Spherical Projections, Shades and Shadows, Perspective and Isometric Projections
