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. 1851 Excerpt: ...all the points S similarly constructed, will be this intersection itself. 68. In order to obtain the tangeot of this curve at the point S, it is sufficient to observe, that during the movement of the cutting plane, the tangent always passes through the point G of the axis of revolution; and, therefore, by drawing the ...
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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. 1851 Excerpt: ...all the points S similarly constructed, will be this intersection itself. 68. In order to obtain the tangeot of this curve at the point S, it is sufficient to observe, that during the movement of the cutting plane, the tangent always passes through the point G of the axis of revolution; and, therefore, by drawing the straight line S G, we shall have the tangent required. 69. Prob. 24.--To construct the intersection of a conical surface upon any given base, with a plane given in position. Solution.--Suppose the vertical plane of projection to be placed perpendicularly to the cutting plane, as it always can be. Let A and a' (pi. VIII. fig. 29) be the projections of the vertex of the cone, or of the center of the conical surface; B C D E, the trace of this surface upon the horizontal plane; fg, the vertical projection of the cutting plane, and G/ its horizontal trace. Imagine a succession of planes perpendicular to the vertical plane of projection to pass through the vertex of the cone: the vertical projections of these planes will be the straight lines a' c drawn through the projection of the vertex; and their horizontal traces will be the straight lines c C perpendicular to L M, which will cut the trace of the conical surface somewhere in the points C, C. These planes will cut the surface in straight lines whose vertical projections will be the straight lines a' c, and whose horizontal projections will be obtained by drawing to the point A, the straight lines C A, C A. The same planes will also intersect the cutting plane in straight lines which will be perpendicular to the vertical plane. The vertical projections of these straight lines will be the points, h, in which fg meets the straight lines a' c, and their horizontal projections will be obtained by let...
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