Descriptive geometry . Fig. 300. Special Case. Tlie given line is parallel to H or V. Let thegiven line A, Fig. 300, be parallel to 77. Assume a secondaryground line, 0\L\, perpendicular to Ah. The line A will thenproject as a point, A? (§ 70). Project the center of the sphereto of, and draw the sphere. The edge views, VXQ and V\T, ofthe required tangent planes may now lie drawn directly throughA{. The plane Q (HQ, VQ) requires no further trace HT is readily obtained, but for Fran auxiliary lineis necessary. The line used here is /;, parallel to the line projection /»,. a
Descriptive geometry . Fig. 300. Special Case. Tlie given line is parallel to H or V. Let thegiven line A, Fig. 300, be parallel to 77. Assume a secondaryground line, 0\L\, perpendicular to Ah. The line A will thenproject as a point, A? (§ 70). Project the center of the sphereto of, and draw the sphere. The edge views, VXQ and V\T, ofthe required tangent planes may now lie drawn directly throughA{. The plane Q (HQ, VQ) requires no further trace HT is readily obtained, but for Fran auxiliary lineis necessary. The line used here is /;, parallel to the line projection /»,. a point, is assumed in V\T. From />, ;l?obtained Bhand Bv. TheF-trace,t2,of B locates a point in I/. 216 DESCRIPTIVE GEOMETRY [XX, § 171 Problem 40. To pass a plane tangent to a double curved surfaceof revolution through a given line. (Special Cases.) Case I. The given line intersects the axis of the Using the point in which the given line intersects. Fig. 301. the axis as a vertex, circumscribe the given surface by a coneof revolution. Pass the required tangent planes through thegiven line tangent to the auxiliary cone. Construction (Fig. 301). The given surface is an oblatespheroid, with its axis perpendicular to H. The given line Aintersects the axis at the point c (c*, c!). Prom c* draw tan-gents to the P-projection of the given surface; these tangentsrepresent the auxiliary cone in the ^projection. The base ofthis cone on H is the circle Bh. The if-traces, HQ and HT, ofthe required tangent planes pass through the JY-trace, su of A,and are tangent to the circle Bh. (Compare Prob. 32, § 162.) XX, § 171] SURFACES OF REVOLUTION 217 The F-traces, VQ and VT, pass through the U-traee, tu of second point on VT is here obtained by finding the F-trace,t2, of the element, E, hi which the plane T is tangent to theauxiliary cone. Case II. TJie given line is parallel to the axis of the surface. Analysis. The axis of the given surface
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