Descriptive geometry . element 0-2, be thegiven point. Find the plane S(HS, VS), which is tangent tothe cone at the point 12 (Prob. 31, § 162). Find the intersec-tion of S with the given plane Q (Prob. 12, § 118). This lineof intersection T(Th, Tv) is the required tangent line. As acheck, it should pass through the point 12, and show tangentto the curve of intersection in each projection (§ 152). E. Development of the Curved Surface of the The entire curved surface, between the vertex andthe base, should be developed first. Any other line drawn onthe surface can then be put in.
Descriptive geometry . element 0-2, be thegiven point. Find the plane S(HS, VS), which is tangent tothe cone at the point 12 (Prob. 31, § 162). Find the intersec-tion of S with the given plane Q (Prob. 12, § 118). This lineof intersection T(Th, Tv) is the required tangent line. As acheck, it should pass through the point 12, and show tangentto the curve of intersection in each projection (§ 152). E. Development of the Curved Surface of the The entire curved surface, between the vertex andthe base, should be developed first. Any other line drawn onthe surface can then be put in. The conical surface is dividedby its elements into pieces bounded by two straight lines anda curve. These pieces are approximately plane triangles, theapproximation being closer the nearer the elements are to-gether. The curved surface may then be developed as if the XXII, § 180] PLANE AND CONE 225 cone were a many-sided pyramid, the triangular faces beingbuilt up from the true lengths of their sides. (See § 89.). Pro. 303 (repeated). Construction. The given conical Burface is divided infoeight triangular pieces by the chosen elements L, 0 226 DESCRIPTIVE GEOMETRY [XXII, § 180 0-8. The true lengths of the elements may be found bythe rule of § 88. The true lengths of 1-2, 2-3, etc. ap-pear directly in the //-projection of the base, the usualapproximation being that the chord equals the arc. As-suming the true lengths found as needed, begin the develop-ment by laying off, on any convenient line, O-l equal tothe true length of 0-1. With 0 and 1 as centers, radiirespectively the true lengths of 0-2 and 1-2, strike arcs inter-secting at 2. Working from 0 and 2, obtain 3 in a similarmanner, and so on. Draw a smooth curve through 1, 2 . .8, 1. To locate the section 11, 12 . . 18, 11 in the development,note that 11 may be located by measuring from 0 the truelength of 0-11, or from 1 the true length of 1-11. By com-paring Figs. 113 and 114, § 88, it will be seen that in thi
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