Descriptive geometry . for obtaining rapidly all the true lengths ofthe elements required in making the development is shown inthe figure. Let the true length of one element, for example1-11, be obtained by revolving the line parallel to V, as shownat l^-llj (Prob. 13, First Method, § 78). Then, since all theelements are parallel, the true length of any element can befound by projecting to the line l-llx, produced if , the true length of 8-28 equals l-^!, and the truelength of 28-18 equals 28J-18J. The developed tangent line, T, is determined from the tri-angle 6-16-s. The point
Descriptive geometry . for obtaining rapidly all the true lengths ofthe elements required in making the development is shown inthe figure. Let the true length of one element, for example1-11, be obtained by revolving the line parallel to V, as shownat l^-llj (Prob. 13, First Method, § 78). Then, since all theelements are parallel, the true length of any element can befound by projecting to the line l-llx, produced if , the true length of 8-28 equals l-^!, and the truelength of 28-18 equals 28J-18J. The developed tangent line, T, is determined from the tri-angle 6-16-s. The point s is located by using its truedistances, s-16 and s-6, from 16 and 6 respectively. Case II. The base of the cylinder lies in P. Construction (Fig. 308). The given cylinder is a cylinderof revolution lying in the third quadrant. It is intersected bythe plane Q. Eight elements have been chosen, indicated by the numbers 1to 8 on the P-projection. Points 12, 13, 14, 15 of the intersec- XXII, §180] PLANE AND CYLINDER 241. Pro. 307 (repeated). 242 DESCRIPTIVE GEOMETRY [XXII, § 180 tion, which lie within the limits of the cylinder, are found, asin the preceding examples, by finding where the chosen ele-ments intersect the plane Q. The plane Q intersects the left-hand base of the cylinder inthe points 19 and 20. To find these points directly, as in thecorresponding case of the cone, Fig. 304, note first that the pro-file trace of Q on the plane of this base would be determinedfrom the points x and ?/, on HQ and VQ respectively (§ 60). The base which is already projected in profile is the right-hand base. Therefore project x and y to xx and yu and obtainthe projected trace, P,Q. The points 19^ and 20p, in whichPXQ intersects the circle, are the profile projections of the re-quired points, which must then be projected back to the left-hand base. The line T is tangent to the section at the point 14. Thisline is the intersection of the given plane Q with the plane #,which is passed tan
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