Descriptive geometry . ectively. Produce «*&*, and * and kr on *. This line produced contains dk. which is found byprojection from d. The point dk being thus .raw dkkk, and proj< I m e*. Draw • . ting th< gon. • These constructions are given mei s ..lustrations of the 150 DESCRIPTIVE GEOMETRY [XV, § 142 method. Other constructions should suggest themselves tothe student. There is often a chance for the exercise of con-siderable ingenuity in solving problems in this manner, espe-cially in the matter of obtaining accuracy in the result. Notethat the ground lme is not esse
Descriptive geometry . ectively. Produce «*&*, and * and kr on *. This line produced contains dk. which is found byprojection from d. The point dk being thus .raw dkkk, and proj< I m e*. Draw • . ting th< gon. • These constructions are given mei s ..lustrations of the 150 DESCRIPTIVE GEOMETRY [XV, § 142 method. Other constructions should suggest themselves tothe student. There is often a chance for the exercise of con-siderable ingenuity in solving problems in this manner, espe-cially in the matter of obtaining accuracy in the result. Notethat the ground lme is not essential in these constructions. Construction by Second Analysis (Fig. 231). Let the completeF-p rejection, avbvcvdvev, and three points, ah, bh, and c*, of theiT-projection be given. By producing the lines ab and be,obtain the plane X, containing these two intersecting lines(Prob. 6, § 106). Points d and e lie in this plane, and d andand ev are known; find dh and eh (Prob. 16, § 133). Connectchdh, dheh, Fig. 231. Corollary 1. To find the true size and shape of a planepolygon. First Analysis. Find one trace of the plane containing the XV, § 142] PROBLEMS OF REVOLUTION 151 polygon. Revolve the polygon about this trace into the corre-sponding coordinate plane. Second Analysis. If any side of the polygon is parallel toone of the coordinate planes, the polygon may be revolvedabout this line as an axis into a position parallel to this coor-dinate plane. Construction by First Analysis (Fig. 231). Each corner ofthe polygon is here revolved about VX into V (Prob. 21,Working Rule, § 138), due regard being had to the relativepositions of the points with respect to the axis VX. Check. Note that, for each side of the polygon, the P~-pro-jection and the revolved position (produced if necessary)must intersect VX at the same point, namely, the P~-trace ofthis line. Construction by Second Analysis (Fig. 230). In this polygon,the line ab is parallel to H. Hence the polygon may be
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