Descriptive geometry . § 106), and then finding the point in which 0intersects this plane (Prob. 13, § 119), let us proceed at once, asin the usual method of Problem 13, to pass through the line 108 XIII, § 123] INTERSECTION OF PLANES 109 C an auxiliary plane perpendicular to H .(or to V). The lineHX, coincident with Ch, is the TZ-trace and edge view of sucha plane. The plane X intersects the line A in point j (seeFig. 178) and the line B in point k. The line D, connecting jand k, must therefore be the line of intersection of the planeX with the plane of the lines A and B. The projection Dvi
Descriptive geometry . § 106), and then finding the point in which 0intersects this plane (Prob. 13, § 119), let us proceed at once, asin the usual method of Problem 13, to pass through the line 108 XIII, § 123] INTERSECTION OF PLANES 109 C an auxiliary plane perpendicular to H .(or to V). The lineHX, coincident with Ch, is the TZ-trace and edge view of sucha plane. The plane X intersects the line A in point j (seeFig. 178) and the line B in point k. The line D, connecting jand k, must therefore be the line of intersection of the planeX with the plane of the lines A and B. The projection Dvintersects C at ev, which, for the same reasoning as that givenin Problem 13, must be one projection of the point in whichC intersects the plane of A and B. Finally, eh is found by pro-jecting from ev. Note that in this solution the position of the ground line isnot essential. It may therefore be omitted. Figure 185 shows how to apply this method to find thepoint in which the profile line cd pierces the plane of the in-. tersecting lines A and B. Pass through cd a profile plane of A and B intersects the profile plane in theline ab. By means of a profile projection it is readily foundthat the lines ab and cd intersect in the point e, the requiredpiercing point. In this figure the ground line is not omitted,since it is necessary in order to find the profile the positions of the projections e* and ev areindependent of the position of the ground line. 110 DESCRIPTIVE GEOMETRY [XIII, § 124 124. The Intersection of Two Limited Plane Surfaces. Let itbe required to find the intersection of the triangle abc, , with the plane, indefinite in length, but limited in widthby the parallel lines J and K. The intersection can be found,without rinding the traces of either plane, by applying thepreceding method, as follows. Using the auxiliary plane Xwhich contains J and is perpendicular to H, we find that theline J intersects the plane of the lines
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