Descriptive geometry . ityof the intersection, planes parallel to H or V are often intro-duced as auxiliaries when the general case fails. Special Case IV. The traces are not parallel, but one orboth pairs fail to intersect within the limits of the Q and R, Fig. 171, be the given planes. The intersectionof the P~-traces of these planes gives the point t, as in thegeneral case. Since HQ and HR do not intersect withinreach, pass the auxiliary plane, X, parallel to H. Planes Xand Q intersect in the line M (Case III); planes X and Rintersect in the line X; the lines M and N intersect i
Descriptive geometry . ityof the intersection, planes parallel to H or V are often intro-duced as auxiliaries when the general case fails. Special Case IV. The traces are not parallel, but one orboth pairs fail to intersect within the limits of the Q and R, Fig. 171, be the given planes. The intersectionof the P~-traces of these planes gives the point t, as in thegeneral case. Since HQ and HR do not intersect withinreach, pass the auxiliary plane, X, parallel to H. Planes Xand Q intersect in the line M (Case III); planes X and Rintersect in the line X; the lines M and N intersect in thepoint c, which is a point in the intersection of the planes Qand R (§ 117). The points t and c determine the required lineof intersection A. In Fig. 172, neither pair of traces intersect within the limitsof the figure. Two auxiliary planes, X and Y, are used, eachof which locates a point on the line of intersection A. Theauxiliary planes may be parallel to either H or V; in thefigure they are taken parallel to Fig. 172. Fig. 17:5. Special Case V. Both planes intersect the ground line atthe same point (Tig. 173). Let Q and R be the given general r-ase fails because the points sand t are point, c, in the required line of intersection, A, may bedetermined by means of the auxiliary plane X parallel to V, asin Fig. 172. An auxiliary plane parallel to H may be used ifprefer icd. 102 DESCRIPTIVE GEOMETRY [XII, § 118 Special Case VI. One of the planes contains the groundline (Fig. 174). Let Q and R be the given planes. R passesthrough the ground line, and is determined by the quadrants through which it passesand its angle with H. Asin Special Case V, thepoints s and t are coinci-dent on the ground additional point in therequired line of intersec-tion may be found by theuse of an auxiliary profileplane of projection, as-sumed anywhere exceptthrough the coincidentpoints s and t. Find theprofile traces, PQ and PR,of the given planes (§ 60). Thes
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