Descriptive geometry . Fm. 183. Q it is sufficient to project one point of A, as for example,point c, which projects at point c. Then the required line B isdrawn through e parallel to the line A. CHAPTER XIII INTERSECTIONS OF PLANES AND SOLIDS BOUNDED BYPLANE FACES 122. A Plane Determined by Two Lines. A plane is com-pletely determined when any two of its lines, not necessarilyits traces, are known (§ 106). Hence, if a plane be given bymeans of any two intersecting or parallel lines in space, it isnot always necessary, nor even desirable, to find its traces inthe solution of a problem in which
Descriptive geometry . Fm. 183. Q it is sufficient to project one point of A, as for example,point c, which projects at point c. Then the required line B isdrawn through e parallel to the line A. CHAPTER XIII INTERSECTIONS OF PLANES AND SOLIDS BOUNDED BYPLANE FACES 122. A Plane Determined by Two Lines. A plane is com-pletely determined when any two of its lines, not necessarilyits traces, are known (§ 106). Hence, if a plane be given bymeans of any two intersecting or parallel lines in space, it isnot always necessary, nor even desirable, to find its traces inthe solution of a problem in which such a plane occurs. 123. The Intersection of a Line with a Plane Determined byTwo Lines. Let it be recpiired to find the point in which the. Fig. 184. line C, Fig. 184, intersects the plane of the intersecting linesA and B. Instead of finding the traces of the plane containingA and B (Prob. 6, § 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 e
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