Descriptive geometry . roundthe base. Find the points in which these elements intersectthe plane Q by passing through them auxiliary planes perpen-dicular to H or V (Prob. 13, Usual Method, § 119). Theplanes here chosen are the planes X, Y. . X, perpendicularto H. The intersection of planes X and Q is the line intersection of Av and the F-projection of the element0-3 locates 13, one point of the required intersection. Theintersection of planes Z and Q is the line C, the projection Cbeing parallel to VQ. Since plane Z contains two elements ofthe cone, the construction locates two points,
Descriptive geometry . roundthe base. Find the points in which these elements intersectthe plane Q by passing through them auxiliary planes perpen-dicular to H or V (Prob. 13, Usual Method, § 119). Theplanes here chosen are the planes X, Y. . X, perpendicularto H. The intersection of planes X and Q is the line intersection of Av and the F-projection of the element0-3 locates 13, one point of the required intersection. Theintersection of planes Z and Q is the line C, the projection Cbeing parallel to VQ. Since plane Z contains two elements ofthe cone, the construction locates two points, 11 on element0-1 and 15 on element 0-5. But the planes Y, M, and X areso situated that in attempting to find their lines of intersectionwith Q, only one point in each line can be found within thelimits of the figure, namely, the points b, d, and e on theground line. 222 XXII, § 180] PLANE AND CONE 223 B. The Common Point. Since the planes X, T, Z, M, and N are perpendicular to H, it follows that the lines of inter-. im [Q, 303 section A, B, C, etc., will have their H-projections coincidentwith HX, IIY, IIZ, etc., respectively. But the lines of inter- 224 DESCRIPTIVE GEOMETRY [XXII, § 180 section A, B, C, etc., are all lines in one plane, namely, theplane Q. Now if a number of lines known to be in the sameplane appear to intersect in a common point in one view, itcan only be because the lines actually intersect in in the other view the lines must also pass through acommon point. In the figure, the iZ-projection of this pointis nh, while nv lies on A. The other F-projections, Bv, D,and Ev, may now be drawn through nv and the points bv, dv,and ev on GL, already determined. The intersections of Bv,Dv, and Ev with the elements lying in the correspondingauxiliary planes locate the remaining points in the curve ofintersection. C. Visibility of the Curve of Intersection. (See§ 177.) In the jff-projection, the point 11, on the highestelement, is evidently visible. This d
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