The essentials of descriptive geometry . t circular cone whose apex is at Q. Through theapex Q pass the plane R perpendicular to Ss. This plane cutsfrom the plane S the line AB, which Hne pierces the surface of thecone at A and B. Since this line is the longest line which can bedrawn common to both the cone and the plane S it will be themajor axis of the curve of intersection. Now through P, themiddle point of AB, draw CO in plane S and perpendicular toAB. This line CO pierces the surface of the cone at the pointsC and D. Since it is the shortest line which can be drawn com-mon to both cone an
The essentials of descriptive geometry . t circular cone whose apex is at Q. Through theapex Q pass the plane R perpendicular to Ss. This plane cutsfrom the plane S the line AB, which Hne pierces the surface of thecone at A and B. Since this line is the longest line which can bedrawn common to both the cone and the plane S it will be themajor axis of the curve of intersection. Now through P, themiddle point of AB, draw CO in plane S and perpendicular toAB. This line CO pierces the surface of the cone at the pointsC and D. Since it is the shortest line which can be drawn com-mon to both cone and plane S, and since it is perpendicular toAB, CD will be the minor axis of the curve of intersection. Tofind its true size revolve the axes of the curve into V about sSand construct the ellipse AyBvCyDv. If the projections of this curve of intersection are required they CONICAL SURFACES 119 may be found by passing other auxiliary planes, such as R,through the apex of the cone and finding points by the methodused to find points A and Fig. 95. Construction. When the axis of the cone is oblique to H andV, the base being any plane curve. In Fig. 96, S is the given plane cutting the cone whose apexis Q. Pass auxihary planes R, \J, V, etc., through 0 perpendicu- I20 ESSENTIALS OF DESCRIPTIVE GEOMETRY lar to H. The auxiliary plane R cuts from the cone one elementand from the plane S the line OM. This Une OM intersects thiselement at F, one point on the curve of intersection. In likemanner the plane U determines the point E of the curve. Now
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