Descriptive geometry . g projections of the circles,the axes of the surface should be perpendicular to one of thecoordinate planes. No figure for this case is deemed necessary. 198. The Intersection of a Sphere with Another Surface. Whenone of two intersecting surfaces is a sphere, the auxiliary sur-faces commonly employed are planes, since every plane sectionof a sphere is a circle. Simple projections of these circles,however, result only when the auxiliary planes are parallel toHoy V. Cases of this kind have already been discussed (§§ 129,131). But planes parallel to H ov Fmay not always cut
Descriptive geometry . g projections of the circles,the axes of the surface should be perpendicular to one of thecoordinate planes. No figure for this case is deemed necessary. 198. The Intersection of a Sphere with Another Surface. Whenone of two intersecting surfaces is a sphere, the auxiliary sur-faces commonly employed are planes, since every plane sectionof a sphere is a circle. Simple projections of these circles,however, result only when the auxiliary planes are parallel toHoy V. Cases of this kind have already been discussed (§§ 129,131). But planes parallel to H ov Fmay not always cut ad-vantageous sections from the second surface. In such cases, the planes are chosen with respect to thesecond surface, and various devices are adopted to avoid pro-jecting the sections of the sphere as ellipses. Two generalmethods are (a) revolution of the auxiliary planes ; (b) theuse of a secondary projection. These methods will be shownin the following two problems. XXVI, § 198] CONICAL FRUSTUM AND CYLINDER 281. Fiu. 329. 282 DESCRIPTIVE GEOMETRY [XXVI, § 198 Problem 50. To find the intersection of a sphere and a cone. Analysis. Planes passed through the vertex of the cone willcut elements from the cone (§ 190), and circles from the these planes be taken perpendicular to one of the coordinateplanes, say to H. Revolve each plane until parallel to V, carry-ing with it the elements cut from the cone, and the circle cut fromthe sphere. The circle will now appear in true shape and the points of intersection of the revolved circle and ele-ments. Obtain their projections by counter-revolution. A convenient axis about which to revolve the planes is a lineperpendicular to // through the vertex of the cone, since allthe planes will contain this line. Construction (Fig. 330). The given surfaces are those ofa cone whose vertex is o, and a sphere whose center is auxiliary planes be passed perpendicular to H through thevertex of the cone. Of these planes,
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