The essentials of descriptive geometry . Fig. 117. plane cuts a circle from each surface. Thus, plane R cuts fromthe cone a circle whose radius is yl and from the other surface acircle whose radius is x2. These two circles intersect at A andB two points on the required curve. By passing other planesparallel to R the curve of intersection may be completely deter-mined. ISO ESSENTIALS OF DESCRIPTIVE GEOMETRY 120. Proposition 38. Given any two surfaces of revolutionwhose axes intersect to find the curve of intersection of Fig. 118. Discussion. If, with the intersection of the axes of
The essentials of descriptive geometry . Fig. 117. plane cuts a circle from each surface. Thus, plane R cuts fromthe cone a circle whose radius is yl and from the other surface acircle whose radius is x2. These two circles intersect at A andB two points on the required curve. By passing other planesparallel to R the curve of intersection may be completely deter-mined. ISO ESSENTIALS OF DESCRIPTIVE GEOMETRY 120. Proposition 38. Given any two surfaces of revolutionwhose axes intersect to find the curve of intersection of Fig. 118. Discussion. If, with the intersection of the axes of the givensurfaces as a center, auxiliary spheres be passed through thesurfaces they wiU cut circles from each surface. These circlesintersect in points on the curve of intersection. SURFACES OF REVOLUTION 151 Construction. In Fig. 118 the sphere is cut by a cone. Theaxes intersect at O. With this point as a center describe a sphereas ABC. This sphere cuts from the given sphere a circle verti-cally projected as a line at ab and from the cone another circlevertically projected as a line at mn. Thesetwo circles intersect at two points, both ofwhich are vertically projected at x andhorizontally projected on the plan view ofcircle AB at x and y. By passing otherspheres and proceeding in the same mannerthe curve of intersection may be completelydetermined. 121. Proposition 39. To develop any sur-face of revolution. Discussion. Theoretically, surfaces ofrevolution are not capable of developmentbut, practically, such surfaces are
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