Descriptive geometry for students in engineering science and architecture; a carefully graded course of instruction . enerators in the , parallelto the \.P. A cone, whose is a circle 3 diameter, has the centre of this circle in theplan of the axis of the cylinder. The axis of the cone is 4 long, and has a plan J long at 45°to XY. Find the plan and elevation of the intersection of the surfaces of the two solids. To obtain the projections of the surface intersections when inclined cones andcylinders, not necessarily right circular ones, interpenetrate, it is necessary to makeuse of sect
Descriptive geometry for students in engineering science and architecture; a carefully graded course of instruction . enerators in the , parallelto the \.P. A cone, whose is a circle 3 diameter, has the centre of this circle in theplan of the axis of the cylinder. The axis of the cone is 4 long, and has a plan J long at 45°to XY. Find the plan and elevation of the intersection of the surfaces of the two solids. To obtain the projections of the surface intersections when inclined cones andcylinders, not necessarily right circular ones, interpenetrate, it is necessary to makeuse of section planes which will have in them straight generator lines on both sur-faces. Hence, when the surfaces of cones are cut by those of other cones, or of cylin-ders, the apex points of the cones must be in the section planes made use of; and in 108 DESCRIPTIVE GEOMETRY the case of cylinders, their axes must be parallel to the section planes. Thus, in , where two cylinders are represented whose given are circles and whoseaxes are directed as indicated by the plans and elevations of generators of their. Fig. 105. surfaces, it is necessary to take any generator of one cylinder, or a parallel to itas ab, ab, and from some point in that line to draw another line, say ac, ac,parallel to the generators of the second cylinder. The of these two linesare h and c respectively, and the plane of the two lines has the line HH for its the generators of both surfaces are parallel to this plane, and hence any plane MORE DIFFICULT CASES OF IXTERPENETRATIOX OF SOLIDS 109 made parallel to this one, and having its crossing the circular of thegiven cyhnders will therefore contain generators of the surfaces of both points in which these generators cut each other are points in the intersectionline of the surfaces, and the plan and elevation of it can in this way be found, asshown. It will be found an advantage to arrange tangent planes to commencewith
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