Descriptive geometry for students in engineering science and architecture; a carefully graded course of instruction . re of sphere A, and another from this point aa found on sphere A, drawn toIII, to limit the radius of the sphere B at bb. The elevations of the points may beobtained by carrying perpendiculars across Al from the plans, instead of usingelevations of generator lines. Both ways are shown in the figure. One checksthe accuracv of the other. 98 DESCRIPTIVE GEOMETRY EXERCISE XXXIX 1. Find two tangent planes to three spheres, the planes not to pass between any of thespheres, and mark t
Descriptive geometry for students in engineering science and architecture; a carefully graded course of instruction . re of sphere A, and another from this point aa found on sphere A, drawn toIII, to limit the radius of the sphere B at bb. The elevations of the points may beobtained by carrying perpendiculars across Al from the plans, instead of usingelevations of generator lines. Both ways are shown in the figure. One checksthe accuracv of the other. 98 DESCRIPTIVE GEOMETRY EXERCISE XXXIX 1. Find two tangent planes to three spheres, the planes not to pass between any of thespheres, and mark the projections of the tangent points on their surfaces. The spheres havetheir centres all at the same level, and these centres are the corners of an equilateral triangle2 side, with no side parallel to the Diameters of the spheres if, i\ and f respectively 2. Three spheres rest on the and touch each other. Their centres are at difTerentdistances from the Their diameters are if, | and f respectively. Find the inclinedplane tangent to all three spheres and mark the projections of the tangent Fig. 97. When the centres of three unequal spheres are at unequal distances fromthe planes of projection and the spheres are not all resting on the , then theline joining the apex points of the enveloping cones will be oblique, and the problembecomes more involved. If, however, the line joining the apex points be consideredin relation to one sphere only, then it becomes a matter of finding the planes con-taining this line and tangent to the one sphere. It will be seen that the tangentplanes found will be tangent to the other spheres, the apex of whose commonenveloping cone is a point in the line. The tangent points, also, having beenobtained on the one sphere, the tangent points on the others may be found as inthe case considered in Fig. 97. Let ah, ah in Fig. 98 be an inclined line, such as that referred to above, andcc the centre of a sphere whose projections are
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