The essentials of descriptive geometry . sion: Second Method. Find the intersections of theplanes of the faces. These lines will be the edges of the inter-section of the two surfaces. Construction. In Fig. 107 a rectangular hopper, base inH 1-2-3-4 and apex 0, intersects a rectangular pipe. The faceof the hopper, 1-4-O, lies in the planer Rr; and this planeintersects U — the plane of the upper face of the pipe — in theline PQ. The portion of PQ between the edges O4 and Oi — orAD — is one side of the opening in the pipe made by the like manner CB may be obtained by finding the interse
The essentials of descriptive geometry . sion: Second Method. Find the intersections of theplanes of the faces. These lines will be the edges of the inter-section of the two surfaces. Construction. In Fig. 107 a rectangular hopper, base inH 1-2-3-4 and apex 0, intersects a rectangular pipe. The faceof the hopper, 1-4-O, lies in the planer Rr; and this planeintersects U — the plane of the upper face of the pipe — in theline PQ. The portion of PQ between the edges O4 and Oi — orAD — is one side of the opening in the pipe made by the like manner CB may be obtained by finding the intersectionof plane U with plane vVv; and with these four points, A, B, C,D, the intersection may be drawn. 109. Proposition 32. To find the intersection of two givencylinders. Discussion. Pass auxiliary planes through the cyhnders cut-ting elements from each. These elements, being in a common 131 132 ESSENTIALS OF DESCRIPTIVE GEOMETRY plane, intersect in points common to both cylinders, or pointson the required curve of Fig. io6. Construction: First Case. When the bases of the givencyhnders he in the same plane. In Fig. io8 one cyKnder is perpendicular to H and the otheroblique to H and V; both have circular bases in H. Pass plane INTERSECTION OF SURFACES 133
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