Descriptive geometry . nd Ff, parallel to ALV. The circle projects as Ci, thecenter coinciding with of, while the diameter is obtained fromthe //-projection. We thus obtain four intersections, lxv, 2^,3^, 4^. These are the projections of four points in the re-quired intersection from which the H- and F-projections may befound. A sufficient number of points to determine the inter-section may be found in a similar manner. In this examplethe intersection consists of two separate curves. 199. The Intersection of any Two Curved Surfaces. As hasbeen mentioned in § 180, it is not always possible to f
Descriptive geometry . nd Ff, parallel to ALV. The circle projects as Ci, thecenter coinciding with of, while the diameter is obtained fromthe //-projection. We thus obtain four intersections, lxv, 2^,3^, 4^. These are the projections of four points in the re-quired intersection from which the H- and F-projections may befound. A sufficient number of points to determine the inter-section may be found in a similar manner. In this examplethe intersection consists of two separate curves. 199. The Intersection of any Two Curved Surfaces. As hasbeen mentioned in § 180, it is not always possible to find a seriesof auxiliary surfaces which will cut simultaneous simple sectionsfrom each of two given surfaces, even when it may be easilypossible to cut simple sections from each surface when taken XXVI, § 199] SPHERE AND CYLINDER 285 separately. Such a case, for example, is that of two surfacesof revolution whose axes are not in the same plane, and which,from the nature of the surfaces, does not fall under any of the. Fig. 331. cases already discussed. The intersection of two suchsurfaces, therefore, may well be taken as illustrative of thegeneral method of finding the intersection of any two curvedsurfaces. 286 DESCRIPTIVE GEOMETRY [XXVI, § 199 Problem 52. To find the intersection of any two curved surfaces.(General Case.) Analysis. It is assumed that neither planes, spheres, norother auxiliary surfaces can be found which will intersectsimultaneously both of the given surfaces in straight lines orcircles ; or at least that a sufficient number of points to deter-mine the required intersection cannot be found in this solution is then effected by means of auxiliary planes(§ 186). Pass each plane so as to intersect, if possible, one ofthe given surfaces in straight lines or circles. Find the inter-section of this plane with the second surface, using secondaryauxiliary planes for the purpose. Xote the points of inter-section of the two sections; they are points on the r
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