Descriptive geometry . nes perpendicular to H. Takefor example the plane X, containing the element 8-18. Theintersection of HX and HQ locates one point, a, in the line ofintersection of these planes. A second point cannot be locatedby the use of VX. A similar situation is found for the planesY, Z, etc. Even if some of the lines of intersection could befound by means of the F-traces of the planes, it would notassist in finding the other lines of intersection, since the com-mon point of the preceding problem is not available. In thiscase, had we begun by taking the auxiliary planes perpendicu-la
Descriptive geometry . nes perpendicular to H. Takefor example the plane X, containing the element 8-18. Theintersection of HX and HQ locates one point, a, in the line ofintersection of these planes. A second point cannot be locatedby the use of VX. A similar situation is found for the planesY, Z, etc. Even if some of the lines of intersection could befound by means of the F-traces of the planes, it would notassist in finding the other lines of intersection, since the com-mon point of the preceding problem is not available. In thiscase, had we begun by taking the auxiliary planes perpendicu-lar to V, we would have been confronted by a similar situation. The method given below is a general one, and may be usedwhen finding the intersection of any ruled surface with aplane. Let L (Lh, Lv) be any arbitrarily chosen line lying in theplane Q. For convenience, this line is usually taken as one ofthe principal lines (§ 99) of the plane. Other conditions gov- XXII, §180] PLANE AND CONICAL FRUSTUM 233 xvy zv j-Kw c. Fig. 30G. 234 DESCRIPTIVE GEOMETRY [XXII, § 180 erning the choice of the line L should be apparent afterobserving the use which is made of it. The line L intersectsthe plane X in the point a (see Fig. 178, § 119). But L lies inthe plane Q. Hence the point x lies in both the planes X andQ, consequently is a point in their line of intersection, A. TheF-projection, Av, must therefore pass through xv in Lv, and isdetermined by xv and the point av, previously noted in theground line. Similarly, the line L intersects the plane Y inthe point y, which must lie in the line of intersection of TandQ; and so on. The F-projections of the lines of intersectionof the auxiliary planes with Q being thus determined, thepoints on the curve of intersection are noted as in the preced-ing problem. C. A Line Tangent to the Curve of See § 178. Construction. The point chosen is 27, lying on the element7-17. The plane S is passed tangent to the frustum at thispo
Size: 1160px × 2154px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometrydescriptive
