Descriptive geometry . Fig. 195. include one through the contour element E of the cylinder;one through the highest element, G; one through the center ofthe torus; and one tangent at the bottom of the torus. Thepoints 7 and 8 of the intersection evidently lie in the plane X,which passes through the center of the torus parallel to V. CHAPTER XIV PROBLEMS INVOLVING THE REVOLUTION OF PLANES 133. A Line Lying in a Given Plane. One method of locatinga line so that it will lie in a given plane is to assume the tracesof the line in the corresponding traces of the plane. This hasalready been explained
Descriptive geometry . Fig. 195. include one through the contour element E of the cylinder;one through the highest element, G; one through the center ofthe torus; and one tangent at the bottom of the torus. Thepoints 7 and 8 of the intersection evidently lie in the plane X,which passes through the center of the torus parallel to V. CHAPTER XIV PROBLEMS INVOLVING THE REVOLUTION OF PLANES 133. A Line Lying in a Given Plane. One method of locatinga line so that it will lie in a given plane is to assume the tracesof the line in the corresponding traces of the plane. This hasalready been explained in § 97. (See Fig. 123.). Fig. 123 (repeated). Another method is to assume one of the projections of theline. As soon as either the H- or the F-projection of a line isassumed, the line becomes definite from the condition that itshall lie in the given plane. Problem 16. Given one projection of a line lying in a plane, tofind the other projection. Analysis. The other projection of the line will be deter-mined if two points on it are found. Whenever it is practi-cable, the simplest points to consider are the two traces, s and t,which lie, respectively, in the horizontal and vertical traces ofthe given planes (§ 90). One trace of the line will be at theintersection of the given projection with the correspondingtrace of the plane, the other projection of this point being inGL. The other trace of the line will be in the other trace ofthe plane, and is determined by a projector drawn from theintersection of the given projection with GL. 125 126 DESCRIPTIVE GEOMETRY [XIV, § 133 Construction (Fig. 196). Let the plane
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