Practical Geometry and Graphics (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1912 Excerpt: ...be the elevation required. 186. To draw the Traces of a Plane which shall contain a given Line and be perpendicular to a given Plane.--Determine the projections of a line to intersect the given liae and be perpendicular to the given plane. Find the traces of a plane to contain these two intersecting lines. These will be the traces required. 187. Given the Inclinations of two intersecting Lines and the Angle between them, to draw their Projections and the Traces of the Plane containing them.--Draw C, A and C, B (Fig. 428) making the angle AC, B equal to the given angle between the lines. From a point A in C, A draw AD making the angle C, AD equal to a, the given inclination of one of the lines. Draw C, D perpendicular to AD. With centre C, and radius C, D describe an arc DEF and draw BF to touch this arc and make the angle C, BF equal to /8, the given inclination of the other line. Join AB. Consider the triangle AC, B to be on the horizontal plane and imagine this triangle to rotate about the side AB until the point C, is at a distance equal to C, D or CtF from the horizontal plane. Denoting the new position of the point C, by C (see the pictorial projection, Fig. 429), the lines CA and CB will be inclined to the horizontal plane at angles equal to a and /8 respectively, and their plans will be equal in length to AD and BF respectively. Hence, if with centre A and radius AD the arc Dc be described, and if with centre B and radius BF the arc Be be described, meeting the former arc at c, Ac and Be will be the plans of the lines required. AB will be the horizontal trace of the plane containing the lines CA and CB. An elevation of the lines on any vertical plane can easily be obtained, since A and B are on the horizontal plane and the distance of. C from the horizo