The essentials of descriptive geometry . Fig. so. the diagonal NhPh and let it intersect the trace rR at a. Nowwhen the plane R returns to its first position Nh revolves to nand the diagonal aBn revolves to ab. Since Ph is on thisdiagonal p, the required plan view of P will be found at thepoint where a perpendicular from Ph to rR intersects ab. Tofind the elevation of P draw first ab, a being on the G. L. since PROBLEMS ON ANGLES 6i A is on the trace rR, and b being on rR. p, the elevation ofP, will be found on ab in a perpendicular to the G. L. from like fashion, 0 may be found and the p
The essentials of descriptive geometry . Fig. so. the diagonal NhPh and let it intersect the trace rR at a. Nowwhen the plane R returns to its first position Nh revolves to nand the diagonal aBn revolves to ab. Since Ph is on thisdiagonal p, the required plan view of P will be found at thepoint where a perpendicular from Ph to rR intersects ab. Tofind the elevation of P draw first ab, a being on the G. L. since PROBLEMS ON ANGLES 6i A is on the trace rR, and b being on rR. p, the elevation ofP, will be found on ab in a perpendicular to the G. L. from like fashion, 0 may be found and the plan and elevation of therequired rectangular opening Fig. si. 52. Corollary. Given a line and a point to draw through thepoint a Hne making a given angle with the given line. Discussion. If a plane be passed through the given point andline it will be the plane of the required angle. If this plane berevolved into H or V the true relation of the point to the Hnewill be shown when they are in the new position. The givenangle may then be constructed. If now the plane be revolved 6a ESSENTIALS OF DESCRIPTIVE GEOMETRY back to its original position the plan and elevation of the requiredangle may be found. Construction. Let the construction be made according tothe discussion. 53. Special Cases, i. To find the size of an angle when oneside is parallel to the G. L. 2. To draw two views of the bisector of an angle. PROBLEMS ON ANGLES 118. Given the triangle ABC, A = o; —3; —2; B = —i; —i; —i;C = —2; —2; —3, to find its true shape and size. 119. The point A = o; o; —3; the point B = +1; o; —i; the pointC = +2; o; —2; the point
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