Items related to Text-book on practical solid or descriptive geometry...
Synopsis
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. 1887 Excerpt: ... 48. To draw the projections of a line which shall pass through a given point, have a given inclination, and be parallel to a givenplane. In the given plane place a line inclined at the given angle by Problem 47. Through the plan and elevation of the given point draw lines parallel to the plan and elevation respectively of this line. These will be the projections required. That the line-whose projections have thus been found fulfils the given conditions is not difficult to see; for it is parallel to a line which has the given inclination, and must therefore have itself the given inclination. Also it can never meet the given plane, for if it did so it could not be parallel to any line in that plane, therefore it is parallel to the plane. PROBLEM 49. To draw the traces of a plane which shall contain a given point, and be parallel to a given plane. Let Hi Vi be the given plane andpp' the given point. Case I. When the traces of the given plane meet within a convenient distance (fig. 91). Fig. 91. Fig. 82. Draw p q parallel to H t and p' q' parallel to X Y, also q q' at right angles to X Y. A line through q' parallel to V. t is the required vertical trace; and a line through the point where this line meets XY parallel to Hi is the required horizontal trace. Case II. When the traces of the given plane do not meet within a convenient distance (fig. 92). In the given plane place a line a b, a' b', inclined at any angle. Draw the projections of a line to pass through P and be parallel to A B. Find the vertical and horizontal traces of the line through P; lines through these parallel to the vertical and horizontal traces respectively of the given plane will be the traces of the required plane. The construction in each case is evidently correct, for if we examine the ...
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