Author: Solomon Woolf

Publisher: Theclassics.Us

Published: 2013-09

Total Pages: 46

ISBN-13: 9781230734927

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 edition. Excerpt: ...by making the perpendicular b"b" equal to c'b'; hence a"b" is the distance required. (4) Bring the plane (Fig. 177), vertically projecting the line which joins the two points, parallel to V by rabattement around any vertical, preferably that passing through (a', a"). This point remains fixed, and the point (b', b") assumes the position (b/,,") by making the perpendicular b'b/ equal to c'rb"; hence a'b/ is the distance required. 189. PROBLEM.--Upon a given line to measure a given distance from either extremity. Let (a', a") be the extremity from which the measurement is to be made (Figs. 178, 179), and (b', b") any other point of the given line. Fig. 178,5' Fig. Itq Bring the line by any of the preceding four methods parallel to either coordinate plane, and measure upon the projection so determined the required length. By a Counter-rotation restore the dividing point (cx cx") to the primitive projections; (a'c', a"c") is the distance sought. II. DISTANCE OF POINT FROM LINE. 190. Problem.--To determine the perpendicular between a point and a line given by their projections., The point and line fixing the position of a plane, their distance from each other may be found by the rabattement of that plane. (1) Let (a a") be the given point, and (b'c', b"c") the given line (Fig. 180) Bring the plane of these two by rabattement around a horizontal, preferably that which passes through the point (a', a"). During rotation this point remains fixed, and the line be assumes the position (b/'c," b/c) (Art. 183); hence, letting fall a perpendicular (a"ox") upon b"c," a"o" is the horizontal projection of the perpendicular sought....