# Plane and Solid Geometry, by G.E. Webster and A. Gardiner

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## Description

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. 1874 edition. Excerpt: ...A Bis 1" from the horizontal plane, and A is 5 from the vertical. Find also distance of B from the vertical. In Fig. 4 draw a' b ' 3" long, at a distance of one inch from X Y parallel to it. From a b ' drop indefinite perpendiculars to X Y. At a distance 5" from X Y, draw a b at an angle of 30 to X Y, and produce it until it meets the perpendicular from b ' in the point b. Then a b is the required plan of the line. The distance from i to X Y is the required distance of the point B from the vertical plane. Problem 5. Given the plan of a line a b, with the distances of the ends of A B above the horizontal plane, to draw the elevation. Suppose the heights of a' and 6' are.5" and 175" respectively: Erect perpendiculars from a and b to a' b', so that a' shall be '5" above X Y; 6' 175" above X Y. Join a' b'. Then a' b' will be the elevation of the line required. This is Evident--first, because the elevation is, from what has previously been given, within the perpendiculars produced from the ends of a b to X Y; secondly, because all distances from the horizontal plane are measured on the vertical and vice versd. Note.--That a b being inclined to the vertical does not at all iffect the measurements on the vertical for the elevation. Problem 6. Given the traces a b' of a line A B, to find its projection. The traces of a line are, as before stated, the points in which a line meets the planes of projection. The line joining a and 6' will be the line in space. From a and 6' draw a a' and 6 6' at right angle to X Y. Join a' b' and a 6. Then a' b ' will be the elevation of the line and a b the plan. Note.--The traces a and b' are simply points. The line joining a & is not the real length of the line in space....show more

## Product details

• Paperback | 26 pages
• 189 x 246 x 1mm | 68g
• United States
• English
• black & white illustrations
• 1236962125
• 9781236962126