Practical geometry, linear perspective, and projection
Thomas Bradley
Paperback
(RareBooksClub.com, May 14, 2012)
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. 1834 Excerpt: ... to the plane of projection; then its vanishing line will pass through C the centre of the picture (21.), and will be parallel to AB; now as all lines perpendicular to the plane (A B) will be parallel to the plane of projection, these lines can have no vanishing point; or the point S will be at an infinite distance-from C (or R; see last figs.); for the radial, V S, of such lines, will be also parallel to the plane of projection, and can consequently never meet it. Let L M be the intersection of a second plane with (AB) as before, then V Y drawn through V parallel to L M, will be the radial of it, and Y will be its vanishing point; this second plane (LM) being supposed perpendicular to (AB),its intersecting line will be perpendicular to A B (Geom. IV. ยง 2. Pr. 18), and is therefore a line passing through N parallel to C V, or perpendicular to A B: and a line through Y also parallel to C V or perpendicular to A B, will be the vanishing line of the plane (L M). If the intersection L M be parallel to A B, the plane (LM) supposed perpendicular to (AB), will be parallel to the plane of projection; and can consequently have neither intersecting nor vanishing line (1. and 23.). III. If the second plane (LM) be not perpendicular to the plane (A B), its vanishing line cannot pass through S, the vanishing point of lines perpendicular to (A B); because no line in (L M) can be perpendicular to (A B), and consequently no line in it can have S for a vanishing point. Let L M be the intersection of the second plane, which is supposed to be inclined to the plane (A B), at any given or known angle: from any point P, in LM, draw P D, P Q, perpendicular and parallel to AB, and make the angle PDQ equal to CRV, or to the angle, which the plane (A B) makes with the plane of ...