Problem XIX
To Find the Vanishing-Point of Steepest Lines in an Inclined Plane Whose Sight-Line Is Given
Let V X, Fig. 49., be the given sight-line.
Produce it to cut the horizontal sight-line in X.
Therefore X is the vanishing-point of horizontal lines in the given inclined plane. (Problem XVIII.)
Join T X, and draw T Y at right angles to T X.
Therefore Y is the rectangular vanishing-point corresponding to X.29
From Y erect the vertical Y P, cutting the sight-line of the inclined plane in P.
All lines drawn to it, as Q P, R P, N P, etc., are the steepest possible in the plane; and all lines drawn to X, as Q X, O X, etc., are horizontal, and at right angles to the lines P Q, P R, etc.
Notes
Then P is the vanishing-point of steepest lines in the plane.
29 That is to say, the vanishing-point of horizontal lines drawn at right angles to the lines whose vanishing-point is X.