TO FIND THE VANISHING-POINT OF STEEPEST LINES IN AN INCLINED PLANE
WHOSE SIGHT-LINE IS GIVEN.
[Illustration: Fig. 49.]
Let _VX_, 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 _TX_, and draw _TY_ at right angles to _TX_.
Therefore _Y_ is the rectangular vanishing-point corresponding to
_X_.[29]
From _Y_ erect the vertical _YP_, cutting the sight-line of the
inclined plane in _P_.
Then _P_ is the vanishing-point of steepest lines in the plane.
All lines drawn to it, as _QP_, _RP_, _NP_, etc., are the steepest
possible in the plane; and all lines drawn to _X_, as _QX_, _OX_,
etc., are horizontal, and at right angles to the lines _PQ_, _PR_,
etc.
[29] That is to say, the vanishing-point of horizontal lines drawn at
right angles to the lines whose vanishing-point is _X_.