PROBLEM XIX.

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_.

The Elements of Perspective arranged for the use of schools and intended to be read in connection with the first three books of Euclid · 第 65 / 91 题