[p 59 ] PROBLEM XIX. TO FIND THE VANISHING-POINT OF STEEPEST LINES IN AN INCLINED PLANE WHOSE SIGHT-LINE IS GIVEN .

[Geometric diagram]
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. (ProblemXVIII.)

Join TX, and draw TY at right angles to TX.

Therefore Y is the rectangular vanishing-point corresponding to X.[Footnote 29]

From Y erect the vertical YP, cutting the sight-line of the inclined plane in P.

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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.