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.[Footnote 29] ]

From Y erect the vertical Y P, 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 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.

[Footnote 29: ] That is to say, the vanishing-point of horizontal lines drawn at right angles to the lines whose vanishing-point is X.] [Return to text]

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[PROBLEM XX.]

TO FIND THE VANISHING-POINT OF LINES PERPENDICULAR TO THE SURFACE OF A GIVEN INCLINED PLANE.