[p 57 ] PROBLEM XVIII. TO FIND THE SIGHT-LINE OF AN INCLINED PLANE IN WHICH TWO LINES ARE GIVEN IN POSITION . [Footnote 28 ]

As in order to fix the position of a line two points in it must be given, so in order to fix the position of a plane, two lines in it must be given.

[Geometric diagram]
Fig.48.

Let the two lines be AB and CD, Fig.48.

[p58]
As they are given in position, the relative horizontals AE and CF must be given.

Then by ProblemXVI. the vanishing-point of AB is V, and of CD, V'.

Join VV' and produce it to cut the sight-line in X.

Then VX is the sight-line of the inclined plane.

Like the horizontal sight-line, it is of indefinite length; and may be produced in either direction as occasion requires, crossing the horizontal line of sight, if the plane continues downward in that direction.

X is the vanishing-point of all horizontal lines in the inclined plane.