PROBLEM XVIII.

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.

Fig. 48.

Let the two lines be A B and C D, Fig. 48.

As they are given in position, the relative horizontals A E and C F must be given.

Then by Problem XVI. the vanishing-point of A B is V, and of C D, V′.

Join V V′ and produce it to cut the sight-line in X.

Then V X 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.