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.
Let the two lines be A B and C D, Fig. 48.
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.
Notes
As they are given in position, the relative horizontals A E and C F must be given.
28 Read the Article on this problem in the Appendix, p. 97, before investigating the problem itself.