TO FIND THE SIGHT-LINE OF AN INCLINED PLANE IN WHICH TWO LINES ARE
GIVEN IN POSITION.[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.
[Illustration: Fig. 48]
Let the two lines be _AB_ and _CD_, Fig. 48.
As they are given in position, the relative horizontals _AE_ and _CF_
must be given.
Then by Problem XVI. 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.
[28] Read the Article on this problem in the Appendix, p. 97, before
investigating the problem itself.