_Obs._ The dividing-points found by the above rule, used with the
ordinary measuring-line, will lay off distances on the retiring
inclined line, as the ordinary dividing-points lay them off on the
retiring horizontal line.
Another dividing-point, peculiar in its application, is sometimes
useful, and is to be found as follows:—
[Illustration: Fig. 47.]
Let _AB_, Fig. 47., be the given inclined line drawn in perspective,
and _Ac_ the relative horizontal.
Find the vanishing-points, _V_ and _E_, of _Ac_ and _AB_; _D_, the
dividing-point of _Ac_; and the sight-magnitude of _Ac_ on the
measuring-line, or _AC_.
From _D_ erect the perpendicular _DF_.
Join _CB_, and produce it to cut _DE_ in _F_. Join _EF_.
Then, by similar triangles, _DF_ is equal to _EV_, and _EF_ is
parallel to _DV_.
Hence it follows that if from _D_, the dividing-point of _Ac_, we
raise a perpendicular and make _DF_ equal to _EV_, a line _CF_, drawn
from any point _C_ on the measuring-line to _F_, will mark the
distance _AB_ on the inclined line, _AB_ being the portion of the
given inclined line which forms the diagonal of the vertical rectangle
of which _AC_ is the base.
[27] The demonstration is in Appendix II., p. 104.