It is evident that if the line _AD_ had been given originally, and we
had been required to draw it, and divide it into three equal parts, we
should have had only to divide its sight-magnitude, _ad′_, into the
three equal parts, _ab′_, _b′c′_, and _c′d′_, and then, drawing to _M_
from _b′_ and _c′_, the line _ad_ would have been divided as required
in _b_ and _c_. And supposing the original line _AD_ be divided
_irregularly into any number_ of parts, if the line _ad′_ be divided
into a similar number in the same proportions (by the construction
given in Appendix I.), and, from these points of division, lines are
drawn to _M_, they will divide the line _ad_ in true perspective into
a similar number of proportionate parts.
The horizontal line drawn through _a_, on which the sight-magnitudes
are measured, is called the “MEASURING-LINE.”
And the line _ad_, when properly divided in _b_ and _c_, or any other
required points, is said to be divided “IN PERSPECTIVE RATIO” to the
divisions of the original line _AD_.
If the line _aV_ is above the sight-line instead of beneath it, the
measuring-line is to be drawn above also: and the lines _b′M_, _c′M_,
etc., drawn _down_ to the dividing-point. Turn Fig. 17. upside down,
and it will show the construction.