[Illustration: Fig. 28.]
Let _AB_, Fig. 28., be the curve.
Inclose it in a rectangle, _CDEF_.
Fix the position of the point _C_ or _D_, and draw the rectangle.
(Problem VIII. Coroll. I.)[20]
Let _CDEF_, Fig. 29., be the rectangle so drawn.
[Illustration: Fig. 29.]
If an extremity of the curve, as _A_, is in a side of the rectangle,
divide the side _CE_, Fig. 29., so that _AC_ shall be (in perspective
ratio) to _AE_ as _AC_ is to _AE_ in Fig. 28. (Prob. V. Cor. II.)
Similarly determine the points of contact of the curve and rectangle
_e_, _f_, _g_.
If an extremity of the curve, as _B_, is not in a side of the
rectangle, let fall the perpendiculars _Ba_, _Bb_ on the rectangle
sides. Determine the correspondent points _a_ and _b_ in Fig. 29., as
you have already determined _A_, _B_, _e_, and _f_.
From _b_, Fig. 29., draw _bB_ parallel to _CD_,[21] and from _a_ draw
_aB_ to the vanishing-point of _DF_, cutting each other in _B_. Then
_B_ is the extremity of the curve.
Determine any other important point in the curve, as _P_, in the same
way, by letting fall _Pq_ and _Pr_ on the rectangle’s sides.
Any number of points in the curve may be thus determined, and the
curve drawn through the series; in most cases, three or four will be
enough. Practically, complicated curves may be better drawn in
perspective by an experienced eye than by rule, as the fixing of the
various points in haste involves too many chances of error; but it is
well to draw a good many by rule first, in order to give the eye its
experience.[22]