We must, in conclusion, investigate the perspective of inclined lines, beginning with a single one given in position. For the sake of completeness of system, I give in Appendix II. Article III. the development of this problem from the second. But, in practice, the position of an inclined line may be most conveniently defined by considering it as the diagonal of a rectangle, as A B in [Fig. 39.], and I shall therefore, though at some sacrifice of system, examine it here under that condition.
If the sides of the rectangle A C and A D are given, the slope of the line A B is determined; and then its position will depend on that of the rectangle. If, as in [Fig. 39.], the rectangle is parallel to the picture plane, the line A B must be so also. If, as in [Fig. 40.], the rectangle is inclined to the [p51] ]picture plane, the line A B will be so also. So that, to fix the position of A B, the line A C must be given in position and magnitude, and the height A D.
Fig. 41.
If these are given, and it is only required to draw the single line A B in perspective, the construction is entirely simple; thus:—
Draw the line A C by [Problem I].
Let A C, [Fig. 41.], be the line so drawn. From
a
and
c