[Footnote 14: ] The student will observe, in practice, that, his paper lying flat on the table, he has only to draw the line T V on its horizontal surface, parallel to the given horizontal line A B. In theory, the paper should be vertical, but the station-line S T horizontal (see its definition above, [page 5]); in which case T V, being drawn parallel to A B, will be horizontal also, and still cut the sight-line in V.
The construction will be seen to be founded on the second [Corollary] of the preceding problem.
It is evident that if any other line, as M N in [Fig. 9.], parallel to A B, occurs in the picture, the line T V, drawn from T, parallel to M N, to find the vanishing-point of M N, will coincide with the line drawn from T, parallel to A B, to find the vanishing-point of A B.
Therefore A B and M N will have the same vanishing-point.
Therefore all parallel horizontal lines have the same vanishing-point.
It will be shown hereafter that all parallel inclined lines also have the same vanishing-point; the student may here accept the general conclusion—“All parallel lines have the same vanishing-point.”
It is also evident that if A B is parallel to the plane of the picture, T V must be drawn parallel to G H, and will therefore never cut G H. The line A B has in that case no vanishing-point: it is to be drawn by the construction given in [Fig. 7.]
It is also evident that if A B is at right angles with the plane of the picture, T V will coincide with T S, and the vanishing-point of A B will be the sight-point.] [Return to text]
[Footnote 15: ] I spare the student the formality of the reductio ad absurdum, which would be necessary to prove this.] [Return to text]
[Footnote 16: ] For definition of Sight-Magnitude, see [Appendix I]. It ought to have been read before the student comes to this problem; but I refer to it in case it has not.] [Return to text]