The Elements of Perspective / arranged for the use of schools and intended to be read in connection with the first three books of Euclid

by John Ruskin

Let them be produced, and meet in P′.

Produce P V, and it will be found to pass through the point P′.

Therefore if A Y (or C Y), [Fig. 45.], be any inclined line drawn in perspective by [Problem XV.], and A C the relative horizontal (A C in [Figs. 39], [40.]), also drawn in perspective.

Through V, the vanishing-point of A V, draw the vertical P P′ upwards and downwards.

Produce A Y (or C Y), cutting P P′ in P (or P′).

Then P is the vanishing-point of A Y (or P′ of C Y).

Fig. 45.

The student will observe that, in order to find the point P by this method, it is necessary first to draw a portion of the given inclined line by [Problem XV]. Practically, it is always necessary to do so, and, therefore, I give the problem in this form.

[p54]
]Theoretically, as will be shown in the analysis of the problem, the point P should be found by drawing a line from the station-point parallel to the given inclined line: but there is no practical means of drawing such a line; so that in whatever terms the problem may be given, a portion of the inclined line (A Y or C Y) must always be drawn in perspective before P can be found.