The Theory and Practice of Perspective

by G. A. Storey

[ X]

The Diagonal

Fig. 45.

From a given point on the base line draw a line at 45°, or half a right angle, to that base. Let P be the given point. Draw a line from P to the point of distance D and this line PD will be at an angle of 45°, or at the same angle as the diagonal of a square. See definitions.

[ XI]

The Square

Draw a square in parallel perspective on a given length on the base line. Let ab be the given length. From its two

extremities a and b draw aS and bS to the point of sight S. These two lines will be at right angles to the base (see [Fig. 43]). From a draw diagonal aD to point of distance D; this line will be 45° to base. At point c, where it cuts bS, draw dc parallel to ab and abcd is the square required.

Fig. 46.	Fig. 47.

We have here proceeded in much the same way as in drawing a geometrical square (Fig. 47), by drawing two lines AE and BC at right angles to a given line, AB, and from A, drawing the diagonal AC at 45° till it cuts BC at C, and then through C drawing EC parallel to AB. Let it be remarked that because the two perspective lines (Fig. 48) AS and BS are at right angles to the base, they must consequently be parallel to each other, and therefore are perspectively equidistant, so that all lines parallel to AB and lying between them, such as ad, cf, &c., must be equal.