It has already been shown that too near a point of distance is objectionable on account of the distortion and disproportion resulting from it. At the same time, the long distance-point must be some way out of the picture and therefore inconvenient. The object of the reduced distance is to bring that point within the picture.
Fig. 85.
In Fig. 85 we have made the distance nearly twice the length of the base of the picture, and consequently a long way out of it. Draw Sa, Sb, and from a draw aD to point of distance, which cuts Sb at o, and determines the depth of the square acob. But
we can find that same point if we take half the base and draw a line from ½ base to ½ distance. But even this ½ distance-point does not come inside the picture, so we take a fourth of the base and a fourth of the distance and draw a line from ¼ base to ¼ distance. We shall find that it passes precisely through the same point o as the other lines aD, &c. We are thus able to find the required point o without going outside the picture.
Of course we could in the same way take an 8th or even a 16th distance, but the great use of this reduced distance, in addition to the above, is that it enables us to measure any depth into the picture with the greatest ease.
It will be seen in the next figure that without having to extend the base, as is usually done, we can multiply that base to any amount by making use of these reduced distances on the horizontal line. This is quite a new method of proceeding, and it will be seen is mathematically correct.