Fig. 224.
Divide the base AB into ten equal parts, and suppose each of these parts to measure 10 feet, S, the point of sight, is placed on the left of the picture near the side, in order that we may get a long line of distance, S ½ D; but even this line is only half the distance we require. Let us therefore take the 16th distance, as shown in our previous illustration of the lighthouse (Fig. 92), which enables us to measure sixteen times the length of base AB, or 1,600 feet. The base ef of the pyramid is 1,600 feet from the base line of the picture, and is, according to our 10-foot scale, 764 feet long.
The next thing to consider is the height of the pyramid. We make a scale to the right of the picture measuring 50 feet from B to 50 at point where BP intersects base of pyramid, raise perpendicular CG and thereon measure 480 feet. As we cannot obtain a palpable square on the ground, let us draw one 480 feet above the ground. From e and f raise verticals eM and fN, making them equal to perpendicular G, and draw line MN, which will be the same length as base, or 764 feet. On this line form square MNK parallel to the perspective plane, find its centre O· by means of diagonals, and O· will be the central height of the pyramid and exactly over the centre of the base. From this point O· draw sloping lines O·f, O·e, O·y, &c., and the figure is complete.
Note the way in which we find the measurements on base of pyramid and on line MN. By drawing AS and BS to point of sight we find Te, which measures 100 feet at a distance of 1,600 feet. We mark off seven of these lengths, and an additional 64 feet by the scale, and so obtain the required length. The position of the third corner of the base is found by dropping a perpendicular from K, till it meets the line eS.
Another thing to note is that the side of the pyramid that faces us, although an equilateral triangle, does not appear so, as its top angle is 382 feet farther off than its base owing to its leaning position.
[ CXXIII]
The Pyramid in Angular Perspective
In order to show the working of this proposition I have taken a much higher horizon, which immediately detracts from the impression of the bigness of the pyramid.