, which mark the required lengths of six feet each at the top of the wall.
[p79]
]PROBLEM X.
This is one of the most important foundational problems in perspective, and it is necessary that the student should entirely familiarize himself with its conditions.
In order to do so, he must first observe these general relations of magnitude in any pyramid on a square base.
Let A G H′, [Fig. 56.], be any pyramid on a square base.
Fig. 56.
The best terms in which its magnitude can be given, are the length of one side of its base, A H, and its vertical altitude (C D in [Fig. 25.]); for, knowing these, we know all the other magnitudes. But these are not the terms in which its size will be usually ascertainable. Generally, we shall have given us, and be able to ascertain by measurement, one side of its base A H, and either A G the length of one of the lines of its angles, or B G (or B′ G) the length of a line drawn from its vertex, G, to the middle of the side of its base. In measuring a real pyramid, A G will usually be the line most easily found; but in many architectural problems B G is given, or is most easily ascertainable.
Observe therefore this general construction.
