If G H is given, describe the circle from H, with distance G H, and it will similarly cut F G in G.
It is especially necessary for the student to examine this construction thoroughly, because in many complicated forms of ornaments, capitals of columns, etc., the lines B G and G H become the limits or bases of curves, which are elongated on the longer (or angle) profile G H, and shortened on the shorter (or lateral) profile B G. We will take a simple instance, but must previously note another construction.
It is often necessary, when pyramids are the roots of some ornamental form, to divide them horizontally at a given vertical height. The shortest way of doing so is in general the following.
Fig. 58.
Let A E C, [Fig. 58.], be any pyramid on a square base A B C, and A D C the square pillar used in its construction.
[p81]
]Then by construction ([Problem X.]) B D and A F are both of the vertical height of the pyramid.
Of the diagonals, F E, D E, choose the shortest (in this case D E), and produce it to cut the sight-line in V.
Therefore V is the vanishing-point of D E.
Divide D B, as may be required, into the sight-magnitudes of the given vertical heights at which the pyramid is to be divided.