ys: "In
what is usually called the Norman period, the general proportions and
outlines of the Churches are reducible to certain rules of setting out
by the plain Square. As Architecture progressed the Square gradually
disappeared, and the proportion of general outline, as well as of
detail, fell in more and more with applications of the Equilateral
Triangle, till the art, having arrived at its culminating point, or
that which is generally acknowledged to be its period of greatest
beauty and perfection in the thirteenth and the beginning of the
fourteenth centuries, again began to decline. With this decline the
Equilateral Triangle was almost lost sight of, and then a mode of
setting out work by diagonal squares was taken up, for such is the
basis found exactly applicable to the work of the fifteenth century,
since which time mathematical proportions have been generally
employed." And after referring to numerous scale drawings of Churches,
windows, doors, and arches, he points out that every student of Church
architecture must pronounce those of the untraceried and traceried
first point to be the most beautiful of all, those of the Norman to be
a degree less so, and those of the perpendicular and debased to be far
inferior to either, and in that analysis we find that the Equilateral
Triangle was used almost exclusively for determining one order (the
Gothic), the Square for another (the Norman), and the Square
diagonally divided for the other (the debased).

Now let me try to describe the wonderful properties of the Vesica
Piscis, so that you may understand the mystery which shrouded it in
the minds of those Mediaeval builders. The rectangle formed by the
length and breadth of this figure, in the simplest form, has several
extraordinary properties; it may be cut into three equal parts by
straight lines parallel to the shorter side, and these parts will all
be precisely and geometrically similar to each other and to the whole
figure,--strangely applicable to the symbolism attached at that time
to the Trinity in Unity,--and the subdivision may be proceeded with
indefinitely without making any change in form. However often the
operation is performed, the parts remain identical with the original
figure, having all its extraordinary properties, the Equilateral
Triangle appearing everywhere, whereas no other rectangle can have
this curious property.

It may also be cut into four equal parts by straight lines parallel to
its