eleton plan upon such a
scale of subdivision that a tracing-board, of 5 feet by 8 feet, would
be divided up into over one million parts, and, as all these
subdivisions are perfect representations of the original Vesica figure
with all its properties, the design of the largest building, with the
minutest detail, could be drafted with absolute accuracy. There are
many other curious properties of this Figure, but they are difficult
to explain without diagrams. I will, however, give one more example of
its creative power. The problem of describing a Pentagon must have
puzzled architects considerably in those early times, but this was
again easily accomplished by means of the Vesica. Albrecht Duerer, the
great designer and engraver, who lived at the end of the fifteenth
century, refers to the Vesica in his works (_Dureri Institutune
Geometricarum_, lib. ii. p. 56) in a way which shows that it was as
commonly known in his time as the Circle, Square, and Triangle. His
instructions for forming a Pentagon are: "Designa circino invariato
tres piscium vesicas" (describe with unchanged compasses three vesicae
piscium). Three similar circles are described with centres at the
angles of an Equilateral Triangle, forming the three Vesicae, by means
of which the Pentagon is drawn, and from which also we get a beautiful
form of arch very common in the thirteenth century (_vide_
illustrations in _Magister Mathesios_). This is also the method used
in that old manuscript of the fifteenth century named "Geometria
deutsch." In this old MS. it is also shown that the easiest method for
finding the centre of a circle, however large, or any segment of a
circle, is by means of the Vesica Piscis. And just as we see so many
Cathedrals of the Middle Ages are stated by antiquarians to have been
planned on the Equilateral Triangle, so do we find the Pentagon
appearing as the basis of Architectural designs of buildings of a
later date, such as Liverpool Castle, Chester Castle, and other
similar structures; but the true means by which each were laid down,
as in the case of the Equilateral Triangle, was again the Vesica
Piscis. A beautiful example of decoration, on the basis of the Vesica,
is seen in the tomb of Edward the Confessor in Westminster Abbey.

I will conclude this subject by quoting from the summing up by Prof.
Kerrich (Principal Librarian to the University of Cambridge in 1820),
in his masterly Essay on Architecture, where he gives the differe