353 
Euclid, in his first problem, describes an equilateral 
triangle upon a given straight line (plate 1, No. 1), and 
this is done by striking two intersecting circles, having 
their centres respectively at the ends of this straight line, 
such straight line being therefore the radius of the circles. 
The arcs of these circles inscribino^ the trianofle are two 
limbs of a spherical equilateral triangle. This is generally 
considered as the actual form of the lancet arch. I am 
prepared to prove that it is not so, and that the spherical 
equilateral triangle is seldom used in lights of the thir- 
teenth century : for this I now assign reasons. 
Euclid treats simply of lines ; but, as in architecture 
mouldings are introduced, the equilateralism is destroyed^ 
and difficulty has thereby arisen in ascertaining which are 
the normal or principal lines. The plan I have adopted 
is this — to consider the outline formed by the light (or 
glazed part of a window) as the normal line, and the suc- 
cessful application of this plan induces the belief that it is 
the only correct one. 
It is evident that, in a continued arcade, the inner line can 
never be a portion of a spherical equilateral triangle, where 
mouldings are introduced, excepting in the instance in which 
the mouldings form a mitre (i. e. the diagonal junction of 
the mouldings — (see plate 1, No. 2), because the diameter 
of the enclosing circle forms the bases of two equilateral 
triangles exactly. I am only acquainted with one example 
approaching to this form, a very early one, in Anselm's 
Tower, Canterbury Cathedral. (See plate 1, No. 2; also 
Britton's Canterbury Cathedral, plate 22.) 
I now proceed to show the impossibility of the spherical 
equilateral triangle existing under any other circumstances, 
by a reference to the Norman arcade in Malmesbury Abbey, 
(plate 1, No. 3.) Here we find the arches formed by inter- 
secting bands, (in the architecture of the thirteenth century, 
31 2 
