s of an infinite number,
passing from the flattest conceivable curve, through the semicircle and
horseshoe, up to the full circle.

The central and the last group are the most important. The central
round, or semicircle, is the Roman, the Byzantine, and Norman arch; and
its relative pointed includes one wide branch of Gothic. The horseshoe
round is the Arabic and Moorish arch, and its relative pointed includes
the whole range of Arabic and lancet, or Early English and French
Gothics. I mean of course by the relative pointed, the entire group of
which the equilateral arch is the representative. Between it and the
outer horseshoe, as this latter rises higher, the reader will find, on
experiment, the great families of what may be called the horseshoe
pointed,--curves of the highest importance, but which are all included,
with English lancet, under the term, relative pointed of the horseshoe
arch.

[Illustration: Fig. XXXII.]

Sec. XV. The groups above described are all formed of circular arcs,
and include all truly useful and beautiful arches for ordinary work. I
believe that singular and complicated curves are made use of in modern
engineering, but with these the general reader can have no concern: the
Ponte della Trinita at Florence is the most graceful instance I know of
such structure; the arch made use of being very subtle, and
approximating to the low ellipse; for which, in common work, a barbarous
pointed arch, called four-centred, and composed of bits of circles, is
substituted by the English builders. The high ellipse, I believe, exists
in eastern architecture. I have never myself met with it on a large
scale; but it occurs in the niches of the later portions of the Ducal
palace at Venice, together with a singular hyperbolic arch, _a_ in Fig.
XXXIII., to be described hereafter: with such caprices we are not here
concerned.

Sec. XVI. We are, however, concerned to notice the absurdity of another
form of arch, which, with the four-centred, belongs to the English
perpendicular Gothic.

Taking the gable of any of the groups in Fig. XXXI. (suppose the
equilateral), here at _b_, in Fig. XXXIII., the dotted line representing
the relative pointed arch, we may evidently conceive an arch formed by
reversed curves on the inside of the gable, as here shown by the inner
curved lines. I imagine the reader by this time knows enough of the
nature of arches to understand that, whatever strength or stability was
gained by th