§ XIV. If the radius with which these intermediate curves are drawn be the base of _f_, the last is the equilateral pointed arch, one of great importance in Gothic work. But between the gable and circle, in all the three figures, there are an infinite number of pointed arches, describable with different radii; and the three round arches, be it remembered, are themselves representatives 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.] § 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. § 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.