§ XI. Many architects, especially the worst, have been very curious in designing out of the way arches,--elliptical arches, and four-centred arches, so called, and other singularities. The good architects have generally been content, and we for the present will be so, with God's arch, the arch of the rainbow and of the apparent heaven, and which the sun shapes for us as it sets and rises. Let us watch the sun for a moment as it climbs: when it is a quarter up, it will give us the arch _a_, Fig. XXXI.; when it is half up, _b_, and when three quarters up, _c_. There will be an infinite number of arches between these, but we will take these as sufficient representatives of all. Then _a_ is the low arch, _b_ the central or pure arch, _c_ the high arch, and the rays of the sun would have drawn for us their voussoirs.
§ XII. We will take these several arches successively, and fixing the top of each accurately, draw two right lines thence to its base, _d_, _e_, _f_, Fig. XXXI. Then these lines give us the relative gables of each of the arches; _d_ is the Italian or southern gable, _e_ the central gable, _f_ the Gothic gable.
§ XIII. We will again take the three arches with their gables in succession, and on each of the sides of the gable, between it and the arch, we will describe another arch, as at _g_, _h_, _i_. Then the curves so described give the pointed arches belonging to each of the round arches; _g_, the flat pointed arch, _h_, the central pointed arch, and _i_, the lancet pointed arch.
§ 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.