But the three-pieced arch is properly representative of all; and the larger and more complicated constructions are merely produced by keeping the central piece for what is called a keystone, and putting additional joints at the sides. Now so long as an arch is pure circular or pointed, it does not matter how many joints or voussoirs you have, nor where the joints are; nay, you may joint your keystone itself, and make it two-pieced. But if the arch be of any bizarre form, especially ogee, the joints must be in particular places, and the masonry simple, or it will not be thoroughly good and secure; and the fine schools of the ogee arch have only arisen in countries where it was the custom to build arches of few pieces. § XV. The typical pure pointed arch of Venice is a five-pieced arch, with its stones in three orders of magnitude, the longest being the lowest, as at _b2_, Plate III. If the arch be very large, a fourth order of magnitude is added, as at _a2_. The portals of the palaces of Venice have one or other of these masonries, almost without exception. Now, as one piece is added to make a larger door, one piece is taken away to make a smaller one, or a window, and the masonry type of the Venetian Gothic window is consequently three-pieced, _c2_. § XVI. The reader knows already where a cusp is useful. It is wanted, he will remember, to give weight to those side stones, and draw them inwards against the thrust of the top stone. Take one of the side stones of _c2_ out for a moment, as at _d_. Now the _proper_ place of the cusp upon it varies with the weight which it bears or requires; but in practice this nicety is rarely observed; the place of the cusp is almost always determined by æsthetic considerations, and it is evident that the variations in its place may be infinite. Consider the cusp as a wave passing up the side stone from its bottom to its top; then you will have the succession of forms from _e_ to _g_ (Plate III.), with infinite degrees of transition from each to each; but of which you may take _e_, _f_, and _g_, as representing three great families of cusped arches. Use _e_ for your side stones, and you have an arch as that at _h_ below, which may be called a down-cusped arch. Use _f_ for the side stone, and you have _i_, which may be called a mid-cusped arch. Use _g_, and you have _k_, an up-cusped arch. § XVII. The reader will observe that I call the arch mid-cusped, not when the cusped point is in the middle of the curve of the arch, but when it is in the middle of the _side piece_, and also that where the side pieces join the keystone there will be a change, perhaps somewhat abrupt, in the curvature.