The sources from which the pointed arch was taken have been more than once alluded to in the preceding pages. It is a subject on which a great deal more has been said and written than was at all called for by the real importance of the question. Scarcely anything was done in pointed architecture which had not already been done in the round-arch styles. Certainly there is nothing which could not have been done, at least nearly as well, and many things much better, by adhering to the complete instead of to the broken arch. The coupling and compounding of piers had already been carried to great perfection, and the assignment of a separate function to each staff was already a fixed principle. Vaulting too was nearly perfect, only that the main vaults were either hexapartite or six-celled, instead of quadripartite, as they afterwards became; an improvement certainly, but not one of much importance. Ribbed vaulting was the greatest improvement which the Mediæval architects made on the Roman vaults, giving not only additional strength of construction, but an apparent vigour and expression to the vault, which is one of the greatest beauties of the style. This system was in frequent use before the employment of the pointed arch. The different and successive planes of decoration were also one of the Mediæval inventions which was carried to greater perfection in the round Gothic styles than in the pointed. Indeed, it is a fact, that except in window tracery, and perhaps in pinnacles and flying buttresses, there is not a single important feature in the pointed style that was not invented and in general use before its introduction. Even of windows, which are the important features of the new style, by far the finest are the circular or wheel windows, which have nothing pointed about them, and which always fit awkwardly into the pointed compartments in which they are placed. In smaller windows, too, by far the most beautiful and constructively appropriate tracery is that where circles are introduced into the heads of the pointed windows. But, after hundreds of experiments and expedients had been tried, the difficulty of fitting these circles into spherical triangles remained, and the unpleasant form to which their disagreement inevitably gave rise, proved ultimately so intolerable, that the architects were forced to abandon the beautiful constructive geometric tracery for the flowing or flamboyant form; and this last was so ill adapted to stone construction, that the method was abandoned altogether. These and many other difficulties would have been avoided, had the architects adhered to the form of the unbroken arch; but on the other hand it must be confessed that the pointed forms gave a facility of arrangement which was an irresistible inducement for its adoption; and especially to the French, who always affected height as the principal element of architectural effect, it afforded an easy means for the attainment of this object.