Hence we see how incontestable was the influence of the cupola upon so-called Gothic architecture. This truth is demonstrated by monuments yet in existence, lapidary documents above suspicion. It cannot be insisted upon too strongly, not merely for the satisfaction of archæeologic accuracy, but more especially as yet another proof that the filiation between the art of the ancients and that of the so-called Romanesque architects is no less evident than that which links together the Romanesque and the so-called Gothic. Of this latter filiation we have a direct proof in the Aquitainian cupola, the parent of those of Angoumois, which in their turn gave birth to the Angevin intersecting arch, and so prepared the way for the flying buttress, which again was to mark a new departure. CHAPTER II THE ORIGIN OF THE INTERSECTING VAULT So early as the eleventh century churches were built with one or several aisles, and in this latter case the side aisles only had ribbed vaults, the nave being covered by a timber roof. The next step was to vault all three aisles, buttressing the barrel-vaulted nave by continuous half-barrel vaults or ribbed vaults over the aisles, and further strengthening it by projecting transverse arches, or _arcs doubleaux_, the whole being crowned by a roof which embraced the side aisles. These cumbrous and timidly constructed buildings were merely imitations of the Roman basilicas. To ensure their solidity they had perforce to be narrow; and the necessary abolition of top lighting made them gloomy. We find then that, before the appearance of the cupola, mediæval architects were perfectly acquainted both with the barrel vault and the ribbed vault, the latter formed, on traditional principles, by the interpenetration of two demi-cylinders. They had even attempted to improve upon the construction by strengthening the line of penetration with a salient rib, giving an elliptic arch. But this rib was purely decorative, for in the Roman vault the stones at the line of intersection, whether ribbed or not, were in complete solidarity with the filling on either side in which they were buried. It follows that we shall seek in vain in the Roman ribbed vault the germ of the intersecting arch, with its essentially active functions. For the origin of the intersecting arch we must turn to the eleventh century. We shall find it in the dressed stone cupola of St. Front, and more especially in its pendentives. Fig. 1 gives the plan of one of the cupolas of St. Front. It is composed of four massive transverse arches, the thrusts of which are received upon four piers united by pendentives (Figs. 2 and 3) passing from the re-entering angles at the spring of the arches to the base of the circular dome itself, each of the concentric courses bearing upon the keys of the _arcs-doubleaux_, and transmitting to them, and therefore to the piers by which they are supported, the weight of the cupola itself.