PENDENTIVE  , the

term given in architecture to the bridging across the angles of a square hall, so as to obtain a circular base for a dome or drain . This may be done by corbelling out in the angles, in which case the pendentive may be a portion of a hemisphere of which the half diagonal of the square hall is the radius; or by throwing a series of arches across the angle, each ring as it rises advancing in front of the one below .and being carried by it during its construction; in this case the base obtained is octagonal, so that corbels or small pendentives are required for each angle of the octagon, unless as in the church of SS . Sergius and Bacchus at Constantinople a portion of the dome is set back; or again, by a third method, by sinking a semicircular niche in the angle . The first system was that employed in St Sophia at Constantinople, and in Byzantine churches generally, also in the domed churches of Perigord and Aquitaine . The second is found in the Sassanian palaces of Serbistan and Firuzabad, and in medieval architecture in England, France and Germany, where the arches are termed " squinches." The third system is found in the mosque at Damascus, and was often adopted in the churches in Asia Minor . There is still another method in which the pendentive and cupola are part of the same hemispherical dome, and in this case the ring courses lie in vertical instead of horizontal planes, examples of which may be found in the vault of Magnesia on Maeander in Asia Minor, and in the tomb at Valence known as le pendenlif de Valence . The problem is one which has taxed the ingenuity of many builders in ancient times; the bas-reliefs found at Nimrud show that in the 9th century B.C. domes were evidently built over square halls, and must have been carried on pendentives of some kind .