SOME of the more characteristic differences between Eastern and Western theology have been noticed in the introduction to the last chapter. It is unnecessary to repeat here what was there said. But there are specific points of difference of historical fact to which it may be well to refer. In the East the history of Eucharistic doctrine is for the most part untouched by controversy. Such controversies as arose concerning the application of the word image to the elements and the direction of the offering of the sacrifice leave unbroken the main stream of belief in the principal aspects of the doctrine. The discussions in the sixteenth century about the teaching of Cyril Lucar were rather the repelling of alien ideas coming in from outside than real difference among theologians properly Eastern. In the West the history from the ninth century to the fifteenth is continually broken by controversy; and from the sixteenth century onwards the literature of the subject is almost wholly controversial. Without going beyond the fifteenth century, there are at best marked differences of view and at worst bitter controversy in the disputes resulting from the teaching of Paschasius Radbert in the ninth century, the conflicts concerning Berengar in the eleventh, the varying types of scholastic thought in the thirteenth, and the questionings and denials and re-assertions of mediæval doctrine in the fourteenth and fifteenth.