Forgotten, believes Dr. Asimov, in the sense of being slighted, even slandered, by Western historians -- but this conscientious recapitulation of Byzantine history is defeated by an excess of detail, a want of emphasis and topical development: ultimately, one remembers not what the Empire stood for but the difficulty of keeping it standing. That Constantinople simply stood, especially against the Arab surge, Dr. Asimov sees as more critical for Christian Europe than the Battle of Tours: he posits wholesale conversion to Islam as the outcome of Moslem penetration in the seventh century. The religious schisms and doctrinal controversies that figured so largely in Byzantine history are attended to carefully here, and that, beside the record per se -- the fortunes of the Empire clarified by maps, each ruler rigorously profiled -- is the chief attraction of the book. By comparison, Jacobs' American Heritage panorama (1969, p. 786, J-308) is more dynamic and focal, Chubb's The Byzantines more fluid and colorful; you can turn to this for greater precision but you can't count on anyone's reading it through. Table of dates and genealogies appended.