The next 3 centuries saw one of the most astonishing growths of an empire known to world history.    Starting from the small walled town of Medina, Moslem rule was extended some 4,000 miles: to the West over Egypt, north Africa, and most of Spain; to the north into Syria, Armenia, and the Caucasus; to the northeast the Islamic armies conquered Persia, Mesopotamia, and Afghanistan; and in the Far East it even made inroads into India.