By the 1st century BC, during the Hellenistic period, the Greeks had begun to develop their own mathematical schemes for predicting the positions of the planets. These schemes, which were based on geometry rather than the arithmetic of the Babylonians, would eventually eclipse the Babylonians' theories in complexity and comprehensiveness and account for most of the astronomical movements observed from Earth with the naked eye. These theories would reach their fullest expression in the Almagest written by Ptolemy in the 2nd century CE. So complete was the domination of Ptolemy's model that it superseded all previous works on astronomy and remained the definitive astronomical text in the Western world for 13 centuries. To the Greeks and Romans, there were seven known planets, each presumed to be circling Earth according to the complex laws laid out by Ptolemy. They were, in increasing order from Earth (in Ptolemy's order and using modern names): the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn.