in Arabia (Eastern Palestine), a Neo-Pythagorean philosopher who flourished in the times of the Antonines, probably from.about 140 to 150 A.D., is noted as the author of Arithmetica (Paris, 1538; Leipsic, 1817; and again in 1861, 1866, and 1867), in which he teaches the pre-existence of numbers before the formation of the world in the mind of the Creator, where they constituted an archetype, in conformity with which he ordered all things. Nicomachus thus reduces the Pythagorean numbers, as Philo reduces the ideas, to thoughts of God. Nicomachus defines number as definite quantity (πλῆθος ἀρισμένον , 1:7). In the θεολογούμενα ἀριθμητικά (which is in the Bibl. of Photius [cod. 187], and is ascribed to this Nicomachus), he expounds the mystical signification of the first ten numbers, according to which number l was God, reason, the principle of form and goodness, and 2 the principle of inequality and change, of matter and evil. etc. The ethical problem for man, he teaches, is solved by retirement from the contact of impurity, and reunion with God. He indirectly exercised no small influence on European studies in the 15th and 16th centuries. Boethius did but abbreviate Nicomachus's larger work on arithmetic, now lost. See Smith, Dict. of Class. Biog. 2:1195; Fabricius, Bibl. Grec. v. 629.