Nicomachus of Gersa, a Neo-Pythagorean philosopher, born at Gersa in Araba Petraea flourished about 100 CE. In his musical treatise he mentions Thrasyllus (d. 36 CE), the astrologer and confidant of Tiberius, and his Arithmetic was translated by Apuleius, who wrote under Antoninus Pius and Marcus Aurelius. He is the author of two extant treatises: 1. Arithmetike eisagonge (Introduction to Arithmetic), a metaphysical account of the theory and properties of numbers and the first work in which arithmetic was treated quite independently of geometry. It was extremely popular, was the subject of commentaries by Iamblichus (ed H. Pistelli, 1894) and others, was translated into Latin by Apuleius (according to Cassidorus, the translation itself being lost) and Boëtius, and was used as a schoolbook down to the Renaissance. 2. Egcheiridion armonikes (Manual of Harmony), complete in one book, to which are erroneously appended as a second book some fragments probably belonging to a larger treatise On Music now lost. It is the oldest authority on the Pythagorean theory of music. Photius also mentions a work by Nicomachus called Arithmetika Theologoumena (The Theology of Arithmetic), written in a spirit of Pythagorean mysticism and Oriental superstition, and setting forth the application of arithmetic, or rather of the first ten numbers, to the origin and attributes of the gods. But the extracts in Photius are now generally attributed to Iamblichus. Other works by Nicomachus were: a Life of Pythagoras and a Collection of Pythagorean Doctrines, the chief source of the life of Pythagoras and the account of his philosophy by Iamblichus.
From the eleventh edition of The Encyclopedia, 1911. Public domain. Some editing has been done for the sake of clarity.