NICOMACHUS OF GERASA

flourished AD 100, , Gerasa, Roman Syria [now Jarash, Jordan] Neo-Pythagorean philosopher and mathematician who wrote Arithmetike eisagoge (Introduction to Arithmetic), an influential treatise on number theory. Considered a standard authority for 1,000 years, the book sets out the elementary theory and properties of numbers and contains the earliest-known Greek multiplication table. In his Arithmetike Nicomachus, unlike Euclid, gave no abstract proofs of his theorems. Instead he merely enunciated the theorems and illustrated them with specific numerical examples. A Latin translation of the Arithmetike by Apuleius of Madaurus (c. AD 125) is lost, but Boethius' version survived and was used as a schoolbook up to the Renaissance. Nicomachus' Encheiridion Harmonikes (Handbook of Harmony) is on the Pythagorean theory of music. He also wrote Theologoumena arithmetikes, 2 vol. (The Theology of Numbers), on the mystic properties of numbers, but only fragments of this work have survived.