Nicomachus of Gerasa Analysis


Hardly anything is known of Nicomachus of Gerasa (nuh-KAHM-uh-kuhs of JEHR-uh-suh) beyond his surviving works. His Arithmītikī eisagōgī (n.d.; Introduction to Arithmetic, 1926) is a general textbook that synthesizes the metaphysics of Plato and Pythagoras, emphasizing mathematics. His Enchiridion harmonikīs (n.d.; Handbook of Harmony, 1967) is also primarily a work of metaphysics. His Theologoumena arithmetikīs (n.d.; theology of arithmetic) survives only in fragments and in a summary by the ninth century Byzantine patriarch and scholar Saint Photius. Among Nicomachus’s lost works are a biography of Pythagoras, a geometry textbook, and perhaps an encyclopedia.


Translated into Latin by both Lucius Apuleius and Boethius, Introduction to Arithmetic remained popular through the Middle Ages and Renaissance. Handbook of Harmony was a key text in both music and astronomy, insofar as it expounded the “harmony of the spheres” theory of planetary motion that Johannes Kepler partially vindicated in his Harmonice Mundi (1619; partial translation Harmonies of the World, 1952). In the twentieth century, philosophers such as Edward Pols have asserted that the most creative eras in human history are Pythagorean eras, that is, eras when the relationship between metaphysics and mathematics is very close.

Additional Resources

Guthrie, Kenneth Sylvan. The Pythagorean Sourcebook and Library. Grand Rapids, Mich.: Phanes, 1987.

Levin, Flora Rose. The Harmonics of Nicomachus and the Pythagorean Tradition. University Park, Pa.: American Philological Association, 1975.

O’Meara, Dominic J. Pythagoras Revived: Mathematics and Philosophy in Late Antiquity. Oxford, England: Clarendon Press, 1989.