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Nicomachus (Greek: Νικόμαχος) (c. 60 – c. 120) was an important mathematician in the ancient world and is best known for his works Introduction to Arithmetic (Arithmetike eisagoge) and Manual of Harmonics in Greek. He was born in Gerasa, Roman Syria (now Jerash, Jordan), and was strongly influenced by Aristotle. He was a Pythagorean.



Nothing is known about the life of Nicomachus except that he was a Pythagorean and that he came from Gerasa. The age in which he lived (c. 100 AD) is only known because he mentions Thrasyllus in his Manual of Harmonics, and because his Introduction to Arithmetic was apparently translated into Latin in the mid 2nd century by Apuleius. As a Neo-Pythagorean, Nicomachus was often more interested in the mystical properties of numbers rather than their mathematical properties.



Introduction to Arithmetic

Introduction to Arithmetic (Greek: Ἀριθμητικὴ εἰσαγωγή), the lesser work on arithmetic. Nicomachus writes extensively on numbers, especially on the significance of prime numbers and perfect numbers and argues that arithmetic is ontologically prior to the other mathematical sciences (music, geometry, and astronomy), and is their cause. Boethius' De institutione arithmetica is in large part a Latin translation of this work.

Manual of Harmonics

Manual of Harmonics (Greek: Ἐνχειρίδιον ἁρμονικῆς). This is the first important music theory treatise since the time of Aristoxenus and Euclid. It provides the earliest surviving record of the story of Pythagoras's epiphany outside a smithy that pitch is determined by numeric ratios. Nicomachus also gives the first in depth account of the relationship between music and the ordering of the universe via the "music of the spheres." Nicomachus's discussion of the governance of the ear and voice in understanding music unites Aristoxenian and Pythagorean concerns, normally regarded as antitheses.[1] In the midst of theoretical discussions, Nicomachus also describes the instruments of his time, also providing a valuable resource. In addition to the Manual, ten extracts survive from what appear to have originally been a more substantial work on music.

Lost Works

The works which are lost are:

  • Art of Arithmetic (Greek: Τεχνη ἀριθμητικῆ), the larger work on arithmetic, mentioned by Photius.
  • A larger work on music, promised by Nicomachus himself, and apparently referred to by Eutocius in his comment on the sphere and cylinder of Archimedes.
  • An Introduction to Geometry, referred to by Nicomachus,[2] although whether it was his work in unclear.
  • Theology of Arithmetic (Greek: Θεολογούμενα ἀριθμητικῆς), on the Pythagorean mystical properties of numbers in two books mentioned by Photius. There is an extant work sometimes attributed to Iamblichus under this title written two centuries later which contains a great deal of material thought to have been copied or paraphrased from Nicomachus' work.
  • A Life of Pythagoras, one of the main sources used by Porphyry and Iamblichus, for their (extant) Lives of Pythagoras.
  • A collection of Pythagorean dogmata, referred to by Iamblichus.
  • On Egyptian festivals (Greek: Περὶ ἑορτῶν Αἰγυπτίων), is mentioned by Athenaeus, but whether by this Nicomachus is uncertain.

See also


  1. ^ Levin, "Nicomachus of Gerasa," Grove Music Online.
  2. ^ Nicomachus, Arithmetica, ii. 6. 1.


  • Flora R. Levin, "Nicomachus of Gerasa," Grove Music Online, visited 3 June 2007.
  • Andrew Barker, editor, Greek Musical Writings vol 2: Harmonic and Acoustic Theory (Cambridge: Cambridge University Press, 1989), pp. 245-69.

External links

1911 encyclopedia

Up to date as of January 14, 2010

From LoveToKnow 1911

There is more than one meaning of Nicomachus discussed in the 1911 Encyclopedia. We are planning to let all links go to the correct meaning directly, but for now you will have to search it out from the list below by yourself. If you want to change the link that led you here yourself, it would be appreciated.

Simple English

Nicomachos or Nicomachus is a Greek name. It can mean:

  • Nicomachus, the father of Aristotle and court physician (doctor) to King Amyntas III of Macedon. Nicomachus died when Aristotle was about 10. Nicomachus wanted Aristotle to follow in his footsteps. But Aristotle did not become a doctor but a philosopher.


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