"Some... agreeing with , believe that the proportion is called harmonic because it attends upon all geometric harmony, and they say that 'geometric harmony' is the cube because it is harmonized in all three dimensions, being the product of a number thrice multiplied together. For in every cube this proportion is mirrored; there are in every cube 12 sides, 8 angles and 6 faces; hence 8, the [harmonic] mean between 6 and 12, is according to harmonic proportion..."
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Note: this harmonic proportion may be expressed as \frac{12}{6}=\frac{12-8}{8-6} or inversely.
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Nicomachus
, or Nicomachus of Gerasa, (Greek: Νικόμαχος; c. 60 – c. 120 CE) was an important ancient Greek mathematician best known for ' and Manual of Harmonics. He was born in , in the Roman province of Syria (now , ). Although a Neopythagorean who wrote about the mystical properties of numbers, Nicomachus was strongly influenced by Aristotle.
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