part in the Pythagorean system as mathematics, or numbers. His idea appears to be, that order or harmony of relation is the regulating principle of the whole universe. He drew out a list of ten pairs of antagonistic elements, and in the octave and its different harmonic relations, he believed that he found the ground of the connexion between them. In his system of the universe fire was the important element, occupying both the centre and the remotest point of it; and being the vivifying principle of the whole. Round the central fire the heavenly bodies he believed to move in a regular circle; furthest off were the fixed stars; and then, in order, the planets, the moon, the sun, the earth, and what he called ἀντίχθων, a sort of other half of the earth, which was a distinct body from it, but moving parallel to it.
The most distant region he called Olympus; the space between the fixed stars and the moon he called κόσμος; the space between the moon and the earth οὐρανός. He, or at least his disciples, taught that the earth revolved on its axis, (though Philolaus taught that its revolutions were not round its axis but round the central fire). The universe itself they considered as a large sphere, and the intervals between the heavenly bodies they thought were determined according to the laws and relations of musical harmony. And from this theory arose the doctrine of the Music of the Spheres; as the heavenly bodies in their motion occasioned a sort of sound depending on their distances and velocities; and as these were determined by the laws of harmonic intervals, the sounds, or notes, formed a regular musical scale.
The light and heat of the central fire he believed that we received through the sun, which he considered a kind of lens: and perfection, he conceived to exist in direct ratio to the distance from the central fire.
The universe, itself, they looked upon as having subsisted from all eternity, controlled by an eternal supreme Deity; who established both limits and infinity; and whom they often speak of as the absolute μονὰς, or unity. He pervaded (though he was distinct from) and presided over the universe. Sometimes, too, he is called the absolute Good,—while the origin of
