[Footnote 31: Philolaus, Fr., p. 62, Boeckh.--Diogen. L. viii. 7, 85.
By [Greek: a(rmoni/a], Philolaus meant the musical octave: and his work included many explanations and comparisons respecting the intervals of the musical scale. (Boeckh, p. 65 seq.)]
[Footnote 32: Aristotel. De Coelo, i. 1, p. 268, a. 10. [Greek: katha/per ga/r phasin oi( Puthago/reioi, to\ pa=n kai\ ta\ pa/nta toi=s tri/sin ô(/ristai; teleutê\ ga\r kai\ me/son kai\ a)rchê\ to\n a)rithmo\n e)/chei to\n tou= panto\s, tau=ta de\ to\n tê=s tria/dos. Dio\ para\ tê=s phu/seôs ei)lêpho/tes ô(/sper no/mous e)kei/nês, kai\ pro\s ta\s a(gistei/as chrô/metha tô=n theô=n tô=| a)rithmô=| tou/tô|] (i. e. three). It is remarkable that Aristotle here adopts and sanctions, in regard to the number Three, the mystic and fanciful attributes ascribed by the Pythagoreans.]
[Footnote 33: Strümpell, Geschichte der theoretischen Philosophie der Griechen, s. 78. Brandis, Handbuch der Gr.-Röm. Phil., sect. 80, p. 467 seq.
The number Five also signified marriage, because it was a junction of the first masculine number Three with the first feminine Two. Seven signified also [Greek: kairo\s] or Right Season. See Aristotel. Metaphys. A. 5, p. 985, b. 26, and M. 4, p. 1078, b. 23, compared with the commentary of Alexander on the former passage.]
[Footnote 34: Aristotel. Ethica Magna, i. 1.]
[Side-note: Pythagorean Kosmos and Astronomy--geometrical and harmonic laws guiding the movements of the cosmical bodies.]
The Pythagoreans conceived the Kosmos, or the universe, as one single system, generated out of numbers.[35] Of this system the central point--the determining or limiting One--was first in order of time, and in order of philosophical conception. By the determining influence of this central constituted One, portions of the surrounding Infinite were successively attracted and brought into system: numbers, geometrical figures, solid substances, were generated. But as the Kosmos thus constituted was composed of numbers, there could be no continuum: each numerical unit was distinct and separated from the rest by a portion of vacant space, which was imbibed, by a sort of inhalation, from the infinite space or spirit without.[36] The central point was fire, called by the Pythagoreans the Hearth of the Universe (like the public hearth or perpetual fire maintained in the prytaneum of a Grecian city), or the watch-tower of Zeus. Around it revolved, from West to East, ten divine bodies, with unequal velocities, but in symmetrical movement or regular dance.[37] Outermost was the circle of the fixed stars, called by the Pythagoreans Olympus, and composed of fire like the centre. Within this came successively,--with orbits more and more approximating to the centre,--the five planets, Saturn, Jupiter, Mars, Venus, Mercury: next, the Sun, the Moon, and the Earth. Lastly, between the Earth and the central fire, an hypothetical body, called the Antichthon or Counter-Earth, was imagined for the purpose of making up a total represented by the sacred number Ten, the symbol of perfection and totality. The Antichthon was analogous to a separated half of the Earth; simultaneous with the Earth in its revolutions, and corresponding with it on the opposite side of the central fire.