The first principle or beginning of Number, was the One or Monas — which the Pythagoreans conceived as including both the two fundamental contraries — the Determining and the Indeterminate.[30] All particular numbers, and through them all things, were compounded from the harmonious junction and admixture of these two fundamental contraries.[31] All numbers being either odd or even, the odd numbers were considered as analogous to the Determining, the even numbers to the Indeterminate. In One or the Monad, the Odd and Even were supposed to be both contained, not yet separated: Two was the first indeterminate even number; Three, the first odd and the first determinate number, because it included beginning, middle, and end. The sum of the first four numbers — One, Two, Three, Four = Ten (1 + 2 + 3 + 4) was the most perfect number of all.[32] To these numbers, one, two, three, four, were understood as corresponding the fundamental conceptions of Geometry — Point, Line, Plane, Solid. Five represented colour and visible appearance: Six, the phenomenon of Life: Seven, Health, Light, Intelligence, &c.: Eight, Love or Friendship.[33] Man, Horse, Justice and Injustice, had their representative numbers: that corresponding to Justice was a square number, as giving equal for equal.[34]
[30] See the instructive explanations of Boeckh, in his work on the Fragments of Philolaus, p. 54 seq.
[31] Philolaus, Fr., p. 62, Boeckh. — Diogen. L. viii. 7, 85.
By ἁρμονία, Philolaus meant the musical octave: and his work included many explanations and comparisons respecting the intervals of the musical scale. (Boeckh, p. 65 seq.)
[32] Aristotel. De Cœlo, i. 1, p. 268, a. 10. καθάπερ γάρ φασιν οἱ Πυθαγόρειοι, τὸ πᾶν καὶ τὰ πάντα τοῖς τρίσιν ὥρισται· τελευτὴ γὰρ καὶ μέσον καὶ ἀρχὴ τὸν ἀριθμὸν ἔχει τὸν τοῦ παντὸς, ταῦτα δὲ τὸν τῆς τριάδος. Διὸ παρὰ τῆς φύσεως εἰληφότες ὥσπερ νόμους ἐκείνης, καὶ πρὸς τὰς ἁγιστείας χρώμεθα τῶν θεῶν τῷ ἀριθμῷ τούτῳ (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.
[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 καιρὸς 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.
[34] Aristotel. Ethica Magna, i. 1.
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.