1. On the Power of Numbers to Explain Phenomena
'There is a gift--so it seems to me--which the gods let fall from their abode, and it was through Prometheus, or someone like him, that it reached mankind, together with a fire exceeding bright. The men of old, who were better than ourselves, passed on this gift in the form of a saying. All things, so it ran, that are ever said to be consist of a one and many, and have in their nature a conjunction of limit and unlimited. This then being the ordering of things we ought, they said, whatever it be that we are dealing with, to assume a single form. . .then we must go from one form to look for two, if the case admits of there being two, otherwise for three or some other number of forms.' (Plato, Philebus 16d)
'And so the Pythagoreans used to invoke the tetrad as their most binding oath: "Nay, by him that gave to our generation the tetraktys, which contains the fount and root of eternal nature" '(A‘tius, I, 3,8)
'For 1 is the point, 2 is the line, 3 the triangle, and 4 the pyramid. . and the same holds in generation too, for the first principle in magnitude is the point, the second the line, the third surface, and the fourth the solid.' (Speusippus in Theologumena Arithmeticae, 84,10, de Falco)
'The sixth tetraktys is of things that grow. The seed is analogous to the the unit and point, growth in length to the dyad and the line, growth in breadth to the triad and the plane, growth in depth to the tetrad and the solid.' (Theo Smyrnaeus 97,17 Hiller)
2. Pythagorean Astronomy
'Those in Italy called Pythagoreans say that at the center is fire, the earth being in effect one
of the planets which moves in a circle about the center and thus produces day and night. They also hold that there is another earth, behind and facing this one, which they call the "counter-earth".' (Aristotle de Caelo 293a7)
ÔThey supposed the whole heaven to be a musical scale and a number...and if there was a gap anywhere they readily made additions so as to make their theory coherent. E.g. as the number 10 is thought to be perfect and to comprise the whole nature of numbers, they say that the bodies which move through the heaven are ten, but as the visible bodies are only nine, to meet this they invent a tenth, the "counter-earth".' (Aristotle, Metaphysics 985b)
3. ÔPythagoreanÕ Medical Ideas
'Health is conserved by equal balance (isonomia) among the powers--wet and dry, cold and
hot, bitter and sweet, etc., disease being produced by the sole dominance (monarchia) of one among them, for the sole dominance of either one of them would be destructive [of the other]. And illness comes about by an excess of heat or cold, from too much or too little food, and in the blood or marrow of the brain. . .health is the proportionate mixture (symmetron krasin) of the qualities.' (Alcmaeon Fr. 4)
4. Philosophy as a Way of Life
'Well, then, if Homer did no public service, is he said to have become during his lifetime
an educational leader in private with pupils who loved him for his company and who handed down a Homeric way of life to their successors-- like Pythagoras who was himself particularly loved on this account and whose successors even today talk of a Pythagorean mode of life and are thought to stand out from others?' (Plato, Republic 600a-b)
'Life, he said, is like a festival; just as some come to the festival to compete, some to ply their trade, but the best come as spectators, so in life the slavish men go hunting for gain or profit, the philosophers for the truth.' (Diogenes Laertius, Lives of the Philosophers VIII, 8).
5. A Letter from Theano, a Pythagorean Woman:
ÔTheano to Euridike, the admirable: What pain possesses your soul? You are disheartened for no other reason than that he with whom you live together has gone to a prostitute and takes pleasure with her. But you should not be in such a way, excellent among women. For, do you not see that when hearing becomes full of the pleasure of an instrument, and is filled with melodious singing, when it is saturated with this, then it loves to hear the flute and it listens with pleasure to the reed pipe. Indeed, is there not a kind of harmony between the flute, lyrical song, and the wondrous ringing of the instrument of most honey-sweet quality? It is also this way for you, as it is for the prostitute with whom your husband keeps company. For, your man gives heed to you in his habits, his nature, and his thought, but at some time when he receives his fill, he will in passing keep company with the prostitute, for to those in whom corrupting juices are stored, there is a certain desire for nourishment not counted among the good thingsÕ. (A translation of the Greek text in Holger Thesleff, The Pythagorean Texts of the Hellenistic Period: Acta Academiae Aboensis, Humaniora Ser. A, vol. 30, no. 1 (Abo: Abo Akademi, 1965).