Archytas Hartenstein, de Archyt. Tar. fragm. Lips. PASSAGES IN PLATO REFERRING TO THE PYTHAGOREANS. Phaedo 62 B. The saying that is uttered in secret rites, to the effect that we men are in a sort of prison, and that one ought not to loose himself from it nor yet to run away, seems to me something great and not easy to see through; but this at least I think is well said, that it is the gods who care for us, and we men are one of the possessions of the gods. Kratyl. 400 B. For some say that it (the body) is the tomb of the soul-I think it was the followers of Orpheus in particular who introduced this word—which has this enclosure like a prison in order that it may be kept safe. Gorg. 493 A. I once heard one of the wise men say that now we are dead and the body is our tomb, and that that part of the soul where desires are, it so happens, is open to persuasion, and moves upward or downward. And, indeed, a clever man--perhaps some inhabitant of Sicily or Italy-speaking allegorically, and taking the word from credible' (Tilavos) and 'persuadable (TIOTIKÓS), called this a jar (ríos); and he called those without intelligence uninitiated, and that part of the soul of uninitiated persons where the desires are, he called its intemperateness, and said it was not watertight, as a jar might be pierced with holes-using the simile because of its insatiate desires. Gorg. 507 E. And the wise men say that one community embraces heaven and earth and gods and men and friendship and order and temperance and righteousness, and for that reason they call this whole a universe, my friend, for it is not without order nor yet is there excess. It seems to me that you do not pay attention to these things, though you are wise in regard to them. But it has escaped your notice that geometrical equality prevails widely among both gods and men. PASSAGES IN ARISTOTLE REFERRING TO THE PYTHA GOREANS. Phys. iii. 4; 203 a 1. For all who think they have worthily applied themselves to such philosophy, have discoursed concerning the infinite, and they all have asserted some first principle of things-some, like the Pythagoreans and Plato, a first principle existing by itself, not connected with anything else, but being itself the infinite in its essence. Only the Pythagoreans found it among things perceived by sense (for they say that number is not an abstraction), and they held that it was the infinite outside the heavens. iii. 4; 204 a 33. the infinite is being, (The Pythagoreans) both hold that and divide it. iv. 6; 213 b 22. And the Pythagoreans say that there is a void, and that it enters into the heaven itself from the infinite air, as though it (the heaven) were breathing; and this void defines the natures of things, inasmuch as it is a certain separation and definition of things that lie together; and this is true first in the case of numbers, for the void defines the nature of these. De coel. i. 1; 268 a 10. For as the Pythagoreans say, the all and all things are defined by threes; for end and middle and beginning constitute the number of the all, and also the number of the triad. ii. 2; 284 b 6. And since there are some who say that there is a right and left of the heavens, as, for instance, those that are called Pythagoreans (for such is their doctrine), we must investigate whether it is as they say. ii. 2; 285 a 10. Wherefore one of the Pythagoreans might be surprised in that they say that there are only these two first principles, the right and the left, and they pass over four of them as not having the least validity; for there is no less difference up and down, and front and back than there is right and left in all creatures. ii. 2; 285 b 23. And some are dwelling in the upper hemisphere and to the right, while we dwell below and to the left, which is the opposite to what the Pythagoreans say; for they put us above and to the right, while the others are below and at the left. ii. 9; 290 b 15. Some think it necessary that noise should arise when so great bodies are in motion, since sound does arise from bodies among us which are not so large and do not move so swiftly; and from the sun and moon and from the stars in so great number, and of so great size, moving so swiftly, there must necessarily arise a sound inconceivably great. Assuming these things and that the swiftness has the principle of harmony by reason of the intervals, they say that the sound of the stars moving on in a circle becomes musical. And since it seems unreasonable that we also do not hear this sound, they say that the reason for this is that the noise exists in the very nature of things, so as not to be distinguishable from the opposite silence; for the distinction of sound and silence lies in their contrast with each other, so that as blacksmiths think there is no difference between them because they are accustomed to the sound, so the same thing happens to men. ii. 9; 291 a 7. What occasions the difficulty and makes the Pythagoreans say that there is a harmony of the bodies as they move, is a proof. For whatever things move themselves make a sound and noise; but whatever things are fastened in what moves or exist in it as the parts in a ship, cannot make a noise, nor yet does the ship if it moves in a river. ii. 13; 293 a 19. They say that the whole heaven is limited, the opposite to what those of Italy, called the Pythagoreans, say; for these say that fire is at the centre and that the earth is one of the stars, and that moving in a circle about the centre it produces night and day. And they assume yet another earth opposite this which they call the counter-earth [avτíx0wv], not seeking reasons and causes for phenomena, but stretching phenomena to meet certain assumptions and opinions of theirs and attempting to arrange them in a system. . . . And farther the Pythagoreans say that the most authoritative part of the All stands guard, because it is specially fitting that it should, and this part is the centre; and this place that the fire occupies, they call the guard of Zeus, as it is called simply the centre, that is, the centre of space and the centre of matter and of nature. iii. 1; 300 a 15. The same holds true for those who construct the heaven out of numbers; for some construct nature out of numbers, as do certain of the Pythagoreans. Metaphys. i. 5; 985 b 23-986 b 8. With these and before them (Anaxagoras, Empedokles, Atomists) those called Pythagoreans applying themselves to the sciences, first developed them; and being brought up in them they thought that the first principles of these (i.e. numbers) were the first principles of all things. And since of these (sciences) numbers are by nature the first, in numbers rather than in fire and earth and water they thought they saw many likenesses to things that are and that are coming to be, as, for instance, justice is such a property of numbers, and soul and mind are such a property, and another is opportunity, and of other things one may say the same of each one. And further, discerning in numbers the conditions and reasons of harmonies also†; since, moreover, other things seemed to be like numbers in their entire nature, and numbers were the first of every nature, they assumed that the elements of numbers were the elements of all things, and that the whole heavens were harmony and number. And whatever characteristics in numbers and harmonies they could show were in agreement with the properties of the heavens and its parts and with its whole arrangement, these they collected and adapted; and if there chanced to be any gap anywhere, they eagerly sought that the whole system might be connected with these (stray phenomena). To give an example of my meaning: inasmuch as ten seemed to be the perfect number and to embrace the whole nature of numbers, they asserted that the number of bodies moving through the heavens were ten, and when only nine were visible, for the reason just stated they postulated the counter-earth as the tenth. We have given a more definite account of these thinkers in other parts of our writings. But we have referred to them here. with this purpose in view, that we might ascertain from them what they asserted as the first principles and in what manner they came upon the causes that have been enumerated. They certainly seem to consider number as the first principle and as it were the matter in things and in their conditions and states; and the odd and the even are elements of number, and of these the one is infinite and the other finite, and unity is the product of both of them, for it is both odd and even, and number arises from unity, and the whole heaven, as has been said, is numbers. A different party in this same school say that the |