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covery. ii. 13; 343. Herakleides and the Pythagoreans asserted that each world [xóoμos] of the stars is air and aether surrounding earth in the infinite aether. And these doctrines are brought out in the Orphic writings, for they construct each world of the stars. ii. 22; 352. The Pythagoreans: The sun is spherical. ii. 23; 353. Plato, Pythagoras, Aristotle: The solstices lie along the slant of the zodiacal circle, through which the sun goes along the zodiac, and with the accompaniment of the tropic circles; and all these things also the globe shows. ii. 24; 354. An eclipse takes place when the moon comes past. ii. 25; 357. Pythagoras: The moon is, a mirrorlike body. ii. 29; 360. Some of the Pythagoreans (according to the Aristotelian account and the statement of Philip the Opuntian) said that an eclipse of the moon takes place, sometimes by the interposition of the earth, sometimes by the interposition of the counter-earth [avríxowv]. But it seems to some more recent thinkers that it takes place by a spreading of the flame little by little as it is gradually kindled, until it gives the complete full moon, and again, in like manner, it grows less until the conjunction, when it is completely extinguished. ii. 30; 361. Some of the Pythagoreans, among them Philolaos, said that the earthy appearance of the moon is due to its being inhabited by animals and by plants, like those on our earth, only greater and more beautiful; for the animals on it are fifteen times as powerful, not having any sort of excrement, and their day is fifteen times as long as ours. But others said that the outward appearance in the moon is a reflection on the other side of the inflamed circle of the sea that is on our earth. ii. 32; 364. Some regard the greater year . . . . as the sixty year period, among whom are Oenopides and Pythagoras.

Aet. Plac. iii. 1; Dox. 364. Some of the Pythagoreans

said that the milky way is the burning of a star that fell from its own foundation, setting on fire the region through which it passed in a circle, as Phaethon was burned. And others say that the course of the sun arose in this manner at the first. And certain ones say that the appearance of the sun is like a mirror reflecting its rays toward the heaven, and therefore it happens at times to reflect its rays on the rainbow in the clouds.

Aet. iii. 2; 366. Some of the followers of Pythagoras say that the comet is one of the stars that are not always shining, but emit their light periodically through a certain definite time; but others say that it is the reflection of our vision into the sun, like reflected images. iii. 14; 378. Pythagoras: The earth, after the analogy of the sphere of the all, is divided into five zones, arctic, antarctic, summer, winter, and equinoctial; of these the middle one he defines to be the middle of the earth, called for this very reason the torrid zone; but the inhabited one [the one between the arctic and the torrid zones] being well-tempered. . .

Aet. iv. 2; Dox. 386. Pythagoras holds that number moves itself, and he takes number as an equivalent for intelligence. iv. 4; 389. Pythagoras, Plato: According to a superficial account the soul is of two parts, the one possessing, the other lacking, reason; but according to close and exact examination, of three parts; for the unreasoning part they divide into the emotions and the desires. (Theodor. v. 20); Dox. 390. The successors of Pythagoras saying that body is a mixture of five elements (for they ranked the aether as a fifth along with the four) held that the powers of the soul are of the same number as these. And these they name intelligence and wisdom and understanding and opinion and senseperception. iv. 5; 391. Pythagoras: The principle of life is about the heart, but the principle of reason and

intelligence is about the head. iv.5; 392. Pythagoras et al. The intelligence enters from without. iv. 7; 392. Pythagoras, Plato: The soul is imperishable. iv. 9; 396. Pythagoras et al.: The sense-perceptions are deceptive. iv. 9; 397. Pythagoras, Plato: Each of the sensations is pure, proceeding from each single element. With reference to vision, it was of the nature of aether; hearing, of the nature of wind; smell, of the nature of fire; taste, of the nature of moisture; touch, of the nature of earth. iv. 14; 405. The followers of Pythagoras and of the mathematicians on reflections of vision : For vision moves directly as it were against the bronze [of a mirror], and meeting with a firm smooth surface it is turned and bent back on itself, meeting some such experience as when the arm is extended and then bent back to the shoulder. iv. 20; 409. Pythagoras, Plato, Aristotle Sound is immaterial. For it is not air, but it is the form about the air and the appearance [êmipaveía] after some sort of percussion which becomes sound; and every appearance is immaterial; for it moves with bodies, but is itself absolutely immaterial;1 as in the case of a bent rod the surface-appearance suffers no change, but the matter is what is bent.

Aet. Plac. v. 1; 415. Pythagoras did not admit the sacrificial part alone (of augury). v. 3; 417. Pythagoras The seed is foam of the best part of the blood, a secretion from the nourishment, like blood and marrow. v. 4; 417. Pythagoras, Plato, Aristotle: The power of seed is immaterial, like intelligence, the moving power; but the matter that is poured forth is material. v. 20; 432. Pythagoras, Plato: The souls of animals called unreasoning are reasonable, not however with active reasoning powers, because of an imperfect mixture of the bodies and because they do not have the power of

1 Cf. Galen, 27; Dox. 615 sq.

speech, as in the case of apes and dogs; for these have intelligence but not the power of speech.

Ar. Did. Ep. Fr. 32; Dox. 467. Apollodoros in the second book Concerning the gods: It is the Pythagorean opinion that the morning and the evening star are the

same.

Theophr. Phys. Op. Fr. 17; Dox. 492. Favorinus says that he (Pythagoras) was the first to call the heavens a universe and the earth round [σтρоyyúλη].

Cic. de Deor. Nat. i. 11; Philod. piet. Fr. c 4 b; Dox. 533. For Pythagoras, who held that soul is extended through all the nature of things and mingled with them, and that from this our souls are taken, did not see that god would be separated and torn apart by the separation of human souls; and when souls are wretched, as might happen to many, then part of god would be wretched; a thing which could not happen.

Hippol. Phil. 2; Dox. 555. There is a second philosophy not far distant from the same time, of which Pythagoras, whom some call a Samian, was the first representative. And this they call the Italian philosophy because Pythagoras fled the rule of Polykrates over the Samians and settled in a city of Italy where he spent his life. The successive leaders of this sect shared the same spirit. And he in his studies of nature mingled astronomy and geometry and music <and arithmetic>. And thus he asserted that god is a monad, and examining the nature of number with especial care, he said that the universe produces melody and is put together with harmony, and he first proved the motion of the seven stars to be rhythm and melody. And in wonder at the structure of the universe, he decreed that at first his disciples should be silent, as it were mystae who were coming into the order of the all; then when he thought they had sufficient education

in the principles of truth, and had sought wisdom sufficiently in regard to stars and in regard to nature, he pronounced them pure and then bade them speak. He separated his disciples into two groups, and called one esoteric, and the other exoteric. To the former he entrusted the more perfect sciences, to the latter the more moderate. And he dealt with magic, as they say, and himself discovered the art of physiognomy. Postulating both numbers and measures he was wont to say that the first principle of arithmetic embraced philosophy by combination, after the following

manner:

Number is the first principle, a thing which is undefined, incomprehensible, having in itself all numbers which could reach infinity in amount. And the first principle of numbers is in substance the first monad, which is a male monad, begetting as a father all other numbers. Secondly the dyad is female number, and the same is called by the arithmeticians even. Thirdly the triad is male number; this the arithmeticians have been wont to call odd. Finally the tetrad is a female number, and the same is called even because it is female.

All numbers, then, taken by classes are fours (for number is undefined in reference to class), of which is composed the perfect number, the decad. For the series, one two three and four, becomes ten, if its own name is kept in its essence by each of the numbers. Pythagoras said that this sacred tetraktys is 'the spring having the roots of ever-flowing nature' in itself, and from this numbers have their first principle. For the eleven and the twelve and the rest derive from the ten the first principle of their being. The four parts of the decad, this perfect number, are called number, monad, power, and cube. And the interweavings and

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