material]. i.14; 812. The followers of Pythagoras held that the universe is a sphere according to the form of the four elements; but the highest fire alone is conical. 1.15; 814. The Pythagoreans call colour the manifesta- tion of matter. 1.16; 914. Bodies are subject to change of condition, and are divisible to infinity. i. 18; 916. (After quotation from Arist. Phys. iv. 4; 212 a 20) And in his first book on the philosophy of Pythagoras he writes that the heaven is one, and that time and wind and the void which always defines the places of each thing, are introduced from the infinite. And among other things he says that place is the immovable limit of what surrounds the world, or that in which bodies abide and are moved; and that it is full when it surrounds body on every side, and empty when it has absolutely nothing in itself. Accordingly it is necessary for place to exist, and body ; and it is never empty except only from the standpoint of thought, for the nature of it in perpetuity is destructive of the interrelation of things and of the combination of bodies; and motions arise according to place of bodies that surround and oppose each other; and no infiniteness is Jacking, either of quantity or of extent. i. 20; 318. Pythagoras said that time is the sphere of what surrounds the world. i. 21; 818. Pythagoras, Plato: Motion is a certain otherness or difference in matter. [This is the common limit of all motion.] i. 24; 920. Pythagoras and all that assume that matter is subject to change assert that genesis and destruction in an absolute sense take place; for from change of the elements and modification and separation of them there take place juxtaposition and mixture, and intermingling and melting together.

Aet. Plac. ii. 1; 827. Pythagoras first named the circumference of all things the universe by reason of the order in it. ii. 4; 990. Pythagoras, Plato, and the Stoics

Pythagoras and τηε Pythagoreans 147

held that the universe is brought into being by god}~ And it is perishable so far as its nature is concerned, for it is perceived by sense, and therefore material ; it will not however be destroyed in accordance with the v foreknowledge and plan of god. u.6; 884. Pythagoras: The universe is made from five solid figures, which are called also mathematical; of these he says that earth has arisen from the cube, fire from the pyramid, air from the octahedron, and water from the icosahedron, and the sphere of the all from the dodecahedron. ii. 9; 338. The followers of Pythagoras hold that there is a void outside the universe into which the universe breathes forth, and from which it breathes in. i. 10; 989. Pythagoras, Plato, Aristotle: The right hand side of the universe is the eastern part from which comes the beginning of motion, and the left hand side is the west. They say the universe has neither height nor depth, in which statement height means distance from below upwards, and depth from above downwards. For none of the distances thus described exist for the universe, inasmuch as it is disposed around the middle of itself, from which it extends toward the all, and with reference to which it is the same on every side. ii. 12; 840. Thales, Pythagoras, and their followers: The sphere of the whole heaven is divided into five circles, which they call zones; the first of these is called the arctic zone and is ever visible ; the second the summer solstice, the third the equinoctial, the fourth the winter solstice, and fifth the antarctic zone, which is invisible. And the ecliptic called the zodiac in the three middle ones is projected to touch the three middle ones. And the meridian crosses all these from the north to the opposite quarter at right angles. It is said that Pythagoras was the first to recognise the slant of the zodiacal circls which Oenopides of Chios appropriated as his own dis- : L2

148 the First Philosophers of Greece

covery. 11.18; 848. Herakleides and the Pythagoreans asserted that each world [κόσμος] 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; 868. 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. 11.24; 854. Aneclipse takes place when the moon comes past. u. 25; 857. Pythagoras: The moon 18,8 mirror- like body. u. 29; 860. 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 [ἀντίχθων]. 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 com- plete full moon, and again, in like manner, it grows less until the conjunction, when it is completely extin- guished. i. 80; 861. 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. wu. 82; 864. Some regard the greater year . . . . as the sixty year period, among whom are Oenopides and Pythagoras.

Aet. Plac. iii. 1; Dox. 864. Some of the Pythagoreang

Pythagoras and the Pythagoreans 149

said that the milky way is the burning ofa 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. 111. 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; 878. 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. 990. 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 sense- perception. iv. 5; 391. Pythagoras: The principle of life is about the heart, but the principle of reason and

150 ‘the First Philosophers of Greece

intelligence is about the head. iv.5; 392. Pythagoras et al.: The intelligence enters from without. iv. 7; 995. Pythagoras, Plato: The soul is imperishable. iv. 9; 396. Pythagoras et al.: The sense-perceptions are deceptive. iv. 9; 997. 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 Pytha- goras 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 [ἐπιφανεία] after some sort of percussion which becomes sound ; and every appearance is immaterial ; for it moves with bodies, but is itself absolutely immaterial ;! as in the case of a bent rod the surface-appearance suffers no change, but the matter is what is bent.

Aet. Plac. ν. 1; 415. Pythagoras did not admit the
sacrificial part alone (of augury). v. 8; 417. Pytha-
goras: 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 ; Doz. 615 aq.

Pythagoras and the Pythagoreans 151

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

Ar. Did. Ep. Fr. 82; 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; Doz. 492. Favorinus
says that he (Pythagoras) was the first to call the heavens
& universe and the earth round [στρογγύλην].

Cic. de Deor. Nat. 1. 11; Philod. piet. Fr. ο 4b; Dox.
538. 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. Thereis a second philo- sophy 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 philo- sophy 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 8 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

152 the First Philosophers οε Greece

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 em-
braced philosophy by combination, after the following
manner :

Number is the first principle, a thing which is unde-
fined, incomprehensible, baving in itself all numbers
which could reach infinity in amount. And the first
principle of numbers is in substance the first monad,
which is 8 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