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Samos, born about 580 B.C., who settled at Crotona in Italy, 529 B.C., and there founded what is known as the Italic school'. He seems to have found in the mysteries and in the Orphic hymns the starting point which Thales had discovered in Homer; and there can be little doubt that his doctrine and system were also in part suggested by his travels in Egypt. He established a sort of religious brotherhood with strict rules and a severe initiation, insisted on training in gymnastics, mathematics and music,

1 There is no one of the early philosophers about whose history and doctrines it is more difficult to ascertain the exact truth than Pythagoras. This is owing in part to the fact that neither Pythagoras himself nor any of his immediate disciples committed their teaching to writing, and also that the earliest Pythagorean treatise, composed by Philolaus a contemporary of Socrates, is only known to us through fragments, the genuineness of which is disputed; but still more it is owing to the luxuriant growth of an apocryphal Pythagorean literature among later eclectic philosophers, who desired to claim the authority of Pythagoras for their own speculations. This was particularly the case with Neo-Pythagoreans and Neo-Platonists, such as Porphyry and Iamblichus, who selected him, as Philostratus had done Apollonius of Tyana, to be the champion of the old religion, and opposed his claims, as prophet and miracleworker, to those put forward by the Christians in the name of their Master or His Apostles. In the account which I have given in the text I have mainly followed Zeller who has examined the evidence with extreme care, testing all later reports by the statements of Plato and Aristotle.

2 It was said by later Pythagoreans that the noviciate lasted for five years, and that absolute silence had to be observed throughout that time. One rule strongly insisted on for all the brotherhood was daily self-examination, as we see by the following lines taken from the miscellaneous collection of Pythagorean precepts entitled the Golden Verses, which Mullach attributes to Lysis, the tutor of Epaminondas, but which, as a collection, are probably of much later date:

and taught the doctrines of immortality and of the transmigration of souls, and the duty of great abstemiousness, if not, as some report, of total abstinence from animal food'. Three points may be noticed about this society, (1) their high ideal of friendship, evinced in the maxims κοινὰ τὰ τῶν φίλων εἶναι; τὸν δὲ φίλον ἄλλον ἑαυτόν, and in the well-known story of the devotion of Damon and Phintias; (2) the admission into their body, as into the Epicurean society of later times, of female associates, of whom the most distinguished was Theano, the wife of Μηδ ̓ ὕπνον μαλακοῖσιν ἐπ ̓ ὄμμασι προσδέξασθαι, πρὶν τῶν ἡμερινῶν ἔργων τρὶς ἕκαστον ἐπελθεῖν· πῇ παρέβην ; τί δ ̓ ἔρεξα; τί μοι δέον οὐκ ἐτελέσθη ; ̓Αρξάμενος δ ̓ ἀπὸ πρώτου ἐπέξιθι, καὶ μετέπειτα

δειλὰ μὲν ἐκπρήξας ἐπιπλήσσει, χρηστὰ δὲ τέρπου.

Plato (Rep. x. 600) bears witness to the marked character of the Pythagorean life (Πυθαγόρειος τρόπος τοῦ βίου) ; and Herodotus (11. 81) connects the religious rites practised by them with those of the Orphic sect and of the Egyptians, ὁμολογέουσι δὲ ταῦτα (the use of linen garments) τοῖσι Ορφικοῖσι καλεομένοισι καὶ Βακχικοῖσι, ἐοῦσι δὲ Αἰγυπτίοισι καὶ Πυθαγορείοισι. (I do not agree with Zeller in putting a comma after Αἰγυπτίοισι.)

1 The earliest notice we have of Pythagoras is contained in some verses of Xenophanes in which allusion is made to his doctrine of metempsychosis. Pythagoras is there said to have interceded for a dog which was being beaten, professing that he recognized in his cries the voice of a friend.

καὶ ποτέ μιν στυφελιζομένου σκύλακος παριόντα
φασὶν ἐποικτεῖραι καὶ τόδε φάσθαι ἔπος

παῦσαι, μηδὲ ῥάπιζ ̓, ἐπειὴ φίλου ἀνέρος ἐστὶ

ψυχή, τὴν ἔγνων φθεγξαμένης αΐων.

It was believed that he retained the memory of his own former transmigrations, and that he had once recognized a shield hanging up in a temple, as one which he had himself carried at Troy under the name of Euphorbus, (see Hor. Od. I. XXVIII. 1. 10).

Pythagoras; (3) the unquestioning submission with which the dicta of the master were received by his disciples, as shown by the famous avròs epa, ipse dixit, which was to them an end of all controversy. The brotherhood, first established at Crotona, soon gained great influence with the wealthier class in that and the neighbouring cities; but after some twenty years of prosperity they seem to have provoked the opposition of the democratic party by their arrogance and exclusiveness. Pythagoras himself is said to have been banished from Crotona and taken refuge at Metapontum. A worse fate overtook his followers about a hundred years later, when their church at Crotona was burnt down, and they themselves massacred with the exception of two. The school appears to have died out altogether about the middle of the 4th century B.C., but revived in the time of Cicero.

The new and startling feature in the Pythagorean philosophy, as opposed to the Ionic systems, was that it found its dpxý, its key of the universe, not in any known substance, but in number and proportion. This might naturally have occurred to one who had listened to the teaching of Thales and Anaximander. After all it makes no difference, he might say, what we take as our original matter, it is the law of development, the measure of condensation, which determines the nature of each thing. Number rules the harmonies of music, the proportions of sculpture and architecture, the movements of the heavenly bodies'. It is Number which makes the universe into a

1 He believed that the intervals between the heavenly bodies corresponded exactly to those of the octave, and that hence arose the Harmony of the Spheres, which mortals were unable to hear, either because it was too powerful for their organs of hearing or be

Kóσμos', and is the secret of a virtuous and orderly life. "Then, by a confusion similar to that which led Heraclitus to identify the law of movement with Fire, the Pythagoreans went on to identify number with form, substance and quality. One, the Monad, evolved out of itself Limit (order), exhibited in the series of odd numbers, and the Unlimited (freedom, expansiveness), the Dyad, exhibited in the series of even numbers, especially of the powers of Two; out of the harmonious mixture of these contraries all particular substances were produced. Again, One was the point, Two the line, Three the plane, Four the concrete solid (but from another point of view, as being the first square number, equal into equal, it was conceived to be Justice). Yet once more, One was the central fire, the hearth of the universe, the throne of Zeus. Around this revolved in regular dance ten spheres; on the outside that of the fixed stars, within this the five planets in their order, then the Sun, the Moon, the Earth, between which and the central fire was interposed the imaginary Anti-Chthon or Counter-Earth, cutting off our view of the central fire and leaving us dependent on the reflection of its light by the Sun, which was not in itself luminous. The separation of the Earth into its two hemispheres was for the purpose of making up the Decad, the symbol of totality. As the Decad was the sum of the first four numbers (1 + 2 + 3 + 4 = 10), special sacredness attached to this group, known under the name Tetractys®.

cause they had never experienced absolute silence. Arist. Cael. II. 9, Plin. N. II. II. 22.

1 Pythagoras is said to have been the first who called the universe by this name.

2 Compare the Pythagorean oath contained in the Golden Verses,

The number Ten was also the number of the Pythagorean categories, or list of contraries, thus given by Aristotle (Met. I. v. 986), Limit and Unlimited, Odd and Even, One and Many, Right and Left, Male and Female, Rest and Motion, Straight and Curved, Light and Darkness, Good and Bad, Square and Oblong.

These mystical extravagances appear to have been the necessary introduction to the sciences of Arithmetic and Geometry, just as Astrology and Alchemy were the introduction to Astronomy and Chemistry. Indeed we find that men like Copernicus and Kepler were to some extent influenced and guided in their investigations by the ideas of Pythagoras. Nor was he himself deficient in knowledge of a more exact kind, if it is true that he was the discoverer of the theorem which we know as the 47th in the first book of Euclid, and was also acquainted with such properties of numbers as are mentioned by Zeller (1. p. 322*).

The Pythagorean doctrine of the soul and of God. is variously reported. If we may trust the oldest accounts, there does not seem to have been any close connexion between the religious and philosophical opinions of

οὐ μὰ τὸν ἡμετέρᾳ γενεᾷ παραδόντα τετρακτύν, παγὰν ἀενάου φύσιος ῥιζώματ ̓ ἔχουσαν. There was of course no end to the fancies which might be connected with numbers. Thus, One was reason, as being unchangeable; Two was opinion, and the earth as the region of opinion; Three was perfection, as comprising in itself beginning, middle, and end; Five was marriage, the union of odd and even. Later Pythagoreans made the Monad God, the Dyad Matter, the Triad the World. For other interpretations, see Zeller I. p. 359* foll. The five regular solids were supposed to be the ultimate forms of the five elements, the cube of earth, pyramid of fire, octahedron of air, icosahedron of water, dodecahedron of the etherial element which encompassed the universe on the outside.

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