(4) And nought can frustrate his almighty power.

But they thought that their opinions deserved to be believed, because he who first promulgated them, was not any casual person, but a God. For this was one of their questions; What was Pythagoras? For they say that he was the Hyperborean Apollo; of which this was an indication, that rising up in the Olympic games, he showed his golden thigh; and also that he received the Hyperborean Abaris as his guest; and was presented by him with the dart on which he rode through the air. But it is said that Abaris came from the Hyperborean regions, in order that he might collect gold for the temple, and that he predicted a pestilence. He also dwelt in temples, and was never seen either to eat or drink. It is likewise said, that rites which purify from evil are performed by the Lacedæmonians, and that on this account Lacedæmon was never infested with pestilence. Pythagoras, therefore, caused this Abaris to acknowledge [that he was more than man,] receiving from him at the same time the golden dart, without which it was not possible for him to find his way. In Metapontum also, certain persons praying that they might obtain what a ship contained that was then sailing into port, Pythagoras said to them, You will then have a dead body. In Sybaris, too, he caught a deadly serpent and dismissed it. In a similar manner likewise in Tyrrhenia, he caught a small serpent, whose bite was fatal. But in Crotona a white eagle, it is said, suffered Pythagoras to stroke it. A certain person also wishing to hear him discourse, he said that he could not, till some sign appeared. And after this a white bear was seen in Cauconia; the death of which he predicted to one who was about to tell him that it was dead. He likewise reminded Myllias the Crotonian that he had been Midas the son of Gordius. And Myllias passed over to the continent of Asia, in order to perform at the sepulchre [of Midas] those rites which had been enjoined him by Pythagoras. It is likewise said, that the person who bought his house, and who dug up that which had been buried in it, did not dare to tell any one what he saw [on this occasion]. But instead of suffering for this offence, he was seized at Crotona for sacrilege, and put to death. For he took away a golden beard which had fallen from a statue. These things therefore, and others of the like kind, are related by the Pythagoreans, in order to render their opinions worthy of belief. And as these are acknowledged to be true, and it is impossible they should have happened to one man, they consequently think it is clear, that what is related of Pythagoras, should be received as pertaining to a being superior to man, and not to a mere man. This also is the meaning of their enigmatical assertion, that man, bird, and another third thing, are bipeds . For the third thing is Pythagoras. Such, therefore, was Pythagoras on account of his piety, and such he was truly thought to be.

(1) Conceiving, however, that the first attention which should be paid to men, is that which takes place through the senses; as when some one perceives beautiful figures and forms, or hears beautiful rythms and melodies, he established that to be the first erudition which subsists through music, and also through certain melodies and rythms, from which the remedies of human manners and passions are obtained, together with those harmonies of the powers of the soul which it possessed from the first. He likewise devised medicines calculated to repress and expel the diseases both of bodies and souls. And by Jupiter that which deserves to be mentioned above all these particulars is this, that he arranged and adapted for his disciples what are called apparatus and contrectations, divinely contriving mixtures of certain diatonic, chromatic, and euharmonic melodies, through which he easily transferred and circularly led the passions of the soul into a contrary direction, when they had recently and in an irrational and clandestine manner been formed; such as sorrow, rage, and pity, absurd emulation and fear, all-various desires, angers, and appetites, pride, supineness, and vehemence.

For he corrected each of these by the rule of virtue, attempering them through appropriate melodies, as through certain salutary medicines. In the evening, likewise, when his disciples were retiring to sleep, he liberated them by these means from diurnal perturbations and tumults, and purified their intellective power from the influxive and effluxive waves of a corporeal nature; rendered their sleep quiet, and their dreams pleasing and prophetic. But when they again rose from their bed, he freed them from nocturnal heaviness, relaxation and torpor, through certain peculiar songs and modulations, produced either by simply striking the lyre, or employing the voice. Pythagoras, however, did not procure for himself a thing of this kind through instruments or the voice, but employing a certain ineffable divinity, and which it is difficult to apprehend, he extended his ears, and fixed his intellect in the sublime symphonies of the world, he alone hearing and understanding, as it appears, the universal harmony and consonance of the spheres, and the stars that are moved through them, and which produce a fuller and more intense melody than any thing effected by mortal sounds.

This melody also was the result of dissimilar and variously differing sounds, celerities, magnitudes, and intervals, arranged with reference to each other in a certain most musical ratio, and thus producing a most gentle, and at the same time variously beautiful motion and convolution. Being therefore irrigated as it were with this melody, having the reason of his intellect well arranged through it, and as I may say, exercised, he determined to exhibit certain images of these things to his disciples as much as possible, especially producing an imitation of them through instruments, and through the mere voice alone. For he conceived that by him alone, of all the inhabitants of the earth, the mundane sounds were understood and heard, and this from a natural fountain itself and root.

He therefore thought himself worthy to be taught, and to learn something about the celestial orbs, and to be assimilated to them by desire and imitation, as being the only one on the earth adapted to this by the conformation of his body, through the dæmoniacal power that inspired him. But he apprehended that other men ought to be satisfied in looking to him, and the gifts he possessed, and in being benefited and corrected through images and examples, in consequence of their inability to comprehend truly the first and genuine archetypes of things. Just, indeed, as to those who are incapable of looking intently at the sun, through the transcendent splendor of his rays, we contrive to exhibit the eclipses of that luminary, either in the profundity of still water, or through melted pitch, or through some darkly-splendid mirror; sparing the imbecility of their eyes, and devising a method of representing a certain repercussive light, though less intense than its archetype, to those who are delighted with a thing of this kind. Empedocles also appears to have obscurely signified this about Pythagoras, and the illustrious and divinely-gifted conformation of his body above that of other men, when he says:

(1) And these indeed were such as philosophized. But the greatest part of his disciples consisted of auditors whom they call Acusmatici , who on his first arrival in Italy, according to Nicomachus, being captivated by one popular oration alone, exceeded two thousand in number. These, with their wives and children, being collected into one very large and common auditory, called Homacoïon, and which for its magnitude resembled a city, founded a place which was universally called Magna Græcia. This great multitude of people likewise, receiving laws and mandates from Pythagoras as so many divine precepts, and without which they engaged in no occupation, dwelt together with the greatest general concord, celebrated and ranked by their neighbours among the number of the blessed.

At the same time, as we have already observed, they shared their possessions in common. Such also was their reverence for Pythagoras, that they numbered him with the Gods, as a certain beneficent and most philanthropic dæmon. And some indeed celebrated him as the Pythian, but others as the Hyperborean Apollo. Some again considered him as Pæon, but others as one of the dæmons that inhabit the moon; and others celebrated him as one of the Olympian Gods, who, in order to benefit and correct the mortal life, appeared to the men of those times in a human form, in order that he might extend to them the salutary light of felicity and philosophy. And indeed a greater good never came, nor ever will come to mankind, than that which was imparted by the Gods through this Pythagoras.

Hence, even now the proverb of the long-haired Samian , is applied to the most venerable man. But Aristotle relates, in his Treatise On the Pythagoric Philosophy, that such a division as the following was preserved by the Pythagoreans among their principal arcana; viz. that of rational animals one kind is a God, another man, and another such as Pythagoras. And indeed they very reasonably apprehended him to be a being of this kind, through whom a right conception and conformable to things themselves was introduced of Gods, heroes, and dæmons; of the world, the all-various motion of the spheres and stars, their oppositions, eclipses, and inequalities, their eccentricities and epicycles; of all the natures contained in the heavens and the earth, together with those that have an intermediate subsistence, whether apparent or occult.

Nor was there anything (in all this variety of information) at all contrary to the phenomena, or the conceptions of intellect. To which we may add, that all such disciplines, theories, and scientific investigations, as truly invigorate the eye of the soul, and purify the intellect from the blindness introduced by studies of a different kind, so as to enable it to perceive the true principles and causes of the universe, were unfolded by Pythagoras to the Greeks. But besides all this, the best polity, popular concord, community of possessions among friends, the worship of the gods, piety to the dead, legislation, erudition, silence, abstinence from animals, continence, temperance, sagacity, divinity, and in one word, whatever is anxiously sought after by the lovers of learning, was brought to light by Pythagoras. On all these accounts, therefore, as I have just now said, he was (every where) so transcendently admired.

(7) Pythagoras likewise used pure and white garments, and in a similar manner white and pure coverlids; for he did not use those that were made of wool. And this custom he also delivered to his auditors. In speaking also of the natures superior to man, he employed honorable appellations, and words of good omen, and upon every occasion made mention of and reverenced the Gods; so that while at supper, he performed libations to the divinities, and ordered his disciples to celebrate with hymns the beings that are above us, every day. He paid attention likewise to rumors and omens, prophecies and lots, and in short, to all casual circumstances. Moreover, he sacrificed to the Gods with millet, cakes, honey-combs, and other fumigations.

But he did not sacrifice animals, nor did any one of the contemplative philosophers. His other disciples, however, viz. the acusmatici, and the politici, were ordered by him to sacrifice animals, such as a cock, or a lamb, or some other animal recently born, but not frequently. At the same time they were prohibited from sacrificing oxen. This also is an indication of the honor which he paid to the Gods, that he exhorted his disciples never to employ the names of the Gods uselessly in swearing. On which account also Syllus, one of the Pythagoreans in Crotona, paid a fine for not swearing, though he could have sworn without violating truth. An oath too such as the following is ascribed to the Pythagoreans, as they were unwilling, through reverence, to name Pythagoras; just as they very much abstained from using the names of the Gods. But they manifested the man through the invention of the tetractys,

(9) Again the Barbarian philosophy knows the world of thought and the world of sense - the former archetypal, and the latter the image of that which is called the model; and assigns the former to the Monad, as being perceived by the mind, and the world of sense to the number six. For six is called by the Pythagoreans marriage, as being the genital number; and he places in the Monad the invisible heaven and the holy earth, and intellectual light. For "in the beginning," it is said, "God made the heaven and the earth; and the earth was invisible." And it is added, "And God said, Let there be light; and there was light." And in the material cosmogony He creates a solid heaven (and what is solid is capable of being perceived by sense), and a visible earth, and a light that is seen. Does not Plato hence appear to have left the ideas of living creatures in the intellectual world, and to make intellectual objects into sensible species according to their genera? Rightly then Moses says, that the body which Plato calls "the earthly tabernacle" was formed of the ground, but that the rational soul was breathed by God into man's face. For there, they say, the ruling faculty is situated; interpreting the access by the senses into the first man as the addition of the soul.

(1) Universally, however, it deserves to be known, that Pythagoras discovered many paths of erudition, and that he delivered an appropriate portion of wisdom conformable to the proper nature and power of each; of which the following is the greatest argument. When Abaris, the Scythian, came from the Hyperboreans, unskilled and uninitiated in the Grecian learning, and was then of an advanced age, Pythagoras did not introduce him to erudition through various theorems, but instead of silence, auscultation for so long a time, and other trials, he immediately considered him adapted to be an auditor of his dogmas, and instructed him in the shortest way in his treatise On Nature, and in another treatise On the Gods. For Abaris came from the Hyperboreans, being a priest of the Apollo who is there worshipped, an elderly man, and most wise in sacred concerns; but at that time he was returning from Greece to his own country, in order that he might consecrate to the God in his temple among the Hyperboreans, the gold which he had collected.

Passing therefore through Italy, and seeing Pythagoras, he especially assimilated him to the God of whom he was the priest. And believing that he was no other than the God himself, and that no man resembled him, but that he was truly Apollo, both from the venerable indications which he saw about him, and from those which the priest had known before, he gave Pythagoras a dart which he took with him when he left the temple, as a thing that would be useful to him in the difficulties that would befal him in so long a journey. For he was carried by it, in passing through inaccessible places, such as rivers, lakes, marshes, mountains, and the like, and performed through it, as it is said, lustrations, and expelled pestilence and winds from the cities that requested him to liberate them from these evils.

We are informed, therefore, that Lacedæmon, after having been purified by him, was no longer infested with pestilence, though prior to this it had frequently fallen into this evil, through the baneful nature of the place in which it was built, the mountains of Taygetus producing a suffocating heat, by being situated above the city, in the same manner as Cnossus in Crete. And many other similar particulars are related of the power of Abaris. Pythagoras, however, receiving the dart, and neither being astonished at the novelty of the thing, nor asking the reason why it was given to him, but as if he was in reality a God himself, taking Abaris aside, he showed him his golden thigh, as an indication that he was not [wholly] deceived [in the opinion he had formed of him;] and having enumerated to him the several particulars that were deposited in the temple, he gave him sufficient reason to believe that he had not badly conjectured [in assimilating him to Apollo].

Pythagoras also added, that he came [into the regions of mortality] for the purpose of remedying and benefiting the condition of mankind, and that on this account he had assumed a human form, lest men being disturbed by the novelty of his transcendency, should avoid the discipline which he possessed. He likewise exhorted Abaris to remain in that place, and to unite with him in correcting [the lives and manners] of those with whom they might meet; but to share the gold which he had collected, in common with his associates, who were led by reason to confirm by their deeds the dogma, that the possessions of friends are common . Thus, therefore, Pythagoras unfolded to Abaris, who remained with him, as we have just now said, physiology and theology in a compendious way; and instead of divination by the entrails of beasts, he delivered to him the art of prognosticating through numbers, conceiving that this was purer, more divine, and more adapted to the celestial numbers of the Gods.

He delivered also to Abaris other studies which were adapted to him. That we may return, however, to that for the sake of which the present treatise was written, Pythagoras endeavoured to correct and amend different persons, according to the nature and power of each. All such particulars therefore as these, have neither been transmitted to the knowledge of men, nor is it easy to narrate all that has been transmitted to us concerning him.

(1) This adaptation therefore of souls was procured by him through music. But another purification of the dianoetic part, and at the same time of the whole soul, through all-various studies, was effected by him as follows: He conceived generally that labor should be employed about disciplines and studies, and ordained like a legislator, trials of the most various nature, punishments, and restraints by fire and sword, for innate intemperance, and an inexhaustible avidity of possessing; which he who is depraved can neither suffer nor sustain. Besides these things also, he ordered his familiars to abstain from all animals, and farther still from certain foods, which are hostile to the reasoning power, and impede its genuine energies. He likewise enjoined them continence of speech, and perfect silence, exercising them for many years in the subjugation of the tongue, and in a strenuous and assiduous investigation and resumption of the most difficult theorems.

Hence also, he ordered them to abstain from wine, to be sparing in their food, to sleep little, and to have an unstudied contempt of, and hostility to glory, wealth, and the like: to have an unfeigned reverence of those to whom reverence is due, a genuine similitude and benevolence to those of the same age with themselves, and an attention and incitation towards their juniors, free from all envy. With respect to the amity also which subsists in all things towards all, whether it be that of Gods towards men through piety and scientific theory, or of dogmas towards each other, or universally of the soul towards the body, and of the rational towards the irrational part, through philosophy, and the theory pertaining to it; or whether it be that of men to each other, of citizens indeed through sound legislation, but of strangers through a correct physiology; or of the husband to the wife, or of brothers and kindred, through unperverted communion; or whether, in short, it be of all things towards all, and still farther, of certain irrational animals through justice, and a physical connexion and association; or whether it be the pacification and conciliation of the body which is of itself mortal, and of its latent contrary powers, through health, and a diet and temperance conformable to this, in imitation of the salubrious condition of the mundane elements;—of the appellation of all these, which are summarily comprehended in one and the same name, that of friendship, Pythagoras is acknowledged to have been the inventor and legislator.

And, in short, he was the cause to his disciples of the most appropriate converse with the Gods, both when they were awake and when asleep; a thing which never takes place in a soul disturbed by anger, or pain, or pleasure, or, by Jupiter, by any other base desire, or defiled by ignorance, which is more unholy and noxious than all these. By all these inventions, therefore, he divinely healed and purified the soul, resuscitated and saved its divine part, and conducted to the intelligible its divine eye, which, as Plato says, is better worth saving than ten thousand corporeal eyes ; for by looking through this alone, when it is strengthened and clarified by appropriate aids, the truth pertaining to all beings is perceived. Referring therefore to this, Pythagoras purified the dianoetic power of the soul. Such also was the form with him of erudition, and these were the things to which he directed his view.

(7) Pythagoras likewise discovered another method of restraining men from injustice, through the judgment of souls, truly knowing indeed that this method may be taught, and also knowing that it is useful to the suppression of justice through fear. He asserted therefore, that it is much better to be injured than to kill a man; for that judgment is deposited in Hades, where the soul, and its essence, and the first nature of beings, are properly estimated. Being desirous, however, to exhibit in things unequal, without symmetry and infinite, a definite, equal, and commensurate justice, and to show how it ought to be exercised, he said, that justice resembles that figure, which is the only one among geometrical diagrams, that having indeed infinite compositions of figures, but dissimilarly disposed with reference to each other, yet has equal demonstrations of power.

Since also, there is a certain justice in making use of another person, such a mode of it as the following, is said to have been delivered by the Pythagoreans: Of associations with others, one kind is seasonable, but another is unseasonable. These likewise are distinguished from each other by difference of age, desert, the familiarity of alliance, and of beneficence, and whatever else there may be of the like kind in the different associations of men with each other. For there is a species of association, viz. of a younger with a younger person, which does not appear to be unseasonable; but that of a younger with an elderly person is unseasonable. For no species of anger, or threatening, or boldness, is becoming in a younger towards an elderly man, but all unseasonable conduct of this kind should be cautiously avoided.

A similar reasoning likewise should be adopted with respect to desert. For it is neither decorous, nor seasonable, to use an unrestrained freedom of speech, or to adopt any of the above-mentioned modes of conduct, towards a man who has arrived at the true dignity of consummate virtue. Conformably to this also, was what he said respecting the association with parents, and likewise with benefactors. He added, that there is a certain various and multiform use of an opportune time. For of those that are enraged and angry, some are so seasonably, but others unseasonably. And again, of those that aspire after, desire, and are impelled to any thing appetible, an opportune time is the attendant on some, and an unseasonable time on others.

And the same thing may be said concerning other passions and actions, dispositions, associations, and meetings. He farther observed, that an opportune time is to a certain extent , to be taught, and also, that what happens contrary to expectation, is capable of receiving an artificial discussion; but that when it is considered universally and simply, none of the above-mentioned particulars pertain to it. Nearly, however, such things are the attendants on it, as follow the nature of opportune time, viz. what is called the florid, the becoming, the adapted, and whatever else there may be homogeneous to these. He likewise asserted, that principle [or the beginning] is in the universe unity, and is the most honorable of things; and that in a similar manner it is so in science, in experience, and in generation.

And again, that the number two is most honorable in a house, in a city, in a camp, and in all such like systems. But that the nature of principle is difficult to be surveyed and apprehended in all the above-mentioned particulars. For in sciences, it is not the province of any casual understanding to learn and judge, by well surveying the parts of things, what the nature is of the principle of these. He added, that it makes a great difference, and that there is danger with respect to the knowledge of the whole of things, when principle is not rightly assumed. For none, in short, of the consequent conclusions can be sane, when the true principle is unknown.

The same thing may also be said respecting a principle of another kind. For neither can a house, or a city, be well instituted, unless each has a true ruler, who governs those that voluntarily submit to him. For it is necessary that in both these the governor should be willing to rule, and the governed to obey. Just as with respect to disciplines, when they are taught with proper effect, it is necessary that there should be a concurrence in the will both of the teacher and learner. For if there is a resistance on the part of either, the proposed work will never be accomplished in a proper manner. Thus therefore, he proved, that it was beautiful to be persuaded by rulers, and to be obedient to preceptors.

But he exhibited the following as the greatest argument through deeds, of the truth of his observations. He went from Italy to Delos, to Pherecydes the Syrian, who had been his preceptor, in order that he might afford him some assistance, as he was then afflicted with what is called the morbus pedicularis, and he carefully attended him to the time of his death, and piously performed whatever rites were due to his dead preceptor. So diligent was he in the discharge of his duties to him from whom he had received instruction.

(6) As they by law are orderly dispos’d;

And reverence thy oath, but honor next

Th’ illustrious heroes.

Hence a certain Pythagorean, being compelled by law to take an oath, yet in order that he might preserve a Pythagoric dogma, though he would have sworn religiously, chose instead of swearing to pay three talents, this being the fine which he was condemned to pay to the defendant. That Pythagoras however thought that nothing was from chance and fortune, but that all events happened conformably to divine providence, and especially to good and pious men, is confirmed by what is related by Androcydes in his treatise on Pythagoric Symbols, of Thymaridas the Tarentine, and a Pythagorean. For when through a certain circumstance he was about to sail from his own country, and his friends who were present were embracing him, and bidding him farewell, some one said to him, when he had now ascended into the ship, May such things happen to you from the Gods, O Thymaridas, as are conformable to your wishes! But he replied, predict better things; for I should rather wish that such things may happen to me as are conformable to the will of the Gods. For he thought it was more scientific and equitable, not to resist or be indignant with divine providence. If, therefore, any one wishes to learn what were the sources whence these men derived so much piety, it must be said, that a perspicuous paradigm of the Pythagoric theology according to numbers, is in a certain respect to be found in the writings of Orpheus. Nor is it to be doubted, that Pythagoras receiving auxiliaries from Orpheus, composed his treatise Concerning the Gods, which on this account also he inscribed the Sacred Discourse, because it contains the flower of the most mystical place in Orpheus; whether this work was in reality written by Pythagoras, as by most authors it is said to have been, or as some of the Pythagoric school who are both learned and worthy of belief assert, was composed by Telauges; being taken by him from the commentaries which were left by Pythagoras himself to his daughter Damo, the sister of Telauges, and which it is said after her death were given to Bitale the daughter of Damo, and to Telauges the son of Pythagoras, and the husband of Bitale, when he was of a mature age. For when Pythagoras died, he was left very young with his mother Theano. In this Sacred Discourse also, or treatise concerning the Gods (for it has both these inscriptions), who it was that delivered to Pythagoras what is there said concerning the Gods, is rendered manifest. For it says: “ that Pythagoras the son of Mnesarchus was instructed in what pertains to the Gods, when he celebrated orgies in the Thracian Libethra, being initiated in them by Aglaophemus; and that Orpheus the son of Calliope, having learnt wisdom from his mother in the mountain Pangæus, said, that the eternal essence of number is the most providential principle of the universe , of heaven and earth, and the intermediate nature; and farther still, that it is the root of the permanency of divine natures, of Gods and dæmons .” From these things, therefore, it is evident that he learnt from the Orphic writers that the essence of the Gods is defined by number. Through the same numbers also, he produced an admirable fore-knowledge and worship of the Gods, both which are especially most allied to numbers. This, however, may be known from hence; for it is necessary to adduce a certain fact, in order to procure belief of what is said. When Abaris performed sacred rites in his accustomed manner, he procured a fore-knowledge of future events, which is studiously cultivated by all the Barbarians, through sacrificing animals, and especially birds; for they are of opinion that the viscera of such animals are subservient to a more accurate inspection. Pythagoras, therefore, not wishing to suppress his ardent pursuit of truth, but to impart it to him through a certain safer way, and without blood and slaughter, and also because he thought that a cock was sacred to the sun, furnished him with a consummate knowledge of all truth, as it is said, through the arithmetical science . He also obtained from piety, faith concerning the Gods. For Pythagoras always proclaimed, that nothing admirable pertaining to the Gods or divine dogmas should be disbelieved , because the Gods are able to accomplish all things. And the divine dogmas in which it is requisite to believe, are those which Pythagoras delivered. Thus, therefore, the Pythagoreans believed in, and assumed the things about which they dogmatised, because they were not the progeny of false opinion. Hence Eurytus the Crotonian, the auditor of Philolaus said, that a shepherd feeding his sheep near the tomb of Philolaus, heard some one singing. But the person to whom this was related, did not at all disbelieve the narration, but asked what kind of harmony it was. Pythagoras himself, also, being asked by a certain person what was indicated by seeming in sleep to converse with his father who was dead, answered that it indicated nothing. For neither, said he, is any thing portended by your speaking with me.

(1) The mode however of teaching through symbols, was considered by Pythagoras as most necessary. For this form of erudition was cultivated by nearly all the Greeks, as being most ancient. But it was transcendently honored by the Egyptians, and adopted by them in the most diversified manner. Conformably to this, therefore, it will be found, that great attention was paid to it by Pythagoras, if any one clearly unfolds the significations and arcane conceptions of the Pythagoric symbols, and thus developes the great rectitude and truth they contain, and liberates them from their enigmatic form. For they are adapted according to a simple and uniform doctrine, to the great geniuses of these philosophers, and deify in a manner which surpasses human conception.

For those who came from this school, and especially the most ancient Pythagoreans, and also those young men who were the disciples of Pythagoras when he was an old man, viz. Philolaus and Eurytus, Charondas and Zaleucus, and Brysson, the elder Archytas also, and Aristæus, Lysis and Empedocles, Zanolxis and Epimenides, Milo and Leucippus, Alcmæon, Hippasus and Thymaridas, and all of that age, consisting of a multitude of learned men, and who were above measure excellent,—all these adopted this mode of teaching, in their discourses with each other, and in their commentaries and annotations. Their writings also, and all the books which they published, most of which have been preserved even to our time , were not composed by them in a popular and vulgar diction, and in a manner usual with all other writers, so as to be immediately understood, but in such a way as not to be easily apprehended by those that read them.

For they adopted that taciturnity which was instituted by Pythagoras as a law, in concealing after an arcane mode, divine mysteries from the uninitiated, and obscuring their writings and conferences with each other. Hence he who selecting these symbols does not unfold their meaning by an apposite exposition, will cause those who may happen to meet with them to consider them as ridiculous and inane, and as full of nugacity and garrulity. When, however, they are unfolded in a way conformable to these symbols, and become obvious and clear even to the multitude, instead of being obscure and dark, then they will be found to be analogous to prophetic sayings, and to the oracles of the Pythian Apollo. They will then also exhibit an admirable meaning, and will produce a divine afflatus in those who unite intellect with erudition.

Nor will it be improper to mention a few of them, in order that this mode of discipline may become more perspicuous: Enter not into a temple negligently, nor in short adore carelessly, not even though you should stand at the very doors themselves . Sacrifice and adore unshod. Declining from the public ways, walk in unfrequented paths. Speak not about Pythagoric concerns without light. And such are the outlines of the mode adopted by Pythagoras of teaching through symbols.

(1) That which follows after this, we shall no longer discuss generally, but direct our attention particularly to the works resulting from the virtues of Pythagoras. And we shall begin in the first place from the Gods, as it is usual to do, and endeavour to exhibit his piety, and the admirable works which he performed. Let this, therefore, be one specimen of his piety, which also we have before mentioned, that he knew what his soul was, and whence it came into the body, and also its former lives, and that of these things he gave most evident indications. After this also, let the following be another specimen; that once passing over the river Nessus with many of his associates, he spoke to it, and the river in a distinct and clear voice, in the hearing of all his followers, answered, Hail Pythagoras!

Farther still, nearly all historians of his life confidently assert, that in one and the same day he was present at Metapontum in Italy, and Tauromenium in Sicily, and discoursed in common with his disciples in both places, though these cities are separated from each other by many stadia both by land and sea, and cannot be passed through in a great number of days. The report, also, is very much disseminated, that he showed his golden thigh to the Hyperborean Abaris, who said that he resembled the Apollo among the Hyperboreans, and of whom Abaris was the priest; and that he did this in order that Abaris might apprehend this to be true, and that he was not deceived in his opinion.

Ten thousand other more divine and more admirable particulars likewise are uniformly and unanimously related of the man : such as infallible predictions of earthquakes , rapid expulsions of pestilence and violent winds, instantaneous cessations of the effusion of hail, and a tranquillization of the waves of rivers and seas, in order that his disciples might easily pass over them. Of which things also, Empedocles the Agrigentine, Epimenides the Cretan, and Abaris the Hyperborean, receiving the power of effecting, performed certain miracles of this kind in many places. Their deeds, however, are manifest. To which we may add, that Empedocles was surnamed an expeller of winds ; Epimenides, an expiator ; and Abaris, a walker on air ; because being carried on the dart which was given to him by the Hyperborean Apollo, he passed over rivers and seas and inaccessible places, like one walking on the air.

Certain persons likewise are of opinion, that Pythagoras did the same thing, when in the same day he discoursed with his disciples at Metapontum and Tauromenium. It is also said, that he predicted there would be an earthquake from the water of a well which he had tasted; and that a ship which was sailing with a prosperous wind, would be merged in the sea. And let these, indeed, be the indications of his piety.

(6) These men also thought it right to adhere to the customs and legal institutes of their ancestors, even though they should be somewhat inferior to other customs and laws. For to fly from the existing laws, and to be studious of innovation, is by no means profitable and salutary. Pythagoras therefore gave many other specimens of piety to the Gods, evincing that his life was conformable to his doctrines. Nor will it be foreign to the purpose to mention one of them, which may serve to elucidate the rest. But I will relate what Pythagoras said and did relative to the embassy from Sybaris to Crotona, about demanding the return of the exiles. For some of his associates were slain by order of the ambassadors, one of whom slew a part of them with his own hands; but another was the son of one of those who had excited the sedition, and who died through disease.

When the Crotonians therefore were deliberating how they should act in this affair, Pythagoras said to his disciples, that he was not willing the Crotonians should be so greatly discordant in this affair, and that in his opinion, the ambassadors should not even lead victims to the altars, much less ought they to drag suppliants [i. e. the exiles] from them. But when the Sybarites came to him with their complaints, and the man who had slain some of his associates with his own hands, was defending his conduct, Pythagoras said, that he should not answer [an homicide]. Hence, some persons accused him of asserting that he was Apollo, because prior to this some one having asked him about a certain object of inquiry, why the thing was so; he in his turn asked the interrogator, if he would think fit to inquire of Apollo when he was delivering oracles to him, why he delivered them?

But to another of the ambassadors who appeared to him to deride his school, in which he taught the return of souls to the supernal realms, and who said that he would give him an epistle to his father, as he was about to descend into Hades, and exhorted him to bring another letter in answer, from his father, when he returned; Pythagoras replied, that he was not about to descend into the abode of the impious, where he clearly knew that murderers were punished. But the ambassadors reviling him, he proceeded to the sea, many persons following him, and there sprinkled himself with marine water. Some one however of the Crotonian counsellors, after reviling the rest of the ambassadors, observed that he understood they had defamed Pythagoras, whom not even a brute would dare to blaspheme, though all animals should again utter the same voice as men, which fables report they did in the beginning of things.

(2) Again, however, assuming a more elevated exordium, I am desirous to exhibit the principles of the worship of the Gods, which Pythagoras and his followers established; viz. that all such particulars as they define with respect to doing or not doing a thing, have for the mark at which they aim, a consent with divinity. This also is with them the principle, [of piety] and their whole life is arranged with a view to follow God . The language, too, of their philosophy is this, that men act ridiculously in exploring good from any other source than the Gods; and that their conduct in this respect resembles that of a man, who in a country governed by a king should reverence one of the magistrates in the city, and neglect him who is the ruler of all of them.

For they were of opinion that such was the conduct of mankind. For since God is, and is the Lord of all things, it is universally acknowledged that good is to be requested of him. For all men impart good to those whom they love, and to those with whom they are delighted; but they give the contrary to good, to those to whom they are contrarily disposed. It is evident, therefore, that those things are to be done, in which God delights. It is, however, not easy for a man to know what these are, unless he obtains this knowledge from one who has heard God, or has heard God himself, or procures it through divine art. Hence also, the Pythagoreans were studious of divination.

For this alone is an interpretation of the benevolence of the Gods. And in short, he will conceive an employment of this kind to be worthy of regard, who believes that there are Gods; but he who thinks that either of these is folly, will also be of opinion that both are foolish. Many of the mandates, however, of the Pythagoreans were introduced from the mysteries; for they did not conceive them to be the productions of arrogance, but to originate from a certain divinity. And in a similar manner, all the Pythagoreans believe such things as are mythologically related of Aristeas the Proconesian, and Abaris the Hyperborean, and other particulars of a like nature. For they consider every thing of this kind to be credible; and of many [such] things they make trial themselves.

They also frequently recollect such-like particulars as appear to be fabulous, as not disbelieving in any thing which may be referred to divinity. A certain person therefore relates, that Eurytus said, that a shepherd feeding his sheep near the tomb of Philolaus, heard some one singing. But the person to whom this was related, did not at all disbelieve the narration, but asked what kind of harmony it was? Both of them, however, were Pythagoreans, and Eurytus was the disciple of Philolaus. It is likewise said, that a certain person told Pythagoras, that he appeared to himself once to converse with his father who was dead, and that he asked Pythagoras what this indicated? Pythagoras replied, that it indicated nothing; but that he had in reality conversed with his father.

As therefore, said he, nothing is signified by my now discoursing with you, so neither is any thing signified by your conversing with your father. Hence, in all particulars of this kind, they did not think that they were stupid, but those that disbelieved in them. For they did not conceive that some things are possible to the Gods, but others impossible, as those fancy who reason sophistically; but they believed that all things are possible to the Gods. And this very assertion is the beginning of the verses, which they ascribe to Linus, and which are as follow:

(4) I think also, it was said by the Pythagoreans, respecting those who teach for the sake of reward, that they show themselves to be worse than statuaries, or those artists who perform their work sitting. For these, when some one orders them to make a statue of Hermes, search for wood adapted to the reception of the proper form; but those pretend that they can readily produce the works of virtue from every nature. The Pythagoreans likewise said, that it is more necessary to pay attention to philosophy, than to parents and agriculture; for it is owing to the latter, indeed, that we live; but philosophers and preceptors are the causes of our living well, and becoming wise, in consequence of having discovered the right mode of discipline and instruction.

Nor did they think fit either to speak or write in such a way, that their conceptions might be obvious to any casual persons; but Pythagoras is said to have taught this in the first place to those that came to him, that, being purified from all incontinence, they should preserve in silence the doctrines they had heard. It is said, therefore, that he who first divulged the theory of commensurable and incommensurable quantities, to those who were unworthy to receive it, was so hated by the Pythagoreans that they not only expelled him from their common association, and from living with them, but also constructed a tomb for him, as one who had migrated from the human and passed into a another life.

Others also say, that the Divine Power was indignant with those who divulged the dogmas of Pythagoras: for that he perished in the sea, as an impious person, who rendered manifest the composition of the icostagonus ; viz. who delivered the method of inscribing in a sphere the dodecaedron, which is one of what are called the five solid figures. But according to others, this happened to him who unfolded the doctrine of irrational and incommensurable quantities. Moreover, all the Pythagoric discipline was symbolic, and resembled enigmas and riddles, consisting of apothegms, in consequence of imitating antiquity in its character; just as the truly divine and Pythian oracles appear to be in a certain respect difficult to be understood and explained, to those who carelessly receive the answers which they give. Such therefore, and so many are the indications respecting Pythagoras and the Pythagoreans, which may be collected from what is disseminated about them.

(8) Conformably likewise to the precepts of their master, the Pythagoreans always rose from bed before the rising of the sun; and never wore a ring in which the image of God was engraved. They also carefully observed to adore the rising sun, and avoided wearing a ring of the above mentioned description, lest they should have it about them at funerals, or in some impure place. In a similar manner, they were attentive to the mandate of Pythagoras, not to do any thing without previous deliberation and disquisition; but to form a plan in the morning of what ought to be done [in the course of the day,] and at night to call to mind the actions of the day, by this means at one and the same time exploring their conduct, and exercising their memory.

Thus too, they observed the precept, that if any one of their associates appointed to meet them at a certain place, they should stay there till he came through the day and the night; in this again, the Pythagoreans being accustomed to remember what was said, and not to speak casually. In short Pythagoras ordered them to be attentive to order and method as long as they lived, and not to blaspheme at the time of death, but to die with propitious words, such as are used by those who are sailing out of port into the Adriatic sea.

(4) There was, however, a certain person named Hippomedon, an Ægean, a Pythagorean and one of the Acusmatici, who asserted that Pythagoras gave the reasons and demonstrations of all these precepts, but that in consequence of their being delivered to many, and these such as were of a more sluggish genius, the demonstrations were taken away, but the problems themselves were left. Those however of the Pythagoreans that are called Mathematici , acknowledge that these reasons and demonstrations were added by Pythagoras, and they say still more than this, and contend that their assertions are true, but affirm that the following circumstance was the cause of the dissimilitude. Pythagoras, say they, came from Ionia and Samos, during the tyranny of Polycrates, Italy being then in a florishing condition; and the first men in the city became his associates.

But, to the more elderly of these, and who were not at leisure [for philosophy], in consequence of being occupied by political affairs, the discourse of Pythagoras was not accompanied with a reasoning process, because it would have been difficult for them to apprehend his meaning through disciplines and demonstrations; and he conceived they would nevertheless be benefited by knowing what ought to be done, though they were destitute of the knowledge of the why : just as those who are under the care of physicians, obtain their health, though they do not hear the reason of every thing which is to be done to them. But with the younger part of his associates, and who were able both to act and learn,—with these he conversed through demonstration and disciplines.

These therefore are the assertions of the Mathematici, but the former, of the Acusmatici. With respect to Hippasus however especially, they assert that he was one of the Pythagoreans, but that in consequence of having divulged and described the method of forming a sphere from twelve pentagons, he perished in the sea, as an impious person, but obtained the renown of having made the discovery. In reality, however, this as well as every thing else pertaining to geometry, was the invention of that man ; for thus without mentioning his name, they denominate Pythagoras. But the Pythagoreans say, that geometry was divulged from the following circumstance: A certain Pythagorean happened to lose the wealth which he possessed; and in consequence of this misfortune, he was permitted to enrich himself from geometry.

But geometry was called by Pythagoras Historia . And thus much concerning the difference of each mode of philosophising, and the classes of the auditors of Pythagoras. For those who heard him either within or without the veil, and those who heard him accompanied with seeing, or without seeing him, and who are divided into interior and exterior auditors, were no other than these. And it is requisite to arrange under these, the political, economic and legislative Pythagoreans.

(1) Of his wisdom, however, the commentaries written by the Pythagoreans afford, in short, the greatest indication; for they adhere to truth in every thing, and are more concise than all other compositions, so that they savour of the ancient elegance of style, and the conclusions are exquisitely deduced with divine science. They are also replete with the most condensed conceptions, and are in other respects various and diversified both in the form and the matter. At one and the same time likewise, they are transcendently excellent, and without any deficiency in the diction, and are in an eminent degree full of clear and indubitable arguments, accompanied with scientific demonstration, and as it is said, the most perfect syllogism; as he will find to be the case, who, proceeding in such paths as are fit, does not negligently peruse them.

This science, therefore, concerning intelligible natures and the Gods, Pythagoras delivers in his writings from a supernal origin. Afterwards, he teaches the whole of physics, and unfolds completely ethical philosophy and logic. He likewise delivers all-various disciplines, and the most excellent sciences. And in short there is nothing pertaining to human knowledge which is not accurately discussed in these writings. If therefore it is acknowledged, that of the [Pythagoric] writings which are now in circulation, some were written by Pythagoras himself, but others consist of what he was heard to say, and on this account are anonymous, but are referred to Pythagoras as their author;—if this be the case, it is evident that he was abundantly skilled in all wisdom.

But it is said that he very much applied himself to geometry among the Egyptians. For with the Egyptians there are many geometrical problems; since it is necessary that from remote periods, and from the time of the Gods themselves, on account of the increments and decrements of the Nile, those that were skilful should have measured all the Egyptian land which they cultivated. Hence also geometry derived its name. Neither did they negligently investigate the theory of the celestial orbs, in which likewise Pythagoras was skilled. Moreover, all the theorems about lines appear to have been derived from thence. For it is said that what pertains to computation and numbers, was discovered in Phœnicia. For some persons refer the theorems about the celestial bodies to the Egyptians and Chaldeans in common.

It is said therefore, that Pythagoras having received and increased all these [theories,] imparted the sciences, and at the same time demonstrated them to his auditors with perspicuity and elegance. And he was the first indeed that denominated philosophy, and said that it was the desire, and as it were love of wisdom. But he defined wisdom to be the science of the truth which is in beings. And he said that beings are immaterial and eternal natures, and alone possess an efficacious power, such as incorporeal essences. But that the rest of things are only homonymously beings, and are so denominated through the participation of real beings, and such are corporeal and material forms, which are generated and corrupted, and never truly are.

And that wisdom is the science of things which are properly beings, but not of such as are homonymously so. For corporeal natures are neither the objects of science nor admit of a stable knowledge, since they are infinite and incomprehensible by science, and are as it were, non-beings, when compared with universals, and are incapable of being properly circumscribed by definition. It is impossible however to conceive that there should be science of things which are not naturally the objects of science. Hence it is not probable that there will be a desire of science which has no subsistence, but rather that desire will be extended to things which are properly beings, which exist with invariable permanency, and are always consubsistent with a true appellation.

For it happens that the perception of things which are homonymously beings, and which are never truly what they seem to be, follows the apprehension of real beings; just as the knowledge of particulars follows the science of universals. For he who knows universals properly, says Archytas, will also have a clear perception of the nature of particulars. Hence things which have an existence are not alone, nor only-begotten, nor simple, but they are seen to be various and multiform. For some of them are intelligible and incorporeal natures, and which are denominated beings; but others are corporeal and fall under the perception of sense, and by participation communicate with that which has a real existence. Concerning all these therefore, he delivered the most appropriate sciences, and left nothing [pertaining to them] uninvestigated.

He likewise unfolded to men those sciences which are common [ to all disciplines ,] as for instance the demonstrative, the definitive, and that which consists in dividing, as may be known from the Pythagoric commentaries. He was also accustomed to pour forth sentences resembling Oracles to his familiars in a symbolical manner, and which in the greatest brevity of words contained the most abundant and multifarious meaning, like the Pythian Apollo through certain oracles, or like nature herself through seeds small in bulk, the former exhibiting conceptions, and the latter effects, innumerable in multitude, and difficult to be understood. Of this kind is the sentence, The beginning is the half of the whole , which is an apothegm of Pythagoras himself.

But not only in the present hemistich, but in others of a similar nature, the most divine Pythagoras has concealed the sparks of truth; depositing as in a treasury for those who are capable of being enkindled by them, and with a certain brevity of diction, an extension of theory most ample and difficult to be comprehended, as in the following hemistich:

(1) After this we must narrate how, when he had admitted certain persons to be his disciples, he distributed them into different classes according to their respective merits. For it was not fit that all of them should equally participate of the same things, as they were naturally dissimilar; nor was it indeed right that some should participate of all the most honorable auditions, but others of none, or should not at all partake of them. For this would be uncommunicative and unjust. While therefore he imparted a convenient portion of his discourses to each, he benefited as much as possible all of them, and preserved the proportion of justice, by making each a partaker of the auditions according to his desert.

Hence, in conformity to this method, he called some of them Pythagoreans, but others Pythagorists; just as we denominate some men Attics, but others Atticists. Having therefore thus aptly divided their names, some of them he considered to be genuine, but he ordained that others should show themselves to be the emulators of these. He ordered therefore that with the Pythagoreans possessions should be shared in common, and that they should always live together; but that each of the others should possess his own property apart from the rest, and that assembling together in the same place, they should mutually be at leisure for the same pursuits. And thus each of these modes was derived from Pythagoras, and transmitted to his successors.

Again, there were also with the Pythagoreans two forms of philosophy; for there were likewise two genera of those that pursued it, the Acusmatici, and the Mathematici. Of these however the Mathematici are acknowledged to be Pythagoreans by the rest; but the Mathematici do not admit that the Acusmatici are so, or that they derived their instruction from Pythagoras, but from Hippasus. And with respect to Hippasus, some say that he was a Crotonian, but others a Metapontine. But the philosophy of the Acusmatici consists in auditions unaccompanied with demonstrations and a reasoning process; because it merely orders a thing to be done in a certain way, and that they should endeavour to preserve such other things as were said by him, as so many divine dogmas.

They however profess that they will not speak of them, and that they are not to be spoken of; but they conceive those of their sect to be the best furnished with wisdom, who retained what they had heard more than others. But all these auditions are divided into three species. For some of them indeed signify what a thing is; others what it especially is; but others, what ought, or what ought not, to be done. The auditions therefore which signify what a thing is, are such as, What are the islands of the blessed? The sun and moon. What is the oracle at Delphi? The tetractys. What is harmony? That in which the Syrens subsist . But the auditions which signify what a thing especially is, are such as, What is the most just thing?

To sacrifice. What is the wisest thing? Number. But the next to this in wisdom, is that which gives names to things. What is the wisest of the things that are with us, [i. e. which pertain to human concerns]? Medicine. What is the most beautiful? Harmony. What is the most powerful? Mental decision. What is the most excellent? Felicity. What is that which is most truly asserted? That men are depraved. Hence they say that Pythagoras praised the Salaminian poet Hippodomas, because he sings: