(2) “It is reported that you philosophize to every one you may happen to meet, and publicly, which Pythagoras did not think fit to do. And these things, indeed, O Hipparchus, you learnt with diligent assiduity, but you have not preserved them; having tasted, O excellent man, of Sicilian delicacies, which you ought not to have tasted a second time. If, therefore, you abandon these, I shall rejoice; but if not, you will be dead in my opinion. For it will be pious to call to mind the divine and human precepts of Pythagoras, and not to make the goods of wisdom common to those, who have not even in a dream their soul purified. For it is not lawful to extend to every casual person, things which were obtained with such great labors, and such diligent assiduity, nor to divulge the mysteries of the Eleusinian Goddesses to the profane.

For those who do either of these, are equally unjust and impious. But it will be well to consider what a great length of time we consumed in wiping away the stains which had insinuated themselves into our breasts, till, after the lapse of some years, we became fit recipients of the doctrines of Pythagoras. For as dyers previously purify garments, and then fix in the colors with which they wish them to be imbued, in order that the dye may not be washed away, and may never become evanescent; after the same manner also that divine man prepared the souls of those that were lovers of philosophy, so that they might not deceive him in any of those beautiful and good qualities which he hoped they would possess.

For he did not impart spurious doctrines, nor snares, in which most of the sophists, who are at leisure for no good purpose, entangle young men; but he possessed a scientific knowledge of things human and divine. These men, however, making his doctrine a pretext, perform many dreadful deeds, ensnaring youth not in a becoming nor yet in a casual way. Hence they render their auditors noxious and precipitate. For they infuse theorems and divine doctrines into confused and turbid manners. Just as if some one should pour pure and clear water into a deep well full of mud; for he would disturb the mud, and destroy the clear water. The same thing likewise takes place between those who teach and those who are taught after this manner.

For dense thickets and which are full of briars surround the intellect and heart of those who have not been purely initiated in disciplines, obscure the mild, tranquil, and reasoning power of the soul, and openly impede the intellective part from becoming increased and elevated. It is requisite likewise to call intemperance and avarice the mothers of these thickets; both which are naturally prolific. From intemperance, therefore, unlawful marriages, [unjust] desires, corruptions, intoxication, preternatural pleasures, and certain vehement appetites blossom forth, and which impel their possessors into profundities and precipices. For now desires have compelled some not to abstain either from their mothers or their daughters, and violating law, their country, city, and king, with their hands as it were bound behind them, they are violently dragged along like slaves to extreme destruction.

But from avarice germinate rapine, robbery, parricide, sacrilege, sorcery, and such other evils at are the sisters of these. In the first place, therefore, it is necessary to purify the woods in which these passions have fixed their abode, with fire and sword, and all the machines of disciplines; and having liberated the reasoning power from such mighty evils, we may then implant in and deliver to it something useful and good.” So great and so necessary was the attention which, according to Pythagoras, ought to be paid to disciplines prior to philosophy. He likewise ordained that a singular honor, and the most accurate investigation, should be given to the teaching and participation of his dogmas, as he judiciously examined the conceptions of those that came to him, by various documents, and ten thousand forms of scientific theory.

(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) NUMEROUS volumes have been written as commentaries upon the secret systems of philosophy existing in the ancient world, but the ageless truths of life, like many of the earth's greatest thinkers, have usually been clothed in shabby garments. The present work is an attempt to supply a tome worthy of those seers and sages whose thoughts are the substance of its pages. To bring about this coalescence of Beauty and Truth has proved most costly, but I believe that the result will produce an effect upon the mind of the reader which will more than justify the expenditure.

(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.

(81) From indisputable facts such as these it is evident that philosophy emerged from the religious Mysteries of antiquity, not being separated from religion until after the decay of the Mysteries. Hence he who would fathom the depths of philosophic thought must familiarize himself with the teachings of those initiated priests designated as the first custodians of divine revelation. The Mysteries claimed to be the guardians of a transcendental knowledge so profound as to be incomprehensible save to the most exalted intellect and so potent as to be revealed with safety only to those in whom personal ambition was dead and who had consecrated their lives to the unselfish service of humanity. Both the dignity of these sacred institutions and the validity of their claim to possession of Universal Wisdom are attested by the most illustrious philosophers of antiquity, who were themselves initiated into the profundities of the secret doctrine and who bore witness to its efficacy.

(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.

(85) The book to which this is the introduction is dedicated to the proposition that concealed within the emblematic figures, allegories, and rituals of the ancients is a secret doctrine concerning the inner mysteries of life, which doctrine has been preserved in toto among a small band of initiated minds since the beginning of the world. Departing, these illumined philosophers left their formulæ that others, too, might attain to understanding. But, lest these secret processes fall into uncultured hands and be perverted, the Great Arcanum was always concealed in symbol or allegory; and those who can today discover its lost keys may open with them a treasure house of philosophic, scientific, and religious truths.

(64) Pythagoras saith: How marvellous is the diversity of the Philosophers in those things which they formerly asserted, and in their coming. together {or agreement], in respect of this small and most common-thing, wherein the precious thing is concealed! And if the vulgar knew, O all ye investigators of this art, the same small and vile thing, they would deem it a lie! Yet, if they knew its efficacy, they would not vilify it, but God hath concealed this from the crowd* lest the world should be devastated.

(2) The rites of Eleusis, with their Mystic interpretations of Nature's most precious secrets, overshadowed the civilizations of their time and gradually absorbed many smaller schools, incorporating into their own system whatever valuable information these lesser institutions possessed. Heckethorn sees in the Mysteries of Ceres and Bacchus a metamorphosis of the rites of Isis and Osiris, and there is every reason to believe that all so-called secret schools of the ancient world were branches from one philosophic tree which, with its root in heaven and its branches on the earth, is--like the spirit of man--an invisible but ever-present cause of the objectified vehicles that give it expression. The Mysteries were the channels through which this one philosophic light was disseminated, and their initiates, resplendent with intellectual and spiritual understanding, were the perfect fruitage of the divine tree, bearing witness before the material world of the recondite source of all Light and Truth.

(13) [paragraph continues] Homerus, as Hesiodus took the subject for his Theogony likewise from thence, which Ovidius took afterwards for a pattern for his Metamorphosis. The knowledge of Nature's secret operations constitutes the principal sense of all these ancient writings, but ignorance framed out of it that external or veiled mythology and the lower class of people turned it into idolatry.

(1) Since it is usual with all men of sound understandings, to call on divinity, when entering on any philosophic discussion, it is certainly much more appropriate to do this in the consideration of that philosophy which justly receives its denomination from the divine Pythagoras. For as it derives its origin from the Gods, it cannot be apprehended without their inspiring aid. To which we may also add, that the beauty and magnitude of it so greatly surpasses human power, that it is impossible to survey it by a sudden view; but then alone can any one gradually collect some portion of this philosophy, when, the Gods being his leaders, he quietly approaches to it. On all these accounts, therefore, having invoked the Gods as our leaders, and converting both ourselves and our discussion to them, we shall acquiesce in whatever they may command us to do.

We shall not, however, make any apology for this sect having been neglected for a long time, nor for its being concealed by foreign disciplines, and certain arcane symbols, nor for having been obscured by false and spurious writings, nor for many other such-like difficulties by which it has been impeded. For the will of the Gods is sufficient for us, in conjunction with which it is possible to sustain things still more arduous than these. But after the Gods, we shall unite ourselves as to a leader, to the prince and father of this divine philosophy; of whose origin and country we must rise a little higher in our investigation.

(1) We shall, therefore, deliver to you the peculiar dogmas of the Assyrians; and also clearly develop to you our own opinions; collecting some things from the infinite writings of the ancients, but others from those particulars which were comprehended by the ancients in one treatise, and pertain to the whole knowledge of divine natures. If also you should propose any philosophic inquiry, we shall discuss it for you, according to the ancient pillars of Hermes, which Plato and Pythagoras knew before, and from thence constituted their philosophy. But such things as exhibit foreign inquiries, or which are contradictory and contentious, we shall assist mildly and aptly, or we shall demonstrate their absurdity. Such, likewise, as proceed conformably to common conceptions, we shall endeavour to discuss in a way perfectly known and clear. And things, indeed, which require the experience of divine operations to an accurate knowledge of them, we shall explain, as far as this is possible to be effected by words alone; but such as are full of intellectual theory, we shall develop with a view to the purification of the soul.

(39) The Neo-Pythagorean school flourished in Alexandria during the first century of the Christian Era. Only two names stand out in connection with it--Apollonius of Tyana and Moderatus of Gades. Neo-Pythagoreanism is a link between the older pagan philosophies and Neo-Platonism. Like the former, it contained many exact elements of thought derived from Pythagoras and Plato; like the latter, it emphasized metaphysical speculation and ascetic habits. A striking similarity has been observed by several authors between Neo-Pythagoreanism and the doctrines of the Essenes. Special emphasis was laid upon the mystery of numbers, and it is possible that the Neo-Pythagoreans had a far wider knowledge of the true teachings of Pythagoras than is available today. Even in the first century Pythagoras was regarded more as a god than a man, and the revival of his philosophy was resorted to apparently in the hope that his name would stimulate interest in the deeper systems of learning. But Greek philosophy had passed the zenith of its splendor; the mass of humanity was awakening to the importance of physical life and physical phenomena. The emphasis upon earthly affairs which began to assert itself later reached maturity of expression in twentieth century materialism and commercialism,

(80) Having thus traced the more or less sequential development of philosophic speculation from Thales to James and Bergson, it is now in order to direct the reader's attention to the elements leading to and the circumstances attendant upon the genesis of philosophic thinking. Although the Hellenes proved themselves peculiarly responsive to the disciplines of philosophy, this science of sciences should not be considered indigenous to them. "Although some of the Grecians," writes Thomas Stanley, "have challenged to their nation the original of philosophy, yet the more learned of them have acknowledged it [to be] derived from the East." The magnificent institutions of Hindu, Chaldean, and Egyptian learning must be recognized as the actual source of Greek wisdom. The last was patterned after the shadow cast by the sanctuaries of Ellora, Ur, and Memphis upon the thought substance of a primitive people. Thales, Pythagoras, and Plato in their philosophic wanderings contacted many distant cults and brought back the lore of Egypt and the inscrutable Orient.

(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:

(43) Although Ammonius Saccus was long believed to be the founder of Neo-Platonism, the school had its true beginning in Plotinus (A.D. 204-269?). Prominent among the Neo-Platonists of Alexandria, Syria, Rome, and Athens were Porphyry, Iamblichus, Sallustius, the Emperor Julian, Plutarch, and Proclus. Neo-Platonism was the supreme effort of decadent pagandom to publish and thus preserve for posterity its secret (or unwritten) doctrine. In its teachings ancient idealism found its most perfect expression. Neo-Platonism was concerned almost exclusively with the problems of higher metaphysics. It recognized the existence of a secret and all-important doctrine which from the time of the earliest civilizations had been concealed within the rituals, symbols, and allegories of religions and philosophies. To the mind unacquainted with its fundamental tenets, Neo-Platonism may appear to be a mass of speculations interspersed with extravagant flights of fancy. Such a viewpoint, however, ignores the institutions of the Mysteries--those secret schools into whose profundities of idealism nearly all of the first philosophers of antiquity were initiated.

(1) Hermes, the God who presides over language, was formerly very properly considered as common to all priests; and the power who presides over the true science concerning the Gods is one and the same in the whole of things. Hence our ancestors dedicated the inventions of their wisdom to this deity, inscribing all their own writings with the name of Hermes. If, therefore, we participate of a portion of this God, adapted and commensurate to our powers, you do well to propose your theological doubts to the priests, as friends, and to make these doubts known to them. I also very properly conceiving that the epistle sent to my disciple Anebo was written to me, shall give you a true answer to your inquiries. For it would not be becoming, that Pythagoras and Plato, Democritus and Eudoxus, and many other of the ancient Greeks, should have obtained appropriate instruction from the sacred scribes of their time, but that you who are our contemporary, and think conformably to those ancients, should be frustrated of your wish by those who are now living, and who are called common preceptors. I, therefore, thus betake myself to the present discussion; and do you, if you please, conceive that the same person to whom you sent the letter returns you an answer. Or, if it should seem fit to you, admit it to be me who discourses with you in writing, or some other prophet of the Egyptians, for this is of no consequence. Or, which I think is still better, dismiss the consideration whether the speaker is an inferior or a superior character, but direct your attention to what is said, so as readily to excite your mind to survey whether what is asserted is true or false.

(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) 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:

(1) It is also said, that Pythagoras was the first who called himself a philosopher; this not being a new name, but previously instructing us in a useful manner in a thing appropriate to the name. For he said that the entrance of men into the present life, resembled the progression of a crowd to some public spectacle. For there men of every description assemble with different views; one hastening to sell his wares for the sake of money and gain; but another that he may acquire renown by exhibiting the strength of his body; and there is also a third class of men, and those the most liberal, who assemble for the sake of surveying the places, the beautiful works of art, the specimens of valor, and the literary productions which are usually exhibited on such occasions.

Thus also in the present life, men of all-various pursuits are collected together in one and the same place. For some are influenced by the desire of riches and luxury; others by the love of power and dominion; and others are possessed with an insane ambition for glory. But the most pure and unadulterated character, is that of the man who gives himself to the contemplation of the most beautiful things, and whom it is proper to call a philosopher. He adds, that the survey of all heaven, and of the stars that revolve in it, is indeed beautiful, when the order of them is considered. For they derive this beauty and order by the participation of the first and the intelligible essence.

But that first essence is the nature of number and reasons [i. e. productive principles,] which pervades through all things, and according to which all these [celestial bodies] are elegantly arranged, and fitly adorned. And wisdom indeed, truly so called, is a certain science which is conversant with the first beautiful objects, and these divine, undecaying, and possessing an invariable sameness of subsistence; by the participation of which other things also may be called beautiful. But philosophy is the appetition of a thing of this kind. The attention therefore to erudition is likewise beautiful, which Pythagoras extended, in order to effect the correction of mankind.