(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.

(11) After Pythagoras of Samos, its founder, the Italic or Pythagorean school numbers among its most distinguished representatives Empedocles, Epicharmus, Archytas, Alcmæon, Hippasus, Philolaus, and Eudoxus. Pythagoras (580-500? B.C.) conceived mathematics to be the most sacred and exact of all the sciences, and demanded of all who came to him for study a familiarity with arithmetic, music, astronomy, and geometry. He laid special emphasis upon the philosophic life as a prerequisite to wisdom. Pythagoras was one of the first teachers to establish a community wherein all the members were of mutual assistance to one another in the common attainment of the higher sciences. He also introduced the discipline of retrospection as essential to the development of the spiritual mind. Pythagoreanism may be summarized as a system of metaphysical speculation concerning the relationships between numbers and the causal agencies of existence. This school also first expounded the theory of celestial harmonics or "the music of the spheres." John Reuchlin said of Pythagoras that he taught nothing to his disciples before the discipline of silence, silence being the first rudiment of contemplation. In his Sophist, Aristotle credits Empedocles with the discovery of rhetoric. Both Pythagoras and Empedocles accepted the theory of transmigration, the latter saying: "A boy I was, then did a maid become; a plant, bird, fish, and in the vast sea swum." Archytas is credited with invention of the screw and the crane. Pleasure he declared to be a pestilence because it was opposed to the temperance of the mind; he considered a man without deceit to be as rare as a fish without bones.

(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.

(4) Of the Leontines, Phrynichus, Smichias, Aristoclidas, Clinias, Abroteles, Pisyrrhydus, Bryas, Evandrus, Archemachus, Mimnomachus, Achmonidas, Dicas, Carophantidas. Of the Sybarites, Metopus, Hippasus, Proxenus, Evanor, Deanax, Menestor, Diocles, Empedus, Timasius, Polemæus, Evæus, Tyrsenus. Of the Carthaginians, Miltiades, Anthen, Odius, Leocritus. Of the Parians, Æetius, Phænecles, Dexitheus, Alcimachus, Dinarchus, Meton, Timæus, Timesianax, Amærus, Thymaridas. Of the Locrians, Gyptius, Xenon, Philodamus, Evetes, Adicus, Sthenonidas, Sosistratus, Euthynus, Zaleucus, Timares. Of the Posidonians, Athamas, Simus, Proxenus, Cranous, Myes, Bathylaus, Phædon. Of the Lucani, Ocellus and Occillus who were brothers, Oresandrus, Cerambus, Dardaneus, Malion. Of the Ægeans, Hippomedon, Timosthenes, Euelthon, Thrasydamus, Crito, Polyctor. Of the Lacones, Autocharidas, Cleanor, Eurycrates. Of the Hyperboreans, Abaris. Of the Rheginenses, Aristides, Demosthenes, Aristocrates, Phytius, Helicaon, Mnesibulus, Hipparchides, Athosion, Euthycles, Opsimus. Of the Selinuntians, Calais.

Of the Syracusans, Leptines, Phintias, Damon. Of the Samians, Melissus, Lacon, Archippus, Glorippus, Heloris, Hippon, Of the Caulonienses, Callibrotus, Dicon, Nastas, Drymon, Xentas. Of the Phliasians, Diocles, Echecrates, Polymnastus, Phanton. Of the Sicyonians, Poliades, Demon, Sostratius, Sosthenes. Of the Cyrenæans, Prorus, Melanippus, Aristangelus, Theodorus. Of the Cyziceni, Pythodorus, Hipposthenes, Butherus, Xenophilus. Of the Catanæi, Charondas, Lysiades. Of the Corinthians, Chrysippus. Of the Tyrrhenians, Nausitheus. Of the Athenians, Neocritus. And of Pontus, Lyramnus. In all, two hundred and eighteen. [And these, indeed, are not all the Pythagoreans, but of all of them they are the most famous. ]

(1) The successor, however, of Pythagoras, is acknowledged by all men to have been Aristæus, the son of Damophon the Crotonian, who existing at the same time as Pythagoras, was seven ages prior to Plato. Aristæus likewise, was not only thought worthy to succeed Pythagoras in his school, but also to educate his children, and marry his wife Theano, because he was eminently skilled in the Pythagoric dogmas. For Pythagoras himself is said to have taught in his school, forty years wanting one, and to have lived nearly one hundred years. But Aristæus, when much advanced in years, relinquished the school; and after him Mnesarchus succeeded, who was the son of Pythagoras. Bulagoras succeeded Mnesarchus, in whose time it happened that the city of the Crotonians was plundered. Gartydas the Crotonian succeeded Bulagoras, on his return from a journey which he had undertaken prior to the war. Nevertheless on account of the calamity of his country, he suffered so much anxiety, as to die prematurely through grief. But it was the custom with the rest of the Pythagoreans, when they became very old, to liberate themselves from the body as from a prison.

(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.

(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.

(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:

(22) Critias: and by recounting the number of years occupied by the events mentioned he tried to calculate the periods of time. Whereupon one of the priests, a prodigiously old man, said, “O Solon, Solon, you Greeks are always children: there is not such a thing as an old Greek.” And on hearing this he asked, “What mean you by this saying?” And the priest replied, “You are young in soul, every one of you. For therein you possess not a single belief that is ancient and derived from old tradition, nor yet one science that is hoary with age.

(5) But after his father Mnesarchus had returned from Syria to Samos, with great wealth, which he had collected from a prosperous navigation, he built a temple to Apollo, with the inscription of Pythius; and took care to have his son nourished with various and the best disciplines, at one time by Creophilus, at another by Pherecydes the Syrian, and at another by almost all those who presided over sacred concerns, to whom he earnestly recommended Pythagoras, that he might be as much as possible sufficiently instructed in divine concerns. He, however, was educated in such a manner, as to be fortunately the most beautiful and godlike of all those that have been celebrated in the annals of history. On the death of his father, likewise, though he was still but a youth, his aspect was most venerable, and his habits most temperate, so that he was even reverenced and honored by elderly men; and converted the attention of all who saw and heard him speak, on himself, and appeared to be an admirable person to every one who beheld him.

Hence it was reasonably asserted by many, that he was the son of a God. But he being corroborated by renown of this kind, by the education which he had received from his infancy, and by his natural deiform appearance, in a still greater degree evinced that he deserved his present prerogatives. He was also adorned by piety and disciplines, by a mode of living transcendency good, by firmness of soul, and by a body in due subjection to the mandates of reason. In all his words and actions, he discovered an inimitable quiet and serenity, not being subdued at any time by anger, or laughter, or emulation, or contention, or any other perturbation or precipitation of conduct; but he dwelt at Samos like some beneficent dæmon.

Hence, while he was yet a youth, his great renown having reached Thales at Miletus, and Bias at Priene, men illustrious for their wisdom, it also extended to the neighbouring cities. To all which we may add, that the youth was every where celebrated as the long-haired Samian , and was reverenced by the multitude as one under the influence of divine inspiration. But after he had attained the eighteenth year of his age, about the period when the tyranny of Policrates first made its appearance, foreseeing that under such a government he might receive some impediment in his studies, which engrossed the whole of his attention, he departed privately by night with one Hermodamas (whose surname was Creophilus, and who was the grandson of him who had formerly been the host, friend, and preceptor in all things of Homer the poet,) to Pherecydes, to Anaximander the natural philosopher, and to Thales at Miletus.

He likewise alternately associated with each of these philosophers, in such a manner, that they all loved him, admired his natural endowments, and made him a partaker of their doctrines. Indeed, after Thales had gladly admitted him to his intimate confidence, he admired the great difference between him and other young men, whom Pythagoras left far behind in every accomplishment. And besides this, Thales increased the reputation Pythagoras had already acquired, by communicating to him such disciplines as he was able to impart: and, apologizing for his old age, and the imbecility of his body, he exhorted him to sail into Egypt, and associate with the Memphian and Diospolitan priests. For he confessed that his own reputation for wisdom, was derived from the instructions of these priests; but that he was neither naturally, nor by exercise, endued with those excellent prerogatives, which were so visibly displayed in the person of Pythagoras. Thales, therefore, gladly announced to him, from all these circumstances, that he would become the wisest and most divine of all men, if he associated with these Egyptian priests.

(1) But here, while he frequented all the Egyptian temples with the greatest diligence and with accurate investigation, he was both admired and loved by the priests and prophets with whom he associated. And having learnt with the greatest solicitude every particular, he did not neglect to hear of any transaction that was celebrated in his own time, or of any man famous for his wisdom, or any mystery in whatever manner it might be performed; nor did he omit to visit any place in which he thought something more excellent might be found. On this account he went to all the priests, by whom he was furnished with the wisdom which each possessed. He spent therefore two and twenty years in Egypt, in the adyta of temples, astronomizing and geometrizing, and was initiated, not in a superficial or casual manner, in all the mysteries of the Gods, till at length being taken captive by the soldiers of Cambyses, he was brought to Babylon.

Here he gladly associated with the Magi, was instructed by them in their venerable knowledge, and learnt from them the most perfect worship of the Gods. Through their assistance likewise, he arrived at the summit of arithmetic, music, and other disciplines; and after associating with them twelve years, he returned to Samos about the fifty-sixth year of his age.