(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) 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.

(1) Pythagoras, therefore, having been benefited by Thales in other respects, and especially having learned from him to be sparing of his time; for the sake of this he entirely abstained from wine and animal food, and still prior to these from voracity, and confined himself to such nutriment as was slender and easy of digestion. In consequence of this, his sleep was short, his soul vigilant and pure, and his body confirmed in a state of perfect and invariable health. In possession of such advantages, therefore, he sailed to Sidon, being persuaded that this was his natural country, and also properly conceiving that he might easily pass from thence into Egypt. Here he conversed with the prophets who were the descendants of Mochus the physiologist, and with others, and also with the Phœnician hierophants.

He was likewise initiated in all the mysteries of Byblus and Tyre, and in the sacred operations which are performed in many parts of Syria; not engaging in a thing of this kind for the sake of superstition, as some one may be led to suppose, but much rather from a love and desire of contemplation, and from an anxiety that nothing might escape his observation which deserved to be learnt in the arcana or mysteries of the Gods. Having been previously instructed therefore in the mysteries of the Phœnicians, which were derived like a colony and a progeny from the sacred rites in Egypt, and hoping from this circumstance that he should be a partaker of more beautiful, divine, and genuine monuments of erudition in Egypt; joyfully calling to mind also the admonitions of his preceptor Thales, he immediately embarked for Egypt, through the means of some Egyptian sailors, who very opportunely at that time landed on the Phœnician coast under mount Carmelus, in whose temple Pythagoras, separated from all society, for the most part dwelt.

But the sailors gladly received him, foreseeing that they should acquire great gain by exposing him to sale. But when, during the voyage, they perceived with what continence and venerable gravity he conducted himself, in conformity to the mode of living he had adopted, they were more benevolently disposed towards him. Observing, likewise, that there was something greater than what pertains to human nature in the modesty of the youth, they called to mind how unexpectedly he had appeared to them on their landing, when from the summit of mount Carmelus, which they knew was more sacred than other mountains, and inaccessible to the vulgar, he leisurely descended without looking back, or suffering any delay from precipices or opposing stones; and that when he came to the boat, he said nothing more than, “Are you bound for Egypt?” And farther, that on their answering in the affirmative, he ascended the ship and sate silent the whole time of the voyage, in that part of the vessel where he was not likely to incommode the occupations of the sailors.

But Pythagoras remained in one and the same unmoved state for two nights and three days, neither partaking of food, nor drink, nor sleep, unless perhaps as he sate in that firm and tranquil condition, he might sleep for a short time unobserved by all the sailors. To which we may add, that when the sailors considered how, contrary to their expectations, their voyage had been continued and uninterrupted, as if some deity had been present; putting all these things together, they concluded that a divine dæmon had in reality passed over with them from Syria into Egypt. Hence, speaking both to Pythagoras and to each other with greater decorum and gentleness than before, they completed, through a most tranquil sea, the remainder of their voyage, and at length happily landed on the Egyptian coast.

Here the sailors reverently assisted him in descending from the ship; and after they had placed him on the purest sand, they raised a certain temporary altar before him, and heaping on it from their present abundance the fruits of trees, and presenting him as it were with the first fruits of their freight, they departed from thence, and hastened to their destined port. But Pythagoras, whose body through such long fasting was become weaker, did not oppose the sailors in assisting him to descend from the ship, and immediately on their departure eat as much of the fruits as was requisite to restore his decayed strength. From thence also he arrived safe at the neighbouring lands, constantly preserving the same tranquillity and modesty of behaviour.

(1) As he therefore thus prepared his disciples for erudition, he did not immediately receive into the number of his associates those who came to him for that purpose, till he had made trial of, and judiciously examined them. Hence in the first place he inquired after what manner they associated with their parents, and the rest of their relatives. In the next place he surveyed their unseasonable laughter, their silence, and their speaking when it was not proper; and farther still, what their desires were, with whom they associated, how they conversed with them, in what they especially employed their leisure time in the day, and what were the subjects of their joy and grief. He likewise surveyed, their form, their mode of walking, and the whole motion of their body.

Physiognomically also considering the natural indications of their frame, he made them to be manifest signs of the unapparent manners of the soul. When, therefore, he had thus made trial of some one, he suffered him to be neglected for three years, in the mean time observing how he was disposed with respect to stability, and a true love of learning, and if he was sufficiently prepared with reference to glory, so as to despise [popular] honor. After this, he ordered those who came to him to observe a quinquennial silence, in order that he might experimentally know how they were affected as to continence of speech, the subjugation of the tongue being the most difficult of all victories; as those have unfolded to us who instituted the mysteries.

During this [probationary] time, however, the property of each was disposed of in common, and was committed to the care of those appointed for this purpose, who were called politicians, economizers, and legislators. And with respect to these probationers, those who appeared to be worthy to participate of his dogmas, from the judgment he had formed of them from their life and the modesty of their behaviour, after the quinquennial silence, then became Esoterics , and both heard and saw Pythagoras himself within the veil. For prior to this they participated of his words through the hearing alone, beyond the veil, without at all seeing him, giving for a long time a specimen of their peculiar manners. But if they were rejected they received the double of the wealth which they brought, and a tomb was raised to them as if they were dead by the homacoï ; for thus all the disciples of the man were called.

And if they happened to meet with them afterwards, they behaved to them as if they were other persons, but said that they were dead, whom they had modelled by education, in the expectation that they would become truly good men by the disciplines they would learn. They also were of opinion that those who were more slow in the acquisition of knowledge, were badly organized, and, as I may say, imperfect and barren. If, however, after Pythagoras had physiognomically considered their form, their mode of walking, and every other motion, and the state of their body, and he had conceived good hope respecting them; after likewise the quinquennial silence, and the orgies and initiations from so many disciplines, together with the ablutions of the soul, and so many and such great purifications produced from such various theorems, through which the sagacity and sanctity of the soul is perfectly ingenerated; if, after all this, some one was found to be still sluggish and of a dull intellect, they raised to such a one in the school a certain pillar and monument, (as they are said to have done to Perialus the Thurian, and Cylon the prince of the Sybarites, who were rejected by them) expelled him from the Homacoïon or auditory, loading him with a great quantity of silver and gold.

For these were deposited by them in common, and were committed to the care of certain persons adapted to this purpose, and who were called Economics, from the office which they bore. And if afterwards they happened to meet with such a one, they conceived him to be any other person, than him who according to them was dead. Hence also Lysis, blaming a certain person named Hipparchus, because he had communicated the doctrines of the Pythagoreans to the profane, and to those who acceded to them without disciplines and theory, says as follows:

(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) 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) This therefore was the form of his wisdom which is so admirable.

It is also said, that of the sciences which the Pythagoreans honored, music, medicine and divination, were not among the least. But they were habitually silent and prompt to hear, and he who was able to hear [in a proper manner] was praised by them. Of medicine, however, they especially embraced the diætetic species, and in the exercise of this were most accurate. And in the first place, indeed, they endeavoured to learn the indications of symmetry, of labor, food, and repose. In the next place, with respect to the preparation of food, they were nearly the first who attempted to employ themselves in it, and to define the mode in which it should be performed. The Pythagoreans likewise employed cataplasms more frequently than their predecessors; but they in a less degree approved of medicated ointments. These however they principally used in the cure of ulcerations. But incisions and burnings they admitted the least of all things. Some diseases also they cured by incantations. Pythagoras, however, thought that music greatly contributed to health, if it was used in a proper manner. The Pythagoreans likewise employed select sentences of Homer and Hesiod for the amendment of souls. But they thought it was necessary to retain and preserve in the memory things which they had learnt and heard; and that it was requisite to be furnished with disciplines and auditions, to as great an extent as there was an ability of learning and remembering; the former of these being the power by which knowledge is obtained, but the latter, the power by which it is preserved. Hence, they very much honored the memory, abundantly exercised, and paid great attention to it. In learning too, they did not dismiss what they were taught, till they had firmly comprehended the first rudiments of it; and they recalled to their memory what they had daily heard, after the following manner: A Pythagorean never rose from his bed till he had first recollected the transactions of the former day; and he accomplished this by endeavouring to remember what he first said, or heard, or ordered his domestics to do when he was rising, or what was the second and third thing which he said, heard, or commanded to be done. And the same method was adopted with respect to the remainder of the day. For again, he endeavoured to recollect who was the first person that he met, on leaving his house, or who was the second; and with whom he in the first, or second, or third place discoursed. And after the same manner he proceeded in other things. For he endeavoured to resume in his memory all the events of the whole day, and in the very same order in which each of them happened to take place. But if they had sufficient leisure after rising from sleep, they tried after the same manner to recollect the events of the third preceding day. And thus they endeavoured to exercise the memory to a great extent. For there is not any thing which is of greater importance with respect to science, experience and wisdom, than the ability of remembering. From these studies therefore, it happened that all Italy was filled with philosophers, and this place, which before was unknown, was afterwards on account of Pythagoras called Magna Græcia. Hence also it contained many philosophers, poets, and legislators. For the rhetorical arts, demonstrative reasonings, and the laws written by them, were transferred from Italy to Greece. Those likewise who make mention of physics, adduce as the principal physiologists Empedocles and the Elean Parmenides. Those too, who wish to cite sentences, pertaining to the conduct of human life, adduce for this purpose the conceptions of Epicharmus. And nearly all philosophers make use of these. Thus much therefore concerning the wisdom of Pythagoras, how in a certain respect he very much impelled all his auditors to the pursuit of it, as far as they were adapted to its participation, and how perfectly it was delivered by him.

(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.

(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) On his return to Samos, however, being known by some of the more aged inhabitants, he was not less admired than before. For he appeared to them to be more beautiful and wise, and to possess a divine gracefulness in a more eminent degree. Hence, he was publicly called upon by his country to benefit all men, by imparting to them what he knew. Nor was he averse to this request, but endeavoured to introduce the symbolical mode of teaching, in a way perfectly similar to the documents by which he had been instructed in Egypt; though the Samians did not very much admit this mode of tuition, and did not adhere to him with that according aptitude which was requisite.

Though no one therefore attended to him, and no one was genuinely desirous of those disciplines which he endeavoured by all means to introduce among the Greeks, yet he neither despised nor neglected Samos, because it was his country, and therefore wished to give his fellow-citizens a taste of the sweetness of the mathematical disciplines, though they were unwilling to be instructed in them. With a view to this, therefore, he employed the following method and artifice. Happening to observe a certain youth, who was a great lover of gymnastic and other corporeal exercises, but otherwise poor and in difficult circumstances, playing at ball in the Gymnasium with great aptness and facility, he thought the young man might easily be persuaded to attend to him, if he was sufficiently supplied with the necessaries of life, and freed from the care of procuring them.

As soon as the youth, therefore, left the bath, Pythagoras called him to him, and promised that he would furnish him with every thing requisite to the support of his bodily exercise, on condition that he would receive from him gradually and easily, but continually, so that he might not be burthened by receiving them at once, certain disciplines, which he said he had learnt from the Barbarians in his youth, but which now began to desert him through forgetfulness and the incursions of old age. But the young man immediately acceded to the conditions, through the hope of having necessary support. Pythagoras, therefore, endeavoured to instruct him in the disciplines of arithmetic and geometry, forming each of his demonstrations in an abacus, and giving the youth three oboli as a reward for every figure which he learnt.

This also he continued to do for a long time, exciting him to the geometrical theory by the desire of honour; diligently, and in the best order, giving him (as we have said) three oboli for every figure which he apprehended. But when the wise man observed that the elegance, sweetness, and connexion of these disciplines, to which the youth had been led in a certain orderly path, had so captivated him that he would not neglect their pursuit though he should suffer the extremity of want, he pretended poverty, and an inability of giving him three oboli any longer. But the youth on hearing this replied, “I am able without these to learn and receive your disciplines.” Pythagoras then said, “But I have not the means of procuring sufficient nutriment for myself.” As it is requisite, therefore, to labour in order to procure daily necessaries and mortal food, it would not be proper that his attention should be distracted by the abacus, and by stupid and vain pursuits.

The youth, however, vehemently abhorring the thought of discontinuing his studies, replied: “I will in future provide for you, and repay your kindness in a way resembling that of the stork: for I in my turn will give you three oboli for every figure.” And from this time he was so captivated by these disciplines, that he alone, of all the Samians, migrated from his country with Pythagoras, having the same name with him, but being the son of Eratocles. There are said to be three books of this Samian On Athletics, in which he orders the Athletæ to feed on flesh instead of dry figs; which books are very improperly ascribed by some to Pythagoras the son of Mnesarchus.

It is likewise said, that about the same time Pythagoras was admired at Delos, when he approached to the bloodless altar, as it is called, of the father Apollo, and worshipped it. After which he went to all the oracles. He likewise dwelt for some time in Crete and Sparta, for the purpose of becoming acquainted with their laws; and, having been an auditor and learner of all these, he returned home in order to investigate what he had omitted. And in the first place, indeed, he established a school in the city, which is even now called the semicircle of Pythagoras; and in which the Samians now consult about public affairs, conceiving it right to investigate things just and advantageous in that place which he had constructed who paid attention to the welfare of all men.

He also formed a cavern out of the city, adapted to his philosophy, in which he spent the greatest part both of the day and night; employing himself in the investigation of things useful in disciplines, framing intellectual conceptions after the same manner as Minos the son of Jupiter. Indeed, he so much surpassed those who afterwards employed his disciplines, that they conceived magnificently of themselves, from the knowledge of theorems of small importance; but Pythagoras gave completion to the science of the celestial orbs, and unfolded the whole of it by arithmetical and geometrical demonstrations. He is, however, to be admired in a still greater degree for what he afterwards accomplished. For when now philosophy had received a great accession, he was admired by all Greece, and the best of those who philosophized came to Samos on his account, in order that they might participate of his erudition.

The citizens likewise employed him in all their embassies, and compelled him to unite with them in the administration of public affairs. However, as he easily saw the difficulty of complying with the laws of his country, and at the same time remaining at home and philosophizing, and considered that all philosophers before him had passed their life in foreign countries, he determined to neglect all political occupations; induced to this, according to the testimony of others, by the negligence of the Samians in what relates to education, and went into Italy, conceiving that place to be his proper country, in which men well disposed towards learning were to be found in the greatest abundance. And such was the success of his journey, that on his arrival at Crotona, which was the noblest city in Italy, he had many followers, amounting, as it is said, to the number of six hundred, who were not only excited by his discourses to the study of philosophy, but also to an amicable division of the goods of life in common; from whence they acquired the appellation of Cœnobitæ .

(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) 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.

(1) Pythagoras, therefore, complying with their wish, is said to have given the boys the following advice: That they should neither revile any one, nor take vengeance on those that reviled. He likewise exhorted them to pay diligent attention to learning, which derives its appellation from their age. He added, that it was easy for a modest youth to preserve probity through the whole of life; but that it was difficult for one to accomplish this, who was not naturally well disposed at that age; or rather it is impossible that he who begins his course from a bad impulse, should run well to the end. Besides this, he observed that boys were most dear to divinity, and hence in times of great drought, they were sent by cities to implore rain from the Gods, in consequence of the persuasion that divinity is especially attentive to children; though such as are permitted to be continually conversant with sacred ceremonies, scarcely obtain purification in perfection.

From this cause also, the most philanthropic of the Gods, Apollo and Love, are universally represented in pictures as having the age of boys. It is likewise acknowledged, that some of the games in which the conquerors are crowned, were instituted on account of boys; the Pythian, indeed, in consequence of the serpent Python being slain by a boy; but the Nemean and Isthmian, on account of the death of Archemorus and Melicerta. Besides what has been said likewise, while the city of Crotona was building, Apollo promised to the founder, that he would give him a progeny, if he brought a colony into Italy; from which inferring that Apollo providentially attended to the propagation of them, and that all the Gods paid attention to every age, they ought to render themselves worthy of their friendship.

He added, that they should exercise themselves in hearing, in order that they may be able to speak. And farther still, that as soon as they have entered into the path in which they intend to proceed to old age, they should follow the steps of those that preceded them, and never contradict those that are older than themselves. For thus hereafter, they will justly think it right that neither should they be injured by their juniors. On account of these exhortations, it must be confessed that he deserved not to be called by his own name, but that all men should denominate him divine.

(4) It is worth while, however, to relate how this report became so prevalent. The Pythian oracle then had predicted to this Mnesarchus (who came to Delphi for the purposes of merchandize, with his wife not yet apparently pregnant, and who inquired of the God concerning the event of his voyage to Syria) that his voyage would be lucrative and most conformable to his wishes, but that his wife was now pregnant, and would bring forth a son surpassing in beauty and wisdom all that ever lived, and who would be of the greatest advantage to the human race in every thing pertaining to the life of man. But, when Mnesarchus considered with himself, that the God, without being interrogated concerning his son, had informed him by an oracle, that he would possess an illustrious prerogative, and a gift truly divine, he immediately named his wife Pythaïs, from her son and the Delphic prophet, instead of Parthenis, which was her former appellation; and he called the infant, who was soon after born at Sidon in Phœnicia, Pythagoras; signifying by this appellation, that such an offspring was predicted to him by the Pythian Apollo.

For we must not regard the assertions of Epimenides, Eudoxus, and Xenocrates, who suspect that Apollo at that time, becoming connected with Parthenis, and causing her to be pregnant from not being so, had in consequence of this predicted concerning Pythagoras, by the Delphic prophet: for this is by no means to be admitted. Indeed, no one can doubt that the soul of Pythagoras was sent to mankind from the empire of Apollo, either being an attendant on the God, of co-arranged with him in some other more familiar way: for this may be inferred both from his birth, and the all-various wisdom of his soul. And thus much concerning the nativity of Pythagoras.

(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) 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.

(4) He performed however what is still more generous than this, by effecting the dissolution of tyranny, restraining the tyrant when he was about to bring the most deplorable calamities on mankind, and liberating Sicily from the most cruel and imperious power. But that it was Pythagoras who accomplished this, is evident from the oracles of Apollo, in which it is predicted that the domination of Phalaris would then be dissolved, when those that were governed by him should become better men, and be more concordant with each other; such as they then became, when Pythagoras was present with them, through the doctrines and instruction which he imparted to them. A greater proof however of the truth of this, is derived from the time in which it happened.

For on the very same day in which Phalaris put Pythagoras and Abaris in danger of death, he himself was slain by stratagem. That also which happened to Epimenides may be an argument of the truth of these things. For as he, who was the disciple of Pythagoras, when certain persons intended to destroy him, invoked the Furies, and the avenging Gods, and by so doing caused all those that attempted his life, to destroy each other;—thus also Pythagoras, who gave assistance to mankind, after the manner and with the fortitude of Hercules, for the benefit of men, punished and occasioned the death of him who had acted in an insolent and disorderly manner towards others; and this through the oracles themselves of Apollo, to the series of which divinity both he and Epimenides spontaneously belonged from their very birth. And thus far, indeed, we have thought it requisite to mention this admirable and strenuous deed, the effect of his fortitude.

(6) It is farther related of the Pythagoreans, that they expelled from themselves lamentation, weeping, and every thing else of this kind; and that neither gain, nor desire, nor anger, nor ambition, nor any thing of a similar nature, became the cause of dissension among them; but that all the Pythagoreans were so disposed towards each other, as a worthy father is towards his offspring. This also is a beautiful circumstance, that they referred every thing to Pythagoras, and called it by his name, and that they did not ascribe to themselves the glory of their own inventions, except very rarely. For there are very few whose works are acknowledged to be their own. The accuracy too, with which they preserved their writings is admirable. For in so many ages, no one appears to have met with any of the commentaries of the Pythagoreans, prior to the time of Philolaus. But he first published those three celebrated books, which Dion the Syracusan is said to have bought, at the request of Plato, for a hundred mina. For Philolaus had fallen into a certain great and severe poverty; and from his alliance to the Pythagoreans, was a partaker of their writings.

(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: