(1) [Trismegistus] ’Tis in this way, Asclepius;—by mixing it, by means of subtle expositions, with divers sciences not easy to be grasped,—such as arithmetic, and music, and geometry. But Pure Philosophy, which doth depend on godly piety alone, should only so far occupy itself with other arts, that it may [know how to] appreciate the working out in numbers of the fore-appointed stations of the stars when they return, and of the course of their procession. Let her, moreover, know how to appreciate the Earth’s dimensions, its qualities and quantities, the Water’s depths, the strength of Fire, and the effects and nature of all these. [And so] let her give worship and give praise unto the Art and Mind of God.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(18) The study of geometry, music, and astronomy was considered essential to a rational understanding of God, man, or Nature, and no one could accompany Pythagoras as a disciple who was not thoroughly familiar with these sciences. Many came seeking admission to his school. Each applicant was tested on these three subjects, and if found ignorant, was summarily dismissed.

(5) Such, then, is the style of the example in arithmetic. And let the testimony of geometry be the tabernacle that was constructed, and the ark that was fashioned, - constructed in most regular proportions, and through divine ideas, by the gift of understanding, which leads us from things of sense to intellectual objects, or rather from these to holy things, and to the holy of holies. For the squares of wood indicate that the square form, producing fight angles, pervades all, and points out security. And the length of the structure was three hundred cubits, and the breadth fifty, and the height thirty; and above, the ark ends in a cubit, narrowing to a cubit from the broad base like a pyramid, the symbol of those who are purified and tested by fire. And this geometrical proportion has a place, for the transport of those holy abodes, whose differences are indicated by the differences of the numbers set down below.

(9) ’Tis mind that all things sees and hears;

What else exists is deaf and blind.

But the precept which is next to this in efficacy is that which exhorts to be beyond measure studious of purifying the intellect, and by various methods adapting it through mathematical orgies to receive something divinely beneficial, so as neither to fear a separation from body, nor, when led to incorporeal natures, to be forced to turn away the eyes, through their most refulgent splendor, nor to be converted to those passions which nail and fasten the soul to the body. And, in short, which urges the soul to be untamed by all those passions which are the progeny of the realms of generation, and which draw it to an inferior condition of being. For the exercise and ascent through all these, is the study of the most perfect fortitude. And such are the instances adduced by us of the fortitude of Pythagoras, and the Pythagoreans.

(2) “There was a man among them [i. e. among the Pythagoreans] who was transcendent in knowledge, who possessed the most ample stores of intellectual wealth, and who was in the most eminent degree the adjutor of the works of the wise. For when he extended all the powers of his intellect, he easily beheld every thing, as far as to ten or twenty ages of the human race.”

(29) "When we consider that he was not only well acquainted with every science, as his works abundantly evince, but that he wrote on almost every subject which is comprehended in the circle of human knowledge, and this with matchless accuracy and skill, we know not which to admire most, the penetration or extent of his mind."

(1) We shall however exhibit a few specimens, and those the most celebrated, of the Pythagoric discipline, and also the monuments of the studies in which those men engaged. In the first place, therefore, Pythagoras in making trial [of the aptitude of those that came to him] considered whether they could echemuthein , i. e. whether they were able to refrain from speaking (for this was the word which he used), and surveyed whether they could conceal in silence and preserve what they had learnt and heard. In the next place, he observed whether they were modest. For he was much more anxious that they should be silent than that they should speak. He likewise directed his attention to every other particular; such, as whether they were astonished by the energies of any immoderate passion or desire.

Nor did he in a superficial manner consider how they were affected with respect to anger or desire, or whether they were contentious or ambitious, or how they were disposed with reference to friendship or strife. And if on his surveying all these particulars accurately, they appeared to him to be endued with worthy manners, then he directed his attention to their facility in learning and their memory. And in the first place, indeed he considered whether they were able to follow what was said, with rapidity and perspicuity; but in the next place, whether a certain love and temperance attended them towards the disciplines which they were taught. For he surveyed how they were naturally disposed with respect to gentleness.

But he called this catartysis , i. e. elegance of manners . And he considered ferocity as hostile to such a mode of education. For impudence, shamelessness, intemperance, slothfulness, slowness in learning, unrestrained licentiousness, disgrace, and the like, are the attendants on savage manners; but the contraries on gentleness and mildness. He considered these things, therefore, in making trial of those that came to him, and in these he exercised the learners. And those that were adapted to receive the goods of the wisdom he possessed, he admitted to be his disciples, and thus endeavoured to elevate them to scientific knowledge. But if he perceived that any one of them was unadapted, he expelled him as one of another tribe, and a stranger.

(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.

(3) For that, in order that a man should be complete in either part, observe that he hath been composed of elements of either part in sets of four;—with hands, and feet, both of them pairs, and with the other members of his body, by means of which he may do service to the lower (that is to say the terrene) world. And to these parts [are added other] four;—of sense, and soul, of memory, and foresight, by means of which he may become acquainted with the rest of things divine, and judge of them. Hence it is brought about that man investigates the differences and qualities, effects and quantities of things, with critical research; yet, as he is held back with the too heavy weight of body’s imperfection, he cannot properly descry the causes of the nature of [all] things which [really] are the true ones.

(3) In a meadow the flowers blooming variously, and in a park the plantations of fruittrees, are not separated according to their species from those of other kinds. If some, culling varieties, have Composed learned collections, Meadows, and Helicons, and Honeycombs, and Robes; then, with the things which come to recollection by haphazard, and are expurgated neither in order nor expression, but purposely scattered, the form of the Miscellanies is promiscuously variegated like a meadow. And such being the case, my notes shall serve as kindling sparks; and in the case of him, who is fit for knowledge, if he chance to fall in with them, research made with exertion will turn out to his benefit and advantage. For it is fight that labour should precede not only food but also, much more knowledge, in the case of those that are advancing to the eternal and blessed salvation by the "strait and narrow way," which is truly the Lord's.

(5) "Philosophy," he said, "to him who heeds it, Noteth, not only in one place alone, After what manner Nature takes her course From Intellect Divine, and from its art; And if thy Physics carefully thou notest, After not many pages shalt thou find, That this your art as far as possible Follows, as the disciple doth the master; So that your art is, as it were, God's grandchild. From these two, if thou bringest to thy mind Genesis at the beginning, it behoves Mankind to gain their life and to advance; And since the usurer takes another way, Nature herself and in her follower Disdains he, for elsewhere he puts his hope. But follow, now, as I would fain go on, For quivering are the Fishes on the horizon, And the Wain wholly over Caurus lies, And far beyond there we descend the crag."

(7) As the geometrician, who endeavours To square the circle, and discovers not, By taking thought, the principle he wants, Even such was I at that new apparition; I wished to see how the image to the circle Conformed itself, and how it there finds place; But my own wings were not enough for this, Had it not been that then my mind there smote A flash of lightning, wherein came its wish. Here vigour failed the lofty fantasy: But now was turning my desire and will, Even as a wheel that equally is moved, The Love which moves the sun and the other stars.

(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 .

(1) If, however, it be necessary, dismissing these particulars, to speak what appears to me to be the truth, you do not rightly infer “ that a knowledge of this mathematical science cannot be obtained, because there is much dissonance concerning it, or because Chæremon, or some other, has written against it .” For if this reason were admitted, all things will be incomprehensible. For all sciences have ten thousand controvertists, and the doubts with which they are attended are innumerable. As, therefore, we are accustomed to say in opposition to the contentious, that contraries in things that are true are naturally discordant, and that it is not falsities alone that are hostile to each other; thus, also, we say respecting this mathematical science, that it is indeed true; but that those who wander from the scope of it, being ignorant of the truth, contradict it. This, however happens not in this science alone, but likewise in all the sciences, which are imparted by the Gods to men.

(5) 'Twas not to know the number in which are The motors here above, or if 'necesse' With a contingent e'er 'necesse' make, 'Non si est dare primum motum esse,' Or if in semicircle can be made Triangle so that it have no right angle. Whence, if thou notest this and what I said, A regal prudence is that peerless seeing In which the shaft of my intention strikes. And if on 'rose' thou turnest thy clear eyes, Thou'lt see that it has reference alone To kings who're many, and the good are rare. With this distinction take thou what I said, And thus it can consist with thy belief Of the first father and of our Delight. And lead shall this be always to thy feet, To make thee, like a weary man, move slowly Both to the Yes and No thou seest not; For very low among the fools is he Who affirms without distinction, or denies, As well in one as in the other case; Because it happens that full often bends Current opinion in the false direction, And then the feelings bind the intellect.

(15) The same holds also of astronomy. For treating of the description of the celestial objects, about the form of the universe, and the revolution of the heavens, and the motion of the stars, leading the soul nearer to the creative power, it teaches to quickness in perceiving the seasons of the year, the changes of the air, and the appearance of the stars; since also navigation and husbandry derive from this much benefit, as architecture and building from geometry. This branch of learning, too, makes the soul in the highest degree observant, capable of perceiving the true and detecting the false, of discovering correspondences and proportions, so as to hunt out for similarity in things dissimilar; and conducts us to the discovery of length without breadth, and superficial extent without thickness, and an indivisible point, and transports to intellectual objects from those of sense.

(1) With respect to the amity, however, which subsists in all things towards all, Pythagoras delivered it in the clearest manner. And, the amity of the Gods indeed towards men, he unfolded through piety and scientific cultivation; but that of dogmas towards each other, and universally of the soul towards the body, and of the rational towards the species of the irrational part, through philosophy, and the theory pertaining to it. With respect to the amity of men also towards each other; that of citizens he delivered through sane legislation, but that of strangers through a correct physiology; and that between man and wife, or children, or brothers, and kindred, through unperverted communion. In short, he unfolded the friendship of all things towards all, and still farther, of certain irrational animals, through justice and a physical connexion and association.

But the pacification and conciliation of the body, which is of itself mortal, and of its latent contrary powers, he unfolded through health, and a diet and temperance conformable to this, in imitation of the salubrious condition of the mundane elements. In all these, however, Pythagoras is acknowledged to have been the inventor and legislator of the summary comprehension of them in one and the same name, which is that of friendship. And indeed he delivered such an admirable friendship to his associates, that even now those who are benevolent in the extreme towards each other, are said to belong to the Pythagoreans. It is necessary therefore to narrate the discipline of Pythagoras respecting these things, and the precepts which he used towards his disciples.