(1) Pythagoras was likewise of opinion that music contributed greatly to health, if it was used in an appropriate manner. For he was accustomed to employ a purification of this kind, but not in a careless way. And he called the medicine which is obtained through music by the name of purification. But he employed such a melody as this about the vernal season. For he placed in the middle a certain person who played on the lyre, and seated in a circle round him those who were able to sing. And thus, when the person in the centre struck the lyre, those that surrounded him sung certain pæans, through which they were seen to be delighted, and to become elegant and orderly in their manners.

But at another time they used music in the place of medicine. And there are certain melodies devised as remedies against the passions of the soul, and also against despondency and lamentation, which Pythagoras invented as things that afford the greatest assistance in these maladies. And again, he employed other melodies against rage and anger, and against every aberration of the soul. There is also another kind of modulation invented as a remedy against desires. He likewise used dancing; but employed the lyre as an instrument for this purpose. For he conceived that the pipe was calculated to excite insolence, was a theatrical instrument, and had by no means a liberal sound. Select verses also of Homer and Hesiod were used by him, for the purpose of correcting the soul.

Among the deeds of Pythagoras likewise, it is said, that once through the spondaic song of a piper, he extinguished the rage of a Tauromenian lad, who had been feasting by night, and intended to burn the vestibule of his mistress, in consequence of seeing her coming from the house of his rival. For the lad was inflamed and excited [to this rash attempt] by a Phrygian song; which however Pythagoras most rapidly suppressed. But Pythagoras, as he was astronomizing, happened to meet with the Phrygian piper at an unseasonable time of night, and persuaded him to change his Phrygian for a spondaic song; through which the fury of the lad being immediately repressed, he returned home in an orderly manner, though a little before this, he could not be in the least restrained, nor would in short, bear any admonition; and even stupidly insulted Pythagoras when he met him.

When a certain youth also rushed with a drawn sword on Anchitus, the host of Empedocles, because, being a judge, he had publicly condemned his father to death, and would have slain him as a homicide, Empedocles changed the intention of the youth, by singing to his lyre that verse of Homer,

(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:

(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.

(2) Nepenthe, without gall, o’er every ill

Oblivion spreads;——

and thus snatched his host Anchitus from death, and the youth from the crime of homicide. It is also related that the youth from that time became the most celebrated of the disciples of Pythagoras. Farther still, the whole Pythagoric school produced by certain appropriate songs, what they called exartysis or adaptation, synarmoge or elegance of manners, and epaphe or contact, usefully conducting the dispositions of the soul to passions contrary to those which it before possessed. For when they went to bed they purified the reasoning power from the perturbations and noises to which it had been exposed during the day, by certain odes and peculiar songs, and by this means procured for themselves tranquil sleep, and few and good dreams. But when they rose from bed, they again liberated themselves from the torpor and heaviness of sleep, by songs of another kind. Sometimes, also, by musical sounds alone, unaccompanied with words, they healed the passions of the soul and certain diseases, enchanting, as they say, in reality. And it is probable that from hence this name epode , i. e. enchantment, came to be generally used. After this manner, therefore, Pythagoras through music produced the most beneficial correction of human manners and lives.

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

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

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

(3) 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. But they are said to have objected to those who expose disciplines to sale; who open their souls like the gates of an inn to every man that approaches to them; and who, if they do not thus find buyers, diffuse themselves through cities, and, in short, hire gymnasia and require a reward from young men for those things which are without price.

Pythagoras, however, concealed the meaning of much that was said by him, in order that those who were genuinely instructed might clearly be partakers of it; but that others, as Homer says of Tantalus, might be pained in the midst of what they heard, in consequence of receiving no delight from thence.

(2) In the next place, I shall speak of the studies which he delivered through the whole of the day to his associates. For those who committed themselves to the guidance of his doctrine, acted in the following manner: they performed their morning walks alone, and in places in which there happened to be an appropriate solitude and quiet, and where there were temples and groves, and other things adapted to give delight. For they thought it was not proper to converse with any one, till they had rendered their own soul sedate, and had co-harmonised the reasoning power. For they apprehended it to be a thing of a turbulent nature to mingle in a crowd as soon as they rose from bed. On this account all the Pythagoreans always selected for themselves the most sacred places. But after their morning walk they associated with each other, and especially in temples, or if this was not possible, in places that resembled them. This time, likewise, they employed in the discussion of doctrines and disciplines, and in the correction of their manners.

(1) Since, however, we are narrating the wisdom employed by Pythagoras in instructing his disciples, it will not be unappropriate to relate that which is proximate in a following order to this, viz. how he invented the harmonic science, and harmonic ratios. But for this purpose we must begin a little higher. Intently considering once, and reasoning with himself, whether it would be possible to devise a certain instrumental assistance to the hearing, which should be firm and unerring, such as the sight obtains through the compass and the rule, or, by Jupiter, through a dioptric instrument; or such as the touch obtains through the balance, or the contrivance of measures;—thus considering, as he was walking near a brazier’s shop, he heard from a certain divine casualty the hammers beating out a piece of iron on an anvil, and producing sounds that accorded with each other, one combination only excepted.

But he recognized in those sounds, the diapason, the diapente, and the diatessaron, harmony. He saw, however, that the sound which was between the diatessaron and the diapente was itself by itself dissonant, yet, nevertheless, gave completion to that which was the greater sound among them. Being delighted, therefore, to find that the thing which he was anxious to discover had succeeded to his wishes by divine assistance, he went into the brazier’s shop, and found by various experiments, that the difference of sound arose from the magnitude of the hammers, but not from the force of the strokes, nor from the figure of the hammers, nor from the transposition of the iron which was beaten. When, therefore, he had accurately examined the weights and the equal counterpoise of the hammers, he returned home, and fixed one stake diagonally to the walls, lest if there were many, a certain difference should arise from this circumstance, or in short, lest the peculiar nature of each of the stakes should cause a suspicion of mutation.

Afterwards, from this stake he suspended four chords consisting of the same materials, and of the same magnitude and thickness, and likewise equally twisted. To the extremity of each chord also he tied a weight. And when he had so contrived, that the chords were perfectly equal to each other in length, he afterwards alternately struck two chords at once, and found the before-mentioned symphonies, viz. a different symphony in a different combination. For he discovered that the chord which was stretched by the greatest weight, produced, when compared with that which was stretched by the smallest, the symphony diapason. But the former of these weights was twelve pounds, and the latter six. And, therefore, being in a duple ratio, it exhibited the consonance diapason; which the weights themselves rendered apparent.

But again, he found that the chord from which the greatest weight was suspended compared with that from which the weight next to the smallest depended, and which weight was eight pounds, produced the symphony diapente. Hence he discovered that this symphony is in a sesquialter ratio, in which ratio also the weights were to each other. And he found that the chord which was stretched by the greatest weight, produced, when compared with that which was next to it in weight, and was nine pounds, the symphony diatessaron, analogously to the weights. This ratio, therefore, he discovered to be sesquitertian; but that of the chord from which a weight of nine pounds was suspended, to the chord which had the smallest weight [or six pounds,] to be sesquialter.

For 9 is to 6 in a sesquialter ratio. In like manner, the chord next to that from which the smallest weight depended, was to that which had the smallest weight, in a sesquitertian ratio, [for it was the ratio of 8 to 6,] but to the chord which had the greatest weight, in a sesquialter ratio [for such is the ratio of 12 to 8.] Hence, that which is between the diapente and the diatessaron, and by which the diapente exceeds the diatessaron, is proved to be in an epogdoan ratio, or that of 9 to 8. But either way it may be proved that the diapason is a system consisting of the diapente in conjunction with the diatessaron, just as the duple ratio consists of the sesquialter and sesquitertian, as for instance, 12, 8, and 6; or conversely, of the diatessaron and the diapente, as in the duple ratio of the sesquitertian and sesquialter ratios, as for instance 12, 9, and 6.

After this manner, therefore, and in this order, having conformed both his hand and his hearing to the suspended weights, and having established according to them the ratio of the habitudes, he transferred by an easy artifice the common suspension of the chords from the diagonal stake to the limen of the instrument, which he called chordotonon . But he produced by the aid of pegs a tension of the chords analogous to that effected by the weights.

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

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

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

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

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

(1) 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.

(4) Similar to these also, were the precepts concerning silence, and which tended to the exercise of temperance. For the subjugation of the tongue, is of all other continence the most difficult. The persuading likewise the Crotonians to abstain from the profane and spurious association with harlots, pertains to the same virtue. And besides this, the correction through music, by means of which Pythagoras restored a young man to temperance, who had become furious through love. The exhortation also, which leads from lascivious insolence, must be referred to the same virtue. And these things Pythagoras delivered to the Pythagoreans, he himself being the cause of them. For they so attended to their bodies, that they might always remain in the same condition, and not at one time be lean, but at another, abounding in flesh.

For they considered this to be an indication of an anomalous life. In a similar manner also with respect to the mind, they were careful that they might not be at one time cheerful, and at another sad, but that they might be mildly joyful with uniformity. But they expelled rage, despondency, and perturbation. And it was a precept with them, that no human casualties ought to be unexpected by those who are endued with intellect, but that they should expect every thing may happen which it is not in their power to prevent. But if at any time they were in a rage, or oppressed with sorrow, or any thing else of this kind, they separated themselves from the rest of their associates, and each by himself alone, endeavoured to digest and heal the passion.

(2) Employing this method, therefore, as a basis, and as it were an infallible rule, he afterwards extended the experiment to various instruments; viz. to the pulsation of patellæ or pans, to pipes and reeds, to monochords, triangles, and the like. And in all these he found an immutable concord with the ratio of numbers. But he denominated the sound which participates of the number 6 hypate : that which participates of the number 8 and is sesquitertian, mese ; that which participates of the number 9, but is more acute by a tone than mese, he called paramese , and epogdous ; but that which participates of the dodecad, nete . Having also filled up the middle spaces with analogous sounds according to the diatonic genus, he formed an octochord from symphonious numbers, viz. from the double, the sesquialter, the sesquitertian, and from the difference of these, the epogdous.

And thus he discovered the [harmonic] progression, which tends by a certain physical necessity from the most grave [i. e. flat] to the most acute sound, according to this diatonic genus. For from the diatonic, he rendered the chromatic and enharmonic genus perspicuous, as we shall some time or other show when we treat of music. This diatonic genus, however, appears to have such physical gradations and progressions as the following; viz. a semitone, a tone, and then a tone; and this is the diatessaron, being a system consisting of two tones, and of what is called a semitone. Afterwards, another tone being assumed, viz. the one which is intermediate, the diapente is produced, which is a system consisting of three tones and a semitone.

In the next place to this is the system of a semitone, a tone, and a tone, forming another diatessaron, i. e. another sesquitertian ratio. So that in the more ancient heptachord indeed, all the sounds, from the most grave, which are with respect to each other fourths, produce every where with each other the symphony diatessaron; the semitone receiving by transition, the first, middle, and third place, according to the tetrachord. In the Pythagoric octachord, however, which by conjunction is a system of the tetrachord and pentachord, but if disjoined is a system of two tetrachords separated from each other, the progression is from the most grave sound. Hence all the sounds that are by their distance from each other fifths, produce with each other the symphony diapente; the semitone successively proceeding into four places, viz. the first, second, third, and fourth. After this manner, therefore, it is said that music was discovered by Pythagoras. And having reduced it to a system, he delivered it to his disciples as subservient to every thing that is most beautiful.

(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) And this indeed is what he said to the young men in the Gymnasium. But when they had told their parents what they had heard, a thousand men having called Pythagoras into the senate-house, and praised him for what he had said to their sons, desired him, if he had any thing advantageous to say to the Crotonians, to unfold it to those who were the leaders of the administration. He was also the first that advised them to build a temple to the Muses, in order that they might preserve the existing concord. For he observed that all these divinities were called by one common name, [the Muses,] that they subsisted in conjunction with each other, especially rejoiced in common honors, and in short, that there was always one and the same choir of the Muses.

He likewise farther observed, that they comprehended in themselves symphony, harmony, rythm, and all things which procure concord. They also evince that their power does not alone extend to the most beautiful theorems, but likewise to the symphony and harmony of things. In the next place, he said it was necessary they should apprehend that they received their country from the multitude of the citizens, as a common deposit. Hence, it was requisite they should so govern it, that they might faithfully transmit it to their posterity, as an hereditary possession. And that this would firmly be effected, if they were equal in all things to the citizens, and surpassed them in nothing else than justice. For men knowing that every place requires justice, have asserted in fables that Themis has the same order with Jupiter, that Dice, i. e. justice, is seated by Pluto, and that Law is established in cities; in order that he who does not act justly in things which his rank in society requires him to perform, may at the same time appear to be unjust towards the whole world.

He added, it was proper that the senators should not make use of any of the Gods for the purpose of an oath, but that their language should be such as to render them worthy of belief even without oaths. And likewise, that they should so manage their own domestic affairs, as to make the government of them the object of their deliberate choice. That they should also be genuinely disposed towards their own offspring, as being the only animals that have a sensation of this conception. And that they should so associate with a wife the companion of life, as to be mindful that other compacts are engraved in tables and pillars, but those with wives are inserted in children. That they should likewise endeavour to be beloved by their offspring, not through nature, of which they were not the causes, but through deliberate choice: for this is voluntary beneficence.

(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.

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

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

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

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

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

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

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

(1) Since, however, we have thus generally, and with arrangement, discussed what pertains to Pythagoras and the Pythagoreans; let us after this narrate such scattered particulars relative to this subject, as do not fall under the above-mentioned order. It is said, therefore, that each of the Greeks who joined himself to this community of the Pythagoreans, was ordered to use his native language. For they did not approve of the use of a foreign tongue. Foreigners also united themselves to the Pythagoric sect, viz. the Messenians, the Lucani, Picentini, and the Romans. And Metrodorus the son of Thyrsus who was the father of Epicharmus, and who transferred the greater part of his doctrine to medicine, says in explaining the writings of his father to his brother, that Epicharmus, and prior to him Pythagoras, conceived that the best dialect, as well as the best harmony of music, is the Doric; that the Ionic and the Æolic participate of the chromatic harmony; but that the Attic dialect is replete with this in a still greater degree. They were also of opinion, that the Doric dialect, which consists of vocal letters, is enharmonic.

(1) After an association of this kind, they turned their attention to the health of the body. Most of them, however, used unction and the course; but a less number employed themselves in wrestling in gardens and groves; others in leaping with leaden weights in their hands, or in pantomime gesticulations, with a view to the strength of this body, studiously selecting for this purpose opposite exercises. Their dinner consisted of bread and honey or the honey-comb; but they did not drink wine during the day. They also employed the time after dinner in the political economy pertaining to strangers and guests, conformably to the mandate of the laws. For they wished to transact all business of this kind in the hours after dinner.

But when it was evening they again betook themselves to walking; yet not singly as in the morning walk, but in parties of two or three, calling to mind as they walked, the disciplines they had learnt, and exercising themselves in beautiful studies. After they had walked, they made use of the bath; and having washed themselves, they assembled in the place where they eat together, and which contained no more than ten who met for this purpose. These, however, being collected together, libations and sacrifices were performed with fumigations and frankincense. After this they went to supper, which they finished before the setting of the sun. But they made use of wine and maze, and bread, and every kind of food that is eaten with bread, and likewise raw and boiled herbs.

The flesh also of such animals was placed before them as it was lawful to immolate; but they rarely fed on fish: for this nutriment was not, for certain causes, useful to them. In a similar manner also they were of opinion, that the animal which is not naturally noxious to the human race, should neither be injured nor slain. But after this supper libations were performed, and these were succeeded by readings. It was the custom however with them for the youngest to read, and the eldest ordered what was to be read, and after what manner. But when they were about to depart, the cup-bearer poured out a libation for them; and the libation being performed, the eldest announced to them the following precepts: That a mild and fruitful plant should neither be injured nor corrupted, nor in a similar manner, any animal which is not noxious to the human race.

And farther still, that it is necessary to speak piously and form proper conceptions of the divine, dæmoniacal, and heroic genera; and in a similar manner, of parents and benefactors. That it is proper likewise to give assistance to law, and to be hostile to illegality. But these things being said, each departed to his own place of abode. They also wore a white and pure garment. And in a similar manner they lay on pure and white beds, the coverlets of which were made of thread; for they did not use woollen coverlets. With respect to hunting they did not approve of it, and therefore did not employ themselves in an exercise of this kind. Such therefore were the precepts which were daily delivered to the disciples of Pythagoras, with respect to nutriment and their mode of living.