(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.

(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.

(531) their ears before their understanding. You mean, I said, those gentlemen who tease and torture the strings and rack them on the pegs of the instrument: I might carry on the metaphor and speak after their manner of the blows which the plectrum gives, and make accusations against the strings, both of backwardness and forwardness to sound; but this would be tedious, and therefore I will only say that these are not the men, and that I am referring to the Pythagoreans, of whom I was just now proposing to enquire about harmony. For they too are in error, like the astronomers; they investigate the numbers of the harmonies which are heard, but they never attain to problems—that is to say, they never reach the natural harmonies of number, or reflect why some numbers are harmonious and others not. That, he said, is a thing of more than mortal knowledge. A thing, I replied, which I would rather call useful; that is, if sought after with a view to the beautiful and good; but if pursued in any other spirit, useless. Very true, he said. Now, when all these studies reach the point of inter-communion and connection with one another, and come to be considered in their mutual affinities, then, I think, but not till then, will the pursuit of them have a value for our objects; otherwise there is no profit in them. I suspect so; but you are speaking, Socrates, of a vast work. What do you mean? I said; the prelude or what? Do you not know that all this is but the prelude to the actual strain which we have to learn? For you surely would not

(530) them are obvious enough even to wits no better than ours; and there are others, as I imagine, which may be left to wiser persons. But where are the two? There is a second, I said, which is the counterpart of the one already named. And what may that be? The second, I said, would seem relatively to the ears to be what the first is to the eyes; for I conceive that as the eyes are designed to look up at the stars, so are the ears to hear harmonious motions; and these are sister sciences—as the Pythagoreans say, and we, Glaucon, agree with them? Yes, he replied. But this, I said, is a laborious study, and therefore we had better go and learn of them; and they will tell us whether there are any other applications of these sciences. At the same time, we must not lose sight of our own higher object. What is that? There is a perfection which all knowledge ought to reach, and which our pupils ought also to attain, and not to fall short of, as I was saying that they did in astronomy. For in the science of harmony, as you probably know, the same thing happens. The teachers of harmony compare the sounds and consonances which are heard only, and their labour, like that of the astronomers, is in vain. Yes, by heaven! he said; and ’tis as good as a play to hear them talking about their condensed notes, as they call them; they put their ears close alongside of the strings like persons catching a sound from their neighbour’s wall 5 —one set of them declaring that they distinguish an intermediate note and have found the least interval which should be the unit of measurement; the others insisting that the two sounds have passed into the same—either party setting

(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) 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:

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

(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.

(36) Timaeus: After that He went on to fill up the intervals in the series of the powers of 2 and the intervals in the series of powers of 3 in the following manner : He cut off yet further portions from the original mixture, and set them in between the portions above rehearsed, so as to place two Means in each interval, —one a Mean which exceeded its Extremes and was by them exceeded by the same proportional part or fraction of each of the Extremes respectively ; the other a Mean which exceeded one Extreme by the same number or integer as it was exceeded by its other Extreme. And whereas the insertion of these links formed fresh intervals in the former intervals, that is to say, intervals of 3:2 and 4:3 and 9:8, He went on to fill up the 4:3 intervals with 9:8 intervals.

(2) All things accord in number:

which he very frequently uttered to all his disciples. Or again, Friendship is equality; equality is friendship . Or in the word cosmos , i. e. the world ; or by Jupiter, in the word philosophy , or in the so much celebrated word tetractys . All these and many other inventions of the like kind, were devised by Pythagoras for the benefit and amendment of his associates; and they were considered by those that understood them to be so venerable, and so much the progeny of divine inspiration, that the following was adopted as an oath by those that dwelt together in the common auditory:

(9) And, in short, it is said that Pythagoras was emulous of the Orphic mode of writing and [piety of] disposition; and that he honored the Gods in a way similar to that of Orpheus, placing them in images and in brass, not conjoined to our forms, but to divine receptacles; because they comprehend and provide for all things; and have a nature and morphe similar to the universe. He also promulgated purifications, and initiations as they are called, which contain the most accurate knowledge of the Gods. And farther still, it is said, that he was the author of a compound divine philosophy and worship of the Gods; having learnt indeed some things from the followers of Orpheus, but others from the Egyptian priests; some from the Chaldæans and Magi; some from the mysteries performed in Eleusis, in Imbrus, Samothracia, and Delos; and some also from those which are performed by the Celtæ, and in Iberia.

It is also said that the Sacred Discourse of Pythagoras is extant among the Latins, and is read not to all, nor by all of them, but by those who are promptly disposed to learn what is excellent, and apply themselves to nothing base. He likewise ordained that men should make libations thrice, and observed that Apollo delivered oracles from the tripod, because the triad is the first number. That sacrifices also should be made to Venus on the sixth day, because this number is the first that partakes of every number , and, when divided in every possible way, receives the power of the numbers subtracted and of those that remain. But that it is necessary to sacrifice to Hercules on the eighth day of the month from the beginning, looking in so doing to his being born in the seventh month.

He further asserted, that it was necessary that he who entered a temple should be clothed with a pure garment, and in which no one had slept; because sleep in the same manner as the black and the brown, is an indication of sluggishness; but purity is a sign of equality and justice in reasoning. He also ordered, that if blood should be found involuntarily spilt in a temple, a lustration should be made, either in a golden vessel, or with the water of the sea; the former of these [i. e. gold] being the most beautiful of things, and a measure by which the price of all things is regulated; but the latter as he conceived being the progeny of a moist nature, and the nutriment of the first and more common matter.

He likewise said, that it was not proper to bring forth children in a temple; because it is not holy that in a temple the divine part of the soul should be bound to the body. He further ordained, that on a festive day neither the hair should be cut, nor the nails paired; not thinking it fit that we should leave the service of the Gods for the purpose of increasing our good. He also said, that a louse ought not to be killed in a temple; conceiving that a divine power ought not to participate of any thing superfluous and corruptible. But that the Gods should be honored with cedar, laurel, cypress, oak, and myrtle; and that the body should not be purified with these, nor should any of them be divided by the teeth.

He likewise ordained, that what is boiled should not be roasted; signifying by this that mildness is not in want of anger. But he would not suffer the bodies of the dead to be burned; following in this the Magi, being unwilling that any thing divine should communicate with a mortal nature. He likewise thought it was holy for the dead to be carried out in white garments; obscurely signifying by this the simple and first nature, according to number and the principle of all things. But above all things he ordained, that an oath should be taken religiously; since that which is behind is long. And he said, that it is much more holy to be injured than to kill a man: for judgment is deposited in Hades, where the soul and its essence, and the first nature of things are [properly] estimated.

Farther still, he ordered that sepulchral chests [i. e. biers] should not be made of cypress, because the sceptre of Jupiter was made of this wood, or for some other mystic reason. He likewise ordained that libations should be performed before the table of Jupiter the Saviour, and of Hercules and the Dioscuri; in so doing celebrating Jupiter as the presiding cause and leader of this nutriment; Hercules, as the power of nature; and the Dioscuri, as the symphony of all things. But he said, that libations should not be offered with closed eyes. For he did not think it fit, that any thing beautiful should be undertaken with shame and bashfulness. Moreover, when it thundered, he ordained that the earth should be touched, in remembrance of the generation of things.

But he ordered that temples should be entered from places on the right hand, and that they should be departed out of from the left hand. For he asserted that the right hand is the principle of what is called the odd number, and is divine; but that the left hand is a symbol of the even number, and of that which is dissolved. And such is the mode which he is said to have adopted in the cultivation of piety. But other particulars which we have omitted concerning it, may be conjectured from what has been said. So that I shall cease to speak further on this subject.

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

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

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

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

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

(4) There was, however, a certain person named Hippomedon, an Ægean, a Pythagorean and one of the Acusmatici, who asserted that Pythagoras gave the reasons and demonstrations of all these precepts, but that in consequence of their being delivered to many, and these such as were of a more sluggish genius, the demonstrations were taken away, but the problems themselves were left. Those however of the Pythagoreans that are called Mathematici , acknowledge that these reasons and demonstrations were added by Pythagoras, and they say still more than this, and contend that their assertions are true, but affirm that the following circumstance was the cause of the dissimilitude. Pythagoras, say they, came from Ionia and Samos, during the tyranny of Polycrates, Italy being then in a florishing condition; and the first men in the city became his associates.

But, to the more elderly of these, and who were not at leisure [for philosophy], in consequence of being occupied by political affairs, the discourse of Pythagoras was not accompanied with a reasoning process, because it would have been difficult for them to apprehend his meaning through disciplines and demonstrations; and he conceived they would nevertheless be benefited by knowing what ought to be done, though they were destitute of the knowledge of the why : just as those who are under the care of physicians, obtain their health, though they do not hear the reason of every thing which is to be done to them. But with the younger part of his associates, and who were able both to act and learn,—with these he conversed through demonstration and disciplines.

These therefore are the assertions of the Mathematici, but the former, of the Acusmatici. With respect to Hippasus however especially, they assert that he was one of the Pythagoreans, but that in consequence of having divulged and described the method of forming a sphere from twelve pentagons, he perished in the sea, as an impious person, but obtained the renown of having made the discovery. In reality, however, this as well as every thing else pertaining to geometry, was the invention of that man ; for thus without mentioning his name, they denominate Pythagoras. But the Pythagoreans say, that geometry was divulged from the following circumstance: A certain Pythagorean happened to lose the wealth which he possessed; and in consequence of this misfortune, he was permitted to enrich himself from geometry.

But geometry was called by Pythagoras Historia . And thus much concerning the difference of each mode of philosophising, and the classes of the auditors of Pythagoras. For those who heard him either within or without the veil, and those who heard him accompanied with seeing, or without seeing him, and who are divided into interior and exterior auditors, were no other than these. And it is requisite to arrange under these, the political, economic and legislative Pythagoreans.

(1) That which follows after this, we shall no longer discuss generally, but direct our attention particularly to the works resulting from the virtues of Pythagoras. And we shall begin in the first place from the Gods, as it is usual to do, and endeavour to exhibit his piety, and the admirable works which he performed. Let this, therefore, be one specimen of his piety, which also we have before mentioned, that he knew what his soul was, and whence it came into the body, and also its former lives, and that of these things he gave most evident indications. After this also, let the following be another specimen; that once passing over the river Nessus with many of his associates, he spoke to it, and the river in a distinct and clear voice, in the hearing of all his followers, answered, Hail Pythagoras!

Farther still, nearly all historians of his life confidently assert, that in one and the same day he was present at Metapontum in Italy, and Tauromenium in Sicily, and discoursed in common with his disciples in both places, though these cities are separated from each other by many stadia both by land and sea, and cannot be passed through in a great number of days. The report, also, is very much disseminated, that he showed his golden thigh to the Hyperborean Abaris, who said that he resembled the Apollo among the Hyperboreans, and of whom Abaris was the priest; and that he did this in order that Abaris might apprehend this to be true, and that he was not deceived in his opinion.

Ten thousand other more divine and more admirable particulars likewise are uniformly and unanimously related of the man : such as infallible predictions of earthquakes , rapid expulsions of pestilence and violent winds, instantaneous cessations of the effusion of hail, and a tranquillization of the waves of rivers and seas, in order that his disciples might easily pass over them. Of which things also, Empedocles the Agrigentine, Epimenides the Cretan, and Abaris the Hyperborean, receiving the power of effecting, performed certain miracles of this kind in many places. Their deeds, however, are manifest. To which we may add, that Empedocles was surnamed an expeller of winds ; Epimenides, an expiator ; and Abaris, a walker on air ; because being carried on the dart which was given to him by the Hyperborean Apollo, he passed over rivers and seas and inaccessible places, like one walking on the air.

Certain persons likewise are of opinion, that Pythagoras did the same thing, when in the same day he discoursed with his disciples at Metapontum and Tauromenium. It is also said, that he predicted there would be an earthquake from the water of a well which he had tasted; and that a ship which was sailing with a prosperous wind, would be merged in the sea. And let these, indeed, be the indications of his piety.

(31) Timaeus: for there must needs be some intermediary bond to connect the two. And the fairest of bonds is that which most perfectly unites into one both itself and the things which it binds together; and to effect this in the fairest manner is the natural property of proportion. For whenever the middle term of any three numbers, cubic or square,

(6) As they by law are orderly dispos’d;

And reverence thy oath, but honor next

Th’ illustrious heroes.

Hence a certain Pythagorean, being compelled by law to take an oath, yet in order that he might preserve a Pythagoric dogma, though he would have sworn religiously, chose instead of swearing to pay three talents, this being the fine which he was condemned to pay to the defendant. That Pythagoras however thought that nothing was from chance and fortune, but that all events happened conformably to divine providence, and especially to good and pious men, is confirmed by what is related by Androcydes in his treatise on Pythagoric Symbols, of Thymaridas the Tarentine, and a Pythagorean. For when through a certain circumstance he was about to sail from his own country, and his friends who were present were embracing him, and bidding him farewell, some one said to him, when he had now ascended into the ship, May such things happen to you from the Gods, O Thymaridas, as are conformable to your wishes! But he replied, predict better things; for I should rather wish that such things may happen to me as are conformable to the will of the Gods. For he thought it was more scientific and equitable, not to resist or be indignant with divine providence. If, therefore, any one wishes to learn what were the sources whence these men derived so much piety, it must be said, that a perspicuous paradigm of the Pythagoric theology according to numbers, is in a certain respect to be found in the writings of Orpheus. Nor is it to be doubted, that Pythagoras receiving auxiliaries from Orpheus, composed his treatise Concerning the Gods, which on this account also he inscribed the Sacred Discourse, because it contains the flower of the most mystical place in Orpheus; whether this work was in reality written by Pythagoras, as by most authors it is said to have been, or as some of the Pythagoric school who are both learned and worthy of belief assert, was composed by Telauges; being taken by him from the commentaries which were left by Pythagoras himself to his daughter Damo, the sister of Telauges, and which it is said after her death were given to Bitale the daughter of Damo, and to Telauges the son of Pythagoras, and the husband of Bitale, when he was of a mature age. For when Pythagoras died, he was left very young with his mother Theano. In this Sacred Discourse also, or treatise concerning the Gods (for it has both these inscriptions), who it was that delivered to Pythagoras what is there said concerning the Gods, is rendered manifest. For it says: “ that Pythagoras the son of Mnesarchus was instructed in what pertains to the Gods, when he celebrated orgies in the Thracian Libethra, being initiated in them by Aglaophemus; and that Orpheus the son of Calliope, having learnt wisdom from his mother in the mountain Pangæus, said, that the eternal essence of number is the most providential principle of the universe , of heaven and earth, and the intermediate nature; and farther still, that it is the root of the permanency of divine natures, of Gods and dæmons .” From these things, therefore, it is evident that he learnt from the Orphic writers that the essence of the Gods is defined by number. Through the same numbers also, he produced an admirable fore-knowledge and worship of the Gods, both which are especially most allied to numbers. This, however, may be known from hence; for it is necessary to adduce a certain fact, in order to procure belief of what is said. When Abaris performed sacred rites in his accustomed manner, he procured a fore-knowledge of future events, which is studiously cultivated by all the Barbarians, through sacrificing animals, and especially birds; for they are of opinion that the viscera of such animals are subservient to a more accurate inspection. Pythagoras, therefore, not wishing to suppress his ardent pursuit of truth, but to impart it to him through a certain safer way, and without blood and slaughter, and also because he thought that a cock was sacred to the sun, furnished him with a consummate knowledge of all truth, as it is said, through the arithmetical science . He also obtained from piety, faith concerning the Gods. For Pythagoras always proclaimed, that nothing admirable pertaining to the Gods or divine dogmas should be disbelieved , because the Gods are able to accomplish all things. And the divine dogmas in which it is requisite to believe, are those which Pythagoras delivered. Thus, therefore, the Pythagoreans believed in, and assumed the things about which they dogmatised, because they were not the progeny of false opinion. Hence Eurytus the Crotonian, the auditor of Philolaus said, that a shepherd feeding his sheep near the tomb of Philolaus, heard some one singing. But the person to whom this was related, did not at all disbelieve the narration, but asked what kind of harmony it was. Pythagoras himself, also, being asked by a certain person what was indicated by seeming in sleep to converse with his father who was dead, answered that it indicated nothing. For neither, said he, is any thing portended by your speaking with me.

(1) The mode however of teaching through symbols, was considered by Pythagoras as most necessary. For this form of erudition was cultivated by nearly all the Greeks, as being most ancient. But it was transcendently honored by the Egyptians, and adopted by them in the most diversified manner. Conformably to this, therefore, it will be found, that great attention was paid to it by Pythagoras, if any one clearly unfolds the significations and arcane conceptions of the Pythagoric symbols, and thus developes the great rectitude and truth they contain, and liberates them from their enigmatic form. For they are adapted according to a simple and uniform doctrine, to the great geniuses of these philosophers, and deify in a manner which surpasses human conception.

For those who came from this school, and especially the most ancient Pythagoreans, and also those young men who were the disciples of Pythagoras when he was an old man, viz. Philolaus and Eurytus, Charondas and Zaleucus, and Brysson, the elder Archytas also, and Aristæus, Lysis and Empedocles, Zanolxis and Epimenides, Milo and Leucippus, Alcmæon, Hippasus and Thymaridas, and all of that age, consisting of a multitude of learned men, and who were above measure excellent,—all these adopted this mode of teaching, in their discourses with each other, and in their commentaries and annotations. Their writings also, and all the books which they published, most of which have been preserved even to our time , were not composed by them in a popular and vulgar diction, and in a manner usual with all other writers, so as to be immediately understood, but in such a way as not to be easily apprehended by those that read them.

For they adopted that taciturnity which was instituted by Pythagoras as a law, in concealing after an arcane mode, divine mysteries from the uninitiated, and obscuring their writings and conferences with each other. Hence he who selecting these symbols does not unfold their meaning by an apposite exposition, will cause those who may happen to meet with them to consider them as ridiculous and inane, and as full of nugacity and garrulity. When, however, they are unfolded in a way conformable to these symbols, and become obvious and clear even to the multitude, instead of being obscure and dark, then they will be found to be analogous to prophetic sayings, and to the oracles of the Pythian Apollo. They will then also exhibit an admirable meaning, and will produce a divine afflatus in those who unite intellect with erudition.

Nor will it be improper to mention a few of them, in order that this mode of discipline may become more perspicuous: Enter not into a temple negligently, nor in short adore carelessly, not even though you should stand at the very doors themselves . Sacrifice and adore unshod. Declining from the public ways, walk in unfrequented paths. Speak not about Pythagoric concerns without light. And such are the outlines of the mode adopted by Pythagoras of teaching through symbols.

(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.

(399) under the circumstances, and acquiescing in the event. These two harmonies I ask you to leave; the strain of necessity and the strain of freedom, the strain of the unfortunate and the strain of the fortunate, the strain of courage, and the strain of temperance; these, I say, leave. And these, he replied, are the Dorian and Phrygian harmonies of which I was just now speaking. Then, I said, if these and these only are to be used in our songs and melodies, we shall not want multiplicity of notes or a panharmonic scale? I suppose not. Then we shall not maintain the artificers of lyres with three corners and complex scales, or the makers of any other many-stringed curiously-harmonised instruments? Certainly not. But what do you say to flute-makers and flute-players? Would you admit them into our State when you reflect that in this composite use of harmony the flute is worse than all the stringed instruments put together; even the panharmonic music is only an imitation of the flute? Clearly not. There remain then only the lyre and the harp for use in the city, and the shepherds may have a pipe in the country. That is surely the conclusion to be drawn from the argument. The preferring of Apollo and his instruments to Marsyas and his instruments is not at all strange, I said. Not at all, he replied. And so, by the dog of Egypt, we have been unconsciously purging the State, which not long ago we termed luxurious. And we have done wisely, he replied. Then let us now finish the purgation, I said. Next in order to harmonies, rhythms will naturally follow, and they should be subject to the same rules, for we ought not to seek out complex systems of metre, or metres of every kind, but rather to discover what rhythms are the expressions of