(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:

(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.

(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.

(18) And in general, Pythagoras, and Socrates, and Plato say that they hear God's voice while closely contemplating the fabric of the universe, made and preserved unceasingly by God. For they heard Moses say, "He said, and it was done," describing the word of God as an act.

(47) Timaeus: the perturbable to the imperturbable; and that, through learning and sharing in calculations which are correct by their nature, by imitation of the absolutely unvarying revolutions of the God we might stabilize the variable revolutions within ourselves. Concerning sound also and hearing, once more we make the same declaration, that they were bestowed by the Gods with the same object and for the same reasons; for it was for these same purposes that speech was ordained, and it makes the greatest contribution thereto; music too, in so far as it uses audible sound,

(10) Further, as an example of music, let us adduce David, playing at once and prophesying, melodiously praising God. Now the Enarmonic s suits best the Dorian harmony, and the Diatonic the Phrygian, as Aristoxenus says. The harmony, therefore, of the Barbarian psaltery, which exhibited gravity of strain, being the most ancient, most certainly became a model for Terpander, for the Dorian harmony, who sings the praise of Zeus thus: "O Zeus, of all things the Beginning, Rule, of, all; O Zeus, I send thee this beginning of hymns."

(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) 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,

(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

(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.

(617) coloured by the reflected light of the seventh; the second and fifth [Saturn and Mercury] are in colour like one another, and yellower than the preceding; the third [Venus] has the whitest light; the fourth [Mars] is reddish; the sixth [Jupiter] is in whiteness second. Now the whole spindle has the same motion; but, as the whole revolves in one direction, the seven inner circles move slowly in the other, and of these the swiftest is the eighth; next in swiftness are the seventh, sixth, and fifth, which move together; third in swiftness appeared to move according to the law of this reversed motion the fourth; the third appeared fourth and the second fifth. The spindle turns on the knees of Necessity; and on the upper surface of each circle is a siren, who goes round with them, hymning a single tone or note. The eight together form one harmony; and round about, at equal intervals, there is another band, three in number, each sitting upon her throne: these are the Fates, daughters of Necessity, who are clothed in white robes and have chaplets upon their heads, Lachesis and Clotho and Atropos, who accompany with their voices the harmony of the sirens—Lachesis singing of the past, Clotho of the present, Atropos of the future; Clotho from time to time assisting with a touch of her right hand the revolution of the outer circle of the whorl or spindle, and Atropos with her left hand touching and guiding the inner ones, and Lachesis laying

(2) "Well, then," enquired Tzŭ Yu, "since the music of earth consists of nothing more than holes, and the music of man of pipes and flutes,—of what consists the music of Heaven?" "The effect of the wind upon these various apertures," replied Tzŭ Ch'i, "is not uniform. But what is it that gives to each the individuality, to all the potentiality, of sound? "Great knowledge embraces the whole: small knowledge, a part only. Great speech is universal: small speech is particular. "For whether when the mind is locked in sleep or whether when in waking hours the body is released, we are subject to daily mental perturbations,—indecision, want of penetration, concealment, fretting fear, and trembling terror. Now like a javelin the mind flies forth, the arbiter of right and wrong. Now like a solemn covenanter it remains firm, the guardian of rights secured. Then, as under autumn and winter's blight, comes gradual decay, a passing away, like the flow of water, never to return. Finally, the block when all is choked up like an old drain,—the failing mind which shall not see light again. "Joy and anger, sorrow and happiness, caution and remorse, come upon us by turns, with ever-changing mood. They come like music from hollowness, like mushrooms from damp. Daily and nightly they alternate within us, but we cannot tell whence they spring. Can we then hope in a moment to lay our finger upon their very Cause?

(115) The Pythagoreans call heaven the Antichthon [the opposite Earth]. And in this land, it is said by Jeremiah, "I will place thee among the children, and give thee the chosen land as inheritance of God Omnipotent; " and they who herit it shall reign over the earth. Myriads on myriads of examples rush on my mind which might adduce. But for the sake of symmetry the discourse must now stop, in order that we may not exemplify the saying of Agatho the tragedian: "Treating our by-work as work, And doing our work as by-work."

(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.

(129) And of the Solar Circles, and of the Lunar, clashings, and of the Aërial Recesses; the Melody of Ether, and of the Sun, and of the phases of the Moon, and of the Air.

(2) Again, however, assuming a more elevated exordium, I am desirous to exhibit the principles of the worship of the Gods, which Pythagoras and his followers established; viz. that all such particulars as they define with respect to doing or not doing a thing, have for the mark at which they aim, a consent with divinity. This also is with them the principle, [of piety] and their whole life is arranged with a view to follow God . The language, too, of their philosophy is this, that men act ridiculously in exploring good from any other source than the Gods; and that their conduct in this respect resembles that of a man, who in a country governed by a king should reverence one of the magistrates in the city, and neglect him who is the ruler of all of them.

For they were of opinion that such was the conduct of mankind. For since God is, and is the Lord of all things, it is universally acknowledged that good is to be requested of him. For all men impart good to those whom they love, and to those with whom they are delighted; but they give the contrary to good, to those to whom they are contrarily disposed. It is evident, therefore, that those things are to be done, in which God delights. It is, however, not easy for a man to know what these are, unless he obtains this knowledge from one who has heard God, or has heard God himself, or procures it through divine art. Hence also, the Pythagoreans were studious of divination.

For this alone is an interpretation of the benevolence of the Gods. And in short, he will conceive an employment of this kind to be worthy of regard, who believes that there are Gods; but he who thinks that either of these is folly, will also be of opinion that both are foolish. Many of the mandates, however, of the Pythagoreans were introduced from the mysteries; for they did not conceive them to be the productions of arrogance, but to originate from a certain divinity. And in a similar manner, all the Pythagoreans believe such things as are mythologically related of Aristeas the Proconesian, and Abaris the Hyperborean, and other particulars of a like nature. For they consider every thing of this kind to be credible; and of many [such] things they make trial themselves.

They also frequently recollect such-like particulars as appear to be fabulous, as not disbelieving in any thing which may be referred to divinity. A certain person therefore relates, that Eurytus 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? Both of them, however, were Pythagoreans, and Eurytus was the disciple of Philolaus. It is likewise said, that a certain person told Pythagoras, that he appeared to himself once to converse with his father who was dead, and that he asked Pythagoras what this indicated? Pythagoras replied, that it indicated nothing; but that he had in reality conversed with his father.

As therefore, said he, nothing is signified by my now discoursing with you, so neither is any thing signified by your conversing with your father. Hence, in all particulars of this kind, they did not think that they were stupid, but those that disbelieved in them. For they did not conceive that some things are possible to the Gods, but others impossible, as those fancy who reason sophistically; but they believed that all things are possible to the Gods. And this very assertion is the beginning of the verses, which they ascribe to Linus, and which are as follow:

(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.

(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.