(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) I, at any rate, am not conscious, when speaking in reply to Greeks or others, of fancying to assist good men, in case they should be able to know and speak the very truth, as it really is in itself. For, when this is correctly demonstrated in its essential nature, according to a law of truth, and has been established without flaw, every thing which is otherwise, and simulates the truth, will be convicted of being other than the reality, and dissimilar, and that which is seeming rather than real. It is superfluous then, that the expounder of truth should contend with these or those. For each affirms himself to have the royal coin, and perchance has some deceptive image of a certain portion of the true. And, if you refute this, first the one, and then the other, will contend concerning the same. But, when the true statement itself has been correctly laid down, and has remained unrefuted by all the rest, every thing which is not so in every respect is cast down of itself, by the impregnable stability of the really true. Having then as I think well understood this, I have not been over zealous to speak in reply to Greeks or to others; but it is sufficient for me (and may God grant this), first to know about truth, then, having known, to speak as it is fitting to speak.

(5) And then I heard: "The ancient and the new Postulates, that to thee are so conclusive, Why dost thou take them for the word divine?" And I: "The proofs, which show the truth to me, Are the works subsequent, whereunto Nature Ne'er heated iron yet, nor anvil beat." 'Twas answered me: "Say, who assureth thee That those works ever were? the thing itself That must be proved, nought else to thee affirms it." "Were the world to Christianity converted," I said, "withouten miracles, this one Is such, the rest are not its hundredth part; Because that poor and fasting thou didst enter Into the field to sow there the good plant, Which was a vine and has become a thorn!" This being finished, the high, holy Court Resounded through the spheres, "One God we praise!" In melody that there above is chanted. And then that Baron, who from branch to branch, Examining, had thus conducted me, Till the extremest leaves we were approaching, Again began: "The Grace that dallying Plays with thine intellect thy mouth has opened, Up to this point, as it should opened be,

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

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

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

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

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

(340) Yes, said Cleitophon, interposing, if you are allowed to be his witness. But there is no need of any witness, said Polemarchus, for Thrasymachus himself acknowledges that rulers may sometimes command what is not for their own interest, and that for subjects to obey them is justice. Yes, Polemarchus,—Thrasymachus said that for subjects to do what was commanded by their rulers is just. Yes, Cleitophon, but he also said that justice is the interest of the stronger, and, while admitting both these propositions, he further acknowledged that the stronger may command the weaker who are his subjects to do what is not for his own interest; whence follows that justice is the injury quite as much as the interest of the stronger. But, said Cleitophon, he meant by the interest of the stronger what the stronger thought to be his interest,—this was what the weaker had to do; and this was affirmed by him to be justice. Those were not his words, rejoined Polemarchus. Never mind, I replied, if he now says that they are, let us accept his statement. Tell me, Thrasymachus, I said, did you mean by justice what the stronger thought to be his interest, whether really so or not? Certainly not, he said. Do you suppose that I call him who is mistaken the stronger at the time when he is mistaken? Yes, I said, my impression was that you did so, when you admitted that the ruler was not infallible but might be sometimes mistaken.

(1) In proof of these things, and witnessing faithfully are the Universe, the Year of time, and Man himself, the Microcosm. He fixed these as testimonies of the Triad, the Heptad, and the Dodecad; the twelve constellations rulers of the world, the Dragon (THELE) Tali which environs the universe, and the microcosm, man. The triad, fire, water, and air; the fire above, the water below, and the air in the midst. The proof of which is that air is a participator with both.

(4) That they exist there only in belief, Upon the which is founded the high hope, And hence it takes the nature of a substance. And it behoveth us from this belief To reason without having other sight, And hence it has the nature of evidence." Then heard I: "If whatever is acquired Below by doctrine were thus understood, No sophist's subtlety would there find place." Thus was breathed forth from that enkindled love; Then added: "Very well has been gone over Already of this coin the alloy and weight; But tell me if thou hast it in thy purse?" And I: "Yes, both so shining and so round That in its stamp there is no peradventure." Thereafter issued from the light profound That there resplendent was: "This precious jewel, Upon the which is every virtue founded, Whence hadst thou it?" And I: "The large outpouring Of Holy Spirit, which has been diffused Upon the ancient parchments and the new, A syllogism is, which proved it to me With such acuteness, that, compared therewith, All demonstration seems to me obtuse."

(340) You argue like an informer, Socrates. Do you mean, for example, that he who is mistaken about the sick is a physician in that he is mistaken? or that he who errs in arithmetic or grammar is an arithmetician or grammarian at the time when he is making the mistake, in respect of the mistake? True, we say that the physician or arithmetician or grammarian has made a mistake, but this is only a way of speaking; for the fact is that neither the grammarian nor any other person of skill ever makes a mistake in so far as he is what his name implies; they none of them err unless their skill fails them, and then they cease to be skilled artists. No artist or sage or ruler errs at the time when he is what his name implies; though he is commonly said to err, and I adopted the common mode of speaking. But to be perfectly accurate, since you are such a lover of accuracy, we should say that the ruler, in so far as he is a ruler, is unerring, and, being unerring, always commands that which is for his own interest; and the subject is required to execute his commands; and therefore, as I said at first and now repeat, justice is the interest of the stronger. Indeed, Thrasymachus, and do I really appear to you to argue like an informer? Certainly, he replied. And do you suppose that I ask these questions with any design of injuring you in the argument? Nay, he replied, ‘suppose’ is not the word—I know it;

(51) To the wise, whose hearts are enlightened, The mere sound of that voice proves its truth." "When you say to a thirsty man, 'Come quickly; This is water in the cup, take and drink it,' Does the thirsty man say, 'This is a vain pretension; Go, remove yourself from me, O vain pretender, Or proceed to give proofs and evidence That this is generic water, and concrete water thereof'? Or when a mother cries to her sucking babe,

(15) Endeavour not to conceal your errors by words, but to remedy them by reproofs. Pythagoras. Stob. p. 146.

It is not so difficult to err, as not to reprove him who errs. Pythagoras. Stob. p. 147.

(51) Timaeus: Now these two Kinds must be declared to be two, because they have come into existence separately and are unlike in condition. For the one of them arises in us by teaching, the other by persuasion; and the one is always in company with true reasoning, whereas the other is irrational; and the one is immovable by persuasion, whereas the other is alterable by persuasion; and of the one we must assert that every man partakes, but of Reason only the gods and but a small class of men. This being so, we must agree that One Kind

(111) They are a proof of the beauty and grace of my beloved.' The other said, "I take not these for a proof, Though they may be a proof to common people." The Sunni said, "When genuine and base coin boast, Saying, 'Thou art false, I am good and genuine,' Fire is the test ultimately, When the two rivals are cast into the furnace." Accordingly both of them entered the furnace, Both leapt into the fiery flame; And the philosopher was burnt to ashes,

(9) The kindred of the Pythagoreans however, were indignant that the Pythagoreans gave their right hand to those of their own sect alone, their parents excepted; and that they shared their possessions with each other in common, but excluded their relations from this fellowship, as if they were strangers. These, therefore, becoming the sources of the dissension, the rest readily fell into hostility against the Pythagoreans. Hippasus, also, Diodorus and Theages said at the same time, that every citizen ought to be a partaker of the magistracy and the assembly, and that the rulers should give an account of their conduct, to those who were elected by lot for this purpose from the multitude. But the Pythagoreans, Alcimachus, Dimachus, Meton and Democedes opposed this, and persevered in prohibiting the dissolution of the polity derived from their ancestors.

Those however, who patronized the multitude, subdued the other party. The multitude therefore, being assembled together, Cylon and Ninon who were rhetoricians accused the Pythagoreans. And of these, one belonged to the class of the rich, but the other was a plebeian. They also divided their harangues between themselves. But of these harangues, the longer being delivered by Cylon, Ninon concluded, pretending that he had explored the arcana of the Pythagoreans, and that he had connected and committed to writing such particulars as were especially calculated to criminate the Pythagoreans, and giving a book to ascribe, he ordered him to read it. But the book was inscribed the Sacred Discourse . And the following is a specimen of what it contained: Friends are to be venerated in the same manner as the Gods; but others are to be treated as brutes. This very sentence also is ascribed to Pythagoras by his disciples, and is by them expressed in verse as follows:

(9) 'That doctrine is not to be obtained by argument, but when it is declared by another, then, O dearest, it is easy to understand. Thou hast obtained it now; thou art truly a man of true resolve. May we have always an inquirer like thee!'

(336) And why, sillybillies, do you knock under to one another? I say that if you want really to know what justice is, you should not only ask but answer, and you should not seek honour to yourself from the refutation of an opponent, but have your own answer; for there is many a one who can ask and cannot answer. And now I will not have you say that justice is duty or advantage or profit or gain or interest, for this sort of nonsense will not do for me; I must have clearness and accuracy. I was panic-stricken at his words, and could not look at him without trembling. Indeed I believe that if I had not fixed my eye upon him, I should have been struck dumb: but when I saw his fury rising, I looked at him first, and was therefore able to reply to him. Thrasymachus, I said, with a quiver, don’t be hard upon us. Polemarchus and I may have been guilty of a little mistake in the argument, but I can assure you that the error was not intentional. If we were seeking for a piece of gold, you would not imagine that we were ‘knocking under to one another,’ and so losing our chance of finding it. And why, when we are seeking for justice, a thing more precious than many pieces of gold, do you say that we are weakly yielding to one another and not doing our utmost to get at the truth? Nay, my good friend, we are most willing and anxious to do so, but the fact is that we cannot. And if so, you people who know all things should pity us and not be angry with us.

(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) Another device there is: prove thou if thou wilt. When thou feelest that thou mayest on nowise put them down, cower thou down under them as a caitiff and a coward overcome in battle, and think that it is but a folly to thee to strive any longer with them, and therefore thou yieldest thee to God in the hands of thine enemies. And feel then thyself as thou wert foredone for ever. Take good heed of this device I pray thee, for me think in the proof of this device thou shouldest melt all to water. And surely me think an this device be truly conceived it is nought else but a true knowing and a feeling of thyself as thou art, a wretch and a filthy, far worse than nought: the which knowing and feeling is meekness. And this meekness obtaineth to have God Himself mightily descending, to venge thee of thine enemies, for to take thee up, and cherishingly dry thine ghostly eyen; as the father doth the child that is in point to perish under the mouths of wild swine or wode biting bears.

(6) These men also thought it right to adhere to the customs and legal institutes of their ancestors, even though they should be somewhat inferior to other customs and laws. For to fly from the existing laws, and to be studious of innovation, is by no means profitable and salutary. Pythagoras therefore gave many other specimens of piety to the Gods, evincing that his life was conformable to his doctrines. Nor will it be foreign to the purpose to mention one of them, which may serve to elucidate the rest. But I will relate what Pythagoras said and did relative to the embassy from Sybaris to Crotona, about demanding the return of the exiles. For some of his associates were slain by order of the ambassadors, one of whom slew a part of them with his own hands; but another was the son of one of those who had excited the sedition, and who died through disease.

When the Crotonians therefore were deliberating how they should act in this affair, Pythagoras said to his disciples, that he was not willing the Crotonians should be so greatly discordant in this affair, and that in his opinion, the ambassadors should not even lead victims to the altars, much less ought they to drag suppliants [i. e. the exiles] from them. But when the Sybarites came to him with their complaints, and the man who had slain some of his associates with his own hands, was defending his conduct, Pythagoras said, that he should not answer [an homicide]. Hence, some persons accused him of asserting that he was Apollo, because prior to this some one having asked him about a certain object of inquiry, why the thing was so; he in his turn asked the interrogator, if he would think fit to inquire of Apollo when he was delivering oracles to him, why he delivered them?

But to another of the ambassadors who appeared to him to deride his school, in which he taught the return of souls to the supernal realms, and who said that he would give him an epistle to his father, as he was about to descend into Hades, and exhorted him to bring another letter in answer, from his father, when he returned; Pythagoras replied, that he was not about to descend into the abode of the impious, where he clearly knew that murderers were punished. But the ambassadors reviling him, he proceeded to the sea, many persons following him, and there sprinkled himself with marine water. Some one however of the Crotonian counsellors, after reviling the rest of the ambassadors, observed that he understood they had defamed Pythagoras, whom not even a brute would dare to blaspheme, though all animals should again utter the same voice as men, which fables report they did in the beginning of things.

(101) He answered, 'The proof is within my heart, Yea, my proofs are hidden in my heart. From weakness of vision you see not the new moon; If I see it, be not angry with me!' Much talk followed, and the people were perplexed Then the first said, 'O friend, within me is a proof I hold it for certain, and the sign of certainty Know this proof is not to be expressed in speech, The secret I labor to express is not revealed When the tears course down my cheeks,

(5) One the false woman is who accused Joseph, The other the false Sinon, Greek of Troy; From acute fever they send forth such reek." And one of them, who felt himself annoyed At being, peradventure, named so darkly, Smote with the fist upon his hardened paunch. It gave a sound, as if it were a drum; And Master Adam smote him in the face, With arm that did not seem to be less hard, Saying to him: "Although be taken from me All motion, for my limbs that heavy are, I have an arm unfettered for such need." Whereat he answer made: "When thou didst go Unto the fire, thou hadst it not so ready: But hadst it so and more when thou wast coining." The dropsical: "Thou sayest true in that; But thou wast not so true a witness there, Where thou wast questioned of the truth at Troy." "If I spake false, thou falsifiedst the coin," Said Sinon; "and for one fault I am here, And thou for more than any other demon." "Remember, perjurer, about the horse," He made reply who had the swollen belly, "And rueful be it thee the whole world knows it."