Presocratic Philosophers

"Περὶ μὲν θεῶν οὐκ ἔχω εἰδέναι οὔθ᾽ ὡς εἰσίν, οὔθ᾽ ὡς οὐκ εἰσίν· πολλὰ γὰρ τὰ κωλύοντα εἰδέναι, ἥ τ᾿ ἀδηλότης καὶ βραχὺς ὢν ὁ βίος τοῦ ἀνθρώπου."

"When they [the Athenians] meet for a consultation on civic art, where they should be guided throughout by justice and good sense, they naturally allow advice from everybody, since it is held that everyone should partake of this excellence, or else that states cannot be."

"Πάντων χρημάτων μέτρον ἄνθρωπον εἶναι, τῶν μὲν ὄντων, ὡς ἔστι, τῶν δὲ μὴ ὄντων, ὡς οὐκ ἔστιν."

"Let thy mind rule thy tongue!"

"Rejoice not in another man's misfortune!"

"Take not thine enemy for thy friend; nor thy friend for thine enemy!"

"Tell not abroad what thou intendest to do; for if thou speed not, thou shalt be mocked!"

"The King that followeth Truth, and ruleth according to Justice, shall reign quietly: but he that doth the contrary, seeketh another to reign for him."

"A fool is known by his Speech; and a wise man by Silence."

"By Silence, the discretion of a man is known: and a fool, keeping Silence, seemeth to be wise."

"He is not rich, that enjoyeth not his own goods."

"True and perfect Friendship is, to make one heart and mind of many hearts and bodies."

"Patience cometh by the grace of the Soul."

"Order thyself so, that thy Soul may always be in good estate; whatsoever become of thy body."

"A good Soul hath neither too great joy, nor too great sorrow: for it rejoiceth in goodness; and it sorroweth in wickedness. By the means whereof, when it beholdeth all things, and seeth the good and bad so mingled together, it can neither rejoice greatly; nor be grieved with over much sorrow."

"When a reasonable Soul forsaketh his divine nature, and becometh beast-like, it dieth. For though the substance of the Soul be incorruptible: yet, lacking the use of Reason, it is reputed dead; for it loseth the Intellective Life."

"It is not proper either to have a blunt sword or to use freedom of speech ineffectually. Neither is the sun to be taken from the world, nor freedom of speech from erudition."

"None can be free who is a slave to, and ruled by, his passions."

"Those alone are dear to Divinity who are hostile to injustice."

"§1. The aim of Book X of Euclid's treatise on the Elements is to investigate the commensurable and incommensurable, the rational and irrational continuous quantities. This science (or knowledge) had its origin in the sect (or school) of Pythagoras, but underwent an important development at the hands of the Athenian, Theaetetus, who had a natural aptitude for this as for other branches of mathematics most worthy of admiration."

"Not one of the philosophical ideas in Part I of the commentary is peculiarly Neoplatonic. The doctrine of the Threeness of things... is found in Aristotle and goes back to the early Pythagoreans or to Homer even; paragraph 8 is mathematical in content rather than philosophical... although there is an allusion in it to the Monad as the principle of finitudes, again a very early Pythagorean doctrine; and these two paragraphs are the source of [Heinrich] Sitter's suggestion of the authorship of Proclus. As a matter of fact, the philosophical notions in Part I have been borrowed for the most part directly from Plato, with two or three exceptions that are Aristotelian... Plato's Theaetetus, Parmenides, and the Laws, are specifically mentioned. The Timaeus forms the background of much of the thought. And the Platonism of a mathematician of the turn of the third century A. D. need not surprise us, if we but recall Aristotle's accusation that the Academy tended to turn philosophy into mathematics."

"§2. Since this treatise (i. e. Book X of Euclid.) has the aforesaid aim and object, it will not be unprofitable for us to consolidate the good which it contains. Indeed the sect (or school) of Pythagoras was so affected by its reverence for these things that a saying became current in it, namely, that he who first disclosed the knowledge of surds or irrationals and spread it abroad among the common herd, perished by drowning: which is most probably a parable by which they sought to express their conviction that firstly, it is better to conceal (or veil) every surd, or irrational, or inconceivable in the universe, and, secondly, that the soul which by error or heedlessness discovers or reveals anything of this nature which is in it or in this world, wanders [thereafter] hither and thither on the sea of nonidentity (i. e. lacking all similarity of quality or accident), immersed in the stream of the coming-to-be and the passing-away, where there is no standard of measurement. This was the consideration which Pythagoreans and the Athenian Stranger held to be an incentive to particular care and concern for these things and to imply of necessity the grossest foolishness in him who imagined these things to be of no account."

"Neither will the horse be adjudged to be generous, that is sumptuously adorned, but the horse whose nature is illustrious; nor is the man worthy who possesses great wealth, but he whose soul is generous."

"It is requisite to defend those who are unjustly accused of having acted injuriously, but to praise those who excel in a certain good."

"The Pythagoreans knew some properties of s... how a plane can be filled by... regular triangles, squares, or regular hexagons, and space by cubes... [They] may also have known the regular oktahedron and dodekahedron—the latter figure because pyrite, found in Italy, crystallizes in dodekahedra, and models... date to Etruscan times."

"It is requisite to choose the most excellent life; for custom will make it pleasant. Wealth is an infirm anchor, glory is still more infirm; and in a similar manner, the body, dominion, and honour. For all these are imbecile and powerless. What then are powerful anchors. Prudence, magnanimity, fortitude. These no tempest can shake. This is the Law of God, that virtue is the only thing that is strong; and that every thing else is a trifle."

"When the wise man opens his mouth, the beauties of his soul present themselves to the view, like the statues in a temple"

"Remind yourself that all men assert that wisdom is the greatest good, but that there are few who strenuously seek out that greatest good."

"Despise all those things which when liberated from the body you will not want; invoke the Gods to become your helpers."

"Wind indeed increases fire, but custom love."

"It is difficult to walk at one and the same time many paths of life."

"While most s emphasized the reality of change — in particular, the Atomists, followers of and Democritus — the Pythagoreans stressed the study of the unchangeable elements in nature and society. In their search for the eternal laws of the universe they studied geometry, arithmetic, astronomy, and music (the '). Their most outstanding leader was Archytas of Tarentum...and to whose school, if we follow... E. [Eva] Frank, much of the Pythagorean brand of mathematics may be ascribed. ...Numbers were divided into classes: odd, even, even-times-even, odd-times-odd, prime and composite, perfect, friendly, triangular, square, pentagonal, etc. ...Of particular importance was the ratio of numbers (logos, Lat. ratio). Equality of ratio formed a proportion. They discriminated between an arithmetical (2b = a + c), geometrical (b^2 = ac), and a harmonical (\frac{2}{b} = \frac{1}{a} + \frac{1}{c}) proportion that they interpreted philosophically and socially."

"[T]he most striking result of the Greeks' faith that the world could be understood in terms of rational principles was the invention of abstract mathematics. The most grandiose ambition they conceived was to explain all the properties of Nature in arithmetical terms alone. This was the aim of the Pythagoreans... [T]hey... knew that the phenomena of the Heavens recurred in a cyclical manner; and... discovered ...that the sound of a vibrating string ...is simply related to the length ...and its 'harmonics' always go with simple fractional lengths. ...[S]ince the Pythagoreans were a religious brotherhood... they thought that this search would lead to more than explanations alone. If one discovered the mathematical harmonies in things, one should... discover how to put oneself in harmony with Nature. ...[T]hey had ...positive grounds for thinking that both astronomy and acoustics were at the bottom arithmetical; and the study of simple fractions was called 'music' right down until the late Middle Ages."

"Not frequently man from man."

"Choose rather to be strong in soul than in body."

"Do not even think of doing what ought not to be done."

"The Neo-Pythagoreans treated all the divisions of philosophy. In Metaphysics they held that the Unit and the (indeterminate) Two are the basis of all things. the Unit being the form, and the Two the matter. ...The Unit being the prior principle may be identified with Deity, and, as such, was thought of either as the former [creator] of indefinite matter into individual things, or, as in Neo-Platonism, as the transcendent origin of the derivative Unit and Two. Another mode of conception was to identify the numbers with the Platonic Ideas and then to think of the Unit as comprehending them in the same manner as the mind comprehends its thoughts and gives them form. In Logic the Neo-Pythagoreans were for the most part imitators of Aristotle. Their Physics was Aristotelian and Stoic. Their Anthropology was Platonic. In Ethics and Politics they merely reechoed the Academy and the Lyceum with Stoic additions. In all this Neo-Pythagoreanism has little originality."

"Dispose thy Soul to all good and necessary things!"

"You will know that wretched men are the cause of their own suffering, who neither see nor hear the good that is near them, and few are the ones who know how to secure release from their troubles. Such is the fate that harms their minds; like pebbles they are tossed about from one thing to another with cares unceasing. For the dread companion Strife harms them unawares, whom one must not walk behind, but withdraw from and flee."

"Holding fast to these things, you will know the worlds of gods and mortals which permeates and governs everything. And you will know, as is right, nature similar in all respects, so that you will neither entertain unreasonable hopes nor be neglectful of anything."

"Nicomachus... mentions the customary Pythagorean divisions of quantum and the science that deals with each. Quantum is either discrete or continuous. Discrete quantum in itself considered, is the subject of Arithmetic; if in relation, the subject of Music. Continuous quantum, if immovable, is the subject of Geometry; if movable, of Spheric (Astronomy). These four sciences formed the of the Pythagoreans. With the (which Nicomachus does not mention) of Grammar, Logic, and Rhetoric, they composed the seven liberal arts taught in the schools of the Roman Empire."

"Why was the Tetraktys so revered? Because to the eyes of the sixth century BC Pythagoreans, it seemed to outline the entire nature of the universe. In geometry — the springboard to the Greeks' epochal revolution in thought — the number 1 represented a point... 2 represented a line... 3 represented a surface... and 4 represented a three-dimensional tetrahedral solid... The Tetraktys, therefore appeared to encompass all the perceived dimensions of space."

"Meditate upon my counsels; love them; follow them; To the divine virtues will they know how to lead thee. I swear it by the One who in our hearts engraved The sacred Tetrad, symbol immense and pure, Source of Nature and model of the Gods."

"Let not sleep fall upon thy eyes till thou has thrice reviewed the transactions of the past day. Where have I turned aside from rectitude? What have I been doing? What have I left undone, which I ought to have done? Begin thus from the first act, and proceed; and, in conclusion, at the ill which thou hast done, be troubled, and rejoice for the good."

"Those who dwelt in the common auditorium adopted this oath: "I swear by the discoverer of the Tetraktys, which is the spring of all our wisdom; The perennial fount and root of Nature.""

"If thy fellows hurt thee in small things, suffer it! and be as bold with them!"

"Many words befall men, mean and noble alike; do not be astonished by them, nor allow yourself to be constrained. If a lie is told, bear with it gently. But whatever I tell you, let it be done completely. Let no one persuade you by word or deed to do or say whatever is not best for you."

"Know that death comes to everyone, and that wealth will sometimes be acquired, sometimes lost. Whatever griefs mortals suffer by divine chance, whatever destiny you have, endure it and do not complain. But it is right to improve it as much as you can, and remember this: Fate does not give very many of these griefs to good people."

"It is certain that the Theory of Numbers originated in the school of Pythagoras."

"The tetrad was called by the Pythagoreans every number, because it comprehends in itself all the numbers as far as to the decad, and the decad itself; for the sum of 1, 2, 3, and 4, is 10. Hence both the decad and the tetrad were said by them to be every number; the decad indeed in energy, but the tetrad in capacity. The sum likewise of these four numbers was said by them to constitute the tetractys, in which all harmonic ratios are included. For 4 to 1, which is a quadruple ratio, forms the symphony bisdiapason; the ratio of 3 to 2, which is sesquialter forms the symphony diapente; 4 to 3, which is sesquitertian, the symphony diatessaron; and 2 to 1, which is a duple ratio, forms the diapason."