Rest satisfied with doing well, and leave others to talk of you as they please.

Above all things reverence thy Self.

Most men and women, by birth or nature, lack the means to advance in wealth and power, but all have the ability to advance in knowledge.

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

Friends share all things.

Having departed from your house, turn not back; for the furies will be your attendants.

Truth is so great a perfection, that if God would render himself visible to men, he would choose light for his body and truth for his soul.

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.

Dear youths, I warn you cherish peace divine, And in your hearts lay deep these words of mine.

Declining from the public ways, walk in unfrequented paths.

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

It is only necessary to make war with five things; with the maladies of the body, the ignorances of the mind, with the passions of the body, with the seditions of the city and the discords of families.

Work at these things, practice them, these are the things you ought to desire; they are what will put you on the path of divine virtue - yes, by the one who entrusted our soul with the tetraktys, source of ever-flowing nature. Pray to the gods for success and get to work.

Man know thyself; then thou shalt know the Universe and God.

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.

Power is the near neighbour of necessity.

Eat not the heart.

There are men and gods, and beings like Pythagoras.

There is geometry in the humming of the strings. There is music in the spacings of the spheres.

The soul of man is divided into three parts, intelligence, reason, and passion. Intelligence and passion are possessed by other animals, but reason by man alone.

Govern your tongue before all other things, following the gods.

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.

As soon as laws are necessary for men, they are no longer fit for freedom.

Practice justice in word and deed, and do not get in the habit of acting thoughtlessly about anything.

A blow from your friend is better than a kiss from your enemy.

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

Number is the ruler of forms and ideas, and the cause of gods and daemons.

Eat not the brain.

There is no word or action but has its echo in Eternity. Thought is an Idea in transit, which when once released, never can be lured back, nor the spoken word recalled. Nor ever can the overt act be erased All that thou thinkest, sayest, or doest bears perpetual record of itself, enduring for Eternity.

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

We ought so to behave to one another as to avoid making enemies of our friends, and at the same time to make friends of our enemies. As quoted in Diogenes Laërtius, Lives and Opinions of Eminent Philosophers, "Pythagoras", Sect. 23, as translated in Dictionary of Quotations (1906) by Thomas Benfield Harbottle, p. 320

The wind is blowing, adore the wind.

Not frequently man from man.

The Athenians are right to accept advice from anyone, since it is incumbent on everyone to share in that sort of excellence, or else there can be no city at all.

When it comes to consideration of how to do well in running the city, which must proceed entirely through justice and soundness of mind.

You, Socrates, began by saying that virtue can't be taught, and now you are insisting on the opposite, trying to show that all things are knowledge, justice, soundness of mind, even courage, from which it would follow that virtue most certainly can be taught.

Man is the measure of all things: of things which are, that they are, and of things which are not, that they are not.

There are two sides to every question.

As touching the gods, I do not know whether they exist or not, nor how they are featured; for there is much to prevent our knowing: the obscurity of the subject and the brevity of human life.

This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth.

But Hermotimus, the Colophonian, rendered more abundant what was formerly published by Eudoxus and Theætetus, and invented a multitude of elements, and wrote concerning some geometrical places. But Philippus the Mendæan, a disciple of Plato, and by him inflamed in the mathematical disciplines, both composed questions, according to the institutions of Plato, and proposed as the object of his enquiry whatever he thought conduced to the Platonic philosophy.

The Platonic doctrine of Ideas has been, in all ages, the derision of the vulgar, and the admiration of the wife. Indeed, if we consider that ideas are the most sublime objects of speculation, and that their nature is no less bright in itself, than difficult to investigate, this opposition in the conduct of mankind will be natural and necessary; for, from our connection with a material nature, our intellectual eye, previous to the irradiations of science, is as ill adapted to objects the most splendid of all, "as the eyes of bats to the light of day.

For this, to draw a right line from every point, to every point, follows the definition, which says, that a line is the flux of a point, and a right line an indeclinable and inflexible flow.

The mathematician speculates the causes of a certain sensible effect, without considering its actual existence; for the contemplation of universals excludes the knowledge of particulars; and he whose intellectual eye is fixed on that which is general and comprehensive, will think but little of that which is sensible and singular.

If two right lines cut one another, they will form the angles at the vertex equal. ...This... is what the present theorem evinces, that when two right lines mutually cut each other, the vertical angles are equal. And it was first invented according to Eudemus by Thales...

A transition, therefore, is not undeservedly made from sense to consideration, and from this to the nobler energies of intellect. Hence, as the certain knowledge of numbers received its origin among the Phœnicians, on account of merchandise and commerce, so geometry was found out among the Egyptians from the distribution of land. When Thales, therefore, first went into Egypt, he transferred this knowledge from thence into Greece: and he invented many things himself, and communicated to his successors the principles of many. Some of which were, indeed, more universal, but others extended to sensibles.

But after these, Pythagoras changed that philosophy, which is conversant about geometry itself, into the form of a liberal doctrine, considering its principles in a more exalted manner; and investigating its theorems immaterially and intellectually; who likewise invented a treatise of such things as cannot be explained in geometry, and discovered the constitution of the mundane figures.

It is told that those who first brought out the irrationals from concealment into the open perished in shipwreck, to a man. For the unutterable and the formless must needs be concealed. And those who uncovered and touched this image of life were instantaneously destroyed and shall remain forever exposed to the play of the eternal waves.

But Eudoxus the Cnidian, who was somewhat junior to Leon, and the companion of Plato, first of all rendered the multitude of those theorems which are called universals more abundant; and to three proportions added three others; and things relative to a section, which received their commencement from Plato, he diffused into a richer multitude, employing also resolutions in the prosecution of these.

Not much younger than these (sc. Hermotimus of Colophon and Philippus of Mende) is Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid: and, further, they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry. He is then younger than pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says.