The games which can be built up from the simple idea of dots and lines... can be a productive source of teaching material. After all, s provided the Pythagoreans and neo-Pythagoreans with important theorems about the summing of series.

Concern should drive us into action and not into a depression.

In this theater of man's life it is reserved only for God and angels to be lookers on.

Ten is the very nature of number. All Greeks and all barbarians alike count up to ten, and having reached ten revert again to the unity. And again, Pythagoras maintains, the power of the number 10 lies in the number 4, the tetrad. This is the reason: if one starts at the unit (1) and adds the successive number up to 4, one will make up the number 10 (1+2+3+4 = 10). And if one exceeds the tetrad, one will exceed 10 too.... So that the number by the unit resides in the number 10, but potentially in the number 4. And so the Pythagoreans used to invoke the Tetrad as their most binding oath: "By him that gave to our generation the Tetractys, which contains the fount and root of eternal nature..."

Pythagoras... assumed as first principles the numbers and symmetries existing among them, which he calls harmonies, and the elements compounded of both, that are called geometrical. ...he says that the nature of Number is the Decad.

Let us not link ourselves with the vilifiers of Plato and the persecutors of Confucius. They were oppressed by citizens who were considered the pride of the country. Thus has the world raised its hand against the great Servitors. Be assured that the Brotherhood formed by Pythagoras appeared dangerous in the eyes of the city guard. Paracelsus was a target for mockery and malignance. Thomas Vaughan seemed to be an outcast, and few wished to meet with him. Thus was the reign of darkness manifested.

If one examines the reasons for the persecution of the best minds of different nations, and compares the reasons for the persecution and banishment of Pythagoras, Anaxagoras, Socrates, Plato, and others, one can observe that in each case the accusations and reasons for banishment were almost identical and unfounded. But in the following centuries full exoneration came, as if there had never been any defamation. It would be correct to conclude that such workers were too exalted for the consciousness of their contemporaries, and the sword of the executioner was ever ready to cut off a head held high. Pericles was recognized in his time only after people had reduced him to a sorry state. Only in that state could his fellow citizens accept him as an equal! A book should be written about the causes of the persecution of great individuals. By comparing the causes is it possible to trace the evil will.

Pythagoras, it seems, did not only call the supreme Deity a monad, but also a tetrad, or tetractys... It is, in the golden verses, said to be the fountain of the eternal nature; and by Hierocles, the maker of all things, the intelligent god, the cause of the heavenly and sensible god, that is, of the animated world or heaven. The later Pythogoreans endeavour to give reasons why God should be called Tetractys, from certain mysteries in the number four; but... much more probable... this name was really nothing else but the tetragrammaton, or that proper name of the supreme God amongst the Hebrews, consisting of four letters; nor is it strange Pythagoras should be so well acquainted with the name Jehovah, since, besides travelling into other parts of the East, he is by Josephus, Porphyry, and others, to have conversed with the Hebrews also.

These thinkers seem to consider that number is the principle both as matter for things and as constituting their attributes and permanent states.

There is nothing so easy but that it becomes difficult when you do it reluctantly.

The oldest, shortest words— "yes" and "no"— are those which require the most thought.

None but a Craftsman can judge of a craft.

Repentance deserveth Pardon.

The best and greatest winning is a true friend; and the greatest loss is the loss of time.

It is better to suffer, than to do, wrong.

He is worst of all, that is malicious against his friends.

Evil destroyeth itself.

Better be mute, than dispute with the Ignorant.

Virtue is harmony.

They thought they found in numbers, more than in fire, earth, or water, many resemblances to things which are and become; thus such and such an attribute of numbers is justice, another is soul and mind, another is opportunity, and so on; and again they saw in numbers the attributes and ratios of the musical scales. Since, then, all other things seemed in their whole nature to be assimilated to numbers, while numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.

Whenever he heard a person who was making use of his symbols, he immediately took him into his circle, and made him a friend.

The apparently ancient reports of the importance of Pythagoras and his pupils in laying the foundations of mathematics crumble on touch, and what we can get hold of is not authentic testimony by the efforts latecomers to paper over a crack, which they obviously found surprising, by the use of various kinds of reconstruction and reinterpretation. On the other hand, there are ancient and unassailable indications of a Greek mathematics antedating Pythagoras and quite outside his sphere of influence.

I wished to show that Pythagoras, the first founder of the vegetable regimen, was at once a very great physicist and a very great physician; that there has been no one of a more cultured and discriminating humanity; that he was a man of wisdom and of experience; that his motive in commending and introducing the new mode of living was derived not from any extravagant superstition, but from the desire to improve the health and the manners of men.

Pythagoras could not have been the discoverer of the relation, because... this property was known and used by scholars and artisans of Oriental lands thousands of years before Pythagoras... While deductive geometry is barely more than twenty-five hundred years old, empirical geometry is probably as old as civilization itself.

Pythagoras did not possess a proof of the theorem which bears his name... he was temperamentally uninterested in proofs of this nature, as may be gleaned from... his numerological deductions. ...the Pythagorean theorem was known to Thales. ...the hypotenuse theorem is a direct consequence of the principle of similitude, and... Thales was fully conversant with the theory of similar triangles. On the other hand, there is no doubt that Pythagoras fully appreciated the metaphysical implications. ...this relation ...was to Pythagoras and the Pythagoreans a basic law of nature, and... a brilliant confirmation of their number philosophy.

Let us suppose that we have set the problem of finding a solution to the equation \scriptstyle x^2=2. \, This is a problem for which the Babylonians around 1700 BC found the excellent approximation \scriptstyle \sqrt{2}. ...This is the identical problem which Pythagoras asserted had no fractional solution and in whose honor he was supposed to have sacrificed a hecatomb of oxen—the problem which caused the existentialist crisis in ancient Greek mathematics. The \scriptstyle \sqrt{2} exists (as the diagonal of the unit square); yet it does not exist (as a fraction)!

A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words, and to-morrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day. — "Ah, so you shall be sure to be misunderstood." — Is it so bad, then, to be misunderstood? Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood.

But there was among them a man of prodigious knowledge who acquired the profoundest wealth of understanding and was the greatest master of skilled arts of every kind; for, whenever he willed with his whole heart, he could with ease discern each and every truth in his ten—nay, twenty—men's lives.

Pythagoras is the founder of European culture in the Western Mediterranean sphere.

There remains no firm basis for the belief that Pythagoras was a geometer and in any case no attestation of his having written anything.

Pythagoras was said to have been the first man to call himself philosopher; in fact, the world is indebted to him for the word philosopher. Before that time the wise men called themselves sages, which was interpreted to mean those who know. Pythagoras was more modest. He coined the word philosopher, which he defined as one who is attempting to find out.

It seems probable that the early Greeks were largely indebted to the Phoenicians for their knowledge of practical arithmetic or the art of calculation, and perhaps also learnt from them a few properties of numbers. It may be worthy of note that Pythagoras was a Phoenician; and according to Herodotus, but this is more doubtful, Thales was also of that race.

But it is, however, in the teachings of Pythagoras that we find the closest and most frequent identities of teachings and argumentation [about as to the nature and position of the Gods], explained as due to Pythagoras himself having visited India and learned his philosophy there, as tradition asserts. In later centuries we find some peculiarly Sânkhyan and Buddhist ideas playing a prominent part in Gnostic thought.

The school of the Pythagoras and those of the Neo-Platonists kept up the tradition for Greece, and we know that Pythagoras gained some of his learning in India, while Plato studied, and was initiated in the schools of Egypt. More precise information has been published of the Grecian schools than of others; the Pythagorean had pledged disciples as well as an outer discipline, the inner circle passing through three degrees during five years of probation.

It is further interesting to remark that the finest characters among women with which ancient Greece presents us were formed in the school of Pythagoras, and the same is true of the men.

The world is always ungrateful to its great men. Florence has built a statue to Galileo, but hardly even mentions Pythagoras. The former had a ready guide in the treatises of Copernicus, who had been obliged to contend against the universally established Ptolemaic system. But neither Galileo nor modern astronomy discovered the emplacement of the planetary bodies. Thousands of ages before, it was taught by the sages of Middle Asia, and brought thence by Pythagoras, not as a speculation, but as a demonstrated science. "The numerals of Pythagoras," says Porphyry, "were hieroglyphical symbols, by means whereof he explained all ideas concerning the nature of all things." Verily, then, to antiquity alone have we to look for the origin of all things. p. 31

Pythagoras called his Gnosis “the knowledge of things that are,” or ἡ γνῶσις τῶν ὄντων, and preserved that knowledge for his pledged disciples only: for those who could digest such mental food and feel satisfied; and he pledged them to silence and secrecy. Occult alphabets and secret ciphers are the development of the old Egyptian hieratic writings, the secret of which was, in the days of old, in the possession only of the Hierogrammatists, or initiated Egyptian priests.

Pythagoras repeats our archaic doctrine when stating that the Ego (Nous) is eternal with Deity; that the soul only passed through various stages to arrive at divine excellence; while thumos returned to the earth, and even the phren, the lower Manas, was eliminated.

I have often admired the mystical way of Pythagoras, and the secret Magic of numbers.

A solitary man is a God, or a beast.

Envy has been, is, and shall be, the destruction of many. What is there, that Envy hath not defamed, or Malice left undefiled? Truly, no good thing.

To use Virtue is perfect blessedness.

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.

Not frequently man from man.

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.

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.

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

Dispose thy Soul to all good and necessary things!

Patience cometh by the grace of the Soul.

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