Philosophers From Greece

"If the Pythagorean metempsychosis should be thoroughly explained and compared with the modern theory of evolution, it would be found to supply every "missing link" in the chain of the latter. But who of our scientists would consent to lose his precious time over the vagaries of the ancients. Notwithstanding proofs to the contrary, they not only deny that the nations of the archaic periods, but even the ancient philosophers had any positive knowledge of the Heliocentric system. The "Venerable Bedes," the Augustines and Lactantii appear to have smothered, with their dogmatic ignorance, all faith in the more ancient theologists of the pre-Christian centuries. But now philology and a closer acquaintance with Sanskrit literature have partially enabled us to vindicate them from these unmerited imputations. In the Vedas, for instance, we find positive proof that so long ago as 2000 B.C., the Hindu sages and scholars must have been acquainted with the rotundity of our globe and the Heliocentric system. Hence, Pythagoras and Plato knew well this astronomical truth; for Pythagoras obtained his knowledge in India, or from men who had been there, and Plato faithfully echoed his teachings."

"Aristotle was no trustworthy witness. He misrepresented Plato, and he almost caricatured the doctrines of Pythagoras. There is a canon of interpretation, which should guide us in our examinations of every philosophical opinion: The human mind has, under the necessary operation of its own laws, been compelled to entertain the same fundamental ideas, and the human heart to cherish the same feelings in all ages. It is certain that Pythagoras awakened the deepest intellectual sympathy of his age, and that his doctrines exerted a powerful influence upon the mind of Plato. His cardinal idea was that there existed a permanent principle of unity beneath the forms, changes, and other phenomena of the universe. Aristotle asserted that he taught that numbers are the first principles of all entities. Ritter has expressed the opinion that the formula of Pythagoras should be taken symbolically, which is doubtless correct."

"It is certain that Pythagoras awakened the deepest intellectual sympathy of his age, and that his doctrines exerted a powerful influence upon the mind of Plato. His cardinal idea was that there existed a permanent principle 'of unity beneath the forms, changes, and other phenomena of the universe. Aristotle asserted that he taught that “ numbers are the first principles of all entities.” Ritter has expressed the opinion that the formula of Pythagoras should be taken symbolically, which is doubtless correct. (p. XV Before the Veil)"

"All was oracular and dogmatic in the school of Pythagoras. He prized and justly prized the greatness of his attainments and discoveries, and had no conception that any thing could go beyond them. He did not encourage, nay, he resolutely opposed, all true independence of mind, and that undaunted spirit of enterprise which is the atmosphere in which the sublimest thoughts are most naturally generated. He therefore did not throw open the gates of science and wisdom, and invite every comer; but on the contrary narrowed the entrance, and carefully reduced the number of aspirants. He thought not of the most likely methods to give strength and permanence and an extensive sphere to the progress of the human mind. For these reasons he wrote nothing; but consigned all to the frail and uncertain custody of tradition. And distant posterity has amply avenged itself upon the narrowness of his policy; and the name of Pythagoras, which would otherwise have been ranked with the first luminaries of mankind, and consigned to everlasting gratitude, has in consequence of a few radical and fatal mistakes, been often loaded with obloquy, and the hero who bore it been indiscriminately classed among the votaries of imposture and artifice."

"It is difficult to imagine any thing more instructive, and more pregnant with matter for salutary reflection, than the contrast presented to us by the character and system of action of Pythagoras on the one hand, and those of the great enquirers of the last two centuries, for example, Bacon, Newton and Locke, on the other. Pythagoras probably does not yield to any one of these in the evidences of true intellectual greatness. In his school, in the followers he trained resembling himself, and in the salutary effects he produced on the institutions of the various republics of Magna Graecia and Sicily, he must be allowed greatly to have excelled them. His discoveries of various propositions in geometry, of the earth as a planet, and of the solar system as now universally recognised, clearly stamp him a genius of the highest order. Yet this man, thus enlightened and philanthropical, established his system of proceeding upon narrow and exclusive principles, and conducted it by methods of artifice, quackery and delusion. One of his leading maxims was, that the great and fundamental truths to the establishment of which he devoted himself, were studiously to be concealed from the vulgar, and only to be imparted to a select few, and after years of the severest noviciate and trial. He learned his earliest lessons of wisdom in Egypt after this method, and he conformed through life to the example which had thus been delivered to him. The severe examination that he made of the candidates previously to their being admitted into his school, and the years of silence that were then prescribed to them, testify this. He instructed them by symbols, obscure and enigmatical propositions, which they were first to exercise their ingenuity to expound. The authority and dogmatical assertions of the master were to remain unquestioned; and the pupils were to fashion themselves to obsequious and implicit submission, and were the furthest in the world from being encouraged to the independent exercise of their own understandings. There was nothing that Pythagoras was more fixed to discountenance, than the communication of the truths upon which he placed the highest value, to the uninitiated. It is not probable therefore that he wrote any thing: all was communicated orally, by such gradations, and with such discretion, as he might think fit to adopt and to exercise."

"The close of the life of Pythagoras was, according to every statement, in the midst of misfortune and violence. Some particulars are related by Iamblichus, which, though he is not an authority beyond all exception, are so characteristic as seem to entitle them to the being transcribed. … Cylon, the richest man, or, as he is in one place styled, the prince, of Crotona, had manifested the greatest partiality to Pythagoras. He was at the same time a man of rude, impatient and boisterous character. He, together with Perialus of Thurium, submitted to all the severities of the Pythagorean school. They passed the three years of probation, and the five years of silence. They were received into the familiarity of the master. They were then initiated, and delivered all their wealth into the common stock. They were however ultimately pronounced deficient in intellectual power, or for some other reason were not judged worthy to continue among the confidential pupils of Pythagoras. They were expelled. The double of the property they had contributed was paid back to them. A monument was set up in memory of what they had been; and they were pronounced dead to the school. … Cylon, from feelings of the deepest reverence and awe for Pythagoras, which he had cherished for years, was filled even to bursting with inextinguishable hatred and revenge. The unparalleled merits, the venerable age of the master whom he had so long followed, had no power to control his violence. His paramount influence in the city insured him the command of a great body of followers. He excited them to a frame of turbulence and riot. He represented to them how intolerable was the despotism of this pretended philosopher. They surrounded the school in which the pupils were accustomed to assemble, and set it on fire. Forty persons perished in the flames. According to some accounts Pythagoras was absent at the time. According to others he and two of his pupils escaped. He retired from Crotona to Metapontum. But the hostility which had broken out in the former city, followed him there. He took refuge in the Temple of the Muses. But he was held so closely besieged that no provisions could be conveyed to him; and he finally perished with hunger, after, according to Laertius, forty days' abstinence."

"What however seems to be agreed in by all his biographers, is that he professed to have already in different ages appeared in the likeness of man: first as Aethalides, the son of Mercury; and, when his father expressed himself ready to invest him with any gift short of immortality, he prayed that, as the human soul is destined successively to dwell in various forms, he might have the privilege in each to remember his former state of being, which was granted him. From Aethalides he became Euphorbus, who slew Patroclus at the siege of Troy. He then appeared as Hermotimus, then Pyrrhus, a fisherman of Delos, and finally Pythagoras. He said that a period of time was interposed between each transmigration, during which he visited the seat of departed souls; and he professed to relate a part of the wonders he had seen. He is said to have eaten sparingly and in secret, and in all respects to have given himself out for a being not subject to the ordinary laws of nature. Pythagoras therefore pretended to miraculous endowments. Happening to be on the sea-shore when certain fishermen drew to land an enormous multitude of fishes, he desired them to allow him to dispose of the capture, which they consented to, provided he would name the precise number they had caught. He did so, and required that they should throw their prize into the sea again, at the same time paying them the value of the fish."

"To give the greater authority and effect to his communications Pythagoras hid himself during the day at least from the great body of his pupils, and was only seen by them at night. Indeed there is no reason to suppose that any one was admitted into his entire familiarity. When he came forth, he appeared in a long garment of the purest white, with a flowing beard, and a garland upon his head. He is said to have been of the finest symmetrical form, with a majestic carriage, and a grave and awful countenance. He suffered his followers to believe that he was one of the Gods, the Hyperborean Apollo, and is said to have told Abaris that he assumed the human form, that he might the better invite men to an easiness of approach and to confidence in him. -->"

"When in the end Pythagoras thought himself fully qualified for the task he had all along had in view, he was no less strict in prescribing ample preliminaries to his own scholars. At the time that a pupil was proposed to him, the master, we are told, examined him with multiplied questions as to his principles, his habits and intentions, observed minutely his voice and manner of speaking, his walk and his gestures, the lines of his countenance, and the expression and management of his eye, and, when he was satisfied with these, then and not till then admitted him as a probationer. It is to be supposed that all this must have been personal. As soon however as this was over, the master was withdrawn from the sight of the pupil; and a noviciate of three and five, in all eight years, was prescribed to the scholar, during which time he was only to hear his instructor from behind a curtain, and the strictest silence was enjoined him through the whole period. As the instructions Pythagoras received in Egypt and the East admitted of no dispute, so in his turn he required an unreserved submission from those who heard him: autos iphae "the master has said it," was deemed a sufficient solution to all doubt and uncertainty."

"One revolution that Pythagoras worked, was that, whereas, immediately before, those who were most conspicuous among the Greeks as instructors of mankind in understanding and virtue, styled themselves sophists, professors of wisdom, this illustrious man desired to be known only by the appellation of a philosopher, a lover of wisdom. The sophists had previously brought their denomination into discredit and reproach, by the arrogance of their pretensions, and the imperious way in which they attempted to lay down the law to the world. The modesty of this appellation however did not altogether suit with the deep designs of Pythagoras, the ascendancy he resolved to acquire, and the oracular subjection in which he deemed it necessary to hold those who placed themselves under his instruction. This wonderful man set out with making himself a model of the passive and unscrupulous docility which he afterwards required from others. He did not begin to teach till he was forty years of age, and from eighteen to that period he studied in foreign countries, with the resolution to submit to all his teachers enjoined, and to make himself master of their least communicated and most secret wisdom.<!-- In Egypt in particular, we are told that, though he brought a letter of recommendation from Polycrates, his native sovereign, to Amasis, king of that country, who fully concurred with the views of the writer, the priests, jealous of admitting a foreigner into their secrets, baffled him as long as they could, referring him from one college to another, and prescribing to him the most rigorous preparatives, not excluding the rite of circumcision. But Pythagoras endured and underwent every thing, till at length their unwillingness was conquered, and his perseverance received its suitable reward."

"To inculcate a pure and a simple mode of subsistence was also an express object of pursuit to Pythagoras. He taught a total abstinence from every thing having had the property of animal life. … He taught temperance in all its branches, and a resolute subjection of the appetites of the body to contemplation and the exercises of the mind; and, by the unremitted discipline and authority he exerted over his followers, he caused his lessons to be constantly observed. There was therefore an edifying and an exemplary simplicity that prevailed as far as the influence of Pythagoras extended, that won golden opinions to his adherents at all times that they appeared, and in all places."

"But this marvellous man in some way, whether from the knowlege he received, or from his own proper discoveries, has secured to his species benefits of a more permanent nature, and which shall outlive the revolutions of ages, and the instability of political institutions. He was a profound geometrician. The two theorems, that the internal angles of every right-line triangle are equal to two right angles, and that the square of the hypothenuse of every right angled triangle is equal to the sum of the squares of the other two sides, are ascribed to him. In memory of the latter of these discoveries he is said to have offered a public sacrifice to the Gods; and the theorem is still known by the name of the Pythagorean theorem."

"Pythagoras was a man of the most various accomplishments, and appears to have penetrated in different directions into the depths of human knowledge. He sought wisdom in its retreats of fairest promise, in Egypt and other distant countries. In this investigation he employed the earlier period of his life, probably till he was forty, and devoted the remainder to such modes of proceeding, as appeared to him the most likely to secure the advantage of what he had acquired to a late posterity. He founded a school, and delivered his acquisitions by oral communication to a numerous body of followers. He divided his pupils into two classes, the one neophytes, to whom was explained only the most obvious and general truths, the other who were admitted into the entire confidence of the master. These last he caused to throw their property into a common stock, and to live together in the same place of resort. He appears to have spent the latter half of his life in that part of Italy, called Magna Graecia, so denominated in some degree from the numerous colonies of Grecians by whom it was planted, and partly perhaps from the memory of the illustrious things which Pythagoras achieved there."

"Around 600 BCE, Pythagoras observed that the tones of a lyre sound most harmonious when the ratio of string lengths forms a simple whole-number fraction. Inspired by such hints, Pythagoras and his followers made a remarkable intuitive leap. They foresaw the possibility of a different kind of world-model, less dependent on the accident of our senses but more in tune with Nature's hidden harmonies, and ultimately more faithful to reality. This is the meaning of... "All things are number.""

"The association between religion and mathematically based science has its origins in the mists of history. ...the very dawn of Western culture in sixth-century B.C. Greece. ...[W]hen the Greeks were turning away from the mythological picture immortalized by Homer and Hesiod, the Ionian philosopher Pythagoras of Samos pioneered a worldview in which mathematics was seen as the key to reality. In place of the mythological gods, Pythagoras painted a picture in which the universe was conceived as a great musical instrument resonating with divine mathematical harmonies. ...[inspiring] mystics, theologians, and physicists ever since. ...But to Pythagoras and his followers, mathematics was the key not simply to the physical world, but more importantly to the spiritual world—for they believed that numbers were literally gods. By contemplating numbers and their relationships, the Pythagoreans sought union with the "divine." For them, mathematics was first and foremost a religious activity."

"It was a maxim of Pythagoras that the two most excellent things for man were to speak the truth, and to render benefits to each other."

"From of old, amid the rage of robbery and blood-lust, it came to wise men's consciousness that the human race was suffering from a malady which necessarily kept it in progressive deterioration. Many a hint from observation of the natural man, as also dim half-legendary memories, had made them guess the primal nature of this man, and that his present state is therefore a degeneration. A mystery enwrapped Pythagoras, the preacher of vegetarianism; no philosopher since him has pondered on the essence of the world, without recurring to his teaching. Silent fellowships were founded, remote from turmoil of the world, to carry out this doctrine as a sanctification from sin and misery."

"It is very important to note that some 2,500 years ago at the least Pythagoras went from Samos to the Ganges to learn geometry…But he would certainly not have undertaken such a strange journey had the reputation of the Brahmins' science not been long established in Europe…"

"It was Pythagoras who first called heaven kosmos, because it is perfect, and "adorned" with infinite beauty and living beings."

"Pythagoras was a man; and with all his imperfections on his head, we shall look among the race of men, for his better, in yain, yea, for his equal, or his second, but in vain. Pythagoras was entirely a Deist, a steady maintainer of the unity of God, and of the eternal obligations of moral virtue. No Christian writings, even to this day, can compete in sublimity and grandeur with what this illustrious philosopher has laid down concerning God, and the end of all our actions; and it is likely, says Bayle, that he would have carried his orthodoxy much farther, had he had the courage to expose himself to martyrdom."

"Pythagoras was a teacher of the purest system of morals ever propounded to man."

"In spite of the dominance of mechanistic thought in the contemporary world, a perplexing residue of the magical tradition still survives in the form of several issues, solutions to which do not appear possible within the context of a purely mechanical view of the world.... It is important to recognize that the materialist, scientific paradigm that dominates the late twentieth century world and provides the basis for its dominant institutions, has its basis in the life and work of Pythagoras, one of the most significant representatives of the perennial philosophy and a founder of the magical tradition. This spirit, which gave rise to our world view, is a spirit that must be recaptured if our civilization is to flourish. The choice is a clear one to many, and was summed up in a book title by the late Pythagorean and futurist Buckminster Fuller, Utopia or Oblivion."

"Number, its kinds; the first kind, intellectual in the divine mind. Number is of two kinds, the Intellectual (or immateriall) and the Scientiall. The intellectuall is that eternal substance of number, which Pythagoras in his discourse concerning the Gods asserted to be the principle most providentiall of all Heaven and Earth, and the nature that is betwixt them. Moreover, it is the root of divine Beings, and of gods, & of Dæmons. This is that which he termed the principle, fountain,and root of all things, and defined it to be that which before all things exists in the divine mind; from which and out of which all things are digested into order, and remain numbred by an indissolube series. For all things which are ordered in the world by nature according to an artificiall course in part and in whole appear to be distinguished and adorn'd by Providence and the All-creating Mind, according to Number; the exemplar being established by applying (as the reason of the principle before the impression of things) the number præxistent in the Intellect of God, maker of the world. This only in intellectual, & wholly immaterial, really a substance according to which as being the most exact artificiall reason, all things are perfected, Time, Heaven, Motion, the Stars and their various revolutions. ...The other kind of number, Scientiall; its principles. Scientiall Number is that which Pythagoras defines the extension and production into act of the seminall reasons which are in the Monad, or a heap of Monads, or a progressian of multitude beginning from Monad, and a regression ending in Monad."

"What seems certain is that Pythagoras developed the idea of mathematical logic... He realized that numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception. This meant he could discover truths which were independent of opinion of prejudice and which were more absolute then any previous knowledge."

"Inasmuch as I have begun to explain to you how much greater was my impulse to approach philosophy in my youth than to continue it in my old age, I shall not be ashamed to tell you what ardent zeal Pythagoras inspired in me. Sotion used to tell me why Pythagoras abstained from animal food, and why, in later times, Sextius did also. In each case, the reason was different, but it was in each case a noble reason. … Pythagoras … held that all beings were inter-related, and that there was a system of exchange between souls which transmigrated from one bodily shape into another. If one may believe him, no soul perishes or ceases from its functions at all, except for a tiny interval – when it is being poured from one body into another."

"The combination of mathematics and theology, which began with Pythagoras, characterized religious philosophy in Greece, in the Middle Ages, and in modern times down to Kant. Orphism before Pythagoras was analogous to Asiatic mystery religions. But in Plato, Saint Augustine, Thomas Aquinas, Descartes, Spinoza, and Kant there is an intimate blending of religion and reasoning, of moral aspiration with logical admiration of what is timeless, which comes from Pythagoras, and distinguishes the intellectualized theology of Europe from the more straightforward mysticism of Asia. It is only in quite recent times that it has been possible to say clearly that Pythagoras was wrong. I do not know of any other man who has been as influential as he was in the sphere of thought. I say this because what appears as Platonism is, when analyzed, found to be in essence Pythagoreanism. The whole conception of an eternal world, revealed to the intellect but not to the senses, is derived from him. But for him, Christians would not have thought of Christ as the Word; but for him, theologians would not have sought logical proofs of God and immortality."

"Personal religion is derived from ecstasy, theology from mathematics, and both are to be found in Pythagoras."

"Pythagoras, as everyone knows, said that "all things are numbers." This statement, interpreted in a modern way, is logical nonsense, but what he meant was not exactly nonsense. He discovered the importance of numbers in music and the connection which he established between music and arithmetic survives in the mathematical terms "harmonic mean" and "harmonic progression." He thought of numbers as shapes, as they appear on dice or playing cards. We still speak of squares or cubes of numbers, which are terms that we owe to him. He also spoke of oblong numbers, triangular numbers, pyramidal numbers, and so on. These were the numbers of pebbles [or calculi] (or as we would more naturally say, shot) required to make the shapes in question."

"Pythagoras transformed the study of geometry into a liberal education, examining the principles of the science from the beginning and probing the theorems in an immaterial and intellectual manner: he it was who discovered the theory of irrationals [or 'proportions'] and the construction of the cosmic figures."

"According to the account of Proclus (Book II. c. 4 ), Pythagoras was the first who gave to Geometry the form of a deductive science, by shewing the connexion of the geometrical truths then known, and their dependence on certain first principles. ...The traditionary account, that Pythagoras was the founder of scientific mathematics, is in some degree, supported by the statement of Diogenes Laertius, that he was chiefly occupied with the consideration of the properties of number, weight, and extension, besides music and astronomy. The passage of Cicero (De Nat. Deor. III. 36) may be referred to as evidence that later writers were unable to give any precise account of the mathematical discoveries of Pythagoras. To Pythagoras, however, is attributed the discovery of some of the most important elementary properties contained in the first book of Euclid's Elements. The very important truth contained in Prop. 47, Book I. is also ascribed to Pythagoras. ...Proclus attributes to him the discovery of that right-angled triangle, the three sides of which are respectively 3, 4, and 5 units. To Pythagoras also belongs the discovery, that there are only three kinds of regular polygons which can be placed so as to fill up the space round a point; namely, six equilateral triangles, four squares, and three regular hexagons. Proclus attributes to him the doctrine of incommensurables, and the discovery of the five regular solids, which, if not due to Pythagoras, originated in his school. In Astronomy he is reputed to have held, that the Sun is the centre of the system, and that the planets revolve round it. This has been called, from his name, the Pythagorean System, which was revived by Copernicus, A.D.1541, and proved by Newton."

"Such things taught he, though advising above all things to speak the truth, for this alone deifies men. For as he had learned from the Magi, who call God Oremasdes, God's body is light, and his soul is truth. He taught much else, which he claimed to have learned from Aristoclea at Delphi."

"He ordained that his disciples should speak well and think reverently of the Gods, muses and heroes, and likewise of parents and benefactors; that they should obey the laws; that they should not relegate the worship of the Gods to a secondary position, performing it eagerly, even at home; that to the celestial divinities they should sacrifice uncommon offerings; and ordinary ones to the inferior deities. (The world he Divided into) opposite powers; the "one" was a better monad, light, right, equal, stable and straight; while the "other" was an inferior duad, darkness, left, unequal, unstable and movable."

"The following became universally known: first, that he maintains that the soul is immortal; second, that it changes into other kinds of living things; third, that events recur in certain cycles and that nothing is ever absolutely new; and fourth, that all living things should be regarded as akin. Pythagoras seems to have been the first to bring these beliefs into Greece."

"It was through philosophy, he said, that he had come to be surprised at nothing."

"The votaries of Pythagoras of Samos have this story to tell of him, that he was not an Ionian at all, but that, once on a time in Troy, he had been Euphorbus, and that he had come to life after death, but had died as the songs of Homer relate. And they say that he declined to wear apparel made from dead animal products and, to guard his purity, abstained from all flesh diet, and from the offering of animals in sacrifice. For that he would not stain the altars with blood; nay, rather the honey-cake and frankincense and the hymn of praise, these they say were the offerings made to the Gods by this man, who realized that they welcome such tribute more than they do the hecatombs note and the knife laid upon the sacrificial basket. For they say that he had of a certainty social intercourse with the gods, and learnt from them the conditions under which they take pleasure in men or are disgusted, and on this intercourse he based his account of nature."

"What appeared here, at the center of the Pythagorean tradition in philosophy, is another view of psyche that seems to owe little or nothing to the pan-vitalism or pan-deism (see theion) that is the legacy of the Milesians."

"Pythagoras and Plato and Boehme and Paracelsus and Thomas Vaughan were men who bore their lamps amidst their fellowmen in life under a hail of nonunderstanding and abuse. Anyone could approach them, but only a few were able to discern the superearthly radiance behind the earthly face. It is possible to name great Servitors of East and West, North and South. It is possible to peruse their biographies; yet everywhere we feel that the superearthly radiance appears rarely in the course of centuries. One should learn from reality. 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. (175)"

"Ah, Pythagoras' metempsychosis, were that true, This soul should fly from me, and I be changed Unto some brutish beast! All beasts are happy, for when they die, Their souls are soon dissolved in elements; But mine must live still to be plagued in hell."

"It may perhaps help us to realize the human side of our Masters if we remember that many of Them in comparatively recent times have been known as historical characters. The Master K.H. for example, appeared in Europe as the philosopher Pythagoras. Before that He was the Egyptian priest Sarthon, and on yet another occasion chief-priest of a temple at Agade, in Asia Minor, where He was killed in a general massacre of the inhabitants by a host of invading barbarians who swooped down upon them from the hills"

"It is impossible to decide whether a particular detail of the Pythagorean universe was the work of the master, or filled in by a pupil—a remark which equally applies to Leonardo or Michelangelo. But there can be no doubt that the basic features were conceived by a single mind; that Pythagoras of Samos was both the founder of a new religious philosophy, and the founder of Science, as the word is understood today."

"The Ionians were optimistic, heathenly materialists... Every philosopher of the period seems to have had his own theory regarding the nature of the universe around him. ...The sixth century scene evokes the image of an orchestra expectantly tuning up, each player absorbed in his own instrument only, deaf to the caterwaulings of the others. Then there is a dramatic silence, the conductor enters the stage, raps three times with his baton, and harmony emerges from the chaos. The maestro is Pythagoras of Samos, whose influence on the ideas, and thereby on the destiny, of the human race was probably greater than that of any single man before or after him."

"Nicomachus concludes his first book with a theorem that indicates that mathematics was not yet free from ethical and æsthetic mixture. From Pythagoras onward two ideas were widespread in Greek, especially Platonic, philosophy. These are that the beautiful and the definite are prior to the ugly and the indefinite, and that from them are formed all the parts and classes of the infinite and indefinite. Nicomachus aims to show that in mathematics the same principle holds good in that from equality may be derived all the species of inequality."

"Pythagoras taught, accordingly, that he had himself been originally Euphorbus, and then Callides, thirdly Hermotimus, fourthly Pyrrhus, and lastly Pythagoras; and that those things which had existed, after certain revolutions of time, came into being again; so that nothing in the world should be thought of as new. He said that true philosophy was a meditation on death; that its daily struggle was to draw forth the soul from the prison of the body into liberty: that our learning was recollection, and many other things which Plato works out in his dialogues, especially in the Phaedo and Timæus. For Plato, after having formed the Academy and gained innumerable disciples, felt that his philosophy was deficient on many points, and therefore went to Magna Græcia, and there learned the doctrines of Pythagoras from Archytas of Tarentum and Timæus of Locris: and this system he embodied in the elegant form and style which he had learned from Socrates. The whole of this, as we can prove, Origen carried over into his book Περὶ ᾿Αρχῶν, only changing the name."

"Pythagoras conceived that the first attention that should be given to men should be addressed to the senses, as when one perceives beautiful figures and forms, or hears beautiful rhythms and melodies. Consequently he laid down that the first erudition was that which subsists through music's melodies and rhythms, and from these he obtained remedies of human manners and passions, and restored the pristine harmony of the faculties of the soul."

"After his father's death, though he was still but a youth, his aspect was so venerable, and his habits so temperate that he was honored and even reverenced by elderly men, attracting the attention of all who saw and heard him speak, creating the most profound impression. That is the reason that many plausibly asserted that he was a child of the divinity. Enjoying the privilege of such a renown, of an education so thorough from infancy, and of so impressive a natural appearance he showed that he deserved all these advantages by deserving them, by the adornment of piety and discipline, by exquisite habits, by firmness of soul, and by a body duly subjected to the mandates of reason. An inimitable quiet and serenity marked all his words and actions, soaring above all laughter, emulation, contention, or any other irregularity or eccentricity; his influence at Samos was that of some beneficent divinity. His great renown, while yet a youth, reached not only men as illustrious for their wisdom as Thales at Miletus, and Bias at Prione, but also extended to the neighboring cities. He was celebrated everywhere as the "long-haired Samian," and by the multitude was given credit for being under divine inspiration."

"No one will deny that the soul of Pythagoras was sent to mankind from Apollo's domain, having either been one of his attendants, or more intimate associates, which may be inferred both from his birth, and his versatile wisdom."

"Much learning does not teach wisdom; otherwise it would have taught Hesiod and Pythagoras, and again Xenophanes and Hecataeus."

"Pythagoras, the son of Mnesarchus, was the most learned of all men of history; and having selected from these writings, he thus formed his own wisdom and extensive learning, and mischievous art."

"Pythagoras was indeed the first man to call himself a philosopher. Others before had called themselves wise (sophos), but Pythagoras was the first to call himself a philosopher, literally a lover of wisdom. More importantly, for Pythagoras and his followers philosophy was not merely an intellectual pursuit, but a way of life, the aim of which was the assimilation to God."

"Some fundamental unity was surely to be discerned either in the matter or the structure of things. The Ionic philosophers chose the former field: Pythagoras took the latter. ...The geometry which he had learnt in Egypt was merely practical. ...It was natural to nascent philosophy to draw, by false analogies, and the use of a brief and deceptive vocabulary,2 enormous conclusions from a very few observed facts: and it is not surprising if Pythagoras, having learnt in Egypt that number was essential to the exact description of forms and of the relations of forms, concluded that number was the cause of form and so of every other quality. Number, he inferred, is quantity and quantity is form and form is quality. Footnote2 Primitive men, on seeing a new thing, look out especially for some resemblance in it to a known thing, so that they may call both by the same name. This developes a habit of pressing small and partial analogies. It also causes many meanings to be at attached to the same word. Hasty and confused theories are the inevitable result."