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one of the earliest and most celebrated sages of Greece, the alleged originator of the name and of the profession of philosopher, and the founder of a sect which enjoyed great and enduring reputation. Notwithstanding the numerous fables which are interwoven with the traditionary accounts of his career, it is certain that none of the elder philosophers of Greece attained higher eminence in speculation, impressed himself more forcibly on the contemporary world, or influenced more widely and more permanently the character of subsequent investigation, Engaged equally and silnultaneously in abstract inquiry and in scientific research, at once theorist and practical politician, and predominant wherever his efforts were directed, he instituted a school, a religious fraternity, a secret society, and a political association, all combined in one body; and he controlled for many years the public movement of the community in which he had fixed his abode. His political asceldency was a potent influence during a considerable part of his life, and was prolonged, in a mitigated and disguised form, through successive generations. His sect survived alike the peculiar circumstances which had favored its original establishment and the violent catastrophe which crushed the primitive association, and, after his characteristic doctrines had been accepted, with modifications and additions, by other schools, devoted itself with marked earnestness to the public and private ethics which had chiefly attracted the regards of the master. His discoveries, or happy conjectures, in mathematics, in astronomy, in music, etc., fascinated Plato, and were largely incorporated into the all-embracing system of Aristotle. Even in cases in which they were questioned, rejected, or almost forgotten by later antiquity, they have been revived by modern philosophy, and may frequently be recognised as furnishing the corner-stones for modern sciences. To Pythagoras have been ascribed the anticipation of the Copernican system, the demonstration of the relation between the squares of the sides of a right-angled triangle, and the determination of the mathematical basis of the theory of music. To him must also be assigned the honor of introducing. however fantastically, numerical relations for the explanation of the laws and operations of the material universe. A man connected so prominently and so effectively with so many important branches of human research and of human action, at the very outset of systematic speculation and systematized activity, may well excite wonder and attract curiosity — a wonder which is converted into amazement by reputed miracles, and a curiosity which is baffled and bewildered bv the accumulation of myths around his name and around all the salient incidents of his career.
I. Life And Labors. — The details of the life and opinions of Pythagoras, as transmitted to us by the ancients, are so confused and contradictory, and are so blended with fantastic fables, that it is impracticable to extract from them a plain, trustworthy, and consistent account (Brucker, Hist. Crit. Phil. i, 991). The founder, in a remote age, of a secret society at once religious and political, philosophical and scientific, afforded an apt frame on which to hang the exaggerations of admiring disciples and the credulous fancies of his own and of other generations. We have no authentic remains and no contemporary memorials of the Samian philosopher. The relics attributed to his earlier followers are not acknowledged to be genuine. The special works of Aristotle and of his pupils, Dicearchus, Aristoxenus, and Heraclides Ponticus, on the subject of the Pythagoreans, were early lost. A few scant notices survive in Herodotus, Heraclitus, Xenophanes, Isocrates, Plato, and Aristotle; but our chief sources of information are the late writers Diogenes Laertius, Porphyry, and lamblichus. Whatever materials may have been accessible to them, they cannot be supposed to have had credible authorities for their compilations. ‘ The loose and uncritical habits of Diogenes do not invite confidence, while the mythical and thaumaturgic proclivities of the Neo-Platonists to provoke constant suspicion. These miracle-mongers would greedily welcome any marvellous legends, and would not be scrupulous about adding embellishments or fictions of their own to the tales of wonder which they might find already in circulation. We are singularly unfortunate in regard to this pioneer in philosophy. Antiquity has bequeathed to us much in regard to him which is absurd as well as incredible; it has left little that can be received without hesitation, to form a portrait of the man, or to furnish an adequate scheme of his doctrines.
The birth of Pythagoras is placed by Mullach in the first year of the 43d Olymnpiad (B.C. 608), on the strength of a legend reported by Eratosthenes and cited by Diogenes Laertius. The same date is deduced, with some uncertainty, from a statement made by Antiochus and preserved by Clemens Alexandrinus. The nativity of Pythagoras is brought dow nearly forty years later bv accepting the declaration of Aristoxenus that he left Samos at the age of forty, in the reign of Polycrates. The difference between these estimates is sufficient to destroy any confidence in either, and distrust is increased by the very dubious character of early Greek chronology; yet each of these deductions has been espoused by eminent scholars. Bentley and Larclher are on the side of Mullach; Dodlwell attaches himself to the declaration of Aristoxenus; Grote, apparently convinced of the inconclusiveness of all reasoning on the subject, aims at the golden mean, and places the birth of Pythagoras about B.C. 580. The only safe conclusion is that the philosopher began to flourish in the secondl half of the 6th century before Christ.
The birthplace of Pythagoras, if less doubtful than the date of his birth, has been monre variously deterrnined. He is usually designated the Samnian. This rests, primarily, upon a passage in Herodotus, in which the curious story of Zamolxis is related. Grote considers the passage decisive. On referring to the text, it will be found that Herodotus says nothing positively of the philosopher's place of birth. The general belief of antiquity, however, accredited Pythagoras to Samos, and it is only this belief that is attested in Isocrates (Bttsil.c. xi). Aristoxenus represented him as a Tyrrhenian from Lemnos or Imbros. Bv some writers he was represented as the son of a Phliasian refugee who settled in Samos. Neanthes regarded him as a Syrian or Tyrian; Theopompus and Aristarchus entertained the opinion of Aristoxenus; Hippobotus and Hermipipus endorsed the common belief.
Contradictions continue to mutltiply. There is no agreement in regard to the paternity of Pythagoras. The accepted tradition presents him as the son of Mnesarchus; Justin, however, names his father Demaratus. Those who assigned a Phliasian origin to his father gave him the name of Marmacus, which Voss and Faber think that Justin blunderingly converted into Demaratus. Tzetzes, a very late author indeed, calls his mother Pythais. His father is variously reputed to have been an engraver of gems and a rich merchant; he may have been both or neither. Two brothers, older than himself, are given to Pythagoras — Eunomus, or, according to other accounts, Eunostes, and Tyrrhenus. These names are very suspicious.
These confusions and perplexities are noticed, not with any desire of exhibiting the numerous opinions which prevailed in relation to the birth of Pythagoras, but to show how uncertain and unauthenticated, even in antiquity, were those points in his history which were least apt to provoke diversity of statement. If there were such differences in such matters, there is little reason to expect trustworthy accounts in regard to more important concerns, where enforced secrecy promoted fanciful conjecture, where the love of the marvellous might indulge itself without check or fiar of detection, and where the character of the school cherished the wildest inventions and encouraged their acceptance. The story is, throughout, involved in fable and in superfetations of fable. Tradition has been wholly unnrestrained in relating the education of Pythagoras. Several teachers have been assigned to him. He is said to have been placed by his uncle Zoilus under the charge of Pherecydes in the island of Lemnos. He is reported to have afterwards attached himself to Hermlodamas, or Leodamas (both names are given), the grandson of Creophylus, the cyclic poet. He is alleged to have been the disciple of Thales, of the Milesian Anaximander, and of the Cretan Epimenides, who is even a more shadowy personage than himself. The true significance of this combination of names may probably be found in the disposition of later times to regard Pythagoras as instructed in all the learning of the Greeks. Yet the accumulation of Hellenic knowledge was not considered a sufficient equipment for his career. He is supposed to have set out, while still young, on extensive travels throlugh the Oriental world, just as the mediaeval sages were believed to have gathered their stores of learning from the Saracenic schools in Spain and in the East.
Egypt seems to have been the first foreign country visited by Pythagoras. He is said to have been commended to Amasis by a letter from his friend Polvcrates, and to have renained in the country long enough to acquire all the wisdom of the Egyptians — their language, arithmetic, geometry, religious rites, etc. During his stay. he is alleged to have been captured by the Persian armies of Cambyses, and to have received the instructions of the Magi; he is also said to have studied astrology with the Chaldtaans, and to have received from the Brahmins in India their peculiar doctrines. This last imagination is apparently a late deduction from the correspondence of the Pythagorean metempsychosis with Hindu tenets. Hermippus and Porphyry ascribe to him also studies among the Jews. He may have visited Crete, and there is no improbability in the supposition that anxiety to note the institutions of Lycurgus may have carried him to Sparta.
After a long and uncertain absence, Pythagoras returned to Samos, and opened a school, at the request of his countrymen, for the dissemination of the marvels of learning which he had collected in his extensive travels. His pupils were few and listless, and his method of teaching — by signs and symbols — irritated rather than enlightened his acolytes. To add mystery to his instructions and a divine sanction to his wisdom, he visited Delos and other oracular shrines. To these journeys may be assigned his appearance at the Olympic Games, and his celebrated invention of the name of "Philosopher," though this is also referred to a conversation with the Tyrant of Phlius, and probably did not originate with him. Having, by these journeys, by frequent intercourse with the divinities, by the pretension of a divine origin and of miraculous gifts, and also by the admiration excited in the congresses of men, extended and heightened his jeputation, Pythagoras came back to Samos, and reopened his school under brighter auspices than before. He gave public instruction in ethical and political philosophy, and freely responded to those who consulted him in regard to the government of the island. But, besides conducting this public academy, he provided a retreat for those who sought and were deemed worthy of more recondite education. Outside of the city he procured a cave, to which he retired with his more select disciples. Here he spent much of the night, as well as of the day, in esoteric instruction, and especially in teaching the wonders of mathematical science. He added the arts of the charlatan to the learning of the scholar and the wisdom of the sage.
Samos, however, proved an uncongenial abode. Whether his philosophical vocation was too much interrupted by the embassies and public duties imposed on him by his countrymen, or the Samians displayed too little aptitude for philosophy; whether he was offended by the tyranny of his friend Polycrates, or imperiled by that of Syloson, the brother and successor of Polycrates, it is vain to inquire. It is sufficient to know, from the universal testimony of antiquity, that Pythagoras abandoned Samos. and migrated to Southern Italy, which proved singularly hospitable to philosophy. But there is as much discrepance in regard to the time mrhen this migration took place as in regard to other circumstances in the life of the Samian teacher; it is placed about B.C. 531 by Fynes Clinton, in 529 by Ueberweg, and other dates are given.
Crotona received the emigrant. He was soon surrounded by numerous admirers, belonging to the wealthier and more influential part of the population. Ile is said to have united these, to the number of three hulndred or more, in a secret organization. Among the earliest consequences of his residence in Crotona is mentioned the complete reformation of the manners and morals of the people, produced by his persuasive address. by the authority of his divine pretensions, by his imposing demeanor, and by his judicious counsels. His disciples were of the rich and noble class, and, by converting them to a more sober and abstemious life, he would necessarily suppress luxury and sensuality; for these are not the vices of poor laborers and "rude mechanicals." Moreover, as the political control was still in the hands of the aristocracy, though already contested, political interest might conspire with religious enthusiasm and philosophical convictions in facilitating a reform requisite to maintain a doubtful ascendency. That aristocratic rule was confirmed by the action of Pythagoras was the belief of later tines; and that Crotona was strengthened by the reformation is shown by its subsequent victory over Sybaris, under Pythagorean leadership. How far the Pythagorean rule was intentionally political, how far Pythagoras directed his secret society to political aims, cannot be ascertained, and has been diversely determined. It has been well observed that a select body of influential men, interested in the maintenance of a specific policy; bound together by the closest ties of opinion, sentiment, and affectionate regard; united, moreover, by secret obligations, would necessarily employ concerted action in public affairs. It should also be observed that the Greek schools, until the close, or nearly the close, of Plato's career, had always a decided political inclination.
It may well be supposed that Pythagoras, who had already tested, at Samos, the efficacy of supernatural claims, would avail himself of like arts to establish his predominance in a new land. He had previously presented himself as a son of Phoebus, and he is said to have been worshipped in Italy, after his death, as the offspring of the Hyperborean Apollo; his golden thigh had been shown to Abaris at the Olympic Games as evidence of his divine descent. The claim was consonant with the whole tenor of Greek genealogy, and is illustrated by many striking parallels in Greece and in other lands. He offered, in confirmation of his doctrine of the transmigration of souls, his recognition, in the temple of Juno at Argos, of the shield of Euphorbus, slain in the Trojan War, whose body he had then inhabited.
"Ipse ego (jam memini) Trojani tempore belli,
Painthoides Euphorbus eram" (Ovid, Met. 15:160, 161).
To the earlier years of his residence at Crotona may be assigned his death, burial, and resurrection, and his report of the wonders of the nether world; to the same time may be referred (though there is really no chronology in these matters) his familiar intercourse with animals, his handling snakes with impunity, his prediction of earthquakes, his control over tempests, his removal of pestilences, etc. To the closing years of his life must be referred his remarkable apparition to his friends at Metapontum and Tarentum simultaneously, and his public conversation with them. It is scarcely surprising that the Neo-Platonists, by whom his biography was composed (or consarcinated), should have presented him as the counterpart and rival of Christ. It is natural that these miraculous endowments should be regarded as the bold inventions of late pagans; but this solution is not satisfactory, as some of them are evidently of much earlier origin, and all of them appear, in modified forms, in other myths in widely separated regions. There are many points in the story of Pythagoras which appear to be only late survivals of primitive superstitions and delusions.
The high and various endowments of Pythagoras, real and fictitious, rendered him singularly successful in the institution of his school at Crotona. The most important, the most credulous, or the most zealous of his pupils were constituted as a secret society, were subjected to the most stringent discipline, and to the most absolute obedience to their inspired teacher. According to some traditions, the property of all was surrendered for the common use. This is scarcely probable, as the age of communism had not vet arrived. The statement may simply indicate that the means of the members were freely employed for common objects, and that the wealthier brethren generously ministered to the requirements of the poorer.
The society seems to have been divided into two classes: the more advanced, or esoterical, and the neophytes, or exoterical. Other divisions are also mentioned, as into Pythagorici, Pythagorei, and Pythagoristc, according to their progress in the studies of the sect, and the intimacy of their communion with their common superior.
The candidates for admission were carefully scrutinized, and great attention was paid to physiognomy and the external indications of moral and mental qualities. If accepted, they had to pass through a long period of probation. It was credited in after-times that they had to maintain silence for five years; that, during this period, they were not allowed to behold the face of the master; and that they were required to undergo other tests of fitness for membership. Silence, or the government of the tongue ( Ἐχεμυθία ), was prescribed as earnestly as by St. James; but the length and degree of the silence required were not uniform in all cases. The fellows of the guild received instruction in all the knowledge then existent, either directly from the scholarch himself, or through the intervention of his more instructed pupils. The esoteric studies have been differently supposed to have been the political theories and the political projects of Pythagoras, and the mystic religious rites, or orgies, which rendered the society a theosophic sect: they were probably the latter. The publication of the characteristic Pythagorean doctrines was absolutely prohibited: and when these were published by Philolaus, in a later age, the procedure was regarded as a grave infraction of Pythagorean proprieties. Daily self-examination, which presupposes habitual meditation, was a constant requirement.
" They summ ' d the actyonns of the daie Eche nyghte before they slept."
Such reverence was paid to the declarations of the master that all contradicticon, cavil, and doubt were unknown. Every difference of opinion was promptly settled by the autocratic dictum, Αὐτὸς Ἔφα .
In the midst of the luxury, sensuality, idleness, and extravagance for which Crotona, like other cities of Magna Graecia, was noted, the greatest restraint was imposed on the elect in regard to all those vices which undermine or fritter away morality. Modesty and simplicity in dress, decorum in behavior, abstemiousness in food, abstinence from meats, beans, and other articles of food, and moderation in all things, iwere earnestly inculcated. The institutions of Pythagoras appear to have been. in many respects, an anticipation of the monastic life of the early mediaeval Benedictines. Healthful recreations for mind and body, music and gymnastics, each of which embraced a large and varied sphere, were zealously prosecuted.
The members of the association were segregated from "the vulgar herd," not merely by their secret organization and higher culture, but also by the pride of learning, of creed, of power, and by the haughty contempt for inferiors which usually attends such pride. The mystic secrecy and the careful separation from the multitude were maintained by signs and enigmatic symbols, which enabled Pythagoreans to recognise each other with certainty and without display.
The best and the latest investigators of the perplexed subject of Pythagoreanism agree in rejecting the opinion that Pythagoras intended to founmd a distinct political organization for the purpose of maintaining aristmocratic authority. Nevertheless, if any weight is to be given to concurrent testimony, or to the natural tendencies of an aristocratic organization held together by secret bonds, or to the existing condition of Greek communities, the Pythagorean fraternity did secure the control of Crotona, and instituted affiliated societies in Metapontum and other neighboring cities. The influence exercised by the Pythagoreans may well have been favorable to private morals, to public virtues, and to general prosperity. But the power of an exclusive, arbitrary, and haughty section of the community, and the constraint imposed by it on the free action as well as on the accustomed passions, the sensual gratifications, and the avidity of license, which is the first manifestation of the spirit of progressive freedom, would be certain to provoke reaction. It would thus be in perfect consonance with the natural order of events that the story should be true which related that, after Pythagoras had taught at Crotona for twenty years, the people made a combined attack upon the coenobitic association assembled in the house of Milo the athlete. Cylon, a noble who had been refused admission into the society, and Ninon were the reputed leaders. The assailants are sometimes said to have been only Crotoniates; at other times they are reputed to have consisted also of deputations from the other cities in which Pythagorean clubs had been established. The coenaculum was burned to the ground, and most of the congregation lost their lives. Accordling to some accounts, Pythagoras himself perished in the flames; accoreding to others, he escaped, retired to Metapontum, and soon after died, or was slain. This calamity is calculated to have happened about B.C. 510, when Pythagoras was ninety-eight years of age, if the earliest late of his nativity be accepted. The same story, however, with the requisite modifications, is told in regard to the Pythagoreans of a later generation. But there are so many and stuch inconsistent narratives of the end of the philosopher, and of the suppression or dispersion of the Pythagorean organization, that no greater certainty can be expected in these matters than is attainable in regard to other points in his career. The whole story is as mythical as the fable of King Arthur and the Knights of the Round Table, though unquestionably encrusting a large substratum of fact. "The stories told of him," savs Cox, "must be classed along with the tales which related the exploits of the Messenian Aristomenes."
Pythagoras was married, and had a family consisting of two sons. Telauges and Mnesarchus, and three daughters or more, Damo, Muia, and Arignote, all of whom became his disciples. Telauges is said to hiave succeedled him in the conduct of' the school. But the disciples appear to have been scattered, the school broken sup, and the sect utterly dissipated as a community, thoupgh its chiefs continued to be named, as late, at least, as Archytas of Tarentum. His wife, and the mother of his children, is usually reported to have been Theano, the daughter of Brontinus of Crotona; but she is called a Cretan, and the daughter of Pythonax, by Suidas. Confusion and discord attend every step of the inquiry.
II. Writings And Doctrines. — All the works ascribed to Pythagoras are spurious beyond all doubt. The Golden Song is not excepted from this censure. David, the scholiast of Aristotle (p. 13, 1. 15-26, r. ed. Brandis), gives the reasons assigned by Pythagoras for his refusal to commit anything to writing, and explicitly assigns the Golden Song to a nameless Pythagorean. This shows how utterly destitute the ancients themselves were of genuine Pythagorean texts, and how uncertain are all sources of information. The earliest documents are the Fragments of Philolaus, whose authenticity is still debated, and the Golden Song, often ascribed to Lysis, but, in all probability, the production of a later age. As Philolaus was the pupil of Archytas and the instructor of Simmias and Cebes, he belonged to the Socratic aera; and, as Lysis was the teacher of Epaminondas, he may be regarded as the contemporary of Plato. The interval must have been considerable between Pythagoras and Philolaus, as Archytas, the instructor of the latter, was regarded as the eigphth in the succession of the Pythagorean scholarchs. Yet the distinctive doctrines of Pythagoras must have been bruited abroad long before the publication of Philolaus; for we find among the fragments of Xenopehanes an epigram on the Pythagorean doctrine of metempsychosis, and Xenophanes was born before the death of Pythagoras. But the doctrines of Pythagoras, deducible from earlier and later writers, cannot be regarded as even a figmentary exposition of a definite system constructed by him. They are only the mutilated expression of his leading principles, as interpreted and expanded by those who claimed to be representatives of his teachings. The remnants of the early Greek inquirers, whether didactic or speculative, exhibit their disposition to employ terse aphorisms for the utterance of their views. This is the tendency of all primitive speculation. While recognising the un-systematic character of the exposition thence resulting, it is well also to remember the commendation and employment of the same mode of communication by Francis Bacon in a period of much ampler knowledge and more diffused intelligence.
Gathering from the unsatisfactory materials that remain the distinctive doctrines of Pythagoras, they appear to be these: The soul is, in its nature, immortal, and akin to divinity. It consists of two parts: the rational, which is alone immortal; and the sensuous, or irrational, which is ultimately mortal. Plants possess the latter. In this distinction may be found the germ of the Aristotelian dogma of three souls: the intelligent, the animal, and the vegetative. The rational soul is pure; the irrational impure, because immersed in matter: both are united in man. The former attests his divine nature and origin; the latter guides and governs his material frame; with which it is united in life, and through which it is diffused. Death is the withdrawal of this complex soul from the corporeal involucre in which it has been enclosed, and which it has animated. The spirit, thus released, dwells in the circumambient air, retaining, in shadowy guise, its former shape, visible as a ghost, or intervening in the affairs of men through dreams and other influences. Souls that have divested themselves in life of the taint of their irrational companion, and of their corporeal environment, enter into enduring bliss, and become wholly divine, apparently without loss of individual nature.
Ἢν Δ᾿ Ἀπολείψας Σῶμα Ἐς Αἰθέῤ Ἐλεύθερον Ἔλθῃς , Ἔσσεαι Ἀθάνατος , Θεὸς Ἄμβροτος , Οὐκ Ἔτι Θνητός ( Carm. Aur 70, 71).
Souls not liberated from the vices and passions of the lower soul, or from the impurities and temptations of their material vesture, float for a time in the air, tormented by the Furies and the ministers of vengeance, till they are allowed a new trial, and are subjected to a new ordeal, by passing into new bodies, human or bestial.
"animam sic semper eandem Esse, sed in varias doceo migraire figuras" (Ovid, Met. 15:171, 172).
The air is always full of souls, undergoing the penal consequences of their sins, and awaiting their descent into new bodies.
" penitusque necesse est Multa din concreta mtdis inolescere miris" (Virgil, A En 6, 737, 738).
This is the noted metempsychosis of Pythagoras, which is usually conceived to have been of Hindu origin, but is often referred to an Egyptian source, though having little correspondence with the metensomatosis or the anacatastasis of Egyptian mythology. It is much more reasonable to consider it a philosophical adaptation of the primitive beliefs in regard to spiritual existence after death (see Tylor, Primitive Culture). It is an obvious deduction from the doctrine of metempsychosis that animal life should be scrupulously regarded, and that animals should not be slaughtered for food. The butcher is a homicide, if not a murderer. It is a natural consequence from the doctrine of disembodied spirits that Pythagoras should have attached great importance to dreams and other spiritual communications. The sanctity of all life, and the consideration of human life as a probation and as a progress to a higher existence, explain his strong condemnation of suicide.
"The Everlasting had fixed His canon ‘ gainst self-slaughter."
(See Thom. Aquin. Summan Theolog. II, ii, qu. 24, art.v.)
Not only the spirits of men are divine, according to Pythagoras, but those of the sun, moon, and stars, which move at such musical intervals from each other, and in such regulated concord, as to produce the music of the spheres-a doctrine welcome to the poetic imagination of Plato.
"Such harmony is in immortal souls.
But while this muddy vesture of decay
Doth grossly close it in, we cannot hear it."
The ontology of Pythagoras was intimately associated with his transcendental theory of numbers. It can scarcely be determined which suggested the other, or by what series of reciprocal reactions both were produced. The cosmogony attributed to him is muchl more manifestly an evolution from the numerical fantasy which has always been held to be the most distinctive part of Pythagoreanism.
Mullach justly observes that the exposition of the significance and potency of numbers in the Pythagorean theory would require an ample volume; hence he notices them very briefly. The like course must be adopted here, and a summary, abridged from an abridgment by Baring-Gould, must suffice.
" 1. The unit, or Monad, is the beginning and end of all. It is the symbol of existence, identity, equalily, conservation, and harmony (comp. Philolai Fragm. 15).
" 2. Two, or the Dyad, is the oirigin of contrasts, the symbol of diversity, division, change, dissorder. "
3. Three, or the Triad, is the first of unequals. It represents God and the soul of man.
4. Four, or the Tetrad, is the most perfect of numbers; the root, or oriagin, of all things, whence the soul derives its eternal nature: hence it furnisles the Pythagorean oath.
Ναὶ Μὰ Τὸν Ἁμετέρᾷ Ψμχᾶ '/ Παραδόντα Τετρακτύν , Παγὰν Ἀενάου Φύσεως ( Carm. Aur. 47, 48)].
" 5. Five, or the Pentad, is everything, supplying the principle of everything, and repelling evil spirits.
" 6. Six, or the Hexad, is the number of good fortune.
" 7. Seven, or the Heptad, is a sacred number, generating good and evil. "
8. Eight, or the Octad, the first cube, is a perfect number. "
9. Nine, or the Ennead, being the square of three, is sacred.
" 10. Ten, or the Decad, the sum of the first four numbers, contains all numeric relations. All science proceeds from it and returns to it (comp. Philolai Fragm. 13)."
Whether numbers constituted the essences of things, or were only similitudes, or symbols, is still in dispute, and was, perhaps, never clearly determined. The language of Aristotle (Met. I, v) is vague and indistinct. That thev were generally employed in ea symbolic sense is apparent. The monad was the first principle of all things, the origin whence all things emanated; it was at once the odd and the even, the limited and the unlimited, God and the universe. The dyad, or first evolution of number, was the even. and represented the interval between limiting extremes. The triad generated the progressive scale of numbers. The tetrad was the union of the triad with the unit, or of the dyad with itself, and indicated geometrical body. The pentad was physical body, with its properties and accidents of sense. Numbers, again, represented points; by the procession of points, lines are formed; by the movement of lines, surfaces; by the progress of surfaces, solids. From these last arise all bodies, and the four elements of earth, air, water, fire, which undergo constant change and reciprocal conversion.
"Nec species sua cuique manet: rerumque novatrix
Ex aliis alias separat Natura figuras.
Nec perit in tanto quicquam, mihi credite, mundo, Sed variat, faciemque novat"
(Ovid, Met. 15:252-255).
A fifth element was added by the pentad; this was the upper air, the surrounding ether, the Quintessence. These five cosmic elements were also symbolized by the five mathematical bodies. The cube was the earth; the pyramid, fire; the octahedron, air; the dodecahedron, space, or ether; and the eicosahedron, water. All were contained within the enveloping sphere. Such are the bare outlines of the Pythagorean cosmogony.
Much more influential than this in the intellectual development of Greece was the moral instruction, which long continued to form a large part of Pythagorean speculation. Morals were divided into two departments: disciplinary, or ethical, for the perfection of the individual; and political, for the furtherance of the common welfare. In both parts, great stress was laid upon the obligation and the benefit of friendship, which extended, also, to the metaphysical and to the material constitution of the universe, producing the harmony of the former, and the attractions, combinations, and absorptions of the latter. The efficacy, in actual life, of the Pythagorean friendship is exemplified by the well-known story of Damon and Pythias. The Pythagorean Symbols belong mainly to practical morals, and exhibit a decided advance on the contemporaneous sentiments of the Greek world. They are unauthentic. Many belong to a later date, many are simply ceremonial, and others are general and traditionary precepts.
Condensed and inadequate as is this summary of the alleged career and teachings of Pythagoras, it reveals the powerful influence exercised by him on the communities with which he was associated, and on the latter generations which professed the adoption of his alleged philosophy. Admitting the utmost confusion and unscertainty in the chronlology of both his biography and his doctrines, and the fabulous nature of much that was ascribed to him, he must yet be deemed worthy of the reputation he left behind him, and is still "claruin et venerabile nomen."
III. Literature. — All the historians of ancient phlilosophy, and all the extended histories of Greece, necessarily treat of Pythagoras with more or less fulness and with more or less discernment. Brucker, as usual, provides an ample accumulation of materials; Ueberlreg is brief but perspicacious; while Ritter is very copious and discreet. Grote's observations are valuable. Of more special sources of information may be enumerated: Mullach, Fragmenta Philosophorum Graecorum (Paris, 187577); Hieroclis Commentarius in Carmenz Aureulm (ap. Mullach, Frany. Plil. Grcec.); Aristotelis Metapysica, lib. i, 9, 12, 13; Diogenes Laertius (ed. Hiibner, Lips. 1828-31, 2 vols.); Porphyrii Pythargorte Vita.; Iamblichi Pythagorce Vitca (ed. Kiessling, Lips. 1813); Fabricii Bibliotheca Grceco, i, 750-804; Mason, ap. Smith. Dict. Greek and Rooman Biog. and Mytl. ss.v.; Schilter, Diss. de Discipl. Pyithatgorae; Terpstra, De Sodclitii Pythagor. Origine (Utrecht, 1824); Wendt, De Rebus Princ. sec. Pythagoram (Lips. 1827); Ritter, Cesch. der pythag. Philosophie (Hamburg, 1826); Krische, De Societatis a Pythag. conduc Scopo Politico (Gottingen, 1830); Beckmann, De Pythagoreor. Reliquiis (Berlin, 1844); also Qucestiones Pythagoricae (Braunsberg, 18521858); Langel, Pythagore, sca Doctrine et son Histoire, in the Revue des Deux Mondes (Paris, 1864); Zeller. Pythagoras und die Pythalgorassage (Leips. 1865); Balzer, Pythagoras der Weise von Samsos (Nordhausen, 1865); Rathgeber, Grossgriechenla und und Pythagoras (Gotha, 1866); Chaignet, Pythagtore (Paris, 1873); Montle, Quelques Maots sur le Philosophe Pythagore (Douai, 1876). (G. F. H.)
The Nuttall Encyclopedia 
A celebrated Greek philosopher and founder of a school named after him Pythagoreans, born at Samos, and who seems to have flourished between 540 and 500 B.C.; after travels in many lands settled at Crotona in Magna Græcia, where he founded a fraternity, the members of which bound themselves in closest ties of friendship to purity of life and to active co-operation in disseminating and encouraging a kindred spirit in the community around them, the final aim of it being the establishment of a model social organisation. He left no writings behind him, and we know of his philosophy chiefly from the philosophy of his disciples.