_Clo._ What is the opinion of Pythagoras concerning wild fowl? _Mal._ That the soul of our grandam might haply inhabit a bird.
It is observed in the golden verses of Pythagoras, that power is never far from necessity. The vigor of the human mind quickly appears when there is no longer any place for doubt and hesitation, when diffidence is absorbed in the sense of danger, or overwhelmed by some resistless passion.--_Johnson._
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.
In the time of Pythagoras that proverbial phrase "Ipse dixit" was introduced into ordinary life.
Remind yourself that all men assert that wisdom is the greatest good, but that there are few who strenuously seek out that greatest good.
Ipse dixit=--He himself (viz. Pythagoras) said it. Assertion without proof.
Oh! the metempsychosis! Oh! Pythagoras, that in bright Greece, two thousand years ago, did die, so good, so wise, so mild; I sailed with thee along the Peruvian coast last voyage--and, foolish as I am, taught thee, a green simple boy, how to splice a rope!
HIPPASUS OF METAPONTUM, Pythagorean philosopher, was one of the earliest of the disciples of Pythagoras. He is mentioned both by Diogenes Laërtius and by Iamblichus, but nothing is known of his life. Diogenes says that he left no writings, but other authorities make him the author of a [Greek: mystikos logos] directed against the Pythagoreans. According to Aristotle (_Metaphysica_, i. 3), he was an adherent of the Heraclitean fire-doctrine, whereas the Pythagoreans maintained the theory that number is the principle of everything. He seems to have regarded the soul as composed of igneous matter, and so approximates the orthodox Pythagorean doctrine of the central fire, or Hestia, to the more detailed theories of Heraclitus. In spite of this divergence, Hippasus is always regarded as a Pythagorean. Entry: HIPPASUS
Granting then that some foreign influence was at work in Essenism, we have four theories offered to us--that this influence was Persian, Buddhist, Pythagorean, or lastly, as maintained by Lipsius, that of the surrounding Syrian heathenism. Each of these views has had able advocates, but it must not be supposed that they are mutually exclusive. If we consider how Philo, while remaining a devout Jew in religion, yet managed to assimilate the whole Stoic philosophy, we can well believe that the Essenes might have been influenced, as Zeller maintained that they were, by Neo-Pythagoreanism. But as Pythagoras himself came from Samos, and his doctrines have a decidedly Oriental tinge, it may very well be that both he and the Essenes drew from a common source; for there is no need to reject, as is so commonly done, the statements of our authorities as to the antiquity of the Essenes. This common source we may believe with Lightfoot to have been the Persian religion, which we know to have profoundly influenced that of Israel, independently of the Essenes. Entry: ESSENES
A steady flow of knowledge from East to West began in the 7th century B.C. A Babylonian sage named Berossus founded a school about 640 B.C. in the island of Cos, and perhaps counted Thales of Miletus (c. 639-548) among his pupils. The famous "eclipse of Thales" in 585 B.C. has not, it is true, been authenticated by modern research;[9] yet the story told by Herodotus appears to intimate that a knowledge of the Saros, and of the forecasting facilities connected with it, was possessed by the Ionian sage. Pythagoras of Samos (fl. 540-510 B.C.) learned on his travels in Egypt and the East to identify the morning and evening stars, to recognize the obliquity of the ecliptic, and to regard the earth as a sphere freely poised in space. The tenet of its axial movement was held by many of his followers--in an obscure form by Philolaus of Crotona after the middle of the 5th century B.C., and more explicitly by Ecphantus and Hicetas of Syracuse (4th century B.C.), and by Heraclides of Pontus. Heraclides, who became a disciple of Plato in 360 B.C., taught in addition that the sun, while circulating round the earth, was the centre of revolution to Venus and Mercury.[10] A genuine heliocentric system, developed by Aristarchus of Samos (fl. 280-264 B.C.), was described by Archimedes in his _Arenarius_, only to be set aside with disapproval. The long-lived conception of a series of crystal spheres, acting as the vehicles of the heavenly bodies, and attuned to divine harmonies, seems to have originated with Pythagoras himself. Entry: A
Even 1000 years after this period, the dog was highly esteemed in Egypt for its sagacity and other excellent qualities; for when Pythagoras, after his return from Egypt, founded a new sect in Greece, and at Croton in southern Italy, he taught, with the Egyptian philosophers, that at the death of the body the soul entered into that of various animals. After the death of any of his favourite disciples he would hold a dog to the mouth of the man in order to receive the departing spirit, saying that there was no animal which could perpetuate his virtues better than that quadruped. It was in order to preserve the Israelites from errors and follies of this kind, and to prevent the possibility of such idolatry being established, that the dog was afterwards regarded with utter abhorrence amongst the Jews, and this feeling prevailed during the continuance of the Israelites in Palestine. Entry: DOG
With the overthrow of this dynasty tyranny disappears from Greece proper for more than a century. During the century and a half which had elapsed since its first appearance the whole aspect of Greek life, and of the Greek world, had changed. The development was as yet incomplete, but the lines on which it was to proceed had been clearly marked out. Political power was no longer the monopoly of a class. The struggle between the "few" and the "many" had begun; in one state at least (Athens) the victory of the "many" was assured. The first chapter in the history of democracy was already written. In the art of war the two innovations which were ultimately to establish the military supremacy of Greece, hoplite tactics and the trireme, had already been introduced. Greek literature was no longer synonymous with epic poetry. Some of its most distinctive forms had not yet been evolved; indeed, it is only quite at the end of the period that prose-writing begins; but both lyric and elegiac poetry had been brought to perfection. In art, statuary was still comparatively stiff and crude; but in other branches, in architecture, in vase-painting and in coin-types, the aesthetic genius of the race had asserted its pre-eminence. Philosophy, the supreme gift of Greece to the modern world, had become a living power. Some of her most original thinkers belong to the 6th century. Criticism had been applied to everything in turn: to the gods, to conduct, and to the conception of the universe. Before the Great Age begins, the claims of intellectual as well as of political freedom had been vindicated. It was not, however, in Greece proper that progress had been greatest. In the next century the centre of gravity of Greek civilization shifts to the western side of the Aegean; in the 6th century it must be looked for at Miletus, rather than at Athens. In order to estimate how far the development of Greece had advanced, or to appreciate the distinctive features of Greek life at this period, we must study Ionia, rather than Attica or the Peloponnese. Almost all that is greatest and most characteristic is to be found on the eastern side of the Aegean. The great names in the history of science and philosophy before the beginning of the 5th century--Thales, Pythagoras, Xenophanes, Heraclitus, Parmenides, Anaximander, Hecataeus; names which are representative of mathematics, astronomy, geography and metaphysics, are all, without exception, Ionian. In poetry, too, the most famous names, if not so exclusively Ionian, are connected either with the Asiatic coast or with the Cyclades. Against Archilochus and Anacreon, Sappho and Alcaeus, Greece has nothing better to set, after the age of Hesiod, than Tyrtaeus and Theognis. Reference has already been made to the greatness of the Ionians as navigators, as colonizers and as traders. In wealth and in population, Miletus, at the epoch of the Persian conquest, must have been far ahead of any city of European Greece. Sybaris, in Magna Graecia, can have been its only rival outside Ionia. There were two respects, however, in which the comparison was in favour of the mother-country. In warfare, the superiority of the Spartan infantry was unquestioned; in politics, the Greek states showed a greater power of combination than the Ionian. Entry: 4
As regards the attitude towards religious images assumed by the primitive Christian Church, several questions have often been treated as one which cannot be too carefully kept apart. There can be no doubt that the early Christians were unanimous in condemning heathen image-worship and the various customs, some immoral, with which it was associated. A form of iconolatry specially deprecated in the New Testament was the then prevalent adoration of the images of the reigning emperors (see Rev. xv. 2). It is also tolerably certain that, if for no other reasons besides the Judaism, obscurity, and poverty of the early converts to Christianity, the works of art seen in their meeting-houses cannot at first have been numerous. Along with these reasons would co-operate towards the exclusion of visible aids to devotion, not only the church's sacramental use of Christ's name as a name of power, and its living sense of his continued real though unseen presence, but also, during the first years, its constant expectation of his second advent as imminent. It was a common accusation brought against Jews and Christians that they had "no altars, no temples, no known images" (Min. Fel. _Oct._ c. 10), that "they set up no image or form of any god" (see Arnob. _Adv. Gent._ vi. I; similarly Celsus); and this charge was never denied; on the contrary Origen gloried in it (_c. Celsum_, bk. 7, p. 386). At a comparatively early date, indeed, we read of various Gnostic sects calling in the fine arts to aid their worship; thus Irenaeus (_Haer._ i. 25. 6), speaking of the followers of Marcellina, says that "they possess images, some of them painted, and others formed from different kinds of material; and they maintain that a likeness of Christ was made by Pilate at that time when Jesus lived among men. They crown these images, and set them up along with the images of the philosophers of the world; that is to say, with the images of Pythagoras and Plato and Aristotle and the rest. They have also other modes of honouring these images after the same manner as the Gentiles" (cf. Aug. _De Haer._ c. 7). It is also well known that the emperor Alexander Severus found a place for several Scripture characters and even for Christ in his lararium (Lamprid. _Vit. Alex. Sev._ c. 29). But there is no evidence that such a use of images extended at that period to orthodox Christian circles. The first unmistakable indication of the public use of the painter's art for directly religious ends does not occur until A.D. 306, when the synod of Elvira, Spain, decreed (can. 36) that "pictures ought not to be in a church, lest that which is worshipped and adored be painted on walls."[1] This canon is proof that the use of sacred pictures in public worship was not at the beginning of the 4th century a thing unknown within the church in Spain; and the presumption is that in other places, about the same period, the custom was looked upon with a more tolerant eye. Indications of the existence of allied forms of sacred Christian art prior to this period are not wholly wanting. It seems possible to trace some of the older and better frescos in the catacombs to a very early age; and Bible manuscripts were often copiously illuminated and illustrated even before the middle of the 4th century. An often-quoted passage from Tertullian (_De Pudic._ c. 10, cf. c. 7) shows that in his day the communion cup was wont to bear a representation of the Good Shepherd. Clement of Alexandria (_Paedag._ iii. 11) mentions the dove, fish, ship, lyre, anchor, as suitable devices for Christian signet rings. Origen (c. _Celsum_, bk. 3) repudiates graven images as only fit for demons. Entry: ICONOCLASTS
the octave scale attributed to Pythagoras, was admitted, to preserve the time-honoured seven strings one note had to be omitted; it was therefore customary to omit the C, which in Greek practice was a dissonance. The Greek names for the strings of seven and eight stringed lyres, the first note being highest in pitch and nearest the player, were as follows: _Nete_, _Paranete_, _Paramese_; _Mese_, _Lichanos_, _Parhypate_, _Hypate_; or _Nete_, _Paranete_, _Trite_, _Paramese_; _Mese_, _Lichanos_, _Parhypate_, _Hypate_--the last four from Mese to Hypate being the finger tetrachord, the others touched with the plectrum. The highest string in pitch was called the last, [Greek: neate]; the lowest in pitch was called the highest, [Greek: hypate], because it was, in theory at least, the longest string. The keynote and thumb string was [Greek: mese], middle; the next lower was [Greek: lichanos], the first finger or lick-finger string; [Greek: trite], the third, being in the plectrum division, was also known as [Greek: oxeia], sharp, perhaps from the dissonant quality to which we have referred as the cause of its omission. The plectrum and finger tetrachords together were [Greek: diapason], through all; in the disjunct scale, an octave. Entry: FIG
The best edition is by Paul Marquard, with German translation and full commentary, _Die harmonischen Fragmente des Aristoxenus_ (Berlin, 1868). The fragments are also given in C.W. Müller, _Frag. Hist. Graec._, ii. 269 sqq.; and R. Westphal, _Melik und Rhythmik d. klass. Hellenenthums_ (2nd vol. edited by F. Saran, Leipzig, 1893). Eng. trans. by H.S. Macran (Oxford, 1902). See also W.L. Mahne, _Diatribe de Aristoxeno_ (Amsterdam, 1793); B. Brill, _Aristoxenus' rhythmische und metrische Messungen_ (1871); R. Westphal, _Griechische Rhythmik und Harmonik_ (Leipzig, 1867); L. Laloy, _Aristoxène de Tarente et la musique de l'antiquité_ (Paris, 1904); See PERIPATETICS, PYTHAGORAS (_Music_) and art. "Greek Music" in Grove's _Dict. of Music_ (1904). For the Oxyrhynchus fragment see _Classical Review_ (January 1898), and C. van Jan in Bursian's _Jahresbericht_, civ. (1901). Entry: ARISTOXENUS
A. _Greek and Graeco-Roman Ethics._--The ethical speculation of Greece, and therefore of Europe, had no abrupt and absolute beginning. The naive and fragmentary precepts of conduct, which are everywhere the earliest manifestation of nascent moral reflection, are a noteworthy element in the gnomic poetry of the 7th and 6th centuries B.C. Their importance is shown by the traditional enumeration of the Seven Sages of the 6th century, and their influence on ethical thought is attested by the references of Plato and Aristotle. But from these unscientific utterances to a philosophy of morals was a long process. In the practical wisdom of Thales (q.v.), one of the seven, we cannot discern any systematic theory of morality. In the case of Pythagoras, conspicuous among pre-Socratic philosophers as the founder not merely of a school, but of a sect or order bound by a common rule of life, there is a closer connexion between moral and metaphysical speculation. The doctrine of the Pythagoreans that the essence of justice (conceived as equal retribution) was a square number, indicates a serious attempt to extend to the region of conduct their mathematical view of the universe; and the same may be said of their classification of good with unity, straightness and the like, and of evil with the opposite qualities. Still, the enunciation of the moral precepts of Pythagoras appears to have been dogmatic, or even prophetic, rather than philosophic, and to have been accepted by his disciples with an unphilosophic reverence as the _ipse dixit_[1] of the master. Hence, whatever influence the Pythagorean blending of ethical and mathematical notions may have had on Plato, and, through him, on later thought, we cannot regard the school as having really forestalled the Socratic inquiry after a completely reasoned theory of conduct. The ethical element in the "dark" philosophizing of Heraclitus (c. 530-470 B.C.), though it anticipates Stoicism in its conceptions of a law of the universe, to which the wise man will carefully conform, and a divine harmony, in the recognition of which he will find his truest satisfaction, is more profound, but even less systematic. It is only when we come to Democritus, a contemporary of Socrates, the last of the original thinkers whom we distinguish as pre-Socratic, that we find anything which we can call an ethical system. The fragments that remain of the moral treatises of Democritus are sufficient, perhaps, to convince us that the turn of Greek philosophy in the direction of conduct, which was actually due to Socrates, would have taken place without him, though in a less decided manner; but when we compare the Democritean ethics with the post-Socratic system to which it has most affinity, Epicureanism, we find that it exhibits a very rudimentary apprehension of the formal conditions which moral teaching must fulfil before it can lay claim to be treated as scientific. Entry: A
CUSP (Lat. _cuspis_, a spear, point), a projecting point, or pointed end. In architecture (Fr. _feuille_, Ital. _cuspide_, Ger. _Knöpfe_), a cusp is the point where the foliations of tracery intersect. The earliest example of a plain cusp is probably that at Pythagoras school, at Cambridge,--of an ornamented cusp at Ely cathedral, where a small roll, with a rosette at the end, is formed at the termination of a cusp. In the later styles the terminations of the cusps were more richly decorated; they also sometimes terminate not only in leaves or foliages, but in rosettes, heads and other fanciful ornaments. The term "feathering" is used of the junction of the foliated cusps in window tracery, but is usually restricted to those cases where it is ornamented with foliage, &c. Entry: CUSP
The method of estimating the area of irregular fields and the cubic contents of granaries, &c., is very faulty. It would be interesting to find material of later date, such as Pythagoras is reported to have studied. Entry: III
In transcribing the Greek notes into our notation, the absolute pitch cannot be represented; the relative positions of the semitones are alone determined. We have already quoted the scale of Pythagoras, the Dorian or true Greek succession:-- Entry: FIG
AURISPA, GIOVANNI (c. 1370-1459), one of the learned Italians of the 15th century, who did so much to promote the revival of the study of Greek in Italy, was born at Noto in Sicily. In 1418 he visited Constantinople, where he remained for some years, perfecting his knowledge of Greek and searching for ancient MSS. His efforts were rewarded by the acquisition of some 250 MSS., with which he returned to Venice. Here he is said to have been obliged to pawn his treasures for 50 gold florins to provide for his immediate wants. Cosimo de' Medici, hearing of his embarrassment, redeemed the MSS. and summoned the owner to Florence. In 1438, at the council of Basel, Aurispa attracted the attention of Pope Eugenius IV., who made him his secretary; he held a similar position under Nicholas V., who presented him to two lucrative abbacies. He died at Ferrara. Considering his long life and reputation Aurispa produced little: Latin translations of the commentary of Hierocles on the golden verses of Pythagoras (1474) and of _Philisci Consolatoria ad Ciceronem_ from Dio Cassius (not published till 1510); and, according to Gesner, a translation of the works of Archimedes. Aurispa's reputation rests upon the extensive collection of MSS. copied and distributed by him, and his persistent efforts to revive and promote the study of ancient literature. Entry: AURISPA
We see from a statement of Cassiodorus that he furnished manuals for the quadrivium of the schools of the middle ages (the "quattuor matheseos disciplinae," as Boetius calls them) on arithmetic, music, geometry and astronomy. The statement of Cassiodorus that he translated Nicomachus is rhetorical. Boetius himself tells us in his preface addressed to his father-in-law Symmachus that he had taken liberties with the text of Nicomachus, that he had abridged the work when necessary, and that he had introduced formulae and diagrams of his own where he thought them useful for bringing out the meaning. His work on music also is not a translation from Pythagoras, who left no writing behind him. But Boetius belonged to the school of musical writers who based their science on the method of Pythagoras. They thought that it was not sufficient to trust to the ear alone, to determine the principles of music, as did practical musicians like Aristoxenus, but that along with the ear, physical experiments should be employed. The work of Boetius is in five books and is a very complete exposition of the subject. It long remained a text-book of music in the universities of Oxford and Cambridge. It is still very valuable as a help in ascertaining the principles of ancient music, and gives us the opinions of some of the best ancient writers on the art. The manuscripts of the geometry of Boetius differ widely from each other. One editor, Godofredus Friedlein, thinks that there are only two manuscripts which can at all lay claim to contain the work of Boetius. He published the _Ars Geometriae_, in two books, as given in these manuscripts; but critics are generally inclined to doubt the genuineness even of these. Professor Rand, Georgius Ernst and A.P. McKinlay regard the _Ars_ as certainly inauthentic, while they accept the _Interpretatio Euclidis_ (see works quoted in bibliography). Entry: BOETIUS
As his history is uncertain, so his doctrines are hard to put together. He does not belong to any one definite school. While, on one hand, he combines much that had been suggested by Parmenides, Pythagoras and the Ionic schools, he has germs of truth that Plato and Aristotle afterwards developed; he is at once a firm believer in Orphic mysteries, and a scientific thinker, precursor of the physical scientists. There are, according to Empedocles, four ultimate elements, four primal divinities, of which are made all structures in the world--fire, air, water, earth. These four elements are eternally brought into union, and eternally parted from each other, by two divine beings or powers, love and hatred--an attractive and a repulsive force which the ordinary eye can see working amongst men, but which really pervade the whole world. According to the different proportions in which these four indestructible and unchangeable matters are combined with each other is the difference of the organic structure produced; e.g. flesh and blood are made of equal (in weight but not in volume) parts of all four elements, whereas bones are one-half fire, one-fourth earth, and one-fourth water. It is in the aggregation and segregation of elements thus arising that Empedocles, like the atomists, finds the real process which corresponds to what is popularly termed growth, increase or decrease. Nothing new comes or can come into being; the only change that can occur is a change in the juxtaposition of element with element. Entry: EMPEDOCLES
LYSIS OF TARENTUM (d. c. 390 B.C.), Greek philosopher. His life is obscure, but it is generally accepted, that in the persecution of the Pythagoreans at Crotona and Metapontum he escaped and went to Thebes, where he came under the influence of Philolaus. The friend and companion of Pythagoras, he has been credited with many of the works usually attributed to Pythagoras himself. Diogenes Laertius viii. 6 gives him three, and Mullach even assigns to him the _Golden Verses_. But it is generally held that these verses are a collection of lines by many authors rather than the work of one man. Entry: LYSIS
APOLLONIUS OF TYANA, a Greek philosopher of the Neo-Pythagorean school, born a few years before the Christian era. He studied at Tarsus and in the temple of Asclepius at Aegae, where he devoted himself to the doctrines of Pythagoras and adopted the ascetic habit of life in its fullest sense. He travelled through Asia and visited Nineveh, Babylon and India, imbibing the oriental mysticism of magi, Brahmans and gymnosophists. The narrative of his travels given by his disciple Damis and reproduced by Philostratus is so full of the miraculous that many have regarded him as an imaginary character. On his return to Europe he was saluted as a magician, and received the greatest reverence from priests and people generally. He himself claimed only the power of foreseeing the future; yet in Rome it was said that he raised from death the body of a noble lady. In the halo of his mysterious power he passed through Greece, Italy and Spain. It was said that he was accused of treason both by Nero and by Domitian, but escaped by miraculous means. Finally he set up a school at Ephesus, where he died, apparently at the age of a hundred years. Philostratus keeps up the mystery of his hero's life by saying, "Concerning the manner of his death, _if he did die_, the accounts are various." The work of Philostratus composed at the instance of Julia, wife of Severus, is generally regarded as a religious work of fiction. It contains a number of obviously fictitious stories, through which, however, it is not impossible to discern the general character of the man. In the 3rd century, Hierocles (q.v.) endeavoured to prove that the doctrines and the life of Apollonius were more valuable than those of Christ, and, in modern times, Voltaire and Charles Blount (1654-1693), the English freethinker, have adopted a similar standpoint. Apart from this extravagant eulogy, it is absurd to regard Apollonius merely as a vulgar charlatan and miracle-monger. If we cut away the mass of mere fiction which Philostratus accumulated, we have left a highly imaginative, earnest reformer who laboured to infuse into the flaccid dialectic of paganism a saner spirit of practical morality. Entry: APOLLONIUS