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pended on seems to have been derived from the writings of Philolaus and Archytas, especially the former (Ritter, l.c. p. 62, &c.). On the philosophy of Archytas Aristotle had composed a treatise in three books, which has unfortunately perished, and had instituted a comparison between his doctrines and those of the Timaeus of Plato (Athen. xii. 12; Diog. Laert. v. 25). Pythagoras resembled greatly the philosophers of what is termed the Ionic school, who undertook to solve by means of a single primordial principle the vague problem of the origin and constitution of the universe as a whole. But, like Anaximander, he abandoned the physical hypotheses of Thales and Anaximenes, and passed from the province of physics to that of metaphysics, and his predilection for mathematical studies led him to trace the origin of all things to number, this theory being suggested, or at all events confirmed, by the ob: servation of various numerical relations, or analogies to them, in the phenomena of the universe. “Since of all things numbers are by nature the first, in numbers they (the Pythagoreans) thought they perceived many analogies to things that exist and are produced, more than in fire, and earth, and water; as that a certain affection of numbers was justice; a certain other affection, soul and intellect; another, opportunity ; and of the rest, so to say, each in like manner; and moreover, seeing the affections and ratios of what pertains to harmony to consist in numbers, since other things seemed in their entire nature to be formed in the likeness of numbers, and in all nature numbers are the first, they supposed the elements of numbers to be the elements of all things” (Arist, Met. i. 5, comp. especially Met. xiii. 3). Brandis, who traces in the notices that remain more than one system, developed by different Pythagoreans, according as they recognised in numbers the inherent basis of things, or only the patterns of them, considers that all started from the common conviction that it was in numbers and their relations that they were to find the absolutely certain principles of knowledge (comp. Philolaus, ap. Stob. Ecl. Phys. i. p. 458; Böckh, Philolaos, p. 62; Stob. l.c. i. p. 10; Böckh, l.c. p. 145, Weddos ow8auds is doubudy érimwel d 6' d'Aéðela oiketov kai a supwrov to două, Yevså), and of the objects of it, and accordingly regarded the principles of numbers as the absolute principles of things; keeping true to the common maxim of the ancient philosophy, that like takes cognisance of like (kaflárep &Aeye kal 6 buwó. Aaos, Sewpmruków re Swra (Töv A6 yov Tów drö täv Maomudrav repryevduevow) ris Táv čaw poorews #xelv rivá ovyyávelav trpos tarny, restep Urd toū duotov to duowv karaxauéávea 6al. Sext. Emp. ade. Math. vii. 92; Brandis, l.c. p. 442). Aristotle states the fundamental maxim of the Pythagoreans in various forms, as, paivovrai Si) kal oirot Tov detouav voussovres doxov elva kai as tany rols oval kal as tra6m Te Rai #ets (Met. i. 5); or, röv dolôuðv elva, row ovariav dirávrov (ibid. p. 987. 19, ed. Bekker); or, toos dpiðuous airious elva, tois àAAous ris ovoias (Met. i. 6. p. 987. 24); nay, even that numbers are things themselves (Ibid. p. 987. 28). According to Philolaus (Syrian. in Arist. Met. xii. 6. p. 1080, b. 16), number is the “dominant and self-produced bond of the eternal continuance of things.” But number has two forms (as Philolaus terms them, ap. Stob. l, c. p. 456; Böckh, l.c. p. 58), or elements (Arist.

Met. i. 5), the even and the odd, and a third, resulting from the mixture of the two, the even-odd (dpriorépurgov, Philol. l.c.). This third species is one itself, for it is both even and odd (Arist. l. c. Another explanation of the dpriorépidoow, which accords better with other notices, is that it was an even number composed of two uneven numbers. Brandis, l.c. p. 465, &c.). One, or unity, is the essence of number, or absolute number, and so comprises these two opposite species. As absolute number it is the origin of all numbers, and so of all things. (Arist. Met. xiii. 4. *w dexa wdvtwo ; Philol. ap. Böckh, Ś 19. According to another passage of Aristotle, Met. xii. 6. p. 1080, b. 7, number is produced ex tou-ov Tov čvás— kal &AAov twos.) This original unity they also termed God (Ritter, Gesch. der Phil. vol. i. p. 389). These propositions, however, would, taken alone, give but a very partial idea of the Pythagorean system. A most important part is played in it by the ideas of limit, and the unlimited. They are, in fact, the fundamental ideas of the whole. One of the first declarations in the work of Philolaus [Philolaus] was, that all things in the universe result from a combination of the unlimited and the limiting (pians 3e év to kórup dpudzøm & dreipw te kal repavóvtwv, kai ÖAos Káguos kal ov aúró révra. Diog. Laërt. viii. 85; Böckh, p. 45); for if all things had been unlimited, nothing could have been the object of cognizance (Phil. l.c.; Böckh, p. 49). From the unlimited were deduced immediately time, space, and motion (Stob. Ecl. Phys. p. 380; Simplic. in Arist. Phys. f. 98, b.; Brandis, l.c. p. 451). Then again, in some extraordinary manner they connected the ideas of odd and even with the contrasted notions of the limited and the unlimited, the odd being limited, the even unlimited (Arist. Met. i. 5, p. 986. a. 18, Bekker, comp. Phys. A usc. iii. 4, p. 203. 10, Bekker). They called the even unlimited, because in itself it is divisible into equal halves ad infinitum, and is only limited by the odd, which, when added to the even, prevents the division (Simpl. ad Arist. Phys. Ausc. iii. 4. f. 105; Brandis, p. 450, note). Limit, or the limiting elements, they considered as more akin to the primary unity (Syrian. in Arist. Mel. xiii. 1). In place of the plural expression of Philolaus (ra repaivovra) Aristotle sometimes uses the singular répas, which, in like manner, he connects with the unlimited (tò are pov. Met. i. 8, p. 990, l. 8, xiii. 3. p. 1091, l. 18, ed. Bekk.). But musical principles played almost as important a part in the Pythagorean system as mathematical or numerical ideas. The opposite principia of the unlimited and the limiting are, as Philolaus expresses it (Stob. l.c. p. 458; Böckh, i.e. p. 62), “neither alike, nor of the same race, and so it would have been impossible for them to unite, had not harmony stepped in.” This harmony, again, was, in the conception of Philolaus, neither more nor less than the octave (Brandis, l.c. p. 456). On the investigation of the various harmonical relations of the octave, and their connection with weight, as the measure of tension, Philolaus bestowed considerable attention, and some important fragments of his on this subject have been preserved, which Böckh has carefully examined (l.c. p. 65–89, comp. Brandis, l.c. p. 457, &c.). We find running through the entire Pythagorean system the idea that order, or harmony of relation, is the regulating principle of the whole universe. Some of the Pythagoreans (but by no means all, as it appears) drew out a list of ten pairs of opposites, which they termed the elements of the universe. (Arist. Met. i. 5. Elsewhere he speaks as if the Pythagoreans generally did the same, Eth. Nic, i. 4, ii. 5.) These pairs were —

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Limit and the Unlimited.

Odd and Even.

One and Multitude.

Right and Left.

Male and Female.

Stationary and Moved.

Straight and Curved.

Light and Darkness.

Good and Bad.

Square and Oblong.

The first column was that of the good elements (Arist. Eth. Nic. i. 4): the second, the row of the bad. Those in the second series were also regarded as having the character of negation (Arist. Phys. iii. 2). These, however, are hardly to be looked upon as ten pairs of distinct principles. They are rather various modes of conceiving one and the same opposition. One, Limit and the Odd, are spoken of as though they were synonymous (comp. Arist. Met. i. 5, 7, xiii. 4, Phys. iii. 5).

o explain the production of material objects out of the union of the unlimited and the limiting, Ritter (Gesch. der Pyth. Phil. and Gesch. der Phil. vol. i. p. 403, &c.) has propounded a theory which has great plausibility, and is undoubtedly much the same as the view held by later Pythagorizing mathematicians; namely, that the éteipov is neither more nor less than void space, and the repaivovta points in space which bound ordefine it (which points he affirms the Pythagoreans called monads or units, appealing to Arist. de Caelo, iii. 1; comp. Alexand. Aphrod. quoted below), the point being the dpxi or principium of the line, the line of the surface, the surface of the solid. Points, or monads, therefore are the source of material existence; and as points are monads, and monads numbers, it follows that numbers are at the base of material existence. (This is the view of the matter set forth by Alexander Aphrodisiensis in Arist, de prim. Phil. i. fol. 10, b.; Ritter, l.c. p. 404, note 3.) Ecphantus of Syracuse was the first who made the Pythagorean monads to be corporeal, and set down indivisible particles and void space as the principia of material existence. (See Stob. Ecl. Phys. p. 308.) Two geometrical points in themselves would have no magnitude; it is only when they are combined with the intervening space that a line can be produced. The union of space and lines makes surfaces; the union of surfaces and space makes solids. Of course this does not explain very well how corporeal substance is formed, and Ritter thinks that the Pythagoreans perceived that this was the weak point of their system, and so spoke of the direpov, as mere void space, as little as they could help, and strove to represent it as something positive, or almost substantial.

But however plausible this view of the matter may be, we cannot understand how any one who compares the very numerous passages in which Aristotle speaks of the Pythagoreans, can suppose that his notices have reference to any such system. The theory which Ritter sets down as that of the

Pythagoreans is one which Aristotle mentions several times, and shows to be inadequate to account for the physical existence of the world, but he nowhere speaks of it as the doctrine of the Pythagoreans. Some of the passages, where Ritter tries to make this out to be the case, go to prove the very reverse. For instance, in De Caelo, iii. 1, after an elaborate discussion of the theory in question, Aristotle concludes by remarking that the number-theory of the Pythagoreans will no more account for the production of corporeal magnitude, than the point-line-and-space-theory which he has just described, for no addition of units can produce either body or weight (comp. Met. xiii. 3). Aristotle nowhere identifies the Pythagorean monads with mathematical points; on the contrary, he affirms that in the Pythagorean system, the monads, in some way or other which they could not explain, got magnitude and extension (Met. xii. 6, p. 1080, ed. Bekker). The kevöv again, which Aristotle mentions as recognised by the Pythagoreans, is never spoken of as synonymous with their àrepov; on the contrary we find (Stoh. Eel. Phys. i. p. 380) that from the firepov they deduced time, breath, and void space. The frequent use of the term répas, too, by Aristotle, instead of repaivovta, hardly comports with Ritter's theory. There can be little doubt that the Pythagorean system should be viewed in connection with that of Anaximander, with whose doctrines Pythagoras was doubtless conversant. Anaximander, in his attempt to solve the problem of the universe, passed from the region of physics to that of metaphysics. He supposed “a primaeval principle without any actual determining qualities whatever; but including all qualities potentially, and manifesting them in an infinite variety from its continually self-changing nature; a principle which was nothing in itself, yet had the capacity of producing any and all manifestations, however contrary to each other—a primaeval something, whose essence it was to be eternally productive of different phaenomena” (Grote, l.c. p. 518; comp. Brandis, l.c. p. 123, &c.). This he termed the ārepov; and he was also the first to introduce the term dox: (Simplic. in Arist. Phys. fol. 6, 32). Both these terms hold a prominent position in the Pythagorean system, and we think there can be but little doubt as to their parentage. The Pythagorean êmepov seems to have been very nearly the same as that of Anaximander, an undefined and infinite something. Only instead of investing it with the property of spontaneously developing itself in the various forms of actual material existence, they regarded all its definite manifestations as the determination of its indefiniteness by the definiteness of number, which thus became the cause of all actual and positive existence (rods doubuous airious elval toss 4AAois tims ovarias, Arist. Met. i. 6). It is by numbers alone, in their view, that the objective becomes cognisable to the subject; by numbers that extension is originated, and attains to that definiteness by which it becomes a concrete body. As the ground of all quantitative and quali. tative definiteness in existing things, therefore, number is represented as their inherent element, or even as the matter (JAm), as well as the passive and active condition of things (Arist. Met. i. 5). But both the repaivovra and the direpov are referred to a higher unity, the absolute or divine unity. And in this aspect of the matter Aristotle speaks of unity as the principium and essence and element of all things (Met. xii. 6, i. 6, p. 987, b. 22); the divine unity being the first principle and cause, and one, as the first of the limiting numbers and the element of all, being the basis of positive existence, and when itself become possessed of extension (Met. xii. 3, p. 1091, a. 15) the element of all that possesses extension (comp. Brandis, l.c. p. 51.1, &c.). In its development, however, the Pythagorean system seems to have taken a twofold direction, one school of Pythagoreans regarding numbers as the inherent, fundamental elements of things (Arist. de Caelo, iii. 1); another section, of which Hippasus seems to have been the head, regarding numbers as the patterns merely, but not as entering into the essence of things (Arist. Met. i. 6. Though Aristotle speaks of the Pythagoreans generally here, there can be no doubt that the assertion, in which the Greek commentators found a difficulty, should be restricted to a section of the Pythagoreans. Comp. Iambl. in Nicom. Arithm. p. 11; Syrian. in Arist. Met. xii. p. 1080, b. 18 ; Simplic. in Phys. f. 104, b. ; Iambl. Pyth. 81; Stob. Ecl. Phys. p. 302; Brandis, l.c. p. 444). As in the octave and its different harmonical A relations, the Pythagoreans found the ground of connection between the opposed primary elements, and the mutual relations of existing things, so in the properties of particular numbers, and their relation to the principia, did they attempt to find the explanation of the particular properties of different things, and therefore addressed themselves to the investigation of the properties of numbers, dividing them into various species. Thus they had three kinds of even, according as the number was a power of two (dpriákis priov), or a multiple of two, or of some power of two, not itself a power of two (reptoodpriov), or the sum of an odd and an even number (dpriorépittov—a word which seems to have been used in more than one sense. Nicom. Arithm. i. 7, 8). In like manner they had three kinds of odd. It was probably the use of the decimal system of notation which led to the number ten being supposed to be possessed of extraordinary powers. “One must contemplate the works and essential nature of number according to the power which is in the number ten; for it is great, and perfect, and all-working, and the first principle (dpxã) and guide of divine and heavenly and human life.” (Philolaus ap. Stob. Eel. Phys. p. 8; Böckh, p. 139.) This, doubtless, had to do with the formation of the list of ten pairs of opposite principles, which was drawn out by some Pythagoreans (Arist. Met. i. 5). In like manner the tetractys (possibly the sum of the first four numbers, or 10) was described as containing the source and root of ever-flowing nature (Carm. Aur. 1. 48). The number three was spoken of as defining or limiting the universe and all things, having end, middle, and beginning, and so being the number of the whole (Arist. de Caelo, i. 1). This part of their system they seem to have helped out by considerations as to the connection of numbers with lines, surfaces, and solids, especially the regular geometrical figures (Theolog. Arithm. 10, p. 61, &c.), and to have connected the relations of things with various geometrical relations, among which angles played an important part. Thus, according to Philolaus, the angle of a triangle was conse

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crated to four deities, Kronos, Hades, Pan, and Dionysus; the angle of a square to Rhea, Demeter, and Hestia; the angle of a dodecagon to Zeus; apparently to shadow forth the sphere of their operations (Procl. in Euclid. Een. i. p. 36; Böckh, l.c. p. 152, &c.). As we learn that he connected solid extension with the number four (Theol. Arithm. p. 56), it is not unlikely that, as others did (Nicom. Arithm. ii. 6), he connected the number one with a point, two with a line, three with a surface (Xpoiá). To the number fire he appropriated quality and colour; to sir life ; to seven intelligence, health, and light; to eight love, friendship, understanding, insight (Theol. Arithm. l. c.). Others connected marriage, justice, &c. with different numbers (Alex. in Arist. Met. i. 5, 13). Guided by similar fanciful analogies they assumed the existence of five elements, connected with geometrical figures, the cube being earth; the pyramid, fire; the octaedron, air; the eikosaedron, water; the dodecaedron, the fifth element, to which Philolaus gives the curious appellation of 3 tãs ordaipas 6Akås (Stob. l.c. i. p. 10; Böckh, l. c. p. 161 ; comp. Plut. de Plac. Phil. ii. 6). In the Pythagorean system the element fire was the most dignified and important. It accordingly occupied the most honourable position in the universe—the extreme (Trépas), rather than intermediate positions; and by cartreme they understood both the centre and the remotest region (to 5’ égyarov kal to uéorov Trépas, Arist. de Caelo, ii. 13). The central fire Philolaus terms the hearth of the universe, the house or watch-tower of Zeus, the mother of the gods, the altar and bond and measure of nature (Stob. l.c. p. 488; Böckh, l.c. p. 94, &c.). It was the enlivening principle of the universe. By this fire they probably understood something purer and more ethereal than the common element fire (Brandis, l.c. p. 491). Round this central fire the heavenly bodies performed their circling dance (xopečev is the expression of Philolaus); — farthest off, the sphere of the fixed stars; then, in order, the five planets, the sun, the moon, the earth and the counter-earth (dvtoz8ww.) —a sort of other half of the earth, a distinct body from it, but always moving parallel to it, which they seem to have introduced merely to make up the number ten. The most distant region, which was at the same time the purest, was termed Olympus (Brandis, l.c. p. 476). The space between the heaven of the fixed stars and the moon was termed káouos ; the space between the moon and the earth oùpavés (Stob. l.c.). Philolaus assumed a daily revolution of the earth round the central fire, but not round its own axis. The revolution of the earth round its axis was taught (after Hicetas of Syracuse ; see Cic. Acad. iv. 39) by the Pythagorean Ecphantus and Heracleides Ponticus (Plut. Plac. iii. 13; Procl. in Tim. p. 281): a combined motion round the central fire and round its own axis, by Aristarchus of Samos (Plut. de Fac. Lun. p. 933). The infinite (direpov) beyond the mundane sphere was, at least according to Archytas (Simpl. in Phys. f. 108), not void space, but corporeal. The physical existence of the universe, which in the view of the Pythagoreans was a huge sphere (Stob. l.c. p. 452,468), was represented as a sort of vital process, time, space, and breath (tvori) being, as it were, inhaled out of the été pov (èrstaåyerúa 3’ &K too dreipov xpóvov te ka? Tvojv kal to keväv, Stob. l.c. p. 380; see espccially Arist. Phys. Ausc. iv. 6; Brandis, l.c. p. 476).

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The intervals between the heavenly bodies were supposed to be determined according to the laws and relations of musical harmony (Nicom. Harm. i. p. 6, ii. 33; Plin. H. N. ii. 20; Simpl. in Arist. de Caelo Schol. p. 496, b. 9, 497. 11). Hence arose the celebrated doctrine of the harmony of the spheres; for the heavenly bodies in their motion could not but occasion a certain sound or note, depending on their distances and velocities; and as these were determined by the laws of harmonical intervals, the notes altogether formed a regular musical scale or harmony. This harmony, however, we do not hear, either because we have been accustomed to it from the first, and have never had an opportunity of contrasting it with stillness, or because the sound is so powerful as to exceed our capacities for hearing (Arist. de Caelo, ii. 9; Porph. in Harm. Ptol. 4. p. 257). With all this fanciful hypothesis, however, they do not seem to have neglected the observation of astronomical phaenomena (Brandis, l.c. p. 481).

Perfection they seemed to have considered to exist in direct ratio to the distance from the central fire. Thus the moon was supposed to be inhabited by more perfect and beautiful beings than the earth (Plut. de Plac. Phil. ii. 30 ; Stob. l.c. i. p. 562; Böckh, l.c. p. 131). Similarly imperfect virtue belongs to the region of the earth, perfect wisdom to the kéguos ; the bond or symbol of connection again being certain numerical relations (comp. Arist. Met. i. 8; Alex. Aphrod. in Arist. Met. i. 7, fol. 14, a.). The light and heat of the central fire are received by us mediately through the sun (which, according to Philolaus, is of a glassy nature, acting as a kind of lens, or sieve, as he terms it, Böckh, l.c. p. 124; Stob. l.c. i. 26; Euseb. Praep. Evang. xv. 23), and the other heavenly bodies. All things partake of life, of which Philolaus distinguishes four grades, united in man and connected with successive parts of the body, — the life of mere seminal production, which is common to all things; vegetable life; animal life; and intellect or reason (Theol. Arithm. 4, p. 22; Böckh, p. 159.) It was only in reference to the principia, and not absolutely in point of time, that the universe is a production; the development of its existence, which was perhaps regarded as an unintermitting process, commencing from the centre (Phil. ap. Stob. l.c. p. 360; Böckh, p. 90, &c.; Brandis, p. 483); for the universe is “imperishable and unwearied ; it subsists for ever; from eternity did it exist and to eternity does it last, one, controlled by one akin to it, the mightiest and the highest.” (Phil, ap. Stob. Ecl. Phys. p. 418, &c.; Böckh, p. 164, &c.) This Deity Philolaus elsewhere also speaks of as one, eternal, abiding, unmoved, like himself (Böckh, p. 151). He is described as having established both limit and the infinite, and was often spoken of as the absolute unity; always represented as pervading, though distinct from, and presiding over the universe: not therefore a mere germ of vital development, or a principium of which the universe was itself a manifestation or development ; sometimes termed the absolute good (Arist. Met. xiii. 4, p. 1091, b. 13, Bekker), while, according to others, good could belong-only to concrete existences (Met. xi. 7, p. 1072, b. 31). The origin of evil was to be looked for not in the deity, but in matter, which pre

vented the deity from conducting every thing to the best end (Theophr. Met. 9. p. 322, 14). With the popular superstition they do not seem to have interfered, except in so far as they may have reduced the objects of it, as well as all other existing beings, to numerical elements. (Plut. de Is... et 0s. 10; Arist. Met. xiii. 5.) It is not clear whether the all-pervading soul of the universe, which they spoke of, was regarded as identical with the Deity or not (Cic. de Nat. Deor. i. 11). It was perhaps nothing more than the ever-working energy of the Deity (Stob. p. 422; Brandis, p. 487, note n). It was from it that human souls were derived (Cie. de Nat. Deor. i. 11, de Sen. 21). The soul was also frequently described as a number or harmony (Plut. de Plac. iv.2; Stob. Eel. Phys. p. 862; Arist. de An. i. 2, 4); hardly, however, in the same sense as that unfolded by Simmias, who had heard Philolaus, in the Phaedo of Plato (p. 85, &c.), with which the doctrine of metempsychosis would have been totally inconsistent. Some held the curious idea, that the particles floating as motes in the sunbeams were souls (Arist. de An. i. 2). In so far as the soul was a principle of hise, it was supposed to partake of the nature of the central fire (Diog. Laërt. viii. 27, &c.). There is, however, some want of uniformity in separating or identifying the soul and the principle of life, as also in the division of the faculties of the soul itself. Philolaus distinguished soul ($vyā) from spirit or reason (vods, Theol. Arith. p. 22 ; Böckh, p. 149; Diog. Laërt. viii. 30, where ppéves is the term applied to that which distinguishes men from animals, vows and 3vués residing in the latter likewise). The division of the soul into two elements, a rational and an irrational one (Cic. Tusc. iv. 5), comes to much the same point. Even animals, however, have a germ of reason, only the defective organisation of their body, and their want of language, prevents its development (Plut. de Plac. v. 20). The Pythagoreans connected the five senses with their five elements (Theol. Arith. p. 27 ; Stob. l.c. p. 1104). In the senses the soul found the necessary instruments for its activity ; though the certainty of knowledge was derived exclusively from number and its relations. (Stob. p. 8 ; Sext. Emp. adr. Math. vii. 92.) The ethics of the Pythagoreans consisted more in ascetic practice, and maxims for the restraint of the passions, especially of anger, and the cultivation of the power of endurance, than in scientific theory. What of the latter they had was, as might be expected, intimately connected with their number-theory (Arist. Eth. Magn. i. 1, Eth. Nic. i. 4, ii. 5). The contemplation of what belonged to the pure and elevated region termed kéduos, was wisdom, which was superior to virtue, the latter having to do only with the inferior, sublunary region (Philol. ap. Stob. Eel. Phys. pp. 490, 488). Happiness consisted in the science of the persection of the virtues of the soul, or in the perfect science of numbers (Clem. Alex. Stron. ii. p. 417; Theo. doret. Serm. xi. p. 165). Likeness to the Deity was to be the object of all our endeavours (Stob. Ecl. Eth. p. 64), man becoming better as he approaches the gods, who are the guardians and guides of men (Plut. de Def. Or. p. 413 ; Plat. Phaed. p. 62, with Heindorf's note), exercising a direct influence upon them, guiding the mind or reason, as well as influencing external circumstances (yevérôa. Yap wirvoiáv riva wapá row Sataviov Stob. Eel. Phys. p. 206; date kal bidvolai rives ral rāon our ép jusveiruv, Arist. Elh. Eud. ii. 8); man's soul being a possession of the gods, confined at present, by way of chastisement, in the body, as a species of prison, from which he has no right to free himself by suicide (Plat. Phaed. p. 61: Cic. de Sen. 20). With the idea of divine influence was closely connected that of the influence of daemons and heroes (Diog. Laërt. viii. 32). Great importance was attached to the influence of music in controlling the force of the passions (Plut. de Is, et 0s. p. 384; Porph. Wit. Pyth. 30; Iambl. 64). Self-examination was strongly insisted on (Cic. de Sen, 11). Virtue was regarded as a kind of harmony or health of the soul (Diog. Laërt. viii. 33). Precepts for the practice of virtue were expressed in various obscure, symbolical forms, many of which, though with the admixture of much that is of later origin, have come down to us in the socalled 'Em xpura and elsewhere (Brandis, l.c. p. 498, note 9). The transmigration of souls was viewed apparently in the light of a process of purification. Souls under the dominion of sensuality either passed into the bodies of animals, or, if incurable, were thrust down into Tartarus, to meet with expiation, or condign punishment. The pure were exalted to higher modes of life, and at last attained to incorporeal existence (Arist. de An, i. 2, 3; Herod. ii. 123; Diog. Laërt. viii. 31 : Lobeck, Aglaoph. p. 893. What we find in Plato, Phaedr. p. 248, b, and in Pindar, Thren. fr. 4, Øymp. ii.68, is probably in the main Pythagorean). As regards the fruits of this system of training or belief, it is interesting to remark, that wherever we have notices of distinguished Pythagoreans, we usually hear of them as men of great uprightness, conscientiousness, and self-restraint, and as capable of devoted and enduring friendship. [See ARchytas; CLEINIAs; DAMon; PHINTIAs.]

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For some account of the very extensive literature connected with Pythagoras, &c., the reader is referred to Fabric. Bibl. Graec. vol. i. pp. 750–804. The best of the modern authorities have been already repeatedly referred to.

Besides a Samian pugilist of the name of Pythagoras, who gained a victory in Ol. 48, and who has been frequently identified with the philosopher, Fabricius (l.c. p. 776, &c.) enumerates about twenty more individuals of the same name, who are, however, not worth inserting. [C.P. M.]

PYTHAGORAS (IIv6ayépas), artists. 1. Of Rhegium, one of the most celebrated statuaries of Greece. Pausanias, who calls him “excellent in the plastic art, if any other was so,” gives the Fo as his artistic genealogy (vi. 4, § 2. s. 4) —

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ficient proof. It is indeed possible, as Sillig proposes, to apply the statement of Pliny to Pythagoras of Samos; but, as Pliny does not say which of the two artists he refers to, it is natural to suppose that he means the more distinguished one. We are inclined to believe that Pliny's reason for placing Pythagoras at this date was the circumstance which he afterwards mentions (l.c. $4), that Pythagoras was in part contemporary with Myron, whose true date was Ol. 87. The genealogy quoted above from Pausanias affords us no assistance, as the dates of the other artists in it depend on that of Pythagoras. Most of the modern writers on ancient art attempt to determine the date of Pythagoras by his statues of Olympic victors. This test is, however, not a certain one; for there are several instances of such statues not having been made until a considerable time after the victory. Still, at a period when art was flourishing, and when the making of these statues formed one of its most important branches, the presumption is that an Olympic victor would not be allowed to remain long without the honour of a statue; and therefore the date of the victory may be taken as a guide to that of the artist, where there is no decisive evidence to the contrary. Now, in the case of Pythagoras, one of his most celebrated works was the statue of the Olympic victor Astylus of Croton, who conquered in the single and double foot-race in three successive Olympiads, and on the last two of these occasions he caused himself to be proclaimed as a Syracusan, in order to gratify Hiero. (Paus. vi. 13. § 1.) Now, supposing (as is natural) that this was during the time that Hiero was king (B. c. 478–467, Ol. 75.3—78. 2), the last victory of Astylus must have been either in Ol. 77, or Ol. 78; or, even if we admit that Hiero was not yet king, and place the last victory of Astylus in Ol. 75 (Müller, Dorier, Chron. tab.), the earliest date at which we should be compelled to place Pythagoras would be about B. c. 480, and, comparing this with Pliny’s date, we should have B. c. 480–430 as the time during which he flourished. This result agrees very well with the indications furnished by his other statues of Olympic victors, by his contest with Myron, and by the statements respecting the character of his art. According to Diogenes Laërtius (viii. 47), Pythagoras was the first who paid special attention to order and proportion in his art; and Pliny states that he was the first who expressed with care and accuracy the muscles and veins and hair (Plin, l.c. §4). Hence it would seem that he was the chief representative of that school of improved development in statuary, which preceded the schools of perfect art which were established at Athens and at Argos respectively by Pheidias and Polycleitus; and that, while Ageladas was preparing the way for this perfection of art in Greece Proper, another school was growing up in Magna Graecia, which attained to its highest fame in Pythagoras; who, in his statues of athletes, practised those very principles of art, as applied to the human figure, which Polycleitus brought to perfection; and who lived long enough to gain a victory over one of the most celebrated masters of the new Attic school, namely Myron. The most important works of Pythagoras, as has just been intimated, appear to have been his statues of athletes. Unfortunately, the passage in s s

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