self by his travels in Greece and Egypt, and probably also by the lessons of Thales and Pherecydes (whose disciple he is said to have been), as well as by those of Anaximander. After having previously attempted to establish a school and a species of philosophical congregation at Samos, he founded one (about 527) at Croto, in Italy, whence his school came to be called the Italic. Besides the improvement of the intellectual, moral, and religious capacities of man, this society had also considerable political influence; which circumstance occasioned its ruin, and the death of its founder, about the year 500. Pythagoras may justly be esteemed a man remarkable for his talents, his discoveries, his plans, and the authority he possessed over others; but the ancient Greeks and Romans invested him with something more than this, amounting to a sort of superstitious reverence. He was the first who assumed the name of philosopher. See Cic. Tusc. Quæst. V. 3, 4. DIOG. LAERT, VIII. 8, and I, 12.

90. He investigated the principles of the mathematical sciences; particularly of Arithmetic, Geometry, Music, and Astronomy; his discoveries in which are of themselves sufficient to immortalize his name. He ascribed an occult power to words and numbers; and the science of arithmetic, which he considered as the key to mathematics, he looked upon as containing also the essence of all philosophical knowledge. From this principle he was led to adopt a sort of Mathematical Philosophy, which gave to his school also the name of Mathematical. We possess only fragments of the speculations of his school on these subjects, in which we are not enabled to distinguish the hand of the master from that of his disciples.

$91.

On the subject of the Pythagorean numbers, see JAC. BRUCKER, Con

1 FR. BUDDEI Diss. de Peregrinationib. Pythagoræ, Jena, 1692, 4to.; and in his Analect. Hist. Philos.

* DIOG. LAERT. I, 118, sqq. Cic. De Div. I, 13.

* About 504, according to Meiners; according to others, 489 B.C. ELIAN. Var. Hist. IV, 17. JAMBLICH. c. 10.

ARISTOT. Metaph. I, 5.

venientia Numerorum Pythagoræ cum Ideis Platonis, Miscell. Hist. Philos.

De Numerorum, quos Arabicos vocant, vera origine Pythagoricâ commentatur CONR. MANNERT, Norimb. 1801, 8vo.

+ C. A. BRANDIS, On the Doctrine of Numbers of the Pythagoreans and Platonists (in the Rhen. Mus. of Hist. Philos. etc. 1828, No. II, s. 208).

AMAD. WENDT, De rerum principiis secundum Pythagoreos Comment. Lips. 1827, 8vo.

Numbers were defined by the Pythagoreans to be the principles (airía) of all things; this school being disposed by their mathematical studies to make the system of external things subordinate to that of numbers, agreeably to their axiom, μίμησιν εἶναι τὰ ὄντα τῶν ἀριθμῶν. Numbers are equal and unequal, ἀρτίοι and περιττοί; the elementary principle of the latter being unity (uovás), that of the former duality (ôvás). Unequal numbers are limited and complete; equal ones unlimited and incomplete. The abstract principle then of all perfection is unity and limitation. (TO TETTEраoμévov); that of imperfection, duality and indeterminateness (TÒ TEIрov). The ten elementary numbers which are represented in the tetractys, and which embrace a complete system of numeration, contain also the elements of a perfect system of nature. (See Arist. Met. I, 5). In this instance they applied the theory of numbers to explain the natures and substances of things, as, in others, to illustrate their formation and origin. But on this subject we are acquainted only with subsequent essays, belonging to a later school.

92. On the World and the Deity. The Pythagoreans, like their predecessors, considered the world to be a harmonious whole (kooμos); consisting, according to a system of Decades, of ten great bodies revolving around a common centre, agreeably to harmonious laws; whence the music of the spheres, and their explanation of the symbolical 1 ARIST. Metaph. I, 3. JAMBLICH. Vit. Pythag. c. xii, p. 120, ex Heraclide Pontic.

5

2 ARIST. Metaph. I, 5, 6; XII, 6, 8.

3 SEXT. EMPIR. Adv. Math. IV, 3.

J. GEO. MICHAELIS. Diss. de Tetracty Pythagoricâ, Francof. ad Viad. 1735. ERH. WEIGIL, Tetractys Pythagorica.

4 SEXTUS, Adv. Mathem. X, 249, sqq.

• AUG. BOECKH, Disputatio de Platonico Systemate Coelestium

lyre of Apollo. The centre, or central fire (the sun), in other words, the seat of Jupiter, Aïòs oikos pvláky, is the most perfect object in nature, the principle of heat, and consequently of life; penetrating and vivifying all things. According to the same system, the stars also are divinities;· and even men, nay, the inferior animals, have a sort of consanguinity with the Divine Being. They considered the dæmones as a race intermediate between gods and men, and attributed to them a considerable agency in dreams and divination: always, however, assigning as ultimate causes of all things, destiny and the deity. They ennobled their notion of the deity by the attribution of certain moral qualities, such as truth and beneficence.1

93. Doctrine of the Soul. The soul also is a number, and an emanation from the central fire, resembling the constellations to which it is allied by its immortality and its constant activity; capable of combining with any body, and compelled by destiny to pass successively through several. This theory of the metempsychosis, borrowed (it is probable) from the Egyptians, Pythagoras appears to have combined with the doctrine of moral Retribution. It is to the Pythagoreans we are indebted for the first attempt, however rude, at an analysis of the operations and faculties of the mind. The Reason and Understanding (vous and Opéves), they placed in the brain; the appetites and the will (Ovuos) in the heart.*

94. The doctrine of Pythagoras embraced also the quesGloborum, et de verâ indole Astronomia Philolaicæ, Heidelberg. 1810, 4to.

1 PLATO Phædon. p. 139, et HEINDORF, ad h. 1. PLUTARCH. De Plac. Philos. I, 3, 7; II, 4._ DIOG. VIII, 27, 21. JAMBLICH. LXXXVI, 137, sqq. PORPHYR. Vitâ Pythag. § 41. ÆLIAN. Var. H. XII, 59. STOB. Ecl. Phys. p. 206.

CONR. DIETR. KOCH, Diss. Unum Theol. Pythagor. Compendium, Helmst. 1710. MICH. MOURGUES, Plan Théologique du Pythagorisme et des autres Sectes, Toulouse, 1712, 2 vols. 8vo.

2 DIOG. LAERT. VIII, 28.

3 HERODOT. II, 123. ARIST. De An. I, 3.? PLUT. De Plac. Philos. IV, 7. JAMBLICH. Vit. Pyth., c. 24. DIOG. LAERT. VIII, 14, 28. 30, 31. STOB. Ecl. I, 1044, sqq.

4 CIC. Tusc. Quæst. I, 17. DIOG. VIIL 30.

STOв. Ecl. Phys.,

p. 878.

tion of Ethics; and the fragments of his which we possess on this subject contain (in symbolical language) many admirable ideas, but of which the principles are not suffi ciently developed. Moral good they identified with unity -evil with multiplicity. Virtue is the harmony and unison of the Soul (Aristot. Eth. Nicom. II, 5; cf. I, 4. Diog. Laert. VIII, 33. Clem. Alex. Strom. IV, c. 23), or, in other words, similitude to God, oμolovia рos TO DELOV. Justice they defined to be ἀριθμὸς ἰσάκις ἴσος; and Right they made to consist in τὸ ἀντιπεπονθός: Friendship was made to consist in community of interests and equality; self-murder was condemned by Pythagoras as a crime against the gods, and the virtue which he especially commended was self-command (katápтvois). But the attention of this school was greatly engaged, and its disciples exer

AMBROS. RHODII, Dial. de Transmigratione Animarum Pythagoricâ. Hafn. 1638, 8vo.

PAGANINI GAUDENTII De Pythagorica Animarum Transmigratione, Pis. 1641, 4to.

Essay of Transmigration, in defence of Pythagoras, Lond. 1692. GUIL. IRHOVII De Palengenesiâ veterum, s. Metempsychosi sic dicta Pythagoricâ, Lib. III, Amst. 1733, 4to.

1 MARC. MAPPI Diss. (Præs. JAC. SCHALLER) de Ethica Pythagoricâ, Argent. 1653; and in the Fragmen. Hist. Philos. of WINDHEIM.

KRISCHE, De societate a Pythagora in urbe Crotoniatanâ conditæ scopo politico, 1830.

CRAMER, De Pythagora, quomodo educaverit atque instituerit.

1833.

MAGN. DAN. OMEISII Ethica Pythagorica, Altd. 1693, 8vo.

FRID. GUIL. EHRENFR. ROST, Super Pythagora Virtutem ad Numeros referente non revocante, Lips. 1803.

FR. BERNII Arcana Moralitatis ex Pythagoræ symbolis collecta, Ferrar. 1669; ed. quartus PAUL Pater. Francf. ad M. 1687·

Jo. MICH. SONNTAG, Diss. de similitudine nostri cum Deo Pythagorico-Platonico, Jen. 1699, 4to.

FR. BUDDEI, Diss. De кalápσe Pythagorico-Platonica, Hal. 1701, 4to; cf. Analect. Hist. Philos. ejusdem.

CH. AUG. ROTH, De Examine conscientiæ Pythagorico vespertino, Lips. 1708, 4to.

Jo. FRIEDEM. SCHNEIDER, Diss. De ävody seu ascensu hominis in Deum Pythagorico, Hal. 1710.

Jo. SCHILTERI, Diss. De Disciplina Pythagoricâ, in his Manuductio Philos. Moralis, Jen. 1676, 8vo.

2 ARIST. Eth. Magn. I, 2.

3 ARIST. Eth. Nicom. I, 1; cf. II, 6; V, 5. DIOG. LAERT. VIII, 33..

cised in an anthropological morality, or asceticism, which pervaded all their system.1

95. We are acquainted with but a small portion of the writings of the old Pythagorean sect, and these are merely commentaries on the opinions of their master. The philosophers belonging to it were Aristaus of Croto, the successor and son-in-law of Pythagoras, according to Jamblichus;2 Teleauges and Mnesarchus, sons of Pythagoras; Alemæon of Croto, particularly distinguished as a naturalist and physician; Hippo of Rhegium, and Hippasus of Metapontum ; (these two last were allied to the Ionic school, by their doctrine of a fundamental and elementary principle of nature); Ecphantus of Syracuse, who inclined to the Atomic school; Clinias, the contemporary of Philolaus, and Epicharmus of Cos, the comedian, called also the Megarean and Sicilian, on account of his residence at those places. Nothing can be advanced with certainty_concerning Ocellus the Lucanian, and Timæus of Locri Epizephyrii, and on that account called Timæus the Locrian. The work attributed to the latter is nothing but an abstract of the Timæus of Plato, and the authenticity of the treatise on the Universe attributed to Ocellus, is even more unquestionably apocryphal. Among the most distinguished Pythagoreans of a later 'Several symbolical precepts are to be found apud PLUTARCH. De Pueror. Educ. fin.; and DIOG. LAERT. VIII, 17.

2 Vita Pythag.

3 Flourished about 496 B.C.

4 Respecting both, consult + MEINERS, Hist. Doctr. de Vero Deo, P. II. p. 312, sqq. The same, in his History of the Sciences among the Greeks and Romans, vol. I, p. 584. The same, in the + Bibl. Philol. of Gött., vol. I, No. I, p. 204; and † TIEDEMANN, Spirit of Speculative Philosophy, vol. I, p. 89.

IIεpi Tns Tou кóσμоν ↓νxñs, printed in the Opusc. Myth. Phys. et Eth. of THOM. GALE, p. 539, sqq., and published by D'ARGENS, Berlin, 1763, 8vo. translated by BARDILI, in the collection of FULLEBORN, No. IX, § 9. On this work, consult + TENNEMANN, System of the Philosophy of Plato, vol, I. p. 93.

* Περί τῆς τοῦ παντός φύσεως, first published in the Opusc. of TΗ. GALE, p. 99, sqq. The same, by BATTEUX, with the work of TIMEUS, Par. 1768, 3 vols. 8vo; and also separately, by D'ARGENS, Berlin, 1792, 8vo; by ROTERMUND, Leips. 1784, 8vo; and lastly, by RUDOLPHÍ. Ocellus Lucanus de Rer. Naturâ, Græcè ; rec., comment. perpet. auxit et vindi. care studuit AUG. FRID. WILH. RUDOLPHI, Leips. 1801, 8vo., translated with a Dissertation on the Genius of Ocellus, by BARDILI, ap. FULLEBORN, Fasc. X, § 1—3.