766 



PYTHAGORAS. 



the ear, but as a science to be reduced to mathe- 

 matical maxims and relations, and allied to astro- 

 nomy. Tradition makes him the inventor of a 

 musical (Pythagorean lyre, octochordum Pytha- 

 gor<t), which, after his death, was engraved in 

 brass, and preserved in the temple of Juno at 

 Samos. The invention of tiie harmonic canon, or 

 monochord an instrument of a single string 

 which served for the measurement of musical inter- 

 vals, has also been ascribed to him by ancient and 

 modern writers. He believed that the heavenly 

 spheres, in which the planets move, dividing the 

 ether in their course, produced tones, and that tiie 

 tones must be different according to their size, 

 velocity, and distance. That these relations were 

 in concord, that these tones produced the most per- 

 fect harmony (music of the spheres), he necessarily 

 believed, in consequence of his notions of the 

 supreme perfection of the universe. The real 

 meaning of this doctrine was, that he regarded the 

 world as a harmonically arranged whole (xotrpos'), in 

 which the relations of numbers were realized. His 

 followers took occasion from this doctrine to say 

 of their master, that he was the only mortal whom 

 the gods had permitted to hear the harmony of the 

 spheres. Geometry, which he had learned in 

 Egypt, he reduced, more than any of his predeces- 

 sors and contemporaries, to the form of a regular 

 science. According to his notion, the geometrical 

 point was simple, the line double, the area three- 

 fold, and solids quadruple ; and in this way, also, 

 he applied the doctrine of numbers. Of the geo- 

 metrical theorems which are ascribed to him, the 

 following are the most important : The three angles 

 of a triangle are together equal to two right 

 angles ; and in a right-angled triangle, the square 

 of the hypothenuse is equal to the sum of the 

 squares of the two sides. This last is still called 

 the Pythagorean theorem (also magister mathescos), 

 although it is doubtful whether Pythagoras invented 

 it. In astronomy he taught the following: The 

 word heaven denotes either the spheres of the fixed 

 stars, or the whole space between the fixed stars 

 and the moon, or the whole world, including both 

 the heavenly spheres and the earth. Agreeably to 

 the arithmetical hypothesis, there are ten heavenly 

 spheres, of which nine are visible to us, viz. the 

 sphere of the fixed stars, the seven spheres of 

 the seven planets (including the sun and moon), 

 and the sphere of the earth. The tenth earth, 

 called by him Anticthon (anti-earth), is invisible, 

 but necessary to the perfection of the harmony of 

 nature, since the decad is the perfection of the 

 numerical harmony. By this anti-earth he explains 

 the eclipses of the moon. In the middle of the 

 universe is the central fire, principle of warmth and 

 life. The earth is one of the planets, moving around 

 the sphere of fire. The atmosphere of the earth is 

 a gross, immovable mass, but the ether is pure, 

 clear, always in motion, and the region of all divine 

 and immortal natures. The distances of the various 

 heavenly spheres from the earth correspond to the 

 proportions of the musical scale. His moon and 

 stars are gods, or inhabited by gods. Pythagoras, 

 therefore, rendered important services to the mathe- 

 matical sciences, and first established a mathematical 

 philosophy. His disciples Philolaus, Archytas, 

 Ecphantus, Ocellus, Timaeus, carried it farther. 

 Philolaus, in particular, whose fragments are the 

 most valuable relics of the Pythagorean school, 

 distinguished himself by his astronomical system. 

 With mathematics were also connected the natural 

 sciences. With respect to philosophy, Pythagoias 

 taught, that true knowledge embraced those subjects 

 which are in their nature immutable, eternal, and 



indestructible, and of which alone it can be proper- 

 ly predicated, that they exist. He who devotes 

 himself to tin's study is a philosopher. The object 

 of philosophy is, by contemplation, to render the 

 human mind similar to the divine, and make it lit 

 to enter the assembly of the gods. For this pur- 

 pose it is necessary to invoke, in prayer, the assis- 

 tance of the Divinity and good demons. Contem- 

 plative wisdom cannot be fully attained without 

 entire abstraction from common things, without 

 entire tranquillity, and freedom of mind. Hence 

 the necessity of founding a society separate from 

 the world, for contemplation and study. The theo- 

 retical philosophy of Pythagoras, which treats of 

 nature and its origin, was enveloped in the most 

 profound obscurity, and we know nothing of it, but 

 what may be conjectured from single intimations 

 of the ancients. In the opinion of Pythagoras, 

 God is the universal spirit, diffused in all directions 

 from the centre, the source of all animal life, the 

 actual and inward cause of all motion, in substance 

 similar to light, the first principle of the universe, 

 incapable of suffering, invisible, indestructible, and 

 to be comprehended by the mind alone. To the 

 Divinity there were subordinate, according to the 

 notions of the Pythagoreans, three kinds of intelli- 

 gences, gods, demons, and heroes, emanations of 

 the supreme God, varying in dignity and perfection, 

 in proportion as they were more or less removed 

 from their source. The heroes he believed to be 

 clothed with a body of subtile matter. Besides 

 these three kinds, there was a fourth the human 

 mind ; likewise an emanation of the Divinity. As 

 God is one, and the origin of all variety, he was re- 

 presented as a monad, and the subordinate spirits as 

 numbers derived from and contained in unity. Thus 

 the numbers of Pythagoras resembled the ideas of 

 Plato, excepting that they are contained in the things 

 themselves. The regions of the air the Pythago- 

 reans thought filled with spirits, demons,and heroes, 

 who were the cause of health or sickness to men 

 and animals, and, by means of dreams and other 

 kinds of divinations, imparted the knowledge of 

 future events. The soul, according to him, was 

 likewise a number, and by numbers it first has per- 

 ception, as Philolaus says, of the world ; it is sin 

 emanation of the central fire, and, consequently, 

 always in motion, and indestructible. Of man, the 

 Pythagoreans believed, at least the later, tliat, since 

 he consisted of an elementary nature, of a divine 01 

 rational principle, he was a microcosm ; that his 

 soul was a self-moving principle, and consisted of 

 two parts, the rational, which was a portion of the 

 universal soul, an emanation of the central fire, 

 and had its seat in the brain, and the irrational, 

 which comprised the passions, and lived in the 

 heart ; that in both, man had something in common 

 with the brutes, who, on account of their bodily 

 structure and the want of language, are incapable 

 of acting reasonably ; that the sensitive soul (Sv/xos ) 

 perishes, but that the rational mind (Qpm, oz/j) is 

 immortal, because it has its origin in an immortal 

 source ; that the latter, when freed from the fetters 

 of the body, assumes an ethereal vehicle, and passes 

 to the habitations of the dead, where it remains till 

 it returns to the world, to dwell in some other 

 human or animal body, and that at last, when suf- 

 ficiently purified, it returns to the source from which 

 it proceeded. This doctrine of the transmigration 

 of souls (metempsychosis), which was originally 

 Egyptian, and connected with the idea ot the 

 reward and puixshment of human actions, was the 

 chief cause why the Pythagoreans killed no animals. 

 His morality Pythagoras taught in symbolic maxims 

 and ascetic precepts, in connexion with his contem 



