PYTHAGORAS 



PYTHON 



511 



upon them, and they had to flee from persecution. 

 How Pythagoras himself died is not exactly known ; 

 his death (according to tradition, at Metapontum) 

 may be placed about 500 B.C. 



The Pythagoreans adhered at first to certain 

 mysteries indeed, the Orphic mysteries ; an 

 examination as to fitness qualified for admis- 

 sion into their number; obedience and silence, 

 abstinence and simplicity in dress and food and 

 'external goods,' and the habit of frequent self- 

 examination were prescribed. The enjoined dis- 

 posal of worldly goods may have helped to foster 

 contemplation and scientific enthusiasm. This at 

 least developed itself in the school. Pythagoras, 

 for example, is said to have practised investiga- 

 tions into harmonies and the properties of numbers. 

 Mathematical investigations were first begun by 

 individuals, and then carried on prominently by 

 the school. Their attention was early turned to 

 the odd and even, to prime numbers, square 

 numbers, &c. ; and from this arithmetical stand- 

 point they cultivated geometrical studies, nnml>er 

 becoming for them the chief principle in space. 

 The elementary relations of harmonies and the 

 regular rotations of the spheres led the Pythagor- 

 eans to think of the cosmic order as a numerical 

 one, and, like the early Greek Realists in philo- 

 sophy, they took number to have a metaphysical 

 significance to be, as Aristotle tells us, not only 

 the form, but the very substance of things: 'All 

 is Number ' came to be their thesis. As numerical 

 proportions are repeated in different things, they 

 regarded numbers also as archetypes, or which 

 things were in a sense the ectypes. They ex- 

 plained the harmonious arrangement of things as 

 that of bodies in a single all-inclusive sphere of 

 reality, moving according to a numerical scheme, 

 the earth itself and the fixed stars all being in 

 progress round the central fire. ( It is interesting 

 to notice this idea so early in science of the move- 

 ment of the earth.) The scheme of revolution was 

 given them first by the decade, each number of 

 which had a peculiar significance, especially the 

 unit, the duad, the square, &c. The table of con- 

 traries they also used in explaining the cosmos ; 

 this included such contrasts as the limited and 

 the unlimited, the even and the odd, one and many, 

 right and left, male and female, light and darkness, 

 and so on. In all this room was naturally given 

 to fanciful and arbitrary speculation, developed 

 later among the Neo-Pythagoreans in such tables 

 as 1, the point ; 2, the line ; 3, the surface ; 

 4, body ; 5, quality ; 6, soul, and so on. To the 

 virtues numbers were also given, justice being the 

 square number ; the soul, too, was in general a 

 harmony chained to the body. As the Pythagor- 

 eans thought the heavenly bodies to be separated 

 from each other by intervals corresponding to the 

 harmonic lengths of strings, they neld that the 

 movement of the spheres gave nse to a pleasing 

 sound called the 'harmony of the spheres.' Of 

 the so-called 'elements' they had also numerical 

 theories, fire being the tetrad, earth the cube, air 

 the octahed, water the equation. 



The great mathematical discover}' of Pythagoras 

 is of course the hypothenuse theorem, where the 

 square is equal to the sum of two squares. 

 'Pythagorean numbers' are such numbers as 

 are related in the way the theorem indicates 

 e.g. 5, 4, and 3 (5 s = 25 = (4 s + 3 s ) = 16 + 9). 

 Various other theorems are closely connected with 

 this cardinal one; these concern chiefly the squares 

 of the various perpendiculars which may be let 

 fall from the different angles of the right-angled 

 triangle upon the hypothenuse and sides. The 

 speculations in general of the Pythagoreans may 

 be regarded from various sides. Their formal 

 principle of number is often said, and with truth, 



to mark a transition from the crude Hylozoism of 

 Thales and the Ionic philosophers to a formal or 

 rational or conceptual contemplation of the world, 

 developed, say, by the Eleatics, and culminating 

 in Plato. Their idea of a quantitative combina- 

 tion of elementary units became a commonplace 

 of Greek speculative cosmology, constituting the 

 ground for a deductive ontology. The conception- 

 general of a measure or proportion in things is, 

 of course, a most pronounced trait in the Greek 

 mind. It is easv to trace in the Pythagorean 

 doctrine of the elements and the contraries and 

 of combination and of spheric completeness all the 

 essential features of Greek cosmology. The influ- 

 ence of Pythagoras and geometrical conceptions 

 over the mind of Plato can hardly be exaggerated. 

 The chief interest of the Pythagoreans doubtless 

 lay in the domain of physics, and their astronomi- 

 cal theories may be said to constitute their capital 

 achievement. If we remember, too, that Pytha- 

 goras is perhaps the first Greek thinker who con- 

 ceived of philosophy as first a life, a life in com- 

 mon, we shall see in this the beginning of the 

 legislative and ethical view of the philosopher's 

 function expressed in the fullest way in Plato's 

 Republic. The ascetic and mystical aspects of 

 Pythagoreanism linked it closely with Platonism 

 in the mind of Christian idealists in later times. 

 See NEOPLATONISM, NEO-PYTHAGOREANISM. 



BIBLIOGRAPHY. The fragments of Philolaus were pub- 

 lished by Buckh in 1819. The brief notices Aristotle gives 

 of the Pythagoreans in the first book of the Metaphysics 

 contain almost all that is of philosophical importance in 

 their theory. Zeller's account is quite exhaustive, and 

 notices most that has been written on the subject ( The 

 fre-Socratie Schools, Eng. trans. 1882). See also Grote's 

 Greece, iv. 525-551; t'haignet, Pythaij. et la Philca. 

 1'nihxii. (1873); James Gow, Short History of Malhe- 

 ma(tc(1884). 



Pytheas of Massilia. See GEOGRAPHY, 

 Vol. V. p. 145. 



Pythia. See DELPHI. 



Pythian Games, one of the four great national 

 festivals of the Greeks, held in the Crisscean plain, 

 near Delphi (anciently called Pytho), are said to 

 have been instituted by Apollo after vanquishing 

 the snaky monster, Python, and were celebrated 

 in his honour every four years. Originally the 

 contests were restricted to singing, with the accom- 

 paniment of cithern-playing; but flute-playing, 

 athletic contests, horseracing, contests in poetry 

 and art were afterwards introduced, and long con- 

 tinued a distinguishing feature of these games, 

 which are believed to have lasted down to nearly 

 the end of the 4th century A.D. The prize was 

 a laurel-wreath and the symbolic palm-branch. 

 Several of Pindar's extant odes relate to victors 

 in the Pythian Games. 



Pythias. See DAMON. 



Python, a name applied to several large ser- 

 pente, especially of the genus Python, which inhabit 

 tropical Asia, Africa, and Australia, and closely 

 resemble both in structure and habit the Boas of 

 the New World. The body is rarely 20 feet in 

 length, usually indeed nearer 10, though often 

 estimated at 40 ; it is plump and very muscular ; 

 the tail is prehensile ; there are beside the anus 

 two rudimentary hind limbs or ' spurs,' which have 

 perhaps a sexual function besides being of use in 

 climbing. The pythons usually lurk near water, 

 among the herbage or on an overhanging tree. 

 They seize small mammals, strangle and crush 

 them in their coils, and swallow them slowly. 

 They do not cover them with saliva before begin- 

 ning to swallow them, reports to this effect being 

 inferences from the appearance of the occasionally 

 disgorged prey. After a heavy meal the serpents 



