PYTHAGOREANS. 



or to the poet. It is faid of Clinius, a Pythagorean, that 

 whenever he perceived himfelf inclined to anger, fpleen, or 

 other reftlefs paflions, he took up his lute, and that it never 

 failed to rcftore the tranquillity of his mind. Of Pytlia- 

 goras himfelf it is related, that he checked a young man, 

 who, in the midll of his revels, was meditating fome aft of 

 Bacchanalian madnefs, by ordcrnig the mufician, who had 

 inflamed liis paflions by Phrygian airs, to change the mufic 

 on a ludden into the (low and folemn Doric mood. If the 

 llories which ar» related by the ancients concerning the 

 wonderful effefts of their mufic are to be credited, we mud 

 acknowledge wc are ftrangers to the method by which thefe 

 effefts were produced. 



Befides arithmetic and mufic, Pythagoras cultivated geo- 

 metry, which he had learned in Egypt ; but he greatly im- 

 proved it, by inveiligating many new theorems, and by 

 digelling its principles, in an order more perfeftly fyfte- 

 niatical than had before been done. Several Grecians, 

 about the time of Pythagoras, applied themfelves to matiie- 

 matical learning, particularly Thales in Ionia. But Py- 

 thagoras feems to have done more than any other philo- 

 fopher of this period towards reducing geometry to a regular 

 fcience. His definition of a point is, a monad or unity 

 with pofition. He taught that a geoinetrical point cor- 

 refponds to unity in arithmetic, a line to two, a fuper- 

 ficies to three, a folid to four. Of the geometrical theo- 

 rems afcribed to Pythagoras, the following are the prin- 

 cipal : that the interior angles of every triangle are together 

 equal to two right angles ; that the only polygons which 

 will fill up the whole fpace about a given point, are the 

 equilateral triangle, the iquare, and the hexagon ; the firft 

 to be taken fix times, the fecond four times, and the third 

 three times ; and that, in reftangular triangles, the fquare 

 of the fide which fubtends the right angle is equal to the 

 two fquares of the fides which contain the right angle. 

 Upon the invention of this latter propofition ( Euclid, 1. i. 

 prop. 47.), Plutarch fays, that Pythagoras offered an ox, 

 others, an hecatomb, to the gods. But this ftory is thought 

 by Cicero inconfiftent with the inttitutions of Pythagoras, 

 which, as he fuppofes, did not admit of animal facrifices. 

 Pythagoras inferred the flature of Hercules from the length 

 of the O'lympic courfe, which meafured fix hundred of his 

 feet. Obferving how much fhorter a courfe fix hundred 

 times the length of the foot of an ordinary-fized man was 

 than the Olympic courfe, he inferred, by the law of pi'o- 

 portion, the length of Hercules's foot ; whence the ufual 

 proportion of the length of the foot to the height of a man 

 enabled him to determine the problem. Pythagoras alfo 

 applied geometrical ideas as fymbolical expreffions of bodies, 

 and of natural principles ; but nothing certain, or intel- 

 ligible, is preferved on this head. 



On altronomy, the doftrine of Pythagoras, or, however, 

 of the ancient Pythagoreans, was as follows : 



The term heaven either denotes the fphere of the fixed 

 ftars, or the whole fpace between the fixed flars and the 

 moon, or the whole world, including both the celellial 

 fphcres and the earth. There are ten celeftial fpheres, nine 



but is one of thofe planets which make their revolution 

 about the fphere of fire. The revolution of Saturn is com- 

 pleted in thirty years, that of .lupiter in twenty, that of 

 Mars in two, that of the Sun, and of Mercury and Venus, 

 in one year. The dillance of tlic feveral celeftial fpheres 

 from the earth correfpond to the proportion of notes in the 

 mufical fcale. The moon and other planetary globes are 

 habitable. The earth is a globe, which admits of anti- 

 podes. 



From feveral of thefe particulars refpefting the aftro- 

 nomical doftrine of Pythagoras, it has been inferred, that 

 he was pofielled of the true idea of the folar fyftem, which 

 wai revived by Copernicus, and has fince been fully cfta- 

 bliflied by Newton. 



From this preparatory (ludy the difciples of the Pytha- 

 gorean fcliool were condufted to the knowledge of natural, 

 theological, and moral fcience. Concerning wifdom, in 

 general, Pythagoras taught, that it is the fcience which is 

 converfaiit with thofe objefts, which are in their nature im- 

 mutable, eternal, and incorruptible, and therefore alone can 

 properly be faid to exift. The man who applies himfelf to 

 this kind of lludy is a philofopher. The end of philofophy 

 is, that the human mind may, by fuch contemplation, be 

 afiTimilated to the divine, and at length be qualified to join 

 the affembly of the gods. In the purfuit of wifdom, the 

 utmoft care muft be taken to raife the mind above the do- 

 minion of the paflions, and the influence of fenfible objefts, 

 and to difengage it from all corporeal imprelfions, that it 

 may be inured to converfe with itfelf, and to contemplate 

 things fpiritual arfd divine. For this purpofe the afliftance 

 of God, and of good daemons, muft be invoked by prayer. 

 Philofophy, as it is converfant with fpeculative truth, or with 

 tlie rules of human conduft, is either theoretical or praftical. 

 Praftical philofophy is only to be ftudied fo far as may be 

 nccellary for the purpofes of life ; theoretical philofophy is 

 the perfeftion of wifdom. Contemplative vs-ifdom cannot 

 be completely attained, without a total abftraftion from the 

 ordinary affairs of life, and a perfeft tranquillity and free- 

 dom of mind. Hence the neceffity of inftituting a fociety, 

 feparated from the world, for the purpofe of contemplation 

 and ftudy. 



Aftive or moral philofophy, which prefcribes rules and 

 precepts for the conduft of life, according to Ariftotle, was 

 firft taught by Pythagoras, and after his death by Socrates. 

 Among the moral maxims and precepts afcribed to Pytha- 

 goras are the following : 



Virtue is divided into two branches, private and public. 

 Private virtue refpefts education, filence, abftinence from 

 animal food, fortitude, fobriety, and prudence. The 

 powers of the mind are reafon and pafiion ; and when the 

 latter is preferved in fubjeftion to the former, virtue is pre- 

 valent. Young perfons fhould be inured to fubjeftion, that 

 they may always find it eafy to fubmit to the authority of 

 reafon. Let them be condufted into the beft courfe of life, 

 and habit will foon render it the moft pleafrnt. Silence is 

 better than idle words. A wife man will prepare himfelf for 

 every thing which is not in his own power. Do v\hat you 



iA which aVe vifible to us ; namely, that of the fixed ftars, judge to be right, whatever the vulgar may think of you ; 

 thofe of the feven planets, and that of the earth ; the tenth if you delpife their praife, dcfpife alfo their cenfure. It is 



is the antichthon, or an invifible fphere oppofite to the 

 earth, which is necellary to complete the harmony of nature, 

 as the decad is the completion of numerical harmony. And 

 this antichthon may be the caufe of the greater number of 

 the eclipfes of the fun than of the moon. Fire holds the 

 middle place in the univerfe ; or, in the midft cf the four 

 elements is placed the fiery globe of unity ; the earth is not 

 without motioD, nor fituated in the centre of the fpheres, 



7 



inconfiftent with fortitude to relinquifh the ilation appointed 

 by the Supreme Lord, before we obtain his permiftion. 

 Sobriety is the ftrength of the foul, for it preferves its rea- 

 fon unclouded by pafiion. No man ought to be cilcemed 

 free, who has not the perfeft command of himfelf. Drun- 

 kennels is a temporary phrenfy. That which is good and 

 becoming is rather to be purfued, than that which is plea- 

 faiit. Tlic defire of fuperfluity is foolifti, becaufe it knows 



no 



