PYTHAGOREANS. 



contemplation. The wliole courfe of mathematical fcicnce 

 may be dividcil into four parts : two refpefting numbers, 

 and two re fpcd'ting magnitude. Number may be confidcred 

 either abllradtedly in itfelf, or as applied to fome oljjttt. 

 The former fcicnce is arithmetic ; of the latter kind is mufic. 

 Magnitude may be confidered as at reft, or as in motion ; 

 the fcicnce which treats of the former is geometry, that 

 wliich treats of the latter is ailronomy. 



Arithm.etic ii. the Boblell fcience ; numbers the firft ob- 

 jeft of ftudy, and a perfeft acquaintance with numbers the 

 higheft good. Numbers are either fcicntific or intelligible. 



Sci-'ntific number is the produftion of tiie powers in- 

 volved in unity, or the progreflion of multitude from the 

 monad or unity, and its return to the fame. Unily and one 

 are to be diftinguidied from each other ; the former being 

 an abftraft conception, the latter belonging to things ca- 

 pable of being numbered. Number it not infinite, but is 

 the fource of that infinite divifibility into equal parts, which 

 is the property of all bodies. 



Intelligible numbers are thofe which fubfiikd in the di- 

 vine mind before all things, from which everything hatli 

 received its form, and which always remain immutably the 

 fame. It is the model, or archetype, after which the world, 

 in all its parts, is framed. Numbers are the caufe of eficiice 

 to beings : tk-: Kjivf/t-; kitix; uvai tk; aVtaf. 



The monad, or unity, is that quantity, which, being de- 

 prived of all number, remains fixed : whence called monad, 

 from TK iJ.mu It IS the fountain of all number. The duad 

 is imperfeft and pafTive, and the caufe of increafe and divi- 

 fion. The triad, compofed of the monad and duad, par- 

 takes of tlie nature of both. The tetrad, tetraftys, or 

 quaternion number, is the moll perfeft. The decad, which 

 is the fum of the four former, comprehends all arithmetical 

 and mufical proportions. 



According to fome writers, the monad denotes the attive 

 principle in nature, or God ; the duad, the paflive prin- 

 ciple, or matter ; the triad, the world formed by the union 

 of the two former ; and the tetratlys, the perfedion of na- 

 ture. Some have underitood by this myfterious number, 

 thai four elements; others, the four faculties of the human 

 mind ; others, the four cardinal virtues ; and others have 

 been fo abfurd as to fuppofe that Pythagoras made ufe of 

 this number to exprefs the name of God, in reference to the 

 word n"in'> by which that name is expreffed in the Hebrew 

 language. But every attempt to unfold this myftery has 

 hitherto been uniucceisful. 



The molt probable explanation of the Pythagoric doc- 

 trine of numbers is, that they were ufed as fyrabolical or 

 emblematical reprelcntatiom; of the firft principles and forms 

 of nature, and particularly of thofe eternal and immutable 

 elfences, to which Plato afterwards gave the appellation of 

 ideas. Not being able, or not chufing, to explain in fimple 

 language the abftraft notions of principles and forms, Py- 

 thagoras feems to have made ufe of numbers, as geometri- 

 cians make ufe of diagrams, to aiTift the conceptions of 

 fcholars. More particularly, conceiving fome analogy be- 

 tween numbers and the intelligent forms which fubfift in the 

 divine mind, he made the former a fymbol of the latter. 

 As numbers proceed from unity, or the monad, as a fimple 

 root, whence they branch out into various combinations, 

 and affnme new properties in their progrefs, fo he con- 

 ceived the different forms of nature to recede, at different 

 diftances, from their common fource, the pure and fimple 

 effence of deity, and at every degree of diftance to afiume 

 certain properties in fome meafure analogous to thofe of 

 number ; and hence he concluded, that the origin of things, 



their emanation from the firft being, and their fubfequeiit 

 progreflion through various orders, if not capable of a per- 

 fedtly cleir explanation, might, however, be illuftrated by 

 'Symbols and refemblances borrowed from numbers. 



Next to numbers, mufic had the chief place in tiie pre- 

 paratory exercifes of the Pythagorean fchool, by means of 

 which the mind was to be raifed above the dominion of the 

 pafiions, and inured to contemplation. Pythagoras con- 

 fidered mufic, not only as an art to be judged of by the ear, 

 but as a fcience to be reduced to mathematical principles 

 ar.d proportions. We have introduced, under the article 

 PvTHA(X)RAs, the manner in which he is faid to have dif- 

 govered the mufical chords, but fhall here fubjoin a more 

 minute account. As Pythagoras was one day refledting upon 

 the fubjeft, happening to pafs by a fmith's forge, where fe- 

 veral men were fucceflively ftriking with tiieir hammers a 

 piece of heated iron upon an anvil, he remarked, that all the 

 founds produced by their llrokes were harmonious except 

 one. The founds, which he obferved to be chords, were 

 the oftave, the fifth, and the third ; but that found which 

 he perceived to lie between the third and the fifth he found 

 to be difcordant. Going into the work-fiiop, he obferved, 

 that the diverfity of founds arofe, not from the form of the 

 hammers, nor from the force with which they were ftruck, 

 nor from the pofition of the iron, but merely from the dif- 

 ference of weight in the hammers. Taking, therefore, the 

 exaft weight of the feveral hammers, he went home, and 

 fufpended four itrings of the fame fubilance, length, and 

 thicknefs, and twifted in the fame degree, and hung a 

 weight at tl e lower end of each, refpedlively equal to the 

 weight of the hammers : upon ftriking the ftrings, he found, 

 that the mufical chords of the ftrings correfp<inded with 

 thofe of the hammers. Hence it is faid, that he proceeded 

 to form a mufical fcale, and to conftruft Itringed inftru- 

 ments. His fcale was, after his death, engraved in brafs, 

 and preferved in the temple of Juno at Samos. 



Pythagoras conceived that the celeftial Spheres in which 

 the planets move, ftriking upon the sether through which 

 they pafs, muft produce a found ( and that this found miift 

 vary, according to the diverfity of their magnitude, velo- 

 city, and relative diftance. Taking it for granted, that 

 every thing refpetling the heavenly bodies is adjufted with 

 perfeft regularity, he further imagined, that all the circum- 

 ftanccs ncceffary to render the founds produced by their 

 motion harmonious, were fixed in fuch exact proportions, 

 that the moit perfect harmony is produced by their revolu- 

 tions. This fanciful dodtrine refpecting the mufic of the 

 fpheres gave rife to the names which Pythagoras applied to 

 mufical tones. The laft note in the mufical odtave he called 

 hypatc, becaufe he fuppofed the fphere of Saturn, the higheft; 

 planet, to give the deepeft tone ; and the higheft note he 

 called mate, from the fphere of the moon, which being the 

 loweft, or nearefl the earth, he imagined, produced the 

 fhrilleft found. In like manner of the reft. It was faid of 

 Pythagoras by his followers, who hefitated at no afiertion, 

 however improbable, which might feem to exalt their maf- 

 ter's fame, that he was the only mortal fo far favoured by 

 the gods as to be permitted to hear the celeftial mufic of the 

 fpheres. Pythagoras applied mufic to the cure of difeafes 

 both bodily and mental. It was, as we have feen, the cuf- 

 tom of his fchool, to compofe their minds for reft in the 

 evening, and to prepare themfelves for adtion in the morn- 

 ing, by fuitable airs, which they performed upon the lute, 

 or other ftringed initruments. The mufic was, however, 

 always accompanied with verfe, fo that it may be doubted, 

 whether the effedl was to be afcribed more to the mufician 



