Part IX.

PTTHAGORAS.
409
incorporeals precede intelligible bodie?* The elements of words, are not words'^ nor of bodies, bodies: but they muft; cither be bodies, or in- corporeal^ therefore they are wholly incorpore¬ al. Neither can we fay, that Atomes are eternal, and therefore, tho’ corporeal, the principles of all things j forfirft, they who affert Homoiome- fia’s, and bulks, and lealls, and indivifibles, to be elements, conceive their fubflance eternal, fo as in that refpecl:, Atomes arc no more elements than they. Again, tho’ it were granted, that Atomes were eternal ^ yet, as they who conceive the world to be unbegotten, and eternal, enquire by an imaginary way, the principles whereof it firft confills ; fo- we (lay the Pythagoreans ) treat¬ ing of Phylick, confidcf in an imaginary way, of what things theife eternal bodies, comprehen- fible only by reafon, conilft. Thus the Univerfe confifti either of bodies or incorporeals ^ we can¬ not fay bodies, for then we muft affign other bo¬ dies whereof they confill 9 and fo proceeding to infinite, we lhall remain without a principle. It refts therefore to affirm, that intelligible bodies confift of incorporeals, which Epicurus confef- feth, faying. By colleiVion of figure, and mag¬ nitude, and rellftance, and gravity, is underllood a Body.
Yet it is not neceffary, that all corporeals pre- exiftent to bodies, be the elements and firft prin¬ ciples of beings. Idea’s (according to Plato) are incorporeals, p-re-exiftent to bodies, and all generated beings have reference to them ^ yet they are not the principles of being ; for every Idea, lingly taken, is faid to be one ^ when we comprehend others with it, they are two, or three, or four. Number therefore is tranfccn- dent to their fubftance, by participation where¬ of, one, two, or more, are predicated of them. Again, folid figures are conceived in the mind before bodies, as having an incorporeal Nature^ yet they are not the principles. Superficies pre¬ cede them in our imagination, for folids confift of fuperficies. But neither are fuperficies the elements .of beings, for they confift of lines lines precede them; numbers precede lines. That which confifts of three lines, is called a Triangle 9 that which of four, a Qliadrangle. Even line it felf, fimply taken, is not conceived without number : but being carried on from one point to another, is conceived in two. As to Numbers, they all fall under the Monad ; for the Duad is one Duad, the Triad one Triad, and the Decad one fummary of number.
This moved Pythagoras to fay. That the prin¬ ciple of all things is the Monad ; by participa¬ tion hereof, every being is termed One j and when we refteSl on a being in its identity, we confider a Monad : but when it receives addition by alterity, it produceth indeterminate Duad, fo called, in diftin£lion from the Arithmetical de¬ terminate Duads ; by participation whereof all Duads are underftood, as Monads by the Monad. Thus there are two principles of be¬ ings, the firft Monad, and the indeterminate Duad.
That thefe are indeed the principles of all things, the Pythagoreans teacli varioufly. Of beings, flay theyj fome are underftood by dif¬ ference 9 others by contrariety : others by rela¬ tion.* Bydiffercnce^zYciho{c\Mhich^rQ confidered
by themfelvesj fubjecled by their proper circum- feription ; as, a man, a horfe, a plant, earth, wa¬ ter, air, fire-, each of theft is confidered abfo- lutely without any. By contrariety^ are thoft which are confidered by contrariety of one to the other - as, good and ill ^ juft, uniuft : profitable unprofitable i facred, profane^ pious impious-* moving, fixt ^ and the like. By relation^ thofe vv inch are confidered by relation to others- as right, left i upwards, downwards ^ double half for right is underftood by a relative habit to lefr* and left by a relative habit to right ; upwards to downwards, and downward to upwards ; and fo of the reft. Thofe which are underftood by contrariety, differ from thofe that are underftood by relation. In contraries, the corruption of the one IS the generation of another ; as, of health iicknefs, motion, and reft. The induftion of licknefs is the expulfion of health, and the in¬ duction of health is the expulfion of iicknefs • the lame in grief and joy, good and ill, and all thines of contrary Natures. But the relative exift toae- ther and perilh together ; for right is nothing, unkfs there be left ^ ^double is nothing, unlefs we underftand the half whereof it is the double: Moi cover, in Contraries there is no mean as bc-^ tween health and iicknefs, life and death, motion and reft. But betwixt Relatives there is a mean - as betwixt greater and lefTer, the mean is equal * -betwixt too much and too little, ft.fficicnt ; be^’ twixt tco fiat and too iharp, concord.
Above theft three kinds, Aofolute, Contrary Relative, there muft neceilarily be fome fupreani Genus- every Genus is before the Species which aie under it. For if the Genus be taken away the Species are taken away alfo ^ but the removal of the Species takes not a^^ay the Genus, the Spe¬ cies depending on the Genus, not the Genus on the Species. The tranfeending Genus of thoft things which are underftood by themfelves ("ac¬ cording to the Pythagoreans) is the One-^ a’s that exifts and is confidered abfoliitely, fo they. Of contraries, equal and unequal, holds the place of a Genus, for in them is confidered the nature of all Contrarieties • as .of reft in equality, it ad¬ mits not intenfion and remiffion 9 of motion in¬ equality, it admits intenfion and remiffion. In like manner, natural inequality, it is the inft:- ble extremity ; preternatural inequality, ic ad¬ mits intenfion and remiffion. The fame of health and ficknefs,^ ftraightnefs and crookednefs. The relative confifts of excels and defed:, as their Ge¬ nus i great and greater, much and more, high and higher, are underftood by excefs -. little and lefs, low and lower, by defed.
Now forafmuch as Ahfolute?^ Contraries and Relatives, appear to be fubordinate to other Ge¬ nus’s, (that is, to One, to Eciuality, and to Lie- quality, to Excefs and Defect) let us examine, whether thofe Genus’s may be reduc’d- to others* Equality is reducible to Oiie, for one is eoual in it felf^ inequality is either in excefs or defeft- of unequals, one e.xceeds, the other is deficient -. Excefs and defeft arc reducible to the indeter¬ minate Duad ^ or the firft excefs and defeft is in two, in the e.xccdent and the deficient. Thus the principles of all things appear in the top above all the reft, the firft xMonad, and the indetermi¬ nate Duad,
Fff 2
Of
VTTHAGORAS.
•4^4
Of thefeis generated the Arithmetical Monad and Daad, from the firfi. Monad, one^ from the Monad and the indeterminate Daad, two ^ the Daad being not yet conflitu'-ed nmonglt Num¬ bers neither was here two, before it was taken out of the indeterminate Duad, of which, toge¬ ther wit!) the Monad, was produced the Daad which is in Numbers. Oat of thefe, in the fame manner proceeded the reft of the Numbers, one continually ffepping forward, the indeterminate Duad generating two, and extending Numbers to an inHuite multitude.
Hereupon they atiirm, that, in principles. Mo¬ nad hath the nature of the efficient caufe, Duad of paffive matter •, and after the fame manner, as they produced Numbers, which con lilts of them, they compofed the World alfo, and all things in it. A. Point is correfpondent to the Monad •, the Monad is indivifiblc, fo is the Pointy the Monad is the principle of Numbers, fo is the Point of Lines. A Line is correfpondent to tlie Duad, both are confidered by tranlition. Aline is length with¬ out breadth, extended betwixt two Points. A Su¬ perficies correfponds to the Triad ^befides length, whereby it was a Duad, it receives a third di- flance, breadth. Again, fetting down three Points, two oppofite, the . third at the juntfurc of the lines made by the two, we reprclent afuperficics. The folid. figure and the body, as a Pyramid, an- fwer the Tetrad ^ if we lay down, as before, three points, and fetover them another point, be¬ hold the Pyramidical form of a folid body, which hath three dimenfions, length, breadth, thick- nefs.
Some there are who affirm, that a Body con- fifts of one point, the point by fluxion makes a Line, the Line by fluxion makes a Superficies, the Superficies moved to thicknefs makes a Body, three ways dimenfurable. This Seft of the Py- thiigoreans differs from the former •, they held, thit of two principles, the Monad and the D lad were made Numbers, of Numbers were made Points, Lines, Superficies, and Solids: Thefe, ^ that all things come from one point, for of it is
made a line, of the line a fuperficics, ofthe fuper- ficies a body.
Thus are folid Bodies produc’d of Numbers precedent to them. Moreover, of them confift Solids, Fire, Water, Air, Earth, and in a word, the whole World, which is governed according to Harmony, as they affirm again, recurring to Numbers, which comprize the proportions that (u\ adverf/Log. confiding of three Concords, the Diatef-
iib. 1. faron, the Diapente, the Diapafon ; the pi'opor- tions of thefe three Concords are found in 'the firif four Numbers, one, two, three, four. The IdiatcfTaron confifts in a felquitertia proportion. The Diapafon in fefquialtcra, the Diapente in duple ^ four being fefquitertius to three, (as con¬ fiding of three and onethird^ hath a Diateffa- ron proportion ; three being felquialtcr to two (as containing two and its half) a Diapente-, four be¬ ing the double ofthe Monad of two, a Diapafon. The Tctraflies affording the analogy of thefe Concords, which make pericH harmony, accor¬ ding to which all things arc governed, they dil’d .A,
The root &nd fountain of eternal Nature.