Part IX.

378
to it felf, and produceth them and the Arith¬ metical knowledge of them. According to the- . union of multitude and communication with it felf , and colligation , it acquireth to it felt Mulick ; For wlfich tcafoiT Arithmetick excels Mu Pick in antiquity, the fold it felf being firlf • divided by the Maker, tiien collefled by pro¬ portions. And again ellablifhing the operation within it felf, according to its ftation, it produ¬ ceth Geonrctry out of it felf, and one ligure, and the principles of all figures, but according to its motion, Sphtrfick : for Ihe is moved by circles, but conlilfs always in the fame manner accor¬ ding to the caufes of thofe circles, the llraight and the circular : And for this reafon likewife Geometry is precedent to Sphatrick, as Station is to Motion.
But forafinuch as the Soul produced thefe Sci¬ ences, not looking on the excitation of Ideas, which is of infinite power, but Upon the boun- (d) ReadK^i- ofthat which is limited (cl) in their feveral 7K yiviu kinds, therefore they fay that they take infinite from multitude and magnitude, and are conver- fant only about finite; For the mind hath placed in her felf all principles both of multitude and magnitude, becanfe being wholly of like parts within her felf, and being one and indivillble, and again divdliblc, and producing the world of Ideas, it doth participate elfential finitenefs and r infinitenefs from the things which it doth nn-
derlfand : But it undcrllands according to that which is finite in them, and not according to the infinitenefs of its life. This is the opinion of the Fythagoreans^ and their divifion of the four Sciences. Hitherto ?roclus.
CHARI.
Number^ its kinds the Jirji kind^ IntelleUual in the Divine Mind.
{a) TV T Umber is of two kinds, the IntelleUual, (^a)mc(im. A- ( or immateiial) and the Sqiential. The rith. Intellednal is that (b ) eternal fubflance of Num- ''g*
bci', which 'Pythagoras in his Difeourfe concern- ^ *
ing the Gods aflerted to be principle 7noJi pro¬ vidential' of all Heaven and Earthy and the nature that is betwixt thetn. Moreover, it is the root of Divine Beings, and of Gods, and of Damons. This is that which he termed (c) the principle^ foun- (0 Thm. tain, and root of all things, and defined it to be that which before all things exijis in the Divine mind-, from which and out of which all things are digefled into order, and remain numbred by (d)(^ Kkm. A- an indijfoluhle feries. fnhm, cap. 5.
For all things which are ordered in the world by nature according to an artificial courfe in part and in wdiole, appear to be diftinguilhed and a- dorn’d by Providence and the All-creating Mind, according to Number 3 the Exemplar being e- flablifhed by applying (as the reafon of the prin- , .
ciple before the imprelfion of things) the num-, her pra^exiftent in the Intelleft of God, maker of the world. This only in Intelledual, and wholly immaterial, really a fubflance according to yvhich as being the moll exaU artificial reafon, all things are perfefled, Time, Heaven, Motion, the Stars, and their various revolutions.
CHAP. II.
SECT. I.
Arithmetick.
(a) N'mn. ’A- (a ) thefe four methods , Which is that
which ought neceffarily to be learned (viz. that which is by nature pi^exi- tle, as a pag. E^nt to the reft and chiefeft, being as it were 30,55, 44, 62, principle, and root, and mother of the reft)? A- 76) cap. 4. rithmetick : Not only for that it is pra^exiftent before the reft in the IntelleQ: of the efficient God, as an ornative and exemplary reafon, according i to which the Maker of the Univerfe caufed all , ■ things to be made out of matter to its proper . , end, as after h- and archetypal pat- (h'\ Read - ^ becaufe being (f) naturally firft ge-
nerated, it together takes away the reft with it v3rc{pp/«5-£j, felf, but is not taken away with them. Thus A- o-tywiV./, &c. nimal is firft in nature before Man : For taking lax. atS- away animal, we take away man, but not in ta- PiTtKn. away man do we take away animal. ( Of
this Nicomachus difeourfeth more largely. 3 As concerning Arithmetick, Timaus affirms (0 Phjfic. 2.- that Pythagoras addilied himfelf chiefly to it : {d)
' Stobxus, that he efieemed it above all others, and brought it to light, reducing it from the ufe of Tra¬ ce) chon. («■) Hence and others, ftylehimr^^
(/) Ong.f.'i.. Inventer of Arithmetick, affirming (/) he was the stob. vbyf, 2, firfl who writ upon this fubjebi among f the Gratci- ahs, which was afterwards more copioufly compofed by Nicomachus. He ftudied this Science exceed- ingly, and fo much did he prefer it above all the reft, that he conceived. The ultimate good of man to confljl in the moji exabl Science of Numbers.
The other kind of Number, Sciential 3 its Principles.
Sciential Number is tlfaf which Pythagoras 'defines the extenfion and produUion into aU of the feminal reajons which are in the (a) Mo- (a) Mider(tt'. nad, or a heap of Monads , or a progrejflon of^l’’ multitude, beginning from Monad, arid a regref- fion ending in Monad.
(b) The Pythagoreans affirmed the expofitive (b) Tbm.Mt- terms, whereby even and odd numbers are un- ‘^P* f* , derftood, to be the principles of CSciential3 Nuni- bers, as of three infenfible things, the Triad,; of ’ four Infenfibles, the Tetrad ; and fo of other ,
numbers.
They, make a difference betwixt the M6nad and One, concerning the Monad to be that which ex- ifts in Intelleauals •, One, in numbers for as (d) (d) Stob.Phyt Moderatus expreffeth it, Aloriad amongft num- 2. bers. One amongft things numbred, one body be¬ ing divifible into infinite: Thus numbers and things numbred differ, as incorporeals and bo- diesj in like manner Two is amongft numbers.
The Duad is indeterminate *, Monad is taken ac¬ cording to equality and mcafure, Duad according id excefs and defeQ : Mean and meafure cannot admit more and lefs, but excefs and defeH: ( fee¬ ing that they proceed to infinite ) admit it, there¬ fore they call the Duad indeterminate (e) holding (e) Themlft. ia Number to be infinite, not that -number which 3* is feparate and incorporeal, but that which is (f)Airift.Fl9r. (f) not feparate from fcnfible things. 4*
G H A P,
T
Jl
IX.
P TT H JG 0 K A S.
CHAP. III.
\ The Two At /ids of Sciential I^unibe/\ Odd
and Ex/en,
f . _ , ■ •* , ' • ■
j naj Euflr.'tt. CScientiall Numbers Tythagora^, afTer-
I m Ethic, i. vv ted Two Orders, One bounded. Odd, the I i’frvj'nfc/o^.s. other infinite, Even.-', (^) Even Number., ("accor- ding jx),-fhePythagorick definition j is that which mt. ‘c3p[V.' 2t once admits divifion into the greateft and the leaft; into the greateft Magnitudes, (for halves are t4§,.S^eareft parK), theleaft in multitude (for Two is the leatt number) according to the natu¬ ral oppofition of.thele two kinds. (W is that which cannot fufter this, but is cut into two un¬ equals.
(c) ThemB. in (c)- Herein the Pythagoreans differ from the Phj/f.^, p/a/c/7/^j', in that they hold not all Number to be
infinite, but only the Even: for ev.en Number is the caufe of feftion into equal parts, , which is in¬ finite, and by its proper Nature geijerates infinity in thofe things in which it exifts.. But it is limi¬ ted by the Odd •, for that being applied to the . Even, hinders its diffeflion into two equal parts.
(d) Macrob. (d) Odd Number is laid to have been found by . staturn. 1. 13. Pythagoras, and tdbe of Mufeuline Virtue, and
proper to the Coeleftial Gods ((^^j to whom they (f) Plutarch facrificed always of that Number,) and to be : deMom.pefi. (f) full and perfefl. ■ Even, is indigent and (gjserv.ad imperfeff, and Female, and proper to the fubterraneous Deities, , to .whom they facrificed Even things. . / ’
(h) Anon in ( h ) Moreover, whatever isi generated of
Odd Number is Male, whatlbever. of Even is bibLhb. 1. for Even Number is fubjeSl to Seflion
and Pafiion, Odd is void of both, and is effica¬ cious •, wherefore they call one the' Male, the
(i) Auon.The(hothQT the Female. ( i) A Number, which. ari-
* % feth out of the Power and Multiplication of
Even and Odd, is called dppsvodvrvf, herma¬ phrodite.
This Opinion Pythagoras feems to have derived i CbJ Piut'.de piornTjarates, his Mafter, (k) who call’d mma.proar. Number, Monad the Father;
and therefore they laid, that thofe Numbers i which refemble. ylD/tizi (wcr. the Odd) are the
fieftv ' .
j Cljsimplic.in (/ j Odd Numbers they called be-
phj/f. lih. ^aufe being added to Squares, they keep the fame Figures; lo Gnomons do in Geometry.
CHAP. IV.
Symbolical Numbers.
(a)Porph.^.‘}2. Pythagoreans (faith Moderatus of
J. Gades, who learnedly comprifed their Opinions in Eleven Books) uling the Mathema¬ tical Sciences as degrees of Preparations to the contemplations of the things that are, were ftu- dioufly addifled to the bufinefs of .Numbers, for . this realbn. Seeing they could not clearly ex¬ plain the firft Forms and Principles in difcourle (thofe being the moft difficult to underhand and exprefs) had recourfe to Numbers for the better explication of their Doflrine, imitating Geome¬ tricians, and fjch as teach to read. For as thele
going about to explain Letters and their Powers, recurr to Marks, laying, That thefe are, as ic were, the firft Elements Learning; neverthelefs afterwards they tell us, That tht;y are not the Elements, but that the true Elements are known by them. And as the Geometricians, not being able to exprefs Incorporeal Forms in words, have recourfe to the Defeription of Figures, faying,
This A is a Triangle, not-meaningrhatthiswhich falleth under the fight is a Triangle, but that which hath the f:tme Figure, and which is by the help thereof, and reprefenteiii the knowledge ^ of a Triangle to theMind. The fame did the P;- in the firft Reafons and Forms; for; feeing they could not in vvords exprefs incorporea I = ' .
forms, and firft principles, they had recourfe to demonftration by Numbers. And thus they cal¬ led the Realbn of Unity, and Indentity, and Equa¬ lity, and the caufe of amicable Gonfpiration, and. of Empathy, and of theConfervation.of the Llni- verfe, which continueth according to the fame, and. in the fame manner, O NE. .. For the one which is in particulars, is fuch united to the parts, and confpiring by participation of the firft caufe. But the twofold Reafbn of diverficy and inequality, and of every thing that isdivifibleand in mutation, and exifts Ibmetimes oneway, Ibme-' times another, they called D U A D, for the na¬ ture of the Duad in particular things is fuchw Thefe Realbns are not only according to the Fy- thagoPeans, and not (acknowledg’d by) others, but we fee that other Philofophers alfo h.ave left certain unitive powers, which comprize all things in the Univerfe ; and amongft them thereare cer¬ tain Realbns of equality, diHimilitude. and diver- fity. . Now thefe Reafons, that the way of teach¬ ing might be more perfpicuous, he called by the names of Monad and Duad-., but ir is all one a- mongft them if it be called biform, or aiqualifbrm^ or diyerfiform.
The lame Realbn is in other Numbers, for eve¬ ry one is ranked according to fome powers. In the Nature of things exifts fbmething. which hath beginning, middle and end. To fuch a form and nature they attributed the number Three, laying,
That viffiatfbever hath a middle is triform ; lb they called every perfect thing. And if any thing be perfebf, they affirm it maketh ufe of this prin¬ ciple, and is adorned according ro it; which,' fince they could not name otherwife, they made ufe of the term Triad to exprefs it; and when they endeavour to bring us to the knowledge there¬ of, they lead us to ic by the ferm of this lyiad. iT he lame in other N umbers. '
Thefe therefore are the Realbns, according to which the forefaid Numbers were placed-, but thefe that follow are comprehended under ona form and power,which they call Decad, q. Dechad, ffrom comprehenfion. d Wherefore they fay, that Ten isaperfebl number, even the moft pet- febl of all numbers, comprehending in it all diffe¬ rence of Numbers, all Realbns, Species and Pro¬ portions. For if the nature of the Univerle be defined according to the Realbns and Proportions of Numbers; and that which is produced, and ^ increafed, and perfebfed, proceed according to the Realbns of Numbers; ^nd the Decad com¬ prehends every Realbn of Number, and every Proportion, and all Species: Why fhould not Nature it felf be termed by the Name of Te:},
C c c a tbs
580
Modtratw apud Stob,
Wyf. I. 2.
PTTHAGORAS. Part IX.
the moll perfeft Number ? Hitherto Mode- ratm.
Thus from the fymbolical ufe of numbers proceeded a multiplicions variety of names, at¬ tributed to them by Pythagoras and his followers. Of which w'e fhall fpeak more particularly, be¬ ginning with the Monad. ^
, - ■ C H A P. V.
The Monad.
TH E Monad is a quantity, which in the de- creafe of multitude, bemg deprived of ail number, rcceiv*eth manfion and ftation; for be¬ low Q;ianticy, Monad cannot retreat. The Mo¬ nad therefore feems to be fo called, either from Handing, or from remaining (fj^kvay) always in the iamer'condition , or from its reparation if tom multitude. '
To the Monad are attributed thefe Names. Mindj (Nicom. Phot. Anon. Tbeo/og. ) htcan{£: the Mind is (table, and every way alike, and hath the preheminence. ( Alex. Aphrod. in Me- tapb. )
Hennaphrodite (Nicom.) it is both Male and Female, Odd and Even, (Macrob. in Somn. Sap. I. 6.) it partakes ot both -Natures V being added to the even, it makes odd, to the. odd, even. {Ariflot. in Pythagorico., cited by Theon. Srnyrn. Ala'them. cap. 5.)
God.^ becaufe it is the beginning and end of all, it felf having neither beginning nor end- Maa'ob. )
. Good., tor fuch is the Nature of one. {Por- phyr. vit. Pyth.)
Matter., receptacle of all., (Nicom.) becaufe it produceth Duad. which is properly Matter. j( Anon. Theol. )
Chaos , Confufion., Contemperation., Ohfcur 'ity , Chafme., Tartarus^ Styx., Uorrour, Jmpermiftion^ Subterraneous Barathrum, Lethe, Rigid Virgin, Atlas, Axis, Siime, Pyr alios, Morpho. ( Nicom. Anon. )
Tower of Jupiter, ( Nicom. ) Cuflody of Ju¬ piter, Throne of Jupiter, ( Simplic. ) from the great power which the Center hath in' the Uni- verfe, being able to reftrain the general Circular Motion, as if the Cuftody of the Maker of all things were conftituted jtlierein. ( Prod, in Ti- maum. com. 4.
Seminal Reafon, (Nicom.) becaufe this one only is one to the Jletractors , and is alone, and the reft are procreated of it, and it is the only .Seminary of all Numbers. ( Mart. Ca- pel. 1.)
Apollo Prophet. ( Nicom. )
Prometheus, as being Author of Life. ( Anon. Theol.)
Geniture, becaufe without' it no number hath being. ( Anon. Theol. )
Subftance , ( Theolog. ) becaufe Subftahee is primary. Alex. Aphr. Alet. i. )
Caufe of Truth, Simple Exemplar, Conjiitution oj Symphony. (Anon. Theolog.)
In Greater and Leffer, Equal-, in Intention and Reiiiiffion, Middle-, in Multitude, Mean, ( Theolog.) in Time, AW, theprefent, (Anon. Theolog.) becaufe it confifts in one part of time
which is always prefent. ( Macrob. in Somn.