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thing；　but　let　us　suppose　the　world　to　be　the　very　image　of　that　whole

of　which　all　other　animals　both　individually　and　in　their　tribes　are

portions。　For　the　original　of　the　universe　contains　in　itself　all

intelligible　beings；　just　as　this　world　comprehends　us　and　all　other

visible　creatures。　For　the　Deity；　intending　to　make　this　world　like

the　fairest　and　most　perfect　of　intelligible　beings；　framed　one

visible　animal　comprehending　within　itself　all　other　animals　of　a

kindred　nature。　Are　we　right　in　saying　that　there　is　one　world；　or

that　they　are　many　and　infinite？　There　must　be　one　only；　if　the

created　copy　is　to　accord　with　the　original。　For　that　which　includes

all　other　intelligible　creatures　cannot　have　a　second　or　companion；　in

that　case　there　would　be　need　of　another　living　being　which　would

include　both；　and　of　which　they　would　be　parts；　and　the　likeness　would

be　more　truly　said　to　resemble　not　them；　but　that　other　which　included

them。　In　order　then　that　the　world　might　be　solitary；　like　the　perfect

animal；　the　creator　made　not　two　worlds　or　an　infinite　number　of　them；

but　there　is　and　ever　will　be　one　only…begotten　and　created　heaven。

　　Now　that　which　is　created　is　of　necessity　corporeal；　and　also

visible　and　tangible。　And　nothing　is　visible　where　there　is　no　fire；

or　tangible　which　has　no　solidity；　and　nothing　is　solid　without　earth。

Wherefore　also　God　in　the　beginning　of　creation　made　the　body　of　the

universe　to　consist　of　fire　and　earth。　But　two　things　cannot　be

rightly　put　together　without　a　third；　there　must　be　some　bond　of　union

between　them。　And　the　fairest　bond　is　that　which　makes　the　most

complete　fusion　of　itself　and　the　things　which　it　combines；　and

proportion　is　best　adapted　to　effect　such　a　union。　For　whenever　in　any

three　numbers；　whether　cube　or　square；　there　is　a　mean；　which　is　to

the　last　term　what　the　first　term　is　to　it；　and　again；　when　the　mean

is　to　the　first　term　as　the　last　term　is　to　the　mean…then　the　mean

becoming　first　and　last；　and　the　first　and　last　both　becoming　means；

they　will　all　of　them　of　necessity　come　to　be　the　same；　and　having

become　the　same　with　one　another　will　be　all　one。　If　the　universal

frame　had　been　created　a　surface　only　and　having　no　depth；　a　single

mean　would　have　sufficed　to　bind　together　itself　and　the　other

terms；　but　now；　as　the　world　must　be　solid；　and　solid　bodies　are

always　compacted　not　by　one　mean　but　by　two；　God　placed　water　and

air　in　the　mean　between　fire　and　earth；　and　made　them　to　have　the　same

proportion　so　far　as　was　possible　（as　fire　is　to　air　so　is　air　to

water；　and　as　air　is　to　water　so　is　water　to　earth）；　and　thus　he　bound

and　put　together　a　visible　and　tangible　heaven。　And　for　these　reasons；

and　out　of　such　elements　which　are　in　number　four；　the　body　of　the

world　was　created；　and　it　was　harmonised　by　proportion；　and

therefore　has　the　spirit　of　friendship；　and　having　been　reconciled

to　itself；　it　was　indissoluble　by　the　hand　of　any　other　than　the

framer。

　　Now　the　creation　took　up　the　whole　of　each　of　the　four　elements；　for

the　Creator　compounded　the　world　out　of　all　the　fire　and　all　the　water

and　all　the　air　and　all　the　earth；　leaving　no　part　of　any　of　them

nor　any　power　of　them　outside。　His　intention　was；　in　the　first

place；　that　the　animal　should　be　as　far　as　possible　a　perfect　whole

and　of　perfect　parts：　secondly；　that　it　should　be　one；　leaving　no

remnants　out　of　which　another　such　world　might　be　created：　and　also

that　it　should　be　free　from　old　age　and　unaffected　by　disease。

Considering　that　if　heat　and　cold　and　other　powerful　forces　which

unite　bodies　surround　and　attack　them　from　without　when　they　are

unprepared；　they　decompose　them；　and　by　bringing　diseases　and　old

age　upon　them；　make　them　waste　away…for　this　cause　and　on　these

grounds　he　made　the　world　one　whole；　having　every　part　entire；　and

being　therefore　perfect　and　not　liable　to　old　age　and　disease。　And

he　gave　to　the　world　the　figure　which　was　suitable　and　also　natural。

Now　to　the　animal　which　was　to　comprehend　all　animals；　that　figure　was

suitable　which　comprehends　within　itself　all　other　figures。

Wherefore　he　made　the　world　in　the　form　of　a　globe；　round　as　from　a

lathe；　having　its　extremes　in　every　direction　equidistant　from　the

centre；　the　most　perfect　and　the　most　like　itself　of　all　figures；

for　he　considered　that　the　like　is　infinitely　fairer　than　the

unlike。　This　he　finished　off；　making　the　surface　smooth　all　around　for

many　reasons；　in　the　first　place；　because　the　living　being　had　no　need

of　eyes　when　there　was　nothing　remaining　outside　him　to　be　seen；　nor

of　ears　when　there　was　nothing　to　be　heard；　and　there　was　no

surrounding　atmosphere　to　be　breathed；　nor　would　there　have　been　any

use　of　organs　by　the　help　of　which　he　might　receive　his　food　or　get

rid　of　what　he　had　already　digested；　since　there　was　nothing　which

went　from　him　or　came　into　him：　for　there　was　nothing　beside　him。　Of

design　he　was　created　thus；　his　own　waste　providing　his　own　food；

and　all　that　he　did　or　suffered　taking　place　in　and　by　himself。　For

the　Creator　conceived　that　a　being　which　was　self…sufficient　would

be　far　more　excellent　than　one　which　lacked　anything；　and；　as　he　had

no　need　to　take　anything　or　defend　himself　against　any　one；　the

Creator　did　not　think　it　necessary　to　bestow　upon　him　hands：　nor　had

he　any　need　of　feet；　nor　of　the　whole　apparatus　of　walking；　but　the

movement　suited　to　his　spherical　form　was　assigned　to　him；　being　of

all　the　seven　that　which　is　most　appropriate　to　mind　and　intelligence；

and　he　was　made　to　move　in　the　same　manner　and　on　the　same　spot；

within　his　own　limits　revolving　in　a　circle。　All　the　other　six　motions

were　taken　away　from　him；　and　he　was　made　not　to　partake　of　their

deviations。　And　as　this　circular　movement　required　no　feet；　the

universe　was　created　without　legs　and　without　feet。

　　Such　was　the　whole　plan　of　the　eternal　God　about　the　god　that　was　to

be；　to　whom　for　this　reason　he　gave　a　body；　smooth　and　even；　having

a　surface　in　every　direction　equidistant　from　the　centre；　a　body

entire　and　perfect；　and　formed　out　of　perfect　bodies。　And　in　the

centre　he　put　the　soul；　which　he　diffused　throughout　the　body；

making　it　also　to　be　the　exterior　environment　of　it；　and　he　made　the

universe　a　circle　moving　in　a　circle；　one　and　solitary；　yet　by

reason　of　its　excellence　able　to　converse　with　itself；　and　needing

no　other　friendship　or　acquaintance。　Having　these　purposes　in　view

he　created　the　world　a　blessed　god。

　　Now　God　did　not　make　the　soul　after　the　body；　although　we　are

speaking　of　them　in　this　order；　for　having　brought　them　together　he

would　never　have　allowed　that　the　elder　should　be　ruled　by　the

younger；　but　this　is　a　random　manner　of　speaking　which　we　have；

because　somehow　we　ourselves　too　are　very　much　under　the　dominion　of

chance。　Whereas　he　made　the　soul　in　origin　and　excellence　prior　to　and

older　than　the　body；　to　be　the　ruler　and　mistress；　of　whom　the　body

was　to　be　the　subject。　And　he　made　her　out　of　the　following　elements

and　on　this　wise：　Out　of　the　indivisible　and　unchangeable；　and　also

out　of　that　which　is　divisible　and　has　to　do　with　material　bodies；

he　compounded　a　third　and　intermediate　kind　of　essence；　partaking　of

the　nature　of　the　same　and　of　the　other；　and　this　compound　he　placed

accordingly　in　a　mean　between　the　indivisible；　and　the　divisible　and

material。　He　took　the　three　elements　of　the　same；　the　other；　and　the

essence；　and　mingled　them　into　one　form；　compressing　by　force　the

reluctant　and　unsociable　nature　of　the　other　into　the　same。　When　he

had　mingled　them　with　the　essence　and　out　of　three　made　one；　he

again　divided　this　whole　into　as　many　portions　as　was　fitting；　each

portion　being　a　compound　of　the　same；　the　other；　and　the　essence。

And　he　proceeded　to　divide　after　this　manner：…First　of　all；　he　took

away　one　part　of　the　whole　＇1＇；　and　then　he　separated　a　second　part

which　was　double　the　first　＇2＇；　and　then　he　took　away　a　third　part

which　was　half　as　much　again　as　the　second　and　three　times　as　much

as　the　first　＇3＇；　and　then　he　took　a　fourth　part　which　was　twice　as

much　as　the　second　＇4＇；　and　a　fifth　part　which　was　three　times　the

third　＇9＇；　and　a　sixth　part　which　was　eight　times　the　first　＇8＇；　and　a

seventh　part　which　was　twenty…seven　times　the　first　＇27＇。　After　this

he　filled　up　the　double　intervals　＇i。e。　between　1；　2；　4；　8＇　and　the

triple　＇i。e。　between　1；　3；　9；　27＇　cutting　off　yet　other　portions

from　the　mixture　and　placing　them　in　the　intervals；　so　that　in　each

interval　there　were　two　kinds　of　means；　the　one　exceeding　and　exceeded

by　equal　parts　of　its　extremes　＇as　for　example　1；　4/3；　2；　in　which　the

mean　4/3　is　one…third　of　1　more　than　1；　and　one…third　of　2　less　than

2＇；　the　other　being　that　kind　of　mean　which　exceeds　and　is　exceeded　by

an　equal　number。　Where　there　were　intervals　of　3/2　and　of　4/3　and　of

9/8；　made　by　the　connecting　terms　in　the　former　intervals；　he　filled

up　all　the　intervals　of　4/3　with　the　interval　of　9/8；　leaving　a

fraction　over；　and　the　interval　which　this　fraction　expressed　was　in

the　ratio　of　256　to　243。　And　thus　the　whole　mixture　out　of　which　he

cut　these　portions　was　all　exhausted　by　him。　This　entire　compound　he

divided　lengthways　into　two　parts；　which　he　joined　to　one　another　at

the　centre　like　the　letter　X；　and　bent　them　into　a　circular　form；

connecting　them　with　themselves　and　each　other　at　the　point　opposite

to　their　original　meeting…point；　and；　comprehending　them　in　a

uniform　revolution　upon　the　same　axis；　he　made　the　one　the　outer　and

the　other　the　inner　circle。　Now　the　motion　of　the　outer　circle　he

called　the　motion　of　the　same；　and　the　motion　of　the　inner　circle

the　motion　of　the　other　or　diverse。　The　motion　of　the　same　he

carried　round　by　the　side　to　the　right；　and　the　motion　of　the

diverse　diagonally　to　the　left。　And　he　gave　dominion　to　the　motion

of　the　same　and　like；　for　that　he　left　single　and　undivided；　but　the

inner　motion　he　divided　in　six　places　and　made　seven　unequal　circles

having　their　intervals　in　ratios　of　two…and