Eudoxussupposedthatthemotionofthesunorofthemoon
　　involves，ineithercase，threespheres，ofwhichthefirstisthe
　　sphereofthefixedstars，andthesecondmovesinthecirclewhich
　　runsalongthemiddleofthezodiac，andthethirdinthecirclewhich
　　isinclinedacrossthebreadthofthezodiac；butthecirclein
　　whichthemoonmovesisinclinedatagreateranglethanthatinwhich
　　thesunmoves。Andthemotionoftheplanetsinvolves，ineachcase，
　　fourspheres，andofthesealsothefirstandsecondarethesameas
　　thefirsttwomentionedaboveforthesphereofthefixedstarsis
　　thatwhichmovesalltheotherspheres，andthatwhichisplaced
　　beneaththisandhasitsmovementinthecirclewhichbisectsthe
　　zodiaciscommontoall，butthepolesofthethirdsphereofeach
　　planetareinthecirclewhichbisectsthezodiac，andthemotionof
　　thefourthsphereisinthecirclewhichisinclinedatanangleto
　　theequatorofthethirdsphere；andthepolesofthethirdsphereare
　　differentforeachoftheotherplanets，butthoseofVenusand
　　Mercuryarethesame。
　　CallippusmadethepositionofthespheresthesameasEudoxus
　　did，butwhileheassignedthesamenumberasEudoxusdidtoJupiter
　　andtoSaturn，hethoughttwomorespheresshouldbeaddedtothe
　　sunandtwotothemoon，ifoneistoexplaintheobservedfacts；
　　andonemoretoeachoftheotherplanets。
　　Butitisnecessary，ifallthespherescombinedaretoexplain
　　theobservedfacts，thatforeachoftheplanetsthereshouldbeother
　　spheresonefewerthanthosehithertoassignedwhichcounteract
　　thosealreadymentionedandbringbacktothesamepositionthe
　　outermostsphereofthestarwhichineachcaseissituatedbelow
　　thestarinquestion；foronlythuscanalltheforcesatworkproduce
　　theobservedmotionoftheplanets。Since，then，thespheres
　　involvedinthemovementoftheplanetsthemselvesare——eightfor
　　SaturnandJupiterandtwenty-fivefortheothers，andoftheseonly
　　thoseinvolvedinthemovementofthelowest-situatedplanetneed
　　notbecounteractedthesphereswhichcounteractthoseofthe
　　outermosttwoplanetswillbesixinnumber，andthesphereswhich
　　counteractthoseofthenextfourplanetswillbesixteen；therefore
　　thenumberofallthespheres——boththosewhichmovetheplanetsand
　　thosewhichcounteractthese——willbefifty-five。Andifonewere
　　nottoaddtothemoonandtothesunthemovementswementioned，
　　thewholesetofsphereswillbeforty-seveninnumber。
　　Letthis，then，betakenasthenumberofthespheres，sothatthe
　　unmovablesubstancesandprinciplesalsomayprobablybetakenasjust
　　somany；theassertionofnecessitymustbelefttomorepowerful
　　thinkers。Butiftherecanbenospatialmovementwhichdoesnot
　　conducetothemovingofastar，andiffurthereverybeingand
　　everysubstancewhichisimmunefromchangeandinvirtueofitself
　　hasattainedtothebestmustbeconsideredanend，therecanbeno
　　otherbeingapartfromthesewehavenamed，butthismustbethe
　　numberofthesubstances。Forifthereareothers，theywillcause
　　changeasbeingafinalcauseofmovement；buttherecannotheother
　　movementsbesidesthosementioned。Anditisreasonabletoinfer
　　thisfromaconsiderationofthebodiesthataremoved；forif
　　everythingthatmovesisforthesakeofthatwhichismoved，and
　　everymovementbelongstosomethingthatismoved，nomovementcan
　　beforthesakeofitselforofanothermovement，butallthe
　　movementsmustbeforthesakeofthestars。Forifthereistobea
　　movementforthesakeofamovement，thislatteralsowillhaveto
　　beforthesakeofsomethingelse；sothatsincetherecannotbean
　　infiniteregress，theendofeverymovementwillbeoneofthe
　　divinebodieswhichmovethroughtheheaven。
　　Evidentlythereisbutoneheaven。Foriftherearemany
　　heavensastherearemanymen，themovingprinciples，ofwhicheach
　　heavenwillhaveone，willbeoneinformbutinnumbermany。But
　　allthingsthataremanyinnumberhavematter；foroneandthesame
　　definition，e。g。thatofman，appliestomanythings，whileSocrates
　　isone。Buttheprimaryessencehasnotmatter；foritiscomplete
　　reality。Sotheunmovablefirstmoverisonebothindefinitionandin
　　number；sotoo，therefore，isthatwhichismovedalwaysand
　　continuously；thereforethereisoneheavenalone。Ourforefathersin
　　themostremoteageshavehandeddowntotheirposteritya
　　tradition，intheformofamyth，thatthesebodiesaregods，andthat
　　thedivineenclosesthewholeofnature。Therestofthetraditionhas
　　beenaddedlaterinmythicalformwithaviewtothepersuasionofthe
　　multitudeandtoitslegalandutilitarianexpediency；theysay
　　thesegodsareintheformofmenorlikesomeoftheotheranimals，
　　andtheysayotherthingsconsequentonandsimilartothesewhich
　　wehavementioned。Butifoneweretoseparatethefirstpointfrom
　　theseadditionsandtakeitalone-thattheythoughtthefirst
　　substancestobegods，onemustregardthisasaninspired
　　utterance，andreflectthat，whileprobablyeachartandeach
　　sciencehasoftenbeendevelopedasfaraspossibleandhasagain
　　perished，theseopinions，withothers，havebeenpreserveduntilthe
　　presentlikerelicsoftheancienttreasure。Onlythusfar，then，is
　　theopinionofourancestorsandofourearliestpredecessorsclearto
　　Thenatureofthedivinethoughtinvolvescertainproblems；for
　　whilethoughtisheldtobethemostdivineofthingsobservedby
　　us，thequestionhowitmustbesituatedinordertohavethat
　　characterinvolvesdifficulties。Forifitthinksofnothing，what
　　istherehereofdignity？Itisjustlikeonewhosleeps。Andifit
　　thinks，butthisdependsonsomethingelse，thensincethatwhich
　　isitssubstanceisnottheactofthinking，butapotencyit
　　cannotbethebestsubstance；foritisthroughthinkingthatits
　　valuebelongstoit。Further，whetheritssubstanceisthefaculty
　　ofthoughtortheactofthinking，whatdoesitthinkof？Eitherof
　　itselforofsomethingelse；andifofsomethingelse，eitherofthe
　　samethingalwaysorofsomethingdifferent。Doesitmatter，then，
　　ornot，whetheritthinksofthegoodorofanychancething？Are
　　therenotsomethingsaboutwhichitisincrediblethatitshould
　　think？Evidently，then，itthinksofthatwhichismostdivineand
　　precious，anditdoesnotchange；forchangewouldbechangeforthe
　　worse，andthiswouldbealreadyamovement。First，then，if’thought’
　　isnottheactofthinkingbutapotency，itwouldbereasonableto
　　supposethatthecontinuityofitsthinkingiswearisometoit。
　　Secondly，therewouldevidentlybesomethingelsemorepreciousthan
　　thought，viz。thatwhichisthoughtof。Forboththinkingandthe
　　actofthoughtwillbelongeventoonewhothinksoftheworstthing
　　intheworld，sothatifthisoughttobeavoidedanditought，for
　　thereareevensomethingswhichitisbetternottoseethantosee，
　　theactofthinkingcannotbethebestofthings。Thereforeitmustbe
　　ofitselfthatthedivinethoughtthinkssinceitisthemost
　　excellentofthings，anditsthinkingisathinkingonthinking。
　　Butevidentlyknowledgeandperceptionandopinionand
　　understandinghavealwayssomethingelseastheirobject，and
　　themselvesonlybytheway。Further，ifthinkingandbeingthought
　　ofaredifferent，inrespectofwhichdoesgoodnessbelongtothought？
　　Fortoheanactofthinkingandtoheanobjectofthoughtarenot
　　thesamething。Weanswerthatinsomecasestheknowledgeisthe
　　object。Intheproductivesciencesitisthesubstanceoressenceof
　　theobject，matteromitted，andinthetheoreticalsciencesthe
　　definitionortheactofthinkingistheobject。Since，then，
　　thoughtandtheobjectofthoughtarenotdifferentinthecaseof
　　thingsthathavenotmatter，thedivinethoughtanditsobjectwillbe
　　thesame，i。e。thethinkingwillbeonewiththeobjectofits
　　thought。
　　Afurtherquestionisleft-whethertheobjectofthedivine
　　thoughtiscomposite；forifitwere，thoughtwouldchangein
　　passingfromparttopartofthewhole。Weanswerthateverything
　　whichhasnotmatterisindivisible-ashumanthought，orratherthe
　　thoughtofcompositebeings，isinacertainperiodoftimeforit
　　doesnotpossessthegoodatthismomentoratthat，butitsbest，
　　beingsomethingdifferentfromit，isattainedonlyinawhole
　　periodoftime，sothroughouteternityisthethoughtwhichhas
　　itselfforitsobject。
　　Wemustconsideralsoinwhichoftwowaysthenatureofthe
　　universecontainsthegood，andthehighestgood，whetherassomething
　　separateandbyitself，orastheorderoftheparts。Probablyinboth
　　ways，asanarmydoes；foritsgoodisfoundbothinitsorderand
　　initsleader，andmoreinthelatter；forhedoesnotdependonthe
　　orderbutitdependsonhim。Andallthingsareorderedtogether
　　somehow，butnotallalike，-bothfishesandfowlsandplants；and
　　theworldisnotsuchthatonethinghasnothingtodowithanother，
　　buttheyareconnected。Forallareorderedtogethertooneend，but
　　itisasinahouse，wherethefreemenareleastatlibertytoact
　　atrandom，butallthingsormostthingsarealreadyordainedfor
　　them，whiletheslavesandtheanimalsdolittleforthecommon
　　good，andforthemostpartliveatrandom；forthisisthesortof
　　principlethatconstitutesthenatureofeach。Imean，forinstance，
　　thatallmustatleastcometobedissolvedintotheirelements，and
　　thereareotherfunctionssimilarlyinwhichallshareforthegoodof
　　thewhole。
　　Wemustnotfailtoobservehowmanyimpossibleorparadoxical
　　resultsconfrontthosewhoholddifferentviewsfromourown，andwhat
　　aretheviewsofthesubtlerthinkers，andwhichviewsareattendedby
　　fewestdifficulties。Allmakeallthingsoutofcontraries。But
　　neither’allthings’nor’outofcontraries’isright；nordothese
　　thinkerstellushowallthethingsinwhichthecontrariesare
　　presentcanbemadeoutofthecontraries；forcontrariesarenot
　　affectedbyoneanother。Nowforusthisdifficultyissolved
　　naturallybythefactthatthereisathirdelement。Thesethinkers
　　howevermakeoneofthetwocontrariesmatter；thisisdonefor
　　instancebythosewhomaketheunequalmatterfortheequal，orthe
　　manymatterfortheone。Butthisalsoisrefutedinthesameway；for
　　theonematterwhichunderliesanypairofcontrariesiscontraryto
　　nothing。Further，allthings，excepttheone，will，ontheviewweare
　　criticizing，partakeofevil；forthebaditselfisoneofthetwo
　　elements。Buttheotherschooldoesnottreatthegoodandthebad
　　evenasprinciples；yetinallthingsthegoodisinthehighest
　　degreeaprinciple。Theschoolwefirstmentionedisrightinsaying
　　thatitisaprinciple，buthowthegoodisaprincipletheydonot
　　say-whetherasendorasmoverorasform。
　　Empedoclesalsohasaparadoxicalview；forheidentifiesthegood
　　withlove，butthisisaprinciplebothasmoverforitbringsthings
　　togetherandasmatterforitispartofthemixture。Nowevenif
　　ithappensthatthesamethingisaprinciplebothasmatterandas
　　mover，stillthebeing，atleast，ofthetwoisnotthesame。Inwhich
　　respectthenisloveaprinciple？Itisparadoxicalalsothatstrife
　　shouldbeimperishable；thenatureofhis’evil’isjuststrife。
　　Anaxagorasmakesthegoodamotiveprinciple；forhis’reason’
　　movesthings。Butitmovesthemforanend，whichmustbesomething
　　otherthanit，exceptaccordingtoourwayofstatingthecase；for，
　　onourview，themedicalartisinasensehealth。Itisparadoxical
　　alsonottosupposeacontrarytothegood，i。e。toreason。Butall
　　whospeakofthecontrariesmakenouseofthecontraries，unlesswe
　　bringtheirviewsintoshape。Andwhysomethingsareperishableand
　　othersimperishable，noonetellsus；fortheymakeallexisting
　　thingsoutofthesameprinciples。Further，somemakeexisting
　　thingsoutofthenonexistent；andotherstoavoidthenecessityof
　　thismakeallthingsone。