matikw suntjevw sa nagkaon n prolaben tw stronomikw sun-
tjevs, lgv d "per te orano ka
"to di msvn tn zdvn liako kklou", ka ti "tn p tw r-
"yw sfaras" ka tw gkeklimnhw "per atn sumbainntvn", rx-
menow to trtou biblou klouyon erskei "fejw tot tn per
"to lou ka selnhw poisasyai lgon, toutstin t per tw kin-
"seiw atn pisumbanonta diejelyen," lgv d plin t per tow
pokatastatikow xrnouw atn, ka tw poyseiw, ka tw malw
ka kribew ka fainomnaw pardouw to te mkouw ka pltouw tw
selnhw, ka per te tn posthmtvn ka megeyn, ka paralljevn
ka sundvn ka panselnvn ka klecevn ka prosnesevn, ka sa
lla kat mrow per n n tow jw mxri to ktou biblou dialam-
bnei, tw tn plann te ka planomnvn pragmateaw proxvren
m dunamnhw neu tw totvn prodialmcevw, di t desyai tw per
atn podejeiw tn erhmnvn per tn lion ka tn selnhn kata-
lmcevn, w n tow ew t prton dhlomen. ti d ka tw atn to-
tvn pragmateaw, lgv d lou te ka selnhw, prohgoumnhn erskei
tn to lou, "w neu plin od t per tn selnhn on te" nte-
lsteron ka kribsteron podeixynai, pe ka mlista tathw o
tpoi k tn kat tw kleceiw atw [tn] to lou poxn kribn
katalambnontai ka p totvn t loip per tw kinseiw atw.
Anagkaou tonun di tata tugxnontow pr tn llvn tn per
tw to lou pragmateaw poisasyai lgon, klouyon erskei pr-
teron tn per atn podeiknumnvn per to niausou xrnou dia-
laben, toutstin n ps xrn p tinow shmeou [tras] rxw to di
msvn tn zdvn rjmenow kinesyai p t at paragnetai. totou
gr ereyntow, ka tn tj moirn to di msvn tn zdvn kklou
ew atn pimerizomnvn, ersketai ato ka t kay' kaston xrnon
mal kinmata: f' n ka t loip pnta per tw kinseiw ato
katalambnei.
Eta re n trpon o palaio per tn eresin to toiotou proun
te ka diefnoun: omenoi gr, fhsn, tow planew straw stnai,
pot mn prw t tropik ka shmerin throntew tn to lou po-
katstasin lttona katelambnonto tn tn atn xrnon tn tje
ka d' mern, pot d t prw t plan stra mezonaw yaw pe-
bllonto.
"Ka tn tn plann strvn sfaran metbasn tina poluxr-
"nion poiesyai", toutstin di makrotrou xrnou, dussnopton di
t lxiston tw kinsevw. deknutai gr kat katn th man moran
meyistamnh ew t pmena ka nanta t tn lvn for, toutstin w
p dusmn p natolw per plouw bebhktaw p to di' mfotrvn
tn plvn to te di msvn ka to shmerino: katalambnetai gr
ka totvn metbasiw per tow to di msvn plouw poteloumnh
kayper ka a tn planomnvn.
Efhsen d tn sfaran atn tn metbasin poiesyai ka ox tow
straw di t t diastmata ka tow prw lllouw sxhmatismow
atow pntote fulttontaw sper ntetupvmnouw p miw sfaraw
perigesyai.
Oti d ka klouyn stin, to prw tow planew straw pokata-
statiko xrnou mezonow katalambanomnou, ew t pmena gesyai
tn tw sfaraw atn metbasin potelesyai, otvw n gnoito d-
lon: stv gr zdiakw kklow ABGD, n d ti tn tropikn sh-
merinn shmevn t A, ka str tiw lgou neken tn plann p' ato
ma t l. e mn on str pntote p to A shmeou mnei, dlon
w ti n t at xrn t te A shmeon ka tn stra liow kinh-
yew lon tn ABGD kklon pikatalmcetai, e d metbasn tina poie-
tai planw, to A shmeou mnontow, okti.
Ka pe tw to lou prw tn plan pokatastsevw mezvn
xrnow katelambneto, fanern ti to lou p to A p t B ew t
pmena kinoumnou, ka planw p t at w ew t pmena
Pepoisyv gr lgou neken w kat t E: dlon on tan liow p
to A tropiko <> shmerino shmeou kinhyew p t at shmeon
poishtai tn pokatstasin, steron, nka n ka tn AE kinhy,
tn prw tn stra poisetai pikatlhmcin ka stai n ploni xrn
tn prw tn plan pokatstasin poihsmenow per tn prw t A
tropikn shmerinn peidper ew t pmena ka p t at t to
lou metabsei ka str keknhtai.
Ektvw d fhsen tow planew straw pokatastseiw mezo-
naw poien to xrnou tn tje d' mern. pe gr prw t tropik
pokatstasiw katalambnetai mern tje d', par t triakosio-
stn toutstin par de
moraw, di t tn merhsan ato maln prodon miw moraw g-
gista katalambnesyai,
d tn plann niausan metbasw stin
katostn moraw a, toutstin detera jhkost l
(2), dlon w n taw tje d' mraiw par t ib detera jhkost prosymen t l (2)
detera jhkost, stai niasiow xrnow tje d' ka jhkostn deu-
trvn kd. ka mezvn stai prw tow planew straw pokat-
stasiw mern tje d'.
Ek tn erhmnvn on parathrsevn nenoun ka tn tn plann
sfaran poiesya tina metbasin ew t pmena. ti d touy' otvw
xei, deknusin ka Ptolemaow n t z' bibl kat tow okeouw
per tn toiotvn tpouw.
"Kat d tn parosan skcin prw odn llow gomeya den po-
"blpontaw tn niausiaon to lou xrnon skopen tn ato to
"lou prw autn ... pokatstasin ..." di gon fhsin t den prw
tina mnonta shmea ka m metakinomena tn pokatstasin skopen,
prw odn teron felomen "rzesyai t niasion xrnon" n
"p tinow kintou shmeou" to sper p' ato grafomnou megstou
ka lojo ka di msvn tn zdvn kklou "p t at paragnetai,
"mnaw rxw dejaw tw toiathw pokatastsevw goumnous"
t toiata shmea kay' o te tropiko ato fptontai per kale
tropik, kay' d shmerinw atn tmnei per plin kale shmerin,
di t tn kklon rxn fsei m xein.
Katalambnetai d kat tn toiotvn shmevn gignmenow di to
n t a' bibl kteyeimnou rgnou di tn krkvn ka tw plin-
ydow, koloyvw tow kese erhmnoiw tw parathrsevw ginomnhw:
ti d tn shmerinn ginmenow katalambnetai ka di krkou n t
to shmerino pipd tn tun xontow tan ato kolh pifneia
skizhtai.
Eta t elogon didskvn to den tn prw tn di msvn tn zdvn
kklon pokatstsin rsyai tn niasion xrnon toutstin n
liow p tinow dhlonti kintou shmeou totou to kklou p
t at paragnhtai, fhsn: ti n te gr mayhmatikteron pisko-
pmen t elogon, "ote okeiotran pokatstasin ersomen tw
"p tn atn sxhmatismn feroshw tn lion ...", toutstin p
borevn p breia p notvn p ntia p shmeraw p tn atn
shmeran ka p' llou tinw p t at.
"Topikw te ka xronikw to toiotou yevroumnou toi prw tn
"rzonta tn meshmbrinn, t megyh tn nuxyhmrvn," toutstin
na p tinow tropiko shmerino shmeou rxmenow liow ki-
nesyai ka p to rzontow to meshmbrino toutstin p na-
tolw dsevw meshmbraw rxhtai, pvw ka p katadhlotrvn t-
pvn parymhsiw to xrnou ggnhtai.
Ka e mn p tinow shmeou to zdiako ka to rzontow rx-
menow jw p to ato shmeou to zdiako genmenow ka p to
ato shmeou plin to rzontow tugxnvn katelambneto, dlon w
n laiw mraiw poieto tn pokatstasin. movw d ka e p to
meshmbrino p tn meshmbrinn. pe d ok p to ato shmeou
to rzontow p t at tn pokatstasin fanetai poiomenow od
plin p to meshmbrino p tn meshmbrinn, kayper k tn thr-
sevn katalambnetai, ll pot mn p to rzontow rjmenow per
tn meshmbrinn tn pokatstasin poiomenow pot d p to meshm-
brino per tn rzonta, dlon gnetai t m n laiw mraiw tn po-
katstasin to lou potelesyai, toutstin m lvn mern tn
niasion xrnon tugxnein ll ka ttarton ggista pilambnein:
ka mlista k tn prw t shmerin pokatastsevn, te ka p
to rzontow p tn meshmbran xrnow p meshmbraw p tn r-
zonta ttartn stin prw asyhsin to nuxyhmrou, per ka kale
mran: t d prw t megyh tn nuxyhmrvn shmanei, ste ka so-
xrnia gnesyai t sunagmena nuxymera ka m mnon sa kat t
plyow tw prthw diastsevw ka tn jw: n gr p tinow shmeou
to di msvn tn zdvn kklou kinhyew liow p t at para-
gnhtai, ka plin jw p t atn, t sunagmena nuxymera tw pr-
thw pokatastsevw o mnon sa stn t plyei tow tw deutraw
ll ka soxrnia, ka jw movw. ka odn stai diforon par tn
nvmalan tn nuxyhmrvn: o gr pntvw t sriyma nuxymera ka
soxrni stin, w jw didskei, ka per to toiotou kefalaou dia-
lambnvn.
xr gr n tow pokatastatikow xrnoiw m mnon w famen
sriymon enai t plyow tn nuxyhmrvn kat tw diastseiw, ll ka
soxrnion: otv gr t k to merismo katalambanmenon mersion
maln knhma t at stai pntote. e gr m soxrnioi een a dia-
stseiw, od t erhmna mal kinmata t at enai sumbsetai,
pe a toiatai kinseiw tn atn lgon xousin prw tow xrnouw.
Eta plin tn erhmnvn rxn t elogon paratiymenow, fhsn:
"ote llaw okeaw rxw p to di msvn tn zdvn" stn laben
" mnaw tw kat t sumbebhkw forizomnaw p tn" erhmnvn
kklvn.
Dlon d ka ti mayhmatikw tn piboln poiomenow tow okeoiw
tw mayhmatikw katexrsato sxhmatismow, ka tpon ka xrnon
pareilhfw: tata gr tw mayhmatikw dia, w ka n rx tw sun-
tjevw t tw mayhmatikw dia forzvn lege: t d "tw kat t
"edh ka tw metabatikw kinseiw poithtow mfanistikn edow sx-
"matw te ka posthtow ka phlikthtow ti te ka tpou ka xrnou
"ka tn movn zhthtikn prxon w mayhmatikn n tiw forseien."
"En te" fhsn plin "fusiktern tiw piskop t okeon" tw
erhmnhw pokatastsevw "ote elogvtran pokatastsin ersei
"to moou per tn ra katastmatos", toutstin to p yerinw
tropw p tn moan yerinn p xeimerinw p xeimerinn p
metopvrinw
p arinw p arinn ka lvw o tn boreiotrvn to shmerino p tw atw peridou prohgomenon plin moraw e d. ka to
tw atw raw p tn atn feroshw tn lion. "ote llaw rxw
" kay' w a rai mlista krnontai" tn kairn ew llouw meta-
ballntvn.
dlon d ti ka ntaya tow okeoiw tw fusikw kate-
xrsato, t mo per tn ra katastmati kataxrhsmenow.
Eta epn tw ataw di' w okeitern stin p tn erhmnvn sh-
mevn pilogzesyai tn niasion xrnon per p tn plann, fhsn:
"met to ka tn prw tow planew straw yevroumnhn pokat-
"stasin topon fanesyai".
Et' jw plin re di' w ataw xr paraitesyai ka t prw tow
planew straw tn toiathn pskecin poiesyai, ka fhsin plin
"ka di' lla" mn topa. toutstin ti, e ka knhtoi tgxanon k
tn prw tn lion atn prtvn sxtvn fsevn t toioton pi-
logizmenoi, di t mhdna tn strvn mte sunodeonta mte kat
tn dimetron t l stsin dnasyai fanesyai, diafvnen mllomen,
tn erhmnvn fsevn m mnon tow tpouw eyw fanizousn, ll
ka kaylou kat tow xrnouw, diamarthynai dunamnvn ka tw dia-
forw neken tn rvn ka tw cevw tn parathrontvn, w k to-
tvn ka tn niausiaon xrnon diforon katalambnesyai.
Eti d mlista ka ti ox stkasin ll knhsin poiontai: odn
gr diferen, eper paj m prw stta tn pokatstasin poiomeya,
prw tow planomnouw straw tn toiathn pskecin poiesyai: pol-
lo te n ka diforoi ggnonto o niasioi xrnoi, diafrvw to lou
kaston n evyen pikatalambnein pikatalambnontow, pe ka
diafrouw poiontai tw kinseiw.
Pepohtai d tn nomasan p to to Krnou strow epn: "n
"s lgou neken tn to Krnou stra ... liow pikatalambnei ..."
pe braxe tiw mlln stin ka totou knhsiw kayper ka tn
plann.
"Di mn d toto proskein omeya, tn eriskmenon di tn th-
"rsevn tn w ni mlista p pleonow diastsevw lambanomnvn
"p tinow tropw shmeraw p tn atn ka fejw xrnon, toton
"gesyai tn niasion to lou."
Di gon t erhmna eloga per to den prw t tropik shmerin
shmea tn pokatstasin rzesyai ka t prw tow planew topa,
klouyon getai tn eriskmenon di tn k pleonow diastsevn
kribestrvn thrsevn p tinow tropw shmeraw p tn atn
xrnon, toton gesyai tn niasion to lou: t d xrsimon to
tw di makrotrou xrnou thrseiw den lambnesyai, jw dhlsomen.
Ka pe erskei yorubomenn pvw tn Ipparxon t ka tw per
t toiata shmea pokatastseiw diafvnen ew tn niasion xrnon
ka mxriw
braxean tugxnousan, kayw ka atw Ipparxow nnon katafa-
netai, ka tathn o par tn atan tn p tn toiotvn shmevn lam-
bnesyai tw pokatastseiw ginomnhn, ll par tw tn rgnvn
di' n poieto tw thrseiw toi kataskeuw par t m strabw ka
kribw at kataskeasyai, par tw diairseiw ka tw yseiw
atn, par tow pilogismow tn thrsevn tow ginomnouw per
tn sunagvgn tn metaj xrnvn, di t m pntvw n at t meshm-
br& tw te tropw tw shmeraw potelesyai n aw mlista t di
tn krkvn ka tw plinydow rganon t kribw katalambnetai,
ka don enai pilogzesyai kat' keno kairo xrnou n trpon n tow
jw pideknumen.
Eta kymenow tw kribw t Ipprx tethrhmnaw metopvrinw
ka arinw shmeraw, fanern poietai ti o pleon tetrtou mrouw
miw mraw erskei tn diaforn
xrnou, ka ti par t rgana ka atw tw thrseiw dnatai ggnesyai
tosath diafvna, k to tn atn shmeran diafroiw rgnoiw
tn mn Ipparxon t auto rgn tethrhknai ginomnhn tn sh-
meran, prton d "n Alejandre& krkon son j katrou mrouw
"paragasyai per e' ran".
kaylou gr n krkow tn dimetron
x m lttona phxn do, ok piskothysetai ato psa kolh
pifneia kayw ka t Ipprx doke ka mn k parathrsevw fa-
nern ggonen, tw skiw ew j lhgoshw di t mezon enai to fvti-
zomnou t fvtzon, ll ka
tn to shmerino ysin xvn, tan p to di msvn tw kurtw pi-
faneaw ato grafomnou kklou liow tugxn.
Oti d par t rgana dnatai tosath diafvna gnesyai pisto-
tai k to tw lojsevw kanonou:
peidper kn t trisxiliost
jakosiost mrei to di tn plvn kat tn diaresin <> ka
tn ysin diamar
ton diforon,
tow
kat t prton to
kaon kinesyai n tetrt
(2). 
Oon meshmbrino
meshmbrino
meshmbrino nt to E t A paralambnvmen, di t t Z kat to
shmerino fermenon kat t A paragnesyai, ka p to di msvn
nt to Z t E paralhmcmeya, ka diafvnsomen p to zdiako
tn EZ perifreian jhkostn ie, di t tn AE lojsevw osan jh-
kostn
(2) katalambnesyai, ka parkeisyai atow tw EZ to z-
diako jhkost ie. ka per mn t shmerin t trisxiliost ja-
kosiost mrei to meshmbrino diamartnontew toutstin tow
(2), tetrt> mrei miw mraw tn diafvn
En d prw tow tropikow throntew tosoton diamrtvmen, e lvn
ggista mern tn diafvnan ersomen, di t tow
(2) jhkostow
to meshmbrino pibllein prw tow tropikow n t at tw lojsevw
kanon to zdiako morai e ggista, peidper taw mn p to
shmerino moraiw pe to zdiako par
morai kg me, taw
(2) jhkostow prtoiw to
meshmbrino p
meron ggista diory
xow ka Ar
ka tow pilogismow
mr>thma per tw thrseiw <...>tai
asyhtn poietai tn nisthta to xrnou per n taw shmeraiw. di
ka fhsi: katoi dunato ntow "m mnon per tw tropikw thrseiw
"ll ka per tw shmerinw gnesya ti ... diamrthma" (dhlad w
mllon per tw tropw to toiotou ginomnou), dunato d ntow ka
mxriw trisxiliosto jakosiosto mrouw per tw thrseiw diamarth-
ynai, klouyon n eh ka tw per tw shmerinw thrseiw tn to
tetrtou mrouw tw mraw poiesyai diafvnan par tw tn rgnvn
tn pilogismn martaw. gnetai d ka per tw yseiw atn dia-
mrthma t m kat tn okean ysin to fsei meshmbrino atw th-
rzesyai, ll ka kat diafrouw tpouw paregklnesyai toi m giw
lambanomnhw tw meshmbrinw eyeaw ka ato to m
krkou m tn prw ryw
d plin ka n di tn n t to shmerino pipd krkvn < ...
tw thrseis> tn shmerinn poimeya di
tw okeaw atn yseiw. ti d, fhsn, ka pleon n diamartsaimen
per tw thrseiw e m par' atw tw erhmnaw yseiw tn rgnvn
kribomen.
Estin d ka erhmnh kat Kllipon perodow tn o
(2), rxn
d elhfen toiath parymhsiw pr
(2) tn tw Alejndrou teleutw. ti mn on perodow kat' atn tn stin o
(2) ka Edhmow Rdiow mmnhtai n tow per gevmetraw at storoumnoiw suntgmasin:
tosotow d at xrnow elhmptai, pe n t tosot law po-
katastseiw sundvn katalambnetai, w n tow jw fanern poi-
somen. dlon d gnetai t ka p to erhmnou xrnou tn rxn e-
lhfnai tw peridouw k tn jw at paratiyemnvn: fhsn gr
t lb' tow tw trthw kat Kllippon peridou roh' enai p tw
Alejndrou teleutw: ka sungontai p tw rxw tw prthw peri-
dou th rpd: di dlon gnesyai pr
(2) tn tw Alejndrou teleu
tw
Ka pe paryeto Ipparxow metopvrinn shmeran gegenhmnhn
t mesonukt, dejomen n trpon stn tn toioton xrnon pilog-
sasyai ka kaylou n m kat' atn tn pr gw meshmbran gnh-
tai shmera kat' kenhn tn okhsin ny
Gegensyv d mn trhsiw podegmatow neken di tn krkvn
tn
shmeraw gnetai liow,
t notitera parodevn, dlon ti mhdpv gegenhmnhw tw toiathw
shmeraw liow ti boreiterow to shmerino tugxnei, gegenhmnhw
d atw notiterow katalambnetai: throntew on tn lion lgou
neken di tn krkvn p tn boreiotrvn to shmerino mllonta
poiesyai tn shmeran, ka labntew k tw kat tn mezona diair-
sevw pson to shmerino fsthken w p to meshmbrino, eta t
jw poihsmenon [ka] tn shmeran ka notiteron gegenhmnon, lam-
bnomen movw ka kat' atn tn meshmbran p to meshmbrino
tn distasin tw p to shmerino p t ntia ato paraxvrsevw
ka tathn esgontew kat t b' seldion to tw lojsevw kanonou
t pibllon at to zdiako kat t
moraw
to metopvrino, f' o xrnou ggonen shmera. ka tathn mer-
santew par t riaon maln to lou knhma ersomen pr psvn
rn ggonen shmera. w felntew p tw kat tn meshmbran
raw
(2), jomen tn pizhtoumnhn ran kay' n gegnhtai shmera,
lambanomnou dhlonti to malo riaou kinmatow, w to niau-
siaou xrnou mern tje d' tugxnontow, ka w to p tw shme-
raw p tn meshmbran xrnou mhdn poiontow diforon mte par
toto t katalambanmenon lepon ew tn to d' pousan, mte par
tn to lou nvmalan: yen ka xr prw tn ggutran to shme-
rino shmeou meshmbran tn sgkrisin to pilogismo poiesyai
oon n mhdpv gegenhmnhw tw shmeraw plhsiateron t kat
tn lion p to meshmbrino shmeon to shmerino, xr pilogzesyai
koloyvw tow erhmnoiw met pson xrnon genhysetai shmera:
otv gr n to metaj xrnou lttonow tugxnontow nepaisyhtotra
ti stai par te tn nvmalan ka t t' tw mraw ginomnh dia-
for.
"All gr tn mn toiotvn odn od' atw Ipparxow oetai
"tugxnein jipiston prw tn pocan tw nisthtow tn niau-
"svn xrnvn, p d tn tw selnhw klecevn ..." ka t jw.
All' k tn mn toiotvn prw t shmerin parathrsevn odn
od atw Ipparxow oetai ggnesyai jilogon diaforn par tn
nisthta to niausou xrnou. "p d tn tw selnhw klecevn
"pilogizmenow erskein oetai ti nvmala tn niausvn xrnvn
"prw t mtron yevroumnh o mezona poietai diaforn mseow ka
"tetrtou mrouw miw mras", per n n diorysew tinow jion,
eper atw exe ka m j atn n paratyetai dieceusmnow katafa-
netai. t mn on
ka xrnow
lecevn tow niausouw xrnouw diafrouw: ka tina
erisk
mrou
(20)' ka d'. fanetai on di to
sfdra ggneto.
Diasfalew on n lloiw per tw thrseiw, lyen eyvw p t mm-
fesyai tow niautow toutstin t to lou pokatastsei w m so-
xronvw poteloumn. trhsen gr Stxun n pnv jyeto t
lb' tei tw g' kat Kllipon peridou prohgomenon, toutstin p
t prw dusmw mrh, to metopvrino shmeou moraw
(2)
(20)': met d
ia th
pe dnaton n n ia tesi tosoton tn Stxun metakekinsyai, t
to lou pokatastsei t ation perh
Pepohtai d tow pilogismow tn thrsevn w n podegmati
mn w p to A p t B ka t G, prohgomena d t npalin, ka
p' ato arinn mn shmerinn t A, metopvrinn d t G, klepousa
d selnh per t metopvrinn kat t E. d liow n t ms xrn
tw klecevw kat dimetron at tugxnvn stai kat t Z, ggion
dhlonti to arino. str d tiw tn plann ggw stv tw selnhw,
d to Stxuow str prohgomenow to G metopvrino stv Y. pe
on tn lion eren p to ato shmeou p t at malw pokayi-
stmenon n mraiw tje d' ggista, thrsaw atn p t arinn para-
genmenon ka pilogismenow k to p tw klecevw p t arinn
xrnou, katalambanomnhw ato malw pardou, pson p to msou
tw klecevw xrnou p tn kat t A shmeran keknhtai, erskei
tn kat t Z to lou poxn, dhlad ka tn kat t E tw selnhw,
kat dimetron tugxnousai, ka ti tn EG. eta pilogismenow pson
selnh
tn rxn tw mptsevw kat to straw yevreto, kayw ka
Ipparxow n t per tw metaptsevw tn tropikn: ka xvn di' r-
ganikw thrsevw pson H str pxei to Y
xuow, sungei ka lhn tn p to Y strow p t G metopvrinn
shmeon.
Ern on tathn tn distasin pot mn moraw e d' pot d
(2)
(20)'
prohgomenon to metopvrino shmeou, ka duntou ntow tn St-
xun moran a ka d' n ndeka tesin metakekinsyai, di t kat r th
deknusyai tow planew moran a metakinoumnouw, eyvw lyen ew
t tn martan tow niausoiw xrnoiw peri
tvn tn dunamnvn tathn mpoisai, t toi tn distasin tw
selnhw prw tn H stra losxersteron katastoxsasyai, tn to
H strow prw tn Y to Stxuow, tn tw paralljevw tw selnhw
prw tn H stra, tn to lou kat mrow nvmalan knhsin tn
p to Z p t A.
Llhye d atn at toto, edta ti o dunatn n tow pilogi-
smow tn diastsevn to Stxuow, prw tn metopvrinn poisasyai:
od' n n tn tw selnhw kat tn kleicin krib poxn eren neu
to tn to lou prolaben, pe ka k tathw katalambnontai: k
gr to xein kat tn mson xrnon tw klecevw tn to lou poxn
katelambneto tn tw selnhw kat dimetron pntvw tugxnousan:
k d tathw, tn to Y ka lhn tn p to Y p t G, toutstin tn
p to Stxuow p t metopvrinn. ste k to xein tn to lou
poxn tn te tw selnhw katelambneto ka k tn erhmnvn
pilogismn tn to Stxuow prw t metopvrinn shmeon dista-
sin.
Atw on ew toto, lgv d ew t erskein kribsteron mllon tn
to lou poxn ka poiesyai tow erhmnouw pilogismow prw tn
katlhmcin tw p to metopvrino diastsevw to Stxuow, para-
lambnvn tw thrseiw tw katalhmfyesaw at pokatastatikow
xosaw tow xrnouw, toutstin n aw to d' tw mraw pousa
[]smfvnow katalambnetai t metaj tn thrsevn xrn, na k
totou, proxervw erskvn k to merhsou malo kinmatow ka t
riaon, pilogzhtai
kinhysetai ka svn tugxnei tmhmtvn, w to lou n tje d' m-
raiw w famen prw t A shmerinn shmeon pokayistamnou, ka k
tw kat t Z to lou poxw ka ti tn loipn katalambnhtai tw
diastseiw to Stxuow prw tn metopvrinn, k tn toiotvn on
parathrsevn t erhmn tp peripesn, mmfetai tow pokata-
statikow to lou xrnoiw, tow p' ato mologhyesi sumfnvw
kateilhmmnoiw t to d' pous&: otv gr o xrnoi tn thrsevn
kat parelambnonto o te to lb' ka mg' touw tw trthw kat
Kllippon peridou, otinew at pnv katelambnonto tw po-
katastseiw poiomenoi sumfnvw t to d' pous& tn erhmnvn
mn mllon dunamnvn tn martan mpoisai.
"All' omai ka tn Ipparxon sunegnvknai mn ka atn ti
"mhdn n tow toiotoiw nestin jipiston ..." ka t jw.
All' polambnei ka tn Ipparxon sunevraknai m tosaton jio-
pstouw gesyai tw toiataw di tn klecevn katalmceiw, w di'
atw nisthtow katagnnai to niausou xrnou, k to mhd deut-
ran diryvsin tw toiathw nisthtow pilelogsyai, kaper prthn
pelogsato tw fainomnhw kribow pardou par tn maln, bebo-
lhsyai
poca tiw gnhtai j atn tw nisthtow to niausou xrnou, m
jiopstouw gntai tw toiataw katalmceiw.
"Kxrhtai gon ka ats" Ipparxow "taw poysesin lou ka
"selnhs" kayper ka Ptolemaow "w miw ka tw atw parxo-
"shw per tn lion nvmalaw." gr ka tw selnhw Ptolemaow
[s] deutran nvmalan potyetai:
ll' otvw ka tathw tw po
yseiw paralambnei w to lou man poiontow nvmalan, tiw
kat mrow nmalow knhsw stin mal kat tn prw t shmerin
ka t tropik shmea katalambanmenon niasion xrnon, kayper
p to di msvn tn zdvn kklou ka to shmerino p tn kat
mrow naforn niso esin a perifreiai atn low d kklow l
sunanafretai, otv ka p tn maln ka tn fainomnvn nvmlvn
pardvn a mn kat mrow mala prodoi niso esin taw fainomnaiw
p d lou to niausou xrnou sh stn mal prodow t fainomn:
katra gr atn tw to lou kklou perixei moraw tj. "ka o-
"dam di t soxronouw potyesyai tw to lou peridous" tow
di tn toiotvn poysevn fodeuomnoiw kolouyontew "t per
"tw kleceiw yevromena jiolg tin diafononta" katalambne-
tai, "per n asyhtn pnu sunbaine" sunepilogizomnvn mn t
par tn nisthta to niausou xrnou diforon "e ka miw mnhw
"moraw tgxanen do d rn ggista shmerinn,"
di t tn se-
lnhn n dusn ggista raiw man moran kinesyai, w k tn per tw
kinseiw atw lexyhsomnvn stai dlon.
Ina d fanern gnhtai t legmenon, stv nt to di msvn
ABGD kklow ka kat dimetron t mn A to G, t d B to D. e on
m n s xrn liow p to A shmeou p t A paragnetai,
jei pot n t at xrn p to A p t D, ste mn paralam-
banntvn atn n s xrn pokayistmenon, ntow ato kat t
D paralambnomen atn kat to A tugxnein, ka tw klecevw po-
teloumnhw tan selnh kat t B , mew atn fsomen ggnesyai
tan kat t G: tw DA on toutstin tw BG gignomnhw moraw a
diamartsomen per tn pfasin to xrnou raw b, di t, w famen,
deknusyai tn selnhn n dusn raiw ggista tn a moran kinou-
mnhn.
Ek tn toiotvn on to Ipprxou thrsevn ka k pleinvn f'
ato gegenhmnvn poiomenow Ptolemaow tn jtasin to niausou
xrnou, katalambnetai ti "n prw n ka t at shmeon to z-
"diako, ka m pot mn prw t tropikn shmerinn shmeon pot
"d prw tow planew stras" poitai tw tn pokatastsevn th-
rseiw, ote nison ersketai t niasion mgeyow: "ote llhn o-
"keiotran" rn pokatastsevw tn tropikn shmerinn
shmevn stn laben lvw tn p tinow to di msvn shmeou "p
"t at plin fereshw tn lion. lvw te gomeya proskein di'
"ploustrvn w ni mlista poysevn t fainmena deiknein f'
"son n mhdn jilogon k tn thrsevn ntippton t toiat pro-
"ysei fanoito."
Apodejaw tn to lou pokatstasin soxrnion pntote po-
teloumnhn, jw re n trpon prskeitai at tn pragmatean tw
prokeimnhw stronomikw suntjevw diejelyen, ka fhsin: "kaylou
"gomeya proskein di' ploustrvn s dunatn poysevn t fai-
"nmena deiknein, f' son n mhdn jilogon" par' at diamart-
noimen taw proxeirotraiw poysesin ka podejesin prosxrmenoi:
filosntomow d n nr, prosxrtai ka taw paxumerestraiw, tan
proxeirterai osai tn kribn mhden asyht atn per tow pi-
logismow tn kinsevn diafrvsin.
"Oti mn tonun prw tropw
"ka tw shmeraw yevromenow pokatastatikw to lou xrnow
"lttvn stn mern tje d' dlon mn ggonen j n ka di' n
"Ipparxow pdeijen. ps d lttvn ox' on te sfalstata la-
"ben," tw to d' prosykhw toutstin tn tje d mern "p pleona
"th parallktou menoshw di t lxiston tw diaforw: ka di
"toto kat tn di makrotrou xrnou sgkrisin tw eriskomnhw tn
"mern pousaw tw atw yevresyai, n de tow metaj tw dia-
"stsevw tesin pimerzein". ka di t lxiston tw diaforw n
p tinow prthw thrsevw tran trhsin lgou neken met th k
poihsmeya ka ervmn ti diforon gegenhmnon w p t latton
tn tje d' mern tugxnontow to niausou xrnou: ka plin met
th dka tran trhsin poihsmeya per stn met l th tw prthw,
eriskmenon diforon ti t at prw asyhsin katalambnetai
t di k tn kateilhmmn di t lxiston w famen tw diaforw,
per diforon xr tow metaj tn thrsevn tesin pimerzein na e-
rvmen t t niaus xrn p t latton tw to d' pousaw pi-
bllon: n on t at diforon ew diafrouw xrnouw pimersvmen,
nison ersomen ka t lepon ew tn to d' tw mraw pousan,
ste ka tn niasion xrnon, soxronou ato kateilhmmnou.
Lambnoito d' n kribsteron xrnow tw to lou pokata-
stsevw f' son n metaj mn te ka n xomen palaiotrvn
thrsevn xrnon plevn erskhtai. o mnon p tw prokeim-
nhw to lou pokatastsevw t toioton pizhten xr ll ka
p tw tn llvn, lgv d tw te selnhw ka tn pnte planvm-
nvn:
t gr par t rgana tn atn tn thrsevn prw kribest-
thn katlhcin "syneian ginmenon diceusma, brax pntote ka t
"at ggista prxon p te to di makro ka to di' lgou xrnou
"fainomnvn, ew lttona mn pimerizmenon xrnon mezon poie t
"niasion mrthma, ew pleona d latton", pe on s makrterow
tugxnei metaj tn thrsevn xrnow, t par tn trhsin ginmenon
diforon t at ggista prxon, ew pleon pimerizmenon nepaisyh-
tteron gnetai.
di toi toto atrkeiw getai tugxnein tow xrnouw
tow te p tn auto thrsevn mxri n exen palaiotrvn, prw t
nepaisyhtteron poien t mrthma:
ste t xrsimon totou
di makrotrvn xrnou par tw to lou pokatastseiw poiesyai
tn sgkrisin tn thrsevn kat do trpouw sumbanei gensyai. pe
gr toi par tw kataskeuw tn rgnvn tw yseiw w famen g-
neta ti diamrthma, kn kribw meyodevntai: ll mn ka nia-
siow xrnow katalambnetai k tn sunexn thrsevn nepaisyt tin
lttvn tn tje d' mern: dlon w xr t mn k tn rgnvn mar-
tanmenon nepasyhton pantpasin poien, t d' k to xrnou paror-
menon lxiston asyhtn, na dunmenon pimerisynai ew tn metaj
tn thrsevn xrnon katdhlon mn pois ka t lepon t niaus
xrn ew t tw pilcevw, ttarton tw mraw.
T d toiata k tn thrsevn tn w ni mlista p pleonow dia-
stsevw lambanomnvn meyodeetai: tn gr thrsevn pleonow xr-
nou distasin xousn, t par t rgana gignmenon diforon t at
pntote ggista prxon s n w famen ew pleona th pimerzhtai,
nepasyhton ka fanw gnetai: t d k to niausou xrnou lepon
lxiston ew t tw pousaw d', asyhtn:
kayper n tow t tesin
mr& mi erskvn prteron ginomnhn tn pokatstasin tw pr t
ttarton pousaw, sungei tn niasion xrnon mern tje d', par
triakosiostn.
Dedeigmnou on ti, s di makrotrou xrnou tn sgkrisin tn
thrsevn poietai, tosot kribsteron tn pizhtomenon niasion
xrnon katalambnetai, re ka poai mlln esin a palaiterai tn
thrsevn ka felousai at ew tn sgkrisin tn kay' autn para-
lambnesyai. ka fhsin: "neken mn on palaithtow a te p tn
"per Mtvna ka Ektmona tethrhmnai yerina tropa ka met to-
"touw a p tn per Arstarxon feloien n ew tn sgkrisin tn
"kay' mw paralambnesyai. neken d to kaylou tw tn tropn
"thrseiw dusdiakrtouw enai",
di t p pol tn lion gxronzein
kat tn atn to meshmbrino krkou tpvn per tw toiataw par-
douw, per k to tw lojsevw kanonou gnetai dlon, peidper prw
tow tropikow lttosin peroxaw parhjhntai a tn lojsevn phli-
kthtew: ka prw totoiw tw par totvn nagrafesaw paxumerste-
ron elfyai "w ka t Ipprx doke, tataw mn parthsmeya:
"sugkexrmeya" d taw p to Ipprxou tethrhmnaiw shmeraiw,
ka to
mnaiw, prw tn sgkrisin tn metrvn: j n erskomen tow t
tesin tow n tje d' mern prteron gegenhmnhn tn shmeran
mr& mi: t gr lb' tei tw trthw kat Kllippon peridou, k-
tyetai Ipparxow metopvrinn shmeran gegenhmnhn "t g' tn
"pagomnvn to mesonuktou to ew tn d' frontow: ka stin to-
"to t roh' p tw Alejndrou teleutw. met d spe th" aguptia-
k, toutstin n tje mern, "t g' tei Antvnnou stin ujg
"tow p tw Alejndrou teleutw, mew thrsamen sfalstata
"plin tn metopvrinn shmeran gegenhmnhn t nt to yr man
"ggista ran met tw to lou natolw. plaben ra pokat-
"stasis", logizomnvn mn tn niasion xrnon mern tje mnvn,
mraw o d' k', di t erhknai met man ggista ran tw to lou
natolw, nt tn piballousn k tw to d' pousaw tow spe te-
sin mern oa d' "w prw t d' pousaw mr& mi leipos t e-
"kostn mros".
Eti te plin sugkrnaw ka tw kat tow atow xrnouw thrhyesaw
Ipprx te ka aut arinw shmeraw t at plin diforon kata-
lambnetai. yen sungei ti n tow t tesin prteron gegnasin a prw
t shmerin shmea pokatastseiw tw prw t d' pilecevw mr&
mi leipos k' mrei prw man.
Eti d e ka m kribew tgxanen, mvw palaithtow neken, ka prw
tw p tn per Mtvna ka Ektmona tethrhmnaw yerinw tropw tn
sgkrisin prw tw f' auto kribw thrhyesaw poihsmenow, t at
toto sxedn erskei: ka di' llvn d pleinvn thrsevn t tosoton
diforon katalambanmenow par tn to d' pousan ginmenon.
Ka ti "... tn Ipparxon ... at pleonkiw sugkatatiymenon: n
"te gr t per niausou megyouw, sugkrnaw tn p Aristrxou te-
"thrhmnhn yerinn tropn t n tei lgonti tw prthw kat Kllip-
"pon peridou, t f' auto plin kribw elhmmn t mg' tei l-
"gonti tw g' kat Kllippon peridou, fhsn otvw: dlon tonun
"ti n tow rme tesin txion ggonen trop tw kat t d' pousaw
"t msei to sunamfotrou j mraw ka nuktw xrnou", w p-
lin t triakosiost ggista mrei tw mraw llepein tn niasion
xrnon par tn to d' pousan.
Plin n t "per mbolmvn mhnn te ka mern" proeipn ti
mn Kllippow sugkrnaw tw auto thrseiw prw tw xaldakw
sungei tn niasion xrnon mern tje ie, tn d mhniaon sunodikn
panselhniakn mern ky l: di ka tn perodon katalambnei
tn o
(2), peidper n t tosot xrn mrai mn sungontai
(69)b
(22)zcny snodoi d Qm ka mrai ky, ka dhlad pokatstasiw
ggista sundvn poteletai: ll ka logizomnou to niausou xr-
nou mhnn sunodikn ib w kay' kaston dvdekathmrion miw sundou
ginomnhw, sungontai n tow o
(2) tesin snodoi
loipo katalepontai mnew sunodiko kh ow fasin mbolmouw, ka
mrai ky w ka atw fasin mbolmouw.
Ka Ipparxow d "n t per mbolmvn mhnn te ka mern" sun-
tgmat fhsin, "ti kat mn tow per Mtvna ka Ektmona" yh-
naouw " niasiow xrnos" mern stin tje ie mz kb ggista, n
fhsin mern "tje d' o
(2)',
kat d Kllippon mern tje d',"
ll mn ka kat' atn tn Ipparxon tje d' par triakosiostn,
w diafrein tow to Ipprxou pilogismow kat mn Mtvna ka
Ektmona o
(2)' ka triakosiost, kat d tn Kllippon triakosiost.
[2]
"w ka n tow t tesin par mn tow per Mtvna llepein mraw e,
"par d Kllippon, mran man", w par mn yhnaoiw mbol-
mouw e, par d lejandresin a.
"Ka sugkefalaiomenow d Ipparxow tw gnmaw auto di tn
"dvn suntagmtvn fhsn otvw: sunttaxa d ka per to niausou
"xrnou n podeiknv ti kay' lion niautw (otow d stin xrnow
"n liow p tinow tropw shmeraw p tn atn paragnetai)
"perixei mraw tje ka d' mrow par triakosiostn".
Totou on otvw xontow, n p tn tje d' mern flvmen t
triakosiostn tw
tn mran ew j metalambanomnhn, poien jhkost prta mn j de-
tera d
(22)gx: n t triakosiostn gnetai detera jhkost ib: "jo-
"men tn niasion xrnon mern tje id mh".
Par' n mersantew tw tw miw pokatastsevw moraw tj, eromen
t mersion maln to lou kat mkow knhma
(130) ny h iz ig ib la.
Epoihsmeya d proxeirteron tn prokemenon merismn tn tr-
pon toton mersantew.
Katabibsantew gr tn tje id mh mern riymn kat tn tw
jhkontdow lgon, ka t genmena
(2) e id mh pisunyntew xri to
kat t a' seldion j riymo, pareykamen n deutr selid pi-
grafnti mern, tn potetagmnon trpon.
Epeita tw to
dion, pegracmeya tn t ggista lttoni ato parakemenon tout-
stin td kb k kat t prton seldion, oon tn n, w prton jh-
kostn, pe ka a tj morai par tw tje id mh merizmenai latton
poiosin tw a moraw. atn d tn tn parakeimnvn kat t b' se-
ldion felntew p tn tj moirn, t loip ne lz m esgontew p-
lin kat t b' seldion tn mern, ka tn parakemenon movw t
ggista ato lttoni kat t a' seldion y tugxnonta prosyntew
t n, pegracmeya t ny.
Atn d plin tn parakemenon t y felntew p tn ne lz m,
t loip n k
(2) mh movw esagagntew kat t b' seldion, t para-
kemena satvw t ggista ato lttoni kat t a' seldion h j-
eymeya jw tn
(130) ny, ka xomen pogegrammnon tn
(130) ny h.
Epeita plin felntew p tn n k
(2) mh t parakemena t h,
ka t loip a md my l
(2) toutstin rd my l
(2) esagagntew movw
kat t b' seldion, t parakemena t ggista ato lttoni i pe-
gracmeya: at d t parakemena t i felntew p tn rd my l
(2)
t loip mg nz h esagagntew movw kat t b' seldion, t para-
kemena t ggista lttoni ato z prosyntew t i, pegracmeya
tn iz jw tn proekteyeimnvn ka gegnasin
(130) ny h iz.
Epeita plin t parakemena t z felntew p tn mg nz h,
t loip a k kd kd, toutstin p kd kd esagagntew kat t b' sel-
dion, t parakemena t ggista ato lttoni
pegracmeya: t d at t i parakemena felntew p tn p kd kd,
t loip iy la n
(2) esagagntew plin kat t tn mern kannion,
ka t parakemena t ggista ato lttoni kat t prton sel-
dion g prosyntew t i, ka tn ig prosyntew tow dh sunaxyesin
sxomen kteyeimnon tn
(130) ny h iz ig.
Epeita plin t parakemena t g felntew p tn iy la n
(2),
ka t loip o
(2) ia l
(2) esagagntew plin ew t b' tn mern seldion,
t parakemena t ggista ato lttoni kat t a' seldion i pe-
gracmeya. at d plin t parakemena t i felntew p tn
o
(2) ia l
(2), ka t loip ie iy h esagagntew ew t tn mern seldion,
t parakemena t ggista ato lttoni t b kat t a' seldion
sunyntew met tn i, t genmena ib proseykamen t prossunaxynti
ka ggonen
(130) ny h iz ig ib.
Epeita plin t parakemena t b felntew p tn ie iy h,
ka t loip rph lh kd esagagntew ew t b' seldion, t parake-
mena t ggista ato lttoni kat t a' seldion l pegracmeya.
at d t t l parakemena felntew p tn rph lh kd ka t
loip
(2) a esagagntew kat t b' seldion, t parakemenon t ggista
ato kat t a' seldion a prosyntew tow l ka t genmena la
prosyntew plin tow proekteyeimnoiw, eramen tn genmenon k to
merismo mersion maln to lou knhma
(130) ny h iz ig ib la: r-
ken gr fhsi mxri tn tosotvn jhkostn, tow merismow gnesyai.
Per tw kay' maln ka gkklion
knhsin poysevw.
Dialabn per to niausou xrnou ka didjaw tn pryesin ka
tn skopn to mayhmatiko, ti prkeitai at dejai t fainmena
n t oran pnta di' maln ka gkuklvn kinsevn potelomena:
maln mn di t llotran enai tw yeithtow atn tn takton
ka nmalon knhsin, gkuklvn d di t dion atn. ka kymenow
tn tw malw to lou kinsevw kanonografan, jw boulmenow
ka per tw di tw tn kklvn poyseiw di' n poietai tw kinseiw
fainomnhw ato nvmlou kinsevw dialaben, ka ti tw totvn
diaforw kanonografan sustsasyai (rmzein gr fhsin ka t sko-
p tn tn toiotvn do kanonvn kyesin prw t p mn tw kat
mrow malw kinseiw k proxerou k tw kysevw tn tw malw
kinsevw kannvn pilogzesyai, p d k tw mjevw atn tw kri-
bew ka fainomnas) eta boulmenow p te to lou ka tw selnhw
ka tn e planvmnvn per tw fainomnhw atn kinsevw dialaben,
pe w famen topon n tow yeoiw ka idoiw prosptein atn tn
takton ka nmalon knhsin, didskei prteron n trpon atn
malw kinoumnvn sumbanei nvmlvw mn atow fanesyai kinou-
mnouw tw to di msvn tn zdvn kklou perifereaw, ka fhsin:
prolaben xr ti "a tn planvmnvn ew t pmena to orano"
toutstin a p dusmn p' natolw "metakinseiw mala mn esi
"psai", toutsti tetagmnai ka mte nesin ptasin pidex-
menai, ll' ae satvw xousai, sotaxw ka gkuklvw fermenai,
kayper ka p' natolw p dsin ew t prohgomena tn lvn for,
di t fsei t toiot sxmati t sunexw ka dion tw kinsevw
prxein. di od taktow nmalow per atow knhsiw, kayper
fanontai pleon ka latton ew t pmena kinomenoi, ti te ka st-
tew ka popodzontew w p tn e planomnvn.
Eta didskvn t lgei t malw atow kinesyai, fhsn plin ti
"a noomenai eyeai perigein tow straw ka tow kklous" kay' n
poiontai tw kinseiw sotaxw periagmenai, saw poiosi tw gvnaw
prw kenoiw tow kntroiw prw ow t teron praw mnon pntote xou-
sai perigontai.
Ina d faner mn gnhtai t legmena, kkesyv ABGD kklow
per kntron
[2] t E, ka dimetron tn AED: ka p' ato kinesyv tiw
str w p to A p t B n tini xrn malw tn AB perifreian.
ka ti n t s xrn malw plin kekinsyv tn BG, shn dhlonti
genomnhn t AB, di t malw ka n s xrn to ato kklou peri-
fereaw atn kekinsyai.
En on kinoumnou to strow p tw kat t A ysevw nosvmen
tn EA eyean per t E kntron sumperiagomnhn at, ka p mn
tn tw EB ysin lambnousan, p d tn tw EG, ka ata sumperiene-
xysontai malw n tow atow soiw xrnoiw ka saw polmcontai
gvnaw tw p AEB, BEG prw t E kntr tw periforw.
All d m stv str p to ABG kklou kinomenow, ll' p
trou kuklskou w to ZHY, kinoumnou ka ato p to ABG kklou
ka t kntron pntote xontow p tw perifereaw ato di ka p-
kuklon atn kale. ka stv ato t kntron kat t A, d str
stv p to Z. ka kinesyv t A kntron to ZHY pikklou malw
n t s xrn tn te AB ka tn BG. ka pezexyvsan a EB, EG
atinew noesyvsan perigousai tn pkuklon ka saw poiosai di t
proeirhmna tw p AEB ka BEG gvnaw.
En on nosvmen ka tn stra n tow soiw xrnoiw malw p
to Z kinhynta p to pikklou tw ZH, HY perifereaw, ka pi-
zejvmen tw GH, GY, ka atai plin sontai p tw toiathw poy-
sevw a noomenai perigein tn stra ka saw polambnousai tw
ZH, HY perifereaw ka ti tw p ZGH, HGY gvnaw prw t G kntr
prw periagvg to strow poteletai.
Di fhsin: "a noomenai perigein tow straw ka tow kklouw
"atn n tow soiw xrnoiw saw gvnaw polambnousi prw tow kn-
"troiw tn periforn": o mnouw d tow pikklouw lgei kinesyai
p tn eyein, ll ka tow kkntrouw w jw p te tw selnhw
ka tn planvmnvn fanern poie.
A d fainmenai nmaloi atn kinseiw
[2] "par tw yseiw tn
"n taw sfaraiw atn kklvn, di' n poiontai tw kinseiw potelon-
"tai".
Eta didskvn kat poaw poyseiw dnatai par tw yseiw ka tw
tjeiw tn kklvn f' n poiontai tw kinseiw proxvren to mayhma-
tiko skopw, toutstin ste malw atn kinoumnvn nvmlvw
fanesyai diejintaw tw to di msvn perifereaw, ka ox t nti
atow prxein llotra tw idithtow atn taktow ka nmalow
knhsiw, fhs:
"t d' ation tw nvmlou fantasaw kat do mlista
"tw prtaw ka plw poyseiw ndxetai gnesyai". tw gr kat
fsin atn malw kinsevw lg yevroumnhw, e mellen fainomnh
knhsiw ka mal tugxnein, p mokntrou kklou t to pantw sfa-
r& ka n t pipd to di msvn potelesyai: otv gr mal
atn prodow ka fainomnh dnato tugxnein, kayper p tw
prthw katagrafw prw t E t kntron to di msvn ka tw cevw
potiyemnhw.
Sumbanei atow toi kat m mokntrvn t ksm kklvn malw
poiesyai tw kinseiw ll kat' kkntrvn, kay' mokntrvn mn, ok
p' atn d, ll p trvn p totvn feromnvn ka t kntra xn-
tvn p' atn, kaloumnvn d w famen pikklvn. kay' katran gr
totvn tn poysevn dunatn enai katalambnetai n tow soiw xr-
noiw malw atn kinoumnvn nsouw fanesyai diejintaw to di
msvn tn zdvn kklou mokntrou t ksmperifereaw.
En te gr p tw erhmnhw to kkntrou poysevw, nosvmen
n sfar& tinw tn e planvmnvn <> ka to lou tw selnhw
kkntron kklon, f' o tn stra fannta kinesyai "tn ABGD, per
"kntron t E ka dimetron tn AED", shmeon d' p' atw tn me-
tran cin, toutstin tn gn, di t sumfvnen tow fainomnoiw sh-
meou lgon xousa atn ka prw t tn planomnvn postmata
potyesyai, mnou to per tn selnhn par toto ginomnou diafrou
tn diryvsin lambnontow, ka to par tn lion di tw kleceiw.
t Z shmeon ka kntron to zdiako tugxnei, peidper mn z-
diakw mkentrw sti t ksm to d ksmou kntron stn g.
"ste ka t mn A shmeon pogeitaton gnesyai", toutstin pleon
p to Z shmeou tw cevw pxon tn kat tw llaw yseiw par-
dvn. "t d D perigeitaton", toutstin latton plin pxon p to
Z kat tn cin tn kat tw llaw yseiw pardvn, di t p tw AD
diamtrou elfyai t Z shmeon, m stin kntron to kklou, ka
mezona gnesyai tn ZA pasn tn p to Z p tn ABGD kklon
diagomnvn eyein, lttona d tn ZD.
Ka "polabntew saw perifereaw tw AB, GD pizejvmen tw
"BE, BZ ka GE, GZ ..." dlon w ti tw malw periagvgw per t E
kntron ginomnhw ka to strow tw AB,
n s xrn dierxomnou, sai sontai ka a p AEB, GED gvnai:
ka pe mezvn stn p AEB tw p AZB, lttvn d p GED
tw p GZD, poll ra lttvn stn p AZB tw p GZD.
Vste nisoi sontai a prw t cei toi prw t kntr to di m-svn tn zdvn kklou ginmenai gvnai, a d prw tow kntroiw gv-
nai tn atn xousi lgon taw perifereaiw. ka ti t p nsvn
gvnin rmena nisa fanetai, ka t mn p meiznvn mezona w n
tow Optikow dexyh. nsouw ra perifereaw fansetai to di m-
svn peilhfw str, pe ka a prw t kntr ato gvnai esn
sai, n s xrn malw saw perifereaw p to kkntrou kinhyew.
Omovw d ka p tw kat' pkuklon poysevw t at plin dei-
xysetai otvw: noesyv gr n sfar& tinw tn erhmnvn strvn
mkentrow kklow t ksm ka
zdvn
syv ciw tn rntvn,
to mokntrou kntron. dimetrow d ato stv AED.
Dlon on ti, n p totou poymeya malw tn stra kinesyai
lgou neken p to A p t B, tn periagvgn poiomenon per t E
kntron, ka pizejvmen tn BE p AEB gvna at stai n -
malw
Epe on tn pyesin smfvnon de enai t skop to mayhmati-
ko, toutstin ste w famen malw atn kinoumnvn nvmlvw
fanesyai diejintaw tn di msvn tn zdvn kklon, pokesyv
str m p to mokntrou kinomenow, ll' p to erhmnou pik-
klou, ka ato malw p tw to BGD mokntrou perifereaw
ew t pmena w p to A p t B, ka t kntron pntote xontow p'
ato ka n t at pipd ato tugxnontow: ka stv erhmnow
pkuklow ZYK per kntron t A, d str p' ato kat t Z,
gnetai p tathw tw poysevw pogeitaton di t mezona enai
tn p to E tw cevw distasin p t Z pasn tn p to ato
shmeou p ti tmma to pikklou, perigeitaton d movw t kat t
Y shmeon di t plin lttona enai tn p to E tw cevw p t
Y distasin pasn
kklou.
Epeidper to ZHYK
pkuklow malw p
mnou to pikklou stato str p tw perifereaw ato tugxnvn
ka oon kat t Z, at mn plin gneto mal periagvg t faino-
mn.
All' pe kinetai, kekinsyv n t at xrn p to pikklou
w ew t pmena malw plin tn ZH perifreian: ka pezexyvsan
a EH, EK. sumbsetai ra to pikklou malw metagagntow tn
stra tn AG perifreian toutstin tn p AEG gvnan, atn kinh-
ynta p to pikklou tn ZH, p tw kat t E cevw fanesyai di
tw EH eyeaw mezona tn p AEH gvnan kekinhmnon tw p AEG
malw.
E d str m p to Z p t H ew t pmena kinoto ll p
to Z ew t prohgomena w p t K, lttona gvnan fansetai ki-
nhyew tn p AEK tw p AEG malw.
On d trpon n taw sfaraiw lou ka selnhw ka tn e pla-
nvmnvn xr pinoen tow kklouw grafomnouw, lgv d tn te kken-
tron ka tn mkentron fronta tn pkuklon, otv deikton: noe-
syv gr t kat tn Aristotlh kukloforhtikn E sma, n te
tn plann sfara ka to lou ka tw selnhw ka tn e pla-
nomnvn p' lllaw kemenai kat tn n tow okeoiw tpoiw lexyhso-
mnhn tjin, periexmenon p tw kurtw pifaneaw n AB k-
klow ka p tw kolhw n GD, per kntron t M.
Ka noesyv n at to lou sfara mkentrow at tugxnousa,
f' w plin kat mn tn ktw kurtn pifneian noesyv EZH k-
klow, kat d tn kolhn YKL, ste t metaj tn kklvn disthma
pxouw toi byouw tugxnein tw liakw sfaraw. ka dixyv di to
M kntrou dimetrow EMH, ka gegrfyv EL kklow faptmenow
tn ZHE, KYL kat
mtrou t J. stai ra erhmnow kkentrow n t sfar&, toiathn xvn
tn ysin f' o w dejamen malw kinomenow str nomlvw fa-
netai diejin tw to di msvn perifereaw. ka pe t' p to E tug-
xnei liow pogeitatow ginmenow p to EZH kklou stn, te d
p to L perigeitatow ginmenow p to YKL, dlon w ka kat
byow kinhysetai n t sfar& ato tn jw podeixyhsomnhn phli-
kthta.
Ina d ka p to mokntrou tn pkuklon frousa pyesiw p'
cin mn gnhtai, pokesyv w p to b' yevrmatow neu to k-
kntrou moa katagraf, ka gegrfyv kat msou to tw lia-
kw sfaraw byouw OPR mkentrow ka p' ato pkuklow per
t O kntron faptmenow tn EZH, YKL kklvn kat t E, Y. fa-
nern on ti kinoumnou to lou p to kklou ka p mn ginomnou
kat t E, p d kat t Y, p d ka kat' llvn ato mern, ka kat'
atn tn pyesin kat byow kinhysetai.
"Ep mn on tw toiaths" toutstin tw erhmnhw ploustraw,
"kat' kkentrthta poysevw, e sumbbhken tn mn laxsthn k-
"nhsin kat t pogeitaton" fanesyai poiomenon tn stra "tn
"d megsthn kat t perigeitaton, pe ka pntote" w p tw
prokeimnhw to kkntrou katagrafw " p AZB gvna" prw t
cei fainomnh "lttvn stn tw p AEB" malw t p ZBE, d
p GZD prw t perige fainomnh mezvn tw p GED malw t
p EGZ, tn maln kinsevn svn dhlad ka soxronvn osn.
"Ep d tw kat' pkuklon poysevw mfterai dnantai" para-
kolouyen, ka kat t pgeion to strow tugxnontow tn megsthn
ka laxsthn knhsin potelesyai, ka kat t pergeion movw. kay-
per p tw prokeimnhw katagrafw, n to pikklou kat to A
tugxnontow ka str p to Z pogeou pokhtai, to pikklou
p to A p t G ew t pmena kinoumnou, e mn str p to Z
pogeou to pikklou movw ew t pmena w p t H kinoto, me-
zona kayw dhlomen tn p AEH fansetai kinhyew tw p AEG
malw, "di t p t at mrh tn te pkuklon ka tn stra tte
"metakinesyai". n d to pikklou ew t pmena w famen tn
maln prodon poioumnou, str ew t prohgomena to pikklou
poitai tn prodon, w p to Z p t K, lttona tw p AEG ma-
lw, "di t p t nanta tw to pikklou metabsevw tn stra
"tte metakinesyai", diafora d sontai tw malw pardou par
tn fainomnhn a p HEZ, KZE.
Ka dlon ti a diafora tn do kinsevn tw te malw ka tw
fainomnhw, p mn tw kat' kkentrthta poysevw prw t perifere&
to kkntrou sunstantai w pnv a p ZBE, EGZ, p d tw kat'
pkuklon prw t kntr to mokntrou w p tw prokeimnhw
katagrafw a p ZEH, ZEK.
Totvn on tn do poysevn tn erhmnon trpon periexousn
"jw kkeno prolhmpton ti p mn tn dissw poioumnvn nvma-
"las", toutstin f' n strvn ok jarke katlhmciw tn erh-
mnvn diaforn prw tn sumfvnan tn k tn thrsevn katalambano-
mnvn atn poxn ll ka traw detai diorysevw, "mfotraw tw
"poyseiw sumbanei sumplkesyai" oone tn pkuklon p to
kkntrou fresyai ka sa lla smfvna prw tn farmogn tn di
tn rgnvn katalmcevn katalambnetai, w n tow okeoiw tpoiw
podsomen.
Ep d tn mi tn erhmnvn diaforn rkoumnvn strvn prw
tn erhmnhn katlhmcin, kayper p to lou, erskomen ka mi
tn erhmnvn pln poysevn rken.
Eta epn mi poi&on tn erhmnvn poysevn rkesyai, dhla-
d w t at fainmena parallktvw atn deiknuousn, dialamb-
nei per tw moithtow atn, ka rxmenow tw toiathw podejevw,
rzetai t kaylou felonta n katr& atn prolambnesyai prw
tn tw moithtow farmogn ka fhsi t at parallktvw fain-
mena dnasyai deiknnai tw erhmnaw poyseiw tan n xei lgon
p tw kat' kkentrthta poysevw ZE metaj tn kntrvn to
te zdiako ka to kkntrou prw tn EA k to kntrou to k-
kntrou toton x tn lgon p tw kat' pkuklon poysevw ZA
k to kntrou
kntrou ka ti n s xrn str tn kkentron kklon knhton
mnonta w ew t pmena malw kinomenow pokaystatai, n
tosot ka pkuklow tn mkentron ew t pmena plin malw
kinomenow pokaystatai ka ti str tn pkuklon, tw mntoi to
strow p to pikklou metabsevw ew t prohgomena toutstin
p to Z p t K ginomnhw ew t Y. ka toiath to strow met-
basiw smfvnon t kat' kkentrthta poysei tn kat' pkuklon
poei ka atw tte prw tow pogeiotroiw mresin lttona poioshw
tn fainomnhn ka krib prodon tw malw, prw d tow perigeio-
troiw mezona: ka ti kat t pgeion n katr& tn laxsthn
prodon, kat d t pergeion tn megsthn w n tow jw podejomen,
per dion tw kat' kkentrthta poysevw katelambneto.
Epeshmnato d tn kkentron metptvton tugxnein, di t p
tw tn llvn poysevw kinomenon atn katalambnesyai, ka don
enai ka tn knhsin ato pilogzesyai.
Eti d ka tn erhmnvn lgvn ka pokatastsevn f' katraw
tn poysevn pokeimnvn t at fainmena parallktvw kay'
katran atn potelesysesyai, deknusin ka di tn grammn "ka
"di tn fodeuomnvn p tw to lou nvmalaw riymn".
[14] Oti d ka n kat t jw sai perifreiai polhmfysin p to
pogeou, pogeiotra fainomnh lttvn stn tw perigeiotraw,
dejomen plin f' katraw tn poysevn ka prteron p tw kat'
kkentrthta.
Estv gr kkentrow kklow ABGD per kntron t E ka dimetron
tn AED, f' w pokesyv t kntron to di msvn t Z. ka peil-
fyvsan p to A pogeou jw do sai perifreiai tw malw kin-
sevw a AB, BG: ka pezexyvsan a EB, EG: ka ti a ZB, ZG. fa-
nern d ti a mn p AEB, BEG gvnai tw malw kinsew esin, a
d p AZB, BZG tw fainomnhw: ka pogeiotra mn p AZB, peri-
geiotra d p BZG. lgv on ti mezvn stn p BZG tw p
AZB.
Epezexyvsan gr a AB, BG. ka pe sh stn AB eyea t BG,
koin d <> BZ, ka bsiw AZ bsevw tw GZ mezvn, gvna ra
p ABZ gvnaw tw p GBZ mezvn stn.
Ekbeblsyv BZ p t H, ka pezexyvsan a AH, GH. ka pe
sh stn AB eyea t BG, koin d BH, ka gvna p ABH gv-
naw tw p HBG mezvn, bsiw ra AH bsevw tw GH mezvn st.
Kesyv t GH sh HY, ka pezexyv YZ: pe on sh stn
GH t HY, koin d HZ, ka gvna p GHZ gvn& t p YHZ sh
stn, pe ka perifreia AB t BG, bsiw ra GZ bsei t YZ sh
stn: ka t GZH trgvnon t YZH: ka a loipa gvnai taw loipaw
gvnaiw: ste ka p GZH gvna sh stn t p YZH: ka loip
p GZB loip t p YZB sh.
Mezvn ra p GZB perigeiotra fainomnh prodow tw p AZB
pogeiotraw fainomnhw.
Omovw d deixysetai ti ka n p to D perigeou saw perife-
reaw polbvmen p to kkntrou tw malw pardou, mezvn stai
perigeiotra fainomnh prodow tw pogeiotraw.
Ina d ka p tw kat' pkuklon poysevw tn atn pdeijin
poihsmeya, stv mn mkentrow t di msvn tn zdvn ka n t
pipd ato kemenow ABG kklow, per kntron t E, ka dimetron
tn AED: d' p' ato fermenow pkuklow ZH. ka pokesyv, tan
mn pkuklow p to A tugxn, ka str kat to Z pogeou.
ka kekinsyv pkuklow malw do saw perifereaw tw AB, BG.
ka n s mn pkuklow tn AB, n tosot ka str p to Z
pogeou p t prohgomena kekinsyv tn ZH, moan ginomnhn t
AB di tn soxronithta tn pokatastsevn. n s d lhn tn AG,
n tosot plin str tn ZY moan atn tugxnousan. ka pe-
zexyvsan a EBZ, EH, EGZ, EY.
Dlon d ti str prteron mn p tw EAZ fainmenow, jw p
tw EH fnh, eta plin p tw EY, ste tw mn p AEB malw
pardou fainomnhn gnesyai tn p AEH, tw d p BEG malw tn
p HEY fainomnhn.
Lgv on ti pogeiotra fainomnh toutstin p AEH, tw peri-
geiotraw fainomnhw toutstin tw p HEY lttvn stn.
Epe gr AG perifreia diplasvn stn tw AB, moa d mn
AG t ZY, d AB t ZH, dipl ra ka ZY tw ZH. tetmsyv ZY
dxa kat t K: katra ra tn ZK, KY sh stn t ZH: pezexyv
KE.
Lgv prton ti p ZEK mezvn stn tw p KEY.
Ekkesyv gr xvrw katagraf mnou to per t G pikklou:
ka pezexyvsan a ZK, KY: ka ti a AL, LY: pe on mezvn stn
ZA eyea tw YL, kesyv t LY sh LM, ka pezexyv EM.
ka pe sh stn LM t LY, koin d LE, ka gvna p MLE
gvn& t p YLE stn sh, pe ka a fejw ataw di t ka tn
ZK perifreian t KY shn enai, bsiw ra ME bsei t YE stn
sh. ka t MLE trgvnon t YLE trign son stai.
Ka a loipa gvnai taw loipaw gvnaiw: sh ra stn p MEL
gvna t p YEL. ste mezvn stn p ZEK tw p KEY.
Eta plin p tw to mokntrou katagrafw, pezexyvsan a HB,
KG. ka pe sh stn p ZGK t p ZBH, sh stn ka loip p
BH. sognion ra stn t EGK trgvnon t EBH trign: ste ka
p GEK gvna sh stn t p BEH.
Mezvn d p GEK tw p KEY. mezvn ra ka p BEH tw
p KEY.
Ka pe sh stn p AEB t p BEG, n p HEB t p KEG
stn sh, loip ra p AEH t p BEK sh stn.
Ka pe mezvn stn p HEB tw p YEK, koinw prosteyeshw
tw p BEY, mezvn ra p HEY tw p BEK. sh d p BEK
t p AEH. mezvn ra p HEY tw p AEH.
Vste pogeiotra fainomnh prodow toutstin p AEH, lttvn
st tw perigeiotraw fainomnhw pardou, toutstin tw p HEY,
per dei dejai.
Omovw d ka n kat t jw katraw tn AB, BG saw pol-
bvmen tw malw pardou to strow perigeiotrou ginomnou, di
tn soxronithta tn kinsevn mezvn deixysetai perigeiotra
fainomnh prodow tw pogeiotraw.
Di ka legen tn mn laxsthn prodon kat t pogeitaton po-
telesyai tn d megsthn kat t perigeitaton, peidper kn bra-
xtata tinew per tata t shmea polhfysin tn svn ka soxro-
nvn maln pardvn, pogeiotra fainomnh prodow pntote lt-
tvn katalambnetai di tn toiotvn dejevn tw perigeiotraw, d
perigeiotth dhlad mezvn.
Ey' jw lambnvn f' katraw tn poysevn tn tn erhmnvn
lgvn moithta ka tn pokatastsevn soxronithta, deknusin ti
kay' katran atn, tan p tw kat' pkuklon str p to po-
geou to pikklou p t prohgomena poitai tn knhsin, megsth
diafor gnetai tw malw kinsevw par tn fainomnhn nmalon
kay' n ka msh toi mal prodow tn strvn yevretai,
toutstin
tan p tw cevw toi to kntrou to di msvn tn zdvn p tn
stra pizeugnumnh eyea prw ryw tugxn t di tn pogevn
ka perigevn diamtrvn.
Kale d tn kat tw toiathw ysevw prodon mshn oone ma-
ln, di t diforon t mal tn fainomnhn tte katalambnesyai
p pol tw atw prw asyhsin menoshw tw par tn nvmalan
diaforw.
Eti d sunapodeknusin ti xrnow n toto t pogeiteron to
di msvn tetarthmrion fanetai kinomenow mezvn stn to xrnou
to n t perigeiteron tetarthmrion fanetai kinomenow, per sum-
banei e p tw kat' kkentrthta poysevw, ka kat tn tn pi-
kklvn d, tan str ew t prohgomena to pikklou poitai tn
knhsin: tan d ew t pmena npalin p tw megsthw kinsevw
toutstin p to pogeou p tn mshn prodon xrnow mezvn po-
teletai to p tw mshw p tn laxsthn, toutstin p t peri-
geiteron, di t p tw toiathw ew t pmena to pikklou to
strow metabsevw ginomnhw, kat mn t pgeion tn megsthn pr-
odon potelesyai kat d t pergeion tn laxsthn, w jw dejomen,
pe ka p tathw tn pogeiotran fainomnhn prodon mezona de-
knumen tw perigeiotraw.
Ey' jw poiomenow tn toiathn pdeijin re plin, "ti mn on
"n n x lgon p EBZ gvna" p tw kteyeimnhw at kat'
kkentrthta katagrafw "prw d ryw, toton xei tn lgon ka
" to par tn nvmalan diafrou perifreia prw tn lon kklon",
peidper mn p AEB gvna mezvn osa ryw, mezona tetarth-
morou perifreian polambnei, d p AZB ry tetarthmrion:
ste ka tn p EBZ peroxn tugxnousan tn erhmnvn gvnin,
tn peroxn tn erhmnvn do periferein polambnein prw t
kntr sunistamnhn.
Eti d katdhlon gnetai t legmenon otvw: pe a mala ka a
kribew poxa p to di msvn lambnontai dhlad ka a diafora,
gegrfyv per t Z kntron LHKD di msvn tn zdvn kklow:
ka di to Z t EB parllhlow xyv ZK: ka dixyvsan a AG, ZB
p t D, L, H shmea. sh ra stn mn p EZK gvna t p AEB
tw malw pardou, d p HZK t p EBZ tw par tn maln k-
nhsin diaforw. ka pe n xousin lgon a gvnai prw lllaw tan
prw tow kntroiw sin toton xousin ka a perifreiai a f' n be-
bkasin, n ra xei lgon <> p HZK prw t kntr to di m-
svn tugxnousa prw tssaraw ryw, toton xei tn lgon ka HK
perifreia prw tn lon kklon. ka stin HK to par tn nvmalan
diafrou: ste n n x lgon to par tn nvmalan diafrou
gvna prw tw d ryw, toton xei tn lgon ka perifreia f' w
bbhken prw t kntr sunistamnh, prw tn lon kklon.
Eta podejaw prw taw erhmnaiw msaiw pardoiw tw megstaw
diaforw sunistamnaw, sunapodeknusin "ti ka AB perifreia
"tiw perixei tn p tw laxsthw kinsevs" toutstin to pogeou
"p tn mshn" prodon "xrnon, mezvn stn tw BG, tiw perixei
"tn p tw mshw ... p tn megsthn ... dusn taw t diforon ... pe-
"riexosaiw perifereaiw."
Epeidper, n di to E t ZB parllhlon ggvmen tn EY, mn
AY sh gnetai t YG: mezvn ra AY tw BG t YB. ste lh
AB tw BG mezvn stn t diplasoni tw YB poteinoshw tn p
YEB gvnan shn t p EBZ t diforon periexos tw nvmalaw.
H ka p tn periferein to di msvn, otvw: p tw kat t
B mshw pardou mal p to zdiako stin kat t K, di t shn
enai tn p AEB gvnan t p AZK d kribw kat t H. ra
HK perifrei stin to par tn nvmalan diafrou. ka pe sh stn
DH perifreia t HL perifere&, ra LH tw KD mezvn stn
t HK. ste lh LK, p to L pogeou p tn kat t K tw mshw
pardou poxn, mezvn stn tw KD p tw atw kat t K poxw
p t pergeion, t diplasoni tw HK, t diforon periexos.
Vste ka kaylou p tw kat' kkentrthta poysevw, n m
mal prodow kayper p tn e planomnvn per t to zdiako
kntron poteltai, ke famen tn maln poxn p to di msvn
tugxnein, nya pptei eyea
to zdiako t ginomn p tw malw periagomnhw ka tw di
tn pogevn: otv gr n tw to zdiako perifereaw moaw sun-
istamnhw t p to kkntrou mal dentvw p to zdiako k-
blletai mal prodow.
Eta jw p tw kat' pkuklon poysevw dejai boulmenow t
at toto sumbann fhsin: "stv mkentrow t ksm" ka n t
pipd to di msvn " ABG, per kntron t D, ka dimetron tn
"ADB: d' n t at pipd fermenow p' ato pkuklow EZH,
"per kntron t A. ka pokesyv str kat t H". p to E po-
geou p t prohgomena to pikklou tn EH perifreian kinhysetai
"tetarthmrion pxvn fanetai to kat t pgeion shmeou", tout-
stin tan p tw cevw p tn stra pizeugnumnh eyea ryn
poi gvnan prw tn di to pogeou ka to perigeou dimetron.
"Ka pezexyvsan te AH ka DH. lgv ti DHG fptetai
"to pikklou: tte gr t pleston gnetai diforon tw malw ki-
"nsevw par tn fainomnhn nmalon".
Ina d safestra gnhtai proeirhmnh pdeijiw, dixyv di to
D LDNMJ dimetrow, prw ryw t DG, f' w pogeitatow ka
perigeitatow str gnetai. ka gegrfyv per t M JN pkuklow
otvw xvn dhlad ste ka tn stra tte kat to J pogeou tug-
xnonta fanesyai perigrafntow to OPR zdiako kat t O. ka
n pkuklow keknhtai tn MA, n tosot ka str p t pro-
hgomena to pikklou tn EH kinhyew ka kat to H tugxnvn,
fainsyv kat t P, pxvn p tw prw t O kat t pgeion po-
xw tn OP tetarthmoriaan perifreian, toutstin tn p ODP prw
t cei ryn gvnan. ka dlon w ti di tn soxronithta tn po-
katastsevn sh stai p MDA gvna tw to pikklou metabsevw,
t p EAH to strow: di toto d ka parllhlow DM
Fhsn on ti "pe mn mal p to pogeou knhsiw perixetai
"p tw EAH" toutstin tw p MDA, di fhsin "sotaxw gr te
"str tn pkuklon ka pkuklow tn mkentron dirxontai: t d
"diforon tw malw kinsevw par tn fainomnhn" nmalon "p
"tw p ADH gvnaw perixetai: "fanern ti ka perox tw p
MDA prw tn p ADH, toutstin p MDH, tn fainomnhn
to strow prodon perixei. pkeitai d at ry: ry ra ka
p DHA, nallj gr, ka sh t fainomn. "ka di toto faptomnh
DHG to pikklou" tn megsthn poietai diaforn tw malw
kinsevw par tn fainomnhn nmalon, toutstin tn p EDH: e
gr tathw mezvn sustaysetai, kpesetai te eyea ka str to
pikklou, per topon: pkeitai gr pntote p' ato kinomenow.
Eti sunapodeiknvn ka p tw toiathw poysevw ti p tw
laxsthw kinsevw p tn mshn xrnow mezvn stn to p tw m-
shw p tn megsthn dus taw t diforon periexosaiw perifereaiw,
xrtai t podejei otvw:
Ekbllvn gr tn DHY ka prw ryw t EZ gagn tn AKY, fh-
sn: "sai mn ggnontai a te p KAH ka ADH gvnai", te n ryo-
gvn trign t ADY, p tw ryw gvnaw p tn bsin kyeton
xyai ka sognia gnesyai t trgvna. ka pe prw tow kntroiw es
tn kklvn a sai gvnai, moa ra stn ka AG perifreia t KH.
ste ka soxrnioi sontai a p' atn mala ka sotaxew kinseiw.
Epe on diafor tw malw kinsevw par tn fainomnhn n-
malon deknuto p ADH gvna toutstin AG perifreia: tat
d soxrniow dexyh KH: tat ka prw tn pdeijin sugxrmenow
deknusin ti tw EH malw pardou xrnow to tw HZ diafrei dus
tow par tn nvmalan diafroiw toutsti dus taw KH perifereaiw.
Ka stin atyen fanern: peidper mn EH mezvn stn tw EK
tetarthmoriaaw t KH, d ZH lttvn tw KZ ka atw tetarth-
moriaaw t at t KH, ste EH tw HZ perxei dus taw KH.
H ka otvw: pe EK mezvn stn tw HZ t KH, ra EH me-
zvn stn tw HZ dus taw KH.
Esti d plin proxeirteron ka otvw podejai ti p tw la-
xsthw kinsevw toutstin to pogeou p tn mshn xrnow, oone
tw MA, to p tw mshw p t pergeion, toutstin to tw AL,
mezvn stn dus taw t diforon periexosaiw, toutsti dus taw AG.
peidper plin shw oshw t MG tw GL MA
stn t GA. ra MA tw AL mezvn st dus taw AG. per dei de-
jai.
Lgv d ka ti DG eyea [ok] fptetai to pikklou kat ti
shmeon metaj tn G, Z. m gr ll' e dunatn faptsyv toi kat
t G p tinow tn metaj tn E, G, ka prteron kat t G. ka kata-
gegrfyv moa katagraf to te mokntrou ka to pikklou:
d HD faptsyv kat t G: ka pezexyv p to A kntrou p tn
fn AG. ry ra stn p AGD. ka n kblvmen tn DG p t
J, stai p AGJ ry gvna n mezoni tmmati mikuklou t AGJ,
per topon. ok ra p to D kntrou to mokntrou fcetai to
pikklou kat t koinn atn shmeon.
Lgv d ti od metaj tn E, G. e gr dunatn, faptsyv kat t
K, w DYK. ka pezexyvsan a AK, AY. ka pe p to A kntrou
p tn kat t K fn pzeuktai AK, ry ra p AKD, mblea
ra p AYD. ka kblhyeshw plin tw YD kat t J stn p
AYJ mblea gvna n mezoni mikuklou t AYJ, per topon. od'
ra metaj tw EG perifereaw stai paf. dexyh d ti od kat
t G. metaj ra tn G, Z.
"Kat d tn ew t pmena tn pikklvn tw p to pogeou
"poiosan periagvgw tn strvn, npalin tn p tw megsthw ki-
"nsevw p tn mshn xrnon mezona ginmenon to p tw mshw p
"tn laxsthn, di t kat t pgeion p tathw tn megsthn pr-
"odon potelesyai."
Lgv on, per at paralleiptai, ti n p to pogeou to
pikklou to strow metbasiw ew t pmena poteltai, p
tw megsthw kinsevw toutstin to pogeou p tn mshn prodon
xrnon mezvn stn to p tw mshw p tn laxsthn toutstin p
t pergeion.
Ina d p katagrafw fanern gnhtai t legmenon, kkesyv
mkentrow ka n t at pipd to di msvn kklow ABGD per
kntron t E ka dimetron tn AED, d p' ato fermenow pkuklow
ZH: ka pokesyv, tan mn pkuklow p to A tugxn, ka
str kat to Z pogeou. kekinsyv pkuklow n soiw xrnoiw do
saw perifereaw malw tw AB, BG, ka n mn pkuklow tn AB
ka str tn ZH moaw osaw, n d plin pkuklow tn AG, ka
str tn ZY moaw plin osaw. ka pe dipl stin AG tw AB
dipl stin ka ZY tw ZH. kesyv t ZH sh ZK, ka pezexyvsan
a BH, EH, GK, KE, EY. movw d tow mprosyen deixysetai ti tw
mn p AEB malw pardou fainomnh stn p AEH, tw d p
BEG malw, fainomnh stn p HEY: ka ti mn p BEH sh
stn t p GEK, d p GEK mezvn tw p KEY. ka pe sh
stn p AEB t p BEG, ll ka p BEH t p GEK, ka
p AEH ra t p BEK stn sh. ka pe mezvn stn p BEH
tw p KEY, pe ka p GEK, koin p HEK, lh ra <> p
BEK lhw tw p HEY mezvn stn. dexyh d ka p BEK sh t
p AEH. ste ka p AEH pogeiotra fainomnh prodow mezvn
stn tw p HEY perigeiotraw, ka di toto e tw pogeiotraw
fainomnhw pardou mezonow poteloumnhw, kat t pgeion, oone
per at t pgeion, megsth prodow potelesysetai, per d at
t pergeion laxsth.
Lgv ti ka p tw megsthw kinsevw toutstin to pogeou
p tn mshn prodon xrnow, mezvn stn to p tw mshw p tn
laxsthn toutstin p t pergeion.
Metakekinsyv d pkuklow ka stv kat t M. ka dixyv EMZ
ka xyv p to E kntrou faptomnh to pikklou EL. ka n
pkuklow tn AM ka str tn ZL moan osan. ra msh to
strow prodow yevrhysetai per t L ato tugxnontow, di t
w famen mprosyen, per tata t shmea f' kann disthma tn
par tn nvmalan diaforn tn atn prw asyhsin ginomnhn, ka
tn fainomnhn prodon tn atn prw asyhsin poien t mal.
Epizexyv ML. ka pe ry stin p MLE, jea d p
EML, mblea ra p ZML: mezvn ra ZL perifreia tw LN.
Ka malw atw str diaporeetai. ra p tw kat t Z
megsthw kinsevw mxri tw kat t L mshw xrnow, mezvn stn to
p tw mshw p tn kat t N laxsthn.
H ka w p to mokntrou ka ato to zdiako: pe mn
ZL moa stn t AM, d LN t MD, ka otvw p tw kat t
A ysevw to pikklou megsthw kinsevw p tn kat t M mshn
Okti d p tw toiathw p to pikklou to strow pardou ka
tw fainomnhw tetarthmrion p to pogeou polambanoshw t
toioton sumbanei.
Dejaw p tn msvn pardvn tn moithta tn erhmnvn poy-
sevn, ey' jw ka p tn kat mrow sumpljaw tw poyseiw, ka
dejaw plin di tn grammn ti "n tow soiw xrnoiw t at paral-
"lktvw sumbanei potelesyai kay' katran atn per te tw ma-
"lw ka tw fainomnaw pardouw, ka ti tw peroxw atn (tout-
"stin t par tn nvmalan diforon)" n te sow n te nisow
kkentrow t mokntr, tn lgvn mnon tn atn pokeimnvn ka
tw soxronithtow tn pokatastsevn (toutstin tan kayw famen
n xei lgon metaj tn kntrvn to te kkntrou ka to di msvn
tn zdvn prw tn k to kntrou, toton x tn lgon ka k
to kntrou to pikklou prw tn k to kntrou to mokntrou: ka
ti n s xrn str tn kkentron kklon metptvton nta malw
ew t pmena kinomenow pokaystatai, n tosot ka pkuklow
tn mkentron ka ti str tn pkuklon, tw p to pogeou
metabsevw ato ew t prohgomena ginomnhs), jw deknusi plin
f' katraw tn poysevn ti "n str saw perifereaw peilhfw
"fanetai p te to pogeou ka to perigeou, son stai kay' ka-
"tran ysin t par tn nvmalan diforon."
Ka kymenow prton kkentron kklon tn ABGD per kntron t
E, ka dimetron tn AEG, f' w t to zdiako kntron t Z, ka
diagagn di tw kat t Z cevw tn BZD na a fainmenai prodoi
p te to pogeou ka to perigeou sai ka penanton tugxnvsin,
ka pizejaw tw EB, ED, ka fanero ntow atyen ti a par tn
nvmalan diafora sai esn, fhsn ti "t at diafr tw faino-
"mnhw perifereaw mezona mn gnesyai tn p to pogeou tw ma-
"lw kinsevw perifreian lttona d tn p to perigeou."
Dejomen on ka t toioton otvw: perigegrfyv gr YKLMNJ
di msvn tn zdvn. ka xyv di to E parllhlow t BZD KOEPJ.
ka dixyv BZD p t L, N shmea, ka ti AEG p t Y, M. ka
pe sh stn prw t B gvna t prw t D, ka nallj ra a p
BEO, DEP sai llloiw esn: ste ka OB perifreia t DP sh
stn. ka pe sh stn p YZL gvna t p AEO, d p MZN
t p MEJ, moiai ra sontai ka mn YL perifreia t AO, d
MN t PG. ste ka AB tw p to pogeou malw pardou peri-
freia, mezvn stn moa tw AO, toutstin tw YL fainomnhw,
t BO par tn nvmalan diafor: otv gr lgei t mezon. d
GD tw p to perigeou malw pardou perifreia lttvn stn
moa tw GP, moaw tugxanoshw t MN fainomn, t DP. ka
stin sh OB t DP, ste t at diafr tn periferein diosou-
sin tn erhmnon trpon a fainmenai prodoi tn maln.
Omovw d kn kat tn B ka R tugxnvn str son pxvn
fanetai p to pogeou ka to perigeou, ste pizeuxyeisn tn
ER, ZR shn gensyai tn p RZG t p BZA, sh stai ka prw
t R diafor t prw t B, di t ka tn p RZG gvnan shn tugx-
nein t p GZD, pei[ta] t p AZB: ste ka loipn tn p RZE
loip t p DZE katalepesyai shn. ka per llaw gvnaw tw
prw t E enai w tn RE prw EZ, otv tn DE prw EZ, katran d
tn prw tow R, D lttona enai ryw. ka di toto sognion gnetai
t ERZ trgvnon t EDZ, ka shn tn prw t R t prw t D, tout-
stin t prw t B.
Ka movw p tw prw t R perigeiotraw ysevw mezvnstn
fainomnh p RZG tw p REG malw t prw t R diafor.
Plin, pe tn toiathn pdeijin p tw kat' pkuklon poysevw
pepohtai w to pikklou mnontow to d strow p' ato kinoumnou,
pe ka kat to ato shmeou to mokntrou to pikklou tugx-
nontow tn stra kat diafrvn tpvn to pikklou parelhfen,
kayper p tw kteyeimnhw at ew tn toiathn dejin katagrafw,
per ox on te di tn soxronithta tn pokatastsevn, poihsmeya
plin ato tn pdeijin w kinoumnou to pikklou tw moaw t
p' ato to strow metabseiw.
Ka stin mn mkentrow ka n t at to di msvn pipd k-
klow ABGL, per kntron t D, ka dimetron kay' n pogeitatw te
ka perigeitatow str gnetai tn ADG. ka gegrfyvsan soi p-
kukloi per t A, G shmea ka kbeblsyv AG p t E, ste tan
pkuklow p to A tugxn, ka str p to E pogeou, tan
d p to G pkuklow, ka str p to H perigeou, di tn so-
xronithta w famen tn pokatastsevn. ka pextv str tn
E', H' pogevn ka perigevn tn pikklvn tw E'Z, H'Y: ka n
str tn E'Z keknhtai n tosot ka pkuklow tn AB, n d
plin str tn H'Y n tosot ka pkuklow tn GL. ka peze-
xyv te DB ka BZ ka DZ ka ti a DL
p ADZ
keitai, ste p miw plin eyeaw tw ZDYM tugxnein tn stra.
Epe on mn p ADB mal stin p to pogeou, d p ADZ
fainomnh, diafor ra stn atn p ZDB. plin pe mn p
GDL mal stin p to perigeou, d p GDY fainomnh, dia-
for ra plin stn atn p YDL.
Lgv on ti sh stn p ZDB diafor t p YDL.
Epezexyv gr BL. ka pe BZ t YL stn sh, stin d
ath ka parllhlow (katra gr atn t AG stn parllhlow di
tn soxronithta tn pokatastsevn) ka ZY ra t BL parllh-
lw stin. sh ra mn p ZDB t p DBL, d p BLD t p
LDY. ll p DBL t p DLB sh stn. ka p BDZ ra t
p LDY sh stn. ste p ZDB, diafor tw p to pogeou
fainomnhw pardou par tn maln, sh stn t p YDL diafor
tw p to perigeou fainomnhw par tn maln.
Omovw d ka n p t at mrh sin o pkukloi, pe ka p
to =hto katagraf p to ato mikuklou to pikklou xei tn
stra pokemenon, oon n nt to per t L pkuklon grcvmen
per t N polabntew saw tw fainomnaw p tw kat t pgeion
ka pergeion ysevw pardouw ka otvw t at dejei katakolou-
yontew, peranomen t prokemenon.
Gegrfyv gr ka per t N OPR pkuklow ka pizeuxyesa DN
dixyv p t O. ka peilfyv t AN moa OR, ste kat t R tug-
xnein tn stra. ka pizeuxyesa plin DR dixyv p t P ka pe-
zexyvsan a NP, NR. ka stv sh p to pogeou fainomnh
p ADZ t p to perigeou fainomn t p GDR. ka pe sh
stn p ADZ t p DZB nallj, d p GDR t p NRP tout-
stin p DPN, sh ra ka p DZB t p DPN. ka per tw
prw tow B, N gvnaw a pleura nlogn esin. a d loipa lttonew
do ryn: sh ra p ZDB diafor t p RDN. ka movw p
ADB p to pogeou mal mezvn stn tw p ADZ fainomnhw,
t p ZDE' diafor: d p NDG prw t perige mal lttvn
tw p RDG fainomnhw t p NDR diafor. deknutai d lttvn
ryw katra tn prw t D gvnin peidper n pizejvmen p
to strow p t pergeion w tn ZH'', lttvn gnetai ryw p
ZH''B, n mezoni osa mikuklou: poll ra ka prw t D. di t
at plin n tn ML pizejvmen, poll plin lttvn stai ryw
p MDL. ka jeaw oshw tw p LYM. di t shn enai tn LY
t LM poll lttvn stn ryw p LDY. ka ti kaylou n
DZ' fpthtai, ryw ginomnhw tw p KZ'D, lttvn ryw stai
prw t D gvna, tn megsthn poiosa par tn nvmalan diaforn.
Per tw to lou fainomnhw
nvmalaw.
Tw tn poysevn moithtow kat tn erhmnon trpon di tn
grammn podedeigmnhw ka sumfnou katalambanomnou tow di
tn thrsevn fainomnoiw to man te enai per tn lion nvmalan,
ka tn p tw laxsthw kinsevw p tn mshn xrnon mezona g-
nesyai to p tw mshw p tn megsthn per dion tw kat' kken-
trthta katelambneto, ka di toto dunato tugxnontow ka kay'
katran atn pidejai t megyh tn kat mrow nvmalin pe
ka p tw kat' pkuklon t toioton sumbanon pedeknuto tan
to strow p to pikklou metbasiw ew t prohgomena ggnetai,
xrtai to proxerou plin neka t kat' kkentrthta poysei
t p tw to strow mnhw kinsevw poteloumn ka ox p do
kayper kat' pkuklon p te tw to pikklou ka tw to strow
p to pikklou.
Eta re per tnow prton nagkan stin tn ew tn toiathn p-
deijin sunteinntvn dialaben ew tn tw fainomnhw nvmalaw kat-
lhcin; per to tw kkentrthtow lgou,
toutstin tna lgon xei
metaj tn kntrvn to di msvn tn zdvn ka to kkntrou prw
tn k to kntrou to kkntrou: k gr tn ew tn toioton lgon
metalmcevn tn n t kkl eyein peranetai t prokemenon: ka
ti kat poou tmmatow to di msvn tn zdvn pptei di tn
kntrvn ka to pogeou ka perigeou eyea, prw t w p okeio-
traw rxw tw kat t pgeion poxw tw par' kasta pardouw dia-
krnein.
"Ddeiktai mn on, fhsn, ka t Ipprx poyemn tn mn p
"arinw shmeraw xrnon mxri yerinw mern qd'
(20)' tn d p yerinw
"tropw mxri metopvrinw shmeraw mern nenkonta do misu",
pe ka k tn kribw at elhmmnvn thrsevn t toioton kate-
lambneto,
ti " metaj tn erhmnvn kntrvn ekostottarton mrow
"stn ggista tw k to kntrou to kkntrou ka ti t pogei-
"taton shmeon prohgetai to yerino tropiko moraw kd
(20)', ovn stn
" di msvn tn zdvn kklow tj," toutstin ti kat tw tn Di-
dmvn pmpthw ka miseaw moraw pptei.
Eti d ka atw Ptolemaow tw erhmnaw dejeiw otvw xosaw
mxri tn kay' atn xrnvn k tn p' ato gegenhmnvn thrsevn
katalambnetai. di fhsin ka stnai tn kkentron: e gr tiw n
ka ato knhsiw, metpipton n n t tosot xrn ka di tn kn-
trvn ka to pogeou ka perigeou dimetrow kay' trou tmmatow
to di msvn tn zdvn, ka okti t pogeitaton shmeon kat
tw tn Didmvn moraw e
(20)' tgxanen, per otvw xon mxriw tn
kay' atn w famen xrnvn katalambnetai.
Omvw d e ka tat t Ipprx doke sungein, pe ermenow
tw kkentrthtow lgow ka to pogeou pox tw stin ka dw
okea tw podejevw tn nvmalin, nagkaon gsato ka atw
tow pilogismow tn podejevn paraysyai, di ka mew, kaper
saf nta tn toioton tpon, o parthsmeya paratiynai. poietai
on tn pdeijin tow erhmnoiw t Ipprx tn tetarthmorvn xr-
noiw prosxrmenow, pe ka at di pleinvn distaktotrvn thr-
sevn t toioton otvw xon katelambneto,
toutstin "t tn mn
"p arinw shmeraw mxri yerinw tropw xrnon mern tugxnein
"qd
(20)', tn d p yerinw tropw mxri metopvrinw shmeraw me-
"rn qb
(20)'", trp toide: kymenow gr "tn di msvn tn z-
"dvn kklon tn ABGD per kntron t E:" ka diagagn "n at
"do diamtrouw prw ryw lllaiw di tn tropikn ka shmerinn
"shmevn tw AG, BD, ka poymenow t mn A shmeon arinn t d
"B yerinn" t d G metopvrinn t d D xeimerinn,
fhsn "ti mn
"on t kntron to kkntrou metaj tn EA ka EB eyein pptei,
"dlon," peidper "t ABG mikklion pleona" perixei "xrnon to
msouw to niausou". dexyh gr totou to mikuklou (lgv
d n liow p arinw shmeraw p metopvrinn shmeran para-
gnetai) xrnow mern tugxnvn rpz, ka di toto mezona miku-
klou to kkntrou perifreian polambnei, ka dhlad t kntron
to kkntrou p to ABG mikuklou pesetai. ka pe plin t AB
p arinw shmeraw p yerinn tropn tetarthmrion pleona peri-
xei xrnon to BG, di t dedexyai t AB mraw perixon qd
(20)' t d
BG qb
(20)', plin t kntron to kkntrou p to AB tetarthmorou
pesetai.
E gr m polambnei t ABG to zdiako mikklion mezon
mikuklou to kkntrou, polmcetai mikklion latton miku-
klou.
Estv d prteron p tw kkeimnhw jw katagrafw t kntron
to kkntrou: kat t
YKLM kkentrow. n s ra xrn liow tte YNKL mikklion
ka t LMSY malw diaporeetai. ll' n t YNKL diaporeetai,
fanetai t ABG mikklion: n d t LMSY, fanetai t GDA.
n s ra xrn t ABG, GDA mikklia to di msvn fanetai dia-
poreumenow, per ntkeitai tow fainomnoiw: dexyh gr k tn thr-
sevn n pleoni t ABG per t GDA.
Omovw d deixysetai ti od p to GDA mikuklou pesetai t
kntron to kkntrou, na latton mikuklou polambn to kkn-
trou t ABG mikklion to zdiako:
to msouw to niausou faneto kinomenow t ABG mikklion.
p to ABG ra mikuklou pesetai t kntron to kkntrou.
Kat t at d deixysetai ti ka p to AB tetarthmorou pe-
setai, toutstin ti metaj tn AE, EB eyein.
Upokesyv on, fhsn, di tata kat t Z. "ka xyv di' mfo-
"trvn tn kntrvn ka to pogeou dimetrow EZH" ste t H
ggnesyai kay' pptei t pogeitaton to kkntrou shmeon. ka
"kntr t Z ka diastmati tuxnti gegrfyv kkentrow to lou
"kklow YKLM" di t dedexyai ti n te mezvn to mokntrou,
n te sow, n te lttvn, t at fainmena parallktvw potelesy-
setai ka kay' katran tn poysevn.
"Ka di to Z xyvsan parllhloi, t mn AG NJO t d BD
"PRS. ka ti xyvsan kyetoi p mn to Y p tn NJO YTU
"p d to K p tn PRS KFX. pe tonun liow tn YKLM
"kkentron malw dierxmenow tn mn YK perifreian" perixousan
tn p tw arinw shmeraw mxri yerinw tropw xrnon dirxetai
n mraiw qd
(20)', peidper n pizejvmen tw ZY ka ZK stai peri-
exomnh p' atn gvna prw t kntr to kkntrou tugxnousa
tw malw pardou, d' p tathw fainomnh ka prw t kntr
to zdiako p AEB toutstin AB perifreia to erhmnou tetar-
thmorou. tn d KL plin kinomenow malw n mraiw qb
(20)' fa-
netai di t at tn BG to tetarthmorou to zdiako p yerinw
tropw p metopvrinn shmeran kinhyew.
All' n mn taw qd
(20)' mraiw malw kinetai moraw qg y, w
k tn kteyeimnvn maln kinsevn katalambnetai: n d taw
qb
(20)' mraiw, kinetai plin malw moraw qa ia. ste ka mn
YK stai moirn qg y, d KL qa. ia. lh d dhlonti YKL moi-
rn rpd k. n t NKO mikklion to kkntrou moirn stin rp.
ka loipa ra sunamfterai te YN ka OL tn loipn sontai
moirn d k. ka pe parllhlw stin NO t YL, n pizejvmen
tn NL, sai sontai a prw ataw ginmenai prw t perifere& gvnai:
ste ka tn NY perifreian t LO gnesyai shn, ka katran moirn
b i tn d tw NY perifereaw dipln toutstin tn YNU, d k, di t
plin tn ON tn YTU dxa te ka prw ryw tmnein. "ste ka tn
"p' atn eyean tn YTU gnesyai d lb, ovn to kkntrou di-
"metrow rk, tn d mseian atw tn YT, toutstin tn EJ.
"Plin pe t YNPK tmma lon dexyh moirn qg y, stin d ka
"t mn YN b i, t d PN tetarthmrion moirn q, ka loip ra
"PK stai
(130) ny, d dipl atw KPX moirn a nh. ste ka p'
"atn eyea KFX toiotvn stai b d, ovn to kkntrou di-
"metrow rk: d mseia atw, KF, toutstin ZJ tn atn a b.
"Edexyh d ka EJ eyea tn atn b i
(2). ka pe t p' a-
"tn sunteynta poie t p tw EZ, stin ka ath mkei b ky l
"ovn" to kkntrou dimetrow rk, d "k to kntrou ato dh-
"lonti j",
ttarton ka ekostn ra mrow stn ggista EZ
metaj tn kntrvn to te di msvn tn zdvn ka to kkntrou, tw
k to kntrou to kkntrou.
"Plin pe ovn EZ dexyh b k
"eyea a b, ka ovn ra stn EZ potenousa rk toiotvn stai
"ka ZJ my m
(2)", metagntvn mn tn lgon kayw n tow pr
totou bibloiw dhlomen: " d p' atw perifreia to grafomnou
"kklou per t EZJ ryognion toiotvn my ovn stn kklow tj.
"ka p ZEJ ra gvna" prw t perifere& osa to perigrafomnou
kklou "ovn mn esin a do rya tj toiotvn stai my, ovn d a
"d rya", w prw t E kntr to zdiako tugxnousa, kd l
ste ka BH to zdiako perifreia moirn stin kd l ovn di
msvn tn zdvn kklow tj.
Tosataw ra moraw prohgetai t kat t H pogeitaton shmeon
to B yerino tropiko. ka fjei dhlonti tn Didmvn moran e l.
Eta ka tn trvn do tetarthmorvn tow xrnouw boulmenow
sunapodeja fhsi: "loipn d pe kteron tn OS, SN to kkntrou
"tetarthmorvn moirn stin q," sti d ka katra tn OL, NY peri-
ferein moirn b i " d MS
(130) ny, ka mn LM" kataleifysetai
"moirn p
(2) na d MY ph my. ll tw mn p
(2) na" to kkntrou
"malw liow dirxetai n mraiw ph h'" w k tw ysevw tn
maln ato kinsevn gnetai dlon: "tw d ph my moraw n m-
"raiw q h' ggista": n di t pnv erhmna pizejvmen tw
ZL ZM [ZY], pe n tn LM to kkntrou malw dirxetai n to-
sot tn GD to zdiako fanetai dierxmenow, n d plin tn
MY to kkntrou, n tosot tn DA to zdiako, "ka tn GD" ra
to zdiako perifreian "tiw stn p metopvrinw shmeraw p
"xeimerinn tropn fansetai dierxmenow liow n mraiw ph h',
"tn d DA tiw stn p xeimerinw tropw p arinn shmeran n
"mraiw q h' ggista. ka erhtai mn t prokemena sumfnvw
"tow p to Ipprxou kateilhmmnoiw."
Ina d ka p tw kat' pkuklon poysevw tw atw phlik-
thtaw dejvmen poteloumnaw, kkesyv plin ABGD zdiakw per
kntron
laiw di tn tropikn ka shmerinn shmevn a AG, BD, ste t mn
A plin pokesyai arinn t d B yerinn t d G metopvrinn t d
D xeimerinn. ka kntr t E ka diastmati tuxnti gegrfyv m-
kentrow t di msvn ZHYK.
Ka pe t mn ABG mikklion fanetai liow diaporeumenow n
mraiw rpz, t d GDA n mraiw roh d', n pleoni ra xrn
liow t ABG mikklion fanetai diaporeumenow per t GDA.
Vste t kntron to pikklou mezon mn to ZHY mikuklou po-
lmcetai lsson d to YKZ. noesyv on t kntron to pikklou p
tn L, M shmevn: ka pizeuxyeisn tn EL, EM, yevresyv liow
p tw di tw cevw eyeaw w tw AEG, tan te kat t A arinn
ka t G metopvrinn, shn poin tn p ZEL gvnan to par tn
nvmalan diafrou t p YEM, peidper p tn kat dimetron
ysevn yevromenow son poie kay' tran ysin t par tn nvmalan
diforon w pnv dejamen.
Ka pe ddotai k tn maln pardvn LHM moirn rpd k,
stin d ka ZHY moirn rp, loip ra katra tn ZL, YM stai
moirn b i.
Plin pe pleoni xrn liow t AB tetarthmrion fanetai kino-
menow per t BG, mezon ra polmcetai pkuklow t LZN, lat-
ton d t NYM. pokesyv on pkuklow tan p tw yerinw tropw
liow yevrtai per t N kntron. ka pezexyv NE, ka LM
parllhlow ginomnh t AG di t shn enai tn ZL t YM. ka di
to N parllhlow xyv t BD NSU. ka pezexyv ES. ka
gegrfyv per t M, N shmea pkuklow shn xvn tn k to kntrou
t ES. ka stv per t N CV. ka dixyv EN p t pgeion, ka
pezexyv NV. ka pokesyv liow kat to V, peidper ka kat
t B yevromenow fairn tw malw pardou faneto.
Ka p mn to L p tn AG kyetow xyv LS, ka dixyv p
t O: p d to N p tn BD NP, ka dixyv p t R.
Epe ddotai LZ perifreia, ddotai ka diplasa atw LZO,
ka p' atn eyea LO ddotai ovn to mokntrou dimetrow
rk. ste ka mseia atw LS toutstin FS stai dedomnh.
Plin pe ddotai k to xrnou LZN tw malw pardou, ddotai
d ka LZ, ll ka ZH tetarthmorou, ka loip ra HN peri-
frei stin dedomnh: ste ka dipl atw NHR ka p' atn
eyea NR ddotai ovn to mokntrou dimetrow rk: ste ka
mseia atw PN toutstin EF stai dedomnh. ll mn ddo-
tai ka FS. ka t p' atn sunteynta poie t p tw ES.
Estai ka ES dedomnh sh osa t k to kntrou to pikklou,
ovn to mokntrou dimetrow rk toutstin ovn k to kntrou
to mokntrou j. ka sunaxysetai movw di tn toiotvn pilogi-
smn b ky l.
Lgv d ti ka kat' atn tn pyesin prohgetai t pgeion tw
yerinw tropw moraw kd
(20)'.
Epe gr sh stn VN t ES, son ra ka t p tw VN t
p tw ES. stin d ka t p tw NP t p tw FE son: ka loipn
ra t p tw VP son stn t p tw FS. stin d sh ka FN t
EP. lh ra VE l t NS stn sh.
Esn d ka parllhloi: ka a VN, ES ra sai esn ka parllhloi.
dixyv SE p t X,
(22)A. sh ra p CNV gvna t p NEX. moa
ra CV t NX. ste, te liow kat to C pogeou tgxanen, tte
t kntron to pikklou n kat to X, d liow yevreto kat t
(22)A.
Lgv on ti B
(22)A moirn stin kd l.
Epe gr ovn stn SE b ky l, toiotvn sungetai EF a b:
ka ovn ra SE rk toiotvn stai EF m y m
(2) ggista, d p'
atw perifreia to grafomnou kklou per t EFS ryognion toio-
tvn my, ovn kklow tj: ka p ESF ra gvna toutstin p
(22)AEB, ovn mn esin a b rya tj, toiotvn stai my: ovn d a
d rya tj
(22)AB perifreia, n pro-
hgetai t kat t
(22)A pgeion tw yerinw tropw moirn stin kd l,
ka pxei tn Didmvn moran e l, per dei dejai.
Plin pokesyv t to pikklou kntron kat t U, tan str
p tw xeimerinw tropw yevrtai.
Epe ka p miw eyeaw fainmenow tw BED diamtrou tan te
p tw yerinw tropw ka tw xeimerinw, son w famen poie kay'
katran ysin t par tn nvmalan diforon, sh ra NH to par
tn nvmalan diafrou t UK, paralllvn osn tn BD, NU. ka
pezexyv EU. ka pe n mn tn MU malw kinetai, fanetai t
YK tetarthmrion diaporeumenow, n d plin tn UL, fanetai t
KZ tetarthmrion diaporeumenow, ka ddotai ra ka loip MU,
ste ka xrnow n t MU tmma toutstin n t KY toi t GD
p metopvrinw shmeraw p xeimerinn tropn fanetai kinomenow
stai doyew.
Plin pe ddotai t KZ tetarthmrion, ddotai d ka ZL, ka
loip ra LK. ddotai d ka KU. ka lh ra U L stai dedomnh
ste ka xrnow n tathn diaporeetai stai dedomnow. ll n
tn UL malw diaporeetai, fanetai t KZ tetarthmrion, toutstin
t DA p xeimerinw tropw p arinn shmeran. ste ka tn loipn
do tetarthmorvn xrnow doysetai koloyvw taw p to kkntrou
phlikthsin.
Dedeigmnvn d tn xrnvn tn te p tn tropn p tw shmeraw
ka p tn shmerin p tw tropw to lou pardvn ka tw to
pogeou ato poxw ka ti to lgou tw kkentrthtow, jw kat
tn totou to lgou phlikthta podeknusin ka di tn riymn
sumfnouw ginomnaw tw phlikthtaw tn kat mrow nvmalin kay'
katran tn poysevn.
Ka prton tn megsthn moirn ginomnhn b kg, kat tw p to
pogeou to kkntrou ka to pikklou tw malw pardou moraw
qb kg: ka kat tw p to pogeou to kkntrou, toutstin tn
Didmvn moraw e l, moraw q ka so, atinw esi kat tw tw Par-
ynou ka tn Ixyvn moraw e l.
Per tw prw t kat mrow tmmata
tn nvmalin kanonopoiaw.
"Eneken d to ka tw kat mros" fainomnaw "nvmlouw kin-
"seis" kat tn nadidmenon xrnon "dnasyai diakrnein", deknusi
"plin f' katraw tn poysevn pw n, miw tn kkeimnvn peri-
"ferein doyeshs", toutstin ete tw malw ete tw fainomnhw
nvmlou ete tw diaforw, "lambnointo ka a loipa".
Ka prteron, p tw kat' kkentrthta poysevw, lambnvn tn
tw malw kinsevw perifreian p to pogeou moirn l, deknusin
tn diaforn moraw a ka jhkostn y, tn d fainomnhn moirn
kh na, di t n tot t mikukl mezona dedexyai tn p to
pogeou maln prodon tw fainomnhw nvmlou t diafor.
Eta p tw fainomnhw deknusi tn diaforn ka tn maln
ka ti plin p tw diaforw tn fainomnhn ka tn maln.
T d at tata ka di tw kat' pkuklon poysevw di tn riy-
mn deknusi sumfnvw t kat' kkentrthta potelomena.
Eti d plin ka p tn perigevn fistn tn lion, t at p-
lin pnta koloyvw podeknusin sumfnvw potelomena kay' kat-
ran tn poysevn.
Ka di tata tn kyesin tw kanonopoiaw tw to lou nvmalaw
boulmenow poisasyai, fhs: "poiklhw on dunamnhw sunstasyai
"kanonopoias" prw t k proxerou mw dnasyai lambnein tw te
malw ka fainomnaw nvmlouw poxw ka ti tw diaforw atn,
pe ka n te tw malw ka fainomnaw kymeya atyen xomen
ka tw diaforw, kn te tn fainomnhn ka tn diaforn, dunmeya
plin k tw okeaw prosyafairsevw xein tn maln, kn te plin
tn maln ka tn diaforn dunmeya movw k tw okeaw prosyafai-
rsevw xein tn fainomnhn,
elogvtra mllon at kyesiw tn
kannvn katefnh taw malaw pardoiw parakeimnaw xousa tw
diaforw, di t ka taw malaw pardoiw okean enai tn tn
yevn etajan, tn d maln pardvn didomnvn jw di tn gram-
mikn dejevn tw diaforw katalambnesyai ka loipw tw fainomnaw.
Oyen kolouysaw t di tw kkentrthtow p tn riymn de-
jei, kayper p tw triakontamoiraw ka p tn loipn kat mrow
postsevn pelogsato tw kst tn maln pardvn piballo-
saw diaforw:
prw mn tow pogeiotroiw tetarthmoroiw, di moirn
(2), di t tw p totvn mikromerestraw diaforen par t grammi-
k tn kay' maln parajhsin lambanomnvn, di t lxiston tw
diaforw
w gnesyai tow totou to tetarthmorou stxouw ie:
prw d tow perigeiotroiw tetarthmoroiw di moirn g,
w gnesyai
ka tow totou tetarthmorou stxouw l. ggonen d p totvn
parajhsiw kat trimoiran, di t tw prw tow perigeiotroiw tetar-
thmoroiw kat mrow diaforw mezonaw gnesyai tn prw tow po-
geiotroiw p tn svn [ka] maln pardvn, kayper ka kyesiw
to kannow fanern poie: t gr prt jamoir& tw malw kinsevw
p to pogeou tugxanos parkeitai diaforw
(130) id, ka perxei
atw deutra tow atow jhkostow id: taw d rod ka rpw moraiw,
atinw esin tw p to perigeou prthw jamoiraw, parkeintai
(130) i
(2) ka perxei plin atw deutra tow atow jhkostow i
(2):
di fhsin ka atw: "peidper mezonw esin a prw tow perigeoiw
"diafora tw peroxw, tn par tn nvmalan piballntvn tow
"soiw tmmasi diaforn tn prw tow pogeoiw ginomnvn" toutstin
peidper mezosi diafrousi prw tow perigeoiw a peroxa tn par
tn nvmalan diaforn, tn prw tow pogeoiw p tn svn tw ma-
lw pardou tmhmtvn, dhlad tn son pexntvn tn pogevn ka
perigevn, w deixysetai mn ka di tn grammn jw t toioton.
Ka p tn llvn d strvn tn toiathn parajhsin tn tetar-
thmorvn pepohtai.
di ka me stxvn tw kyseiw tn kannvn pa-
ryhken.
Eti d t prokemenon to lou kannion pepohken selidvn g
ka paryhken n mn tow prtoiw do tow tw malw kinsevw riy-
mow, tn erhmnon trpon parhujhmnouw: n d t trt t kst
okevw pibllonta tmmata tw prosyafairsevw to par tn nv-
malan diafrou. ka stin to kannow kyesiw toiath.
Epe on kyesiw to toiotou kannow kat saw peroxw kteyei-
mnaw xei kat t prta do seldia tw tn pogeiotrvn ka peri-
geiotrvn tetarthmorvn malw pardouw, tw mn tn pogeiotrvn
w famen kay' jamoiran, tw d tn perigeiotrvn kat trimoiran:
a d kat t trton seldion parakemenai tw nvmalaw diafora
ox saiw diafrousin ll' n tow pogeiotroiw tmmasin n lttosin
tn parajhsin lambnousin, a d n tow perigeiotroiw n mezosi tn
mevsin: ka ti plin w famen p tn svn tw malw pardou
periferein, a kat t pergeia tn kat t pgeia mezonaw diaforw
poiontai par tn nvmalan: peirasmeya di tn grammn kaston
tn toiotvn podejai kay' katran tn poysevn.
Ka prton p tw kat' kkentron, ti n tow pogeiotroiw tmmasin
a perigeiterai tn pogeiotrvn n lttosin diaforaw parhjhntai,
n d tow perigeiotroiw n mezosi tn mevsin lambnousin.
Estv gr kkentrow kklow ABGD, per dimetron tn AD, f' w
pokesyv t mn to kkntrou kntron t E t d to zdiako t Z,
ka polhmfyeisn p to A pogeou do svn periferein tw malw
pardou tn AB, BG, pezexyvsan a BE, GE, ka ti a ZB, ZG.
Lgv prton ti mezvn stn p EGZ gvna tw p EBZ.
Dixyv gr BZ p t K ka pezexyvsan a EK, GK. pe mezvn
stn GZ tw ZK di t prw t pogeiotr tmmati pokesyai t G,
mezvn stn ka p ZKG gvna tw p ZGK. stin d ka lh p
EGK t p EKG sh, di t shn enai tn EG t EK: ka loip ra
p EGZ loipw tw p EKZ mezvn stn, sh d p EKZ t p
EBZ: mezvn ra ka p EGZ tw p EBZ, per dei dejai.
Ka pe tw mn p AEB gvnaw tw malw pardou diafor stin
par tn p BZA fainomnhn <> p ZBE, lhw d tw p AEG
malw pardou diafor stin par tn p GZA fainomnhn p
ZGE, dlon ti mn tw AB perifereaw tw malw pardou diafor
stin prw t B gvna, d tw AG perifereaw p EGZ gvna:
ka perox ra tw AG perifereaw prw tn AB toutstin BG dia-
for par tn nvmalan pepohtai ka tn peroxn perxei p
EGZ gvna tw prw t B.
Lgv on ti p EGZ gvna lttvn stn dipl tw prw
t B, na lttosin sin parhujhmnai kat tn to kannow tw nv-
malaw kyesin p tn pogeiotrvn tmhmtvn a perigeiterai.
Epe gr p GEA dipl stin tw p BEA, ka a p GZE, EGZ
ra diplasonw esin tn p BZE, EBZ. ka pe n tow mprosyen
pedeknumen tn p GZB mezona tw p BZA, ra p GZA mezvn
stn dipl tw p BZA, ka loip ra p ZGE lttvn stn
dipl tw p ZBE, per dei dejai: ra tw perigeiotraw malw
pardou diafor lttoni parhjhtai tw pogeiotraw.
Lgv ti kn prw t perige saw perifereaw polbvmen tw
malw pardou, tw perigeiotraw diafor n mezosin tn mevsin
poietai tw pogeiotraw.
Apeilfyvsan gr ka p to D perigeou to kkntrou sai peri-
freiai tw malw pardou a DH, HY, ka pezexyvsan a EY, EH,
ZY, ZH. movw plin deixysetai ti ka prw t Y gvna mezvn
stn tw prw t H, diaxyeshw tw ZY p tn ntikeimnhn perifreian,
ka pizeuxyeisn p tn H ka E eyein p t gegonw prw t peri-
fere& shmeon. ka pe n tow mprosyen pedejamen tn p DZH
perigeiotran fainomnhn prodon mezona tw p HZY pogeiotraw,
ra p YZD tw p HZD lttvn stn dipl, toutstin a p
ZEY, EYZ tn p ZEH, EHZ lttonw esin dipla. dipl d p
YED tw p HED. loip ra p EYZ tw p EHZ lttvn stn
<> dipl. ste prw t H gvna mezvn stn miseaw tw prw
t Y. ka pe lhw mn tw YD perifereaw diafor stin prw t Y
gvna, tw d HD perifereaw diafor stin prw t H gvna, ka
perox ra tw YD perifereaw prw tn HD toutstin YH tn
peroxn tw Y gvnaw prw tn H pepohtai. ka stin perox atn
tw prw t H gvnaw lttvn. ste mn YH pogeiotra perifreia
lttona tw prw t H gvnaw diaforn par tn nvmalan pepohtai,
d HD perigeiotra mezona.
Mezosin ra diaforaw mevsan a prw tow perigeiotroiw tm-
masi perigeiterai mala prodoi tn pogeiotrvn, koloyvw t
to kannow kysei.
Eti d deikton, per polepetai tn proteyntvn, ti p tn
svn p to pogeou ka to perigeou maln pardvn a prw t
perige diafora mezonw esi tn prw t poge.
Ekkesyv gr plin ABGD kkentrow kklow per kntron t E
ka dimetron tn AED, f' w elfyv t to zdiako kntron t Z.
ka peilfyvsan do sai perifreiai tw malw pardou p te to
A pogeou ka to D perigeou a AB, GD, ka pezexyvsan movw
a EB, EG, BZ, ZG ka dixyv ZB p t H, ka pezexyv GH. lgv
ti mezvn stn p ZGE gvna tw p ZBE.
Epe gr mezvn stn p GZD gvna tw p BEA, pe ka tw
p GED, mezvn d p BEA tw p BZE toutstin tw p DZH,
poll ra p GZD mezvn stn tw p DZH. ste p GZA
lepousa ew tw do ryw lttvn stn tw p HZA. ZG ra e-
yea ggin stin tw di to kntrou tw ZEA per ZH. mezvn ra
GZ tw ZH. ste ka p GHZ mezvn stn tw p ZGH. ra p
GZB lttvn stn dipl tw p GHB. dipl d p BEG tw p
GHB: p gr tw atw perifereaw bebkasin: mezvn ra p
BEG tw p BZG. ka sai a kat korufn tn BEY, YGZ trignvn.
loip ra p EGZ loipw tw p EBZ mezvn stn. a ra peri-
geiterai mala prodoi tn svn ka pogeiotrvn mezonaw pote-
losin tw par tn nvmalan diaforw.
Di ka tw mn pogeiotraw w famen kat' jamoiran paryhke
tw d perigeiotraw kat trimoiran.
Eti d jw ka p tw kat' pkuklon poysevw dejomen t erh-
mna sumfnvw t kat' kkentrthta poysei potelomena.
Estv gr mkentrow ka n t at pipd to di msvn tn z-
dvn kklow ABGD per kntron t E, ka dimetron tn DEA. ka pei-
lfyvsan p to A do sai perifreiai AB, BG, ka gegrfyvsan per
t A, B, G soi pkukloi, ste tan mn kat to A tugxn pkuklow
tn stra enai p to Z pogeou, tan d kat t B, p to H, kinh-
ynta tn ZH moan osan t AB, tan d kat to G, p to Y, kinh-
ynta tn ZY moan plin t AG.
Oti mn on p tw toiathw ysevw a perigeiterai diafora n
lttosin peroxaw parhjhntai, dlon, pe ka tn p GEY gvnan
pedeknumen n tow prsyen nya ka xvrw tn to pikklou kata-
grafn jeymeya lttona osan dipln tw p BEH.
Lgv d ti ka n p to D, nya to pikklou tugxnontow
kat t N pergeiow str gnetai di tn soxronithta tn pokata-
stsevn, saw perifereaw polbvmen, a perigeiterai diafora n
mezosin peroxaw tn mevsin lambnousin.
Apeilfyvsan gr sai a DK, KL ka gegrfyvsan plin o per
t D, K, L pkukloi. ka pextvsan o strew moaw perifereaw
p tn pogevn tn pikklvn taw p to mokntrou tn pikklvn,
ka stvsan kat tn J, M.
Ka pe dipl stin LD tw KD, dipl stin ka N' J tw MO:
kesyv t MO sh JP. ka pizeuxyesa EP, dixyv p t R, ka
pezexyvsan a RJ, RN'. ka pe mezvn stn RN' tw RJ, kesyv
t RJ sh RS. ka pezexyv ES. ka pe sh stn RJ t RS,
koin d RE, ka gvna prw t R gvn& t prw t R sh, pe ka
perifreia perifere&: bsiw ra EJ bsei t ES stn sh, ka t
trgvnon son, ka a loipa gvnai taw loipaw. ste ka p SER
gvna t p REJ: ra p N'EJ gvna lssvn stn diplw tw
p REN' toutstin tw p KEM. ka movw tow p to kkntrou
erhmnoiw, pe lhw tw DA tw malw pardou perifereaw diafor
stin par tn nvmalan p N'EJ, tw d DK, p KEM: ka
tw ra peroxw atn perox. ste tw KL perifereaw tw
malw pardou diafor stin p JER. ka stin [] lttvn tw
p MEK. ste ka mn KL pogeiotra perifreia lttona dia-
forn tw nvmalaw pepohtai, d KD perigeiotra mezona. me-
zosin ra diaforaw ka p tathw tw poysevw n tow perigeio-
troiw tmmasin a perigeiterai mala prodoi tn mevsin lambnou-
sin tn pogeiotrvn koloyvw t to kannow kysei.
Epe on a p to pogeou mxri tw mshw pardou kat mrow
par tn nvmalan diafora p t latton sunistmenai katalamb-
nontai, p d tw mshw pardou mxriw to N perigeou p tn mezon,
ektvw ka kat mn atn tn mshn prodon tn stsin poiontai,
per d atn nepasyhtoi tugxnousin.
Eti d deixysetai per polepetai tn prokeimnvn ka p tathw
tw poysevw, toutstin ti p tn svn maln pardvn p to
pogeou ka perigeou a prw t perige diafora mezonw esin
tn prw t poge.
Ekkesyv gr plin ABGD mkentrow per kntron t E ka di-
metron tn AED, ste tan mn pkuklow kat to A tugxn ka tn
stra enai p to pogeou: tan d kat to D, p to perigeou.
ka peilfyvsan do sai perifreiai tw malw pardou a AB, GD
ka gegrfyvsan o pkukloi per t B, G shmea. ka pokesyv
str kat tn H ka Y, ste tw ZH ka YK saw lllaiw enai
ka moaw taw AB, GD, di tn soxronithta tn pokatastsevn.
ka pezexyvsan a HE, YE.
Lgv ti p YEG perigeiotra diafor mezvn st tw p HEZ
pogeiotraw.
Hxyv gr di to H t BE parllhlow HL, ka pezexyv LM.
sh ra stn ZH perifreia t LM: per dlon gnetai pizeuxye-
shw tw ZL. ll ZH perifreia t YK sh stn. ka LM ra peri-
freia sh st t YK: ste ka a p' atw eyeai LM, YK sai
esn. ka pe sh stn ZH perifreia t YK perifere&, sh stn
ka p ZML gvna t p Z'KY. ka loip ra p LME loip
t p YKE sh stn. pe on mn YK eyea t LM sh stn,
stin d ka KE t ME sh, ka gvna gvn& ka bsiw bsei, ka t
trgvnon t trign: ste ka p KEY gvna sh stn t p
MEL. mezvn ra p YEK perigeiotra diafor tw p ZEH po-
geiotraw.
Per tw kat tn mshn to lou
prodon poxw.
Ep d pshw didaskalaw ka maysevw rxw tinaw xr pro#fist-
nai f' n t met tw rxw klouya de pragmateesyai. dlon w
ti ka tw kysevw tn kinsevn nagkaon n eh rxw tinaw po-
kesyai.
a d tw kinsevw rxa esin xrnow te ka tpow. xr ra
laben tn te xrnon ka tn tpon f' o tow kannaw tn kinsevn
Ptolemaow sunestsato.
Esti d mn xrnow p to a' touw Nabonassrou to tn Per-
sn basilvw yy a' raw
(2)' plhrvyeshw w prw tn metran kat'
Agupton Alejndreian, di t p totou xein atn ka tw nagra-
fw tn palain thrsevn diaszomnaw.
Loipn on eh n eren n tot t xrn ka kat poou tmmatow
to di msvn tn zdvn kklou to lou mal prodow tgxanen:
o mnon d p to lou ll ka p tw selnhw ka tn e planvmnvn
t toioton metaxeirzetai, p te tn auto distaktotrvn thr-
sevn katalambanmenow kat poou tmmatow to zdiako pizhto-
menow str tugxnei ka sungvn tn p Nabonassrou xrnon mxri
tw auto thrsevw ka k tn kteyeimnvn tw malw kinsevw ka-
nnvn lambnvn t t tosot xrn pibllonta mal kinmata
met kklouw ka nakmptvn p tw kateilhmmnhw to zdiako
kat tn trhsin poxw, katalambnetai t tmma pexen ew t
a' tow Nabonassrou yy a' tw meshmbraw pizhtomenow str.
Poiomenow on ntaya tn toiathn katlhmcin ktyetai a ye-
rhma di' o podeknusin ti "tan tn metopvrinn shmeran liow
"poitai, prohgetai pntvw to perigeou to kkntrou malw ki-
"nomenow moraw jg k, pxei d to pogeou ew t pmena" tw
loipw ew t mikklion moraw riw m. eta jw labn k thrsevw
metopvrinn shmeran gegenhmnhn t iz' tei Adriano yr z met
do raw shmerinw tw meshmbraw, fhsn: pexen ra liow kat
toton tn xrnon to pogeou malw moraw riw m.
ka sunagagn
tn xrnon tn p to prtou touw Nabonassrou mxri tw prokei-
mnhw thrsevw tn tugxnonta voy ka mern jw ka rn sh-
merinn b, ka labn tn maln knhsin met kklouw to tsou xr-
nouw moirn sunagomnhn sia ke ka feln atn p tn riw m
moirn nw kklou moraw tj prosyew, tw loipw met tn faresin
moraw sje ie koloyvw fhsen pxein tn lion malw to po-
geou toutstin tn kat tow Didmouw moirn e l kat t a' tow
Nabonassrou yy a' tw meshmbraw: ka di toto pxein tn Ixy-
vn malw tw prthw moraw jhkost me.
Per tw liakw chfoforaw.
Diejelyn per te tn to lou maln pardvn ka tn par tn
fainomnhn nvmalan diaforn ka to kat tn sstasin tw prag-
mateaw xrnou ka tw kat' atn p to pogeou mshw poxw f'
w a met tn sstasin prodoi tn rxn elfasi ka pw di tn
grammn tw malw pardou doyeshw te par tn nvmalan diafor
ddotai ka kribw ato prodow ka t npalin, jw didskei pw
n ka di tw kanonikw kysevw fodevmen tn kat tn par' kasta
xrnon to lou maln ka met tw nvmalaw krib ka fainomnhn
prodon.
Prokesyv d mn kaylou tn te to lou ka tw selnhw ka ti
tn e planvmnvn chfoforan poisasyai p to ly' touw Dioklh-
tiano kat' lejandraw toi kay' llhnaw tub i pr d rn kairi-
kn tw n Alejandre& meshmbraw: kat
prw tn toioton mn xrnon o kannew sunestyhsan farmouy e' met
ka' ran tw n t d' meshmbraw, di t tn pokatstasin to kay'
llhnaw prw aguptouw niausou xrnou gegensyai t e' tei tw
Agostou basileaw, ka sungesyai th j kenou to xrnou mxri
to prokeimnou ly, tmz, peidper t mn p Agostou p
Dioklhtiano th stn tig, p d to e' Agostou th sungein met
tn p Dioklhtiano tn ly t erhmna th tmz, tetraethrdaw
d p
(2) saiw mraiw proelhfen kat' aguptouw xrnow tn kay' l-
lhnaw ka kat lejandraw di tn to tetrtou tw mraw pou-
san. di prosyntew t kat lejandraw kteyeimn xrn tub i'
r& g' atinw esin p tw n t yy a' meshmbraw mrai rkh
rai ka, tw p
(2) mraw, sxomen tn kat' aguptouw xrnon p tw
n t yy a' meshmbraw mern sid ka rn ka.
Sungetai d p Nabonassrou otow tn
(22)ajy ka tn erhmnvn
mern sid ka rn ka kairikn, prw n xrnon lambnomen pr-
ton tn maln ka krib to lou poxn tnde tn trpon: esgon-
tew gr prteron ew t tn ktvkaidekaethrdvn kannion t
(22)ajy th,
ka labntew t totvn lttona ggista parakemena kat t a' sel-
dion th vi pografmeya w prton keflaion: peita t loip ew
t
(22)ajy th esagagntew plin kat t at a' seldion tn ktvkai-
dekaethrdvn, ka labntew movw t ggista lttona atn para-
kemena snb pegracmeya w b' keflaion: ti d ka t polei-
fynta th pl z trton keflaion: jw d plin ka tw si mraw
mhnn z w d' keflaion pareykamen: ka tw loipw d w e': ka
ti tn ka' ran w
(2)'.
Ka pogracmenoi jw tn otvw kteyeimnvn kefalavn tow
parakeimnouw okevw tn maln kinsevn riymow w poggraptai,
na m makrologmen, ka sunagagntew ka poisantew moraw, ka
ti d ka tw moraw, ka kbllontew kklon kklouw, tn polipn-
ta tn moirn ka tn jhkostn riymn katalambanmenon tia nd
pegracmeya: prosyntew w pexen liow p to pogeou n t
tw rxw Nabonassrou xrn moraw sje ie, tw sunaxyesaw met
kklon moraw siz y sxomen w pexen liow p to pogeou ma-
lw kinomenow ew t pmena: w kbllontew p to erhmnou po-
geou tn kat tow Didmouw moirn e l kst zd didntew
moraw l, eromen tn maln to lou prodon kat tn prokemenon
xrnon pxousan to Agkerv moraw ib ly.
Ina d ka tn krib toi fainomnhn ato poxn pilogismeya,
eshggomen tn atn
tw malw pardou riymn toutstin tn
siz y ew t tw nvmalaw kannion kat t prta seldia perixei
tow tn maln pardvn riymow, pe ka totoiw a par tn nv-
malan diafora parkeintai. ka tn parakeimnhn at j nalgou
n t g' selid moran a ky ggista prosyntew at di t mezona
atn tugxnonta tn to mikuklou moirn rp pptein ew t met
t pergeion mikklion nya p to perigeou fainomnh prodow
mezvn stn tw malw, tw sunaxyesaw moraw sih lh kbllontew
plin p tn kat tow Didmouw moirn e l, sxomen ka tn krib
toi fainomnhn to lou prodon xousan to Agkerv moraw id h.
Per tw sumfvnaw tn kat tn
sntajin ka tn prxeiron chfoforin.
Ina d ka tn di tw kysevw tn proxervn kannvn to lou
chfoforan smfvnon t di tw Suntjevw kateilhmmn dejvmen
poteloumnhn, kyhsmeya prton t pibllonta kat tn tn pro-
xervn kannvn kyesin t prokeimn xrn keflaia.
Estin d tde: ekosipentaethrdaw xk
(2): th pl k: mn far-
mouy: mrai e: rai p meshmbraw k ka a.
Ka pleonzei otow xrnow to kat tn Sntajin kteyeimnou
niaut ka mhn ka mr&. n gr prosymen totoiw t p Nabo-
nassrou vw Filppou rxw to met Aljandron tn Ktsthn, f'
o xrnou ka prxeirow kann tn sstasin elhfen, th ukd, sun-
axysetai p Nabonassrou mxri to prokeimnou ly' touw Dioklh-
tiano th
(22)ao ka mrai sme ka rai ka peidper ka atn
tn Farmouy pografmeya ka tw e mraw, nt tn kat tn
p tw Suntjevw to lou chfoforan kteyeimnvn tn
(22)ajy ka
mern sid ka rn ka. w pleonzein w famen tn kat tn
prxeiron kteyeimnon xrnon to kat tn Sntajin niaut ka mhn
ka mr&, per klouyn stin, peidper ka
kat tn prxeiron t
t a' tei tn ekosipentaethrdvn parakemena rjb i tn pr tw
sustsew sti to proxerou p Nabonassrou vw rxw Filppou
tn ukd, w n tow ew tn lgon to proxerou pomnmasin pe-
dejamen. ka di toto t tow k
(2) tesin parakemena tn ekosi pnte
tn enai kinmata,
p d tw Suntjevw okti, ll t tow ih
tesin parakemena atn tn ih st kinmata ka t tn l
(2) tn
l
(2): w pleonzein tn to proxerou kyesin niaut n. ka p tn
mhnn d plin n tow proxeroiw t mn Yy,
(130)
(130) parkeitai, t
d Favf t to Yy knhma. ti d ka p tn mern p mn tn
proxervn t a' mra
(130)
(130) parkeitai, t d b' t tw a': p d tw
Suntjevw t to a' mhnw knhma t prt mhn parkeitai, ka t
to b' t b', ka jw koloyvw: movw d ka p tn mern, w
plin klouyon enai tn kyesin tn to xrnou p to proxerou
kannow pleonzein mhn ka mr&.
Ekymenoi on tn erhmnon p to proxerou xrnon perixonta
ekosipentaethrdvn mn th xk
(2) pl d th k ka mna Farmouy
ka mran e' ka ran p meshmbraw ka', ka parayntew atow
okevw t mal kinmata kat tn to Proxerou kyesin, ka sunaga-
gntew movw t jhkost ka tw moraw w poggraptai, tn sun-
axynta riymn tn siz y moirn met kklon kbllontew p tn
kat tow Didmouw moirn e l, jomen koloyvw tow p tw Sun-
tjevw pilogismow pxonta tn lion msvw to Agkerv moran
ib ly.
Ina d plin ka tn krib ka fainomnhn ato poxn lbvmen,
eshggomen tn atn tn siz y moirn riymn ew t tw nvmalaw
ato kannion kat tn prtvn do selidvn, ka tn parakeimnhn
at kat t g' seldion moran a ka jhkost ky prosyntew at
di t mezona atn enai moirn rp, ka tw genomnaw moraw sih lh
kbalntew plin p tn kat tow Didmouw moirn e l, sxomen
tn kat tn prokemenon poxn to lou kat to Agkerv moran
id h sumfnvw t p tw Suntjevw chfofor&.
Ey' jw kat tn toiathn to lou poxn meteilfamen tn ka
ran kairikn ew shmerinw tnde tn trpon: labntew gr prteron
p to di' Alejandreaw trtou klmatow tow sunanaferomnouw t p
tn prokeimnvn to Agkerv moirn id h mxri to Karknou tn
atn moirn to mikuklou xrnouw sunagomnouw rna ia, ka to-
touw mersantew par tw kairikw raw ib tw mraw jomen tow
pibllontaw tw ken t mr& riaouw kairikow merinow xrnouw
ib l
(2), tow d loipow ew tow l xrnouw tn do shmerinn rn xr-
nouw iz kd nukterinow. ka pollaplasisantew tw mn merinw raw
y, a esin j mn met meshmbran, trew d p natolw, p tow
merinow raouw xrnouw ib l
(2) tw d nukterinw raw ib p tow
nukterinow riaouw xrnouw iz kd, ka tw p mesonuktou raw
(2) p to iz kd tw d p natolw raw p tow ib l
(2) ka tow
sunagomnoiw prostiyntew tow p meshmbraw p mesonktion xr-
nouw rp, ka tow sunagomnouw plin k te tn merinn ka nukte-
rinn rn xrnouw tkb ib mersantew par tow tw shmerinw
mraw riaouw xrnouw ie, sxomen plyow rn shmerinn ka
(20)'
ggista, aw ka xrhsmeya prw tn to lou kribestran chfoforan.
En d tra to di' Alejandreaw meshmbrino okhsiw f'
tn kairikn xrnon paralambnomen, tw kat mkow atn peroxw
t ginmenon mrow raw shmerinw, tan mn natolikvtra tw
Alejandreaw nadoyesa okhsiw felomen tn kese kateilhmm-
nvn shmerinn rn, tan d dusmikvtra prosysomen. ka k to
otv plin katalambanomnou prw tn n Alejandre& meshmbrinn
xrnou poihsmeya tn to lou chfoforan.
Per tw nisthtow tn nuxyhmrvn.
Apodejaw t per tw kinseiw to lou yevromena, jw bole-
tai dialaben ti tata t kairik ka fainmena mn nuxymera ok
stin sa llloiw toi mal, ll diallttousi kat t msa.
Kathnxyh d' p tn toiathn pskecin di t t kteyeimna at
mal kinmata kat' saw peroxw tn parajhsin elhfnai dhlad
w tn nuxyhmrvn soxronvn ntvn. to toiotou m otvw xontow
katalambanomnou, boletai on tw katalmceiw poisasyai tn gino-
mnvn diaforn par t mezona ka lttona at katalambnesyai
tn nooumnvn maln, na tw piballosaw atow prosyafairseiw
poiomenow ew mal at metgvn, koloyvw t tn maln pardvn
kysei t totoiw pibllonta mal kinmata lambnvn, prw tata
ka tw kribew ka fainomnaw poxw metaxeirzetai.
Mllvn on t toioton jetzein, fhs: "t mn on per tn lion
"mnon yevromena sxedn tata" n eh. t gr prolhfynta, lgv
d per te to megyouw to niausou ato xrnou, f' o ka tw ma-
lw ato kinseiw kanonikw jyeto, ka per tw nvmlouw ka faino-
mnaw pardouw, ka ti per tw diaforw atn k tn kay' atn ka
prw atn yevroumnvn pdeijen.
Estin d ka lla per tn lion yevromena <> k tw ato
prw teron sxsevw podeknutai, oon w snodoi ka panslhnoi ka
kleceiw k tn prw tn selnhn sxsevn: ka
tow fejw per tn lion
dthw ka Ermo <> k tw
deiknmena, w n tow per atn fanern stai.
T d sxedn erhtai di t ka tw paralljeiw ato k tn per
atn poteloumnvn nepaisytouw poien tw diaforw par tw
erhmnaw ato kribew ka fainomnaw pardouw.
Eta w suntelon at prw tn pokeimnhn tw nisthtow tn
nuxyhmrvn pragmatean, didskei prteron t stin ksmou peristrof
ka t kairikn ka plw yevromenon nuxymeron ka t maln.
Ka fhsi ksmou mn peristrofn enai tn man periforn to sh-
merino, toutstin tan ti shmeon ato p tinow rzontow meshm-
brino w p katadhlotrvn tpvn rxmenon fresyai p t at
to rzontow to meshmbrino shmeon pokaysthtai.
Nuxymeron d plw toutstin kaylou kairikn, tan liow p
to rzontow natllvn p to meshmbrino mesourann p tn
atn natoln mesournhsin plin paragnhtai, per perixei xr-
nouw miw to shmerino peristrofw ka ti tw sunanerxomnhw ato
summesouranoshw t nvml to lou kinsei, tiw ka at
pilambanomnh to shmerino perifreia nisow kay' ksthn gnetai
w k tn jw didaxyhsomnvn pilogismn stai dlon.
Epe on mn to ksmou peristrof plhmcin ok xei to sh-
merino t d tuxn kairikn nuxymeron plhmcin nmalon xei, fh-
sn:
"maln mn on nuxymeron gnetai di tata t perixon prodon
"tn tw miw peristrofw to shmerino xrnvn tj ka ti nw xr-
"nou jhkostn ny ggista, sa n t tosot msvw liow piki-
"netai."
H ka otvw: pe t nuxymeron mezn stin tw to ksmou peri-
strofw di tn ew t pmena to lou metbasin, ka o xrnoi tw
forw per tn mgiston tn paralllvn tn tow ploiw tw sfaraw
grafomnvn yevrontai, oone tn shmerinn w n tow mprosyen dh-
lomen, nagkan stin, e mllei soxrnia enai t nuxymera, met
tn man peristrofn to shmerino ka shn ato perifreian kay'
ksthn mran nafresyai tn meshmbrinn: ste tn tj xrnvn
to shmerino pimerizomnvn ew tje id mh mraw to niausou
xrnou, stai met tn man peristrofn pilambanomnhn <
(130)> ny
ggista, sh tw sti ka to lou mal knhsiw to di msvn tn
zdvn toi to kkntrou kklou movw ew t erhmnon niasion tn
mern plyow pimerisyntow.
Di ka fhsin: "ka ti nw xrnou jhkostn ny ggista, sa n
"t tosot msvw liow pikinetai."
"Anmalon d t perixon prodon tn tw miw peristrofw to
"shmerino xrnvn tj ka ti tn toi sunanaferomnvn summesou-
"ranontvn t nvml to lou pikinmati."
toto d t met
tn man peristrofn to shmerino sunanafermenon summesoura-
non ato tmma t prw tn zdiakn yevroumn nvml to lou
kinsei nison ngkh ggnesyai kat do trpouw: prton mn mezoni
p d lssoni to zdiako perifere& tn prosyafaresin tw nv-
malaw sunanafresyai summesouranen, ka nison ngkh w famen
gnesyai, peidper ka fainomnh to lou nmalow knhsiw o
toiathn xousa tjin katalambnetai w saw kay' ksthn mran
to shmerino sunanafresyai at summesouranen: deteron d
ti e ka sai san a pilambanmenai to zdiako perifreiai ote
n tow soiw xrnoiw sunejrxonto tn meshmbrinn ote mn naf-
ronto tn rzonta, w k tw tn naforikn xrnvn kanonografaw
gnetai dlon, to toiotou sumbanontow k tw to di msvn prw
tn shmerinn gklsevw.
Dlon d ti ka sumpeplegmnai esn a erhmnai diafora di t
met nvmlouw fanesyai, ti ka diafroiw xrnoiw w famen sum-
mesouranen, aw ka mlista prosxrtai podokimzvn tw sunanafo-
rw.
Ka nepasyhtow mn gnetai j katrou ka sunamfotrvn tn
toiotvn do trpvn sunagomnh diafor tn fainomnvn nuxyhmrvn
par t mal w to nw nuxyhmrou, kayper p tn to g' seli-
dou tw ryw sfaraw naforn to Proxerou Kannow stn den,
nya ka k tw sumplokw tn do nvmalin ginomnh diafor par-
keitai, w n t ew tn lgon to proxerou pomnmati pedeknumen.
o mezona gr ersomen tn parajhsin jhkostn deutrvn la g-
gista gnesyai miw raw shmerinw ggista, di t t ttarton
atn toutstin t z
(20)' d' don enai paralambnesyai w xrnouw
jhkost tan prta: tan d detera w prta detera: ste t
z
(20)' d' jhkost detera paralambanmena w prta ggnetai tn tw
a raw shmerinw jhkostn prtvn Q, ri
(2)' ggista, w famen,
per t n nuxyhmr pibllei pe ka t mi mor& tw p to z-
diako to lou pardou: " d k pleinvn nuxyhmrvn pisunago-
"mnh asyht".
Eta zhtn tn k tw sumplokw ginomnhn megsthn diaforn p
tn pleinvn nuxyhmrvn, r prteron lkh tw stin par mnhn
tn to lou nvmalan ginomnh ka kat povn tmhmtvn to zdia-
ko poteletai. ti d movw per tn atn re ka p tn sunana-
forn ka summesouransevn. di fhsin:
"par mn on tn liakn
"nvmalan t pleston gnetai diforon p tn p miw tn msvn
"to lou kinsevn p tn tran diastsevn".
msaw pardouw
kale w p to zdiako tw metaj tn pogevn ka perigevn te-
tarthmoriaaw diastseiw toutstin tw te kat tn Parynon ka tow
Ixyaw moraw e l, di t per tata t shmea tn lion fanesyai
malw poiomenon tn knhsin, tw diaforw w famen nepaisytou
ginomnhw.
Fhsn on kaston tn mikuklvn tn p tn toiotvn msvn
pardvn poiesyai par tn to lou nvmalan tn megsthn diaforn
tn fainomnvn nuxyhmrvn par t mal xrnvn d
(20)' d', prw llhla
d t at mikklia poiesyai tn tn fainomnvn nuxyhmrvn dia-
forn tow diplasoiw xrnoiw, y
(20)' ggista.
Eta ka tn atan pgvn fhsn plin "di t ka tn to lou
"fainomnhn prodon par tn maln, kat mn t prw t poge
"mikklion d
(20)' d' moraw llepein, kat d t prw t perige
"pleonzein taw ataw."
Ina d ka tn totvn pdeijin di tn grammn poihsmeya, k-
kesyv ABGD kkentrow to lou kklow, per kntron t E ka di-
metron tn EG, f' w elfyv t to zdiako kntron t Z. ka
xyv p' ato t AZG prw ryw BZD. ka perigegrfyv HYKL
zdiakw. ka dixyv YBZDL, ste t mn H kat t pgeion tug-
xnein toutstin kat tw tn Didmvn moraw, e l, t d Y p tw
kat tn Parynon moraw e l mshw pardou, t d K p tw kat t
pergeion to Tojtou moraw e l, ka ti t D kat tw traw mshw
pardou tn Ixyvn moirn tn atn. ka pezexyvsan a BE, ED.
Dlon d ti tn mn AB to kkntrou tmma moirn stin qb kg,
di t ka tn prw t Z gvnan ryn tugxnousan moirn enai q, tn
d prw t B dedexyai moirn b kg. tataiw d shn osan tn p
AEB sungesyai tn p t at moirn qb kg'. ka lon ra t BAD
pogeiteron to kkntrou tmma sunaxysetai moirn rpd m
(2).
All' n toto liow malw kinetai, fanetai t YHL mik-
klion diaporeumenow moirn rp.
Vste prw t pogeiotr to zdiako mikukl pleonzei t
mal kinmata tn fainomnvn tmmasin d
(20)' d' ggista. plin pe
t BGD to kkntrou tmhmtvn loipn stin ew tn lon kklon
met tw rpd m
(2) moraw roe id, stin d ka t YKL to zdiako
mikklion moirn rp, ka n t BGD malw kinetai, fanetai t
YKL. nleicen ra ntaya t mal kinmata t tn fainomnvn tm-
masin d
(20)' d' ggista.
Vste ka prw llhla t prw t poge mal kinmata tn prw
tow perigeoiw diafrei tow diplasoiw tmmasi y
(20)' ggista.
Lgv ti tow tosotoiw xrnoiw koloyvw ka t otvw sunagme-
na fainmena nuxymera prw t mal ka ti prw llhla tn moan
diaforn poiontai.
Epe gr n t BAD to kkntrou tmma malw liow diapo-
reetai moirn tugxnon rpd m
(2), fanetai tw to YHL mikuklou
to di msvn moraw rp nvmlvw diaporeumenow, n d plin t
BGD moirn tugxnon roe id malw diaporeetai, fanetai tw to
YKL mikuklou moraw rp, n pleoni d xrn t BAD malw diapo-
reetai per t BGD, n pleoni ra xrn fanetai t YHL to di
msvn mikklion diaporeumenow per t YKL: e d n s xrn j
malo faneto kteron atn diaporeumenow, parhkoloyei ka
kteron atn fanesyai parodeonta n xrnoiw rp. ste n pleosi
xrnoiw toi tmmasin d m
(2) toutstin d
(20)' d' ggista liow t
DHY pogeiteron to zdiako mikklion fanetai kinomenow nv-
mlvw per sunbainen atn malw at fanesyai kinomenon: ka
movw n lttosi xrnoiw toi tmmasin tow soiw fanetai t YKL
to di msvn perigeiteron mikklion nvmlvw diaporeumenow
per sunbainen atn malw at fanesyai kinomenon.
Ka fainmena mn gnetai nuxymera t pilambnonta met tw
to ksmou peristrofw tn xrnon tw fainomnhw to lou pardou,
mal d t pilambnonta tn xrnon se malw faneto to di
msvn t mikklia diaporeumenow n xrnoiw rp.
Ka diafrei xrnow to xrnou tosotoiw tmmasin soiw diaf-
rei ka fainomnh to lou nmalow knhsiw tw malw, toutstin
tmmasin d m
(2).
Vste ka t pilambnonta nuxymera tn xrnon tw p to L
mikuklou fainomnhw nvmlou pardou tn pilambanntvn tn
xrnon se malw at faneto diaporeumenow perjei tosot
xrn n s nafretai diafor tw fainomnhw to lou par tn
maln, toutstin n s nafrontai a d
(20)' d' morai to di msvn
tn zdvn kklou.
t d pilambnonta tn xrnon tw
YKL mikuklou fainomnhw pardou tn pilambanntvn tn xrnon
tn se malw at faneto kinomenow llecei t xrn tw na-
forw tn d
(20)' d' moirn. lllvn d t prw t pogeiotr miku-
kl fainmena nuxymera tn prw t perigeiotr mikukl dio-
sousin tow diplasoiw tn d
(20)' d' moirn tw naforw xrnvn, tou-
tstin y
(20)' ggista moraiw naforw xrnoiw.
Eklesen d tw tw malw to lou pardou moraw ka xrnouw,
di t poxesyai w par tn to lou mnhn nvmalan ginomnhw tw
diaforw okti d ka par tw sunanaforw tw summesouranseiw,
ka di toto w m gkeklimnon paralambnesyai tn di msvn prw
tn shmerinn ll tn atn at tugxnonta, pe ka a par tw
sunanaforw tw summesouranseiw diafora par tn gklisin to
di msvn prw tn shmerinn potelontai, ka dhlad sodunamen
tw tw malw pardou moraw tow to shmerino xrnoiw, pe nw
ka to ato ginomnou to di msvn t shmerin, a sai tw ma-
lw pardou to lou morai soxronvw nafrontai tn rzonta
sunejrxontai tn meshmbrinn kayper ka to shmerino.
H ka suntomteron otvw: pe w famen, p tn p natolw
rxn tn nuxyhmrvn, m ginomnhw par tw sunanaforw diaforw,
p tn p meshmbraw rxn m ginomnhw par tw summesouran-
seiw diaforw, soduname di msvn tn zdvn kklow t shmerin:
ka di toto n kinetai liow malw, tathn ka pilambnei t
maln nuxymeron met tn to ksmou peristrofn, n d nvmlvw
tathn plin pilambnei t nmalon ka fainmenon nuxymeron met
tn to ksmou peristrofn: dlon w n n tini mr& kinhy malw
moran a n d tr& nvmlvw moran a ka jhkostn a katran
totvn pilmcetai kteron tn nuxyhmrvn met tn peristrofn.
ka diosei t nuxymeron to nuxyhmrou t tosot xrn n s
t jhkostn a tw peroxw tn kinsevn nafretai diejrxetai
tn meshmbrinn.
Omovw d ka p pleinvn nuxyhmrvn, diafrei to lou
mal knhsiw tw nvmlou, tathw t nafor mesouransei diosei
ka t nuxymera tn nuxyhmrvn.
ka pe tw nvmlou ka faino-
mnhw kinsevw par tn maln diafor w dejamen o plen stin
moirn d
(20)' d' ggista, dlon w t totvn nafor mesouransei
diosei t fainmena nuxymera tn maln,
prw llhla d t fain-
mena tow diplasoiw.
Gnetai d ka par tw prw tn rzonta tn nuxyhmrvn poka-
tastseiw toutstin tw sunanaforw sugkatadseiw megsth tn
maln nuxyhmrvn par t kairik diafor p tn p tn tropikn
shmevn forizomnvn mikuklvn toutstin p tn p rxw to
Agkerv movw p Karknou: "ka nyde gr a katrou totvn
"tn mikuklvn sunanafora" diafrousi tn maln, toutstin tn
se malw nrxonto j' sou atow piballntvn xrnvn soiw dia-
frei ka megsth laxsth mra tw shmerinw kay' kaston kl-
ma: lllvn d ow megsth tw laxsthw.
Oon w p to trtou di' Alejandreaw klmatow, pe megsth
mra n nafretai t p Karknou p Agkerv mikklion, rn
stin shmerinn id xrnvn d si, d laxsth mra, n naf-
retai t p Agkerv p Karknon mikklion, rn i xrnvn d rn:
dlon w ti tn tw shmerinw mraw xrnvn rp diafrousi xrnoiw
l, raiw d do, saiw diafrousi a id rai tw megsthw mraw ka
tw laxsthw tn shmerinn rn ib: lllvn d tow
diplasoiw xrnoiw j raiw d d, saiw diafrousi a tw megsthw
plin mraw rai id tn tw laxsthw rn i. ka dlon w ti
diafrousin lllvn t erhmna mikklia kat tw naforw xrnoiw
tosotoiw soiw ka megsth mra tw laxsthw diafrei. ka pe
t mn fainmena nuxymera kat tow sunanenexyntaw katr tn
to zdiako mikukl xrnouw poteletai, t d mal kat tow
j malo w famen krnouw rp, dlon w ti ka t mn fainmena
nuxymera diosousi tn maln xrnoiw l, lllvn d t fainmena
xrnoiw j.
Eti d gnetai plin ka par tw prw tn meshmbrinn tn nu-
xyhmrvn pokatastseiw toutstin tw summesouranseiw plesth
diafor tn maln nuxyhmrvn prw t fainmena nmala p do
tn katrvyen potrou tn tropikn dvdekathmorvn prw do t
katrvyen potrou tn shmerinn, di t t mn katrvyen tn
tropikn t plest pleonzein par tn mshn piboln (toutsti
par t kat mson diforon, t n pleosin ka lttosin xrnoiw sun-
ejrxesyai tn meshmbrinn, otinw esi
(2) ka kz n:> plin j
malo atn sunejerxomnvn sriymon gnontai taw kat do dvde-
kathmria) xrnoiw d
(20)' ggista:
merinn llepein sxedn tow atow.
Oon pe t to Karknou ka t tn Didmvn dvdekathmrion,
katrvyen nta tw yerinw tropw, summesouranosin mftera to
shmerino xrnoiw jd lb, di t kteron summesouranen xrnoiw
lb i
(2): o d kat tn mson lgon w famen summesouranontew kst
esn xrnoi l: ste diafrousin a fainmenai summesouranseiw tn
kat mson lgon toi maln xrnoiw d
(20)' ggista.
Plin pe t to Krio ka t tn Ixyvn dvdekathmrion katrvyen
nta to ato shmerino summesouranosin xrnoiw ne m, di t
kteron summesouranen xrnoiw kz n, w k tn tw ryw sfaraw
sunanaforn gnetai dlon, fanern ti ka tata t dvdekathmria
faire tn msvw pilambanomnvn xrnvn j, xrnouw d
(20)'.
Epe on tn msvn xrnvn j, t mn katrvyen tn tropikn
do dvdekathmria perxei kat tw fainomnaw summesouranseiw
xrnoiw d
(20)' ggista, t d katrvyen to shmerino llepei sxedn
tow atow, dlon w ti lllvn a fainmenai summesouranseiw
tn katrvyen tn tropikn do dvdekathmorvn prw t katrvyen
tn shmerinn do dvdekathmria diafrousin xrnoiw y ggista:
ka di toto, koloyvw tow p tn naforn erhmnoiw, diafrei
ka t fainmena nuxymera tn maln xrnoiw d
(20)', lllvn d tow
diplasoiw xrnoiw y.
Eta podokimzei tw prw to rzontow rxw tn nuxyhmrvn,
di t tw sunanaforw sugkatadseiw p tn atn to zdiako
tmhmtvn diafrouw gnesyai kay' kaston klma, ka don enai ka tw
k tw sumplokw tn do nvmalin ginomnaw diaforw f' kstou
pilogzesyai: ka di t tw naforw fejw kolouyen w famen
taw diaforaw tn megstvn laxstvn mern, tn d diaforn
totvn ka mxri polln rn p tn boreiotrvn klimtvn ginomnvn,
dlon w ti ka a p tn sunanatoln sugkatadsevn diafora p
tn gklsevn ka mxri polln rn poisousin tn diafvnan.
Ep d tn summesouransevn at stai diafor kat mrow:
ka plin at megsth kat psaw tw gklseiw xrnvn tugxnousa
y, ka mhd tow tw liakw nvmalaw sunagomnouw xrnouw y
(20)',
kaper ligstouw ntaw te d mhd dimorou raw tugxnontaw, per-
bllousa, prw ow prohgoumnvw ka tn nuxyhmrvn nvmala po-
teletai, di t ka prw tn to lou prodon at yevresyai: di
ka tw rxw tn nuxyhmrvn p tn mesouransevn sunestsato
toutstin p meshmbraw, ka ox p tn natoln dsevn.
Ka a mn mgistai diafora tn nuxyhmrvn par te tn to lou
nvmalan ka par tw summesouranseiw diai kay' kaston trpon
hrhntai kayw pedejamen.
Gnetai d ka k tw mjevw tw to lou nvmalaw ka tw par
tw summesouranseiw, di t w famen sumpeplxyai atw pntote,
plesth diafor "p tn kat mfotraw tw erhmnaw diaforw
"toi prosyetikn ma fairetikn" ginomnvn: o gr n troiw
mnon to lou nvmala tmmasin faire n troiw d tn sum-
mesouransevn n troiw plin ka troiw prostiyasin, ll' pou
mn ka ma fairosin, o do trpoi kat tn sumplokn w "p Udro-
"xou msou mxri Xhln tmmatow," pou d ka prostiyasin w
"p Skorpou mxri msou Udroxou": ka fairosi mn kat tn mjin
p tn erhmnvn fairetikn xrnouw h g', prostiyasi d tow a-
tow p tn prosyetikn, peidper mn k tw liakw mnhw nv-
malaw ginomnh diafor xrnvn g
(137) katalambnetai, d k tw
par tw summesouranseiw xrnvn d m, w k tw mjevw mfotrvn
tn nvmalin sungesyai tow xrnouw h g'.
Oti d p to p msou Udroxou tmmatow, toutstin p pente-
kaidekthw moraw to Udroxou mxri to tlouw tn Xhln faire
to lou nvmala xrnouw g
(137) p d tw rxw Skorpou mxriw
tw ie' to Udroxou prostyhsi tow atow g
(137), otvw stai dlon.
Estv gr kkentrow to lou kklow ABGD per kntron t E ka
dimetron tn AEG f' w elfyv t to di msvn tn zdvn kntron
t Z, ste t mn A gnesyai t pogeitaton t d G t perigeitaton.
ka gegrfyv per t Z HYKL zdiakw, ste kblhyeshw tw AG
p t H, K, t mn H gnesyai kat tw tn Didmvn moraw e l, t d
K kat tw to Tojtou moraw tw atw. ka pokesyv t Y kat
tw rxw to Skorpou, t d L kat tw ie' moraw to Udroxou. ka
pezexyvsan a ZY, ZL, EB, ED.
Ka pe HY to zdiako sungetai moirn rmd l ovn a d
rya tj, ka pe taw malaw pardoiw parkeintai a par tn nv-
malan diafora, stai AB to kkntrou perifreia toutstin p
AEB gvna moirn rme ng, peidper a tataiw parakemenai tw
par tn nvmalan diaforw tw p EBZ gvnaw moraw a ka jhko-
stn kg faireyesai p' atn poiosi tn p HZY fainomnhn tn
prokeimnvn moirn rmd l.
Plin pe HYL to di msvn perifreia sungetai moirn smy l,
stai ka AGD mal p to kkntrou prodow moirn smz i
(2),
pe ka n tataiw prosymen tw parakeimnaw ataw tw par tn
nvmalan diaforw moraw b id, poiosin tw erhmnaw moraw smy l
tw fainomnhw pardou.
Estin d ka di tn n tow ew toto t biblon pareilhmmnvn
at di tn grammikn dejevn fdvn p tw kribow poxw tn
maln eren.
Vste ka taw loipaw ew tn lon kklon tw LH fainomnhw pardou
moraiw ri l pibllousin a loipa tw DA malw morai rib md.
pballon d ka tw HY fainomnhw pardou moraiw rmd l a tw AB
malw morai rme ng. taw ra tw LHY p msou Udroxou mxriw
Xhln tlouw fainomnhw pardou moraiw sne pibllousi tw DAB malw pardou morai snh lz. ka di toto faire fainomnh pr-
odow tw malw kat t erhmnon to di msvn tmma moraw g lz,
(2) fhsin g
(137) ggista.
Fanern d ti ka loipn t YKL p rxw Skorpou mxri msou
Udroxou prostyhsi tw atw moraw g
(137) ggista. fhsen d ka
ntaya tw g
(137) moraw ka xrnouw, di t w famen sodunamen
tn di msvn tn zdvn kklon t shmerin tan par mnhn tn
to lou nvmalan ggnhtai diafor tow nuxyhmroiw.
Oti d ka [t] par tw summesouranseiw t mn p msou Udro-
xou mxri Xhln tmma faire xrnouw d
(137) t d p rxw Skor-
pou mxri msou Udroxou prostyhsi tow atow, otvw stai dlon.
En gr tw p tw ie' moraw to Udroxou mxri to tlouw tn
Xhln sunagomnaw moraw sne esaggvmen, w dejamen n tow ew
t b' biblon pomnmasin, ew tn p' ryw tw sfaraw rzonta,
ersomen taw tosataiw moraiw summesouranontaw tow shmerinow
xrnouw sn iy ka frkasin dhlad xrnouw d
(137) ggista: tosotoiw
gr lssonw esin o sn iy xrnoi tn sne moirn to zdiako.
dlon d ti ka taw loipaw to zdiako moraiw re summesourano-
sin to shmerino o loipo xrnoi ry ma, pe ka low zdiakw
l t shmerin sugxrone. ka prosteykasin ntaya o summesou-
ransantew xrnoi taw to zdiako moraiw tow souw xrnouw d
(137).
ka ggonen mn dlon ti ka par tw mesouranseiw tn mn p msou
Udroxou mxri Xhln tmma faire xrnouw d
(137), t d p rxw
Skorpou mxri msou Udroxou prostyhsin tow souw xrnouw d
(137).
Afrei d ka to lou nvmala tw malw ato kinsevw p to
ato tmmatow nya kat tw summesouranseiw froun moraw g
(137),
ka ti prosetyei tw atw f' n plin ka a summesouranseiw prow-
etyesan.
ste ka k tw mjevw tn do nvmalin sungetai t
pleston diforon tn xrnvn par tn maln to lou knhsin xr-
nvn h g': to mn p msou Udroxou mxri Xhln fairontow a-
tow, to d p Skorpou mxri msou Udroxou prostiyntow tow
souw.
Ka pe t mn fainmena nuxymera prw tow shmerinow k tw
sumplokw xrnouw yevretai, t d mal prw tn maln w famen
to lou prodon: ka t p msou ra Udroxou mxri Xhln fain-
mena nuxymera tn maln llecei xrnoiw h g' toutstin miw raw
(20)' ih', t d p Skorpou mxri msou Udroxou pleonsei tow
soiw.
Prw llhla d, toutstin tn fainomnvn diafor tw tn maln
diaforw diosei tow diplasoiw tn h g' xrnoiw, soiw ka nleipon
plenazon o kay' kteron tn erhmnvn tmhmtvn k tw sumplokw
fainmenoi xrnoi tn maln toutstin xrnoiw i
(2)
(137), ran d man y'.
Oti d diafor tn fainomnvn tw diaforw tn maln diafrei
tow diplasoiw tn h g' xrnvn, otvw stai dlon.
Epe gr p msou Udroxou mxri Xhln to lou mal pr-
odow katelambneto moirn snh lz ka tathw frei to lou
nvmala moraw g lz, tw d nvmlou to lou kinsevw moirn
sne frei par tw summesouranseiw diafor moraw d ma, dlon
w ti k tw sumplokw tn do nvmalin morai h ih fairo-
menai p tn snh lz tw malw pardou to lou, poisousin tn
k tw sumplokw tn do nvmalin pibllousan tow fainomnoiw
nuxyhmroiw
Skorpou mxri msou Udroxou tw malw pardou moraiw r kg
prostiyasin, a loipa ew tn kklon tn k tw sumplokw moirn
Ka dlon w o k tw sumplokw tn do nvmalin xrnoi sn iy
p msou Udroxou mxri Xhln tmmatow, tn k tw sumplokw
xrnvn ry ma tn p Skorpou mxri msou Udroxou fainomnvn
nuxyhmrvn diafrousin xrnoiw rm lh: a d tw malw pardou
morai p msou Udroxou mxri Xhln snh lz, tn tw malw
ra kg tn p Skorpou mxri msou Udroxou diafora rnz id,
o esin tn maln nuxyhmrvn.
Ka diafrousin a rm lh tn rnz id, i
(2) l
(2), w fhsin i
(2)
(137) ggista,
diplasvn osn tn h ih tw diaforw tn sn iy k tw fainomnhw
sumplokw par tw snh lz tw malw.
T d tn i
(2)
(137) xrnvn diforon stin ra shmerin a ka y',
"p mn lou ka tn e planvmnvn parormenon odn n svw a-
"syht katablptoi" tn neu tw to tosotou diakrsevw tn fai-
nomnvn katlhmcin, di t n t tosot xrn tn lion do pou
jhkost kinesyai, tow d loipow ka latton.
"Ep d tw selnhw, di t tw kinsevw atw txow jilogon
"
(2) gigno-
mnhn, di t n t tosot xrn t mgista atn tosata ggista
kinoumnhn katalambnesyai.
Dlon d mn gensetai ti ka t erhmna tmmata tn megsthn
sumplokn tn do nvmalin tw nisthtow nuxyhmrvn diaforn
perixousin, k tn kat tn prxeiron p' ryw tw sfaraw trtvn
selidvn nya ka a toiatai diafora pilelogismnai parkeintai,
w n t ew tn lgon tn proxervn kannvn pomnmati dhlomen.
Per tw prw t mal nuxymera
tn rn diakrsevw.
"Ina on ka tn kay' poiandpote distasin" tn p meshmbraw
mesonuktou kairikn ka plw yevroumnvn nuxyhmrvn "ew mal
"nuxymera kaypaj metalambnvmen, piskecmeya" prteron kat
te tn rxn ka t tlow tw didomnhw to xrnou diastsevw n di-
djamen trpon, "kat povn stn to di msvn tn zdvn kklou
"moirn liow malw te kinomenow ka nvmlvs". ka pogra-
cmenoi tn posthta tn tw malw diastsevw moirn ka jhkostn
ka ti tn tw nvmlou ka fainomnhw (tiw dhlonti perixei tn
man diaforn tn do tn poiousn tn nisthta tn nuxyhmrvn,
lgv d tn par tn to lou nvmalan), eta plin tathn tn n-
malon distasin "esenegkntew ew tw p' ryw tw sfaraw sunana-
"forw piskecmeya psoiw summesouransousin xrnoiw to shmeri-
"no a tw nvmlou diastsevw morai". ka dlon ti o otv kat.
lambanmenoi xrnoi tn sumplokn perixousin tn do diaforn tn
fainomnvn nuxyhmrvn par t mal, lgv d tn te par tn to
lou nvmalan ka tn par tw summesouranseiw.
Oon pe gr o k tn p' ryw tw sfaraw naforn lhmfyntew
xrnoi fairosin tn tw kribow to lou diastsevw moirn par
tw summesouranseiw, d kribw to lou distasiw diafrei tw
malw par tn to lou nvmalan, o ra k tn p' ryw tw sfa-
raw naforn lhmfyntew xrnoi diafrousin tw malw to lou dia-
stsevw, par te tw summesouranseiw ka par tn to lou nv-
malan.
Labntew on tn peroxn tn otvw ereyntvn xrnvn ka tn
tw malw diastsevw to lou moirn, tathw t ie' jomen pst
mrei raw diosousin t kairik ka plw yevromena nuxymera tn
maln, w tw kay' kteron trpon diaforw, e ka kay' autn g-
gneto, suntiyemnhw mhdn asyhtn diforon poioshw t k tw sum-
plokw fainomn.
Toto on t katalambanmenon mrow tw raw, n mn t plyow
tn fainomnvn xrnvn toutstin tn k tw sumplokw tn do nv-
malin pleon tn tw malw diastsevw to lou moirn, prost-
yemen t dedomn kairik xrn.
Oon w p nw nuxyhmerino, pe xrnow to fainomnou nu-
xyhmrou plen stin to malo, t fainmenon n stin maln ka
mrow rn: ste koloyvw tn prsyesin p tw toiathw diakrsevw
poiontew ew mal nuxymera, t kairik metalambnomen.
En d latton t plyow tn xrnvn tn tw malw diastsevw
to lou moirn, fairomen p to doyntow kairiko xrnou.
Plin gr movw e xrnow to fainomnou nuxyhmrou lttvn stn
to malo, t fainmenon nuxymeron n stin maln par ti mrow
raw: ste koloyvw plin p tathw tw diakrsevw fairontew
ew mal nuxymera t kairik metalambnomen.
Pepohtai d Ptolemaow tn sgkrisin tw tn fainomnvn nv-
mlvn xrnvn diastsevw prw tn to lou maln knhsin, nt tn
piballntvn tow malow nuxyhmroiw, di t sa enai t pilamban-
mena to shmerino tmmata met tn man peristrofn t mal
nuxyhmr t to lou mal pardou, w pnv erhken "sa ka
liow msvw n t tosot xrn pikinetai".
En d, fhsn, plin p tw tn maln nuxyhmrvn diastsevw
t kairik proairmeya lambnein, npalin tn prosyafaresin poih-
smeya. tan gr o[on] k tw sumplokw tn nvmalin eriskmenoi
xrnoi, otinw esin tn fainomnvn nuxyhmrvn, pleouw sin tn tw
malw diastsevw to lou moirn, felomen p to xrnou tw
malw tn nuxyhmrvn diastsevw, t k tw peroxw ginmenon m-
row raw shmerinw: peidper plin n t n fainmenon nuxymeron
mezon to nw malo, lgomen t n maln n enai fainmenon
par ti mrow raw. ste koloyvw ka ntaya tw fairsevw p
tn nvmlvn ginomnhw t mal lambnetai. tan d plin lttonew
sin o k tw sumplokw xrnoi tn tw malw diastsevw moirn,
prosysomen t tn maln nuxyhmrvn plyei t tw raw mrow:
peidper plin n t n maln nuxymeron mezon to nw faino-
mnou, lgomen t maln n enai fainmenon ka ti mrow raw, ste
ka ntaya koloyvw tw prosysevw ginomnhw jomen p tn ma-
ln nuxyhmrvn t kairik ka nmala.
Epeita pe sumbanei mw ka tn p to a' touw Nabonassrou
xrnon mxri dedomnou tinw metalambnein prw tina tn erhmnvn
nuxyhmrvn xrnon, pomimnskei mw ka tn kat toton tn xrnon
to lou maln ka krib poxn, ka fhsin: "pexen" d ew tn
erhmnhn "poxn to a' touw Nabonassrou yy a'" raw
(2) liow
malw "w mikr prsyen pedejamen tn Ixyvn moraw
(130) me. kri-
"bw d moraw g h", peidper ka sje ie moraw tte pxvn
to pogeou, prosetyei t mal pard tn plesthn diaforn tn
b kg moirn.
Ina d ka p podegmatow faner mn gnhtai t erhmna, poih-
smeya ka tn toiathn dikrisin p to ato xrnou f' o ka tn
chfoforan to lou poihsmeya.
Ka prokesyv p tw tn fainomnvn nvmlvn nuxyhmrvn dia-
stsevw t mal pilogsasyai. pe on eromen p to prw tw
shmerinw raw lhmfyntow mn xrnou malw tn lion pxonta
to Agkerv moran ib lh kribw d id h: pexen d w famen
ka n t rx Nabonassrou malw mn tn Ixyvn
(130) me, kribw
d g h: ka sungetai p tw malw poxw p tn maln moirn
tia ng: d p tw fainomnhw p tn fainomnhn moirn tia: aw
summesouranosin p' ryw tw sfaraw to shmerino xrnoi ti ie,
lttonew ntew tn tw malw diastsevw tia ng, mor& a lh, tout-
stin miw raw y' ggista.
Toto t mrow felntew p tn kat tn proekteyeimnon mn
xrnon ka
(20)' rn shmerinn, sxomen tn prw t mal nuxymera
diakekrimnon p tw rxw tw Nabonassrou basileaw yy a tw
meshmbraw, tn aguptiakn ajy ka mern sid ka rn ka g' k',
xrhsmeya mlista prw tw pisunagvgw tn maln tw selnhw
kinsevn, di t tn toiathn dikrisin dnasyai per tn tw selnhw
prodon asyhtn poiesyai diaforn, di t tw kinsevw atw w
famen txow.