Aristotelis Opera selecta

Analitica Posteriora

ANALUTIKVN USTERVN A

    Psa didaskala ka psa myhsiw dianohtik k pro#- parxoshw gnetai gnsevw. fanern d toto yevrosin p pasn: a te gr mayhmatika tn pisthmn di totou to trpou paragnontai ka tn llvn ksth texnn. movw d ka per tow lgouw o te di sullogismn ka o di' pagvgw: mfteroi gr di proginvskomnvn poi- ontai tn didaskalan, o mn lambnontew w par junin- tvn, o d deiknntew t kaylou di to dlon enai t kay' kaston. w d' atvw ka o =htoriko sumpeyousin: gr di paradeigmtvn, stin pagvg, di' nyumhmtvn, per st sullogismw. dixw d' nagkaon proginskein: t mn gr, ti sti, pro#polambnein nagkaon, t d, t t legmenn sti, juninai de, t d' mfv, oon ti mn pan fsai pofsai lhyw, ti sti, t d tr- gvnon, ti tod shmanei, tn d monda mfv, ka t sh- manei ka ti stin: o gr movw totvn kaston dlon mn. Esti d gnvrzein t mn prteron gnvrsanta, tn d ka ma lambnonta tn gnsin, oon sa tugxnei nta p t kaylou o xei tn gnsin. ti mn gr pn tr- gvnon xei dusn ryaw saw, prodei: ti d tde t n t mikukl trgvnn stin, ma pagmenow gnrisen. (nvn gr toton tn trpon myhsw sti, ka o di to msou t sxaton gnvrzetai, sa dh tn kay' kasta tugx- nei nta ka m kay' pokeimnou tinw.) prn d' paxynai laben sullogismn trpon mn tina svw faton psta- syai, trpon d' llon o. gr m dei e stin plw, toto pw dei ti do ryw xei plw; ll dlon w d mn pstatai, ti kaylou pstatai, plw d' ok pstatai. e d m, t n t Mnvni prhma sumbsetai: gr odn maysetai oden. o gr d, w g tinew gxeirosi lein, lekton. r' odaw pasan duda ti rta o; fsantow d pronegkn tina duda n ok et' enai, st' od' rtan. lousi gr o fskontew ednai p- san duda rtan osan, ll' n sasin ti duw. katoi sasi mn oper tn pdeijin xousi ka o labon, la- bon d' ox pantw o n edsin ti trgvnon ti riymw, ll' plw kat pantw riymo ka trignou: odema gr prtasiw lambnetai toiath, ti n s odaw riy- mn s odaw eygrammon, ll kat pantw. ll' odn (omai) kvlei, manynei, stin w pstasyai, sti d' w gnoen: topon gr ok e od pvw manynei, ll' e d, oon manynei ka w. Epstasyai d omey' kaston plw, ll m tn sofistikn trpon tn kat sumbebhkw, tan tn t' atan omeya ginskein di' n t prgm stin, ti kenou ata st, ka m ndxesyai tot' llvw xein. dlon tonun ti toiotn ti t pstasya sti: ka gr o m pistmenoi ka o pistmenoi o mn oontai ato otvw xein, o d' pist- menoi ka xousin, ste o plw stin pistmh, tot' dnaton llvw xein. E mn on ka terow sti to pstasyai trpow, steron romen, famn d ka di' podejevw ednai. p- deijin d lgv sullogismn pisthmonikn: pisthmonikn d lgv kay' n t xein atn pistmeya. e tonun st t p- stasyai oon yemen, ngkh ka tn podeiktikn pistmhn j lhyn t' enai ka prtvn ka msvn ka gnvrimvtrvn ka protrvn ka atvn to sumpersmatow: otv gr son- tai ka a rxa okeai to deiknumnou. sullogismw mn gr stai ka neu totvn, pdeijiw d' ok stai: o gr poisei pistmhn. lhy mn on de enai, ti ok sti t m n pstasyai, oon ti dimetrow smmetrow. k prtvn d' napodektvn, ti ok pistsetai m xvn pdeijin a- tn: t gr pstasyai n pdeijiw sti m kat sumbe- bhkw, t xein pdeijn stin. ati te ka gnvrimtera de enai ka prtera, atia mn ti tte pistmeya tan tn atan edmen, ka prtera, eper atia, ka progi- nvskmena o mnon tn teron trpon t juninai, ll ka t ednai ti stin. prtera d' st ka gnvrimtera dixw: o gr tatn prteron t fsei ka prw mw prteron, od gnvrimteron ka mn gnvrimteron. lgv d prw mw mn prtera ka gnvrimtera t ggteron tw a- sysevw, plw d prtera ka gnvrimtera t porrte- ron. sti d porrvttv mn t kaylou mlista, gguttv d t kay' kasta: ka ntkeitai tat' llloiw. k pr- tvn d' st t j rxn okevn: tat gr lgv prton ka rxn. rx d' stn podejevw prtasiw mesow, mesow d w m stin llh protra. prtasiw d' stn po- fnsevw t teron mrion, n kay' nw, dialektik mn movw lambnousa poteronon, podeiktik d ri- smnvw yteron, ti lhyw. pfansiw d ntifsevw po- teronon mrion, ntfasiw d ntyesiw w ok sti metaj kay' atn, mrion d' ntifsevw t mn t kat tinw kat- fasiw, t d t p tinw pfasiw. Amsou d' r- xw sullogistikw ysin mn lgv n m sti dejai, mhd' ngkh xein tn mayhsmenn ti: n d' ngkh xein tn tion mayhsmenon, jvma: sti gr nia toiata: toto gr mlist' p tow toiotoiw eyamen noma lgein. ysevw d' mn poteronon tn morvn tw ntifsevw lamb- nousa, oon lgv t ena ti t m ena ti, pyesiw, d' neu totou rismw. gr rismw ysiw mn sti: tye- tai gr riymhtikw monda t diareton enai kat t posn: pyesiw d' ok sti: t gr t sti monw ka t e- nai monda o tatn. Epe d de pisteein te ka ednai t prgma t toioton xein sullogismn n kalomen pdeijin, sti d' otow t tad enai j n sullogismw, ngkh m mnon proginskein t prta, pnta nia, ll ka ml- lon: ae gr di' prxei kaston, ken mllon pr- xei, oon di' filomen, keno flon mllon. st' eper smen di t prta ka pisteomen, kkena smen te ka pisteomen mllon, ti di' kena ka t stera. ox on te d pisteein mllon n oden m tugxnei mte edw mte bltion diakemenow e tgxanen edw. sumbsetai d toto, e m tiw prognsetai tn di' pdeijin pisteun- tvn: mllon gr ngkh pisteein taw rxaw psaiw tis to sumpersmatow. tn d mllonta jein tn pi- stmhn tn di' podejevw o mnon de tw rxw mllon gnvrzein ka mllon ataw pisteein t deiknumn, ll mhd' llo at pistteron enai mhd gnvrimteron tn ntikeimnvn taw rxaw j n stai sullogismw tw nantaw pthw, eper de tn pistmenon plw met- peiston enai. Enoiw mn on di t den t prta pstasyai o doke pistmh enai, tow d' enai mn, pntvn mntoi pdeijiw enai: n odteron ot' lhyw ot' nagkaon. o mn gr poymenoi m enai lvw pstasyai, otoi ew peiron jio- sin ngesyai w ok n pistamnouw t stera di t prtera, n m sti prta, ryw lgontew: dnaton gr t peira dielyen. e te statai ka esn rxa, tataw gnstouw enai podejew ge m oshw atn, per fasn enai t pstasyai mnon: e d m sti t prta ednai, od t k totvn enai pstasyai plw od kurvw, ll' j poysevw, e kena stin. o d per mn to pstasyai mologosi: di' podejevw gr enai mnon: ll pntvn enai pdeijin odn kvlein: ndxesyai gr kkl gne- syai tn pdeijin ka j lllvn. Hmew d famen ote psan pistmhn podeiktikn enai, ll tn tn msvn napdeikton (ka toy' ti nagkaon, fanern: e gr ngkh mn pstasyai t prtera ka j n pdeijiw, statai d pote t mesa, tat' napdeikta ngkh enai) tat t' on otv lgomen, ka o mnon pistmhn ll ka rxn pistmhw ena tin famen, tow rouw gnv- rzomen. kkl te ti dnaton podeknusyai plw, d- lon, eper k protrvn de tn pdeijin enai ka gnvrimv- trvn: dnaton gr sti t at tn atn ma prtera ka stera enai, e m tn teron trpon, oon t mn prw mw t d' plw, nper trpon pagvg poie gnri- mon. e d' otvw, ok n eh t plw ednai kalw ri- smnon, ll dittn: ox plw tra pdeijiw, gino- mnh g' k tn mn gnvrimvtrvn. sumbanei d tow lgousi kkl tn pdeijin enai o mnon t nn erhmnon, ll' odn llo lgein ti tot' stin e tot' stin: otv d pnta =dion dejai. dlon d' ti toto sumbanei trin rvn te- yntvn. t mn gr di polln di' lgvn nakmptein fnai odn diafrei, di' lgvn d' duon. tan gr to A ntow j ngkhw t B, totou d t G, to A ntow stai t G. e d to A ntow ngkh t B enai, totou d' ntow t A (toto gr n t kkl), kesyv t A f' o t G. t on to B ntow t A enai lgein st t G enai l- gein, toto d' ti to A ntow t G sti: t d G t A t at. ste sumbanei lgein tow kkl fskontaw enai tn pdeijin odn teron pln ti to A ntow t A stin. otv d pnta dejai =dion. O mn ll' od toto dunatn, pln p totvn sa llloiw petai, sper t dia. nw mn on keimnou ddeiktai ti odpot' ngkh ti enai te- ron (lgv d' nw, ti ote rou nw ote ysevw miw teye- shs), k do d ysevn prtvn ka laxstvn ndxetai, eper ka sullogsasyai. n mn on t te A t B ka t G phtai, ka tat' llloiw ka t A, otv mn nd- xetai j lllvn deiknnai pnta t athynta n t prt sxmati, w ddeiktai n tow per sullogismo. ddeiktai d ka ti n tow lloiw sxmasin o gnetai sullogismw o per tn lhfyntvn. t d m ntikath- goromena odamw sti dejai kkl, st' peid lga toi- ata n taw podejesi, fanern ti kenn te ka dna- ton t lgein j lllvn enai tn pdeijin ka di toto pntvn ndxesyai enai pdeijin. Epe d' dnaton llvw xein o stin pistmh plw, nagkaon n eh t pisthtn t kat tn podeiktikn pi- stmhn: podeiktik d' stn n xomen t xein pdeijin. j nagkavn ra sullogismw stin pdeijiw. lhpton ra k tnvn ka povn a podejeiw esn. prton d dior- svmen t lgomen t kat pantw ka t t kay' at ka t t kaylou. Kat pantw mn on toto lgv n m p tinw mn tinw d m, mhd pot mn pot d m, oon e kat pantw nyrpou zon, e lhyw tnd' epen nyrvpon, lhyw ka zon, ka e nn yteron, ka yteron, ka e n ps gramm stigm, satvw. shmeon d: ka gr tw nstseiw otv fromen w kat pantw rvtmenoi, e p tini m, e pote m. Kay' at d' sa prxei te n t t stin, oon trign gramm ka gramm stigm ( gr osa atn k totvn st, ka n t lg t lgonti t stin nuprxei), ka soiw tn parxntvn atow at n t lg nuprxousi t t sti dhlonti, oon t ey prxei gramm ka t periferw, ka t perittn ka rtion riym, ka t prton ka snyeton, ka spleu- ron ka termhkew: ka psi totoiw nuprxousin n t lg t t sti lgonti nya mn gramm nya d' ri- ymw. movw d ka p tn llvn t toiay' kstoiw kay' at lgv, sa d mhdetrvw prxei, sumbebhkta, oon t mousikn leukn t z. ti m kay' pokei- mnou lgetai llou tinw, oon t badzon tern ti n ba- dzon st ka t leukn , d' osa, ka sa tde ti shmanei, ox tern ti nta stn per stn. t mn d m kay' pokeimnou kay' at lgv, t d kay' pokeimnou sum- bebhkta. ti d' llon trpon t mn di' at prxon kst kay' at, t d m di' at sumbebhkw, oon e badzontow strace, sumbebhkw: o gr di t badzein stracen, ll sunbh, famn, toto. e d di' at, kay' at, oon e ti sfattmenon pyane, ka kat tn sfagn, ti di t sfttesyai, ll' o sunbh sfatt- menon poyanen. t ra legmena p tn plw pisth- tn kay' at otvw w nuprxein tow kathgoroumnoiw nuprxesyai di' at t sti ka j ngkhw. o gr ndxetai m prxein plw t ntikemena, oon gramm t ey t kamplon ka riym t perittn t rtion. sti gr t nanton strhsiw ntfasiw n t at gnei, oon rtion t m perittn n riymow petai. st' e ngkh fnai pofnai, ngkh ka t kay' at prxein. T mn on kat pantw ka kay' at divrsyv tn trpon toton: kaylou d lgv n kat pantw te prx ka kay' at ka at. fanern ra ti sa kaylou, j ngkhw prxei tow prgmasin. t kay' at d ka at tatn, oon kay' atn t gramm prxei stigm ka t ey (ka gr gramm), ka t trign trgvnon do rya (ka gr kay' at t tr- gvnon do ryaw son). t kaylou d prxei tte, tan p to tuxntow ka prtou deiknhtai. oon t do ryw xein ote t sxmat sti kaylou (katoi sti dejai kat sxmatow ti do ryw xei, ll' o to tuxntow sxmatow, od xrtai t tuxnti sxmati deiknw: t gr tetrgvnon sxma mn, ok xei d do ryaw sas) t d' soskelw xei mn t tuxn do ryaw saw, ll' o prton, ll t trgvnon prteron. tonun t tuxn prton deknutai do ryw xon tion llo, tot prt prxei kaylou, ka pdeijiw kay' at totou kaylou st, tn d' llvn trpon tin o kay' at, od to soske- low ok sti kaylou ll' p plon. De d m lanynein ti pollkiw sumbanei diamar- tnein ka m prxein t deiknmenon prton kaylou, doke deknusyai kaylou prton. patmeya d tathn tn pthn, tan mhdn laben nteron par t kay' kaston [ t kay' kasta], mn, ll' nnumon p diafroiw edei prgmasin, tugxn n w n mrei lon f' deknutai: tow gr n mrei prjei mn pdei- jiw, ka stai kat pantw, ll' mvw ok stai totou pr- tou kaylou pdeijiw. lgv d totou prtou, toto, p- deijin, tan prtou kaylou. e on tiw dejeien ti a r- ya o sumpptousi, djeien n totou enai pdeijiw di t p pasn enai tn ryn. ok sti d, eper m ti d sai gnetai toto, ll' pvson sai. ka e trgvnon m n llo soskelw, soskelw n dkei prxein. ka t nlogon ti ka nallj, riymo ka gramma ka stere ka xrnoi, sper deknut pote xvrw, nde- xmenn ge kat pntvn mi podejei deixynai: ll di t m enai nomasmnon ti tata pnta n, riymo mkh xrnoi stere, ka edei diafrein lllvn, xvrw lambneto. nn d kaylou deknutai: o gr gramma riymo prxen, ll' tod, kaylou potyentai prxein. di toto od' n tiw dej kay' kaston t trgv- non podejei mi tr& ti do ryw xei kaston, t spleuron xvrw ka t skalhnw ka t soskelw, opv ode t trgvnon ti do ryaw, e m tn sofistikn tr- pon, od kay' lou trignou, od' e mhdn sti par tata trgvnon teron. o gr trgvnon oden, od pn trgvnon, ll' kat' riymn: kat' edow d' o pn, ka e mhdn stin ok oden. Pt' on ok ode kaylou, ka pt' oden plw; dlon d ti e tatn n trign enai ka so- pler kst psin. e d m tatn ll' teron, prxei d' trgvnon, ok oden. pteron d' trgvnon soskelw prxei; ka pte kat toy' prxei pr- ton; ka kaylou tnow pdeijiw; dlon ti tan fai- roumnvn prx prt. oon t soskele xalk trign prjousi do rya, ll ka to xalkon enai faire- yntow ka to soskelw. ll' o to sxmatow pratow. ll' o prtvn. tnow on prtou; e d trignou, kat toto prxei ka tow lloiw, ka totou kaylou stn p- deijiw. E on stin podeiktik pistmh j nagkavn r- xn ( gr pstatai, o dunatn llvw xein), t d kay' at prxonta nagkaa tow prgmasin (t mn gr n t t stin prxei: tow d' at n t t stin prxei kathgoroumnoiw atn, n yteron tn ntikeimnvn ngkh prxein), fanern ti k toiotvn tinn n eh podei- ktikw sullogismw: pan gr otvw prxei kat sumbebhkw, t d sumbebhkta ok nagkaa. H d otv lekton, rxn yemnoiw ti pdeijiw nagkavn st, ka e poddeiktai, ox on t' llvw xein: j nagkavn ra de enai tn sullogismn. j lh- yn mn gr sti ka m podeiknnta sullogsasyai, j nagkavn d' ok stin ll' podeiknnta: toto gr dh podejew stin. shmeon d' ti pdeijiw j nagkavn, ti ka tw nstseiw otv fromen prw tow oomnouw po- deiknnai, ti ok ngkh, n omeya lvw ndxesyai llvw nek ge to lgou. dlon d' k totvn ka ti e- yeiw o lambnein omenoi kalw tw rxw, n ndojow prtasiw ka lhyw, oon o sofista ti t psta- syai t pistmhn xein. o gr t ndojon mn rx stin, ll t prton to gnouw per deknutai: ka tlhyw o pn okeon. ti d' j nagkavn enai de tn sullogi- smn, fanern ka k tnde. e gr m xvn lgon to di t oshw podejevw ok pistmvn, eh d' n ste t A kat to G j ngkhw prxein, t d B t mson, di' o pedexyh, m j ngkhw, ok ode diti. o gr sti toto di t mson: t mn gr ndxetai m enai, t d sum- prasma nagkaon. ti e tiw m ode nn xvn tn lgon ka szmenow, szomnou to prgmatow, m pilelhsm- now, od prteron dei. fyareh d' n t mson, e m nagkaon, ste jei mn tn lgon szmenow szomnou to prgmatow, ok ode d. od' ra prteron dei. e d m fyartai, ndxetai d fyarnai, t sumbanon n eh dunatn ka ndexmenon. ll' stin dnaton otvw xonta ednai. Otan mn on t sumprasma j ngkhw , odn kv- lei t mson m nagkaon enai di' o dexyh (sti gr t nagkaon ka m j nagkavn sullogsasyai, sper ka lhyw m j lhyn): tan d t mson j ngkhw, ka t sumprasma j ngkhw, sper ka j lhyn lh- yw e (stv gr t A kat to B j ngkhw, ka toto kat to G: nagkaon tonun ka t A t G prxein): tan d m nagkaon t sumprasma, od t mson nagkaon on t' enai (stv gr t A t G m j ng- khw prxein, t d B, ka toto t G j ngkhw: ka t A ra t G j ngkhw prjei: ll' ox pkeito). Epe tonun e pstatai podeiktikw, de j ngkhw pr- xein, dlon ti ka di msou nagkaou de xein tn p- deijin: ok pistsetai ote diti ote ti ngkh keno e- nai, ll' oޮsetai ok edw, n polb w nagkaon t m nagkaon, od' oޮsetai, movw n te t ti ed di msvn n te t diti ka di' msvn. Tn d sumbebhktvn m kay' at, n trpon div- rsyh t kay' at, ok stin pistmh podeiktik. o gr stin j ngkhw dejai t sumprasma: t sumbebhkw gr ndxetai m prxein: per to toiotou gr lgv sum- bebhktow. katoi porseien n tiw svw tnow neka tata de rvtn per totvn, e m ngkh t sumprasma enai: odn gr diafrei e tiw rmenow t tuxnta eta epeien t sumprasma. de d' rvtn ox w nagkaon enai di t rvthmna, ll' ti lgein ngkh t kena lgonti, ka lhyw lgein, n lhyw prxonta. Epe d' j ngkhw prxei per kaston gnow sa kay' at prxei ka kaston, fanern ti per tn kay' at parxntvn a pisthmonika podejeiw ka k tn toiotvn esn. t mn gr sumbebhkta ok nagkaa, st' ok ngkh t sumprasma ednai diti prxei, od' e e eh, m kay' at d, oon o di shmevn sullogi- smo. t gr kay' at o kay' at pistsetai, od diti (t d diti pstasya sti t di to atou pstasyai). di' at ra de ka t mson t trt ka t prton t ms prxein. Ok ra stin j llou gnouw metabnta dejai, oon t gevmetrikn riymhtik. tra gr sti t n taw po- dejesin, n mn t podeiknmenon, t sumprasma (toto d' st t prxon gnei tin kay' at), n d t ji- mata (jimata d' stn j n): trton t gnow t poke- menon, o t pyh ka t kay' at sumbebhkta dhlo pdeijiw. j n mn on pdeijiw, ndxetai t at enai: n d t gnow teron, sper riymhtikw ka gev- metraw, ok sti tn riymhtikn pdeijin farmsai p t tow megyesi sumbebhkta, e m t megyh riymo esi: toto d' w ndxetai p tinvn, steron lexysetai. d' riymhtik pdeijiw e xei t gnow per p- deijiw, ka a llai movw. st' plw ngkh t at enai gnow p, e mllei pdeijiw metabanein. llvw d' ti dnaton, dlon: k gr to ato gnouw ngkh t kra ka t msa enai. e gr m kay' at, sumbebhkta stai. di toto t gevmetr& ok sti dejai ti tn nantvn ma pistmh, ll' od' ti o do kboi kbow: od' ll pistm t traw, ll' sa otvw xei prw llhla st' enai yteron p yteron, oon t ptik prw gevmetran ka t rmonik prw riymhti- kn. od' e ti prxei taw grammaw m gramma ka k tn rxn tn dvn, oon e kallsth tn grammn eyea e nantvw xei t perifere: o gr t dion gnow atn, prxei, ll' koinn ti. Fanern d ka n sin a protseiw kaylou j n sullogismw, ti ngkh ka t sumprasma dion enai tw toiathw podejevw ka tw plw epen po- dejevw. ok stin ra pdeijiw tn fyartn od' pistmh plw, ll' otvw sper kat sumbebhkw, ti o kay' lou ato stin ll pot ka pw. tan d' , ngkh tn tran m kaylou enai prtasin ka fyartn-fyar- tn mn ti stai ka t sumprasma oshw, m kaylou d ti t mn stai t d' ok stai f' n st' ok sti sul- logsasyai kaylou, ll' ti nn. movw d' xei ka per rismow, peper stn rismw rx podejevw pdeijiw ysei diafrousa sumprasm ti podejevw. a d tn pollkiw ginomnvn podejeiw ka pistmai, oon selnhw klecevw, dlon ti mn toiod' esn, e esn, d' ok e, kat mrow esn. sper d' kleiciw, sa- tvw tow lloiw. Epe d fanern ti kaston podejai ok stin ll' k tn kstou rxn, n t deiknmenon prx keno, ok sti t pstasyai toto, n j lhyn ka napodektvn deixy ka msvn. sti gr otv dejai, sper Brsvn tn tetragvnismn. kat koinn te gr deiknousin o toiotoi lgoi, ka tr prjei: di ka p' llvn far- mttousin o lgoi o suggenn. okon ox keno psta- tai, ll kat sumbebhkw: o gr n frmotten p- deijiw ka p' llo gnow. Ekaston d' pistmeya m kat sumbebhkw, tan kat' keno ginskvmen kay' prxei, k tn rxn tn kenou keno, oon t dusn ryaw saw xein, prxei kay' at t erhmnon, k tn rxn tn totou. st' e kay' at kkeno prxei prxei, ngkh t mson n t at suggene& enai. e d m, ll' w t rmonik di' riymhtikw. t d toiata deknutai mn satvw, diafrei d: t mn gr ti traw pist- mhw (t gr pokemenon gnow teron), t d diti tw nv, w kay' at t pyh stn. ste ka k totvn fanern ti ok stin podejai kaston plw ll' k tn k- stou rxn. ll totvn a rxa xousi t koinn. E d fanern toto, fanern ka ti ok sti tw k- stou daw rxw podejai: sontai gr kenai pntvn rxa, ka pistmh kenvn kura pntvn. ka gr p- statai mllon k tn nteron atvn edw: k tn protrvn gr oden, tan k m atiatn ed atvn. st' e mllon ode ka mlista, kn pistmh kenh eh ka mllon ka mlista. d' pdeijiw ok farmttei p' llo gnow, ll' w erhtai a gevmetrika p tw mhxanikw ptikw ka a riymhtika p tw r- monikw. Xalepn d' st t gnnai e oden m. xalepn gr t gnnai e k tn kstou rxn smen m: per st t ednai. omeya d', n xvmen j lhyinn tinn sullogismn ka prtvn, pstasyai. t d' ok stin, ll suggen de enai tow prtoiw. Lgv d' rxw n kst gnei tataw w ti sti m ndxetai dejai. t mn on shmanei ka t prta ka t k totvn, lambnetai, ti d' sti, tw mn rxw ngkh lambnein, t d' lla deiknnai: oon t monw t t ey ka trgvnon, enai d tn monda laben ka mgeyow, t d' tera deiknnai. Esti d' n xrntai n taw podeiktikaw pistmaiw t mn dia ksthw pistmhw t d koin, koin d kat' nalogan, pe xrsimn ge son n t p tn pistmhn gnei: dia mn oon grammn enai toiand ka t ey, koin d oon t sa p svn n fl, ti sa t loip. kann d' kaston totvn son n t gnei: tat gr poi- sei, kn m kat pntvn lb ll' p megeyn mnon, t d' riymhtik p' riymn. Esti d' dia mn ka lambnetai enai, per pistmh yevre t prxonta kay' at, oon mondaw riymhtik, d gevmetra shmea ka grammw. tata gr lambnousi t enai ka tod enai. t d totvn pyh kay' at, t mn shmanei kaston, lambnousin, oon mn riymhtik t perittn rtion tetrgvnon kbow, d gevmetra t t logon t keklsyai neein, ti d' sti, deiknousi di te tn koinn ka k tn podedei- gmnvn. ka strologa satvw. psa gr podeiktik pistmh per tra stn, sa te enai tyetai (tata d' st t gnow, o tn kay' at payhmtvn st yevrhtik), ka t koin legmena jimata, j n prtvn pode- knusi, ka trton t pyh, n t shmanei kaston lam- bnei. naw mntoi pistmaw odn kvlei nia totvn paro- rn, oon t gnow m potyesyai enai, n fanern ti stin (o gr movw dlon ti riymw sti ka ti cuxrn ka yermn), ka t pyh m lambnein t shmanei, n d- la: sper od t koin o lambnei t shmanei t sa p svn felen, ti gnrimon. ll' odn tton t ge fsei tra tat sti, per te deknusi ka deknusi ka j n. Ok sti d' pyesiw od' athma, ngkh enai di' at ka doken ngkh. o gr prw tn jv lgon p- deijiw, ll prw tn n t cux, pe od sullogismw. e gr stin nstnai prw tn jv lgon, ll prw tn sv lgon ok e. sa mn on deikt nta lambnei a- tw m dejaw, tat', n mn dokonta lambn t man- ynonti, potyetai, ka stin ox plw pyesiw ll prw kenon mnon, n d mhdemiw noshw djhw ka nantaw noshw lambn t at, atetai. ka tot dia- frei pyesiw ka athma: sti gr athma t penanton to manynontow t dj, n tiw podeiktn n lam- bn ka xrtai m dejaw. O mn on roi ok esn poyseiw (odn gr enai m lgetai), ll' n taw protsesin a poyseiw, tow d' rouw mnon junesyai de: toto d' ox pyesiw (e m ka t koein pyesn tiw enai fsei), ll' svn ntvn t kena enai gnetai t sumprasma. (od' gevmtrhw ceud potyetai, sper tinw fasan, lgontew w o de t ce- dei xrsyai, tn d gevmtrhn cedesyai lgonta podi- aan tn o podiaan eyean tn gegrammnhn ok eyean osan. d gevmtrhw odn sumperanetai t tnde enai grammn n atw fyegktai, ll t di totvn dh- lomena.) ti t athma ka pyesiw psa w lon w n mrei, o d' roi odteron totvn. Edh mn on enai n ti par t poll ok ngkh, e pdeijiw stai, enai mntoi n kat polln lhyw e- pen ngkh: o gr stai t kaylou, n m toto : n d t kaylou m , t mson ok stai, st' od' pdeijiw. de ra ti n ka t at p pleinvn enai m mnumon. t d m ndxesyai ma fnai ka pofnai odema lambnei pdeijiw, ll' n d dejai ka t sump- rasma otvw. deknutai d labosi t prton kat to m- sou, ti lhyw, pofnai d' ok lhyw. t d mson o- dn diafrei enai ka m enai laben, w d' atvw ka t trton. e gr dyh, kay' o nyrvpon lhyw epen, e ka m nyrvpon lhyw, ll' e mnon nyrvpon zon e- nai, m zon d m, stai [gr] lhyw epen Kallan, e ka m Kallan, mvw zon, m zon d' o. ation d' ti t prton o mnon kat to msou lgetai ll ka kat' llou di t enai p pleinvn, st' od' e t mson ka at sti ka m at, prw t sumprasma odn diafrei. t d' pan fnai pofnai ew t dnaton pdeijiw lambnei, ka tata od' e kaylou, ll' son kann, kann d' p to gnouw. lgv d' p to gnouw oon per gnow tw podejeiw frei, sper erhtai ka prteron. Epikoinvnosi d psai a pistmai lllaiw kat t koin (koin d lgv ow xrntai w k totvn po- deiknntew, ll' o per n deiknousin od' deiknousin), ka dialektik psaiw, ka e tiw kaylou peirto dei- knnai t koin, oon ti pan fnai pofnai, ti sa p svn, tn toiotvn tta. d dialektik ok stin otvw rismnvn tinn, od gnouw tinw nw. o gr n rta: podeiknnta gr ok stin rvtn di t tn ntikeimnvn ntvn m deknusyai t at. ddeiktai d toto n tow per sullogismo. E d t at stin rthma sullogistikn ka pr- tasiw ntifsevw, protseiw d kay' ksthn pistmhn j n sullogismw kay' ksthn, eh n ti rthma pisthmonikn, j n kay' ksthn okeow gnetai sullo- gismw. dlon ra ti o pn rthma gevmetrikn n eh od' atrikn, movw d ka p tn llvn: ll' j n deknuta ti per n gevmetra stn, k tn atn deknutai t gevmetr&, sper t ptik. movw d ka p tn llvn. ka per mn totvn ka lgon fe- kton k tn gevmetrikn rxn ka sumperasmtvn, per d tn rxn lgon ox fekton t gevmtr gevmtrhw: movw d ka p tn llvn pisthmn. ote pn ra kaston pistmona rthma rvthton, oy' pan t rvtmenon pokriton per kstou, ll t kat tn pistmhn diorisynta. e d dialjetai gevmtr gev- mtrhw otvw, fanern ti ka kalw, n k totvn ti deikn: e d m, o kalw. dlon d' ti od' lgxei gevmtrhn ll' kat sumbebhkw: st' ok n eh n gevmetrtoiw per gevmetraw dialekton: lsei gr falvw dialegmenow. movw d ka p tn llvn xei pisthmn. Epe d' sti gevmetrik rvtmata, r' sti ka gevmtrhta; ka par' ksthn pistmhn t kat tn gnoian tn poan gevmetrik stin; ka pteron kat tn gnoian sullogismw k tn ntikei- mnvn sullogismw, paralogismw, kat gevmetran d, <> j llhw txnhw, oon t mousikn stin rthma gevmtrhton per gevmetraw, t d tw paralllouw sumpptein oesyai gevmetrikn pvw ka gevmtrhton l- lon trpon; dittn gr toto, sper t rruymon, ka t mn teron gevmtrhton t m xein [sper t rruymon], t d' teron t falvw xein: ka gnoia ath ka k tn toiotvn rxn nanta. n d tow maymasin ok stin movw paralogismw, ti t mson stn e t dittn: kat te gr totou pantw, ka toto plin kat' llou lgetai pantw (t d kathgoromenon o lgetai pn), tata d' stin oon rn t nosei, n d tow lgoiw lanynei. ra pw kklow sxma; n d grc, dlon. t d; t ph kklow; fanern ti ok stin. O de d' nstasin ew at frein, n prtasiw paktik. sper gr od prtasw stin m stin p pleinvn (o gr stai p pntvn, k tn kaylou d' sullogisms), dlon ti od' nstasiw. a ata gr pro- tseiw ka nstseiw: n gr frei nstasin, ath gnoit' n prtasiw podeiktik dialektik. Sumbanei d' nouw sullogstvw lgein di t lam- bnein mfotroiw t pmena, oon ka Kainew poie, ti t pr n t pollaplas& nalog&: ka gr t pr tax genntai, w fhsi, ka ath naloga. otv d' ok sti sullogismw: ll' e t taxst nalog& pe- tai pollaplsiow ka t pur taxsth n t kinsei naloga. note mn on ok ndxetai sullogsasyai k tn elhmmnvn, t d' ndxetai, ll' ox rtai. E d' n dnaton k cedouw lhyw dejai, =dion n n t na- lein: ntstrefe gr n j ngkhw. stv gr t A n: totou d' ntow tad stin, oda ti stin, oon t B. k totvn ra dejv ti stin keno. ntistrfei d mllon t n tow maymasin, ti odn sumbebhkw lambnousin (ll ka tot diafrousi tn n tow dialgois) ll' rismow. Ajetai d' o di tn msvn, ll t proslam- bnein, oon t A to B, toto d to G, plin toto to D, ka tot' ew peiron: ka ew t plgion, oon t A ka kat to G ka kat to E, oon stin riymw posw ka peirow toto f' A, perittw riymw posw f' o B, riymw perittw f' o G: stin ra t A kat to G. ka stin rtiow posw riymw f' o D, r- tiow riymw f' o E: stin ra t A kat to E. T d' ti diafrei ka t diti pstasyai, prton mn n t at pistm, ka n tat dixw, na mn trpon n m di' msvn gnhtai sullogismw (o gr lambnetai t prton ation, d to diti pistmh kat t prton ation), llon d e di' msvn mn, ll m di to atou ll tn ntistrefntvn di to gnvri- mvtrou. kvlei gr odn tn ntikathgoroumnvn gnvri- mteron enai note t m ation, st' stai di totou pdeijiw, oon ti ggw o plnhtew di to m stlbein. stv f' G plnhtew, f' B t m stlbein, f' A t ggw enai. lhyw d t B kat to G epen: o gr plnhtew o stlbousin. ll ka t A kat to B: t gr m stlbon ggw sti: toto d' elfyv di' pagv- gw di' asysevw. ngkh on t A t G prxein, st' poddeiktai ti o plnhtew ggw esin. otow on sul- logismw o to diti ll to ti stn: o gr di t m stlbein ggw esin, ll di t ggw enai o stlbousin. gxvre d ka di yatrou yteron deixynai, ka stai to diti pdeijiw, oon stv t G plnhtew, f' B t ggw enai, t A t m stlbein: prxei d ka t B t G ka t A t B, ste ka t G t A [t m stl- bein]. ka sti to diti sullogismw: elhptai gr t prton ation. plin w tn selnhn deiknousin ti sfai- roeidw, di tn ajsevn e gr t ajanmenon otv sfairoeidw, ajnei d' selnh, fanern ti sfairoei- ds otv mn on to ti ggonen sullogismw, npalin d teyntow to msou to diti: o gr di tw ajseiw sfairoeidw stin, ll di t sfairoeidw enai lamb- nei tw ajseiw toiataw. selnh f' G, sfairoeidw f' B, ajhsiw f' A. f' n d t msa m ntistrfei ka sti gnvrimteron t nation, t ti mn deknutai, t diti d' o. Eti f' n t mson jv tyetai. ka gr n totoiw to ti ka o to diti pdeijiw: o gr lgetai t ation. oon di t ok napne toxow; ti o zon. e gr toto to m napnen ation, dei t zon enai ation to napnen, oon e pfasiw ata to m prxein, katfasiw to prxein, sper e t sm- metra enai t yerm ka t cuxr to m gianein, t smmetra enai to gianein, movw d ka e katfa- siw to prxein, pfasiw to m prxein. p d tn otvw podedomnvn o sumbanei t lexyn: o gr pan napne zon. d sullogismw gnetai tw toia- thw ataw n t ms sxmati. oon stv t A zon, f' B t napnen, f' G toxow. t mn on B pant prxei t A (pn gr t napnon zon), t d G o- yen, ste od t B t G oyen: ok ra napne to- xow. okasi d' a toiatai tn atin tow kay' per- boln erhmnoiw: toto d' sti t plon postsanta t m- son epen, oon t to Anaxrsiow, ti n Skyaiw ok e- sn alhtrdew, od gr mpeloi. Kat mn d tn atn pistmhn ka kat tn tn msvn ysin atai diafora esi to ti prw tn to diti sullogismn: llon d trpon diafrei t diti to ti t di' llhw pistmhw kteron yevren. toiata d' stn sa otvw xei prw llhla st' enai yteron p yte- ron, oon t ptik prw gevmetran ka t mhxanik prw stereometran ka t rmonik prw riymhtikn ka t fainmena prw strologikn. sxedn d sunnumo e- sin niai totvn tn pisthmn, oon strologa te ma- yhmatik ka nautik, ka rmonik te mayhmatik ka kat tn kon. ntaya gr t mn ti tn asyh- tikn ednai, t d diti tn mayhmatikn: otoi gr xousi tn atvn tw podejeiw, ka pollkiw ok sasi t ti, ka- yper o t kaylou yevrontew pollkiw nia tn kay' kaston ok sasi di' nepiskecan. sti d tata sa tern ti nta tn osan kxrhtai tow edesin. t gr maymata per edh stn: o gr kay' pokeimnou tinw: e gr ka kay' pokei- mnou tinw t gevmetrik stin, ll' ox ge kay' pokeim- nou. xei d ka prw tn ptikn, w ath prw tn gevme- tran, llh prw tathn, oon t per tw ridow: t mn gr ti fusiko ednai, t d diti ptiko, plw to kat t myhma. polla d ka tn m p' lllaw pisthmn xousin otvw, oon atrik prw gevmetran: ti mn gr t lkh t perifer bradteron gizetai, to atro ednai, diti d to gevmtrou. Tn d sxhmtvn pisthmonikn mlista t prtn stin. a te gr mayhmatika tn pisthmn di totou frousi tw podejeiw, oon riymhtik ka gevmetra ka ptik, ka sxedn w epen sai to diti poiontai tn skcin: gr lvw w p t pol ka n tow ple- stoiw di totou to sxmatow to diti sullogismw. ste kn di tot' eh mlista pisthmonikn: kuritaton gr to ednai t diti yevren. eta tn to t stin pistmhn di mnou totou yhresai dunatn. n mn gr t ms sxmati o gnetai kathgorikw sullogismw, d to t stin pistmh katafsevw: n d t sxt gnetai mn ll' o kaylou, t d t sti tn kaylou stn: o gr p sti zon dpoun nyrvpow. ti toto mn kenvn odn prosdetai, kena d di totou katapuknotai ka ajetai, vw n ew t mesa ly. fanern on ti ku- ritaton to pstasyai t prton sxma. Vsper d prxein t A t B nedxeto tmvw, otv ka m prxein gxvre. lgv d t tmvw prxein m prxein t m enai atn mson: otv gr okti stai kat' llo t prxein m prxein. tan mn on t A t B n l tin , ka mfv, ok ndxetai t A t B prtvw m prxein. stv gr t A n l t G. okon e t B m stin n l t G (gxvre gr t mn A enai n tini l, t d B m enai n tot), sullo- gismw stai to m prxein t A t B: e gr t mn A pant t G, t d B mhden, oden t B t A. movw d ka e t B n l tin stin, oon n t D: t mn gr D pant t B prxei, t d A oden t D, ste t A oden t B prjei di sullogismo. tn atn d trpon deixysetai ka e mfv n l tin stin. ti d' ndxetai t B m enai n l st t A, plin t A n t B, fanern k tn sustoixin, sai m pal- lttousin lllaiw. e gr mhdn tn n t A G D su- stoix& kat mhdenw kathgoretai tn n t B E Z, t d' A n l st t Y sustox nti, fanern ti t B ok stai n t Y: palljousi gr a sustoixai. movw d ka e t B n l tin stin. n d mhdteron n l mhden, m prx d t A t B, ngkh tmvw m prxein. e gr stai ti mson, ngkh yteron a- tn n l tin enai. gr n t prt sxmati n t ms stai sullogismw. e mn on n t prt, t B stai n l tin (katafatikn gr de tn prw toto gensyai prtasin), e d' n t ms, pteron tuxen (prw mfotroiw gr lhfyntow to sterhtiko gnetai sul- logismw: mfotrvn d' pofatikn osn ok stai). Fanern on ti ndxeta te llo ll m prxein t- mvw, ka pt' ndxetai ka pw, erkamen. Agnoia d' m kat' pfasin ll kat diye- sin legomnh sti mn di sullogismo ginomnh pth, ath d' n mn tow prtvw prxousin m prxousi sumbanei dixw: gr tan plw polb prxein m prxein, tan di sullogismo lb tn p- lhcin. tw mn on plw polcevw pl pth, tw d di sullogismo pleouw. m parxtv gr t A mh- den t B tmvw: okon n sullogzhtai prxein t A t B, mson labn t G, pathmnow stai di sul- logismo. ndxetai mn on mfotraw tw protseiw e- nai ceudew, ndxetai d tn tran mnon. e gr mte t A mhden tn G prxei mte t G mhden tn B, e- lhptai d' katra npalin, mfv ceudew sontai. g- xvre d' otvw xein t G prw t A ka B ste mte p t A enai mte kaylou t B. t mn gr B dnaton enai n l tin (prtvw gr lgeto at t A m pr- xein), t d A ok ngkh psi tow osin enai kaylou, st' mfterai ceudew. ll ka tn tran ndxetai lhy lambnein, o mntoi potran tuxen, ll tn A G: gr G B prtasiw e ceudw stai di t n mh- den enai t B, tn d A G gxvre, oon e t A ka t G ka t B prxei tmvw (tan gr prtvw kat- hgortai tat pleinvn, odteron n odetr stai). diaf- rei d' odn, od' e m tmvw prxei. H mn on to prxein pth di totvn te ka otv gnetai mnvw (o gr n n ll sxmati to pr- xein sullogisms), d to m prxein n te t pr- t ka n t ms sxmati. prton on epvmen posa- xw n t prt gnetai, ka pw xousn tn prot- sevn. ndxetai mn on mfotrvn ceudn osn, oon e t A ka t G ka t B prxei tmvw: n gr lhfy t mn A t G mhden, t d G pant t B, ceudew a protseiw. ndxetai d ka tw traw ceudow oshw, ka tathw potraw tuxen. gxvre gr tn mn A G lhy enai, tn d G B ceud, tn mn A G lhy ti o psi tow osin prxei t A, tn d G B ceud ti dnaton prxein t B t G, mhden prxei t A: o gr ti lhyw stai A G prtasiw: ma d, e ka esn mfterai lhyew, ka t sumprasma stai lhyw. ll ka tn G B ndxetai lhy enai tw traw oshw ceudow, oon e t B ka n t G ka n t A stn: ngkh gr yteron p yteron enai, st' n lb t A mhden t G prxein, ceudw stai prtasiw. fa- nern on ti ka tw traw ceudow oshw ka mfon stai ceudw sullogismw. En d t ms sxmati law mn enai tw protseiw mfotraw ceudew ok ndxetai: tan gr t A pant t B prx, odn stai laben t mn tr pant yatr d' oden prjei: de d' otv lambnein tw protseiw ste t mn prxein t d m prxein, eper stai sul- logismw. e on otv lambanmenai ceudew, dlon w nan- tvw npalin jousi: toto d' dnaton. p ti d' ka- tran odn kvlei ceud enai, oon e t G ka t A ka t B tin prxoi: n gr t mn A pant lhfy pr- xon, t d B mhden, ceudew mn mfterai a prot- seiw, o mntoi lai ll' p ti. ka npalin d teyn- tow to sterhtiko satvw. tn d' tran enai ceud ka poteranon ndxetai. gr prxei t A pant, ka t B prxei: n on lhfy t mn A l prxein t G, t d B l m prxein, mn G A lhyw stai, d G B ceudw. plin t B mhden prxei, od t A pant prjei: e gr t A, ka t B: ll' ox pr- xen. n on lhfy t G t mn A l prxein, t d B mhden, mn G B prtasiw lhyw, d' tra ceu- dw. movw d ka metateyntow to sterhtiko. gr mh- den prxei t A, od t B oden prjei: n on lh- fy t G t mn A l m prxein, t d B l prxein, mn G A prtasiw lhyw stai, tra d ceudw. ka plin, pant t B prxei, mhden la- ben t A prxon cedow. ngkh gr, e t B pant, ka t A tin prxein: n on lhfy t mn B pant prxein t G, t d A mhden, mn G B lhyw stai, d G A ceudw. fanern on ti ka mfotrvn osn ceudn ka tw traw mnon stai sullogismw path- tikw n tow tmoiw. En d tow m tmvw prxousin [ m prxou- sin], tan mn di to okeou msou gnhtai to cedouw sullogismw, ox on te mfotraw ceudew enai tw protseiw, ll mnon tn prw t mezoni kr. (lgv d' okeon mson di' o gnetai tw ntifsevw sul- logismw.) parxtv gr t A t B di msou to G. pe on ngkh tn G B katafatikn lambnesyai sul- logismo ginomnou, dlon ti e ath stai lhyw: o gr ntistrfetai. d A G ceudw: tathw gr nti- strefomnhw nantow gnetai sullogismw. movw d ka e j llhw sustoixaw lhfyeh t mson, oon t D e ka n t A l sti ka kat to B kathgoretai pan- tw: ngkh gr tn mn D B prtasin mnein, tn d' tran ntistrfesyai, sy' mn e lhyw, d' e ceudw. ka sxedn ge toiath pth at sti t di to okeou msou. n d m di to okeou msou gnh- tai sullogismw, tan mn p t A t mson, t d B mhden prx, ngkh ceudew enai mfotraw. lhptai gr nantvw w xousin a protseiw, e ml- lei sullogismw sesyai: otv d lambanomnvn mf- terai gnontai ceudew. oon e t mn A l t D pr- xei, t d D mhden tn B: ntistrafntvn gr totvn sullogismw t' stai ka a protseiw mfterai ceu- dew. tan d m p t A t mson, oon t D, mn A D lhyw stai, d D B ceudw. mn gr A D lhyw, ti ok n n t A t D, d D B ceudw, ti e n lhyw, kn t sumprasma n lhyw: ll' n cedow. Di d to msou sxmatow ginomnhw tw pthw, mfotraw mn ok ndxetai ceudew enai tw protseiw law (tan gr t B p t A, odn ndxetai t mn pant t d mhden prxein, kayper lxyh ka prte- ron), tn tran d' gxvre, ka potran tuxen. e gr t G ka t A ka t B prxei, n lhfy t mn A prxein t d B m prxein, mn G A lhyw stai, d' tra ceudw. plin d' e t mn B lhfyeh t G prxon, t d A mhden, mn G B lhyw stai, d' tra ceudw. En mn on sterhtikw tw pthw sullogismw, erhtai pte ka di tnvn stai pth: n d kata- fatikw, tan mn di to okeou msou, dnaton mfot- raw enai ceudew: ngkh gr tn G B mnein, eper stai sullogismw, kayper lxyh ka prteron. ste A G e stai ceudw: ath gr stin ntistrefomnh. movw d ka e j llhw sustoixaw lambnoito t mson, w- per lxyh ka p tw sterhtikw pthw: ngkh gr tn mn D B mnein, tn d' A D ntistrfesyai, ka pth at t prteron. tan d m di to okeou, n mn t D p t A, ath mn stai lhyw, tra d ceudw: gxvre gr t A pleosin prxein ok stin p' llhla. n d m t D p t A, ath mn e dlon ti stai ceudw (katafatik gr lambnetai), tn d D B ndxetai ka lhy enai ka ceud: odn gr kvlei t mn A t D mhden prxein, t d D t B pant, oon zon pistm, pistmh d mousik. od' a mte t A mhden tn D mte t D mhden tn B. [fanern on ti m ntow to msou p t A ka mfo- traw gxvre ceudew enai ka potran tuxen.] Posaxw mn on ka di tnvn gxvre gnesyai tw kat sullogismn ptaw n te tow msoiw ka n tow di' podejevw, fanern. Fanern d ka ti, e tiw asyhsiw klloipen, ngkh ka pistmhn tin kleloipnai, n dnaton laben, eper manynomen pagvg podejei, sti d' mn pdei- jiw k tn kaylou, d' pagvg k tn kat mrow, dnaton d t kaylou yevrsai m di' pagvgw (pe ka t j fairsevw legmena stai di' pagvgw gn- rima poien, ti prxei kst gnei nia, ka e m xv- rist stin, toiond kaston), paxynai d m xontaw a- syhsin dnaton. tn gr kay' kaston asyhsiw: o gr ndxetai laben atn tn pistmhn: ote gr k tn ka- ylou neu pagvgw, ote di' pagvgw neu tw a- sysevw. Esti d pw sullogismw di trin rvn, ka mn deiknnai dunmenow ti prxei t A t G di t pr- xein t B ka toto t G, d sterhtikw, tn mn tran prtasin xvn ti prxei ti llo ll, tn d' tran ti ox prxei. fanern on ti a mn rxa ka a le- gmenai poyseiw ata esi: labnta gr tata otvw ngkh deiknnai, oon ti t A t G prxei di to B, plin d' ti t A t B di' llou msou, ka ti t B t G satvw. kat mn on djan sullogizomnoiw ka mnon dialektikw dlon ti toto mnon skepton, e j n ndxetai ndojottvn gnetai sullogismw, st' e ka m sti ti t lhye& tn A B mson, doke d enai, di totou sullogizmenow sullelgistai dialektikw: prw d' lyeian k tn parxntvn de skopen. xei d' otvw: peid stin at mn kat' llou kathgoretai m kat sumbebhks lgv d t kat sumbebhkw, oon t leu- kn pot' ken famen enai nyrvpon, ox movw lgontew ka tn nyrvpon leukn: mn gr ox tern ti n leu- kw sti, t d leukn, ti sumbbhke t nyrp enai leuk stin on nia toiata ste kay' at kathgoresyai. Estv d t G toioton at mn mhkti prxei ll, tot d t B prt, ka ok stin llo metaj. ka plin t E t Z satvw, ka toto t B. r' on toto ngkh stnai, ndxetai ew peiron ޡnai; ka plin e to mn A mhdn kathgoretai kay' at, t d A t Y prxei prt, metaj d mhden protr, ka t Y t H, ka toto t B, ra ka toto stasyai ngkh, ka tot' ndxetai ew peiron ޡnai; diafrei d toto to pr- teron tosoton, ti t mn stin, ra ndxetai rjamn p toiotou mhden prxei tr ll' llo ken, p t nv ew peiron ޡnai, yteron d rjmenon p toiotou at mn llou, kenou d mhdn kathgoretai, p t ktv skopen e ndxetai ew peiron ޡnai. Eti t metaj r' ndxetai peira enai rismnvn tn krvn; lgv d' oon e t A t G prxei, mson d' atn t B, to d B ka to A tera, totvn d' lla, ra ka tata ew peiron ndxetai ޡnai, dnaton; sti d toto sko- pen tat ka e a podejeiw ew peiron rxontai, ka e stin pdeijiw pantow, prw llhla peranetai. Omovw d lgv ka p tn sterhtikn sullogismn ka protsevn, oon e t A m prxei t B mhden, toi prt, stai ti metaj protr ox prxei (oon e t H, t B prxei pant), ka plin totou ti ll protr, oon e t Y, t H pant prxei. ka gr p totvn peira ow prxei protroiw, statai. Ep d tn ntistrefntvn ox movw xei. o gr stin n tow ntikathgoroumnoiw o prtou kathgoretai teleutaou pnta gr prw pnta tat ge movw xei, et' stn peira t kat' ato kathgoromena, et' mfter sti t porhynta peira: pln e m movw ndxetai nti- strfein, ll t mn w sumbebhkw, t d' w kathgoran. Oti mn on t metaj ok ndxetai peira enai, e p t ktv ka t nv stantai a kathgorai, dlon. lgv d' nv mn tn p t kaylou mllon, ktv d tn p t kat mrow. e gr to A kathgoroumnou kat to Z peira t metaj, f' n B, dlon ti ndxoit' n ste ka p to A p t ktv teron trou kathgo- resyai ew peiron (prn gr p t Z lyen, peira t metaj) ka p to Z p t nv peira, prn p t A lyen. st' e tata dnata, ka to A ka Z dnaton peira enai metaj. od gr e tiw lgoi ti t mn sti tn A B Z xmena lllvn ste m enai metaj, t d' ok sti laben, odn diafrei. gr n lbv tn B, stai prw t A prw t Z peira t metaj o. f' o d prton peira, et' eyw ete m eyw, odn diaf- rei: t gr met tata peir stin. Fanern d ka p tw sterhtikw podejevw ti st- setai, eper p tw kathgorikw statai p' mftera. stv gr m ndexmenon mte p t nv p to st- tou ew peiron ޡnai (lgv d' staton at mn ll mhden prxei, ken d llo, oon t Z) mte p to prtou p t staton (lgv d prton at mn kat' llou, kat' kenou d mhdn llo). e d tat' sti, ka p tw pofsevw stsetai. trixw gr deknutai m prxon. gr mn t G, t B prxei pant, d t B, oden t A. to mn tonun B G, ka e to trou diastmatow, ngkh badzein ew mesa: kathgorikn gr toto t disthma. t d' teron dlon ti e ll ox pr- xei protr, oon t D, toto desei t B pant pr- xein. ka e plin ll to D protr ox prxei, keno desei t D pant prxein. st' pe p t nv sta- tai dw, ka p t A stsetai, ka stai ti prton ox prxei. Plin e t mn B pant t A, t d G mhden, t A tn G oden prxei. plin toto e de de- jai, dlon ti di to nv trpou deixysetai di totou to trtou. mn on prtow erhtai, d dete- row deixysetai. otv d' n deiknoi, oon t D t mn B pant prxei, t d G oden, e ngkh prxein ti t B. ka plin e toto t G m prjei, llo t D prxei, t G ox prxei. okon pe t prxein e t nvtrv statai, stsetai ka t m prxein. O d trtow trpow n: e t mn A t B pant prxei, t d G m prxei, o pant prxei t G t A. p- lin d toto di tn nv erhmnvn movw deixysetai. kenvw mn d statai, e d' otv, plin lcetai t B t E prxein, t G m pant prxei. ka toto p- lin movw. pe d' pkeitai stasyai ka p t ktv, dlon ti stsetai ka t G ox prxon. Fanern d' ti ka n m mi d deiknhtai ll p- saiw, t mn k to prtou sxmatow, t d k to deutrou trtou, ti ka otv stsetai: peperasmnai gr esin a do, t d peperasmna peperasmenkiw ngkh pepe- rnyai pnta. Oti mn on p tw stersevw, eper ka p to pr- xein, statai, dlon. ti d' p' kenvn, logikw mn yevrosin de fanern. Ep mn on tn n t t sti kathgoroumnvn dlon: e gr stin rsasyai e gnvstn t t n enai, t d' peira m sti dielyen, ngkh pepernyai t n t t sti kathgoromena. kaylou d de lgomen. sti gr e- pen lhyw t leukn badzein ka t mga keno jlon enai, ka plin t jlon mga enai ka tn nyrvpon ba- dzein. teron d sti t otvw epen ka t kenvw. tan mn gr t leukn enai f jlon, tte lgv ti sum- bbhke leuk enai jlon stn, ll' ox w t pokeme- non t jl t leukn sti: ka gr ote leukn n oy' per leukn ti gneto jlon, st' ok stin ll' kat sumbe- bhkw. tan d t jlon leukn enai f, ox ti tern t sti leukn, ken d sumbbhke jl enai, oon tan t mousikn leukn enai f (tte gr ti nyrvpow leukw stin, sumbbhken enai mousik, lgv), ll t jlon st t pokemenon, per ka gneto, ox tern ti n per jlon jlon t. e d de nomoyetsai, stv t otv lgein kathgoren, t d' kenvw toi mhdamw kathgoren, kathgoren mn m plw, kat sumbebh- kw d kathgoren. sti d' w mn t leukn t kathgoro- menon, w d t jlon t o kathgoretai. pokesyv d t kathgoromenon kathgoresyai e, o kathgoretai, plw, ll m kat sumbebhkw: otv gr a pode- jeiw podeiknousin. ste n t t stin ti poin po- sn prw ti poion ti psxon po pot, tan n kay' nw kathgorhy. Eti t mn osan shmanonta per keno per ken ti shmanei kay' o kathgoretai: sa d m o- san shmanei, ll kat' llou pokeimnou lgetai m sti mte per keno mte per ken ti, sumbe- bhkta, oon kat to nyrpou t leukn. o gr stin nyrvpow ote per leukn ote per leukn ti, ll zon svw: per gr zn stin nyrvpow. sa d m osan shmanei, de kat tinow pokeimnou kathgoresyai, ka m ena ti leukn ox tern ti n leukn stin. t gr edh xairtv: teretsmat te gr sti, ka e stin, odn prw tn lgon stn: a gr podejeiw per tn toi- otvn esn. Eti e m sti tde tode poithw kkeno totou, mhd poithtow poithw, dnaton ntikathgoresyai lllvn otvw, ll' lhyw mn ndxetai epen, ntikathgorsai d' lhyw ok ndxetai. gr toi w osa kathgorhy- setai, oon gnow n diafor to kathgoroumnou. tata d ddeiktai ti ok stai peira, ot' p t ktv ot' p t nv (oon nyrvpow dpoun, toto zon, toto d' teron: od t zon kat' nyrpou, toto d kat Kallou, toto d kat' llou n t t stin), tn mn gr osan pasan stin rsasyai tn toiathn, t d' peira ok sti diejel- yen noonta. st' ot' p t nv ot' p t ktv peira: kenhn gr ok stin rsasyai w t peira kathgoretai. w mn d gnh lllvn ok ntikathgorhysetai: stai gr at per at ti. od mn to poio tn llvn odn, n m kat sumbebhkw kathgorhy: pnta gr tata sumbbhke ka kat tn osin kathgoretai. ll d ti od' ew t nv peira stai: kstou gr kathgore- tai n shman poin ti posn ti ti tn toiotvn t n t os&: tata d peprantai, ka t gnh tn kathgorin peprantai: gr poin posn prw ti poion psxon po pot. Upkeitai d n kay' nw kathgoresyai, at d atn, sa m t sti, m kat- hgoresyai. sumbebhkta gr sti pnta, ll t mn kay' at, t d kay' teron trpon: tata d pnta kay' pokeimnou tinw kathgoresya famen, t d sumbe- bhkw ok enai pokemenn ti: odn gr tn toiotvn t- yemen enai ox tern ti n lgetai lgetai, ll' at llou ka toto kay' trou. ot' ew t nv ra n kay' nw ot' ew t ktv prxein lexysetai. kay' n mn gr lgetai t sumbebhkta, sa n t o- s& kstou, tata d ok peira: nv d tat te ka t sumbebhkta, mftera ok peira. ngkh ra ena ti o prtn ti kathgoretai ka totou llo, ka toto stasyai ka ena ti okti ote kat' llou protrou ote kat' kenou llo prteron kathgoretai. Ew mn on trpow lgetai podejevw otow, ti d' llow, e n prtera tta kathgoretai, sti totvn p- deijiw, n d' stin pdeijiw, ote bltion xein gxvre prw at to ednai, ot' ednai neu podejevw, e d tde di tnde gnrimon, tde d m smen mhd bltion xomen prw at to ednai, od t di totvn gnrimon pisthsmeya. e on sti ti ednai di' podejevw plw ka m k tinn mhd' j poysevw, ngkh stasyai tw kathgoraw tw metaj. e gr m stantai, ll' stin e to lhfyntow pnv, pntvn stai pdeijiw: st' e t peira m gxvre dielyen, n stin pdeijiw, tat' ok esmeya di' podejevw. e on mhd bltion xomen prw at to ednai, ok stai odn pstasyai di' podejevw plw, ll' j poysevw. Logikw mn on k totvn n tiw pisteseie per to lexyntow, nalutikw d di tnde fanern suntomte- ron, ti ot' p t nv ot' p t ktv peira t kat- hgoromena ndxetai enai n taw podeiktikaw pistmaiw, per n skciw stn. mn gr pdeijw sti tn sa prxei kay' at tow prgmasin. kay' at d dittw: sa te gr [n] kenoiw nuprxei n t t sti, ka ow at n t t stin prxousin atow: oon t riym t perit- tn, prxei mn riym, nuprxei d' atw riy- mw n t lg ato, ka plin plyow t diairetn n t lg t to riymo nuprxei. totvn d' odtera n- dxetai peira enai, oy' w t perittn to riymo (p- lin gr n t peritt llo eh nuprxen pr- xonti: toto d' e sti, prton riymw nuprjei pr- xousin at: e on m ndxetai peira toiata pr- xein n t n, od' p t nv stai peira: ll mn ngkh ge pnta prxein t prt, oon t riym, kkenoiw tn riymn, st' ntistrfonta stai, ll' ox pertenonta): od mn sa n t t stin nuprxei, od tata peira: od gr n eh rsasyai. st' e t mn kathgoromena kay' at pnta lgetai, tata d m peira, staito n t p t nv, ste ka p t ktv. E d' otv, ka t n t metaj do rvn e pe- perasmna. e d toto, dlon dh ka tn podejevn ti ngkh rxw te enai, ka m pntvn enai pdeijin, per famn tinaw lgein kat' rxw. e gr esn rxa, ote pnt' podeikt ot' ew peiron on te badzein: t gr enai totvn poteronon odn llo stn t enai mh- dn disthma meson ka diareton, ll pnta diairet. t gr ntw mbllesyai ron, ll' o t proslam- bnesyai podeknutai t podeiknmenon, st' e tot' ew peiron ndxetai ޡnai, ndxoit' n do rvn peira me- taj enai msa. ll tot' dnaton, e stantai a kat- hgorai p t nv ka t ktv. ti d stantai, ddei- ktai logikw mn prteron, nalutikw d nn. Dedeigmnvn d totvn fanern ti, n ti t at dusn prx, oon t A t te G ka t D, m kat- hgoroumnou yatrou kat yatrou, mhdamw m kat pantw, ti ok e kat koinn ti prjei. oon t so- skele ka t skalhne t dusn ryaw saw xein kat koinn ti prxei ( gr sxm ti, prxei, ka ox teron), toto d' ok e otvw xei. stv gr t B kay' t A t G D prxei. dlon tonun ti ka t B t G ka D kat' llo koinn, kkeno kay' teron, ste do rvn metaj peiroi n mpptoien roi. ll' dna- ton. kat mn tonun koinn ti prxein ok ngkh e t at pleosin, eper stai mesa diastmata. n mn- toi t at gnei ka k tn atn tmvn ngkh tow rouw enai, eper tn kay' at parxntvn stai t koi- nn: o gr n j llou gnouw ew llo diabnai t dei- knmena. Fanern d ka ti, tan t A t B prx, e mn sti ti mson, sti dejai ti t A t B prxei, ka stoixea totou sti tat ka tosay' sa msa stn: a gr mesoi protseiw stoixea, psai a kaylou. e d m stin, okti stin pdeijiw, ll' p tw rxw dw ath stn. movw d ka e t A t B m prxei, e mn stin mson prteron ox prxei, stin p- deijiw, e d m, ok stin, ll' rx, ka stoixea tosat' stin soi roi: a gr totvn protseiw rxa tw po- dejew esin. ka sper niai rxa esin napdeiktoi, ti st tde tod ka prxei tde td, otv ka ti ok sti tde tod od' prxei tde td, sy' a mn ena ti, a d m ena ti sontai rxa. Otan d d dejai, lhpton to B prton kathgoretai. stv t G, ka totou movw t D. ka otvw e badzonti odpot' jvtrv prtasiw od' prxon lambnetai to A n t deiknnai, ll' e t mson puknotai, vw diareta gnhtai ka n. sti d' n tan meson gnhtai, ka ma prtasiw plw me- sow. ka sper n tow lloiw rx plon, toto d' o tat pantaxo, ll' n brei mn mn, n d mlei desiw, llo d' n ll, otvw n sullogism t n prtasiw mesow, n d' podejei ka pistm now. n mn on tow deiktikow sullogismow to prxontow odn jv pptei, n d tow sterhtikow, nya mn de prxein, odn totou jv pptei, oon e t A t B di to G m (e gr t mn B pant t G, t d G mhden t A): p- lin n d ti t G t A oden prxei, mson lhpton to A ka G, ka otvw e poresetai. n d d dejai ti t D t E ox prxei t t G t mn D pant prxein, t d E mhden [ m pant], to E odpot' jv pesetai: toto d' stn de prxein. p d to trtou trpou, ote f' o de ote de stersai odpot' jv badietai. Oshw d' podejevw tw mn kaylou tw d kat mrow, ka tw mn kathgorikw tw d sterhtikw, mfi- sbhtetai potra beltvn: w d' atvw ka per tw po- deiknnai legomnhw ka tw ew t dnaton goshw po- dejevw. prton mn on piskecmeya per tw kaylou ka tw kat mrow: dhlsantew d toto, ka per tw deiknnai legomnhw ka tw ew t dnaton epvmen. Djeie mn on tx' n tisin d skoposin kat mrow enai beltvn. e gr kay' n mllon pistmeya pdeijin beltvn pdeijiw (ath gr ret podejevs), mllon d' pistmeya kaston tan at edmen kay' at tan kat' llo (oon tn mousikn Korskon tan ti Korskow mousikw tan ti nyrvpow mousikw: movw d ka p tn llvn), d kaylou ti llo, ox ti at tetxhken pideknusin (oon ti t soskelw ox ti soskelw ll' ti trgvnon), d kat mrow ti at: e d beltvn mn kay' at, toiath d' kat mrow tw kaylou mllon, ka beltvn n kat mrow pdeijiw eh. ti e t mn kaylou m sti ti par t kay' kasta, d' pdeijiw djan mpoie ena ti toto kay' pode- knusi, ka tina fsin prxein n tow osi tathn, oon trignou par t tin ka sxmatow par t tin ka riymo par tow tinw riymow, beltvn d' per n- tow m ntow ka di' n m pathysetai di' n, sti d' mn kaylou toiath (prontew gr deiknousin sper per to n lgon, oon ti n ti toioton stai n lgon ote gramm ot' riymw ote steren ot' p- pedon, ll par tat ti): e on kaylou mn mllon ath, per ntow d' tton tw kat mrow ka mpoie djan ceud, xervn n eh kaylou tw kat mrow. H prton mn odn mllon p to kaylou to kat mrow terow lgow stn; e gr t dusn ryaw prxei m soskelw ll' trgvnon, edw ti soskelw t- ton oden at edw ti trgvnon. lvw te, e mn m ntow trgvnon eta deknusin, ok n eh pdeijiw, e d ntow, edw kaston kaston prxei mllon oden. e d t trgvnon p plon st, ka atw lgow, ka m kay' mvnuman t trgvnon, ka prxei pant trign t do, ok n t trgvnon soskelw, ll t soskelw trgvnon, xoi toiataw tw gvnaw. ste kaylou edw mllon oden prxei kat mrow. beltvn ra kay- lou tw kat mrow. ti e mn eh tiw lgow ew ka m mvnuma t kaylou, eh t' n odn tton nvn tn kat mrow, ll ka mllon, s t fyarta n kenoiw st, t d kat mrow fyart mllon, ti te odema ngkh polambnein ti enai toto par tata, ti n dh- lo, odn mllon p tn llvn sa m t shmanei ll' poin prw ti poien. e d ra, ox pdei- jiw ata ll' kovn. Eti e pdeijiw mn sti sullogismw deiktikw a- taw ka to di t, t kaylou d' atiteron ( gr kay' at prxei ti, toto at at ation: t d kaylou prton: ation ra t kaylou): ste ka pdeijiw bel- tvn: mllon gr to atou ka to di t stin. Eti mxri totou zhtomen t di t, ka tte omeya ednai, tan m ti ti llo toto ginmenon n: tlow gr ka praw t sxaton dh otvw stn. oon tnow neka lyen; pvw lb trgrion, toto d' pvw pod feile, toto d' pvw m diks: ka otvw ntew, tan mhkti di' llo mhd' llou neka, di toto w tlow famn l- yen ka enai ka gnesyai, ka tte ednai mlista di t lyen. e d movw xei p pasn tn atin ka tn di t, p d tn sa atia otvw w o neka otvw smen mlista, ka p tn llvn ra tte mlista smen, tan mhkti prx toto ti llo. tan mn on ginskvmen ti tttarsin a jv sai ti soskelw, ti lepetai di t t soskels ti trgvnon, ka toto, ti sxma e- ygrammon. e d toto mhkti diti llo, tte mlista smen. ka kaylou d tte: kaylou ra beltvn. Eti s n mllon kat mrow , ew t peira mpptei, d kaylou ew t plon ka t praw. sti d', mn peira, ok pistht, d peprantai, pistht. ra ka- ylou, mllon pistht kat mrow. podeikt ra mllon t kaylou. tn d' podeiktn mllon mllon pdeijiw: ma gr mllon t prw ti. beltvn ra kaylou, peper ka mllon pdeijiw. Eti e aretvtra kay' n toto ka llo kay' n toto mnon oden: d tn kaylou xvn ode ka t kat mrow, otow d tn kay- lou ok oden: ste kn otvw aretvtra eh. Eti d de. t gr kaylou mllon deiknnai st t di msou dei- knnai ggutrv ntow tw rxw. gguttv d t me- son: toto d' rx. e on j rxw tw m j rxw, mllon j rxw tw tton kribestra pdeijiw. sti d toiath kaylou mllon: krettvn n eh ka- ylou. oon e dei podejai t A kat to D: msa t f' n B G: nvtrv d t B, ste di totou kaylou mllon. All tn mn erhmnvn nia logik sti: mlista d dlon ti kaylou kurivtra, ti tn protsevn tn mn protran xontew smen pvw ka tn stran ka xomen dunmei, oon e tiw oden ti pn trgvnon dusn ryaw, od pvw ka t soskelw ti do ryaw, dunmei, ka e m ode t soskelw ti trgvnon: d tathn xvn tn prtasin t kaylou odamw oden, ote dunmei ot' nerge&. ka mn kaylou noht, d kat mrow ew asyhsin teleut. Oti mn on kaylou beltvn tw kat mrow, to- say' mn ersyv: ti d' deiktik tw sterhtikw, nte- yen dlon. stv gr ath pdeijiw beltvn tn llvn tn atn parxntvn, j lattnvn athmtvn po- ysevn protsevn. e gr gnrimoi movw, t ytton gnnai di totvn prjei: toto d' aretteron. lgow d tw protsevw, ti beltvn j lattnvn, kaylou de: e gr movw eh t gnrima enai t msa, t d pr- tera gnvrimtera, stv mn di msvn pdeijiw tn B G D ti t A t E prxei, d di tn Z H ti t A t E. movw d xei t ti t A t D prxei ka t A t E. t d' ti t A t D prteron ka gnv- rimteron ti t A t E: di gr totou keno po- deknutai, pistteron d t di' o. ka di tn lat- tnvn ra pdeijiw beltvn tn llvn tn atn par- xntvn. mfterai mn on di te rvn trin ka prot- sevn do deknuntai, ll' mn ena ti lambnei, d ka enai ka m ena ti: di pleinvn ra, ste xervn. Eti peid ddeiktai ti dnaton mfotrvn osn sterhtikn tn protsevn gensyai sullogismn, ll tn mn de toiathn enai, tn d' ti prxei, ti prw tot de tde laben. tw mn gr kathgorikw ajanomnhw tw podejevw nagkaon gnesyai pleouw, tw d sterhtikw dnaton pleouw enai miw n panti sullogism. stv gr mhden prxon t A f' svn t B, t d G pr- xon pant t B. n d d plin ajein mfotraw tw protseiw, mson mblhton. to mn A B stv t D, to d B G t E. t mn d E fanern ti kathgorikn, t d D to mn B kathgorikn, prw d t A sterhtikn ketai. t mn gr D pantw to B, t d A oden de tn D prxein. gnetai on ma sterhtik prtasiw t A D. d' atw trpow ka p tn trvn sullogismn. e gr t mson tn kathgorikn rvn kathgorikn p' mftera: to d sterhtiko p ytera sterhtikn nagkaon enai, ste ath ma toiath gnetai prtasiw, a d' llai kathgo- rika. e d gnvrimteron di' o deknutai ka pistteron, deknutai d' mn sterhtik di tw kathgorikw, ath d di' kenhw o deknutai, protra ka gnvrimvtra osa ka pistotra beltvn n eh. ti e rx sullogismo kaylou prtasiw mesow, sti d' n mn t deiktik kata- fatik n d t sterhtik pofatik kaylou pr- tasiw, d katafatik tw pofatikw protra ka gnvrimvtra (di gr tn katfasin pfasiw gn- rimow, ka protra katfasiw, sper ka t enai to m enai): ste beltvn rx tw deiktikw tw sterhtikw: d beltosin rxaw xrvmnh beltvn. ti rxoeidestra: neu gr tw deiknuoshw ok stin ste- rhtik. Epe d' kathgorik tw sterhtikw beltvn, dlon ti ka tw ew t dnaton goshw. de d' ednai tw diafor atn. stv d t A mhden prxon t B, t d G t B pant: ngkh d t G mhden prxein t A. otv mn on lhfyntvn deiktik sterhtik n eh pdeijiw ti t A t G ox prxei. d' ew t dnaton d' xei. e doi dejai ti t A t B ox prxei, lhpton prxein, ka t B t G, ste sumbanei t A t G prxein. toto d' stv gnrimon ka mologomenon ti dnaton. ok ra on te t A t B prxein. e on t B t G mologetai prxein, t A t B dnaton pr- xein. o mn on roi movw tttontai, diafrei d t potra n gnvrimvtra prtasiw sterhtik, pteron ti t A t B ox prxei ti t A t G. tan mn on t sumprasma gnvrimteron ti ok stin, ew t dnaton gnetai pdeijiw, tan d' n t sullogism, podeiktik. fsei d protra ti t A t B ti t A t G. prtera gr sti to sumpersmatow j n t sumprasma: sti d t mn A t G m prxein sum- prasma, t d A t B j o t sumprasma. o gr e sumbanei nairesya ti, toto sumprasm stin, kena d j n, ll t mn j o sullogismw stin n otvw x ste lon prw mrow mrow prw lon xein, a d t A G ka B G protseiw ok xousin otv prw lllaw. e on k gnvrimvtrvn ka protrvn krettvn, es d' mfterai k to m ena ti pista, ll' mn k protrou d' j strou, beltvn plw n eh tw ew t dnaton sterhtik pdeijiw, ste ka tathw beltvn kathgorik dlon ti ka tw ew t dnatn sti beltvn. Akribestra d' pistmh pistmhw ka protra te to ti ka diti at, ll m xvrw to ti tw to diti, ka m kay' pokeimnou tw kay' pokeimnou, oon riymhtik rmonikw, ka j lattnvn tw k prow- ysevw, oon gevmetraw riymhtik. lgv d' k prosy- sevw, oon monw osa yetow, stigm d osa yetw: ta- thn k prosysevw. Ma d' pistmh stn nw gnouw, sa k tn pr- tvn sgkeitai ka mrh stn pyh totvn kay' at. tra d' pistmh stn traw, svn a rxa mt' k tn a- tn my' terai k tn trvn. totou d shmeon, tan ew t napdeikta ly: de gr at n t at gnei e- nai tow podedeigmnoiw. shmeon d ka totou, tan t deiknmena di' atn n tat gnei si ka suggen. Pleouw d' podejeiw enai to ato gxvre o mnon k tw atw sustoixaw lambnonti m t sunexw mson, oon tn A B t G ka D ka Z, ll ka j traw. oon stv t A metabllein, t d' f' D kinesyai, t d B desyai, ka plin t H remzesyai. lhyw on ka t D to B ka t A to D kathgoren: gr dmenow kinetai ka t kinomenon metabllei. plin t A to H ka t H to B lhyw kathgoren: pw gr dmenow remzetai ka remizmenow metabllei. ste di' trvn msvn ka ok k tw atw sustoixaw sullogismw. o mn ste mh- dteron kat mhdetrou lgesyai tn msvn: ngkh gr t at tini mfv prxein. piskcasyai d ka di tn llvn sxhmtvn saxw ndxetai to ato gensyai sullogismn. To d' p txhw ok stin pistmh di' podejevw. ote gr w nagkaon oy' w p t pol t p txhw stn, ll t par tata ginmenon: d' pdeijiw ya- trou totvn. pw gr sullogismw di' nagkavn di tn w p t pol protsevn: ka e mn a prot- seiw nagkaai, ka t sumprasma nagkaon, e d' w p t pol, ka t sumprasma toioton. st' e t p txhw my' w p t pol mt' nagkaon, ok n eh ato pdeijiw. Od di' asysevw stin pstasyai. e gr ka stin asyhsiw to toiode ka m tod tinow, ll' asynesya ge nagkaon tde ti ka po ka nn. t d kaylou ka p psin dnaton asynesyai: o gr tde od nn: o gr n n kaylou: t gr e ka pantaxo kaylou famn enai. pe on a mn podejeiw kaylou, tata d' ok stin asynesyai, fanern ti od' pstasyai di' asy- sevw stin, ll dlon ti ka e n asynesyai t tr- gvnon ti dusn ryaw saw xei tw gvnaw, zhtomen n pdeijin ka ox sper fas tinew pistmeya: asyne- syai mn gr ngkh kay' kaston, d' pistmh t t kaylou gnvrzein stn. di ka e p tw selnhw ntew vrmen ntifrttousan tn gn, ok n deimen tn atan tw klecevw. syanmeya gr n ti nn klepei, ka o diti lvw: o gr n to kaylou asyhsiw. o mn ll' k to yevren toto pollkiw sumbanon t kaylou n yh- resantew pdeijin exomen: k gr tn kay' kasta plei- nvn t kaylou dlon. t d kaylou tmion, ti dhlo t ation: ste per tn toiotvn kaylou timivtra tn a- sysevn ka tw nosevw, svn teron t ation: per d tn prtvn llow lgow. Fanern on ti dnaton t asynesyai pstasya ti tn podeiktn, e m tiw t asynesyai toto lgei, t pistmhn xein di' podejevw. sti mntoi nia nagmena ew asysevw kleicin n tow problmasin. nia gr e vrmen ok n zhtomen, ox w edtew t rn, ll' w xontew t kaylou k to rn. oon e tn alon tetruph- mnhn vrmen ka t fw diin, dlon n n ka di t kaei, t rn mn xvrw f' ksthw, nosai d' ma ti p pasn otvw. Tw d' atw rxw pntvn enai tn sullogismn dnaton, prton mn logikw yevrosin. o mn gr lh- yew esi tn sullogismn, o d ceudew. ka gr e stin lhyw k ceudn sullogsasyai, ll' paj toto gnetai, oon e t A kat to G lhyw, t d mson t B ce- dow: ote gr t A t B prxei ote t B t G. ll' n totvn msa lambnhtai tn protsevn, ceudew sontai di t pn sumprasma cedow k ceudn enai, t d' lhy j lhyn, tera d t ceud ka tlhy. eta od t ceud k tn atn autow: sti gr ceud llloiw ka nanta ka dnata ma enai, oon t tn dikaiosnhn enai dikan deilan, ka tn nyrvpon ppon bon, t son mezon latton. Ek d tn keimnvn de: od gr tn lhyn a ata rxa pntvn. terai gr polln t gnei a rxa, ka od' farmttousai, oon a mondew taw stigmaw ok farmttousin: a mn gr ok xousi ysin, a d xousin. ngkh d ge ew msa rmttein nvyen ktvyen, tow mn esv xein tow d' jv tn rvn. ll' od tn koinn rxn on t' ena tinaw j n panta deixysetai: lgv d koinw oon t pn fnai pofnai. t gr gnh tn ntvn tera, ka t mn tow posow t d tow poiow prxei mnoiw, mey' n deknutai di tn koinn. ti a rxa o poll lttouw tn sumperasmtvn: rxa mn gr a protseiw, a d protseiw proslambanomnou rou m- ballomnou esn. ti t sumpersmata peira, o d' roi peperasmnoi. ti a rxa a mn j ngkhw, a d' n- dexmenai. Otv mn on skopoumnoiw dnaton tw atw enai peperasmnaw, pervn ntvn tn sumperasmtvn. e d' llvw pvw lgoi tiw, oon ti ad mn gevmetraw ad d logismn ad d atrikw, t n eh t legmenon llo pln ti esn rxa tn pisthmn; t d tw atw f- nai geloon, ti ata ataw a ata: pnta gr otv ggnetai tat. ll mn od t j pntvn deknusyai tion, tot' st t zhten pntvn enai tw atw rxw: lan gr ehyew. ote gr n tow fanerow maymasi toto gnetai, ot' n t nalsei dunatn: a gr mesoi pro- tseiw rxa, teron d sumprasma proslhfyeshw gne- tai protsevw msou. e d lgoi tiw tw prtaw msouw protseiw, tataw enai rxw, ma n kst gnei stn. e d mt' j pasn w don deknusyai tion my' otvw t- raw sy' ksthw pistmhw enai traw, lepetai e sug- genew a rxa pntvn, ll' k tvnd mn tad, k d tvnd tad. fanern d ka toy' ti ok ndxetai: ddei- ktai gr ti llai rxa t gnei esn a tn diaf- rvn t gnei. a gr rxa ditta, j n te ka per : a mn on j n koina, a d per diai, oon riymw, mgeyow. T d' pisthtn ka pistmh diafrei to dojasto ka djhw, ti mn pistmh kaylou ka di' nagkavn, t d' nagkaon ok ndxetai llvw xein. sti d tina lhy mn ka nta, ndexmena d ka llvw xein. dlon on ti per mn tata pistmh ok stin: eh gr n dnata llvw xein t dunat llvw xein. ll mn od now (lgv gr non rxn pistmhs) od' pistmh napdeiktow: toto d' stn plhciw tw msou protsevw. lhyw d' st now ka pistmh ka dja ka t di totvn leg- menon: ste lepetai djan enai per t lhyw mn ce- dow, ndexmenon d ka llvw xein. toto d' stn p- lhciw tw msou protsevw ka m nagkaaw. ka mo- logomenon d' otv tow fainomnoiw: te gr dja b- baion, ka fsiw toiath. prw d totoiw odew oe- tai dojzein, tan ohtai dnaton llvw xein, ll' p- stasyai: ll' tan enai mn otvw, o mn ll ka llvw odn kvlein, tte dojzein, w to mn toiotou djan osan, to d' nagkaou pistmhn. Pw on sti t at dojsai ka pstasyai, ka di t ok stai dja pistmh, e tiw ysei pan oden n- dxesyai dojzein; kolouysei gr mn edw d doj- zvn di tn msvn, vw ew t mesa ly, st' eper kenow ode, ka dojzvn oden. sper gr ka t ti dojzein sti, ka t diti: toto d t mson. e mn otvw polcetai t m ndexmena llvw xein sper [xei] tow rismow di' n a podejeiw, o dojsei ll' pi- stsetai: e d' lhy mn enai, o mntoi tat ge atow prxein kat' osan ka kat t edow, dojsei ka ok pistsetai lhyw, ka t ti ka t diti, n mn di tn msvn dojs: n d m di tn msvn, t ti mnon dojsei; to d' ato dja ka pistmh o pntvw stn, ll' sper ka ceudw ka lhyw to ato tr- pon tin, otv ka pistmh ka dja to ato. ka gr djan lhy ka ceud w mn tinew lgousi to ato enai, topa sumbanei aresyai lla te ka m doj- zein dojzei ceudw: pe d t at pleonaxw lge- tai, stin w ndxetai, sti d' w o. t mn gr smmetron enai tn dimetron lhyw dojzein topon: ll' ti dimetrow, per n a djai, t at, otv to ato, t d t n enai katr kat tn lgon o t at. movw d ka pistmh ka dja to ato. mn gr otvw to zou ste m ndxesyai m enai zon, d' st' ndxesyai, oon e mn per nyrpou stn, d' nyrpou mn, m per d' nyrpou. t at gr ti n- yrvpow, t d' w o t at. Fanern d' k totvn ti od dojzein ma t at ka pstasyai ndxetai. ma gr n xoi plhcin to llvw xein ka m llvw t at: per ok ndxetai. n ll mn gr kteron enai ndxetai to ato w e- rhtai, n d t at od' otvw on te: jei gr plh- cin ma, oon ti nyrvpow per zon (toto gr n t m ndxesyai enai m zon) ka m per zon: toto gr stv t ndxesyai. T d loip pw de dianemai p te dianoaw ka no ka pistmhw ka txnhw ka fronsevw ka sofaw, t mn fusikw t d yikw yevraw mlln stin. H d' gxnoi stin estoxa tiw n skpt xrn to msou, oon e tiw dn ti selnh t lamprn e xei prw tn lion, tax nenhse di t toto, ti di t lm- pein p to lou: dialegmenon plous gnv diti da- nezetai: diti floi, ti xyro to ato. pnta gr t atia t msa [] dn t kra gnrisen. t lamprn enai t prw tn lion f' o A, t lmpein p to lou B, selnh t G. prxei d t mn seln t G t B, t lmpein p to lou: t d B t A, t prw tot' enai t lamprn, f' o lmpei: ste ka t G t A di to B.

Analitici secondi B

Copyright 2002 Giovanni Ferrero