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Система философии математики Аристотеля

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A?enoioaeue ?iaeeeny a 384a. ae.i.y. a a?a/aneii ai?iaea Noaae?a.
Aeoaieia i?iaeioeeaeueiia i?ienoiaeaeaiea A?enoioaeyeiiiaine?iaaeinue
oai, /oi ii aue nuiii ecaanoiiai a?a/a Ieeiiaoa.Auoue a?a/ai
icia/aei a Ae?aaiae A?aoeee caieiaoue aieueoia iauanoaaiiia
iieiaeaiea, e Ieeiiao aue ecaanoai anae Iaeaaeiiee. A?enoioaeue, ii
neiaai i/aaeaeoeaa, n iieiaeinoe aueiaac?a/iiai
aeaea.Ooaeiuaaue,eiae ooaeua iiae, iaeaiueeea aeaceee oaiaeyaee.Ii caoi
ethaee iaeaoueny, iinee ii ianeieueei aei?iaeoia?noiae e aeaeae
iaiau/ioth i?e/aneo. Ainieouaaynue a naiueaa?a/a, e iiyoiio nai
caieiaynue iaaeaoeeiie, A?enoioaeue, iaeiaei,ia noae i?iooaneiiaeueiui
a?a/ai. Ii iaaeaoeeia inoaeanue aeeyiaai ia anth aeeciue ianoieueei
?iaeiie e iiiyoiie iaeanoueth, /oi aiineaaenoaee a naieo o?oaeiaeoeo
oeeinianeeo o?aeoaoao ii aeaaoiiyniaiey ia i?eia?ao ec iaaeeoeeineie
i?aeoeee. I?eaoaa n naaa?a A?aoeee, A?enoioaeue a naiii ?aiiai
aic?anoa (a 17eao ) aioae a oeieo Ieaoiia.Ii aue nia?aa
i?eioeeieaeueiui ieaoiieeii, a aiineaaenoaee ioioae io no?iaiai
ieaoiiecia. Ia?aua ni/eiaiey A?enoioaey a noaiao Ieaoiiianeie
Aeaaeaiee, eoaea ii iinooiaao, ioee/athony neeiiiinoueth aai
e ?eoi?eea,eioi?ie ii aiineaaenoaee i?icaieiaeny anth aeeciue. A
364 aiaeo aei i.y. A?enoioaeue ano?a/aaony n Ieaoiiii, e iie
iauaeenue aei naiie nia?oe Ieaoiia, o.a. a oa/aiee 17 eao.
A?enoioaeue i?aaenoaaeyeny Ieaoiio ?aoeaui eiiai, eioi?iai
i?eoiaeeony naea?aeeaaoue ocaeie.Iaeioi?ua aioe/iua enoi/ieee i?yii
aiai?yo ia oieueei i ?anoiaeaeaiee, ii e aeaaea i iai?eycie iaaeaeo
aeaoiy oeeinioaie. Ieaoii neeueii ia iaeia?ye naienoaaiiie A?enoioaeth
iaia?u aea?aeaoue naay e iaeaaaoueny.A?enoioaeue i?eaeaaae
aieueoia aieiaiea naiaio aiaoiaio aeaeo, a Ieaoii n/eoae ,/oi yoi
iai?eaieaii enoeiiiio oeeinioo. Ii A?enoioaeue ii – aeaeeiiio aua e
aea?cei iaiaaeae ia Ieaoiia, /oi a aeaeueiaeoai i?eaaei e
nicaeaieth A?enoioaeai nianoaaiiie oeieu.Ca ana yoe nii?u,
aeia?iaeooiue Ieaoii neacae, /oi “A?enoioaeue iaiy a?ueaao, eae
ninoiie aea?aaaiie naith iaoue”.A Ieaoiiianeie oeiea A?enoioaeue
iieo/aao aaaeiaeoea iniiau ciaiee, iaeaaeay eioi?uie, aiineaaenoaee,
ii ioe?uaaao iai?ioea Ieaoiiiaie naith nianoaaiioth oeieo, e
noaiiaeony caacyoui i?ioeaieeii naiaai o/eoaey. Eiy A?enoioaey a
ie?iaie eeoa?aoo?a iaiin?aaenoaaiii naycaii n eiaiai Ieaoiia.Iii?iaoai
?anniio?aoue oeeinioeth A?enoioaey e niioianoe aa n oeeinioeae
Ieaoiia. Oeaio?aeueiay eaeay oeeinioee Ieaoiia – yeaein – ia?aoea e
A?enoioaeth ii/oe oeaeeeii.Ie Ieaoii, ie A?enoioaeue ia iuneeo
aauae aac eo eaeae, eee yeaeinia. Any oeeinioey Nie?aoa, a caoai e
Ieaoiia i?ienoaeaea ec i?aeoeee e aeeciaiiie iaiaoiaeeiinoe,
auoiaey a /enoi oai?aoe/aneoth iaeanoue eeoue a aunoai naiai
i?iyaeaiee – a o/aiee ia eaeayo. Ii Ieaoiio, ie? aauae ,
aini?eieiaaiue iin?aaenoaii /oanoa, ia anoue ie? enoeiii
nouanoaothuaai: /oanaaiiua aaue iai?a?uaii ?iaeaeathony e iiaeaatho,
eciaiythony e aeaeaeoony, a ieo iao ie/aai iinoiyiiiai,
i?i/iiai, niaa?oaiiiai e enoeiiiai.E ana aea aaue ia iieiinoueth
ioaeaeaiu io enoeiii nouanoaothuaai, iie ana eaeei-oi ia?acii i?e/anoiu
aio.A eiaiii: anai,/oi a ieo anoue enoeiii nouiiai, ooaa?aeaeaao
Ieaoii,/oanoaaiiua aaue iaycaiu naiei i?e/eiai.Yoe i?e/eiu – oi?iu
aauae, ia aini?eieiaaiua /oanoaaie, iinoeaaaiua oieueei oiii,
aanoaeaniua e aan/onoaaiiua.Ieaoii iacuaaao eo “aeaeaie” eee ai?acaei
?aaea “eaeayie”.”Aeaeu”,”eaeae” c?eiua oiii oi?iu aauae.Eaaeaeiio
eeanno i?aaeiaoia /oanoaaiiiai ie?a, iai?eia? eeanno “eiiae”
niioaaonoaoao a aanoaeaniii ie?a iaeioi?ue “aeae”, eee “eaeay” –
“aeae” eiiy,”eaeay” eiiy. Yoio “aeae” oaea ia iiaeao auoue iinoeaaai
/oanoaaie, eae iau/iue eiiue, ii iiaeao auoue eeoue nica?oeaai
oiii, e oiio aea oiii, oi?ioi iiaeaioiaeaiiui e oaeiio
iinoeaeaieth. Yoe “eaeae” eee, “yeaeinu” ia ?iaeaeathony, ia oie?atho,
ia ia?aoiaeyo ia a eaeia ae?oaia ninoiyiea. Nouanoaoao “oea?noai
eaeae” 1.Eaeae aunoeo ii oeaiinoe eaoaai?ee auoey. Nthaea aoiaeyo
oaeea iiiyoey, eae e?anioa, ni?aaaaeeeainoue, enoeia. 2.Aeaeaeaiea
oece/aneeo yaeaiee – eaeae aeaeaeaiey, iieiy, naaoa, caoea e o.i.
3.Eaeae ?ac?yaeia nouanoa – eaeae aeeaioiiai,/aeiaaea. 4.Eaeae aeey
i?aaeiaoia i?iecaiaeeiuo /aeiaa/aneeie oneeeyie – eaeae noiea,e?iaaoe
e o.i. 5.Eaeae iaoee – eaeae /enae, ?aaainoaa,ioiioaiey.
I?eioeeiu nouanoaiaaiey eaeae: a)eaeath aeaeaao eaeay; a)eaeay
yaeyaony ia?acoeii , ace?ay ia eioi?ua, Aeaieo? oai?ee ie? aauae; a)
eaeay yaeyaony oeaeueth, e eioi?ie eae e aunoaio aeaao no?aieony
ana nouanoaothuaa. Ie? aauae e ie? eaeae iauaaeeiyao aeooa Einiina.
Iia canoaaeyao eaeae i?enoonoaiaaoue a aauao e iaiai?io. Iaaeaeo ie?ii
aauae e ie?ii eaeae – aiaeanoai – Aeaieo?. A?enoioaeue ?aoeoaeueii
e?eoeeoao i?eioeeieaeueiue io?ua eaeae aaue io naiie aaue. Eaeay
aaue, ii A?enoioaeth iaoiaeeony aioo?e naiie aea aaue.Oacen i i?aauaaiee
eaeae aaue aioo?e naiie aea aaue anoue oi iniiaiia e
i?eioeeieaeueiia, a /ai caeeth/aaony iniiaiia ?acee/ea iaaeaeo
Ieaoiiianeie e A?enoioaeaaneie oeieao. Eaeay aaue, ii A?enoioaeth
,iaycaoaeueii anoue iaeioi?iai ?iaea iauiinoue, o.a. yeaein ai anao
niuneao. Ii yeaein aaue ,anoue ia oieueei iaiauaiiinoue aa
ioaeaeueiuo yeaiaioia. Ii i?aaenoaeeyao niaie aua e ia/oi
aaeeie/iia.Yoie aaeeie/iinoueth aeaiiue yeaein aaue ioee/aaony io
ae?oaeo yeaeinia, e , neaaeiaaoaeueii, io anyeeo ae?oaeo aauae.
Yeaein aaue, aoaeo/e iaeie iauiinoueth e iaeie aaeeie/iinoueth, a
oi aea naiia a?aiy yaeyaony e ii?aaeaeaiiiai ?iaea
oeaeueiinoueth. Niaa?oaiii iaaiciiaeii io?uaaoue iauaa io
aaeeie/iiaie,aaeeie/iia io iauaai.O.a. oaeaeea eaeie-oi iaeei iiiaio
oeaeueiinoe , oai naiui iu eeeaeaee?oai naio oeaeueiinoue.Niya,e
i?eia?o e?uoo n aeiia, aeii ia?anoaao auoue oeaeueiui, e nianoaaiii
aiai?y ia?anoaao auoue aeiiii. Naia o/aiea i aaue eae i?aaiecia
A?enoioaeue eceaaae iiiai ?ac e ?aciuie niiniaaie.Ii auaeaeyao
/aou?a i?e/eiu,eee /aou?a i?eioeeia ethaie aaue , iiieiaaiie eae
i?aaieci. Ia?aue i?eioeei – i oii, /oi yeaein aaue aiana ia yaeyaony
aa caiaaaniie nouiinoueth, ii oaeie aa nouiinoueth, eioi?ay
iaoiaeeony a iae oa naiie e aac eioi?ie aiiaua iaeuecy iiiyoue, /oi
oaeia aeaiiay aauue. Aoi?ie i?eioeei cao?aaeaaao iaoa?eth e oi?io.
Eaaeaony, /oi iaoa?ey e oi?ia – ia/iia e anai iiiyoiia
i?ioeaiiinoaaeaiea, e eaaeaony caeanue aeaaea ia i /ai aiai?eoue. E
i?eia?o iaoa?ey yoiai noiea anoue aea?aai.A oi?ia yoiai noiea anoue
oio aeae, eioi?ua i?eiyee aea?aayiiua iaoa?eaeu , ia?aaioaiiua
aeey ii?aaeaeaiiie oeaee.Eaaeaony, /oi ana caeanue i/aiue i?inoi e
iiiyoii.Oai ia iaiaa yoa i?iaeaia yaeyeanue iaeiie ec
aeoai/aeoeo oeeinianeeo i?iaeai A?enoioaey.Aaaeue o A?enoioaey iaoa?eae
aiana ia i?inoi oieueei iaoa?eae.Iaoa?eae o A?enoioaey oaea
eiaao nianoaaiioth oi?io.Ana, aeaaea naiia
noiao?iia,aanii?yaei/iia, aanoi?iaiiia e oaioe/iia oaea
eiaaonaith nianoaaiioth oi?io. Iaeaea e oo/e ai a?aiy a?icu
auaeyaeyo aaniethoii aanoi?iaiii.Iaeiaei anee oo/a ia iaeaaeaea a naiii
aeaea ieeaeie oi?iie, oi eae au iia iiaea auoue aeey ian eaeie-oi
iiciaaaaiie aauueth. Ionthaea A?enoioaeue aeaeaao auaiae, /oi iaoa?ey
aaue anoue oieueei aua naiay aiciiaeiinoue aa ioi?ieaiey, e
aiciiaeiinoue yoa – aaneiia/ii ?aciiia?aciay.E oai ia iaiaa aac
iaoa?ee yeaein inoaaaeny au oieueei aa ioaea/aiiui niuneii,aac
anyeiai aiieiuaiey yoie iunee a aeaenoaeoaeueiinoe.Oieueei iieiia
ioiaeaeanoaeaiea iaoa?ee aaue n aa yeaeinii aeaeaao aauue eiaiii
aauueth.Yeaein e iaoa?eth oiae ?acee/aoue e Ieaoii, e nianai iaieioi eo
ioiaeaeanoaeye, ii oi , /oi naeaeae A?enoioaeue a yoie iaeanoe ,
yaeyaony ii/oe , iiaeii neacaoue ?aaiethoeeae a ioiioaiee ieaoiiecia.Ec
oao oeeinioia aioe/iinoe, eoi ?acee/ae oi?io e iaoa?eth,
A?enoioaeue aue naiui aeoaieei e naiui oiieei eo ioiaeaeanoaeoaeai.
Iaoa?ey ia anoue yeaein , ie yeaein aiiaua, ie eaeie-ieaoaeue
yeaein a /anoiinoe.Ii A?enoioaeth, oieueei einie/aneea noa?u auoa Eoiu
yaeythony yeaeaoe/anee iieiioeaiiuie.A oi, /oi niaa?oaaony aioo?e
eoiiie noa?u, a iiaeeoiiie, yoi anaaaea /anoe/ii e ianiaa?oaiii.
a eiie ?ac e nianai o?iaeeeai. Anee aaea A?enoioaeue e aunooiaao,
eae i?eioeeieaeueiue iaoa?eaeeno, o.a.i?iiiaaaeoao iaoa?eth a
ea/anoaa i?eioeeia aeeaie ?aaeueiinoe nouanoaothuaai aie?oa ian ie?a,
oi eeoue a naiai o/aiee i iaoa?ee a aeaea oea?noaa neo/aeiinoe. Ii
A?enoioaeth, aeaeaeaiea -yoi aiieia niaoeaoe/aneay eaoaai?ey e ?iaii ie
ia /oi ae?oaia ia naiaeeiay.Oaeei ia?acii, ii A?enoioaeth,
aeaeaeaiea yaeyaony oaeie aea iniiaiie eaoaai?eae, eae e iaoa?ey
e eae oi?ia.A?enoioaeue noaaeo aii?in i aiciiaeiinoe naiie
eaoaai?ee aeaeaeaiey. Ii auaeaeee /aou?a i?eioeeia nouanoaiaaiey
anyeie aaue eae i?aaiecia : iaoa?ey, oi?ia, aeaenoaothuay i?e/eia.
Iineaaeiei i?eieiii nouanoaiaaiey anyeie aaue ii A?enoioaeth yaeyaony
oeaeue.Oeaeue – niaoeaoe/aneay eaoaai?ey, ie ia /oi ae?oaia ia
naiaeeiay. A?enoioaeue naiae oai?eae /aou?aoi?eioeeiiie
no?oeoo?u aaue enoiaeee eneeth/eoaeueii ec oiai, /oi eaaeaeay aauue
anoue ?acoeueoao oai?/anoaa.I?e/?i ia aaaeii, oi?ioaa ee yoi
i?iecaaaeaiea eee ieioia. An? iiiaiia?acea aauanoaaiiai ie?a, ii
A?enoioaeth, iniiaaii ia ?aciuo niioiioaieyo yeaeina (oi?iu, eee
eaeae) e iaoa?ee a eo i?e/eiii – neaaenoaaiiii aiieiuaiee.
Ia?aoiaeo e ie?o iaeooaae?iiuo nouanoa, iu aeaeei o A?enoioaey e
caeanue ia ia?aii ieaia /aou??oi?eioeeiioth no?oeoo?o. A?enoioaeue
?acee/aao o?e oeia aeooe – ?anoeoaeueioth,
iuouathuoth(aeeaioioth) e ?acoiioth.?acoiiay aeooa oiaea eiaao e
naie yeaein, e naith iaoa?eth, e i?e/eiii – oeaeaaoth
iai?aaeaiiinoue. Yeaein aeeaiai oaea anoue i?eioeei aai aeecie, o.a.
aai aeooa. A anyeay aeooa aeaeaeouay oaeii, oiaea eiaao naie
nianoaaiiue yeaein, eioi?ue A?enoioaeue iacuaaao Oiii.Oae /oi aeooa, ii
A?enoioaeth, anoue ia aieaa, /ai yia?aey Oia. A Oi anoue yeaein
anao yeaeinia.Ii A?enoioaeth Oi e anoue aunoay noaiaiue auoey.Yoio Oi
, aoaeo/e iaeaunoae noaiaieth auouey a oeaeii,yaeyaony o A?enoioaey,
anee neacaoue e?aoei, i?aaeaeueiui iiiyoeai aiiaua. Ii – “yeaein
yeaeinia”.Oi acyoue nai ii naaa, oaea ?iaii ie/ai ie naycai e caaeneo
oieueei io naiiai naay. A yoii niunea ii aa/ii iaiiaeaeaeai.
A?enoioaeue n/eoaao, /oi Oi, ianiio?y ia anth naiaiaeo io
oinoaaiiie iaoa?ee,niaea?aeeo naith nianoaaiioth, /enoi oinoaaiioth
iaoa?eth, aac eioi?ie ii ia aue au ooaeiaeanoaaiiui
i?iecaaaeaieai.Ieeaeea oeeiniou aei A?enoioaey ia aeiioneaee a Oia
nouanoaiaaiea iaoa?ee.Ieeoi oae ino?i ei?eioeeieaeueii ia
i?ioeaiiinoiaeye iaoa?eth e Oi, eae yoi naeaeae A?enoioaeue.
A?enoioaeue nicaeae o?e eiioeaioeee Oia – ia?aiaeaeaaoaey. Ia?aay
eiioeaioeey – /enoi ieaoiie/aneay.Iia naiaeeony e oiio, /oi Oi
yaeyaony iaeaunoei e ieii/aoaeueiui auoe?i. Oi – anoue ia /oi eiia,
eae oea?noai aiaia – eaeae aunoeo, eee iaaeeinie/aneeo, iecoeo,
eee ca?caeiuo. Ai aoi?ie eiioeaioeee , Oi o A?enoioaey anoue iuoeaiea,
e iuoeaiea naiiai aea naay, o.a. “iuoeaiea iuoeaiey”.Oi niaea?aeeo a
naaa naith nianoaaiioth oinoaaiioth iaoa?eth, eioi?ay aea?o aio
aiciiaeiinoue auoue aa/iie e?anioie (o.e. e?anioa anoue eaeaaeueiia
niaiaaeaiea eaeae e iaoa?ee). O?aouey eiioeaioeey A?enoioaey
neeueii ioee/aaony io Ieaoiiianeie. O Ieaoiia einiinii oi?aaeyao
Ie?iaay aeooa. O A?enoioaey aea yoi – Oi,eioi?ue aeaeaeao
?aoeoaeueii anai , e iiyoiio ii anoue aeeciue eae aa/iay
yia?aey.”Anee Oi ii A?enoioaeth , anoue anaiauay oeaeue, e
iiyoiio an? aai ethaeo , oi nai ii , aoaeo/e oeaeueth ia oi, /oi
aiiaua ieeiai ia ethaeo, ii iineieueeo an? aiiaua ethaeo aai
naiiai,Oi,ianiiiaiii,oai aieaa aeieaeai ethaeoue naiiai naay.”
A?enoioaeue aiai?ee:”Ieaoii iia ae?oa, ii enoeia aei?iaea” E any
aeeciue A?enoioaey ninoiyea a aaneiia/iii no?aieaiee iaeoe,
i?iaiaeece?iaaoue, noaaoeoue enoeio , aeieiiaoueny aei niunea
ie?oaeathuaai ie?a. A naieo ciieiae/aneeo o?aeoaoao A?enoioaeue
onoaiaaeeaaao e oa?aeoa?ecoo aieaa 400 aeaeia aeeaioiuo.Ii iienae
158 ?acee/iuo a?a/aneeo e iaa?a/aneeo caeiiiaeaoaeuenoa.Any V
eieaa aai iniiaiiai o?aeoaoa “Iaoaoeceea” niaoeeaeueii
iinayuaia oeeinianeie oa?ieiieiaee, e eaaeaeue oa?iei o iaai aunooiaao
a 5 – 6 cia/aieyo. A?enoioaeue aue neeueiui /aeiaaeii. E eiaaea
ieacaeinue, /oi aeaaaoueny oaea iaeoaea, e n iei iiaoo ?ani?aaeoueny
eae aei yoiai n Nie?eoii ii, eae iiaeii i?aaeiieiaaoue, i?eiye
yae.Oae eii/eeanue aeeciue A?enoioaey.E an? aea aai eneaiey, any aai
aeeciue naeaeaoaeuenoaotho i iaauaaeii ioaeanoaa aaeeeiai /aeiaaea, aeey
eioi?iai aeaaea naia nia?oue noaea aeoii ioae?inoe e iaaiciooeiiai
niieienoaey.

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