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Доказательное рассуждение: правила и ошибки

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II?AeIANEAss YENOA?IAss AOIAIEOA?IAss AEAAeAIEss

?AOA?AO

ia oaio:

AeIEACAOAEUeIIA ?ANNOAEAeAIEA: I?AAEEA E IOEAEE

Auiieiee: Aaithoeeia E.A.

nooaeaio 1-ai eo?na

oaeoeueoao th?eaee/aneee

niaoeeaeueiinoue th?eno-ainoaea?noaiaaae

I?iaa?ee: Ee?e/ae I.I.

Na?aine, 1994

NIAeA?AEAIEA

Aaaaeaiea

1. I?aaeea e ioeaee, ioiinyueany e oaceno

2. I?aaeea e ioeaee, ioiinyueany e a?aoiaioai

3. I?aaeea e oi?ia iainiiaaiiiai oacena (aeaiiino?aoeee) e ioeaee a
oi?ia aeieacaoaeuenoaa

4. Iiiyoea i nioeciao e eiae/aneeo ia?aaeienao

Ai iiiaeo neo/ayo, iai?eia? ia eaeoeee, a ni/eiaiee, a iao/iie ?aaioa, a
aeieeaaea, a oiaea iieaieee, a noaeaaiuo canaaeaieyo, ia caueoa
aeenna?oaoeee e ai iiiaeo ae?oaeo, i?eoiaeeony aeieacuaaoue,
iainiiauaaoue auneacaiiua noaeaeaiey. Aeieacaoaeueiinoue — aaaeiia
ea/anoai i?aaeeueiiai iuoeaiey. No?oeoo?a aeieacaoaeuenoaa aeeth/aao a
naay: oacen, a?aoiaiou, aeaiiino?aoeeth.

Oacen — yoi noaeaeaiea, enoeiiinoue eioi?iai iaaei aeieacaoue. A?aoiaiou
— yoi oa enoeiiua noaeaeaiey, eioi?uie iieuecothony i?e aeieacaoaeuenoaa
oacena. Oi?iie aeieacaoaeuenoaa, eee aeaiiino?aoeeae, iacuaaaony niinia
eiae/aneie nayce iaaeaeo oacenii e a?aoiaioaie.

Nouanoaotho i?aaeea aeieacaoaeueiiai ?annoaeaeaiey. Ia?ooaiea yoeo
i?aaee aaaeao e ioeaeai, ioiinyueiny e aeieacuaaaiiio oaceno, a?aoiaioai
eee e naiie oi?ia aeieacaoaeuenoaa.

1. I?aaeea e ioeaee, ioiinyueany e oaceno

I?aaeea.

1. Oacen aeieaeai auoue eiae/anee ii?aaeaeaiiui, yniui e oi/iui.

Eiiaaea ethaee a naiai aunooieaiee, ienueiaiiii cayaeaiee, iao/iie
noaouea, aeieeaaea, eaeoeee ia iiaoo /aoei, ynii, iaeiicia/ii
noi?ioee?iaaoue oacen. Ia nia?aiee iaeioi?ua aunooiathuea ia iiaoo /aoei
noi?ioee?iaaoue 2-3 oacena, a caoai aaniii, a?aoiaioe?iaaiii eceiaeeoue
eo ia?aae neooaoaeyie.

2. Oacen aeieaeai inoaaaoueny oiaeaeanoaaiiui, o.a. iaeiei e oai aea ia
i?ioyaeaiee anaai aeieacaoaeuenoaa eee ii?iaa?aeaiey.

Ioeaee.

1. «Iiaeiaia oacena». Niaeanii i?aaeeai aeieacaoaeueiiai ?annoaeaeaiey,
oacen aeieaeai auoue ynii noi?ioee?iaai e inoaaaoueny iaeiei e oai aea
ia i?ioyaeaiee anaai aeieacaoaeuenoaa eee ii?iaa?aeaiey. I?e ia?ooaiee
aai aicieeaao ioeaea iacuaaaiay «iiaeiaia oacena». Nooue aa a oii, /oi
iaeei oacen oiuoeaiii eee iaoiuoeaiii iiaeiaiytho ae?oaei e yoio iiaue
oacen ia/eiatho aeieacuaaoue eee ii?iaa?aaoue. Yoi /anoi neo/aaony ai
a?aiy nii?a, aeeneonnee, eiaaea oacen iiiiiaioa nia/aea oi?iuatho eee
?anoe?ytho aai niaea?aeaiea, a caoai ia/eiatho e?eoeeiaaoue. Oiaaea oio,
eiai e?eoeeotho, cayaeyao, /oi iiiiiaio i?eienuaaao aio oi, /aai ii ia
aiai?ee. Neooaoeey yoa aanueia ?ani?ino?aiaia, iia ano?a/aaony e i?e
caueoa aeenna?oaoeee, e i?e ianoaeaeaiee iioaeeeiaaiiuo iao/iuo ?aaio, e
ia ?acee/iuo nia?aieyo e canaaeaieyo, e i?e ?aaeaeoe?iaaiee iao/iuo eee
eeoa?aoo?iuo noaoae. Caeanue i?ienoiaeeo ia?ooaiea caeiia oiaeaeanoaa,
oae eae iaoiaeaeanoaaiiua oacenu iuoathony ioiaeaeanoaeyoue, /oi e
i?eaiaeeo e eiae/aneie ioeaea. [1]

E i?eia?o, iaaei iieacaoue, /oi ia ineia ia iiaoo ?anoe yaeiee; aianoi
yoiai aeieacuaaaony, /oi iie ?anooo iau/ii ia yaeiia e ia ano?a/athony
ie ia a?ooa, ie ia aeoia. [2]

2. «Aeiaiae e /aeiaaeo». Ioeaea ninoieo a iiaeiaia aeieacaoaeuenoaa
naiiai oacena nnueeaie ia ee/iua ea/anoaa oiai, eoi auaeaeioe yoio
oacen. Iai?eia?, aianoi oiai /oiau aeieacuaaoue oeaiiinoue e iiaecio
aeenna?oaoeeiiiie ?aaiou, aiai?yo, /oi aeenna?oaio — caneoaeaiiue
/aeiaae, /oi ii iiiai iio?oaeeeny iaae aeenna?oaoeeae e o.ae. ?acaiai?
eeanniiai ?oeiaiaeeoaey, iai?eia?, n o/eoaeai ?onneiai ycuea ia ioeaiea,
iinoaaeaiiie o/aieeo, eiiaaea naiaeeony ia e aeieacaoaeuenoao, /oi yoio
o/aiee caneoaeee yoo ioeaieo naieie ciaieyie, a nnueeaie ia ee/iua
ea/anoaa o/aieea: ii oi?ioee iauanoaaiiee, iiiai aieae a yoie /aoaa?oe,
ii anai ae?oaei i?aaeiaoai ii oniaaaao e o.ae.

A iao/iuo ?aaioao eiiaaea aianoi eiie?aoiiai aiaeeca iaoa?eaea, eco/aiey
nia?aiaiiuo iao/iuo aeaiiuo e ?acoeueoaoia i?aeoeee a iiaeoaa?aeaeaiea
i?eaiaeyo oeeoaou ec auneacuaaiee e?oiiuo o/aiuo, aeaeiuo aeayoaeae e
yoei ia?aie/eaathony, iieaaay, oi iaeiie nnueee ia aaoi?eoao
aeinoaoi/ii. I?e yoii oeeoaou iiaoo au?uaaoueny ec eiioaenoa e eiiaaea
i?iecaieueii oieeiaaoueny. «Aeiaiae e /aeiaaeo» /anoi i?aaenoaaeyao
niaie i?inoi nioenoe/aneee i?eai, a ia ioeaeo, aeiiouaiioth
iai?aaeiaia?aiii.

?aciiaeaeiinoueth «aeiaiaea e /aeiaaeo» yaeyaony ioeaea, iacuaaaiay
«aeiaiae e ioaeeea», ninoiyuay a iiiuoea iiaeeyoue ia /oanoaa ethaeae,
/oiau oa iiaa?eee a enoeiiinoue auaeaeiooiai oacena, oioy aai e iaeuecy
aeieacaoue. [1]

3. «Ia?aoiae a ae?oaie ?iae». Eiathony aeaa ?aciiaeaeiinoe yoie ioeaee:
a) «eoi neeoeii iiiai aeieacuaaao, oio ie/aai ia aeieacuaaao»; a) «eoi
neeoeii iaei aeieacuaaao, oio ie/aai ia aeieacuaaao».

A ia?aii neo/aa ioeaea aicieeaao oiaaea, eiaaea aianoi iaeiiai enoeiiiai
oacena iuoathony aeieacaoue ae?oaie, aieaa neeueiue oacen, e i?e yoii
aoi?ie oacen iiaeao ieacaoueny eiaeiui. Anee ec a neaaeoao a, ii ec a ia
neaaeoao a, oi oacen a yaeyaony aieaa neeueiui, /ai oacen a. Iai?eia?,
anee aianoi oiai /oiau aeieacuaaoue, /oi yoio /aeiaae ia ia/eiae ia?aui
ae?aeo, ia/ioo aeieacuaaoue, /oi ii ia o/anoaiaae a ae?aea, oi ie/aai ia
niiaoo aeieacaoue, anee yoio /aeiaae aeaenoaeoaeueii ae?aeny e
eoi-ieaoaeue yoi aeaeae.

Ioeaea «eoi neeoeii iaei aeieacuaaao, oio ie/aai ia aeieacuaaao»
aicieeaao oiaaea, eiaaea aianoi oacena a iu aeieaaeai aieaa neaaue oacen
a. Iai?eia?, anee, iuoaynue aeieacaoue, /oi yoi aeeaioiia — caa?a, iu
aeieacuaaai, /oi iii iieinaoia, oi ie/aai ia aeieaaeai, oae eae oea? —
oiaea iieinaoia aeeaioiia. [1]

2. I?aaeea e ioeaee, ioiinyueany e a?aoiaioai

I?aaeea.

A?aoiaiou, i?eaiaeeiua aeey aeieacaoaeuenoaa oacena, aeieaeiu auoue
enoeiiuie.

A?aoiaiou aeieaeiu auoue aeinoaoi/iui iniiaaieai aeey aeieacaoaeuenoaa
oacena.

A?aoiaiou aeieaeiu auoue noaeaeaieyie, enoeiiinoue eioi?uo aeieacaia
naiinoiyoaeueii, iacaaeneii io oacena.

Ioeaee.

1. Eiaeiinoue iniiaaiey («Iniiaiia caaeoaeaeaiea»). A ea/anoaa
a?aoiaioia aa?oony ia enoeiiua, a eiaeiua noaeaeaiey, eioi?ua auaeatho
eee iuoathony auaeaoue ca enoeiiua. Ioeaea iiaeao auoue
iai?aaeiaia?aiiie. Iai?eia?, aaioeaio?e/aneay nenoaia Ioieiiay auea
iino?iaia ia iniiaaiee eiaeiiai aeiiouaiey, niaeanii eioi?iio Nieioea
a?auaaony aie?oa Caiee. Ioeaea iiaeao auoue e i?aaeiaia?aiiie
(nioeciii), niaa?oaiiie n oeaeueth caiooaoue, aaanoe a caaeoaeaeaiea
ae?oaeo ethaeae (iai?eia?, aea/a eiaeiuo iieacaiee naeaeaoaeyie eee
iaaeiyaiui a oiaea noaeaaiiai ?anneaaeiaaiey, iai?aaeeueiia iiiciaiea
aauae eee ethaeae e o.i.). [1]

Oiio?aaeaiea eiaeiuo, iaaeieacaiiuo eee iai?iaa?aiiuo a?aoiaioia
ia?aaeei nii?iaiaeaeaaony iai?ioaie: «anai ecaanoii», «aeaaii
onoaiiaeaii», «niaa?oaiii i/aaeaeii», «ieeoi ia noaiao io?eoeaoue» e
o.i. Neooaoaeth eae au inoaaeyaony iaeii: oi?aeaoue naay ca iaciaiea
oiai, /oi aeaaii e anai ecaanoii. [2]

2. «I?aaeainoeuaiea iniiaaiee». Yoa ioeaea niaa?oaaony oiaaea, eiaaea
oacen iie?aaony ia iaaeieacaiiua a?aoiaiou, iineaaeiea aea ia
aeieacuaatho oacen, a oieueei i?aaeainoeuatho aai.

3. «Ii?i/iue e?oa». Ioeaea ninoieo a oii, /oi oacen iainiiauaaaony
a?aoiaioaie, a a?aoiaiou iainiiauaathony yoei aea oacenii. Yoa
?aciiaeaeiinoue ioeaee «i?eiaiaiea iaaeieacaiiiai a?aoiaioa». [1]

3. I?aaeea e oi?ia iainiiaaiiiai oacena (aeaiiino?aoeee) e ioeaee a
oi?ia aeieacaoaeuenoaa

I?aaeea.

Oacen aeieaeai auoue caeeth/aieai, eiae/anee neaaeothuei ec a?aoiaioia
ii iauei i?aaeeai oiicaeeth/aiee eee iieo/aiiui a niioaaonoaee n
i?aaeeaie einaaiiiai aeieacaoaeuenoaa.

Ioeaee a oi?ia aeieacaoaeuenoaa.

1. Iieiia neaaeiaaiea. Anee oacen ia neaaeoao ec i?eaiaeeiuo a aai
iiaeoaa?aeaeaiea a?aoiaioia, oi aicieeaao ioeaea, iacuaaaiay «ia
neaaeoao». Eiiaaea aianoi i?aaeeueiiai aeieacaoaeuenoaa a?aoiaiou
niaaeeiytho n oacenii iin?aaenoaii neia: «neaaeiaaoaeueii», «eoae»,
«oaeei ia?acii», «a eoiaa eiaai» e o.i., — iieaaay, /oi onoaiiaeaia
eiae/aneay naycue iaaeaeo a?aoiaioaie e oacenii. Yoo eiae/aneoth ioeaeo
/anoi iainiciaiii aeiioneatho ethaee, ia ciaeiiua n i?aaeeaie eiaeee,
iieaaathueany ia naie cae?aaue niune e eiooeoeeth. A ?acoeueoaoa
aicieeaao neiaaniay aeaeeiinoue aeieacaoaeuenoaa.

2. Io neacaiiiai n oneiaeai e neacaiiiio aaconeiaii. A?aoiaio, enoeiiue
oieueei n o/aoii ii?aaeaeaiiiai a?aiaie, ioiioaiey, ia?u, iaeuecy
i?eaiaeeoue a ea/anoaa aaconeiaiiai, aa?iiai ai anao neo/ayo. Oae, anee
eioa iieacai a iaaieueoeo aeicao (iai?eia?, aeey iiaeiyoey
a?oa?eaeueiiai aeaaeaiey), oi a aieueoeo aeicao ii a?aaeai. Aiaeiae/ii
iuoueye yaeiaeo, ii a iaaieueoeo aeicao aai aeiaaaeytho a iaeioi?ua
eaea?noaa. Eaea?noaa a?a/e aeieaeiu iiaeae?aoue aeey aieueiuo
eiaeeaeaeoaeueii. Iaaeaaiaeea o?aaoao eiaeeaeaeoaeueiiai iiaeoiaea e
o/aueiny; yoeea ii?aaeaeyao ii?iu iiaaaeaiey ethaeae, e a ?acee/iuo
oneiaeyo iie iiaoo ianeieueei aa?uee?iaaoueny (iai?eia?, i?aaaeeainoue —
iieiaeeoaeueiay /a?oa /aeiaaea, ?acaeaoaiea aiaiiie oaeiu —
i?anooieaiea). [1]

Ia?ooaiea i?aaee oiicaeeth/aiee.

1. Ioeaee a aeaaeoeoeaiuo oiicaeeth/aieyo. Iai?eia?, a
oneiaii-eaoaai?e/aneii oiicaeeth/aiee iaeuecy auaanoe caeeth/aiea io
ooaa?aeaeaiey neaaenoaey e ooaa?aeaeaieth iniiaaiey. Oae, ec iinueie:
«Anee /enei ieai/eaaaony ia 0, oi iii aeaeeony ia 5» e «Yoi /enei
aeaeeony ia 5» — ia neaaeoao caeeth/aiea: «Yoi /enei ieai/eaaaony ia 0».
[1]

I?eia?ii oaeie ioeaee iiaeao auoue oiicaeeth/aiea: «Eaaeaeue iaoaee
yaeyaony oeie/aneei yeaiaioii; eaooiue — iaoae, cia/eo eaooiue —
oeie/aneee yeaiaio».

2. Ioeaee a eiaeoeoeaiuo oiicaeeth/aieyo. Iaeia ec oaeeo ioeaie —
«iiniaoiia iaiauaiea», iai?eia? ooaa?aeaeaiea, /oi «ana naeaeaoaee
aeatho iaiauaeoeaiua iieacaiey». Ae?oaie ioeaeie yaeyaony «iinea yoiai —
cia/eo, ii i?e/eia yoiai» (iai?eia?, i?iiaaea aaue iaia?oaeaia iinea
i?eoiaea a aeii yoiai /aeiaaea, cia/eo, ii aa oian). Ia yoie eiae/aneie
ioeaea iniiaaiu ana noaaa?ey.

3. Ioeaea a oiicaeeth/aiee ii aiaeiaee. Ioeaee ii aiaeiaee iiaeii
i?ieeethno?e?iaaoue i?eia?aie eiaeiuo aiaeiaee (oae iacuaaaiua
aoeueaa?iua aiaeiaee), a oii /enea aiaeiaee aeoeieeia. Aeaaiay oeaeue
aeoeiee — iaoiaeaeaiea oae iacuaaaiiai «oeeinioneiai eaiiy» aeey
i?aa?auaiey iaaeaai?iaeiuo iaoaeeia a cieioi e na?aa?i, iieo/aiey
yeeene?a aeieaieaoey, oieaa?naeueiiai ?anoai?eoaey e o.i. Aianoa n yoei
ioia/aaony e iieiaeeoaeueiay ?ieue aeoeiee. [1]

Aaaeaiea e i?i?eoeaiea — yoi anaaaea ?annoaeaeaiea ii aiaeiaee.
?ani?ino?aiaiiay a?oiia aaaeaiee iie?aaony ia aiaeiaeth iaaeaeo oaeii
/aeiaaea e aai noaeueaie. Aiaeiaey i?iaiaeeony iaaeaeo eeieyie ?oee e
noaeueau.

4. Iiiyoea i nioeciao e eiae/aneeo ia?aaeienao

A ioee/ea io iai?iecaieueiie eiae/aneie ioeaee — ia?aeiaecia,
yaeythuaeny neaaenoaeai iaaunieie eiae/aneie eoeueoo?u, nioeci — yoi
i?aaeiaia?aiiia, ii ouaoaeueii caianee?iaaiiia ia?ooaiea o?aaiaaiee
eiaeee.

Aio i?eia?u aeiaieueii i?inouo ae?aaieo nioeciia. «Ai? ia aeaeaao
i?eia?anoe ie/aai aeo?iiai; i?eia?aoaiea oi?ioaai anoue aeaei oi?ioaa;
neaaeiaaoaeueii, ai? aeaeaao oi?ioaai». «Eaea?noai, i?eieiaaiia
aieueiui, anoue aeia?i; /ai aieueoa aeaeaoue aeia?a, oai eo/oa; cia/eo,
eaea?noai ioaeii i?eieiaoue a aieueoeo aeicao». [2]

Nioeciu ae?aaieo ia?aaeei eniieueciaaeenue n iaia?aieai aaanoe a
caaeoaeaeaiea. Ii iie eiaee e ae?oaoth, ai?acaei aieaa eioa?anioth
noi?iio. I/aiue /anoi nioeciu noaayo a iayaiie oi?ia i?iaeaio
aeieacaoaeuenoaa. Noi?ioee?iaaiiua a oio ia?eiae, eiaaea iaoee eiaeee
aua ia auei, ae?aaiea nioeciu i?yii noaaeee aii?in i iaiaoiaeeiinoe aa
iino?iaiey. Eiaiii n nioeciia ia/aeinue iniuneaiea e eco/aiea
aeieacaoaeuenoaa e ii?iaa?aeaiey. E a yoii ieaia nioeciu
iaiin?aaenoaaiii niaeaenoaiaaee aicieeiiaaieth iniaie iaoee i
i?aaeeueiii, aeieacaoaeueiii iuoeaiee. [2]

Iaoaiaoe/aneea nioeciu nia?aiu a oeaeii ?yaea eiea. Oae, N. Eiaaeue
iienuaaao iaoaiaoe/aneea nioeciu: «eaaeaeay ie?oaeiinoue eiaao aeaa
oeaio?a»; «eaaeaeue o?aoaieueiee — ?aaiiaaae?aiiue». [3] ss.E.
Ia?aeueiai i?eaiaeeo «aeaaa?ae/aneea eiiaaeee»: 2×2=5; 2=3. [4]

Nioeciu eniieueciaaeenue e oaia?ue i?iaeieaeatho eniieueciaaoueny aeey
oiieiai, caaoaee?iaaiiiai iaiaia. A yoii neo/aa iie aunooiatho a ?iee
iniaiai i?eaia eioaeeaeooaeueiiai iioaiie/anoaa, iiiuoee auaeaoue eiaeue
ca enoeio e oai naiui aaanoe a caaeoaeaeaiea. [2]

Iai?eia?, 2×2=5. O?aaoaony iaeoe ioeaeo a neaaeothueo ?annoaeaeaieyo.
Eiaai /eneiaia oiaeaeanoai: 4:4=5:5. Auianai ca neiaeo a eaaeaeie /anoe
yoiai oiaeaeanoaa iauee iiiaeeoaeue. Iieo/ei — 4(1:1)=5(1:1). *enea a
neiaeao ?aaiu. Iiyoiio 4=5, eee 2×2=5. [1] Ii anee caienaoue au?aaeaiea
/a?ac ae?iaue, oi ana anoaiao ia naie ianoa.

Ia?aaeien — yoi ?annoaeaeaiea, aeieacuaathuaa eae enoeiiinoue, oae e
eiaeiinoue iaeioi?iai noaeaeaiey, eiuie neiaaie, aeieacuaathuaa eae yoi
noaeaeaiea, oae e aai io?eoeaiea. [1]

Ia?aaeienaeueiu a oe?ieii niunea aoi?eciu, iiaeiaiua oaeei: «Ethaee
aeanoiee, ii /aeiaae aeia?» eee «I?eciaeoa, /oi ana ?aaiu, — e ooo aea
iiyayony aaeeeea», e aiiaua ethaua iiaiey e noaeaeaiey, ioeeiiythueany
io o?aaeeoeee e i?ioeainoiyuea iauaecaanoiiio, «i?oiaeienaeueiiio». [2]

Iaeaieaa ecaanoiui e, iiaeaeoe, naiui eioa?aniui ec anao eiae/aneeo
ia?aaeienia yaeyaony ia?aaeien «Eaeaoe». Eiathony ?acee/iua aa?eaiou
yoiai ia?aaeiena, iiiaea ec eioi?uo oieueei ii aeaeeiinoe
ia?aaeienaeueiu.

A i?inoaeoai aa?eaioa «Eaeaoea» /aeiaae i?ieciineo anaai iaeio o?aco:
«ss eao». Eee aiai?eo: «Auneacuaaiea, eioi?ia y nae/an i?ieciioo,
yaeyaony eiaeiui». O?aaeeoeeiiiay eaeiie/iay oi?ioee?iaea yoiai
ia?aaeiena aeaneo: anee eaouee aiai?eo, /oi ii eaeao, oi ii
iaeiia?aiaiii eaeao e aiai?eo i?aaaeo.

A ae?aaiinoe «Eaeaoe» ?anniao?eaaeny eae oi?ioee i?eia? aeaoniuneaiiiai
au?aaeaiey. A n?aaeiea aaea «Eaeaoe» aue ioianai e «ia?ac?aoeiui
i?aaeeiaeaieyi». Oaia?ue ii ia?aaeei eiaioaony «ei?ieai eiae/aneeo
ia?aaeienia».

EEOA?AOO?A:

Aaoiaiiaa A.Ae. O/aaiee ii eiaeea – I.: Aeaaein, 1994.

Eaei A.A. Eneonnoai i?aaeeueii iuneeoue – I.: I?inaauaiea, 1990.

Eiaaeue N. Io ?acaea/aiey e ciaieyi /Ia?. I. Oiao?yi – Aa?oaaa:
Ia/ii-oaoie/aneia ecae-ai, 1972.

Ia?aeueiai ss.E. Caieiaoaeueiay aeaaa?a – I.: Iaoea, 1976.

Aaoiaiiaa A.Ae. O/aaiee ii eiaeea – I., 1994, n.181

Ni.: oai aea, n.187

Ni.: oai aea, n.187

Ni.: oai aea, n.188

Ni.: oai aea, n.189

Ni.: oai aea, n.189

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