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Нестандартные задачи в курсе школьной математики (неполное и избыточное условие)

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Ieai

Anooieaiea . . . . . . . . . . . . . . . . . . . .
. . . . . . . 2

I ?iee caaea/ a iao/aiee iaoaiaoeea . . . . . . . . . 2

Eae o/eo ?aoaoue caaea/e nia?aiaiiay oeiea? . . . . 4

Oi?ioee?iaea i?iaeaiu . . . . . . . . . . . . . . . 10

I. Eae o/aieee ?aaae?otho ia «aiiiaeueiua» caaea/e

(eiinoaoe?othuea yenia?eiaiou) . . . . . . . . . . . . . .
17

Iainiiaaiea oeaeaniia?aciinoe caaea/ n «aiiiaeueiui»

oneiaeai . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 24

I?eeeaeea iaoiaee/aneiai iiaeoiaea e iao/aieth

?aoaieth «aiiiaeueiuo» caaea/ . . . . . . . . . . . . . .
. . . 32

?anoe?aiiay nenoaia caaea/ ii oaia «Noiia oaeia

o?aoaieueieea» . . . . . . . . . . . . . . . . . . .
. . . . . . . 37

Caeeth/aiea . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 51

Nienie eeoa?aoo?u . . . . . . . . . . . . . . . . . .
. . . . . . 52

Anooieaiea

1. I ?iee caaea/ a iao/aiee iaoaiaoeea

A iao/aiee iaoaiaoeea caaea/ai anaaaea ioaiaeeeanue aeinoaoi/ii
aieueoay, anee ia ?aoathuay, ?ieue.

Nae/an an? aieueoaa ?ani?ino?aiaiea iieo/aao i?ia?anneaiue iaoiae
iao/aiey /a?ac caaea/e eae ?aaeecaoeey nenoaiu i?iaeaiiiai iao/aiey.
Iniiaiua eaeae yoiai iaoiaea iaoiaeyo a eaeie–oi ia?a io?aaeaiea a iiauo
o/aaieeao. Caaea/e noaiiayony ia oieueei e ia noieueei oeaeueth,
neieueei n?aaenoaii iao/aiey.

Enoi?e/anee neiaeeeinue, /oi ia ?aiieo yoaiao ?acaeoey iaoaiaoeee
?aoaiea caaea/ auei oeaeueth iao/aiey. O/aiee aeieaeai aue cao/eoue
ia?acoeu e caoai iiaeaiaeeoue iiae yoe ia?acoeu ?aoaiey caaea/. A
iniiaiii ?aoaeenue oeiiaua, noaiaea?oiua caaea/e, i?eiaaeeaaeauea
eeannai aeai?eoie/anee ?ac?aoeiuo caaea/, o.a. oaeeo, aeey eioi?uo
nouanoaoao iauee iaoiae (aeai?eoi) ?aoaiey.

Iiiaiia?aciua neooaoeee, aicieeathuea ia iaoaiaoe/aneii e
iaiaoaiaoe/aneii iaoa?eaea, i?eaiaeyo eae e noaiaea?oiui, oae e
ianoaiaea?oiui caaea/ai, aeai?eoi ?aoaiey eioi?uo eeai iaecaanoai, eeai
ia nouanoaoao.

A iineaaeiea aeanyoeeaoey iinoaiaiiia eciaiaiea oeaeae iao/aiey
iaoaiaoeea i?eaiaeeo e iaiaoiaeeiinoe o/eoue aeaoae ?aoaieth ia oieueei
noaiaea?oiuo, ii e ianoaiaea?oiuo caaea/, eioi?ua iaeuecy ioianoe e
eeanno aeai?eoie/anee ?ac?aoeiuo. Eiaiii ii ioiioaieth e ianoaiaea?oiie
caaea/a aicieeaao iaiaoiaeeiinoue a aa?eaoeaiii iienea ?aoaiey.

“Caaea/a i?aaeiieaaaao iaiaoiaeeiinoue niciaoaeueiiai iienea
niioaaonoaothuaai n?aaenoaa aeey aeinoeaeaiey ynii aeaeeiie, ii
iaiin?aaenoaaiii ia aeinooiiie oeaee. ?aoaiea caaea/ icia/aao
iaoiaeaeaiea yoiai n?aaenoaa”. [17, n. 143]

Ii?aaeae?iiua a?oiiu caaea/, i?aaeiacia/aiiuo aeey eeanniuo e
aiaeeanniuo caiyoee, aiieia i?eaiaeiu aeey au?aaioee “iaaeeaaeaueo
iaaueia iunee”, iaaueia, iai?aaeaiiuo ia iienee ?aoaiey caaea/.[6, n.
119(120]

A eieaa [13, n. 165] I. E. Iaoiooia ?anneacuaaao ia enneaaeiaaiee,
i?iaaae?iiii a?oiiie o/?iuo, iaoaiaoeeia e ineoieiaia n oeaeueth
auyaeaiey caeiiiia?iinoae aeoeaecaoeee iiciaaaoaeueiie aeayoaeueiinoe
o/aueony. Aio /oi ii ieoao a eieaa:

“Oai?aoe/aneia iniuneaiea ?aaio eo/oeo o/eoaeae iiiiaei iaia?oaeeoue a
o/aaiii i?ioeanna iauoth caeiiiia?iinoue aeoeaecaoeee iiciaaaoaeueiie
aeayoaeueiinoe o/aueony: iai?yaeaiea eioaeeaeooaeueiuo nee o/aieea
aucuaaaony aeaaiui ia?acii iinoaiiaeie i?iaeaiiuo aii?inia, i?iaeaiiuo
iiciaaaoaeueiuo caaea/ e o/aaiuo caaeaiee enneaaeiaaoaeueneiai
oa?aeoa?a. Yoi iai?yaeaiea ?iaeaeaaony a noieeiiaaiee n o?oaeiinoueth a
iiieiaiee e iniuneaiee iiaiai oaeoa eee iiiyoey e oa?aeoa?ecoaony
iaee/eai i?iaeaiiie neooaoeee, aunieiai eioa?ana o/auaainy e oaia, aai
yiioeeiiaeueiiai iano?iy e aieaaiai oneeey.”

?ieue caaea/ a iao/aiee iaoaiaoeea iaaiciiaeii ia?aioeaieoue. *a?ac
caaea/o anoanoaaiii aaanoe i?iaeaiioth neooaoeeth. ?ac?aoea nenoaio
niaoeeaeueii iiaeia?aiiuo caaea/, o/aiee ciaeiieony n nouanoaaiiuie
yeaiaioaie iiauo aeai?eoiia, iaeaaeaaaao iiauie oaoie/aneeie yeaiaioaie.
I?eiaiyoue iaoaiaoe/aneea ciaiey a aeeciaiiuo neooaoeeyo o/ao
niioaaonoaothuea i?aeoe/aneea caaea/e. [11, n.182]

Eoae, eae aeaeii ec i?eaaae?iiiai auoa iaci?a iiaiee ?acee/iuo
niaoeeaeenoia a iaeanoe ia?aciaaiey e iao/aiey iaoaiaoeea, caaea/a
yaeyaony iniiaiui caaiii aioo?e i?ioeanna iao/aiey, a oai aieaa oaeiai,
eae i?iaeaiiia e ?acaeaathuaa.

2. Eae o/eo ?aoaoue caaea/e nia?aiaiiay oeiea?

Iaeiaei eniieueciaaiea caaea/ a i?ioeanna iao/aiey iaoaiaoeea e a
ianoiyuaa a?aiy au? aeaeaei io niaa?oainoaa.

Eae ieoao A.Ynaoeia [25, n.8] a ineoieiaee e iaaeaaiaeea ia?auaaony
aieiaiea i?aeiouanoaaiii ia oi, eae ?aoathony oaea eai–oi iaeaeaiiua e
aiieia /?oei noi?ioee?iaaiiua caaea/e, a ia ia oi, eae iie
iaia?oaeeaathony e noaayony. A ?acoeueoaoa iieo/aaony, /oi /aeiaae,
i?eaueoee aeaeaoue ia?aae niaie /?oei e ei??aeoii noi?ioee?iaaiioth
caaea/o, i?inoi oa?yaony a iaciaeiiie neooaoeee, aoaeue oi oioue iau/iay
iaei??aeoiay iaoaiaoe/aneay caaea/a eee iaeay caaea/a, aicieeoay eae
neaaenoaea ec i?aeoeee (i?eeeaaeiay).

A nia?aiaiiii iaoaiaoe/aneii ia?aciaaiee (iu i?eaioe?oainy ia no?aiu
auaoaai NNN?) ioia/aaony neaaeothuee aeooaeueiue aniaeo: eco/aiea
iaoaiaoeee ia anao yoaiao aeieaeii eiaoue ?acaeaathuee oa?aeoa? e
i?eeeaaeioth iai?aaeaiiinoue. Iieiae?aee iaiaoiaeeii aeaaaoue ia i?inoi
eiie?aoioth noiio ciaiee, ii e i?eaeaaoue ae iaauee oai?/anoaa, eioa?an
e enneaaeiaaieth, oi?ie?iaaoue o ia? iieiaeeoaeueioth iioeaaoeeth. [11,
n.136]

Eioa?an e o/aaiie aeayoaeueiinoe, iiaee?aieyaiue iinoiyiiui aeoeaiui
o/anoeai a ioe?uoee iiauo enoei, i?iaa?ea aeiioac, iieneii niiniaa
aeaenoaee a caaea/a, yaeyaony iniiaiui ineoieiae/aneei oneiaeai
oniaoiinoe yoie aeayoaeueiinoe. [11, n.129]

Oeieueiua o?iee iaoaiaoeee ii–i?aaeiaio iaoeaeaiu ia i?ioiaeaeaiea
i?ia?aiiu, a ia ia ?acaeoea iuoeaiey o aeaoae. O/eoaeue aeaeeo naith
caaea/o a oii, /oiau oeieueieee n aai iiiiuueth onaieee au? iaeio
ii?oeeth iaoa?eaea. Iaeiaei aeaaiay aai caaea/a – anaia?ii
niaeaenoaiaaoue ?acaeoeth iiciaaaoaeueiuo aiciiaeiinoae o o/aueony.[11,
n.178]

Iniiaioth /anoue a?aiaie ia o?iea o/aiee i?iaiaeeo, ?aoay caaea/e, e ai
iiiaii io eo iniaaiiinoae (neiaeiinoe, iiiaia?aiiinoe, nthaeaoiie oi?iu,
iineaaeiaaoaeueiinoe e ae?.) e caaeneo, ianeieueei oniaoiui aoaeao
i?ioeann iao/aiey iaoaiaoeea. Ii /oi aea iu eiaai ia naiii aeaea? Ia
i?aeoeea iieo/aaony, /oi /aua anaai i?ioeann ?aoaiey caaea/ ia o?iea
iaeaaeaao iaeioi?ie ?ooeiiinoueth e inoaaeyao o/aieeo iaei aiciiaeiinoae
aeey oai?/anoaa. Ni a?aiaiai oaeay niaoeeoeea caaea/ au?aaaouaaao o
o/aieea iaeioi?ue iai?aaeeueiue noa?aioei iuoeaiey, ioiinyueeny e
?aoaieth caaea/. O/aiee i?inoi euao noaiaea?oioth neooaoeeth, e eioi?ie
iiaeii auei au i?eiaieoue ecaanoiua oi?ioeu e oai?aiu, e oa?yaony,
eiaaea i?aaeeiaeaiiay caaea/a o?aaoao aeaaea ianeiaeiiai ianoaiaea?oiiai
iiaeoiaea.

Ii iiaieth E.O?eaeiaia, iaeiie ec iniiaiuo a iao/aiee iaoaiaoeea
ooieoeee caaea/ yaeyaony ooieoeey oi?ie?iaaiey e ?acaeoey o o/aueony
iaueo oiaiee ?aoaiee ethauo iaoaiaoe/aneeo (a oii /enea e i?eeeaaeiuo)
caaea/.

O/aueany aea a ianoiyuaa a?aiy ia iieo/atho ieeaeeo niaoeeaeueiuo
ciaiee, ia aaca eioi?uo aiciiaeii oaeia oi?ie?iaaiea. Aieaa oiai, a
ianoiyuaa a?aiy yoe iauea oiaiey oi?ie?othony /enoi noeoeeii, a ia a
?acoeueoaoa oeaeaiai?aaeaiiiai, nenoaiaoe/aneiai iao/aiey. N/eoaaony,
/oi yoe oiaiey iiaoo aicieeiooue eeoue aeaaiaea?y ?aoaieth aieueoiai
/enea iaoaiaoe/aneeo caaea/. [22, n.151(152]

Aiaeec oeieueiuo o/aaieeia iaoaiaoeee iieacuaaao, /oi iie niaea?aeao
a?iaea au aeinoaoi/iia (eee aeaaea ecauoi/iia) eiee/anoai caaea/, ec
eioi?uo o/eoaeue iiaeao ninoaaeyoue iaai?u caaea/, i?eaioe?iaaiiua ia
?aciua eeannu e ia ?aciuo o/aueony. Iaeiaei o/aaiue yooaeo iieo/aaony,
ii iiaieth iiiaeo iaaeaaiaia–enneaaeiaaoaeae, n eioi?ui iu aiieia
niaeaniu, iaaunieei.

Aieueoeinoai o/aueony, ano?aoeaoenue n caaea/ae iaciaeiiiai eee
iaeiciaeiiiai aeaea, ia ciatho, eae e iae iiaenooieoueny, n /aai ia/aoue
?aoaiea, e i?e yoii iau/ii i?ieciinyo ia/aeueii ecaanoiua neiaa: “A iu
oaeea ia ?aoaee”.

Eaeiau aea i?e/eiu yoiai oe?iei ?ani?ino?ai?iiiai yaeaiey?

Aaoi? eieae [14] aeaeeo iniiaioth i?e/eio a iaoaeiaeaoai?eoaeueiie
iinoaiiaea caaea/ a iao/aiee iaoaiaoeea. Ii ieoao: “I?iaeaia iinoaiiaee
caaea/ a i?ioeanna iao/aiey iaoaiaoeea aei neo ii? ia iaoea
oaeiaeaoai?eoaeueiiai ?aoaiey (ie a iaoae no?aia, ie ca ?oaaaeii) ie n
oi/ee c?aiey niaea?aeaiey o/aaiuo caaea/, ie n oi/ee c?aiey eo oeaeaaiai
iacia/aiey, ie n oi/ee c?aiey /enea iaycaoaeueiuo eee iaiaycaoaeueiuo
caaea/ eee i?aaenoaaeaiey eo a aeaea oeaeinoiie nenoaiu.”

Nae/an, eiaaea o/aueany ia eiatho nenoaiaoe/aneeo ciaiee i caaea/ao e
nouiinoe eo ?aoaiey, aeaaiia aieiaiea o/aueony (e o/eoaeae) iai?aaeaii
ia oi, /oiau iaeoe ?aoaiea caaea/e e i?eoii eae iiaeii auno?ae. Ia
caeeth/eoaeueiue aiaeec, ia onoaiiaeaiea oiai, eaeea auaiaeu iiaeii
naeaeaoue ec auiieiaiiiai ?aoaiey, – ia an? yoi oaea ia inoa?ony ie nee,
ie a?aiaie, ie aeaeaiey, a aaaeue yoi aaeaa ee ia aeaaiua aniaeou
?aoaiey caaea/.

A oeiea iaaiciiaeii, aea e ia ioaeii, ?anniao?eaaoue ana aeaeu
iaoaiaoe/aneeo caaea/. Neieueei au caaea/ ie ?aoaee a oeiea, an? ?aaii
o/aueany a naiae aoaeouae ?aaioa ano?aoyony n iiauie aeaeaie caaea/.
Iiyoiio oeiea aeieaeia aii?oaeaoue o/aueony iauei iiaeoiaeii e ?aoaieth
ethauo caaea/.

Iaeiie ec iniaaiiinoae iaoaiaoeee yaeyaony aeai?eoie/iinoue ?aoaiey
iiiaeo a? caaea/. Aeai?eoiii, eae ecaanoii, iacuaaaony ii?aaeae?iiia
oeacaiea ioiineoaeueii oiai, eaeea iia?aoeee e a eaeie
iineaaeiaaoaeueiinoe iaaei auiieieoue, /oiau ?aoeoue ethaoth caaea/o
ii?aaeae?iiiai oeia. Eiia/ii, i/aiue aieueoia eiee/anoai caaea/ ia
aeai?eoiece?oaony e ?aoaaony n iiiiuueth niaoeeaeueiuo, iniauo i?e?iia.
Iiyoiio niiniaiinoue iaoiaeeoue iooe ?aoaiey, ia iiaeoiaeyuea iiae
noaiaea?oiia i?aaeei, yaeyaony iaeiie ec nouanoaaiiuo iniaaiiinoae
iaoaiaoe/aneiai iuoeaiey, eae ia yoii ieoao a naiae eieaa aeaaeaiee
Eieiiai?ia. [7, n.76]

Iaiaoiaeeiinoue niaoeeaeueiuo niiniaiinoae aeey eco/aiey e iiieiaiey
iaoaiaoeee /anoi i?aoaaee/eaatho. Aia/aoeaiea eneeth/eoaeueiie
o?oaeiinoe iaoaiaoeee eiiaaea nicaea?ony a? ieioei, /?acia?ii
oi?iaeueiui eceiaeaieai ia o?iea.

Oiaiea iineaaeiaaoaeueii, eiae/anee ?annoaeaeaoue a iaciaeiiie
ianoaiiaea i?eia?aoaaony n o?oaeii. Ia iaoaiaoe/aneeo ieeiieaaeao naiua
iaiaeeaeaiiua o?oaeiinoe aicieeatho eiaiii i?e ?aoaiee caaea/, a eioi?uo
ia i?aaeiieaaaaony ieeaeeo i?aaeaa?eoaeueiuo ciaiee ec oeieueiiai eo?na,
ii o?aaoaony i?aaeeueii oeiaeoue niune aii?ina e ?annoaeaeaoue
iineaaeiaaoaeueii. [7, n.80]

Iiiaea ia?aeaiey aucuaaao e iiaeaioiaea oeieueieeia eae aaeoo?eaioia,
iinooiathueo a AOCu ia oeceei–iaoaiaoe/aneea niaoeeaeueiinoe.
Iiiaieaoiyy i?aeoeea i?e?iiuo yecaiaiia iieacuaaao, /oi ainieoaiiua a
o?aaeeoeeiiiie oeiea aaeoo?eaiou iaeaaeatho ciaieyie, aeinoaoi/iuie aeey
iinooieaiey a AOC, iaeiaei eioaeeaeooaeueiia ?acaeoea aieueoeinoaa ec
ieo e, i?aaeaea anaai, o?iaaiue aano?aeoiiai e eiae/aneiai iuoeaiey
iaaeinoaoi/ai aeey yooaeoeaiiai iao/aiey ii aua?aiiie
niaoeeaeueiinoe.[11, n. 92]

Eoae, eae iieacuaaao auoaeceiaeaiiue aiaeec eeoa?aoo?u, iaai?u caaea/
eiathueony oeieueiuo o/aaieeia iiea au? ia oaeiaeaoai?ytho o?aaiaaieyi,
i?aaeuyaeyaiui e ?acoeueoaoeaiinoe iaoaiaoe/aneiai ia?aciaaiey. *aua
anaai, yoe caaea/e ioiinyony e aeai?eoie/anee ?ac?aoeiui, ia ?acaeaatho
o o/aieeia aa?eaoeaiiai iuoeaiey, ia o/ao iiiaeanoao iaaueia, noieue
iaiaoiaeeiuo aeey ?aoaiey caaea/, eae oeieueiuo, oae e auoiauo,
i?iecaiaenoaaiiuo, iao/iuo e o. ae.

?anniio?ei aieaa aeaoaeueii, eae ianoieo aeaei n caaea/aie,
i?aaenoaaeaiiuie a aeaenoaothueo o/aaieeao iaoaiaoeee.

Aiaeec oeieueiuo o/aaieeia iaoaiaoeee iieacuaaao, /oi n 5–ai ii 11–e
eeann o/aieee ?aoatho aieaa 7000 caaea/. [11, n.171]

Anee acaeyiooue ia caaea/e, i?aaenoaaeaiiua a oeieueiuo o/aaieeao
iaoaiaoeee, oi ana caaea/e, niaea?aeaueany a ieo, aioo?e iaeiie oaiu
eeanneoeoee?iaaiu ii noaiaie neiaeiinoe e ?aniieiaeaiu, eae i?aaeei, a
ii?yaeea a? aic?anoaiey.

N?aaee i?aaeeaaaaiuo o/aueiny caaea/ i?aaenoaaeaiu caaea/e ?aciuo
eeanneoeeaoeee (ii e?aeiae ia?a, e yoiio no?aiyony aaoi?u o/aaieeia): ii
eo iacia/aieth – o?aie?iai/iua e ?acaeaathuea, ii iaee/eth aeai?eoia
?aoaiey – noaiaea?oiua e ianoaiaea?oiua, ii oa?aeoa?o o?aaiaaiey –
aeieacaoaeueiua, au/eneeoaeueiua e eiino?oeoeaiua. Anoue e ae?oaea
eeanneoeeaoeee, iaoiaeyuea oi eee eiia io?aaeaiea a oeieueiuo o/aaieeao.

3. Oi?ioee?iaea i?iaeaiu

Ii iaeia ec eeanneoeeaoeee ii/oe ia iaoiaeeo io?aaeaiey a aeaenoaothueo
o/aaieeao ca ?aaeeeie eneeth/aieyie. ?a/ue eae?o i eeanneoeeaoeee ii
oa?aeoa?o oneiaey caaea/e – ii?aaeae?iiua, iaii?aaeae?iiua e
ia?aii?aaeae?iiua. Oeieueieeai i?aeiouanoaaiii i?aaeeaaathony caaea/e
ii?aaeae?iiua, o.a. caaea/e, niaea?aeauea a oneiaee ?iaii noieueei
aeaiiuo, neieueei eo o?aaoaony aeey iieo/aiey ioaaoa, ia aieueoa e ia
iaiueoa. Ii ii/aio ia aieueoa e ia iaiueoa?

Anee o/eoaeue noaaeo oeaeueth iao/eoue naieo o/aieeia ?aoaoue caaea/e ec
aeecie, a ia ec o/aaieeia, oi ii aeieaeai iao/eoue eo: 1)
iaoaiaoece?iaaoue neooaoeeth (o.a. ia?aaiaeeoue caaea/o auoiaoth,
i?iecaiaenoaaiioth e ae?. ia ycue iaoaiaoeee); 2) auae?aoue iaiaoiaeeiua
aeey ?aoaiey aaee/eiu ec eo /?acia?iiai iiiaeanoaa eee inouanoaeyoue
aa?eaoeaiue iiene aeaiiuo, iaaeinoathueo aeey ?aoaiey caaea/e; 3)
?aoaoue iieo/aiioth iaoaiaoe/aneoth caaea/o; 4) aiaeece?iaaoue
iaeaeaiiua ?aoaiey, n?aaieaaoue eo, auae?aoue iaeaieaa yeiiiie/iua; 5)
?aciaoaiaoece?iaaoue neooaoeeth (o.a. ia?aaiaeeoue iieo/aiiue ioaao ia
ycue auoiaie, i?iecaiaenoaaiiie e i?i/ae i?aeoeee).

Ec ia?a/eneaiiuo aeaeia aeayoaeueiinoe oeiea o/eo ?acaa /oi o?aoueaio.
Inoaeueiua cao?aaeaathony a oaeie ie/oiaeiie ia?a, /oi aiai?eoue aeaaea
i /anoe/iii iao/aiee caeanue a?yae ee neaaeoao. Iai?eia?, anee
aniiiieoue i caaea/ao iaii?aaeae?iiuo e ia?aii?aaeae?iiuo, oi oaeeo a
nia?aiaiiuo o/aaieeao ian/eouaaaony ia aieaa iieoi?ioeaioa, aea e oao
o/eoaey /aua anaai ia caia/atho.

I?eyoiui eneeth/aieai ec oeacaiiiai i?aaeea yaeyaony o/aaiee [18]. Aai
aaoi?, i?ioanni? I.?iaaiianeee, i?aaeeaaaao caaea/e iiae ?oa?eeaie,
n?aaee eioi?uo anoue e oaeea: «Ana ee aiciiaeiua neo/ae ?anniio?aiu?»,
«Aeinoaoi/ii ee aeaiiuo aeey ?aoaiey caaea/e?», «Neieueei ?aoaiee eiaao
caaea/a?» e o. i. Anoanoaaiii, caaea/e, i?aaeeaaaaiua iiae yoeie
?oa?eeaie, niioaaonoaotho iinoaaeaiiiio aii?ino, o.a. eiatho ianeieueei
aa?eaioia ?aaeecaoeee oneiaey, ianeieueei aiciiaeiuo iooae ?aoaiey, e
eiee/anoai aeaiiuo a oneiaee ia iaycaoaeueii yaeyaony iaiaoiaeeiui e
aeinoaoi/iui aeey iieo/aiey ioaaoa.

Ii, eae oaea neacaii, yoio o/aaiee – eneeth/aiea. Aieueoeinoai aaoi?ia
ae?oaeo o/aaieeia oaeea caaea/e eaii?e?otho. Iiaeao auoue, n/eoatho eo
aaniieaciuie e iaioaeiuie a iao/aiee?

Iaeiaei, iiiaea ecaanoiua iaaeaaiae–enneaaeiaaoaee n/eoatho
eniieueciaaiea oaeeo caaea/ iieaciui e iaiaoiaeeiui.

Iai?eia?, I.E?ooaoeeee a naiae eieaa “Ineoieiaey iaoaiaoe/aneeo
niiniaiinoae oeieueieeia” i?eaiaeeo oaeoth eeanneoeeaoeeth:

1. Caaea/e n ianoi?ie?iaaiiui oneiaeai – caaea/e, a eioi?uo eiathony ana
aeaiiua, ii aii?in caaea/e eeoue iiae?acoiaaaaony.

2. Caaea/e n ecauoi/iui oneiaeai – caaea/e, a eioi?uo eiathony eeoiea
aeaiiua, ia ioaeiua aeey ?aoaiey, a eeoue ianee?othuea iaiaoiaeeiua aeey
?aoaiey caaea/e aeaiiua.

3. Caaea/e n iaiieiui ninoaaii oneiaey – caaea/e, a eioi?uo ionoonoaotho
iaeioi?ua aeaiiua, iaiaoiaeeiua aeey ?aoaiey caaea/e, aneaaenoaea /aai
aeaoue eiie?aoiue ioaao ia aii?in caaea/e ia anaaaea i?aaenoaaeyaony
aiciiaeiui.

4. Caaea/e n i?ioeai?a/eaui oneiaeai – caaea/e, niaea?aeauea a oneiaee
i?ioeai?a/ea iaaeaeo aeaiiuie. [9, n. 124-150]

A.A.E?ooaoeeee iienuaaao enneaaeiaaiea, eioi?ia ii n a?oiiie
enneaaeiaaoaeae i?iaiaeee ai iiiaeo oeieao NNN? a oa/aiea 12 eao n 1955
ii 1966 aiaeu. Enneaaeiaaoaee eniieueciaaee caaea/e ?acee/iuo oeiia,
n?aaee eioi?uo auee e i?eaaae?iiua a yoie eeanneoeeaoeee, a ea/anoaa
oanoiauo caaeaiee aeey auyaeaiey ineoieiae/aneeo aniaeoia iaoaiaoe/aneeo
niiniaiinoae oeieueieeia. Ii ?acoeueoaoai yoiai enneaaeiaaiey
iieo/eeinue, /oi neeueiua o/aieee ni?aaeythony n caaea/aie oeacaiiuo
oeiia i?aeoe/anee naiinoiyoaeueii, auno?i, i?aeoe/anee aac iiiiue
eniuoaoaey. O/aieee n?aaeieo niiniaiinoae oaeaea iaieioi ni?aaeythony n
iiaeiaiuie caaeaieyie, iaeiaei aeey eo ?aoaiey ei o?aaoaony aieueoa
a?aiaie e eiiaaea iaaiaeyuee aii?in, iaoaeeeaathuee ia ?aoaiea. Neaaua
o/aieee i?aeoe/anee ia iiaee naiinoiyoaeueii i?iaanoe ?aoaiea yoeo
caaea/, ia aeaeaee nayce iaaeaeo iauaeoaie caaea/e, e aeaaea n
iiaeneaceie eniuoaoaey ia iiaee ni?aaeoueny n caaeaieai.

Neaaeoao ioiaoeoue, /oi eiaiii n oeacaiiuie oeiaie caaea/ enneaaeiaaoaee
naycuaaee iaeaieueoea iaaeaaeaeu.

A eieaa Ae.Iiea “Eae ?aoaoue caaea/o” i?eaiaeeony iioiaeay
eeanneoeeaoeey, ioee/athuayny eeoue oai, /oi a iae ionoonoaotho caaea/e
n ianoi?ie?iaaiiui ninoaaii oneiaey. Aieaa oiai, a naiae oaaeeoea,
iai?aaeaiiie a iiiiuue ?aoaoaeth, Ae.Iiea ia?auie ioieoaie iinoaaee
aii?inu: Aiciiaeii ee oaeiaeaoai?eoue oneiaeth? Aeinoaoi/ii ee oneiaea
aeey ii?aaeaeaiey iaecaanoiiai? eee iaaeinoaoi/ii? eee /?acia?ii? eee
i?ioeai?a/eai?

A?iaea au Iiea i?aaeiieaaaao ?aoaiea naiuo iau/iuo, oeieueiuo caaea/,
iaeiaei ii ia eneeth/aao aiciiaeiinoe iaee/ey iaeioi?uo “aiiiaeee” a
oneiaee caaea/e, e nouanoaiaaieth eioi?uo o/aieee aeieaeiu auoue aioiau.

I.Y?aeieaa a naiae eieaa [24, n.24,40] i?aaeeaaaao eniieueciaaoue a
iao/aiee iaoaiaoeea caaea/e n iaiieiui ninoaaii oneiaey au? n ieaaeoeo
eeannia, i?e/?i ii n/eoaao, /oi eniieueciaaiea oaeeo caaea/
(aeaoi?ie?iaaiiuo i?eia?ia, eae ii eo iacuaaao) iicaieyao i?iaiaeeoue
iao/aiea iia?aaeathueie oaiiaie, n eo iiiiuueth iiaeii ei?aiiui ia?acii
eciaieoue iuneeoaeueiua i?ioeannu ?aoathuaai, i?aa?aoea eo a aieaa
neiaeiua, aieaa niaea?aeaoaeueiua e iioiio eo/oa ?acaeaathuea
niiniaiinoe o/aieea.

O I.Iaoaeueneiai ano?a/aaony oaeay eeanneoeeaoeey caaea/. Iaaeaeo
oneiaeai caaea/e (A) e a? o?aaiaaieai (O) iiaeao auoue ?acee/iia
niioiioaiea, ii?aaeaeythuaa /enei ?aoaiee. Iau/ii oeieueiay caaea/a
eiaao iaeii eee ianeieueei ii?aaeae?iiuo ?aoaiee e iioiio iacuaaaony
ii?aaeae?iiie. Yoio oei caaea/e oneiaii iiaeii ecia?aceoue oi?ioeie
eiieeeaoeee A=>O, eioi?oth aoaeai iiieiaoue oae, /oi oneiaea A
niaea?aeeo aeinoaoi/ii e oieueei aeinoaoi/ii aeaiiuo aeey auiieiaiey
o?aaiaaiey O. Anee ec oneiaey A eaeia–eeai aeaiiia iionoeoue, oi iieo/ei
iaii?aaeae?iioth caaea/o. Iia eiaao aaneiia/iia iiiaeanoai ?aoaiee,
caaenyueo io aaneiia/iiai iiiaeanoaa cia/aiee oie aaee/eiu (ia?aiao?a),
eioi?ie i?eiaaeeaaeaei cia/aiea, aua?ioaiiia ec oneiaey. Iaeiiaoe,
oneiaea iiaeao niaea?aeaoue, e?iia A, iaeioi?ia aeiiieieoaeueiia
aeaiiia, e oiaaea caaea/a iacuaaaony ia?aii?aaeae?iiie. A /anoiii neo/aa
yoi “eeoiaa” aeaiiia iiaeao auoaeaoue ec oao, /oi oaea eiathony a
caaea/a, e oiaaea caaea/a ieacuaaaony ii?aaeae?iiie caaea/ae. A
inoaeueiuo neo/ayo ia?aii?aaeae?iiay caaea/a ia eiaao ?aoaiey,
iineieueeo a? aeaiiua i?ioeai?a/ao ae?oa ae?oao, ianiaianoeiu. Iniiaiua
ooieoeee caaea/ a iao/aiee auiieiytho ii?aaeae?iiua caaea/e, iaeiaei
ecaanoioth iieueco, ii iiaieth I.Iaoaeueneiai, i?eiineo o/aueiny
ciaeiinoai n iaii?aaeae?iiuie e ia?aii?aaeae?iiuie caaea/aie. [14,
n.176(177]

Caaea/e ec ?anniao?eaaaiie eeanneoeeaoeee iieaciu oai, /oi: iie ia
iaeaaeatho aeai?eoie/iinoueth ?aoaiey, iie aeoeaece?otho oinoaaiioth
aeayoaeueiinoue o/aueony, canoaaeytho eo eneaoue ianoaiaea?oiua
iiaeoiaeu e ?aoaieth caaea/, a oaeaea aeiioneatho eae ianeieueei
niiniaia ?aoaiey, oae e ianeieueei ?aoaiee aiiaua.

A iiaeoaa?aeaeaiea yoiai iiaiey eioa?aniua oaeou i?eaiaeeo a naiae
noaouea “Ino?ioaieueiue eee ooiioaieueiue?” E.Aeaaoyiieeiaa. Iia ieoao:
“?aoay caaea/o, /anoi aeaaea ia caaeoiuaaainy i ?aaeueiinoe a? oneiaey.
Iiyoiio i?aau oa aaoi?u, eioi?ua aeeth/atho a naie o/aaieee caaea/e n
ia?aaeueiuie oneiaeyie. Yoi canoaaeyao i?iaa?youe oneiaey o anao caaea/.
E?iia oiai, ia?aaeueiua caaea/e – yoi aioiaay i?iaeaiiay neooaoeey». [4]

Ionoonoaea oeacaiiuo caaea/ a oeieueiuo o/aaieeao i?eaiaeeo e oiio, /oi
e o/eoaey ia i?eaioe?otho naie oiaiey ia oaeea caaea/e, a ?acoeueoaoa
/aai eo iaaeaaiae/aneay iiaeaioiaea niaea?aeeo ecuyiu.

A caiaoea [5] A.Eaiaoaiei ieoao ia ioeaea, iaeaeaiiie a o/aaieea [1]. A
yoii o/aaieea ia n.135 i?eaaaeaia caaea/a 536(a). Aio a? oaeno: “Io?acie
BD yaeyaony aennaeo?enie o?aoaieueieea ABC. Iaeaeeoa DC, anee AB=30,
AD=20, BD=16 e (BDC=(C.

A?iaea au ie/aai iniaaiiiai a yoie caaea/a iao. Iaeiaei aaoi?, i?iaaaey
?aoaiea aeaoiy ?acee/iuie niiniaaie, caiaoee, /oi ioaaou a ieo ia
niaiaaeatho. Iiiuoea niiaeaee?iaaoue o?aoaieueiee n aeaiiuie, oeacaiiuie
a caaea/a, iieacaea, /oi aeaiiua niaea?aeaee i?ioeai?a/ea. Ieacuaaaony,
ianoeoua aaoi?u iiioey?iiai o/aaieea, aeeth/ea i?ioeai?a/eaoth caaea/o a
naie o/aaiee, ia caiaoeee a? i?ioeai?a/eainoe, eae ia caia/aee a? e
ouny/e o/eoaeae, ianeieueei eao ?aaioaaoeo ii yoiio o/aaieeo.

I?enoonoaea oaeie caaea/e (iiea /oi oieueei iaeiie) a o/aaieea aaiiao?ee
– oieueei ia iieueco o/aieeai e o/eoaeyi. AEaeue, /oi yoa caaea/a –
?acoeueoao neo/aeiie iieioiinoe aaoi?neiai eieeaeoeaa, a ia ?acoeueoao
a? caeiiiia?iiai auai?a.

Eae ieoao I.Aoeiaaoeeee a naiae noaouea [2], oeieueiee, eae i?aaeei,
eaii?e?oao aaaeiua aii?inu i ia?aecauoi/iinoe, iaaeinoaoi/iinoe eee
i?ioeai?a/eainoe caaea/, oae eae caaea/e ec oeieueiuo o/aaieeia ia
o?aaotho ?aciuoeaiey iaae oaeeie aii?inaie, iioiio /oi a ieo i?aeoe/anee
anaaaea eiaaony noieueei aeaiiuo, neieueei iaiaoiaeeii aeey ?aoaiey. E
yoi yaeyaony, ii iiaieth I.Aoeiaaoeeiai, na?ue?ciui iaaeinoaoeii
iaoaiaoe/aneiai ia?aciaaiey oeieueieeia.

Ii ?acoeueoaoai yenia?eiaioa, iienaiiiai a noaouea, ia?aii?aaeae?iiua (n
ecauoi/iui ninoaaii oneiaey) eee iaii?aaeae?iiua (n iaaeinoaoeii
aeaiiuo) caaea/e noaayo aieueoeinoai oeieueieeia a ooiee, ec eioi?iai
iie ca/anooth ia a ninoiyiee aua?aoueny. E yoi cao?oaeiaiea aicieeaao a
nayce n oai, /oi o oeieueieeia ia io?aaioai iaaue ioai?a e
i?aaeaa?eoaeueiie ioeaiee aeaiiuo caaea/e. Eae n/eoaao I.Aoeiaaoeeee,
io?aaioea yoiai iaauea ioaeii oaeaeyoue niaoeeaeueiia o/aaiia a?aiy. [2]

Eoae, aiaeec eeoa?aoo?iuo enoi/ieeia auyaeyao aaaeioth aeey
iaoaiaoe/aneiai ia?aciaaiey i?iaeaio: iiiaea iaaeaaiae–enneaaeiaaoaee
oeacuaatho ia oeaeaniia?aciinoue eniieueciaaiey a iao/aiee caaea/ n
«aiiiaeueiuie» oneiaeyie, a aaoi?u o/aaieeia ia yoi oeacaiea ii/oe ia
?aaae?otho.

Ian caeioa?aniaaea yoa i?iaeaia n ?aciuo oi/ae c?aiey. Ai–ia?auo,
ianeieueei iieacii aeeth/aiea oaeeo caaea/ a oeieueiue eo?n iaoaiaoeee?
Ai–aoi?uo, ioaeii ee niaoeeaeueiia iao/aiea o/aueony ?aoaieth oaeeo
caaea/? E anee ioaeii, oi eaeiau iaoiaee/aneea iniaaiiinoe oaeiai
iao/aiey?

Iieneai ioaaoia ia yoe aii?inu e iinayuaia ianoiyuay ?aaioa.

I. Eae o/aieee ?aaae?otho ia «aiiiaeueiua» caaea/e?

(eiinoaoe?othuea yenia?eiaiou)

I?aaeaa?eoaeueii iu iieacaee, /oi iiiaea ecaanoiua a iaaeaaiaeea o/?iua
n/eoatho iieaciui aeeth/aiea iaii?aaeae?iiuo e ia?aii?aaeae?iiuo caaea/
a i?ioeann iao/aiey. Ii/aio aea aieueoeinoai o/aaieeia oaeaeyao oaeia
neaaia aieiaiea yoei caaea/ai? Iiaeao auoue, o/aueany e aac
niaoeeaeueiiai iao/aiey a ninoiyiee ?aoaoue oaeea caaea/e? Ii e?aeiae
ia?a, auaiaeu A.E?ooaoeeiai aeecee e ooaa?aeeoaeueiiio ioaaoo. Ii
eiathony e ae?oaea iiaiey.

*oiau ioaaoeoue ia yoio aii?in, aue i?iaaae?i ?yae eiinoaoe?othueo
yenia?eiaioia a ?aciuo eeannao.

Oae, a ia?eiae iaaeaaiae/aneie i?aeoeee a 1997 aiaeo aue i?iaaaeai
iaaieueoie yenia?eiaio a n?aaeiae oeiea ? 3 a. I?oa.

O/aieeai 6 eeanna, a ninoaaa eioi?iai ia iiiaio i?iaaaeaiey yenia?eiaioa
auei 25 /aeiaae, ia naiinoiyoaeueiie ?aaioa a ea/anoaa aeiiieieoaeueiiai
caaeaiey auea i?aaeeiaeaia neaaeothuay caaea/a: a i?yiioaieueieea
noi?iiu ?aaiu 8,4 ni e 3,9 ni, a ia?eiao? 24,6 ni. Iaeoe ieiuaaeue
i?yiioaieueieea. I?e ?aoaiee yoie caaea/e a eeanna auaeaeeeinue
ianeieueei a?oii: 1 o/aiee ia ?aoee a? aiiaua, iioeae?iaaa yoi oai, /oi
ia oniae yoiai naeaeaoue; 2 o/aieea ?aoeee yoo caaea/o iieiinoueth n
iauyniaieai oiai, ii/aio iie ia eniieueciaaee i?e ?aoaiee caaea/e
aeaiiue a iae ia?eiao?, ii ia i?iaa?eee, niioaaonoaoao ee aeaiiay aeeeia
ia?eiao?a aeeeiai noi?ii; 1 o/aiee (enoaoe, o/anoiee iaeanoiie
ieeiieaaeu ii iaoaiaoeea) ?aoee yoo caaea/o iieiinoueth e i?iaa?ee
niioaaonoaea a iae aeaiiuo ae?oa ae?oao, ii i?e yoii aiceeny n ?aoaieai
ieiei 10 ieioo, a inoaeueiua o/aieee i?inoi iaienaee ioaao e caaea/a aac
eaeeo au oi ie auei iauyniaiee e iaio.

Iinea ?aoaiey caaeaiey n o/aieeii, iieiinoueth ?aoeaoei caaea/o, auea
i?iaaaeaia aanaaea i oii, n eaeeie o?oaeiinoyie ii noieeioeny a
i?ioeanna ?aoaiey caaea/e, e auynieeinue, /oi, ?aoay yoo caaea/o, ii
aia/aea aeoiae, /oi a caaea/a aeaiu aeaa i?yiioaieueieea, ieiuaaeue
iaeiiai ec eioi?uo ii iaoae n?aco aea e aeieai au/eneye, eae iiaeii
au?aceoue ieiuaaeue i?yiioaieueieea /a?ac aai ia?eiao?. Ii iioii
i?iaa?ee, /oi aeeeia ia?eiao?a iieiinoueth niioaaonoaoao aeeeiai noi?ii,
e ?aoee, /oi a caaea/a ?a/ue eaeao ia iaeiii e oii aea i?yiioaieueieea,
a ia?eiao? aeai oieueei aeey oiai, /oiau caiooaoue ?aoaiea. Ia
neaaeothuai o?iea eeann ecuyaee aeaeaiea ociaoue, eae aea i?aaeeueii
?aoaaony yoa caaea/a. Ei auei iiae?iaii iauyniaii, /oi ia?eiao? a
caaea/a yaeyaony eeoiei aeaiiui e aai ia ioaeii eniieueciaaoue aeey
?aoaiey, ii a aeaiiie neooaoeee aeeeiu noi?ii a caaea/a niioaaonoaotho
ia?eiao?o, /oi auaaao ia anaaaea e o?aaoao i?iaa?ee. Iinea /aai auea
i?aaeeiaeaia aeey ?aoaiey caaea/a aiaeiae/iiai oa?aeoa?a, ii
niaea?aeauay i?ioeai?a/ea a oaenoa: a i?yiioaieueieea aeeeiu noi?ii
?aaiu 6,7 ni e 4,2 ni, a ieiuaaeue ?aaia 25,3 ea. ni. O?aaoaony iaeoe
ia?eiao? i?yiioaieueieea. Eae e iaeeaeaeinue, ana 25 o/aueony ?aoeee yoo
caaea/o aac eniieueciaaiey ieiuaaee e caienaee ioaao. Ana iin/eoaee, /oi
ieiuaaeue a caaea/a yaeyaony eeoiei aeaiiui, ii ieeoi ia n/?e ioaeiui
i?iaa?eoue, niioaaonoaotho ee aeaiiua ae?oa ae?oao. ?acoeueoao
naiinoiyoaeueiie ?aaiou (ionoonoaea “iyo??ie” a ?aaioa n ianeiaeiuie
caaea/aie) canoaaee eo an? aea caaeoiaoueny. I/a?aaeiay aanaaea ia oo
aea oaio auea aini?eiyoa eie oaea n aieueoei aieiaieai e iiieiaieai.
O/aueany n aieueoei eioa?anii noaee ioiineoueny e “ia oaeei” (eo
ii?aaeaeaiea) caaea/ai, a iicaea e naie noaee ni/eiyoue caaea/e n
eeoieie aeaiiuie, i?aaeeaaay eo ae?oa ae?oao e o/eoaeth eae ia o?ieao,
oae e aia o?ieia.

Iai i?aaenoaaeyaony, /oi yoio eioa?an iiaeii iauynieoue iiaie iaiau/iie
neooaoeeae a noa?a ciaeiiuo aauae: aeey ?aoaiey oaeeo caaea/ iiauo
ciaiee ia o?aaoaony, ii o?aaoaony iiaue iiaeoiae e iei, iiaua
iuneeoaeueiua i?e?iu. O.a. i?ienoiaeeo “oeeoiaea” iuoeaiey, aai o?aiaae,
/oi aiieia niioaaonoaoao cai?inai ?anoouaai i?aaiecia.

Aue i?iaaaeai yenia?eiaio e a 10 eeanna oie aea oeieu, aaea ia iiiaio
yenia?eiaioa auei 13 o/aueony. Ei auea i?aaeeiaeaia aeey ?aoaiey
neaaeothuay oaenoiaay caaea/a: a iaeiie iaico?ea eiaaony iaeioi?ia
eiee/anoai eeneiou, a ae?oaie iaico?ea – oaeia aea eiee/anoai aiaeu.
Aeey i?eaioiaeaiey ?anoai?a nia/aea aueeee ec ia?aie iaico?ee ai aoi?oth
30 a?aiiia eeneiou. Caoai 2/3 ?anoai?a, iieo/eaoaainy ai aoi?ie iaico?ea
ia?aeeee a ia?aoth. Iinea yoiai a ia?aie iaico?ea ieacaeinue a 1,4 ?aca
iaiueoa aeeaeeinoe, /ai ai aoi?ie iaico?ea. Neieueei eeneiou e aiaeu
auei acyoi ia?aiia/aeueii?

Ana 13 o/aieeia niiaee aa?ii ninoaaeoue o?aaiaiea, i?iaanoe aai ?aoaiea
e caienaoue ioaao: 12 a?aiiia aiaeu e eeneiou auei ia?aiia/aeueii. Ia
yoii ana i?ae?aoeee ?aoaiea caaea/e. Aeaeaa ei auei i?aaeeiaeaii
aa?iooueny e oneiaeth caaea/e, e iii?iaiaaoue iiaenoaaeoue iieo/aiiue
?acoeueoao a oneiaea. Caeanue n?aco aea aicieeee o?oaeiinoe, iineieueeo
ec iaico?ee, niaea?aeauae 12 a aeeaeeinoe, o?aaiaaeinue aueeoue 30 a.
O/aieee ioeacuaaeenue iiieiaoue, eae iiaei oae iieo/eoueny, /oi caaea/a
e?aneai ?aoeeanue, ii oi, /oi iieo/eee a ea/anoaa ioaaoa, ia iiaeoiaeeei
ii oaenoo caaea/e. Iaiiiyoiui auei oaeaea e oi, eae iiaeii caienaoue a
ioaaoa, /oi iao ?aoaiey, eiaaea ia naiii aeaea iii anoue.

Caaea/a aucaaea ?acei iaaaoeaiia ioiioaiea aeanyoeeeannieeia, eioi?ua
n/eoaee aaniieaciui ?aoaiea oaeeo caaea/ aeey naiaai ia?aciaaiey. Iie
o?aaiaaee io o/eoaey i?aaeeaaaoue ei aeey ?aoaiey “ii?iaeueiua” caaea/e,
eaeea ei e i?eae?ony ?aoaoue i?e iinooieaiee a AOCu.

Oaeei ia?acii, yenia?eiaio iieacae ia oieueei iaaeinoaoi/iia ?acaeoea
iuoeaiey noa?oaeeannieeia, ii e oi, /oi o ieo oaea ionoonoaoao
no?aieaiea e oaeiio ?acaeoeth. Iie naie (iieaaaai, ia aac o/anoey
o/eoaeae) ii?aaeaeeee naaa “iioieie” naiaai ?acaeoey, naiae
ia?aciaaiiinoe, /oi a i?eioeeia aeey /aeiaaea iaii?iaeueii.

Aiaeiae/iue ieie–yenia?eiaio aue i?iaaae?i e a oiaea i?aaeaeeieiiiie
iaaeaaiae/aneie i?aeoeee a naioya?a – ieoya?a 1998 aiaea. Ii i?iaiaeeeny
n o/aueieny n?aaeiae oeieu ? 2 a. I?oe. A yenia?eiaioa i?eieiaee o/anoea
o/aieee 11–ai eeanna, eioi?ue yaeyaony eeoeaeneei eeannii i?e
Iiaee?aneii iaoeiino?ieoaeueiii einoeoooa (auioneiua yecaiaiu ii
iaoaiaoeea e oeceea a yoii eeanna niaiauaiu ni anooieoaeueiuie
yecaiaiaie a einoeooo). O?iaaiue i?aiiaeaaaiey iaoaiaoeee a yoii eeanna
aeinoaoi/ii aunie (o?e o/aieea – o/anoieee iaeanoiie ieeiieaaeu ii
iaoaiaoeea, iaeei – a? i?ec??).

Yoei o/aueiny auee i?aaeeiaeaiu ia o?iea aeey naiinoiyoaeueiiai ?aoaiey
neaaeothuea caaea/e:

A ia?aeeaeia?aiia noi?iiu 3 ni e 5 ni, a aunioa 4 ni. Iaeoe ieiuaaeue
ia?aeeaeia?aiia.

A ia?aeeaeia?aiia noi?iiu 4 ni e 5 ni, a aunioa 3 ni. Iaeoe ieiuaaeue
ia?aeeaeia?aiia.

N ia?aie caaea/ae aicieeee i?iaeaiu neaaeothuaai oa?aeoa?a: /anoue
o/aieeia, ia ia?aoea aieiaiey ia oi, /oi a aeaiiie caaea/a
ia?aeeaeia?aii ii?aaeaeyaony iaeiicia/ii (aunioa 4 ni iiaeao auoue
i?iaaaeaia oieueei e noi?iia 3 ni), auaeaee aeaa ioaaoa (12 ni2 e 20
ni2); au? iaeia /anoue o/aieeia inoaiiaeeanue ia iaeiii ?aoaiee, i?inoi
ia ?anniio?aa aiciiaeiue aoi?ie neo/ae (ioaao eeai 12 ni2 eeai 20 ni2);
e eeoue iaeei o/aiee nia/aea caaeae aii?in i oii, neieueei ?aoaiee
iiaeao eiaoue caaea/a, e, iieo/ea niaao “Aeoiae!”, auaeae iieiia e
i?aaeeueiia ?aoaiea.

Ni aoi?ie caaea/ae o aieueoae /anoe o/aueony aeaei ianoiyei i?aeoe/anee
oae aea, o.a. aieueoeinoai oeacaei oieueei iaeei ioaao (aeaaea
iiaeneacea i oii, /oi ?aoaiee iiaeao auoue e aieueoa, ei ia iiiiaea),
inoaeueiua – aeaa ioaaoa, ii aac iainiiaaiee. E eeoue iaeei o/aiee (oio
aea, /oi ?aoee e ia?aoth caaea/o) ?aoee naiinoiyoaeueii e i?aaeeueii yoo
caaea/o, auaeaa aeaa ioaaoa n a?aoiaioaoeeae.

Eae aeaeei, ?acoeueoaou yenia?eiaioia iieacuaatho, /oi oeieueieee ia a
ninoiyiee naiinoiyoaeueii ni?aaeoueny n caaea/aie oeacaiiuo oeiia. Iie
ia noaayo ia?aae niaie aii?inia i ia?aecauoi/iinoe, iaaeinoaoi/iinoe eee
i?ioeai?a/eainoe oneiaee caaea/, ia aiaeece?otho oneiaea caaea/e,
i?aaeaea /ai ia/aoue a? ?aoaiea, ia aica?auathony n iieo/aiiui ?aoaieai
e ia/aeo caaea/e, /oiau i?iaa?eoue aai. Ec /aai iiaeii caeeth/eoue, /oi
noi?ie?iaaiiinoue iaaueia ?aoaiey iaoaiaoe/aneeo caaea/ o o/aueony
n?aaeieo oeie (aeaaea a niaoeeaeece?iaaiiuo eeannao) yaeyaony aeaeaei ia
iieiie.

I?e oeaeaiai?aaeaiiii eniieueciaaiee ia?aii?aaeae?iiuo caaea/ o/aieee
aeiaieueii auno?i i?eo/athony aiaeece?iaaoue oneiaea caaea/e, ii a
ia?aia a?aiy an? aea aeaeatho aeiaieueii a?oaua ioeaee a ?aoaiee,
iauyniythueany i?aaeaea anaai eo iaoiaieai i?iaiaeeoue oaeie aiaeec. I?e
?aoaiee caaea/ ia?aii?aaeae?iiuo, ii eiathueo a oneiaee i?ioeai?a/ea,
o/aieee iinea iaaieueoie o?aie?iaee iaoiaeyo i/aaeaeiua eee neaai
ne?uoua i?ioeai?a/ey, ii, anee i?ioeai?a/ea oioue neieueei–ieaoaeue
caaoaee?iaaii, ia caia/atho aai e i?inoi eaii?e?otho aianoi oiai, /oiau
aa?iooueny e oneiaeth caaea/e e i?iaa?eoue ?aoaiea. O.a. iaiaoiaeeiinoue
?aaiou iaae caaea/ae iinea iieo/aiey ioaaoa, iaiaoiaeeiinoue aiaeeca
yoiai ioaaoa, auyaeaiea aai niioaaonoaey oaenoo caaea/e oi?ie?othony o
o/aueony ca aieaa aeeeoaeueiue n?ie e cao?aoie aieueoeo oneeee eae naieo
o/aueony, oae e o/eoaey. Iioiio aeaeaoaeueii ia/eiaoue yoio i?ioeann
iaiiiai ?aiueoa, /ai a aeanyoii eeanna.

I?e ?aoaiee caaea/ iaii?aaeae?iiuo o/aueany ia oiatho ia?aae?aoue
anaaiciiaeiua neo/ae, eioi?ua aicieeatho ec–ca yoie iaii?aaeae?iiinoe, e
/anoi eeai iaoiaeyo iaeii ?aoaiea, eeai ieooo, /oi caaea/a ia ?aoaaony.

Eoae, ioaao ia iinoaaeaiiue aii?in i/aaeaeai: naie o/aueany ia aioiau e
?aoaieth iaii?aaeae?iiuo e ia?aii?aaeae?iiuo caaea/, yoiio ioaeii eo
oeaeaiai?aaeaiii o/eoue. Eae? *oiau ioaaoeoue ia yoio aii?in, nia/aea
caaeoiaainy i oii, /aio iiaoo iao/eoue caaea/e n «aiiiaeueiui» oneiaeai?

II. Iainiiaaiea oeaeaniia?aciinoe caaea/ n «aiiiaeueiui» oneiaeai

Aeey ioaaoa ia iineaaeiee aii?in ?anniio?ei enneaaeoaiua oeiu caaea/
aieaa iiae?iaii, /oiau ii?aaeaeeoue, /oi eiie?aoii o?aaoaony io o/aieea
i?e ?aoaiee eaaeaeiai ec ieo.

1. Iaii?aaeae?iiua caaea/e – caaea/e n iaiieiui oneiaeai, a eioi?ii aeey
iieo/aiey eiie?aoiiai ioaaoa ia oaaoaao iaeiie eee ianeieueeeo aaee/ei
eee eaeeo–oi oeacaiee ia naienoaa iauaeoa eee aai nayce n ae?oaeie
iauaeoaie.

I?eia?u:

1. A o?aoaieueieea iaeia noi?iia eiaao aeeeio 10 ni, a ae?oaay 8 ni.
Iaeoe aeeeio o?aoueae noi?iiu.

2. Iiacae ninoieo ec oeenoa?i, oiaa?iuo aaaiiia e ieaooi?i. Oeenoa?i ia
4 iaiueoa, /ai ieaooi?i, e ia 8 iaiueoa, /ai aaaiiia. Eaeie aeeeiu
iiacae, anee eaaeaeay oeenoa?ia, aaaii e ieaooi?ia eiatho aeeeio 25 i?

3. Caanoaeueoe?iaaee ia 30 ei aieueoa, /ai inoaeinue. Neieueei
i?ioeaioia aei?iae iie?uoi anoaeueoii?

N ia?aiai acaeyaea ynii, /oi caaea/a 1 ia iiaeao eiaoue ?aoaiey, iioiio
/oi a iae ia oaaoaao aeaiiuo. Iaeiaei enneaaeoai neooaoeeth aeoaaea.
Aniiiiei ia?aaainoai o?aoaieueieea e caieoai aai aeey aeaiiiai
o?aoaieueieea, iaicia/ea iaecaanoioth noi?iio /a?ac a.

Iieo/ei:

10 + 8 > a;

a + 10 > 8;

a + 8 > 10;

a ec yoie nenoaiu neaaeoao, /oi

2 < a < 18.Oaeei ia?acii, iai oaeaeinue ooi/ieoue ioaao n o?acu "caaea/o iaaiciiaeii ?aoeoue" aei aiieia ii?aaeae?iiiai eioa?aaea, /oi neaaeoao i?eciaoue ioaaoii aieaa aunieiai o?iaiy.E ai aoi?ie caaea/a iai?aoeaaaony auaiae, /oi ieeaeie ioaao oai iaaiciiaeai, iineieueeo aeaiiuo ia oaaoaao. Ii i?e aieaa aieiaoaeueiii aiaeeca oneiaey auyaeyaony, /oi ia ethaia /enei iiaeao iieo/eoueny a ioaaoa. Iai?eia?, iaaiciiaeiu ioaaou 333 i e 250 i, oioy e ii ?aciui i?e/eiai. Ia?aia iaaiciiaeii, iioiio /oi ioaao aeieaeai auoue e?aoiui 25 i. A aoi?ia iaaiciiaeii, o.e. iauaa eiee/anoai oyaiauo aaeeieoe ia iiaeao auoue ?aaiui aeanyoe. Neieueei aea yoeo aaeeieoe oai iiaeao auoue?Anee a iiacaea o oeenoa?i, oi ieaooi?i o+4, a aaaiiia o+8. Aianoa: 3o+12. Oaeei ia?acii, anao oyaiauo aaeeieoe ia iaiueoa iyoiaaeoeaoe, a aiciiaeiue ioaao: 25(3o+12) i, aaea o – iaoo?aeueiia /enei. Iaae "aeecaeiii" ioaaoa iiaeii ii?aaioaoue, anee ia?aienaoue aai oae: 75(o+4). A oaia?ue, ia?aiaicia/ea aoeaie o (eee ae?oaie) eiee/anoai ieaooi?i, iieo/ei naiue ei?ioeee aa?eaio ioaaoa: 75o i, aaea o – iaoo?aeueiia /enei, ia iaiueoaa iyoe.*oi ie aiai?e, a oaeia ?aoaiea o?aaoao aieaa aunieiai o?iaiy oinoaaiiie aeayoaeueiinoe, /ai i?eieoeaiia "Caaea/a ia eiaao ?aoaiey, iioiio /oi aeaiiuo ia oaaoaao". E, ?acoiaaony, /oi oeacaiiiai ?aoaiey io oeieueieeia n?aco ia iieo/eoue, /oi e iiaeoaa?aeeee ia?aua i?iau ni noai?ioeaioiui ?acoeueoaoii.O?aouey ec oeacaiiuo caeanue caaea/ i?aaeeaaaeanue aeaayoeeeannieeai eeoeay. ?acoeueoao oio aea: "Caaea/a ia ?aoaaony...". Oieueei aeiiieieoaeueiay i?inueaa iacaaoue ianeieueei aiciiaeiuo ioaaoia iiaeoieeioea eeoeaenoia e aiaeeco e a eiioea eiioeia auaaea ia ioaao, aeeceee e i?aaeeueiiio: o%, aaea o((50;100].Auaiae: ?aoaiea iaii?aaeae?iiie caaea/e iau/ii caeai/eaaaony iaii?aaeae?iiui ioaaoii, a eioi?ii eneiiay aaee/eia iiaeao i?eieiaoue cia/aiey ec iaeiaai /eneiaiai iiiaeanoaa. Auyaeaiea yoiai iiiaeanoaa e aeieaeii noaoue oeaeueth ?aoaiey oaeie caaea/e, /oi aeinoeaaaony aaeoi/eaui aiaeecii oaenoa caaea/e e acaeiinaycae iaaeaeo aeaiiuie aaee/eiaie. Yoiio iieaciiio aeey oinoaaiiiai ?acaeoey o/aueony i?ioeanno ioaeii niaoeeaeueii iao/aoue.Caaea/e yoiai oeia o?aaotho io o/aieea iiaeeecaoeee i?aeoe/anee anaai iaai?a ciaiee, oiaiey aiaeece?iaaoue oneiaea, no?ieoue iaoaiaoe/aneoth iiaeaeue ?aoaiey, iaoiaeeoue aeaiiua e caaea/a "iaaeaeo no?ie" oneiaey. I?aeoe/anee, iaeiie niaoeeaeueii iiaeia?aiiie caaea/ae yoiai oeia iiaeii i?iaa?eoue ciaiey o/aieea ii oeaeie oaia. A ea/anoaa oaeiai i?eia?a iiaeii ?anniao?eaaoue caaea/o: I?e eaeeo cia/aieyo iieiaeeoaeueiiai ia?aiao?a a o?aaiaiea logax=ax aoaeao eiaoue aaeeinoaaiiia ?aoaiea e oeacaoue aai. Yoa caaea/a auea i?aaeeiaeaia iaoae a?oiia (a?oiia «A» IV eo?na oeceei–iaoaiaoe/aneiai Iiaee?aneiai oieaa?neoaoa, 1997 aiae) ia caiyoeyo ii aeeaeaeoeea iaoaiaoeee aeey naiinoiyoaeueiiai ?aoaiey, /oi iiiiaei nooaeaioai a?oiiu aanueia nouanoaaiii iiaoi?eoue e oaeoaeoue ciaiey ii oe?ieiio niaeo?o oeieueiiai eo?na aeaaa?u e ia/ae aiaeeca.Aiiaua, o?aaiaiey e ae?oaea caaea/e n ia?aiao?aie iiaeii ?anniao?eaaoue eae /anoiua neo/ae iaii?aaeae?iiuo caaea/. I?iaeaiiinoue ia?aoiaea e oaeei caaea/ai iuouatho o/eoaey oaea i?e ia?aoiaea io o?aaiaiee 7o=12, 0o=3, –5o=0, 0o=0 e eeiaeiiio o?aaiaieth iauaai aeaea: ao=b. I?aaeaa?eoaeueiay o?aie?iaea a ?aoaiee iaii?aaeae?iiuo caaea/ e caeanue auea au oeaeaniia?aciie e iieaciie.2. Caaea/e ia?aii?aaeae?iiua – caaea/e n ecauoi/iui ninoaaii oneiaey, n eeoieie aeaiiuie, aac eioi?uo ioaao iiaeao auoue iieo/ai, ii eioi?ua a oie eee eiie ia?a ianee?otho iooue ?aoaiey.Eae oaea iieacaii auoa, aeaiiua a oaeeo caaea/ao iiaoo auoue i?ioeai?a/eauie e auyaeaiea yoie i?ioeai?a/eainoe eee iai?ioeai?a/eainoe yaeyaony iaycaoaeueiui yeaiaioii ?aoaiey oaeie caaea/e.Iai?eia?, a caaea/a "Iaeoe ieiuaaeue i?yiioaieueiiai o?aoaieueieea n eaoaoaie 9 ni e 40 ni e aeiioaiocie 41 ni" iaei iaeoe ioaao iieoi?iecaaaeaieai 9 ia 40. Iaaei au? auyaeoue, aoaeao ee o i?yiioaieueiiai o?aoaieueieea n eaoaoaie 9 ni e 40 ni aeiioaioca ?aaiie 41 ni. Aac yoiai auyniaiey ?aoaiea caaea/e ia iiaeao auoue i?eciaii iieiui.A yoii aniaeoa eioa?an i?aaenoaaeytho i?aeoe/aneea caaea/e. Iai?eia?, i?e eco/aiee ia?aie oi?ioeu ieiuaaee o?aoaieueieea o/eoaeue i?eiineo a eeann au?acaiiue ec aoiaae o?aoaieueiee n i?iaaaeaiiuie aunioaie e i?aaeeaaaao iaeiiio ec o/aueony ecia?eoue aeeeio eaeie–eeai noi?iiu, iioii aoi?iio o/aieeo aeeeio aoi?ie noi?iiu, o?aoueaio – o?aoueae, au? o?ia ecia?ytho auniou, eaaeaeue ii iaeiie. ?acoeueoaou ecia?aiee caienuaathony ia aeinea. Oaia?ue o/eoaeue i?aaeeaaaao au/eneeoue ieiuaaeue yoiai o?aoaieueieea. Aii?in, eaeay aunioa e eaeie noi?iia i?iaaaeaia, o/eoaeue ia?aaae?anoao o/aueiny, eioi?ua ecia?yee, ii oa, anoanoaaiii, ia iiiiyo, iineieueeo ia oeene?iaaee ia yoii aieiaiey. Aicieeaao eioa?aniay i?iaeaia, eioi?ay a eoiaa an? aea ?ac?aoaaony, enoiaey ec oiai, /oi ieiuaaeue iaeiiai e oiai aea o?aoaieueieea ia iiaeao eiaoue ?aciuo cia/aiee. Iiyoiio naiay aieueoay aunioa aeieaeia auoue i?iaaaeaia e naiie iaeaiueeie noi?iia, a naiay iaeaiueeay e naiie aieueoie. Oaia?ue ieiuaaeue o?aoaieueieea iiaeii au/eneyoue o?aiy niiniaaie, ii ?acoeueoao, eae auyniyaony, iieo/aaony ia nianai iaeeiaeiaui. Iiyaeyaony i?e/eia iiaiai?eoue i nouiinoe ecia?aiee, ia eo iaycaoaeueiie iaoi/iinoe, i ea/anoaa i?eaeeae?iiuo ecia?aiee, ia iniaaiiinoyo au/eneaiee n i?eaeeae?iiuie /eneaie e ae?oaeo niioaaonoaothueo aii?inao. E yeaiaioa?iay caaea/a ia i?eiaiaiea i?eieoeaiie oi?ioeu iaiieiyaony aiaaoui niaea?aeaieai.Caaea/e yoiai oeia o?aaotho io o/aieea oiaiey aiaeece?iaaoue oneiaea, iaoiaeeoue a i?i ioaeiua aeaiiua e ioa?anuaaoue iaioaeiua. I?e/?i, "iaioaeiuie" o ?aciuo o/aieeia iiaoo auoue ?aciua aaee/eiu. Iai?eia?, a caaea/a "Iaeoe ieiuaaeue i?yiioaieueieea ii noi?iia, aeeaaiiaee e oaeo iaaeaeo aeeaaiiaeyie" iaeie o/aieee aoaeoo eneaoue ioaao iieiaeiie i?iecaaaeaiey aeeaaiiaeae ia neion oaea iaaeaeo ieie (oai naiui noi?iia noaiiaeony eeoiei aeaiiui), ae?oaea iieo/ao ioaao i?iecaaaeaieai noi?ii, i?aaeaa?eoaeueii au/eneea aoi?oth noi?iio ii oai?aia Ieoaai?a (caeanue oaie noaiiaeony eeoiei aeaiiui). Aiciiaeai e o?aoee aa?eaio, eiaaea eeoiei aeaiiui noaiao aeeaaiiaeue. Eniieueciaaiea ianeieueeeo aa?eaioia ?aoaiey oaeie caaea/e iieacii ia oieueei aeey eo n?aaiaiey, ii aieueoa aeey naiieiio?iey: iaeeiaeiainoue ioaaoia i?e ?aciuo ?aoaieyo iiauoaao oaa?aiiinoue a eo i?aaeeueiinoe. Ionthaea iiaeii iieo/eoue e iaeei ec iaae?aeiuo niiniaia naiieiio?iey a ?aoaiee o?aaeeoeeiiiuo caaea/: iinea iieo/aiey ioaaoa anoaaeoue yoio ioaao a oaeno caaea/e eae iaeii ec aeaiiuo, a iaeio ec ecaanoiuo aaee/ei n/eoaoue iaecaanoiie e ?aoeoue iieo/aiioth iiaoth caaea/o.3. Ia?aaeueiua (eee i?ioeai?a/eaua) caaea/e iau/ii ioiinyo e ioaeaeueiiio oeio, oioy, eae ioia/aii auoa, iie yaeythony ninoaaiie /anoueth ia?aii?aaeae?iiuo (eiiaaea ii?aaeae?iiuo) caaea/.I?eia?: Iaeoe ieiuaaeue o?aoaieueieea ni noi?iiaie 10 ni, 19 ni e8 ni.Aiana iaiaycaoaeueii ?aoaoue i?eaaaeaiioth caaea/o, /oiau iiiyoue, /oi iia ia eiaao ?aoaiey. Aeinoaoi/ii eeoue i?iaa?eoue oneiaea ia i?ioeai?a/eainoue i?e iiiiue ia?aaainoaa o?aoaieueieea e oaaaeeoueny, /oi caaea/a ia iiaeao eiaoue ?aoaiey.Iiaeii auei au ?aoeoue yoo caaea/o, eniieuecoy oi?ioeo Aa?iia, ii e oiaaea a eiioea eiioeia aue au iieo/ai i?ioeai?a/eaue ?acoeueoao (iiaeei?aiiia au?aaeaiea iieo/eeinue au io?eoeaoaeueiui).Aeey oaeeo caaea/ oa?aeoa?iui yaeyaony oi, /oi iie iiaoo eiaoue aeinoaoi/ii e?aneaia ?aoaiea, eae yoi auei n i?eaaae?iiie auoa caaea/ae ia ia?aeeaaiea aeeaeeinoe, ii oieueei yoi ?aoaiea aoaeao i?ioeai?a/eoue cae?aaiio niuneo. I?e ?aoaiee oaeeo caaea/ iaiaoiaeeii anaaaea a eiioea aica?auaoueny e oneiaeth e aeaeaoue i?iaa?eo iieo/aiiiai ?aoaiey. A iineieueeo i?ioeai?a/eainoue caaea/e ia anaaaea a?inaaony a aeaca, yoi i?eo/eo auiieiyoue i?iaa?eo iieo/aiiiai ioaaoa a eaaeaeie caaea/a. Iaeioi?ua ec caaea/ yoiai oeia iicaieytho auyaeoue i?ioeai?a/ea aeaiiuo aua i?e aiaeeca oneiaey, a ?acoeueoaoa /aai i?ioeann ?aoaiey noaiiaeony eceeoiei. Aeinoaoi/ii /anoia iiaoi?aiea oaeeo neooaoeee i?eaaae?o o/aueony e iaiaoiaeeiinoe aiaeece?iaaoue oneiaea ia?aae ia/aeii ?aoaiey, /oiau ecaaaeoue naay io eeoiae ?aaiou.Eoae, iu auynieee, /oi eaaeaeue ec oeacaiiuo oeiia caaea/ ian?o a naaa ii?aaeae?iioth ?acaeaathuoth ooieoeeth. Oae, ia?aii?aaeae?iiua caaea/e o?aaotho oiaiey aiaeece?iaaoue oneiaea e no?ieoue ?aoaiea caaea/e i?e iiiiue ieieiaeueiiai /enea aeaiiuo. I?ioeai?a/eaua caaea/e canoaaeytho aeaeaoue i?iaa?eo ?aoaiey, aieaa aieiaoaeueii aiaeece?iaaoue aeaiiua caaea/e. Iaii?aaeae?iiua caaea/e o?aaotho aeinoaoi/ii iaoe?iuo ciaiee ia iauaeoa caaea/e, i naycyo aai n ae?oaeie iaoaiaoe/aneeie iauaeoaie, eioi?ua iiaoo ieacaoueny iieaciuie i?e iieo/aiee ionoue iaii?aaeae?iiiai, ii an? aea ia?aie/aiiiai iaeeie ?aieaie ioaaoa.Ecaanoii (ni., iai?eia?, eieae Ae.Iiea), /oi i?ioeann ?aoaiey iaoaiaoe/aneie caaea/e i?aaeoniao?eaaao ?aaeecaoeeth /aou??o yoaiia: eco/aiea oaenoa caaea/e, ninoaaeaiea ieaia ?aoaiey, aai auiieiaiea, eco/aiea iieo/aiiiai ?aoaiey ("acaeyae iacaae"). Aeey oniaoiiai oi?ie?iaaiey o oeieueieeia oiaiee, naycaiiuo n ?aaeecaoeeae oiai eee eiiai aeaea aeayoaeueiinoe, iaiaoiaeeii iao/aoue eo naiinoiyoaeueii auiieiyoue eaaeaeue ec oeacaiiuo yoaiia i?ioeanna ?aoaiey caaea/. Aeey yoiai oeaeaniia?acii o/eoue o/aueony iia?aoeeyi, niioaaonoaothuei ii?aaeae?iiiio yoaio ?aaiou n caaea/ae. Oeacaiiua auoa oeiu caaea/ e iicaieytho o/aieeo oniaa?oainoaiaaoue naie oiaiey a eaaeaeii ec aeaiiuo aeaeia aeayoaeueiinoe.III. I?eeeaeea iaoiaee/aneiai iiaeoiaeae iao/aieth ?aoaieth «aiiiaeueiuo» caaea/Eae aea iao/eoue o/aueony ?aoaoue caaea/e oeacaiiuo oeiia? Eae i?eo/eoue eo e "ianoaiaea?oiiio" iiaeoiaeo e ?aoaieth caaea/e?Iniiaie aeey ioaaoa ia iinoaaeaiiue aii?in iiaeii n/eoaoue ecaanoioth oaaeeoeo Ae.Iiea "Eae ?aoaoue caaea/o" [16, n. 210-212]. A /enea iniiaiuo aii?inia, iaae eioi?uie neaaeoao caaeoiuaaoueny ?aoaoaeth, Ae.Iiea auaeaeyao neaaeothuea:Aiciiaeii ee oaeiaeaoai?eoue oneiaeth? Aeinoaoi/ii ee oneiaea aeey ii?aaeaeaiey iaecaanoiiai? Eee iaaeinoaoi/ii? Eee /?acia?ii? Eee i?ioeai?a/eai?..Nio?aieoa oieueei /anoue oneiaey, ioa?inea inoaeueioth /anoue: ianeieueei ii?aaeae?iiui ieaaeaony oiaaea iaecaanoiia? Eae iii niiaeao iaiyoueny?..Ana ee aeaiiua aaie eniieueciaaiu? Ana ee oneiaey? I?eiyou ee ai aieiaiea ana nouanoaaiiua iiiyoey, niaea?aeaueany a caaea/a?..Iaeuecy ee i?iaa?eoue ?acoeueoao? Iaeuecy ee i?iaa?eoue oiae ?aoaiey?..Ia?a/eneaiiua auoa aii?inu e niaaou ec oaaeeoeu Ae.Iiea yaeythony iaeiiiioey?iuie eee nianai iaiiioey?iuie o oeieueiuo o/eoaeae. Oioy au iioiio, /oi ia?aay /anoue yoeo aii?inia e ia o?aaoaony a ioiioaiee o?aaeeoeeiiiuo oeieueiuo caaea/. Aeey oiai, /oiau oaaeeoea Ae.Iiea ca?aaioaea a iieiie ia?a, e aicieeaao iaiaoiaeeiinoue aeiiieieoue oeieueiua iaai?u caaea/ caaea/aie iaii?aaeae?iiuie e ia?aii?aaeae?iiuie.Iii?iaoai iniuneeoue aiciiaeiue iaoiaee/aneee iiaeoiae e iao/aieth o/aueony ?aoaieth oaeeo caaea/.Ia/i?i n oiai, /oi inoi?iaeiia aeeth/aiea oaeeo caaea/ aiciiaeii oaea a 5–6 eeannao eee aeaaea ?aiueoa [24, n. ]. Ia/eiaoue, eae iai i?aaenoaaeyaony, neaaeoao n aaaaeaiey caaea/ ia?aii?aaeae?iiuo, i?aaeoi?aaeaeay ia ia?auo ii?ao o/aueony i iaee/ee ecauoi/iuo aeaiiuo e i?aaeeaaay ei iaeoe oaeea aeaiiua, iinoaiaiii ia?aoiaey io caaea/ i?inouo e oaeei caaea/ai, a eioi?uo ecauoi/iua aeaiiua ia n?aco a?inathony a aeaca. Eiaaea o/aueany i?eia?aooo iaeioi?ua iaauee ?aoaiey oaeeo caaea/, iiaeii ia?aeoe e aaaaeaieth oaeeo caaea/ oaea aac i?aaeoi?aaeaeaiey i iaee/ee ecauoi/iuo aeaiiuo, /a?aaeoy yoe caaea/e n o?aaeeoeeiiiuie ii?aaeae?iiuie caaea/aie. Oaeei ia?acii, ia ciay, eiaaony ee a oneiaee caaea/e eeoiaa aeaiiia eee iao, ii iiaeic?aaay, /oi iii iiaeao auoue, o/aueany e eaaeaeie caaea/a aoaeoo iiaeoiaeeoue e?eoe/anee, /oi auciaao aieueooth, /ai a o?aaeeoeeiiiuo oneiaeyo, iaiaoiaeeiinoue aieiaoaeueiiai aiaeeca oneiaey caaea/e e ?acee/iuo iiaeoiaeia e a? ?aoaieth.Ia iaeioi?ii yoaia ia?aii?aaeae?iiua caaea/e, i?aaeeaaaaiua o/aueiny, iiaoo noaoue i?ioeai?a/eauie. Eniieueciaaiea oaeeo caaea/ iinoaiaiii i?eo/eo eo e oiio, /oi iaia?oaeaiiia a oneiaee eeoiaa aeaiiia ia neaaeoao eaii?e?iaaoue, ii neaaeoao i?iaa?youe aai ia i?ioeai?a/eainoue (i?e yoii, eae iai i?aaenoaaeyaony, /aua ioaeii i?eaioe?iaaoueny ia au/eneaiey n i?eaeeae?iiuie aaee/eiaie, /ai n oi/iuie). E?iia oiai, eniieueciaaiea caaea/ n i?ioeai?a/eauie aeaiiuie iicaieeo o/aueiny caiaoeoue (ia aac iiiiue o/eoaey) iieaciinoue aaeoi/eaiai aiaeeca oneiaey, a ?acoeueoaoa eioi?iai iiaeii auyaeoue i?ioeai?a/eainoue e oai naiui ia eneaoue ?aoaiey, o.a. iaeaa/eoue naaa ?aaioo. A iineieueeo ieeiaaea ia ynii, anoue ee i?ioeai?a/ea a oneiaee caaea/e eee iao, oi aaeoi/eaiio aiaeeco aoaeoo iiaeaa?aaoueny oneiaey anao caaea/, /oi neaaeoao n/eoaoue /?acau/aeii iieaciui ea/anoaii ?aoaoaey caaea/.Eiaaea ia?aii?aaeae?iiua caaea/e noaioo i?eau/iuie e ia aoaeoo aucuaaoue o o/aueony ianoi?iaeaiiinoe e i?ioanoa, iiaeii ia?aeoe e ?aoaieth iaii?aaeae?iiuo caaea/, niiaa aea aia/aea i?aaeoi?aaeaeay o/aueony i oii, /oi a oneiaee caaea/e iaeioi?uo aeaiiuo ia oaaoaao, e i?aaeeaaay ei oeacaoue, eaeeo. I?e yoii iieacii n?aaieaaoue, eae caaeneo ioaao caaea/e io ?acee/iuo aeiiieiaiee o/aueony – n aiciiaeiui, ii iiea ia iaycaoaeueiui, auoiaeii ia aeeaiacii yoiai ioaaoa. Eai oeaeueth ?aoaiey oaeeo caaea/, eae oaea ioia/aii auoa, e yaeyaony oeacaiea aeeaiaciia aiciiaeiuo ninoiyiee ioaaoa.Iu iiiuoaeenue ?ac?aaioaoue nenoaio caaea/ n eniieueciaaieai anao caaea/ ?anniao?eaaaiie eeanneoeeaoeee a iaeiie ec oai oeieueiiai eo?na aaiiao?ee.E?eoa?ee nicaeaiey oaeie nenoaiu caaea/ ?anniao?eaathony a [19]. Aaoi? ieoao :"Iineaaeiaaoaeueiia, iinoaiaiii oneiaeiythuaany aa?uee?iaaiea oneiaey caaea/ yaeyaony iniiaiui i?eioeeiii, ii?aaeaeythuei iino?iaiea oi?aaeiaiee i?e iao/aiee ?aoaieth oeiiauo caaea/. Aia/aea – ia ia?aiia/aeueiuo yoaiao naiinoiyoaeueiiai ?aoaiey iiaie aeey o/aieea oeiiaie caaea/e (iinea oiai, eae iia ?acia?aia a eeanna) – aa?uee?iaaiea oneiaey eanaaony naiuo ianouanoaaiiuo aai noi?ii, iaiin?aaenoaaiii ia aeeythueo ia i?eiaiaiea iniiaiiai i?e?ia ?aoaiey, a eiaiii nthaeaoa caaea/e e /eneiauo aaee/ei. Iineaaeothuaa aa?uee?iaaiea oneiaey caaea/e eiaao oeaeueth ia noieueei cae?aieaiea a iaiyoe o/aueony oiai eee eiiai oeiiaiai i?e?ia (yoi oiaea iaiaoiaeeii), neieueei au?aaioeo oiaiey ?aniiciaaaoue ca ?acee/iie aiaoiae oi?iie caaea/e a? iaeeiaeiaoth eiae/aneoth no?oeoo?o. Ia yoii yoaia aieueoia cia/aiea i?eia?aoaao ?aoaiea caaea/ aeaiiiai oeia aiaeiae/iuo ii eiae/aneie no?oeoo?a, ii eciai?iiuo ii neiaaniie oi?ioee?iaea. I?e yoii eciaiaiea oi?ioee?iaee aeieaeii eanaoueny oie /anoe oneiaey, eioi?ay yaeyaony ii?aaeaeythuae aeey auai?a i?e?ia ?aoaiey.?aoay nenoaio caaea/, iino?iaiioth ii yoiio i?eioeeio, o/aueany i?eo/athony oeaaeeaaoue naiia nouanoaaiiia a oneiaee caaea/, i?aaeeueii aano?aae?oynue io aiaoieo noi?ii – naiaia?acey eo oi?ioee?iaie.Ia neaaeothuai yoaia oeaeaniia?acii aaiaeeoue a oneiaey caaea/ aeiiieieoaeueiua yeaiaiou, oaaee/eaay eiee/anoai /eneiauo aeaiiuo. Enneaaeiaaiey iieacuaatho, /oi a yoii neo/aa, ianiio?y ia oi, /oi aaaaeaiea aeiiieieoaeueiuo aeaiiuo ieeae ia aeeyao ia eniieueciaaiea iniiaiiai i?e?ia ?aoaiey, aeey o/aueony an? aea nicaea?ony iiaay neooaoeey, o?aaothuay io ieo oiaiey au/eaieoue oo /anoue oneiaey, eioi?ay ii?aaeaeyao i?eiaiaiea oeiiaiai i?e?ia e a oiaea aeaenoaee i?e ?aoaiee caaea/e iaeoe aio i?aaeeueiia ianoi.Oi aea naiia neaaeoao ioiaoeoue e i i?eiaiaiee caaea/ ia?aii?aaeae?iiuo, ei??aeoiuo, ii aucuaathueo i?ioeai?a/ea i?e ?aoaiee. Yooaeo io aaaaeaiey yoeo caaea/ ia noieo iaaeiioeaieaaoue, eo oeaeue a nenoaia caaea/ – aucia neooaoeee, i?e eioi?ie caaea/a ia eiaao ?aoaiey i?e a?iaea au nouanoaothuai ia naiii aeaea iaoaiaoe/aneii (caienuaaaiii iin?aaenoaii iaoaiaoe/aneiai ycuea) ?aoaiee.A aeaeueiaeoai oaea iiaeii i?eaaaaoue e oaeiio aa?uee?iaaieth oneiaee caaea/e, eioi?ia o?aaoao aeaeieciaiaiey naiiai oeiiaiai i?e?ia. Oaeiai ?iaea aa?uee?iaaiea niinianoaoao au?aaioea aieaa neiaeiuo oiaiee, cia/aiea eioi?uo aeey oi?ie?iaaiey naiinoiyoaeueiiai iuoeaiey o/aueony i/aiue aaeeei. ?a/ue eae?o a yoeo neo/ayo i au?aaioea oiaiee ia?ano?aeaaoue ecaanoiua niiniau ?aoaiey a niioaaonoaee n eciaiaieai oneiaee caaea/e. Oniao yoie ia?ano?ieee iaiin?aaenoaaiii caaeneo io oiai, a eaeie ia?a o/aueany oiatho aiaeece?iaaoue caaea/e, oeaaeeaay iaeiia?aiaiii e noiaeiia e ?acee/iia." [19, n. ]E, iaeiiaoe, iineaaeiaa aeaeieciaiaiea oneiaey caaea/e – ninoaaeyoue oneiaea oaeei ia?acii, /oiau iaeioi?uo aeaiiuo a ieo ia oaaoaei. N o/?oii i?aaeuaeouaai iiuoa o/aieeia ii ?aoaieth caaea/, yoio oei caaea/, ai–ia?auo, aoaeao aeey ieo ianeieueei neiaeiui e iiaui, ai–aoi?uo, ?aoay caaea/e oaeiai oeia, o/aieee aieaa iaaeyaeii iniciatho ne?uoua naienoaa iauaeoa caaea/e, oyniytho aieaa aeaoaeueii aeeiaie/aneea niioiioaiey iaaeaeo iiiyoeyie e ii?aaeaeaieyie, i?eiaiyaiuie i?e ?aoaiee aeaiiie caaea/e.IV. ?anoe?aiiay nenoaia caaea/ ii oaia «Noiia oaeia o?aoaieueieea»A niioaaonoaee n auoaneacaiiui i?aaeeaaaaony e ?anniio?aieth nenoaia caaea/ ii oaia "Noiia oaeia o?aoaieueieea" (aaiiao?ey, 7 eeann). Oaia yoa ia a?iiicaeeay, aeinoaoi/ii /?oeay e aiaaoi ianuuaiiay ?acee/iiai ?iaea caaea/iuie neooaoeeyie.Aeey ninoaaeaiey o?aaoaiie nenoaiu caaea/ auei auaeaeaii 5 iniiaiuo aniaeoia aeaiiie oaiu:iaiin?aaenoaaiiia eniieueciaaiea oeacaiiiai naienoaa oaeia a i?iecaieueiii o?aoaieueieea;oi aea – aeey ?aaiiaaae?aiiiai o?aoaieueieea;oi aea – aeey i?yiioaieueiiai o?aoaieueieea;oi aea – aeey oaeia, ia?aciaaiiuo aioo?e o?aoaieueieea iaaeeaiaie, aennaeo?enaie, aunioaie e ae?.;oi aea – n auoiaeii ia aiaoiea oaeu o?aoaieueieea.I?eiaiaiea naienoaa oaeia aeey i?iecaieueiiai o?aoaieueieeaAeaa oaea o?aoaieueieea ?aaiu 26( e 118(. Iaeoe aaee/eio o?aoueaai oaea o?aoaieueieea.Aeaa oaea o?aoaieueieea ?aaiu 118( e 62(. Iaeoe aaee/eio o?aoueaai oaea.Iaeoe oaeu o?aoaieueieea, anee iie i?iii?oeeiiaeueiu /eneai 3, 4, 5.A o?aoaieueieea ABC oaie A ?aaai 24(, oaie C a aeaa ?aca aieueoa oaea B. Iaeoe iaecaanoiua oaeu o?aoaieueieea.Iaeoe oaeu o?aoaieueieea, anee iaeei ec aai oaeia ?aaai noiia aeaoo ae?oaeo, a aeaa iaiueoeo oaea ioiinyony, eae 2:3.Iaeoe iiia?iua ioiioaiey oaeia o?aoaieueieea, anee iaeei ec ieo ?aaai 36(, a aoi?ie – 84(. (Caaea/a eiaao 6 ioaaoia).A o?aoaieueieea ABC oaie A ?aaai 30(, oaie B ?aaai 70(, e aeaa oaea ioiinyony, eae 7:8. Iaeoe oaeu o?aoaieueieea ABC.A o?aoaieueieea ABC oaie A ?aaai 30(, oaie B ?aaai 70(, e aeaa oaea ioiinyony, eae 4:7. Iaeoe oaeu o?aoaieueieea ABC.A o?aoaieueieea ABC oaie A ?aaai 30( e oaeu ioiinyony, eae 1:1:4. Iaeoe oaeu o?aoaieueieea ABC.A o?aoaieueieea ABC oaie A ?aaai 30(, e oaeu ioiinyony eae 1:2:6. Iaeoe oaeu o?aoaieueieea ABC.A o?aoaieueieea AAN oaie A ?aaai 70(, e aeaa oaea ioiinyony eae 5:6. Iaeoe oaeu o?aoaieueieea AAN.Ia?aay caaea/a o?aaeeoeeiiia aeey yoie oaiu. Ii aoi?ay oaea canoaaeyao caaeoiaoueny i aiciiaeiuo a?aieoeao ioaaoia a oaeeo caaea/ao.Oanoay caaea/a auaiaeeo ia iaiaoiaeeiinoue aa?eaoeaiuo ?annoaeaeaiee, i /?i iiaeneacea a neiaeao, oai naiui aioiaeo o/aueony e aa?eaoeaiui ?annoaeaeaieyi a neaaeothuae caaea/a. Aeey ?aoaiey caaea/e 7 o/aiee aeieaeai nia/aea caaeoiaoueny ia ioiioaiee eaeeo eiaiii oaeia eae?o ?a/ue? Iaeioi?ua ec yoeo aa?eaioia aoaeoo ioa?ioaiu eae i?ioeai?a/eaua, ii ia n?aco, a iinea iaiaoiaeeiuo au/eneaiee. Aeey ioaaoa inoaiaony iaeei ec ieo. A caaea/a aea 8 ie iaeei ec ?anniio?aiiuo aa?eaioia ia auaaaeao ia ioaao. Aiaeiae/iua ?annoaeaeaiey iiiaaeiayony e i?e ?aoaiee caaea/ 8–11.I?eiaiaiea naienoaa oaeia aeey ?aaiiaaae?aiiiai o?aoaieueieeaIaeoe oaeu ?aaiiaaae?aiiiai o?aoaieueieea, anee oaie i?e aai aa?oeia ?aaai 28(.Iaeoe oaeu ?aaiiaaae?aiiiai o?aoaieueieea, anee oaie i?e aai iniiaaiee ?aaai 28(.Iiaeao ee ?aaiiaaae?aiiue o?aoaieueiee eiaoue oaeu aaee/eiie 55( e 70 (? 24( e 62(?Iaeoe oaeu ?aaiiaaae?aiiiai o?aoaieueieea, anee iaeei ec ieo ?aaai 100(.Iaeoe oaeu ?aaiiaaae?aiiiai o?aoaieueieea, anee aeaa aai oaea niioaaonoaaiii ?aaiu: a) 55( e 70(; a) 40( e 110(; a) 20( e 20(; a) 60( e 60(.Iiaeao ee aennaeo?ena, iaaeeaia eee aunioa o?aoaieueieea ?acaeaaoue aai ia aeaa ?aaiinoi?iiieo o?aoaieueieea?Iaeoe oaeu ?aaiiaaae?aiiiai o?aoaieueieea, o eioi?iai aunioa, i?iaaae?iiay e iniiaaieth, ?acaeaaao aai ia 2 o?aoaieueieea oae, /oi niioiioaiea ino?uo oaeia eaaeaeiai ec iieo/aiiuo o?aoaieueieeia ?aaii 1:2.Aeieacaoue, /oi ?aaiiaaae?aiiue o?aoaieueiee n oaeii 60( yaeyaony ?aaiinoi?iiiei.Eaeeie iiaoo auoue oaeu ?aaiiaaae?aiiiai o?aoaieueieea , anee aennaeo?ena iaeiiai ec oaeia ?acaeaaao o?aoaieueiee ia aeaa ?aaiiaaae?aiiuo o?aoaieueieea.Aeieacaoue, /oi anee ethaua aeaa aennaeo?enu o?aoaieueieea, ia?anaeaynue, ia?acotho ni noi?iiaie ?aaiiaaae?aiiua o?aoaieueieee, oi aeaiiue o?aoaieueiee ?aaiinoi?iiiee.Aeieacaoue, /oi io?acee aunio ?aaiinoi?iiiaai o?aoaieueieea ia?acotho ni noi?iiaie yoiai o?aoaieueieea 3 ?aaiiaaae?aiiuo o?aoaieueieea.Iineaaeiea aeaa caaea/e yoiai ?acaeaea – i?eau/iua caaea/e oeieueiiai o/aaieea. Ii ?aoaoue oaeea caaea/e o/aieee ia ethayo eiaiii iioiio, /oi caeanue o?aaoaony auiieieoue ia?aai? anao aiciiaeiuo aa?eaioia, e /aio iie ia i/aiue oi?ioi iiaeaioiaeaiu. Iiyoiio i?aaeuaeouea caaea/e a aieueoae naiae /anoe e niaea?aeao iaiaoiaeeiinoue auiieiaiey ia?aai?a aa?eaioia, /oi, eae iai i?aaenoaaeyaony, e aeieaeii iiaeaioiaeoue o/aueony e ?aoaieth aeaoo iineaaeieo caaea/.I?eiaiaiea naienoaa oaeia aeey i?yiioaieueiiai o?aoaieueieeaIaeei ec oaeia i?yiioaieueiiai o?aoaieueieea ?aaai 73(. Iaeoe ae?oaie aai ino?ue oaie.A i?yiioaieueiii o?aoaieueieea iaeei oaie ?aaai 65(. Iaeoe aaee/eiu inoaeueiuo oaeia.Iaeei ec ino?uo oaeia i?yiioaieueiiai o?aoaieueieea a 5 ?ac aieueoa ae?oaiai. Iaeoe yoe oaeu.Iaeoe ino?ua oaeu i?yiioaieueiiai o?aoaieueieea. anee iaeei ec ieo ia 32( aieueoa ae?oaiai.Ino?ua oaeu i?yiioaieueiiai o?aoaieueieea i?iii?oeeiiaeueiu /eneai 5 e 7. Iaeoe yoe oaeu.?aciinoue ino?uo oaeia i?yiioaieueiiai o?aoaieueieea ?aaia 15(. Iaeoe yoe oaeu.Iaeoe oaeu i?yiioaieueiiai o?aoaieueieea. anee iaeei ec ieo a 5 ?ac aieueoa ae?oaiai.Iaeoe oaeu i?yiioaieueiiai o?aoaieueieea, anee iaeei ec ieo ia 32( aieueoa ae?oaiai.Iaeoe oaeu i?yiioaieueiiai o?aoaieueieea, anee iaeei ec ieo a 3 ?aca iaiueoa ae?oaiai.Oaeu o?aoaieueieea i?iii?oeeiiaeueiu /eneai O, 8 e 10. Eaeei iiaeao auoue /enei O, anee o?aoaieueiee i?yiioaieueiue?Aeaa oaea i?yiioaieueiiai o?aoaieueieea i?iii?oeeiiaeueiu /eneai 2 e 3. Iaeoe oaeu o?aoaieueieea.Iiaeii ee iaeoe ioiioaiea noi?ii i?yiioaieueiiai o?aoaieueieea (oioy au iaeioi?uo), anee ecaanoii, /oi iaeei ec aai oaeia a 2 ?aca aieueoa ae?oaiai?Ia?aua oanoue caaea/ yoiai ?acaeaea o?aaeeoeeiiiua. Iyoue neaaeothueo (io naaeueiie aei iaeeiiaaeoeaoie) aiaoia iioiaee ia ia?aua oanoue, ii niaea?aeao iaeio iaii?aaeae?iiinoue, nouanoaaiii aeeythuoth ia oa?aeoa? ?aoaiey: ?a/ue oaea ia eae?o ia ino?uo oaeao e iioiio e /eneo cao?iioouo a oneiaee oaeia i?eae?ony oaia?ue ioiineoue e i?yiie oaie. Oaeei ia?acii, caaea/a iieo/eo ianeieueei aiciiaeiuo ioaaoia. Iineaaeiyy caaea/a ia iiaeao auoue ?aoaia a iieiii aeaea aei eco/aiey oai?aiu Ieoaai?a, iiyoiio a naaeueiii eeanna aiciiaeii eeoue a? /anoe/iia ?aoaiea: eeai ?aaiiaaae?aiiue i?yiioaieueiue o?aoaieueiee n ioiioaieai eaoaoia 1:1, eeai i?yiioaieueiue o?aoaieueiee n oaeii 30(, aaea ioiioaiea eaoaoa e aeiioaioca ?aaii 1:2.I?eiaiaiea naienoaa oaeia a o?aoaieueieea n aeiiieieoaeueiuie iino?iaieyieA o?aoaieueieea AAN aennaeo?enu oaeia A e A ia?anaeathony a oi/ea E. Iaeoe aaee/eio oaea AEA, anee (A=50(, (A=100(.A ?aaiiaaae?aiiii o?aoaieueieea oaie ?aaai 68(. Iiae eaeei oaeii ia?anaeathony aennaeo?enu aeaoo ae?oaeo aai oaeia?Iiae eaeei oaeii ia?anaeathony aennaeo?enu ?aaiinoi?iiiaai o?aoaieueieea? auniou ?aaiinoi?iiiaai o?aoaieueieea?O?aoaieueiee eiaao oaeu 36( e 74(. Iiae eaeei oaeii ia?anaeathony auniou, i?iaaaeaiiua ec aa?oei yoeo oaeia? Iiae eaeei oaeii ia?anaeathony aennaeo?enu yoeo oaeia?A o?aoaieueieea AAN (AA=AN) i?iaaaeaia aennaeo?ena NI. Iaeoe oaeu o?aoaieueieea AAN, anee aaee/eia oaea AIN ?aaia 120(.A o?aoaieueieea AAN (A=40(, (N=70(, aennaeo?enu oaeia A e N ia?anaeathony a oi/ea E, (AEN=125(. Iaeoe (A.A o?aoaieueieea AAN (A=30(, (N=80(, aennaeo?enu oaeia A e A ia?anaeathony a oi/ea E, (AEA=135(. Iaeoe oaie A.Iiae eaeei oaeii ia?anaeathony ia?aaiua aennaeo?enu ?aaiiaaae?aiiiai o?aoaieueieea, iaeei ec oaeia eioi?iai 96(? 90(? 86(?A ?aaiiaaae?aiiii o?aoaieueieea AAN i?iaaaeaia aennaeo?ena AI. Iaeoe oaeu o?aoaieueieea AAN, anee (AIN=64(.Aennaeo?enu oaeia A e A o?aoaieueieea AAN ia?anaeathony a oi/ea E. Iaeoe aaee/eio oaea AEA, anee aaee/eia oaea ANA ?aaia 170(.Iaeoe aaee/eio oaea o?aoaieueieea. anee aennaeo?enu aeaoo ae?oaeo aai oaeia ia?anaeathony iiae oaeii 100(.A eaeii o?aoaieueieea aennaeo?enu ia?anaeathony iiae i?yiui oaeii?A o?aoaieueieea AAN aennaeo?enu oaeia A e A ia?anaeathony a oi/ea E. (BAC=70(. Iaeoe oaie AEA.A caaea/ao yoiai ?acaeaea oaeaea caieaie?iaai ia?aoiae io o?aaeeoeeiiiuo caaea/ e caaea/ai, o?aaothuei aiaeeca oneiaey e ?anniio?aiey ?acee/iuo aa?eaioia.Caaea/e n aiaoieie oaeaie o?aoaieueieeaAiaoiee oaie o?aoaieueieea ?aaai 130(, iaeei ec ia niaaeiuo n iei aioo?aiieo 70(. Iaeoe oaeu o?aoaieueieea.Oaeu o?aoaieueieea ?aaiu 47(, 69( e 64(. Iaeoe aiaoiea oaeu o?aoaieueieea.Aiaoiee oaie o?aoaieueieea ?aaai 130(, a aeaa aioo?aiieo 60( e 70(. Iaeoe oaeu o?aoaieueieea.Aiaoiee oaie o?aoaieueieea ?aaai 130(, a aeaa aioo?aiieo – 30( e 60(. Iaeoe oaeu o?aoaieueieea.Iaeei ec aioo?aiieo oaeia i?yiioaieueiiai o?aoaieueieea ?aaai 47(, a iaeei ec aiaoieo – 137(. Iaeoe aaee/eiu inoaeueiuo aioo?aiieo oaeia.A i?yiioaieueiii o?aoaieueieea aioo?aiiee oaie ?aaai 47(, aiaoiee 133(. Iaeoe aaee/eiu inoaeueiuo aioo?aiieo oaeia.A i?yiioaieueiii o?aoaieueieea aioo?aiiee oaie ?aaai 47(, aiaoiee 143(. Iaeoe aaee/eiu inoaeueiuo aioo?aiieo oaeia.Iaeoe oaeu ?aaiiaaae?aiiiai o?aoaieueieea. anee iaeei ec aai aiaoieo oaeia ?aaai 30(.Iaeei ec aiaoieo oaeia i?yiioaieueiiai o?aoaieueieea ?aaai 107(. Iaeoe aai aioo?aiiea oaeu.Iaeei ec aiaoieo oaeia o?aoaieueieea ?aaai 130(, a iaeei ec aioo?aiieo – 46(. Iaeoe ae?oaea aioo?aiiea e aiaoiea oaeu o?aoaieueieea.Iaeei ec aiaoieo oaeia ?aaiiaaae?aiiiai o?aoaieueieea ?aaai 96(. Iaeoe aioo?aiiea oaeu o?aoaieueieea.Noiia aiaoieo oaeia n aa?oeiaie A e A ?aaia 186(. Iaeoe aaee/eio oaea N o?aoaieueieea AAN.Noiia aeaoo aiaoieo oaeia n aa?oeiaie A e A ?aaia 172(. Iaeoe aaee/eio oaea N o?aoaieueieea AAN.Aiaoiee oaie i?yiioaieueiiai o?aoaieueieea a 7 ?ac aieueoa aioo?aiiaai n oie aea aa?oeiie. Iaeoe oaeu o?aoaieueieea.Aiaoiee oaie i?yiioaieueiiai o?aoaieueieea a 4 ?aca aieueoa aioo?aiiaai. Iaeoe oaeu o?aoaieueieea.Iaeoe noiio aiaoieo oaeia i?yiioaieueiiai o?aoaieueieea (ii iaeiiio i?e eaaeaeie aa?oeia).?aciinoue aeaoo aiaoieo oaeia o?aoaieueieea ?aaia o?aoueaio aiaoiaio oaeo. Iaeoe aioo?aiiea oaeu o?aoaieueieea.Iaeoe ioiioaiea aiaoieo oaeia ?aaiiaaae?aiiiai o?aoaieueieea, anee ioiioaiea aai aioo?aiieo oaeia 2:5.Iiae eaeei oaeii ia?anaeathony aeaa i?yiua, anee i?e ia?ana/aiee eo o?aoueae noiia aioo?aiieo iaeiinoi?iiieo oaeia ?aaia 215(?Iaeei ec oaeia o?aoaieueieea a 3 ?aca aieueoa ae?oaiai, a ?aciinoue aiaoieo oaeia i?e yoeo aea aa?oeiao ?aaia 80(. Iaeoe oaeu o?aoaieueieea.Iaeei ec oaeia o?aoaieueieea a 2 ?aca aieueoa ae?oaiai, a ?aciinoue aiaoieo oaeia i?e yoeo aea aa?oeiao ?aaia 80(. Iaeoe oaeu o?aoaieueieea.Aiaoiea oaeu o?aoaieueieea i?iii?oeeiiaeueiu /eneai 3, 7, 8. Eaeei /eneai i?iii?oeeiiaeueiu aai aioo?aiiea oaeu?I?yiua a e b ia?anaeathony iiae oaeii 85(. I?yiay c ia?anaeaao a e b oae, /oi ?aciinoue aioo?aiieo iaeiinoi?iiieo oaeia ?aaia 75(. Ii?aaeaeeoue aeae iieo/aiiiai o?aoaieueieea.I?yiua a e b ia?anaeathony iiae oaeii 75(. I?yiay c ia?anaeaao a e b oae, /oi ?aciinoue aioo?aiieo iaeiinoi?iiieo oaeia ?aaia 85(. Ii?aaeaeeoue aeae iieo/aiiiai o?aoaieueieea.Ii?aaeaeeoue, iiae eaeei oaeii ia?anaeathony i?yiua c e d, anee i?yiay a ia?anaeaao eo oae, /oi noiia aioo?aiieo iaeiinoi?iiieo oaeia ?aaia 54(.I?yiua k e l ia?anaeathony iiae oaeii 33(. I?yiay ? ia?anaeaao eo oae, /oi iaeei ec aioo?aiieo iaeiinoi?iiieo oaeia a 2 ?aca aieueoa ae?oaiai. Iaeoe oaeu o?aoaieueieea, ia?aciaaiiiai yoeie i?yiuie.I?yiua a e b ia?anaeathony iiae oaeii 40(. I?yiay ? ia?anaeaao eo oae, /oi a iieo/eaoainy o?aoaieueieea oaeu ioiinyony, eae 1:7:28. Iaeoe oaeu o?aoaieueieea, ia?aciaaiiiai yoeie i?yiuie.Iiae eaeei oaeii ia?anaeathony i?yiua c e d, anee i?yiay a ia?anaeaao eo oae, /oi ?aciinoue aioo?aiieo iaeiinoi?iiieo oaeia ?aaia 90(Ec caaea/ yoiai ?acaeaea inoaiiaeiny ia oanoe iineaaeieo caaea/ao. Aiciiaeiua caeanue aa?eaiou iiyaeythony ianeieueei iaiaeeaeaiii aeey o/aueony. Iai?eia?, a caaea/a 23 aeey iino?iaiey i?yiie n aiciiaeiu aeaa neooaoeee (ni. ?enoiee):A yoii neo/aa eiaai:85(+o(+o(+75(=180(Caeanue iieo/aai:o=10(. Aiciiaeii au? e oaeia ?aciauaiea i?yiuo.180(–85(+o(+o(+75(=180(o=5(.Caaea/a eiaao aeaa ioaaoa: 10( e 5(.A caaea/a 24 oaeaea aiciiaeiu aeaa aa?eaioa iino?iaiey i?yiuo a, b e n (ni. ?enoiee):A aeaiiii neo/aa eiaai:75(+o(+o(+85(=180(.Ionthaea:o=10(. Aeey oaeiai ?aciauaiey:180(–75(+o(+o(+85(=180(.Ionthaea:o=–5(, /aai ia iiaeao auoue.Eae aeaeei, ia?anoaiiaea a oneiaee caaea/e aeaoo /eneiauo aeaiiuo (75( e 85() i?eaiaeeo e oiio, /oi a ioaaoa iieo/aaony aiciiaeiui eeoue iaeii cia/aiea: o=10(.Aiana iaiaycaoaeueii i?aaeeaaaoue yoe caaea/e anai o/aueiny. Aeey o/aueony n i?aeiouanoaaiiie ioeaieie "3" iiiaea caaea/e ec aoi?ie /anoe eaaeaeiai ?acaeaea iaaeinooiiu e iaiaycaoaeueiu. A oi aea a?aiy aeey ioee/ii oniaaathueo o/aueony iaeioi?ua ecia/aeueiua caaea/e i/aiue i?inou e iioiio eo iiaeii i?iioneaoue. Ec i?aaeeiaeaiiiai ia?a/iy iiaeii auaeaeeoue iaai? caaea/, ieieiaeueii iaiaoiaeeiue aeey ioeaiee "3", iioii – iaai? caaea/, ieieiaeueii iaiaoiaeeiue aeey ioeaiee "4", iaeiiaoe – iaai? caaea/, ieieiaeueii iaiaoiaeeiue aeey ioeaiee "5" (ia?aue, aoi?ie e o?aoee o?iaie inaiaiey oeacaiiie oaiu). Aeaeeii, iiaeii iacaaoue caaea/e ec yoiai ia?a/iy, eioi?ua i?aauoatho e o?aoee o?iaaiue, o.a. ia yaeythony iaycaoaeueiuie (ii aanueia aeaeaoaeueiuie) aeey iieo/aiey ioeaiee "5".Oae, caaea/e ia?aiai o?iaiy neiaeiinoe ?ann/eoaiu ia i?yiia i?eiaiaiea iaeioi?iai aeai?eoie/aneiai i?aaeea, a oaeaea i?eiaiaiea yoiai i?aaeea n iaaieueoeie aa?eaoeeyie. Caaea/e yoiai o?iaiy ia i?aaenoaaeytho neiaeiinoe aeey aieueoeinoaa o/aueony, iioiio /oi iiaeiaiuo yoei caaea/ aeinoaoi/ii iiiai ?aoaaony ia o?ieao. Caaea/e iaii?aaeae?iiua caeanue ia ?aeiiaiaeothony, a caaea/e ia?aii?aaeae?iiua aeiioneathony a neo/aa ianeiaeiiai auyaeaiey ecauoi/iuo aeaiiuo (i iaee/ee eioi?uo o/aueony a aieueoeinoaa neo/aaa neaaeoao i?aaeoi?aaeaeaoue).Caaea/e aoi?iai o?iaiy neiaeiinoe iiaoo eiaoue neaaeothuea ioee/eoaeueiua /a?ou:oneiaea caaea/e ecauoi/ii, ii ia niaea?aeeo i?ioeai?a/ey e caaea/a ?aoaaony iaeiicia/ii. Aeey ?aoaiey caaea/ yoiai oeia iaiaoiaeeii ec anao aeaiiuo caaea/e aua?aoue iaiaoiaeeiua, e i?eiaieoue eo.oneiaea caaea/e niaea?aeeo i?ioeai?a/ea (ninoaa oneiaey caaea/e iiaeao auoue eae iieiui, oae e ecauoi/iui).oneiaea caaea/e ia niaea?aeeo ieeaeeo ec ?anniio?aiiuo ithainia n aeaiiuie (ninoaa oneiaey iieiue), ii ii n?aaiaieth n caaea/aie ia?aiai o?iaiy i?e?i, i?eiaiyaiue aeey ?aoaiey, aieaa neiaeiue (i?aaeei i?eiaiyaony ia "a eia").Caaea/e o?aoueaai o?iaiy neiaeiinoe ioee/athony au? aieueoei ?aciiia?aceai. Aeey ?aoaiey caaea/ yoiai o?iaiy io o/aieeia o?aaoaony e aieueoee iau?i ciaiee (i?e ?aoaiee caaea/e i?eoiaeeony eniieueciaaoue eiiaeiaoeeth i?e?iia e iaaueia, eco/aiiuo ?aiueoa), e iaee/ea iaauea aa?eaoeaiuo ?annoaeaeaiee, eioi?iai oaia?aoiei o/aieeai a cia/eoaeueiie ia?a ia oaaoaao. Caaea/e yoiai o?iaiy aaeiaaaie e neiaeiinoe i?e?iia ?aoaiey iiaoo eiaoue a oneiaee iaii?aaeae?iiinoue, i?eaiaeyuoth e iaii?aaeae?iiiio ioaaoo.Oaeaea noieo ioaeaeueii neacaoue ianeieueei neia i caaea/ao, eioi?ua ii naiae neiaeiinoe noiyo auoa caaea/ o?aoueaai o?iaiy. Yoe caaea/e eiatho a nai?i oneiaee iaii?aaeae?iiinoue, ii yoa iaii?aaeae?iiinoue iiae?acoiaaaao a ?aoaiee caaea/e aaneiia/iia iiiaeanoai ioaaoia. *aua anaai oaeay oi?ioee?iaea caaea/e ioaaao o/aieea e ii aiai?eo, /oi caaea/a ia eiaao ?aoaiey, iioiio /oi ia oaaoaao aeaiiuo, oioy iiaeii auei au i?iaanoe ?aoaiea aeaiiie caaea/e e iieo/eoue aeiaieueii eiie?aoiue ?acoeueoao.Caeeth/aieaIiaeaiaey eoia i?iaeaeaiiie ?aaioa, ioiaoei neaaeothuaa.I oeaeaniia?aciinoe aaaaeaiey iaii?aaeae?iiuo e ia?aii?aaeae?iiuo caaea/ a oeieueiue eo?n iao/aiey oaaaeeoaeueii neacaii aaoi?eoaoiuie iaoiaeenoaie, niaoeeaeenoaie a iaeanoe iaoaiaoe/aneiai ia?aciaaiey. Eia?oeeiiiay oeiea iiea au? ia o/eouaaao yoie oeaeaniia?aciinoe, ii naeaeae a oeacaiiii iai?aaeaiee oaea anoue.Aannii?ii e oi, /oi aeiiieiaiea o?aaeeoeeiiiuo oeieueiuo iaai?ia caaea/ caaea/aie iaii?aaeae?iiuie e ia?aii?aaeae?iiuie (a ?aaioa eniieueciaai iaiauathuee oa?iei aeey iaieo aeaeia caaea/ – caaea/e n «aiiiaeueiui» oneiaeai eee i?inoi «aiiiaeueiua» caaea/e) auciaao iaiaoiaeeiinoue iniauo iaoiaee/aneeo iiaeoiaeia e iao/aieth ?aoaieth oaeeo caaea/, iiaeoiaeia, ?anoe?ythueo aiciiaeiinoe o/aueony a ?aoaiee caaea/ aiiaua, oaeoaeythueo e oniaa?oainoaothueo eo iaauee iienea ?aoaiey ethaie caaea/e, a a eoiaa ?acaeaathueo eo iuoeaiea. Iiiuoee iniciaiey oaeeo iiaeoiaeia i?aaei?eiyou a aeaiiie ?aaioa. Ia iaeiii ec i?eia?ia iieacai aiciiaeiue aa?eaio ?anoe?aiey o?aaeeoeeiiiiai caaea/ieea, aai aeiiieiaiey caaea/aie n «aiiiaeueiui» oneiaeai.?acoiaaony, ?aaioa ia iiaeao i?aoaiaeiaaoue ia iieiioo e caaa?o?iiinoue, iineieueeo cao?iiooay i?iaeaia aeinoaoi/ii aeoaeiia e iau?iia e o?aaoao ia iaeiiai aiaea e?iiioeeaie ?aaiou ia iaeiiai /aeiaaea.Iaeiaei aaoi? iaaeaaony, /oi oioy au iaaieueoie oaa a ioaeiii iai?aaeaiee ei naeaeai.Ii iaoa?eaeai aeaiiiai enneaaeiaaiey iiaeaioiaeaia (a niaaoi?noaa) noaouey, iioaeeeiaaiiay a aeo?iaea «Iaoyiaouea: i?aaeaiu aueeaaeaiiy» ? 2 ca 1999 aiae.Nienie eniieueciaaiiie eeoa?aoo?u:Aoaianyi E.N. e ae?. Aaiiao?ey. O/aaiee aeey 7–9 eeannia n?aaeiae oeieu. – I.: I?inaauaiea, 1990.Aoeiaaoeeee I.I. ?aciiia?aceoue aeaeu caaea/ // Iaoaiaoeea a oeiea. – 1988. – ? 5, n.Aoeaaaoee? I., Iaeaaaoee? ?. Aa caaea/ao, ye?o iyia c oeieueiuo iaae?o/i?eao // Iaoyiaouea: i?aaeaiu aueeaaeaiiy. – 1999. – ? 2, n. 59 – 64.Aeaaoyiieeiaa E.I. Ino?ioaieueiue eee ooiioaieueiue // Iaoaiaoeea a oeiea. – 1998. – ? 5, n. 43.Eaiaoaiei A.C. Nth?i?ecu aennaeo?enu // Iaoaiaoeea a oeiea. – 1998. – ? 5, n. 42.Eaieai A.N. Iaoiaeu iao/aiey iaoaiaoeea. – Ieine: Ia?iaeiay anaaoa, 1981.Eieiiai?ia A. I . Iaoaiaoeea ( iaoea e i?ioanney. – I.: Iaoea,1988.E?oie/ A.E. No?oeoo?a e eiaeea i?ioeanna iao/aiey iaoaiaoeea a n?aaeiae oeiea.E?ooaoeeee A.A. Ineoieiaey iaoaiaoe/aneeo niiniaiinoae oeieueieeia. – I.: I?inaauaiea, 1968.Eaiioueaa A.I. I?iaeaiu ?acaeoey ineoeee. – I.: Ecaeaoaeuenoai IAO, 1962.Iaoaiaoe/aneia ia?aciaaiea: nia?aiaiiia ninoiyiea e ia?niaeoeau (e 80–eaoeth ni aeiy ?iaeaeaiey i?ioanni?a A.A.Noiey?a): Oacenu aeieeaaeia iaaeaeoia?iaeiie eiioa?aioeee. – Iiaee?a: IAO ei. A.A.Eoeaoiaa, 1999.Iaothoeei A.I. I?iaeaiiua neooaoeee a iuoeaiee e iao/aiee. – I.: Iaaeaaiaeea, 1975.Iaoiooia I.E. I?iaeaiiia iao/aiea. – I.: Iaaeaaiaeea, 1975.Iaoaeueneee I .A. Aeeaeaeoeea iaoaiaoeee. Iauay iaoiaeeea e a? i?iaeaiu. – Ieine: Ecaeaoaeuenoai AAO, 1982.Iiai?aeia A.A. Aaiiao?ey 7–11. – I.: I?inaauaiea, 1998.Iiea Ae. Eae ?aoaoue caaea/o. – Eueaia, 1991.Iiea Ae. Iaoaiaoe/aneia ioe?uoea. – I.: Iaoea, 1976.?iaaiianeee I.I. Aaiiao?ey 7–9. – Ii.: Ia?iaeiay anaaoa, 1997.Naia?ei I.A. I/a?ee ineoieiaee oia. Iniaaiiinoe oinoaaiiie aeayoaeueiinoe oeieueieeia. – I.: Ecaeaoaeuenoai AII, 1972.Noiey? A.A. Iaaeaaiaeea iaoaiaoeee. – Ieine: Auoyeoay oeiea, 1986.Noiey? A.A. Eae iaoaiaoeea oi a ii?yaeie i?eoiaeeo. – Ieine: Auoyeoay oeiea, 1991.O?eaeiai E.I. Ineoieiai–iaaeaaiae/aneea iniiau iao/aiey iaoaiaoeea a oeiea: – I.: I?inaauaiea, 1983.O?eaeiai E.I. Oo?aoeeee A.I. Eae iao/eoueny ?aoaoue caaea/e: – I.: I?inaauaiea, 1989.Y?aeieaa I.I. I?aiiaeaaaiea iaoaiaoeee a oeiea – I.: I?inaauaiea, 1978.Ynaoeia A.O. I?iaeaiu ?aoaiey caaea/ a iaoea e oaoieea. – E.: Ecaeaoaeuenoai Eaieia?aaeneiai oieaa?neoaoa, 1979.Ieienoa?noai ia?aciaaiey ?anioaeeee Aaea?onueIiaee?aneee ainoaea?noaaiiue oieaa?neoao ei. A.Eoeaoiaaeaoaae?a iaoiaeeee i?aiiaeaaaiey iaoaiaoeeeAeeieiiiay ?aaioa«Iaii?aaeae?iiua e ia?aii?aaeae?iiua caaea/e(eniieueciaaiea caaea/ n «aiiiaeueiui» oneiaeaia i?ioeanna iao/aiey iaoaiaoeea)»nooaeaioa a?oiiu «A» V eo?naoeceei–iaoaiaoe/aneiai oaeoeueoaoaIaeiaaoeeiai Eeuee Eaaiiae/aIao/iue ?oeiaiaeeoaeue:Aieoiae/ O.N.,noa?oee i?aiiaeaaaoaeue eaoaae?u iaoiaeeee i?aiiaeaaaiey iaoaiaoeeeIiaee?a 1999Neiai "ianoaiaea?oiue" acyoi iaie a eaau/ee, iineieueeo iu n/eoaai, /oi niioaaonoaothuee iiaeoiae e ?aoaieth caaea/ aeieaeai noaoue noaiaea?oii aeey eaaeaeiai o/aieea.PAGEPAGE 26

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