IIEOAANUeEEE I?NUeEEE IAOe?IIAEUeIEE E?OeAE ? 1
?AOA?AO IA OAIO :
«ETHAeEIA A NA?O? CAOE?A»
I?AeAIOOAAA O?OEUeIA IEAENAIAe? TH??EIAE*, A?OIA O – 41
IIEOAAA
1998
UI OAEA CAOE ?
O?ce/ia i?e?iaea an?o caoe?a, iacaeaaeii a?ae /anoioe, iaeia e oa ae :
oea i?oaei? eieeaaiiy, ye? iioe?ththoueny o oiio na?aaeiaeu?, a yeiio
aiie caoaeaeai?. O iia?o?? caoeia? oaee? iioe?ththoueny o aeaeyae?
?ica?aeii? (noa?e/ii?) oaee?. Caoeiaa noa?e/ia oaeey caiiaith? ana
a?eueoee ia’?i, ine?eueee eieeaaiiy /anoeiie iia?o?y, coiiaeai?
aeaea?aeii caoeo, ia?aaeathoueny ana c?inoath/?e ian? iia?o?y. Ie caeeee
aei oiai, ui caoeia? oaee? iioe?ththoueny a on? aiee a?ae ?o aeaea?aea.
Iai?eeeaae, eiee ni?aa? a?oeno, oi eiai iaeiaeiai, /e iaeaea iaeiaeiai
/ooe nia?aaeo, caieo ? iaa?oue ccaaeo; caoe ne?eiee /e a?oa?e
?icoiaeeoueny a on? aiee. Oiio aiai?youe, ui aeaea?aea /ooieo caoeiaeo
oaeeue ia iai?yieai?. sseui caoeiaa oaeey i?ioiaeeoue /a?ac ii??aiyii
iaaaeeeee ioa??, oi aiia iioe?th?oueny a on? aiee, a ia eaea iai?yieaiei
io/eii, iia i?ii?iue na?oea, ui i?iiee /a?ac ae??i/eo o iai?ici?iio
ae?ai?. Ooi aoeeoe?, i?iieeath/e /a?ac a?aee?eoo eaaoe?eo, i?aeoe/ii
iaeiaeiai /ooe o an?o oi/eao e?iiaoe, a ia eeoa i?ioe a?eia.
Ie aeia?a cia?ii, ui i?iiai? na?oea ooai?ththoue /?oe? o?i? iai?ici?eo
i?aaeiao?a, yeui oe? i?aaeiaoe ciaoiaeyoueny ia oeyoo i?iiai?a. A oie
aea /an caoee ia ooai?ththoue oaeeo o?iae, o anyeiio ?ac? oiae?, eiee
?ici??e ia?aoeiae ia aeoaea aaeee?. Caoeia? oaee? i?ae «iao?eathoue»
ia?aoeiaee. Oae, iai?eeeaae, ie aeineoue aeia?a /o?ii ni?a?iciiaieea a
e?n?, iacaaaeath/e ia oa, ui a?i o oeae /an iiaea aooe cae?eoee
aea?aaaie. *ei aea iiynieoe, ui caoe ? na?oei, iath/e oaeeueao i?e?iaeo,
aeaiiino?othoue oae?, i?yii i?ioeeaaei? aeanoeaino? ? Uia ?ic?a?aoeny a
oeueiio, iiaa?iaiinue aei iiiyooy aeiaaeeie oaee?.
?c ni?aa?aeiioaiiy (((( aeieeaa?, ui /ei a?eueoa /anoioa caoeo, oei
iaioa aeiaaeeia caoeiai? oaee?. A oa?eoa? iioe?aiiy oaeeue a?ey
ia?aoeiae ?noioii caeaaeeoue a?ae ni?aa?aeiioaiiy i?ae ?ici??aie
ai?aoeiaee ? aeiaaeeiith oaee?. sseui ?ici??e ia?aoeiaee iae? ii??aiyii
c aeiaaeeiith oaee? aai ni?anoaai? c iath, oi oaee? iao?eathoue
ia?aoeiaeo, ia aeath/e o?i?. Oae, oaee? ia iiaa?oi? aiaee a?eueii
iao?eathoue noaaeeie i/a?aoo. Ca oiano? ae noiaie /e aaeee? eaiai? oaee?
ia caoiaeyoue.
Oaee? /ooieo caoe?a cae/aeii iathoue aeiaaeeio aeecueei e?eueeio
aeanyoe?a naioeiao??a, aea iiaeooue aeinyaaoe aeiaaeeie 15 – 20 i. Oiio
i?aaeiaoe, ?ici??e yeeo ia ia?aaeuothoue 15 – 20 i, ia ? ia?aoeiaeaie
aeey iioe?aiiy caoeiaeo oaeeue, aiie ?o iao?eathoue, ia aeath/e caoeiai?
o?i?. Aeiaaeeie ae na?oeiaeo oaeeue aei??ththoueny aeanyoeoeny/ieie
/anoeaie i?e?iao?a, oiio an? i?aaeiaoe, ui ian ioi/othoue, a ii??aiyii?
c aeiaaeeiith na?oeiaeo oaeeue iaaecae/aeii aaeee? ? aeathoue /?oe?
o?i?.
ssE AEI??TH?OUeNss CAOE ?
Aeey ii/aoeo – aea? eieiiee ??aiinoae, caea?oueny, ia cian?i
cae/aeieo.
30 + 30 = 33
30 + 20 ( 30
70 + 70 = 73
70 + 60 ( 70
100 + 100 = 103
100 + 90 ( 100
E?aa eieiiea ??aiinoae a?aeia?aaea? (oiiaii) ?acoeueoaoe noioaaiiy
aoaeoo ae?? aeaio iaeiaeiaeo aeaea?ae ooia aai a?a?aoe??, eieeaaeueia
iiooaei?noue yeeo ae?aaeaia a aeaoeeaaeao. sse aa/eii, iacaeaaeii a?ae
aaee/eie eieeaaeueiiai ??aiy eiaeiiai c iaeiaeiaeo aeaea?ae, noia?iee
caoeiaee ??aaiue aeaio aeaea?ae caaaeaee ia 3 aeaoeeaaee ia?aaeuo?
??aaiue aoaeue-yeiai c ie?aii acyoeo aeaea?ae.
Ae?oaa ae eieiiea a?aeiineoueny aei neeaaeaiiy aoaeo?a aeaio aeaea?ae
c iii?oii a?ae??ciyth/eieny eieeaaeueieie iiooaeiinoyie. Aeaeii, ui yeui
??aaiue neaaoiai aeaea?aea ia 10 (aai a?eueoa) aeaoeeaae a?ae??ciy?oueny
a?ae ??aiy a?eueo iiooaeiiai aeaea?aea, oi noia?iee ??aaiue i?aeoe/ii
??aiee ??aith ie?aii acyoiai a?eueo iiooaeiiai aeaea?aea.
sseui ?ioaineai?noue iaeiiai caoeo o 10 ?ac?a a?eueoa ca
?ioaineai?noue ae?oaiai, oi eaaeooue, ui ??aaiue oeueiai caoeo ia iaeio
iaeeieoeth aeua ??aiy ae?oaiai caoeo. Oey iaeeieoey ??aiy caoeo iacaaia
aaeii – ia /anoue Ieaenaiae?a A?aeaia Aaeea, yeee neiino?othaaa oaeaoii.
aoeo aei??aith? 10-12 Ao/i2
? iaceaa?oueny ii?iaii /ooiino?. Oeae ??aaiue caoeo i?eeiyoi ca ioeue
aae. I?e ca?eueoaii? ?ioaineaiino? a 10 ?ac?a ??aaiue caoeo a aaeao
c?inoa ia iaeio iaeeieoeth, yeui ?ioaineai?noue c?inoa? a 100 ?ac?a, oi
??aaiue caoeo c?inoa? ia 2 aaee, i?e ca?eueoaii? ?ioaineaiino? a 1000
?ac?a – ia 3 aaee ? o.ae. Oaea oeaea – eiaa?eoi?/ia – aoea ia?aia oiio,
ui niinoa?aaeaiiy aeacothoue ia i?iii?oe?ei?noue ao/iino? caoeo,
ni?eeiyoiai aooii, eiaa?eoiia? o?ce/ii? ?ioaineaiino?. Aeey iiai?oiai
oyaeaiiy i?i oaeee niin?a ii??aiyiiy caoe?a iaaaaeaii a?aeiiino? i?i
?ioaineaiino? ? ??ai? aeayeeo caoe?a.(Aeea. oaaeeoeth.)
Aae – caiaaeoi aaeeea iaeeieoey, oiio ia i?aeoeoe? cae/aeii
ei?enoothoueny a 10 ?ac?a iaioith – aeaoeeaaeii (0,1 aaea). Ci?ia caoeo
ia 1 aeaoeeaae (aeA) – oea i?eaeecii iaeiaioa ci?ia, yeo iiaea aeyaeoe
ii?iaeueia aooi. A inoaiiueiio ?yaeeo oaaeeoe? iaaaaeaii cia/aiiy ii?iao
aeieeiaiiy aeioeeiaiai a?ae/oooy caoeo. Eiee ?ioaineai?noue caoeo
aeinyaa? 1 Ao/i2, oi aooi ia eeoa /o? caoe, aea ? a?ae/oaa? oene.
Iaa?oue oe??a iiaea a?ae/oaaoe caoe oaei? ?ioaineaiino?. sseui
?ioaineai?noue iaaaaaoi ia?aaeuo? 1 Ao/i2, oi a?ae/oaa?oueny a?eue o
aon?.
Oaaeeoey ?ioaineaiinoae oa ??ai?a caoeo.
Aeaea?aei caoeo ?ioai -neai., Ao/i2 .
??aaiue caoeo, aae.
Ii??a /ooiino? 10-12 0
Niie?eia aeeoaiiy 10-11 1
Ooi niie?eiiai naaeo 10-10 2
Ia?aai?oaiiy noi??iie aacaoe 10-9 3
Iaae?iiy e?aiaeue ia a?aenoai? iaeiiai iao?a 10-9 3
Cae/aeiee ooi o aoaeeieo 10-8 4
Oeoa ?iciiaa 10-8 4
Ieeinin 10-7 5
Cae/aeia ?iciiaa 10-6 6
?aae?i 10-5 7
AEaaaee aoee/iee ooi 10-4 8
Ii?cae ia anoaeaae? 10-3 9
Ooi o aaaii? iao?i 10-2 10
A??i 10-1 11
Ii??a aeioeeiaiai a?ae/oooy 1 12
Eiaeai c ian iaiaeiaeiai /ooeeaee aei caoe?a ??cieo /anoio. Aea yeui
aano?aaoaaoeny a?ae iaoeo ?iaeea?aeoaeueieo ? a?eiaeo iniaeeainoae, oi
iiaeia aaaaeaoe, ui aooi ethaeeie caeaoia ni?eeiaoe caoeia? oaee? a
?ioa?aae? /anoio a na?aaeiueiio 16 Aoe – 20 eAoe. Caoee, /anioa yeeo
iaioa 16 Aoe ? aeua 20 eAoe, iaoa aooi acaaae? ia ni?eeia?. Ethaeeia ?o
i?inoi ia /o?. Caoeia? oaee? c /anoioith iaioa 16 Aoe ae?noaee iacao
?io?acaoeo, a c /anoioith a?eueoa 20 eAoe – oeueo?acaoeo. Inoaii?i /anii
o oaoi?oe? aeei?enoiaothoue caoeia? oaee? iniaeeai aaeeei? /anoioe –
a?ae 109 aei 1013 Aoe, ye? iaceaathoue a?ia?caoeaie. Aeey ?a?no?aoe??
ia/ooieo caoe?a canoiniaothoueny niaoe?aeuei? i?eeaaee.
A ye? caoee /othoue oaa?eie ? Aeaye? oaa?eie ? eiiaoe ni?eeiathoue
caoee, /anoioa yeeo ia?aaeuo? 20 eAoe. Ii?nueea naeiea, niaa, n??a ieoa,
ai?noe ni?eeiathoue oeueo?acaoeia? oaee? c /anoioith aei 100 eAoe.
Iaiaei ? e oaeeo oaa?ei, ui nai? aei?ii?iththoue oeueoa?caoe, yeee
cai?ith? ?i c??. Iaea?eueo ?icaeiooa oeueo?acaoeiaa aa/aiiy o eaoth/eo
ieoae ? aeaeueo?i?a.
OEUeO?ACAOE
Ia a?aei?io a?ae cae/aeieo caoe?a oeueo?acaoee iathoue cia/ii iaioo
aeiaaeeio oaeeue. Aiane?aeie oeueiai aiie aeathoue oeueo?acaoeia? o?i? ?
?o iiaeia iaea?aeaoe o aeaeyae? aocueeeo io/e?a, ye? ca aiaeia??th ?c
na?oeiaeie i?eeiyoi iaceaaoe oeueo?aaoeiaeie io/eaie. Oaeei /eiii,
iiaeia aaaaeaoe, ui oeueo?acaoe iioe?th?oueny a iaeii??aeiiio
na?aaeiaeu? i?yiie?i?eii, ia iaeia? ia?aoeiae, ?ici??e yeeo cia/ii
ia?aaeuothoue aeiaaeeio oaee?.
C oeueo?acaoeii, ye ? c ?ioeie aeaeaie oaeeue, niinoa??aathoueny
caeiieaiiy, a?aeaeaaiiy, aeeo?aeoe?y oa iiaeeiaiiy.
I?e caeiieaii? oa iaae?ii? oeueo?acaoeiaeo oaeeue i?ae eooii
a?aeaoaa?oueny oe?eaaa yaeua – ooai?aiiy i?iaeieueieo ? iiia?a/ieo
oaeeue iaeii/anii.
Iaee?aua oeueo?acaoe iiaeeia?oueny aacaie, o?eaie c iaeith i?oaei?noth
(ieanoiane), ii?enoeie o?eaie (aoia, ei?ie), a??oa – ??aeeiaie, iaea??oa
– oaa?aeeie o?eaie.
Oeueo?acaoe aeoaea oe?iei aeei?enoiao?oueny. ?niothoue oeueo?acaoeia?
: ??caiiy, caa?thaaiiy, iayiiy, eoae?iiy, /euaiiy, oeiaethaaiiy ieeo ?
ooiaio, i?enei?aiiy oaoiieia?/ieo i?ioean?a, aiooaaiiy noniaic?e ?
aioeuen?e, eiio?ieue yeino?, aa/aiiy, aoieieaoe?y ? o.ae.
Aeei?enoiao?oueny oaeiae oeueo?acaoe o o?i??, iaoaeo?a??, aeaeo?ii?oe?
oa iaaeeoeei?.
sse aea ae?? oeueo?acaoe iaethaeeio ? Iaaeeee – oai?aoeee ? i?aeoeee
ia oea ieoaiiy iiee ui eaoaai?e/ii? a?aeiia?ae? ia aeathoue. Oi/i?oa,
iaei? aaaaeathoue oeueo?acaoe aeoaea aoaeoeaiei ? aaniethoii aacia/iei,
?io? – iaaiaee. Iiynieoe oaeo neooaoe?th iiaeia a iniiaiiio oei,
ui oeueo?acaoe i?eeoia o iaaeeoeeio cian?i iaaeaaii (iaoa??aee 1987 ?.)
Ioaea, oe?eeii i?e?iaeii, ui aaaaoi i?iaeai ooo ua ia ciaeoee
inoaoi/iiai ?ica’ycaiiy. Iathoue ?aoe?th o? niaoe?ae?noe, ye?
iaaieioothoue ia oai?/iio i?aeoiae? aei aeei?enoaiiy oeueo?acaoeo o
iaaeeoeei?, ai a a?eueoino? aeiaaee?a e?eoaaiiy ? ae?aaiinoeee c eiai
aeiiiiiaith aeathoue o?eueee iiceoeai? ?acoeueoaoe. Aaaeeeai eeoa a??ii
i?ae?a?aoe ?ici??, aeice, iaoiae ? i?eeaaee. Aeico, ye i?aaeei,
aeae?athoue aeey na?aaeiuei? ?ioaineaiino? ca o?eaae?noth aieeao
oeueo?acaoeo. *anoioo oeueo?acaoeiaeo eieeaaiue iae?athoue a caeaaeiino?
a?ae aeeaeie ?icoaooaaiiy oai?iai i?aaia. *ei ieae/a /anoioa, oei aeeaoa
i?iieeathoue a o?ei oeueo?acaoeia? eieeaaiiy, oiio iae/ano?oa
aeei?enoiaothoue /anoioo 0,8 – 1 IAoe.
Iaaei??i? aeice oeueo?acaoeo ia ae?iaieoeoa? iaaaoeaii aieeaathoue ia
i?aai?ci ethaeeie. O oeo, ooi ii?ooo? i?aaeea oaoi?ee aaciaee, iiaea
ii/aoeny i?ioan?eia caoai?thaaiiy. Oiio ii?aoeueiaothoueny aoaeoeai?
caoiaee ii ai?iouea? c oe?aeeeaei aieeaii oeueo?acaoeo ia ethaeeio.
?IO?ACAOE
?io?acaoe – oea eieeaaiiy /anoioe ieae/a 16 Aoe. Aeyaeaii, ui
?io?acaoe iaaoaii aieeaa? ia i?aai?ci ethaeeie ? ioi/oth/a na?aaeiaeua.
Oea coiiaeaii oei, ui /anoioa ?io?acaoeo ni?aiaaea? c aeaniith /anoioith
i?aaeiaoa, a oea, ye iai a?aeiii – yaeua ?aciiaino. Oea ? ? iniiaiith
i?e/eiith caoaiiai aieeao ?io?acaoeo ia ioi/oth/a na?aaeiaeua. Oaee?
??cii? /anoioe iaaaoeaii aieeaathoue ia ??ci? i?aaie ethaeeie, ia ??ci?
eiino?oeoe??.
Anoaiiaeaii, ui ?io?acaoe iiaeia caaaneoe ca aeiiiiiaith /ooieo caoe?a
a?eueoi? iiooaeiino?.
A?IA?CAOE
Aei aa?oiueiai ei?aeiio oeueo?acaoeiaeo oaeeue i?aeoiaeyoue oaee?
a?ia?caoeiaiai ae?aiaciio (109 – 1013 Aoe). I?oaei? eieeaaiiy oeeo
/anoio iaceaathoueny a?ia?caoeii (aai oeueo?a-oeueo?acaoeii). Ca
o?ce/iith i?e?iaeith a?ia?caoe i?/ei ia a?ae??ciy?oueny a?ae
oeueo?acaoeo. Aea caaaeyee a?eueo aenieei /anoioai, a ioaea, iaioei
aeiaaeeiai oaeeue cia/ii a?eueo ?noioieie ? aca?iiae?? a?ia?caoeo c
na?aaeiaeuai, eiai eaac?/anoeieaie – aeaeo?iiaie, oioiiaie, iaaiiiaie
oa ?i. A?ia?caoe aeeth/a? iaeanoue /anoio, a?aeiia?aeieo /anoioai
aeaeo?iiaai?oieo oaeeue aeaoeeiao?iaiai, naioeiao?iaiai ? i?e?iao?iaiai
ae?aiacii?a. I?e ii?iaeueiiio oeneo ? e?iiaoi?e oaiia?aoo?? aeiaaeeia
a?ia?caoeiai? oaee? iaeiiai ii?yaeeo c aeiaaeeiith a?eueiiai i?ia?ao
iieaeoe a iia?o?? ? oiio a?ia?caoe o na?aaeiaeu? iaeaea ia
iioe?th?oueny. (A?ia?aoe c /anoioith 100 i?e?a?ae?a aa?oe iiaeeia?oueny
iano?eueee, ui iiai?noth caoooa? aaea a?ey naii? iiaa?oi? aeaea?aea
a?ia?caoeo. A?ia?caoe oaei? /anoioe ua ia io?eiaiee. Aea aaea io?eiaiee
a?ia?caoe c /anoioith 25 i?e?a?ae?a Aoe iiaea ?iciianthaeaeoaaoenue ia
aeoaea ei?ioe? a?aenoai? ? oi, iai?eeeaae, o?eueee a e?enoaeao eaa?oeo
i?e aeoaea iecueeeo oaiia?aoo?ao, aeecueeeo aei aaniethoiiai ioey).
OOI
Eoe?aoe?e Ea? (? noie?ooy i.a.) : «Oe?aeeeaiai aaaaoi iai a aooa ?aea».
O.?iaa?neaa (i?aceaeaio VI I?aeia?iaeiiai eiia?ano c aeonoeee, OO
noie?ooy
i.a.) : «Ooi – oea yae».
«Ooi – oea a?aeoiaee oeea?e?caoe??. Oae caaaeaii ae oe? a?aeoiaee aei
i?i?ioio !»
«Oeoeiu oi/o, oeoeiu. Ia?au, /oi ee, iaiaeaeaiu ?» Aicianainueeee
On? oe? aeneiaethaaiiy a??i?. Ooi – oea aeoaea oe?aeeeaa yaeua. A?i
aeoaea iaaaoeaii aieeaa? ia ethaeeio. C oeueiai i?eaiaeo i?iaaaeaii
/eneai? aeine?aee. Iaeei aeoaea oe?eaaee aeine?ae aoei i?iaaaeaii a
Aa?iai??. Ethaeae iii?noeee a caoeiiai?iieeio e?iiaoo. O ieo i?ney aeiy
i?aoe? a oeeo oiiaao niinoa??aaeinue iia??oaiiy iano?ith ? naiiii/oooy.
Ioaea, a?aenooi?noue ooio oaae ? oe?aeeeaei /eiieeii. Oiio ??aaiue ooio
ia iiaeiai aeoiaeeoe ca iaai? ?aiee.
Aeei?enoaia e?oa?aoo?a :
?.A.Oi?aaei «Ca ei?aeiiaie /ooiiai»
N.O.Aii/a?aiei «Ia/ooi? caoee – o?oaea??»
?.?.Eethe?i «Aeeaiee na?o caoeo»
?.Oaeei? «Ooi»
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