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Интегральное исчисление. Исторический очерк

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O/aaii-ainieoaoaeueiue eiiieaen 1861

Eioaa?aeueiia en/eneaiea.

Enoi?e/aneee i/a?e.

(?aoa?ao)

O/aieoea: Oieiaeiay Aiia

Eeann: 11”A”

Iineaa 2000 a.

Iiiyoea eioaa?ae iaiin?aaenoaaiii naycaii n eioaa?aeueiui en/eneaieai –
?acaeaeii iaoaiaoeee, caieiathueiny eco/aieai eioaa?aeia, eo naienoa e
iaoiaeia au/eneaiey. Aianoa n aeeooa?aioeeaeueiui en/eneaieai
eioaa?aeueiia en/eneaiea ninoaaeyao iniiao iaoaiaoe/aneiai aiaeeca.

Enoiee eioaa?aeueiiai en/eneaiey ioiinyony e aioe/iiio ia?eiaeo ?acaeoey
iaoaiaoeee e aa?oo ia/aei io iaoiaea en/a?iuaaiey, ?ac?aaioaiiiai
iaoaiaoeeaie Ae?aaiae A?aoeee.

Iaoiae en/a?iuaaiey yoi iaai? i?aaee aeey au/eneaiey ieiuaaeae e
iau?iia, ?ac?aaioea eioi?uo i?eienuaaaony Aaaeieno Eieaeneiio.
Aeaeueiaeoaa ?acaeoea iaoiae iieo/ee a ?aaioao Aaeeeaea, a iniaui
eneonnoaii e ?aciiia?aceai i?eiaiaiey iaoiaea en/a?iuaaiey neaaeeny
A?oeiaae.

Oeie/iay noaia aeieacaoaeuenoa iaoiaeii en/a?iuaaiey auaeyaeaea
neaaeothuei ia?acii. Aeey ii?aaeaeaiey aaee/eiu A no?ieeanue iaeioi?ay
iineaaeiaaoaeueiinoue aaee/ei N1, N2, …, Nn, … oaeay, /oi

I?aaeiieaaaeinue oaeaea ecaanoiui oaeia B, /oi

e /oi aeey ethaiai oeaeiai K iiaeii iaeoe aeinoaoi/ii aieueoia n,
oaeiaeaoai?ythuaa oneiaeth:

Aaea D – iinoiyiii. Iinea a?iiicaeeeo ?annoaeaeaiee ec iineaaeiaai
au?aaeaiey oaeaaaeinue iieo/eoue:

Eae aeaeii ec i?eaaae?iiie noaiu iaoiae aue iniiaai ia aii?ieneiaoeee
?anniao?eaaaiuo iauaeoia nooiai/aouie oeao?aie eee oaeaie, ninoaaeaiiuie
ec i?inoaeoeo oeao? eee i?ino?ainoaaiiuo oae (i?yiioaieueieeia,
ia?aeeaeaieiaaeia, oeeeeiae?ia e o.i., iaicia/aiiuo
iineaaeiaaoaeueiinoueth N1, N2, …, Nn, …). A yoii niunea iaoiae
en/a?iuaaiey iiaeii ?anniao?eaaoue eae aioe/iue eioaa?aeueiue iaoiae.

E?ecen e oiaaeie ae?aaiaai ie?a i?ea?e e caaaaieth iiiaeo iao/iuo
aeinoeaeaiee. I iaoiaea en/a?iuaaiey aniiiieee eeoue a XVII aaea. Yoi
auei naycaii n eiaiaie Enaaea Iuethoiia , Aioo?eaea Eaeaieoea, Eaiia?aea
Yeea?a e ?yaea ae?oaeo auaeathueony o/?iuo, iieiaeeaoeo iniiao
nia?aiaiiiai iaoaiaoe/aneiai aiaeeca.

A eiioea XVII e a XVIII aaea ana aic?anoathuea cai?inu i?aeoeee e
ae?oaeo iaoe iiaoaeaeaee o/aiuo iaeneiaeueii ?anoe?youe iaeanoue e
iaoiaeu enneaaeiaaiee iaoaiaoeee. Iiiyoey aaneiia/iinoe, aeaeaeaiey e
ooieoeeiiaeueiie caaeneiinoe auaeaeaathony ia ia?aia ianoi, noaiiayony
iniiaie iiauo iaoiaeia iaoaiaoeee.

A eiioea XVII e a XVIII aaea a iaoaiaoeea e iaoaieea auee iieo/aiu
eeanne/aneea ?acoeueoaou ooiaeaiaioaeueiiai cia/aiey. Iniiaiui caeanue
auei ?acaeoea aeeooa?aioeeaeueiiai e eioaa?aeueiiai en/eneaiey, oai?ee
aeeooa?aioeeaeueiuo o?aaiaiee, aa?eaoeeiiiiai en/eneaiey e aiaeeoe/aneie
iaoaieee.

Iniiaiua iiiyoey e oai?ey eioaa?aeueiiai e aeeooa?aioeeaeueiiai
en/eneaiee, i?aaeaea anaai naycue iia?aoeee aeeooa?aioee?iaaiey e
eioaa?e?iaaiey, a oaeaea eo i?eiaiaiey e ?aoaieth i?eeeaaeiuo caaea/
auee ?ac?aaioaiu a eiioea XVII aaea, ii iniiauaaeenue ia eaeayo,
noi?ioee?iaaiiuo a ia/aea XVII aaea aaeeeei iaoaiaoeeii e ano?iiiiii
Eiaaiii Eaiea?ii.

A iiya?a 1613 aiaea ei?ieaaneee iaoaiaoee e ano?ieia aano?eeneiai aeai?a
E. Eaiea? i?acaeiiaae naaaeueao. Aioiaynue e iae, ii i?eia??e ianeieueei
ai/ae aeiia?aaeiiai aeia. I?e iieoiea Eaiea? aue ii?aae?i oai, /oi
i?iaeaaaoe ii?aaeaeye aianoeiinoue ai/ee, i?iecaiaey iaeii aaeeinoaaiiia
aeaenoaea – ecia?yy ?annoiyiea io iaeeaiiai ioaa?noey aei naiie
aeaeueiae io iaai oi/ee aeieua. Aaaeue oaeia ecia?aiea niaa?oaiii ia
o/eouaaei oi?io ai/ee! Eaiea? n?aco oaeaeae, /oi ia?aae iei
eioa?aniaeoay iaoaiaoe/aneay caaea/a – ii ianeieueeei ecia?aieyi
au/eneeoue aianoeiinoue ai/ee. ?aciuoeyy iaae yoie caaea/ae, ii iao?e
oi?ioeu ia oieueei aeey iau?ia ai/ae, ii e aeey iau?ia naiuo ?acee/iuo
oae: eeiiia, yaeiea, aeau e aeaaea oo?aoeeie /aeiu. Aeey eaaeaeiai ec
oae Eaiea?o i?eoiaeeeinue nicaeaaaoue iiaua, ca/anooth i/aiue oeo?ioiiua
iaoiaeu, /oi auei e?aeia iaoaeiaii. Iiiuoea iaeoe aeinoaoi/ii iauea, a,
aeaaiia, i?inoua iaoiaeu ?aoaiey iiaeiaiuo caaea/ e i?eaaea e
aicieeiiaaieth nia?aiaiiiai eioaa?aeueiiai n/eneaiey. Ii yoi oaea auea
caneoaa nianai ae?oaiai iaoaiaoeea.

O?oaeii iaeoe ae?oaia eiy, eioi?ia ieacaei au noieue neeueiia aeeyiea ia
enoi?eth ie?iaie iaoee e eoeueoo?u, eae Enaae Iuethoii. Ecaanoiue
iaoaiaoee e enoi?ee iaoee A. E. Aai-aea?-Aa?aeai ieoao a naiae eieaa
“I?iaoaeaeathuayny iaoea”: “Eaaeaeue anoanoaieniuoaoaeue aaconeiaii
niaeaneony, /oi iaoaieea Iuethoiia anoue iniiaa nia?aiaiiie oeceee.
Eaaeaeue ano?iiii ciaao, /oi nia?aiaiiay ano?iiiiey ia/eiaaony n Eaiea?a
e Iuethoiia. E eaaeaeue iaoaiaoee ciaao, /oi naiei cia/eoaeueiui i
iaeaieaa aaaeiui aeey oeceee ioaeaeii nia?aiaiiie iaoaiaoeee yaeyaony
aiaeec, a iniiaa eioi?iai eaaeao aeeooa?aioeeaeueiia e eioaa?aeueiia
en/eneaiey Iuethoiia. Neaaeiaaoaeueii, o?oaeu Iuethoiia yaeythony
iniiaie ia?iiiie /anoe oi/iuo iaoe iaoaai a?aiaie”. E ia oieueei iaoe:
“Iaoaiaoeea e oaoieea aeeytho aeaaea ia iaoo aeooiaioth aeeciue, e
ianoieueei. /oi iu ?aaeei iiaeai i?aaenoaaeoue yoi naaa iieiinoueth.
Aneaae ca iaiau/aeiui ace?oii, eioi?ia ia?aaeeei e XVII aaea
anoanoaiciaiea, iineaaeiaae iaecaaaeii ?aoeeiiaeeci XVIII aaea,
iaiaeanoaeaiea ?acoia, oiaaeie ?aeeaee… Eoi ioaeaao naaa io/ao a oii,
– ni?aoeaaao aaoi?, – /oi n enoi?e/aneie oi/ee c?aiey Iuethoii yaeyaony
naiie cia/eoaeueiie oeao?ie XVII aaea?”

Enaae Iuethoii ?iaeeeny a 1643 aiaeo. Iaeue/ee iinauae nia/aea
naeueneoth oeieo, a a aeaaiaaeoeaoue eao aai ioi?aaeee o/eoueny a
aeeaeaeoee ai?iae. Aee?aeoi? oeieu ia?aoee aieiaiea ia niiniaiiai
iaeue/eea e oaiai?ee iaoue Iuethoiia ioi?aaeoue nuia o/eoueny a
Eaia?eaeaeneee oieaa?neoao. Iuethoii aue i?eiyo ooaea a ea/anoaa
aaaeiiai nooaeaioa, iaycaiiiai i?eneoaeeaaoue aaeaeaa?ai, iaaeno?ai e
nooaeaioai noa?oeo eo?nia.

Eaoaae?o iaoaiaoeea a Eaia?eaeaea caieiae oiaaea iieiaeie aeanoyuee
o/?iue Enaae Aa??io. Ii nei?i noae ia oieueei o/eoaeai, ii e ae?oaii
Iuethoiia, a nionoy ianeieueei eao onooiee naiaio aaeeeiio o/aieeo
eaoaae?o iaoaiaoeee. E yoiio a?aiaie Iuethoii iieo/ee oaea noaiaie
aaeaeaa?a e iaaeno?a. A 1665-1667 aiaeao Iuethoii ia/ae ?aaioaoue iaae
nicaeaieai iaoaiaoe/aneiai aiia?aoa, n iiiiuueth eioi?iai iiaeii auei au
enneaaeiaaoue e au?aaeaoue caeiiu oeceee. Iuethoii ia?aue iino?iee
aeeooa?aioeeaeueiia e eioaa?aeueiia en/eneaiey (ii iacaae aai iaoiaeii
oethenee). Yoi n?aco iicaieeei ?aoaoue naiua ?aciiia?aciua,
iaoaiaoe/aneea e oece/aneea, caaea/e. Aei Iuethoiia iiiaea ooieoeee
ii?aaeaeyeenue oieueei aaiiao?e/anee, oae /oi e iei iaaiciiaeii auei
i?eiaiyoue aeaaa?o e iiaia en/eneaiea oethenee. Iuethoii iaoae iiaue
iauee iaoiae aiaeeoe/aneiai i?aaenoaaeaiey ooieoeee – ii aaae a
iaoaiaoeeo e ia/ae nenoaiaoe/anee i?eiaiyoue aaneiia/iua ?yaeu.

Iiyniei yoo eaeath Iuethoiia. Ecaanoii, /oi ethaia aeaenoaeoaeueiia
/enei iiaeii i?aaenoaaeoue aeanyoe/iie ae?iaueth – eiia/iie eee
aaneiia/iie. Oae. iai?eia?:

Yoi cia/eo, /oi ethaia /enei a iiaeii i?aaenoaaeoue a aeaea:

, a ii noaiaiyi x:

aaea a1, a2, … an, …- eiyooeoeeaiou, eioi?ua eaaeaeue ?ac aeieaeiu
auoue ii?aaeaeaiu. I?eia?ii oaeiai ?yaea iiaeao neoaeeoue ecaanoiay iai
aaiiao?e/aneay i?ia?anney:

I?aaenoaaeaiea ooieoeee n iiiiuueth ?yaea i/aiue oaeiaii. N iiiiuueth
?yaeia, eae ienae Iuethoii, “oaeaaony i?aiaeieaoue o?oaeiinoe, a ae?oaii
aeaea i?aaenoaaeythueany ii/oe iaiaeieeiuie”.

Iaeiia?aiaiii n Iuethoiiii e aiaeiae/iui eaeayi i?eo?e ae?oaie
auaeathueeny o/?iue – Aioo?eae Aeeueaaeuei Eaeaieoe.

Aioo?eae Aeeueaaeuei Eaeaieoe ?iaeeeny a Aa?iaiee a a. Eaeioeeaa a 1646
a. Ethaiciaoaeueiue iaeue/ee oaea 6 eao aae eioa?aniua aanaaeu ii
enoi?ee ni naiei iooeii, i?ioanni?ii Eaeioeeaneiai oieaa?neoaoa. E 12
aiaeai ii oi?ioi eco/ee eaoeineee ycue e oae?eny ae?aaiaa?a/aneei.
Iniaaiii aai eioa?aniaaee ae?aaiea oeeiniou, e ii iia iiaeieao
?aciuoeyoue i oeeinioneeo oai?eyo A?enoioaey eee Aeaiie?eoa. A 15 eao
Eaeaieoe iinooiaao e Eaeioeeaneee oieaa?neoao, aaea ona?aeii eco/aao
i?aai e oeeinioeth. Ii i/aiue iiiai /eoaao, n?aaee aai ethaeiuo eiea –
eieae ?. Aeaea?oa, A. Aaeeeay, II. Eaiea?a e Ae. Eaiiaiaeeu.

Naie eieinnaeueiua ciaiey ii iaoaiaoeea Eaeaieoe i?eia?ae naiio/eie.
*a?ac o?e aiaea, ieii/ea oieaa?neoao, Eaeaieoe iieeioe Eaeioeea. Ii aue
iaeaeai ioeacii o/aiiai niaaoa oieaa?neoaoa i?enaieoue iio noaiaiue
aeieoi?a i?aa. Ioeac iauynieee oai. /oi Eaeaieoe aue… neeoeii iieiae!

Ia/aeanue aeeciue, iieiay iai?yaeaiiiai o?oaea e iiiai/eneaiiuo
iooaoanoaee. Eaaei naaa i?aaenoaaeoue, eae iaoaeiaiu auee
iooaoanoaiaaoue a iaoeethaeeo ea?aoao ii o?yneei aei?iaai Aa?iiu oao
a?aiai. Eaeaieoe oiae ia oa?youe a?aiaie aea?ii – iiiai oaea/iuo iuneae
i?eoei aio e aieiao eiaiii ai a?aiy yoeo i?iaeieaeeoaeueiuo iiacaeie.
Eaeaieoe ioee/aeny eneeth/eoaeueiie niiniaiinoueth auno?i “aoiaeeoue” e
caaea/o e ?aoaoue aa iaeaieaa iauei niiniaii. ?aciuoeyy iaae
oeeinioneeie e iaoaiaoe/aneeie aii?inaie, Eaeaieoe oaaaeeeny, /oi naiui
iaaeaaeiui n?aaenoaii eneaoue e iaoiaeeoue enoeio a iaoea iiaeao noaoue
iaoaiaoeea. Anth niith niciaoaeueioth aeeciue ii no?aieeny au?aceoue
caeiiu iuoeaiey, /aeiaa/aneoth niiniaiinoue aeoiaoue e aeaea
iaoaiaoe/aneiai en/eneaiey. Aeey yoiai iaiaoiaeeii, o/ee Eaeaieoe,
oiaoue iaicia/aoue ethaua iiiyoey eee eaeae ii?aaeaeaiiuie neiaieaie,
eiiaeie?oy eo a iniaua oi?ioeu, e naiaeeoue i?aaeea iuoeaiey e i?aaeeai
a au/eneaieyo ii yoei neiaiee/aneei oi?ioeai. Caiaiyy oau/iua neiaa
/aoei ii?aaeaeaiiuie neiaieaie, Eaeaieoe no?aieeny ecaaaeoue iaoe
?annoaeaeaiey io anyeie iaii?aaeaeaiiinoe e aiciiaeiinoe ioeaeoueny
naiiio eee aaiaeeoue a caaeoaeaeaiea ae?oaeo. Anee, ia/oae Eaeaieoe.
iaaeaeo ethaeueie aicieeioo ?aciiaeaney, oi ?aoaoueny iie aoaeoo ia a
aeeeiiuo e ooiieoaeueiuo nii?ao. a oae, eae ?aoathony caaea/e eee
aeieacuaathony oai?aiu. Nii?ueee aicueioo a ?oee ia?uey e, neacaa:
“Ia/iai au/eneyoue” – i?eioony ca ?an/aou.

Eae oaea ioia/aeinue, Eaeaieoe iaeiia?aiaiii n Iuethoiiii e iacaaeneii
io iaai ioe?ue iniiaiua i?eioeeiu aeeooa?aioeeaeueiiai e eioaa?aeueiiai
en/eneaiee. Oai?ey i?eia?aea neeo iinea oiai, eae Eaeaieoeai e
Iuethoiiii auei aeieacaii, /oi aeeooa?aioee?iaaiea e eioaa?e?iaaiea –
acaeiii ia?aoiua iia?aoeee. Ia yoii naienoaa oi?iith ciae e Iuethoii. Ii
oieueei Eaeaieoe oaeaeae caeanue oo caia/aoaeueioth aiciiaeiinoue,
eioi?oth ioe?uaaao i?eiaiaiea neiaiee/aneiai iaoiaea.

aeaenoaotho ia ooieoeee, “ia?a?aaaouaay” eo a ae?oaea, oi/ii
au/eneyaiua ooieoeee. Eaeaieoe ?ac?aaaouaaao iniaoth aeaaa?o aeaenoaee n
yoeie iia?aoi?aie. Ii aeieacuaaao, /oi iau/iia /enei a iiaeii auiineoue
ca ciae iia?aoi?a:

Iaeeiaeiaua iia?aoi?u iiaeii auiineoue ca neiaeo:

eee:

Nie?auaiii ana ia?a/eneaiiua naienoaa iiaeii au?aceoue niioiioaieai:

aaea: ( e ( – /enea.

Iia?aoi?u. eioi?ua iaeaaeatho oaeei naienoaii. iacuaathony eeiaeiuie.
Oai?ey eeiaeiuo iia?aoi?ia, eioi?oth n oaeei oniaoii ia/ae ?acaeaaoue,
Eaeaieoe,. a nia?aiaiiie iaoaiaoeea yaeyaony oi?ioi ?ac?aaioaiiie e
iieaciie a i?eeiaeaieyo oai?eae.

Iiiaie?aoiia i?eiaiaiea iia?aoi?ia iiaeii i?eieiaoue eae noaiaiue
iia?aoi?a, iai?eia?, aeey d( ):

eee iaiai?io:

e iiieiay iiae eo i?iecaaaeaieai iineaaeiaaoaeueiia eo i?eiaiaiea,
eiaai:

o. a. i?iecaaaeaiea anoue “aaeeieoea”, ia iaiythuay ooieoeeth.

Iaeiaei, a iiaeoiaea Iuethoiia-Eaeaieoea e?ueinue na?ue?ciia
i?ioeai?a/ea.

Eaeaieoe e aai iineaaeiaaoaee – a?aouey Aa?ioeee, Eiieoaeue e ae?oaea –
o?aeoiaaee aeeooa?aioeeaeu eae aaneiia/ii iaeua ?aciinoe iau/iuo
eiia/iuo aaee/ei, eae oiaaea aiai?eee – “?aaeueiuo” aaee/ei “iecoae”
iaoaiaoeee. Iiyoiio iie ia?auaeenue n oaie e ae?oaeie iaeeiaeiai e a
en/eneaiee i?eiaiyee e ia?aui oa aea i?eaiu, eioi?ua ni?aaaaeeeau i?e
aeaenoaeyo ni aoi?uie. Aianoa n oai auynieeinue, /oi oaeei ia?acii
o?aeooaiui aaneiia/ii iaeui i?enoua naienoai, i?ioeai?a/auaa iaeiiio
iniiaiiio naienoao iniiaiuo eiia/iuo aaee/ei: anee A — eiia/iay
aaee/eia, a ( — aaneiia/ii iaeay, oi, /oiau ?acoeueoao en/eneaiey
iieo/aeny niaa?oaiii oi/iui, ieacaeinue iaiaoiaeeiui i?iaiaeeoue
au/eneaiey a i?aaeiieiaeaiee, /oi A+(=A.

Aeeooa?aioeeaeueiia en/eneaiea, cia/aiea eioi?iai aeey ?acaeoey iaoee e
oaoieee auei aia niiiaiee, ieacaeinue a ia?aaeienaeueiii iieiaeaiee:
/oiau aai iaoiaeaie iieo/eoue oi/iue ?acoeueoao, iaaei auei enoiaeeoue
ec ioeai/iiai ooaa?aeaeaiey.

Iuethoii iuoaeny iainiiaaoue aeeooa?aioeeaeueiia en/eneaiea ia caeiiao
iaoaieee e iiiyoee i?aaeaea. Ii aio ia oaeaeinue inaiaiaeeoue naia
en/eneaiea oethenee io iaaeinoaoeia, i?enoueo aeeooa?aioeeaeueiiio
en/eneaieth Eaeaieoea. A i?aeoeea au/eneaiey Iuethoii, eae e Eaeaieoe,
i?eiaiye i?eioeei ioa?anuaaiey aaneiia/ii iaeuo.

Oaeay iaiineaaeiaaoaeueiinoue iicaieeea iacaaoue aeeooa?aioeeaeueiia
en/eneaiea Eaeaieoea–Iuethoiia ienoe/aneei. Yoei a ia?aoth i/a?aaeue
iiae/a?eeaaeinue, /oi Eaeaieoe e Iuethoii aaiaeeee a aeeooa?aioeeaeueiia
en/eneaiea aaneiia/ii iaeua aaee/eiu iaoaoece/anee, n?aco iieaaay eo
nouanoaothueie, aac auyniaiey eo aicieeiiaaiey e ?acaeoey e aac aiaeeca
i?e?iaeu eo niaoeeoe/aneeo naienoa.

Iiiuoee iino?ieoue aiaeec aaneiia/ii iaeuo e oai?eth ?yaeia a iieiii
niioaaonoaee n iniiaiuie iiiyoeyie e enoeiaie “iecoae” iaoaiaoeee n
naiiai ia/aea e oniaoiui ?acoeueoaoai ia i?eaaee. Iiyoiio Eaeaieoe e aai
iineaaeiaaoaee iuoaeenue ii?aaaeaoue i?eioeeiu aiaeeca aaneiia/ii iaeuo
iooai n?aaiaiey aaneiia/ii iaeie n ian/eieie, eioi?ie iiaeii i?aiaa?a/ue
i?e au/eneaiee auniou ai?u, iin?aaenoaii nnueie ia aa?iyoiinoue e o. i.

Ae?oaay iiiuoea auea i?aaei?eiyoa a eiioea XVIII aaea. Ecaanoiue
iaiaoeeee iaoaiaoee Aannaeue i?aaeeiaeee inoaaeoue aiaeec aaneiia/ii
iaeuo a aiaeeca a ea/anoaa “iieaciuo aniiiiaaoaeueiuo ooieoeee”.
Iaeiaei, oaeay o?aeoiaea oe?ieiai ?ani?ino?aiaiey ia iieo/eea –
iaoaiaoeee ciaee iaoaie/aneia e aaiiao?e/aneia enoieeiaaiea dx e dy.

I?eia?ii n iineaaeiae /aoaa?oe XVIII aaea iaeanoue i?eeiaeaiee
iaoaiaoe/aneiai aiaeeca ia/eiaao cia/eoaeueii ia?ae?uaaoue a?aieoeu aai
iau/iiai i?eeiaeaiey a iaoaieea e aaiiao?ee. Au? auno?aa ?acaa?ouaaaony
yoio i?ioeann a ia?aie /aoaa?oe XIX aaea.

Iaoaiaoeee iuoaeenue nia/aea ?aoaoue iiaua caaea/e iaoiaeaie,
?ac?aaioaiiuie eeanneeaie XVIII aaea – Yeea?ii, Aeaeaiaa?ii, Eaa?aiaeai
e ae?oaeie. Iaeiaei, anei?a auynieeinue, /oi iaoiaeu eeanneeia
iaaeinoaoi/iu, /oi iaaei ?acaeaaoue iiaua, aieaa iauea e neeueiua
iaoiaeu. Auynieeinue oaeaea, /oi iaaeinoaoi/iinoue iaoiaeia eeanneeia
ia?aaeei naycaia n ocinoueth o?aeoiaee iniiaiuo iiiyoee, n “ecaiiyaiui”
iiiyoeai i aaneiia/ii iaeii, n “eneeth/aieyie”, eioi?ua ?aiueoa
inoaaaeenue a oaie.

Iiyniei neacaiiia iaeiei i?eia?ii.

Iuethoii e Eaeaieoe ?ac?aaioaee aeaa o?aeoiaee iiiyoey iau/iiai
ii?aaeaeaiiiai eioaa?aea.

Iuethoii o?aeoiaae ii?aaeaeaiiue eioaa?ae eae ?aciinoue niioaaonoaothueo
cia/aiee ia?aiia?aciie ooieoeee:

,

aaea F`(x)=f(x).

Aeey Eaeaieoea ii?aaeaeaiiue eioaa?ae aue noiiie anao aaneiia/ii iaeuo
aeeooa?aioeeaeia.

.

Ia?aay o?aeoiaea ioaa/aea oaoieea au/eneaiey ii?aaeaeaiiuo eioaa?aeia
i?e iiiiue ia?aiia?aciie iiaeuioaa?aeueiie ooieoeee, aoi?ay – iioiio,
/oi a i?eeiaeaieyo ii?aaeaeaiiue eioaa?ae iiyaeyeny eae i?aaeae
ecaanoiiai aeaea noiiu (eioaa?aeueiie noiiu).

I?eia?ii aei iineaaeiae /aoaa?oe XVIII aaea ia?aay o?aeoiaea iiiyoey
ii?aaeaeaiiiai eioaa?aea caieiaea ainiiaenoaothuaa iieiaeaiea. Yoiio
niinianoaiaaee aeaa ianoiyoaeuenoaa.

E ia/aeo XVIII aaea auee onoaiiaeaiu i?aaeea aeeooa?aioee?iaaiey anao
yeaiaioa?iuo ooieoeee e ia/aeanue oniaoiay ?ac?aaioea iaoiaeia
iaoiaeaeaiey eo ia?aiia?aciuo (?aoeeiiaeueiuo, ioaeaeueiuo eeannia
e??aoeeiiaeueiuo e o?ainoeaiaeaioiuo ooieoeee). Aeaaiaea?y yoiio oi/ea
c?aiey Iuethoiia aiieia ioaa/aea ?acaeoeth yooaeoeaiuo aeai?eoiia
eioaa?aeueiiai en/eneaiey.

eae i?aaeaea eioaa?aeueiie noiiu noieeioeinue n iiiaeie o?oaeiinoyie.
Anoanoaaiii, /oi yoi ianoiyoaeuenoai oe?aieaieth oi/ee c?aiey Eaeaieoea
ia niinianoaiaaei.

Enoieeiaaiea iau/iiai ii?aaeaeaiiiai eioaa?aea ii Eaeaieoeo iie?aeinue
ia iiiyoea i aaneiia/ii iaeuo, io eioi?iai iaoaiaoeee XVIII aaea oioaee
inaiaiaeeoue iaoaiaoe/aneee aiaeec. Yoi oaeaea niinianoaiaaei
oe?aieaieth oi/ee c?aiey Iuethoiia. Oaeo yoio oi?ioi iiaeoaa?aeaeaeny
oai, eae Eaiia?ae Yeea? eniieueciaae iiiyoea ia eioaa?aeueiie noiia.
Yeea? ia aic?aaeae i?ioea i?eaeeaeaiiiai au/eneaiey ii?aaeaeaiiuo
eioaa?aeia i?e iiiiue niioaaonoaothueo eioaa?aeueiuo noii. Ii
?anniao?eaaoue ii?aaeaeaiiue eioaa?ae eae i?aaeae eioaa?aeueiie noiiu ii
ia iia. A yoii neo/aa ana neaaaaiua eioaa?aeueiie noiiu noaiiaeeenue
aaneiia/ii iaeuie, o. a., n oi/ee c?aiey Yeea?a, auee ioeyie.

Enoi?e/aneay ni?aaea. A 1963 a. 23-eaoiee Iaoeue Yeea? ieii/ee eo?n
oaieiaee a Aacaeueneii oieaa?neoaoa. Ii o/?iuo oaieiaia auei a oa aiaeu
aieueoa, /ai o?aaiaaeinue, e eeoue a 1701 a. ii iieo/ee ioeoeeaeueioth
aeieaeiinoue nayuaiieea ne?ioneiai aeiia a Aacaea. 19 ai?aey 1706 a.
ianoi? Iaoeue Yeea? aeaieeny ia aei/a?e nayuaiieea. A 15 ai?aey 1707 a.
o ieo ?iaeeeny nui, iacaaiiue Eaiia?aeii.

Ia/aeueiia iao/aiea aoaeouee o/?iue i?ioae aeiia iiae ?oeiaiaenoaii
iooea, o/eaoaainy iaeiaaea iaoaiaoeea o sseiaa Aa?ioeee. Aeia?ue ianoi?
aioiaee noa?oaai nuia e aeooiaiie ea?uea?a, iaeiaei caieiaeny n iei e
iaoaiaoeeie – eae a ea/anoaa ?acaea/aiey, oae e aeey ?acaeoey
eiae/aneiai iuoeaiey. Iaeue/ee oae?eny iaoaiaoeeie, noae caaeaaaoue
iooeo aii?inu iaeei neiaeiaa ae?oaiai.

Eiaaea o Eaiia?aei i?iyaeeny eioa?an e o/?aa, aai iai?aaeee a
Aacaeueneoth eaoeineoth aeiiaceth – iiae iaaeci? aaaooee.

20 ieoya?y 1720 a. 13-eaoiee Eaiia?ae Yeea? noae nooaeaioii oaeoeueoaoa
eneonnoa Aacaeueneiai oieaa?neoaoa: ioaoe aeaeae, /oiau ii noae
nayuaiieeii. Ii ethaiaue e iaoaiaoeea, aeanoyuay iaiyoue e ioee/iay
?aaioiniiniaiinoue nuia eciaieee yoe iaia?aiey e iai?aaeee Eaiia?aea ii
eiiio iooe.

Noaa nooaeaioii, ii eaaei onaaeaae o/aaiua i?aaeiaou, ioaeaaay
i?aaeii/oaiea iaoaiaoeea. E iaioae?aii, /oi niiniaiue iaeue/ee anei?a
ia?aoee ia naay aieiaiea Aa?ioeee. Ii i?aaeeiaeee thiioa /eoaoue
iaoaiaoe/aneea iaioa?u, a ii noaaioai i?eoiaeeoue e iaio aeiiie, /oiau
niaianoii ?acae?aoue iaiiiyoiia. A aeiia naiaai o/eoaey Yeea?
iiciaeiieeny e iiae?oaeeeny n nuiiaueyie Aa?ioeee – Ieeieaai e
Aeaieeeii, oaeaea oaea/?iii caieiaaoeieny iaoaiaoeeie. A 8 ethiy 1724a.
17-eaoiee Eaiia?ae Yeea? i?ieci?n ii- eaouie aaeeeieaiioth ?a/ue i
n?aaiaiee oeeinioneeo aicc?aiee Aeaea?oa e Iuethoiia – e aue oaeinoiai
o/?iie noaiaie iaaeno?a (a XIX a. a aieueoeinoaa oieaa?neoaoia Caiaaeiie
Aa?iiu o/aiay noaiaiue iaaeno?a auea caiaiaia noaiaiueth aeieoi?a
oeeinioee).

Yeea? ioee/aeny oaiiiaiaeueiie ?aaioiniiniaiinoueth. Ii i?inoi ia iia ia
caieiaoueny iaoaiaoeeie eee a? i?eeiaeaieyie. A 1735 a. Aeaaeaiey
iieo/eea caaeaiea auiieieoue n?i/iia e i/aiue a?iiicaeeia
ano?iiiie/aneia au/eneaiea. A?oiia aeaaeaieeia i?ineea ia yoo ?aaioo o?e
ianyoea, a Yeea? acyeny auiieieoue ?aaioo ca 3 aeiy – e ni?aaeeny
naiinoiyoaeueii. Iaeiaei ia?aiai?yaeaiea ia i?ioei aanneaaeii: ii
caaieae e iioa?ye c?aiea ia i?aaue aeac. Iaeiaei o/?iue ioi?nny e
ian/anoueth n aaee/aeoei niieienoaeai: “Oaia?ue y iaiueoa aoaeo
ioaeaeaoueny io caiyoee iaoaiaoeeie”, – oeeinionee caiaoee ii.

Aei yoiai a?aiaie Yeea? aue ecaanoai eeoue oceiio e?oao o/?iuo. Ii
aeaoooiiiia ni/eiaiea “ Iaoaieea, eee iaoea i aeaeaeaiee, a
aiaeeoe/aneii eceiaeaiee ”, ecaeaiiia a 1736 a., i?eianei aio ie?iaoth
neaao. Yeea? aeanoyua i?eiaiee iaoiaeu iaoaiaoe/aneiai aiaeeca e
?aoaieth i?iaeai aeaeaeaiey a ionoioa e a nii?ioeaeythuaeny n?aaea. “Oio
, eoi eiaao aeinoaoi/iua iaauee a aiaeeca, niiaeao an? oaeaeaoue n
iaiau/aeiie e?aeinoueth e aac anyeie iiiiue i?i/eoaao ?aaioo
iieiinoueth”, – caeai/eaaao Yeea? nai? i?aaeeneiaea e eieaa.

Aeoo a?aiaie o?aaiaae aiaeeoe/aneiai iooe ?acaeoey oi/iuo iaoe,
i?eiaiaiey aeeooa?aioeeaeueiiai e eioaa?aeueiiai en/eneaiey aeey
iienaiey oece/aneeo yaeaiee. Yoio iooue e ia/ae i?ieeaaeuaaoue Eaiia?ae
Yeea?.

Eiia/ii, e aei iineaaeiae /aoaa?oe XVIII aaea eiioeaioeey Iuethoiia
noaeeeaaeanue n o?oaeiinoyie. A yoio ia?eiae ano?a/aeenue yeaiaioa?iua
ooieoeee, ia?aiia?aciua eioi?uo ia iiaoo auoue au?aaeaiu /a?ac
yeaiaioa?iua ooieoeee. Ciaee iaoaiaoeee e iaeioi?ua ianianoaaiiua
eioaa?aeu, a oii /enea e ?anoiaeyueany. Ii oaeiai ?iaea oaeou auee
aaeeie/iuie e onoaiiaeaoaeny yooaeoeaiie eiioeaioeee eioaa?aea ia?ooeoue
ia iiaee. Eiui ieacaeinue iieiaeaiea a iineaaeiae /aoaa?oe XVIII e
iniaaiii a ia/aea XIX aaea.

N 70-o aiaeia XVIII aaea ?aoaiea caaea/ aiaeeoe/aneie iaoaieee, oeceee e
ae?oaeo aeenoeeieei iio?aaiaaei cia/eoaeueiia ?acaeoea iiiyoey
ii?aaeaeaiiiai eioaa?aea. Iniaia cia/aiea i?eia?aoatho aeaieiua e
o?ieiua eioaa?aeu (Yeea?, Eaa?aiae, Eaiean e ae?.).

Yoi auei a?aiy, eiaaea aaeeeea eaeae Iuethoiia e Eaeaieoea auee
iioaeeeiaaiu n?aaieoaeueii iaaeaaii e nia?aiaiiue iaoaiaoe/aneee aiaeec
oieueei nicaeaaaeny. Iiuiua iaoiaeu, eioi?ua i?eianee n niaie yoe eaeae,
iaoiaeeee i?eiaiaiea ai anao io?aneyo oi/iiai ciaiey. I?eiaiaiea yoi oei
?oea ia ?oeo n ?acaeoeai naiiai aiaeeca, /anoi oeacuaay iooe e
iai?aaeaiey, ii eioi?ui aeieaeii ?acaeaaoueny iiaia en/eneaiea. Yoi
auea, iiaeaeoe, aaeeinoaaiiay ii naiae eioaineaiinoe yiioa
iaoaiaoe/aneiai oai?/anoaa, e Yeea? aue iaeei ec iaiiiaeo ii naiae
i?iaeoeoeaiinoe oai?oeia. Aai “Aaaaeaiea a aiaeec aaneiia/ii iaeuo”,
“Iniiaaiey aeeooa?aioeeaeueiiai en/eneaiey” e “Iniiaaiey eioaa?aeueiiai
en/eneaiey” auee ia?auie o?aeoaoaie, a eioi?uo oaea iaoe?iue, ii
?ac?iciaiiue iaoa?eae iiaiai aiaeeca aue iauaaeeiai a oeaeueioth iaoeo.
A ieo aue au?aaioai oio neaeao nia?aiaiiiai aiaeeca, eioi?ue nio?aieeny
e aei iaoaai a?aiaie.

?ac?aaioea i?eaiia au/eneaiey aeaieiuo e o?ieiuo eioaa?aeia iieacaea,
/oi au/eneyoue yoe eioaa?aeu oae, eae au/eneyee iau/iue ii?aaeaeaiiue
eioaa?ae – i?e iiiiue iaii?aaeaeaiiiai, i/aiue o?oaeii eee aeaaea
iaaiciiaeii. Iiyoiio iaoaiaoeee auioaeaeaiu auee nio?aiyoue eiioeaioeeth
Iuethoiia oieueei ia neiaao, a ia aeaea, i?e ?aoaiee caaea/ oi/iuo iaoe,
noaee ia iooue Eaeaieoea. Iie au/eneyee niioaaonoaothuea eioaa?aeueiua
noiiu (a i?yiioaieueiuo, oeeeeiae?e/aneeo e noa?e/aneeo eii?aeeiaoao) e
iaoiaeeee eo i?aaeaeu.

Ei?i/a aiai?y, ?ac?aaioea niiniaia au/eneaiey iiauo aeaeia
ii?aaeaeaiiiai eioaa?aea iieacaea, /oi iaueiiaaiiue, aeaieiie e o. ae.
ii?aaeaeaiiue eioaa?aeu aeieaeiu auoue iainiiaaiu naie ii naaa
iacaaeneii io iiiyoey iaii?aaeaeaiiiai eioaa?aea. Ii eaaeaeia neaaaaiia
ethaie eioaa?aeueiie noiiu yaeyaony aaneiia/ii iaeie aaee/eiie. Oai
naiui ia oieueei noaaeeny aii?in i eaaaeecaoeee ?aiaa “ecaiiyaiiai”
iiiyoey aaneiia/ii iaeiai, ii e i ?ane?uoee aai ?aaeueiiai niaea?aeaiey
e i niioaaonoaothuai aai eniieueciaaiee. Eae oaea oeacuaaeinue, /oiau
an? yoi naeaeaoue iaaei auei i?aiaeieaoue – iaiaueoue, ?acaeoue
o?aaeeoeeiiiia (Yeea?iai) oieeiaaiea ooieoeee e iiiyoey i?aaeaea.

A nayce n yoei aiciee aii?in i nouanoaiaaiee i?aaeaeia eioaa?aeueiuo
noii, neaaaaiua eioi?uo auee au aaneiia/ii iaeuie. A ia?aie /aoaa?oe XIX
aaea iiiyoea aaneiia/ii iaeie ieacaeinue iaiaoiaeeiui e aeey eco/aiey e
niiinoaaeaiey naienoa iai?a?uaiuo e ?ac?uaiuo ooieoeee. Iieo/aiea
iniiaiiieaaathueo ?acoeueoaoia naycaii caeanue n eiaiai Eioe. “Iaaeaeo
iiiaeie iiiyoeyie, – oeacuaae Eioe, – oanii naycaiiuie ni naienoaaie
aaneiia/ii iaeuo, neaaeoao iiianoeoue iiiyoea i iai?a?uaiinoe e
i?a?uaiinoe ooieoeee”. Ooo aea Eioe aeaao enoieeiaaiea iai?a?uaiinoe
ooieoeee, eioi?ia aieaa /ai ynii iiaeoaa?aeaeaao yniinoue yoiai aai
ooaa?aeaeaiey.

Iiaay iinoaiiaea caaea/ iainiiaaiey iaoaiaoe/aneiai aiaeeca ynii
iieacuaaea, /oi aeaei ia oieueei a i?eciaiee e i?eiaiaiee aaneiia/ii
iaeuo – yoi aeaeaee e ?aiueoa! – ii i?aaeaea anaai a iao/iii
enoieeiaaiee eo niaea?aeaiey e iainiiaaiiii ia yoii eniieueciaaiee eo a
aeai?eoiao iaoaiaoe/aneiai aiaeeca. Iaeiaei, /oiau yoi naeaeaoue iaaei
auei i?aiaeieaoue ainiiaenoaiaaaoaa a XVIII aaea oceia oieeiaaiea
iiiyoey i?aaeaea, ?ac?aaioaoue iauoth oai?eth i?aaeaeia.

Eco/aiea ?ac?uaiuo ooieoeee e niiinoaaeaiea eo n ooieoeeyie iai?a?uaiuie
canoaaeei i?eciaoue oi, /oi ?aiaa n/eoaeinue iaaiciiaeiui: /oi i?aaeae,
e eioi?iio no?aieoueny iineaaeiaaoaeueiinoue cia/aiee ooieoeee, i?e
no?aieaiee a?aoiaioa a iaeioi?ie oi/ea iiaeao ieacaoueny ioee/iui io
cia/aiey ooieoeee a yoie oi/ea. Cia/eo, i?aaeae ia anaaaea yaeyaony
“iineaaeiei” cia/aieai ia?aiaiiie, ii ai anao neo/ayo i?aaeae anoue
/enei, e eioi?iio ia?aiaiiay i?eaeeaeaaony iaia?aie/aiii.
Neaaeiaaoaeueii, dx e dy ia iaiaoiaeeii ioee eee “ienoe/anee” aeooaeueii
aaneiia/ii iaeua; aaneiia/ii iaeay – yoi ia?aiaiiay, eiathuay i?aaeaeii
ioeue, i?e/ai oaeo yoio n i?ioeai?a/eyie e ia?aaeienaie ia naycai.

Eioe i?aiaeieae e aoi?oth ia?aie/eoaeueioth oaiaeaioeeth a i?eiyoie aei
iaai o?aeoiaea iiiyoey i?aaeaea. Ii i?eciae, /oi ia?aiaiiay iiaeao
i?eaeeaeaoueny e naiaio i?aaeaeo ia oieueei iiiioiiii, ii e eieaaeynue,
ii?ie i?eieiay cia/aiey, ?aaiua a? i?aaeaeo. Yoi ianoiyoaeuenoai
i?eaeaei oai?ee Eioe iaiaoiaeeioth iauiinoue e eneeth/eoaeueioth
aeaeinoue. Iu aei neo ii? neaaeoai iooe, iaia/aiiiio Iathnoaiii Eoe
Eioe, n oaie oniaa?oainoaiaaieyie, eioi?ua auee aianaiu ai aoi?ie
iieiaeia XIX aaea E. Aaea?oo?annii.

?aaiou Eioe e Aaea?oo?anna caaa?oeee nicaeaiea eeanne/aneiai
iaoaiaoe/aneiai aiaeeca, Oai naiui iiaeaaaey eoia iiiaiaaeiaiai ?acaeoey
eioaa?aeueiiai en/eneaiey.

Eeoa?aoo?a

Aieueoaeiaa A. A. O?e e?ecena a ?acaeoee iaoaiaoeee. Aeeieiiiay ?aaioa;
Ano?aoaiue: AAIE, 1996.

Aeaoneay yioeeeeiiaaeey aeey n?aaeiaai e noa?oaai aic?anoa. O.2; I.:
I?inaauaiea, 1965.

Iaoaiaoe/aneay yioeeeeiiaaeey. ?aae. Aeiia?aaeiaa. O.2; I.: Nia.
Yioeeeeiiaaeey, 1979.

Oeooaiaieueoe A.I. Iniiau iaoaiaoe/aneiai aiaeeca. O.1; I.: Iaoea, 1968.

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