1. Ieaie?iaaiea o?aaeoi?ee.
1.1 Iainiiaaiea iaiaoiaeeiinoe aaoiiaoe/aneiai
ieaie?iaaiey e ioneaaeeaaiey o?aaeoi?ee.
Iaeaieaa aaaeiui iai?aaeaieai aaoiiaoecaoeee ?aaiou ea?uea?iiai
o?ainii?oa yaeyaony aaoiiaoecaoeey aeaeaeaiey naiinaaeia a ianoao
?aca?ocee. A nayce n oai, /oi a eiioo?a oi?aaeaiey i?enoonoaoao /aeiaae,
ionoonoaoao aa?aioey a neaaeothueo aniaeoao:
auai? iioeiaeueiie o?aaeoi?ee;
oi/iinoue inoaiiaee a oi/ea ?aca?ocee (ioeaea iiaeao i?eaanoe e aaa?ee);
ianiaeaniaaiiinoue iai?a?ia naiinaaeia a ciia ?aca?ocee;
Aeey ono?aiaiey oeacaiiuo i?iaeai o?aaoaony aaoiiaoece?iaaoue iino?iaiea
o?aaeoi?ee. Aaoiiaoecaoeey iino?iaiey o?aaeoi?ee e neaaeiaaiey ii iae
oneiaeiyaony neaaeothueie oaeoi?aie:
neiaeiinoue e ia iinoiyinoai ieiuaaeee;
neo/aeiue oa?aeoa? o?aaeoi?ee;
iaiaoiaeeiinoue o/eouaaoue aeeiaie/aneea e aaiiao?e/aneea iniaaiiinoe
naiinaaea;
ionoonoaea ia ianoiinoe oa?aeoa?iuo oi/ae e i?eaioe?ia;
iaaiciiaeiinoue i?aaeaa?eoaeueiiai oeacaiey o?aaeoi?ee ia ianoiinoe ec –
ca oyae?euo oneiaee ?aaiou ecaanoiuo n?aaenoa, oeacuaathueo o?aaeoi?ee
(aieueoea iannu naiinaaeia, ?aaioa aoeueaeica?a, ieioea iiaiaeiua
oneiaey e ae?.).
Aeey oaea/iie ?aaiou NAA iaiaoiaeeii e?iia nicaeaiey iioeiaeueiie
o?aaeoi?ee au? e ioneaaeeaaoue i?aaeeueiinoue aeaeaeaiey ii iae, a
oaeaea iia?aoeaii aiineoue a ia? eciaiaiey ii ia?a iaeiieaiey aeaiiuo i
ianoiinoe e eciaiaiey ?aniieiaeaiey i?aiyonoaee. A nayce n yoei a
?ac?aaaouaaaiie NAA aaaaeaiu iiaenenoaiu i?eaioaoeee e i?ia?aiiiia
ii?aaeaeaiea eii?aeeiao e i?eaioaoeee naiinaaea ii n/eneaieth.
Eniieueciaaiea aeaoo iacaaeneiuo enoi/ieeia eioi?iaoeee ia i?eaioaoeee
naiinaaea iicaieyao iiauneoue iaae?aeiinoue NAA e iia?aoeaiinoue
i?aaeinoaaeaiey aeaiiuo i?ia?aiiai e nenoaiai, eioi?ua a oaeeo aeaiiuo
ioaeaeathony. Aaoiiaoe/aneia ioneaaeeaaiea i?ioiaeaeaiey ii
caieaie?iaaiiie o?aaeoi?ee iicaieeo aia?aiy ia?aeeth/eoue ?aaeeiu
ieaie?iaaiey o?aaeoi?ee e i?ioiaeaeaiey ii iae.
O?aaiaaiey e o?aaeoi?ee e
e aeai?eoio auai?a o?aaeoi?ee.
Noi?ie?iaaiiay i?ia?aiiii o?aaeoi?ey aeieaeia oaeiaeaoai?youe
neaaeothuei o?aaiaaieyi:
Aeieaeia o/eouaaoue aaiiao?e/aneea e oaoiieiae/aneea iniaaiiinoe
o?ainii?oiiai n?aaenoaa aeey eioi?iai ieaie?oaony o?aaeoi?ey. I?e
?an/?oa iiai?ioa aeieaeai auoue o/o?i oaoiieiae/aneee ?aaeeon
(ieieiaeueiue ?aaeeon iiai?ioa ON), nei?inoue ON, eiyooeoeeaio
noeaieaiey e ae?oaea aiaoiea e aioo?aiiea oaeoi?u, aeeythuea ia
aeeiaieeo ON.
Aeieaeia i?ioiaeeoue ia ?annoiyiee io i?aiyonoaee, aeinoaoi/iii aeey
ii?iaeueiiai aaciianiiai i?iacaea.
Aeieaeia auoue eae iiaeii ei?i/a e niaea?aeaoue ieieioi iiai?ioia.
Iiai?iou aeieaeiu auoue oaeeie, /oi au naiinaae ia ieo ia caiineei,
cia/eo ii ia?a eciaiaiey nei?inoe a? aeae iiaeao iaiyoueny.
I?e aeaeaeaiee caaeiei oiaeii iia aeieaeia eaaei caaeaaaoueny , oi/ii e
eaaei ioneaaeeaaoueny.
A niioaaonoaee n oeacaiiuie o?aaiaaieyie aeai?eoi aeieaeai
oaeiaeaoai?youe neaaeothuei o?aaiaaieyi:
iaeneiaeueiia auno?iaeaenoaea;
iaaieueoay iio?aaiinoue a i?ioeanni?iii a?aiaie;
aeieaeai oiaoue aini?iecaiaeeoue i?yiua i?inoaeoea e?eaua ii eioi?ui
iiaeao aeaeaaoueny naiinaae;
aeieaeai o/eouaaoue iniaaiiinoe ieaie?iaaiey aeaeaeaiey caaeiei oiaeii.
A nayce n yoei i?eiaieiu aeai?eoiu ieaie?iaaiey o?aaeoi?ee ii ea?oa
ianoiinoe.
Aaiiao?e/aneea iniaaiiinoe ?aaeecaoeee aeai?eoiia.
Aeey aeaiiino?aoeee oeacaiiuo iniaaiiinoae, iaian?i ia ieeeeiao?iaoth
aoiaao ai?eciioaeueioth i?iaeoeeth naiinaaea. Aeey iaeaieaa oaeiaiie
aii?ieneiaoeee ?aaeueiie i?iaeoeee aaoiiiaeey auaa?ai ioiioaiea aeeeiu
i?iaeoeee e a? oe?eia ?aaiui 9:5. (?en. 2.1) Aeey auyaeaiey e?eoa?ey
aiciiaeiinoe i?iacaea iiae oaeii 450 ?aniieiaeei i?iaeoeeth
aaoinaiinaaea iiae oaeii 450 e iiiaoei caiyoua ath eaaae?aou ni noi?iiie
a iaeio aeene?aoo. Iia??iooue oaeei ia?acii naiinaae caieiaao ieiuaaeue
11 o 11 aeene?ao. I?e ethaie ae?oaie i?eaioaoeee naiinaae caei?o
i?yiioaieueiee caaaaeiii iaiueoae ieiuaaee e iaeneiaeueiie aeeeiu,
neaaeiaaoaeueii anee oeaio? naiinaaea iiaeii ?aniieiaeeoue a eaaae?aoa
11 o 11 aeene?ao oae, /oiau a i?i ia auei i?aiyonoaee, cia/eo o?aaeoi?ey
iiaeao i?ioiaeeoue /a?ac aeaiioth oi/eo. A oeaeyo iiauoaiey
auno?iaeaenoaey aeaeaoaeueii i?iecaanoe iiene e oeacaiea oaeeo oi/ae aei
ia/aea iienea o?aaeoi?ee /oiau ecaaaeaoue iiaoi?iuo iieneia i?aiyonoaee
a eaaae?aoa.
Aeey ii?aaeae?iiinoe ia ea?oa aoaeoo ii?aaeaeyoueny eeoue
aaiiao?e/aneea ianoa oeaio?ia aaoiiiaeey.
I?e ?anniio?aiee e?eoa?eaa ?ac?aoaiey iiai?ioa, iaian?i ia ea?oo
iieiaeaiea naiinaaea aei e iinea iiai?ioa, e i?iaaaeai ie?oaeiinoe oaeei
ia?acii, /oiau ioaaoeoue ana i?iiaaeooi/iua iieiaeaiey e?aeieo oi/ae
aaoinaiinaaea. Niaaeeiea ia/aeueioth e eiia/ioth oi/ee iiai?ioa
iineaaeiaaoaeueiinoueth eeaoie – aeene?ao ia ea?oa iaeaieaa aeeceeo e
iieo/aiiie aeoaa iiaeii oaeaeaoue, /oi aeeeia i?yiiai o/anoea ia ea?oa,
ia?aeeaeueiiai inyi aeieaeia auoue ia iaiaa iaeiie aeene?aou, a aeeia
iaeeiiiiai o/anoea – ia iaiaa o??o.
Neaaeiaaoaeueii noieo i?aaeienaoue aeai?eoiai, /oiau oi/ea eceiia
o?aaeoi?ee iaoiaeeeanue ia a ?aaeueiii ia/aea iiai?ioa, a auea niauaia
iacaae ia oeacaiiia auoa eiee/anoai aeene?ao a caaeneiinoe io
iai?aaeaiey. Neaaeoao oaeaea cai?aoeoue eceii o?aaeoi?ee a neo/aa
aeeaaiiaeueiiai aeaeaeaiey iaiaa /ai a naie aeene?aoao io i?aaeuaeouaai
eceiia e o??o aeene?aoao i?e aeaeaeaiee aaeieue inae.
2.4 E?aoeee iaci? eiathueony aeai?eoiia
ieaie?iaaiey o?aaeoi?ee e eo n?aaieoaeueiay oa?aeoa?enoeea.
2.4.1 Iaoiae i?iaiuo o?aaeoi?ee.
Iaoiae caeeth/aaony a oii, /oi i?ia?aiia ioo?i i?inoiai ia?aai?a
o?aaeoi?ee iuoaaony iaeoe eo/ooth. Ai a?aiy iienea iiaeii aaanoe
aeiiieieoaeueiua e?eoa?ee, iicaieythuea ioa?anuaaoue caaaaeiii ooaeoea
o?aaeoi?ee, e oai naiui yeiiiieoue a?aiy. I?ia?aiiii o?aaeoi?ey
i?aaenoaaeyaony a aeaea aeeiaie/aneiai nienea – noaea. I?e aeaeaeaiee
aia??ae ia iaeei oaa a noae aeiaaaeyaony eioi?iaoeey i oiaea e i caiyoie
iiceoeee. Anee anoue iaiaoiaeeiinoue aa?iooueny iacaae ia ianeieueei
iieae, oi niioaaonoaothuaa eiee/anoai iieae ecaeaeaaony ec noaea a
ii?yaeea «ia?aue aio?e – iineaaeiee auoae».
Anee a aeaiiii aa?eaioa i?ia?aiia oaeaeinue aeia?aoueny aei oeaee, oi
iaeaeaiiue ia?o?oo n?aaieaaaony n iaeaeaiiui ?aiaa (anee ii anoue) e ec
aeaoo nio?aiyaony eo/oee ia?o?oo e aai ia?aiao?u. Yoi iicaieyao
ioa?anuaaoue i?iiaaeooi/iua aa?eaiou anee iie iaauatho auoue ooaeoeie,
/ai oaea eiathueeny. Iinea eaaeaeiai oiaea i?ia?aiia i?iniao?eaaao
o?aaeoi?eth iacaae, /oi iicaieyao ecaaaeaoue eeoieo iiai?ioia.
Aeey oaeianoaa ?aaiou i?ia?aiiu i?aaeiieaaaaony, /oi aiciiaeii oieueei
ainaiue iai?aaeaiee ia?aiauaiey n oaaii 450 . I?ia?aiia o?aieo
o??oia?iue iannea ioeaiie a eioi?ue aiineo eioi?iaoeeth i oaeouae
ioeaiea oiaea /a?ac aeaiioth iiceoeeth a caaeaiiii iai?aaeaiee. Anee
iiaay ioeaiea aieueoa eee ?aaia eiathuaeny a y/aeea ianneaa, oi
iineaaeiee oiae ioa?anuaaaony e aeaeaaony iiiuoea oiaea a ethaii ae?oaii
aeiionoeiii iai?aaeaiee.
Anee ec oaeouae iiceoeee iao aa?eaioia oiaea, oi aeaeaaony oiae iacaae.
Anee iiaay ioeaiea iaiueoa noa?ie, oi ia cia/aiea a y/aeea ianneaa
aoaeao ia ia? caiaiaii. Oaeei ia?acii a oeacaiiii ianneaa o?aieony
eioi?iaoeey i eo/oeo aa?eaioao aeaeaeaiey. Yoi iicaieyao eniieueciaaoue
a? i?e neaaeothueo oeeeeao ieaie?iaaiey o?aaeoi?ee, anee ia i?iecioei
cia/eoaeueiuo eciaiaiee ia ianoiinoe (iai?eia? i?e eciaiaiee iiceoeee
naiinaaea). Neaaeoao ia?aoeoue aieiaiea ia oi, /oi a aeaiiii aeai?eoia
aa?eaio o?aaeoi?ee eae aaeeiia oeaeia ia?ae/ai, a iannea ioeaiie –
aoi?e/ai.
Au? iaeiei i?e?iii, oeo/oathuei aeai?eoi yaeyaony ooieoeey oeaee (io
eii?aeeiao iiceoeee e iai?aaeaiey). A? cia/aiea oai iaiueoa, /ai aeeaea
noaiao ON, ia?aianoeaoenue n caaeaiiie iiceoeee a caaeaiiii iai?aaeaiee.
I?e ?anniio?aiee iai?aaeaiey ia?aae?athony a ii?yaeea aic?anoaiey
ooieoeee oeaee.
Iieo/aiiay ii aeai?eoio o?aaeoi?ey aoaeao i?eieoeaia e iiyoiio aoaeao
ioaeaeaoueny a naeaaeeaaiee.
Aeaaiui iaaeinoaoeii aeaiiiai aeai?eoia yaeyaony ieceia auno?iaeaenoaea.
2.4.2 Iaeiineieiay iae?iiiay naoue.
Aeai?eoi caeeth/aaony a oii, /oi aeey eaaeaeiai ec aiciiaeiuo
(oaoie/anee) iai?aaeaiee ninoaaeythony ioeaiee, a eioi?uo o/eouaaaony:
?annoiyiea aei aeeaeaeoaai caia/aiiiai i?aiyonoaey a aeaiiii iai?aaeaiee
(/ai aeaeueoa i?aiyonoaea – oai auoa ioeaiea).
Nea/ie ?annoiyiee (neooaoeey, eiaaea i?inaao iaaeaeo i?aiyonoaeyie a
aeaiiii iai?aaeaiee ia iaia?oaeai, ii i?e ia?aoiaea io iaeiie oi/ee
i?aiyonoaey e ninaaeiae iaia?oaeai cia/eoaeueiue ia?aiaae ?annoiyiee aei
i?aiyonoaey): /ai aieueoa nea/ie – oai aieueoa ioeaiea.
Iaee/ea i?aiyonoaey ?yaeii (anee iaia?oaeaii i?aiyonoaea ?yaeii n
aaoiiiaeeai, oi aaiaeeony oaeay io?eoeaoaeueiay ioeaiea, /oi iacaaeneii
io inoaeueiuo ioeaiie yoi iai?aaeaiea aeaeaeaiey aeieaeii auoue
eneeth/aii).
Iai?aaeaiea ia oeaeue (/ai aeeaea eo/, i?iaaae?iiue ec oaeouae oi/ee
?aniieiaeaiey aaoiiiaeey i?ieaeao ieiei oi/ee oeaee, oai aieueoa
ioeaiea).
I?aaeuaeouaa iai?aaeaiea aeaeaeaiey (iaeaieueooth ioeaieo aoaeao eiaoue
i?aaeuaeouaa iai?aaeaiea aeaeaeaiey, aeey inoaeueiuo iai?aaeaiee – /ai
aeaeueoa io i?aaeuaeouaai iai?aaeaiey – oai ieaea ioeaiea).
Iieo/aiiua ioeaiee oiiiaeathony ia niioaaonoaothuea eo ?iaeo aaniaua
eiyooeoeeaiou e iieo/aiiua cia/aiey noiie?othony. Auae?aaony oaeia
iai?aaeaiea aeaeaeaiey, aeey eioi?iai iieo/aiiay noiia aoaeao
iaeneiaeueiie. Aa?uee?oy aaniaua eiyooeoeeaiou iu iiaeai iieo/eoue
?aciua aa?eaiou o?aaeoi?ee aeey iaeiie e oie aea ea?ou.
Yoio aeai?eoi i?ino i?e i?ia?aiiiie ?aaeecaoeee, ii eiaao neaaeothuea
iaaeinoaoee: i?eieoeaiay o?aaeoi?ey, iaaiciiaeii ieaie?iaaiea n?aco anae
o?aaeoi?ee eee oioy au n?aaieoaeueii aieueoie a? /anoe a nayce n
ionoonoaeai caiiieiaiey aeaeueiaeoeo aa?eaioia aeaeaeaiey, ia iicaieyao
o/anoue iaee/ea o/anoea aeaeaeaiey caaeiei oiaeii, aieueoie iau?i
au/eneaiee n eniieueciaaieai /enae n ieaaathuae caiyoie, iaaiciiaeiinoue
iiaeia?aoue aaniaua eiyooeoeeaiou oae, /oi au ia ethaie ea?oa (eee ec
ethaie oi/ee ea?ou) auea iaeaeaia iioeiaeueiay o?aaeoi?ey.
I?aaeeaaaaiue aeai?eoi.
Iniiaiuie iauaeoaie ia?aaioee aeey yoiai aeai?eoia yaeythony ea?oa e
iannea ioeaiie (ni. aeai?eoi i?iaiuo o?aaeoi?ee), eioi?ue yaeyaony
ia?ae/iui, a ii iaio aoaeao iino?iaia iioeiaeueiay o?aaeoi?ey. Aeaaiie
caaea/ae i?aaeeaaaaiiai aeai?eoia auno?i e i?aaeeueii caiieieoue iannea
ioeaiie. Eae e a aeai?eoia i?iaiuo o?aaeoi?ee (i. 2.3.1) iannea ioeaiie
yaeyaony o??oia?iui. Caiieiaiea aaae?ony ioo?i iienea ii?aaeae?iiuo
y/aae ianneaa e caienueth a ieo ioeaiee, niioaaonoaothuae ioeaiea oiaea
ia i?aaeuaeouoth y/aeeo i/a?aaeiiio oiaeo. Iineieueeo iannea ioeaiie
i/aiue aaeee e o/eouaay iaaeeaiiue aeinooi e yeaiaioai yoiai
(o??oia?iiai) ianneaa aeaaiie caaea/ae i?ia?aiiu yaeyaony onei?aiea
iienea eeaoie ec eioi?uo iiaeii naeaeaoue i/a?aaeiua oiaeu. Aeaiiay
caaea/a oniaoii ?aoaaony n iiiiuueth noaeiiiaeiaiuo no?oeoo? aeaiiuo. A
oeaeyo iiauoaiea auno?iaeaenoaey i?ia?aiia, ?aaeecothuay oiiiyiooue
aeai?eoi ?aaeeciaaia ia Annaiaea?a [2].
N?aaieoaeueiay oa?aeoa?enoeea
i?eaaae?iiuo aeai?eoiia.
N?aaieoaeueiay oa?aeoa?enoeea i?eaaae?iiuo aeai?eoiia i?eaaaeaia a
oaaeeoea 2.1
Oaaeeoea 2.1 N?aaiaiea aeai?eoiia ieaie?iaaiey o?aaeoi?ee.
E?eoa?ee Iaeiaiiaaiea aeai?eoia
Iae?iiiay naoue I?iaiuo o?aaeoi?ee I?aaeeaaaaiue aeai?eoi
1 2 3 4
O?aaiaaiey e iaiyoe 6*n2 /enae n ieaaathuae caiyoie
18*Xmax *Ymax aaeo
?aaeeco-aiinoue ia ycuea ieceiai o?iaiy
Iaoaeiaii
Oaeiaii
Ea/anoai iieo/aiiie o?aaeoi?ee Ia aa?aioe?oaony Aa?aioe?oaony
A?aiy ?aaiou Caaeneo io 6*n2 Iaii?aaeae?iii Iaaieueoia, /ai aeeaea e
eiioeo – oai auno?aa
Iieiioa eniieueciaaiey eioi?iaoeee Eniieuecoao oieueei aeaeeiue a
aeaiiue iiiaio o/anoie iiey
Iieo/aiiay eioi?iaoeey eniieuecoaony iieiinoueth
Neiaeiinoue aaeaioaoeee Ia o?aaoaony Aeey aaeaioaoeee o?aaoaony caiaia
ea?ou a iaiyoe YAI.
Aeeyiea oi?iu ciiu iniio?a Ii?iaeueii i?eiaiei oieueei i?e iaci?a ia
3600
Ia aeeyao
Io /aai caaeneo aeene?aoa Io eiee/anoaa iai?aaeaiee n Io o?aaoaiuo
oi/iinoe, auno?iaeaenoaey, ea/anoaa o?aaeoi?ee
O/?o o/anoea aeaeaeaiey caaeiei oiaeii
Iaaiciiaeai
Eaaei auiieiyaony.
Aeaeueiaeoay iioeiecaoeey Ia o?aaoaony O?aaoaony «n?acaiea» oaeia
A nayce n yoei aue ?ac?aaioai aeai?eoi ieaie?iaaiey o?aaeoi?ee,
iicaieythuee auno?i niaaeeieoue aeaa oi/ee iiaa?oiinoe e?ao/aeoae
eeieae, i?iaaae?iiie n o/?oii eaaei aaiaeeiuo e eaaei ?aaeecoaiuo
e?eoa?eaa iioeiaeueiinoe. E?iia oiai ?ac?aaioaiiue aeai?eoi eaaei
iicaieyao o/anoue aaiiao?e/aneea iniaaiiinoe o?ainii?oiiai n?aaenoaa e
eaaei e iei aaeaioe?oaony.
3 Iienaiea i?aaeeaaaaiiai aeai?eoia
aaoiiaoe/aneiai iino?iaiey o?aaeoi?ee
e iaaeaaoeee ii n/eneaieth.
3.1 I?aaeaa?eoaeueiia ieaie?iaaiea o?aaeoi?ee.
A ?ac?aaioaiiii aeai?eoia no?ieony ea?oa ianoiinoe a aeene?aoao
1,25o1,25 i (naycaii n aaeaeaaoiui ioia?aaeaieai naiinaaea ia ea?oa),
n/eoaaony, /oi naiinaae caieiaao ia ea?oa ieiuaaeue 5o9 aeene?ao.
O?aaeoi?ey, iieo/aaiay ii aeai?eoio yaeyaony o?aaeoi?eae oeaio?a
naiinaaea. Aiciiaeiinoue ia?aiauaiey oeaio?a naiinaaea ia iiaoth
iiceoeeth ii?aaeaeyaony aiciiaeiinoueth iiceoeeiie?iaaiey oeaio?a
naiinaaea a aeaiiie oi/ea, i?e yoii o/eouaaaony ethaay aiciiaeiay
i?eaioaoeey naiinaaea.
Aeey onei?aiey ieaie?iaaiey i?aaeiieaaaaony, /oi naiinaae iiaeao
iiai?a/eaaoue ia oaie 450 . o. a. Iu iieo/aai ainaiue aiciiaeiuo
iai?aaeaiee ia?aiauaiey naiinaaea. O?aaeoi?ey no?ieony ii neaaeothuei
e?eoa?eyi: ieieiaeueiay aeeeia, ieieiaeueiia eiee/anoai iia?ioia.
Aeai?eoi caeeth/aaony a neaaeothuai:
1) ninoaaeyaony iannea 8 o a x b, aaea a e b – noi?iiu i?yiioaieueieea,
a eioi?ue aienuaaaony ea?oa.
2) ia?aae ia/aeii iienea yoio iannea caiieiyaony ioeyie;
3) ii?aaeaeyaony oi/ea eiioea o?aaeoi?ee;
4) n/?o/ee ?annoiyiey e eneaoaeue onoaiaaeeaaaony ia iieue;
ec iaeaeaiiie oi/ee aeaeaaony oaa a ethaii aiciiaeiii iai?aaeaiee;
anee oaa ia?aeeaeueii inyi eii?aeeiao – e n/?o/eeo ?annoiyiey
i?eaaaeyaony 10, eia/a – 14;
7) cia/aiea n/?o/eea caienuaaaony a y/aeeo N x X x Y, aaea N –
iai?aaeaiea; X, Y – eii?aeeiaou oaeouae iiceoeee;
eneaoaeue oaaee/eaaaony ia 1;
i?ienoiaeeo iiene y/aae ni cia/aieai ?aaiui eneaoaeth;
anee oaeay y/aeea iaeaeaia (aeai?eoi a? iienea i?eaaae?i ia ieaeaoa
AeI.98.YIO.514.004), io ia? aeaeathony oiaeu ai anao aiciiaeiuo
iai?aaeaieyo, i?e yoii n/?o/eee ?annoiyiee niioaaonoaothuei ia?acii
iiaeeoeoee?othony e caienuaathony a iiaua y/aeee;
anee eneaoaeue aeinoea aoiaea oaaee/eaaai n/?o/ee aeinoeaeaiee ia 1,
eia/a ia?aoiae e ioieoo 8;
anee n/?o/ee aeinoeaeaiee ?aaai iaiaa aeaoo ia?aoiaeei e ioieoo 8;
ia?aoiue iiene ia?o?ooa: a oi/ea aoiaea iaoiaeei iai?aaeaiea, ioeaiea
?annoiyiey eioi?iai ieieiaeueia;
aeaeaai oiae iaano?a/o yoiio iai?aaeaieth;
anee aeinoeaee aoiaea – eiiaoe;
iouneeaaai iai?aaeaiea, ioeaiea ?annoiyiey a eioi?ii ieieiaeueia;
ia?aoiae e ioieoo 14.
I?eaaae?iiue aeai?eoi oaeaea ecia?aae?i ia ieaeaoa AeI.98.YIO.514.003.
?aaeueiue iiai?io naiinaaea ia ea?oa e a aeaea o?aaeoi?ee iiaeaee?oaony
o/anoeii eiiaiiie (i?eeiaeaiea 2), niaea?aeauei eceii ia (450 (a
caaeneiinoe io iai?aaeaiey) i?aaeiieaaaaony, /oi iiai?io ia/eiaaony
(caeai/eaaaony) ?aiueoa (iicaea) oi/ee eceiia aeey i?oiaiiaeueiiai
ia?aiauaiey ia iaeio aeene?aoo, a aeey iaeeiiiiai e inyi eii?aeeiao ia
o?e. Aeae iiai?ioa ia ea?oa i?eaaae?i ia ?en. 3.1. Eeethno?aoeey
iiaeai?a /enae, o/eouaathueo aaiiao?e/aneea ia?aiao?u i?eaaaeaia a
i?eeiaeaiee 2. A nayce n yoei aeeeia i?yiiai ai?eciioaeueiiai o/anoea
aeiioneaaony ia iaiaa o??o oaaia, a iaeeiiiiai – ia iaiaa naie oaaia.
I?eaeeceoaeueiue aeae ianneaa a eiioea o?aaeoi?ee ii ieii/aiee ?aaiou
aeai?eoia aoaeao eiaoue aeae, iieacaiiue ia ?enoiea 3.2 (o?aaeoi?ey
i?ioiaeeo /a?ac cae?aoaiiua eeaoee cae?aoaiiua eeaoee). A ?acoeueoaoa
?aaiou aeai?eoia aoaeao iieo/aia o?aaeoi?ey, i?aaenoaaeythuay niaie
iacaieioooth eiiaiioth, ninaaeiea caaiuey eioi?ie iaeeiiaiu ae?oa
ioiineoaeueii ae?oaa ia oaie (450 . A?aiy ?aaiou yoiai aeai?eoia ia
i?ioeanni?a PENTIUM S – 75 i?eaeeceoaeueii 0,2 n., anee o/anoue, /oi
aeey i?iacaea io ia/aea aei eiioea o?aaoaony caioneaoue aeai?eoi eeoue
iaeiaaeaeu, oi auno?iaeaenoaea aai iiaeii n/eoaoue aeinoaoi/iui.
Iienaiiue aeai?eoi i?eiaiei ia oieueei e naiinaaeo, ii e iinea
aaiiao?e/aneie aaeaioaoeee e ethaiio o?ainii?oiiio n?aaenoao, a
/anoiinoe ii iicaieeo aeaeaaoueny o?ainii?oiiio ?iaioo a
iaaeaoa?ieie?iaaiiie (ia ?acaeoie ia eaa?oaeu) n?aaea.
A nayce n oai, /oi iiene eiie?aoiiai /enea a o??oia?iii ianneaa,
niaea?aeauai aeanyoee ouny/ /enae neeoeii aeieia, aue i?eiai?i noaeiaue
iaoiae iaeiieaiey eii?aeeiao e iai?aaeaiee. Ii caeeth/aaony a
neaaeothuai. A iaeanoe aeaiiuo i?ia?aiiu auaeaeaii oanoiaaeoeaoue
iaeeiaeiauo iaeanoae aeey o?aiaiey aeaiiuo. Yoe iaeanoe iii/a??aeii
caiieiythony aeaiiuie i eii?aeeiaoao, iai?aaeaiee e aeeeia iineaaeiaai
?iaiiai o/anoea. I?e ia?aaioea iaeia ec oanoiaaeoeaoe iaeanoae neoaeeo
enoi/ieeii aeaiiuo, a inoaeueiua iaeaieeaatho eioi?iaoeeth i iiauo
aeinoeaioouo eeaoeao. Ii ieii/aiee ia?aaioee iaeiie iaeanoe i?ia?aiia
i?enooiaao e ecaea/aieth aeaiiuo ec neaaeothuae, a iaeanoue,
ia?aaioaiiay oieueei /oi eniieuecoaony aeey iaeiieaiey neaaeothuae
ii?oeee aeaiiuo. Aeey oi?iuaiey ianeoaeeaaiey iaeanoae eniieuecoaony
iannea aeane?eioi?ia, a eioi?ii o?aieony eioi?iaoeey ia aae?ana iaeanoe
e i aeoaeia a? caiieiaiey, a oaeaea aaaae?i niaoeeaeueiue oeaa, eioi?ue
onoaiaaeeaaaony i?e en/a?iaiee oaeouae iaeanoe noaea.
89
?en 3.2. I?eaeeceoaeueiue aeae ianneaa a eiioea o?aaeoi?ee ii ieii/aiee
?aaiou aeai?eoia.
3.2 Naeaaeeaaiea iiai?ioia.
Ii ieii/aiee ia?ae/iiai ieaie?iaaiey o?aaeoi?ee (i 3.1) iu aoaeai
eiaoue i?aaeaa?eoaeueioth o?aaeoi?eth, i?aaenoaaeythuoth niaie
eiiaiioth, eaaeaeia ec caaiueaa eioi?ie iia??iooi ia oaie (450
ioiineoaeueii i?aaeuaeouaai caaia. Aeaiiay o?aaeoi?ey eiaao ieceia
ea/anoai ii n?aaiaieth n aeinoeaeeiie, iiyoiio o?aaoaony i?iecaanoe
naeaaeeaaiea («n?acaiea oaeia»). Eiaiii yoi e aoaeao auiieiyony i?e
aoi?e/iii ieaie?iaaiee.
A oeaeyo yeiiiiee a?aiaie, aeai?eoi naeaaeeaaiey aoaeao caioneaoueny
aeey aeeaeaeoaai iiai?ioa (eae eneeth/aiea e aeey neaaeothuaai). I?e
naeaaeeaaiee i?ia?aiia aoaeao iuoaoueny i?iaanoe o?aaeoi?eth iaaeaeo
ethauie aeaoiy oi/eaie aei ia/aea aeeaeaeoaai iiai?ioa (aeai?eoi
eioa?iieyoeee i?yiie i?eaaae?i ia ieaeaoa AeI.98.YIO.514.005) e iinea
aai ieii/aiey. I?e yoii i?ia?aiia ia/i?o n ieieiaeueiiai naeaaeeaaiey
(iaeia oaea/iia naeaaeeaaiea aieaa aa?iyoii), a caoai iiiuoaaony
oaeeeieoue io?acie naeaaeeaaiey. I?e yoii io?acie naeaaeeaaiey aoaeao
i?iaiaeeony /a?ac eeaoee ia eioi?uo aiciiaeii iaoiaeaeaiea oeaio?a
naiinaaea e i?eaioaoeey naiinaaea a ethaii iai?aaeaiee. I?eia?u
naeaaeeaaiey i?eaaaeaiu ia ieaeaoa AeI.98.YIO.514.005.
A ?acoeueoaoa oaea/iiai naeaaeeaaiey (?en.3.3 – 3.5), aianoi iiai?ioia
ia (450 aicieeioo aeaa iiai?ioa ia oaie iaiaa 450 e io?acie
naeaaeeaaiey. A nayce n oai, /oi a i?ia?aiio, auiieiythuoth ia?aoth
noaaeeth ieaie?iaaiey ia caeiaeaiu iiai?iou ia yoe oaeu ((1 e (2),
aeai?eoi naeaaeeaaiey ii oi?ioeai aeieaeai aoaeao ii?aaeaeeoue oi/eo
ia/aea iiai?ioa (r1 e r2). Oeacaiiua ia ?en. 3.3 aaee/eiu iaeae?i ii
oi?ioeai 3.1 – 3.5.
(3.1);
(3.2);
(3.3);
r1=R*tg((1/2) (3.4);
r2=R*tg((2/2) (3.5).
A neo/aa iiai?ioa, ecia?aaeaiiiai ia ?enoiea 3.4, aaee/eiu, aai
ii?aaeaeythuea, ?ann/eoaai ii oi?ioea 3.6 e 3.7:
(3.6)
(3.7).
Eae a ia?aii, oae e ai aoi?ii neo/ayo eeiey l i?iaiaeeony oaeei ia?acii,
/oiau iia ia i?ioiaeeea /a?ac eeaoee, ia eioi?ua cai?au?i auacae
naiinaaea. A neo/aa aeey ?enoiea 3.6 ii oi?ioeai 3.8 e 3.9:
(3.8);
(3.9).
Aiciiaeia neooaoeey, eiaaea eiiaoe naeaaeeaaiey iiai?ioa niaiaaeaao n
ia/aeii naeaaeeaaiey neaaeothuaai iiai?ioa (?en 3.6). A yoii neo/aa oaie
((5) iaaeaeo io?aceaie naeaaeeaaiey l1 e l2 au/eneyaony ii oi?ioea 3.7,
a oi?aaeaeaiea iiai?ioa ii oi?ioea 3.4 (3.5), ii n (5 aianoi (2
A neo/aa, anee naeaaeeaaiea aeaiiiai iiai?ioa i?iecaanoe ia
-43-
oaeaeinue, oi ia/eiaoue iiai?io o?aaoaony ia iaeio aeene?aoo ?aiueoa
oi/ee eceiia ia ea?oa (i?e aei iiai?ioa aeaeaeaiee ia?aeeaeueii inyi
eii?aeeiao), e ia o?e aeene?aou ?aiueoa i?e aeaeaeaiee aei iiai?ioa iiae
oaeii e inyi. Oaeei ia?acii ria?? =1,875i (ie?oaeei aei 2 i), a
riiaeoaeii =4,375 i (ie?oaeei aei 4,5 i).
A nayce n oai, /oi ?aaeueiay i?eaioaoeey naiinaaea ia?aae naeaaeeaaieai
aoaeao ioee/aoueny io oeene?iaaiiie,
o?aaoaony ei??aeoe?iaaoue oaeu ia eioi?ua aeieaeai iiaa?iooue naiinaae e
?annoiyiey eioi?ua ii aeieaeai i?iaoaoue aei iiai?ioa, /oi au aueoe ia
iaeaeaiiue io?acie naeaaeeaaiey. Iaoiaeeea aaaaeaiey oaeie ei??aeoeee
iieacaia ia ieaeaoa AeI.98.YIO.514.004. A
i?eaaae?iiuo ieaea ?enoieao (3.7 a, a, a, a) e oi?ioeao aaaaeaiu
neaaeothuea iaicia/aiey: (’ – oaie iaaeaeo iai?aaeaieyie ieaie?oaiii aei
iiai?ioa o?aaeoi?ee e ?aaeueiie i?eaioaoeeae naiinaaea; ( – oaie iaaeaeo
iai?aaeaieai ieaie?oaiie o?aaeoi?ee e io?aceii naeaaeeaaiey;
( – oaie iaaeaeo ?aaeueiui iai?aaeaieai naiinaaea e io?aceii
naeaaeeaaiey; o – ?aaeueiia ?annoiyiea aei iiai?ioa; k – eiee/anoai
aeene?ao aei eceiia; d – -aeeeia iaeiie aeene?aou. Iaoiaeeea auai?a
oi?ioeu aeey ?an/?oa aeaiiuo ei??aeoeee i?eaaaeaia a oaaeeoea 3.1.
Oaaeeoea 3.1. Auai? ?an/?oiuo oi?ioe aeey iieo/aiey aeaiiuo ei??aeoeee
Iiia?
?enoiea Oi?ioea aeey au/eneaiey ( Oi?ioea aeey au/eneaiey o
3.8 a (=(-(’ o=kd*sin(()/sin(()
3.8 a (=(+(’ o=kd*sin(()/sin(()
3.8 a (=(-(’ o=1.41*kd*sin((+45)/sin(()
3.8 a (=(-(’ o=1.41*kd*sin((-45)/sin(()
Ieaie?iaaiea o?aaeoi?ee a ciia ?acai?ioa
e ieiei oi/ee ?aca?ocee.
E ianoo ?aca?ocee naiinaae aeieaeai iiaeuacaeaoue caaeiei oiaeii,
iaeiaei iaeneioi ?annoiyiey a ianoao ?aca?ocee ii i?iacaeaao ia?aaeiei
oiaeii neaaeiaaoaeueii, nenoaia aaoiaiaeaeaiey naiinaaea o?aaoaony
ii?aaeaeeoue eii?aeeiaou oi/ee niaiu iai?aaeaiey aeaeaeaiey e oi/ae
nii?yaeaiey ?aciuo o/anoeia o?aaeoi?ee, e?iia oiai nenoaia
aaoiaiaeaeaiey aeieaeia ca?aiaa ?aniieaaaoue /anoe o?aaeoi?ee ia
ianoiinoe, /oiau i?aaeoniio?aoue e ecaaaeaoue iaacaeu ia i?aiyonoaey e
auacaeu a ciiu, ia ii?aaeaeyaiua eae i?aiyonoaey.
Ieaie?iaaiea niaiu iai?aaeaiey a ianoao ?aca?ocee naiinaaea eiaao
neaaeothuea o?oaeiinoe:
aa?iyoiinoiue oa?aeoa? eii?aeeiao e iai?aaeaiey iineaaeiaai
i?yiiai o/anoea aeaeaeaiey ia?aaeiei oiaeii;
aunieea o?aaiaaiey (a nayce n iaiaoiaeeiinoueth iiauneoue aaciianiinoue)
e oi/iinoe o?aaeoi?ee aeaeaeaiey caaeiei oiaeii e aunieea o?aaiaaiey e
oi/iinoe ii?aaeaeaiey eii?aeeiao eiioea o/anoea aeaeaeaiey caaeiei
oiaeii
iaiaoiaeeiinoue ieieiecaoeee noiia?iie aeeeiu io?acea aei niaiu
ia?aaeiaai oiaea ia caaeiee e aeeeiu io?acea aeaeaeaiey caaeiei oiaeii;
ia?aie/aiey ia i?aaeaeueioth aeeeio io?acea aeaeaeaiey caaeiei oiaeii;
A nayce n oneiaeyie, i?eaaae?iiuie auoa oi/ea niaiu iai?aaeaiey
aeieaeia auae?aoueny ii neaaeothuei e?eoa?eyi:
O/anoie aeaeaeaiey caaeiei oiaeii aeieaeai auoue e?ao/aeoei.
Aeaeaeaieth aei e iinea ?aaa?na ia aeieaeiu iaoaoue i?aiyonoaey.
3) Oi/ea niaiu iai?aaeaiey aeieaeia auoue eae iiaeii aeeaea e ianoo
?aca?ocee.
4) Aaoiiiaeeue ia aeieaeai iieeaeaoue i?aaeaeu ?aai/ae ieiuaaeee.
N o/aoii auoa neacaiiiai iiaeii naeaeaoue auaiae, /oi aaiiao?e/aneei
ianoii oi/ae (oeaio?ia naiinaaea) niaiu iai?aaeaiey aeaeaeaiey i?e
iiaeuacaea e aeaiiiio ianoo ?aca?ocee aeieaeia auoue oaeay e?eaay,
eioi?ay au eiaea oaie iaeeiia a oi/ea iaeneiaeueii oaeae?iiie io oi/ee
?aca?ocee ?aaiue 0, a a oi/ea, aeeaeaeoae e oi/ea ?aca?ocee – 900
.Oaeeie naienoaaie iaeaaeaao i?inoaeoay aeey aiaeeca e?eaay – naaiaio
yeeeina, ?aniieiaeaiiue iaaeaeo aeaoiy aai iieoinyie e i?eaioe?iaaiiue
oae, /oi au iaeia aai iieoinue ieai/eaaeanue ia ?annoiyiee aieueoai eee
?aaiui iieiaeia oe?eiu naiinaaea io i?ioeaiiieiaeiie noi?iiu ieiuaaeee
?aca?ocee e eanaoaeueiay, i?iaaaeaiiay e oi/ea yeeeina, ?aniieiaeaiiie
ia ?annoiyiee io oi/ee ?aca?ocee aeinoaoi/iii aeey eni?aaeaiey
iaoi/iinoe i?eaioaoeee naiinaaea (ia?aie/eaaao iaeoth iieoinue), auea
ia?iaiaeeeoey?ia a?aieoea ?aai/ae ieiuaaeee a oi/ea ?aca?ocee. Neaaeoao
ioiaoeoue, /oi iinea niaiu iai?aaeaiey naiinaae iiaeao aeaeaaoueny ii
yoiio yeeeino eae ii ca?aiaa ii?aaeae?iiiio o/anoeo o?aaeoi?ee,
eniieuecoy ca?aiaa ?ann/eoaiiua ?aaeeiu ?aaiou aeaeaaoaeae e oi?iiciie
nenoaiu.
Ieaie?iaaiea o?aaeoi?ee ia/eiaaony n iino?iaiey yeeeina (o?aaiaiea eiaao
aeae (3.10)).
(3.10).
Aieueoay aai iieoinue (a) auae?aaony enoiaey ec oe?eiu ieiuaaeee aeey
iai?a?a, a iaeay (b) oaeei ia?acii, /oiau iaeiaiueoee ?aaeeon
e?eaeciu yeeeina aue ia iaiaa oaoiieiae/aneiai ?aaeeona. Yeeein yaeyaony
iii?iie e?eaie, e neoaeeo aeey ii?aaeaeaiey oi/ee ?acai?ioa.
Nii?yaathuay aeoaa yaeyaony /anoueth ie?oaeiinoe, eiathuae ?aaeeon
iacia/eoaeueii aieueoee oaoiieiae/aneiai e no?ieony oae, /oiau iia
eanaeanue yeeeina e i?yiiai io?acea, io eioi?iai e ia/eiaaony
ieaie?iaaiea o?aaeoi?ee ?acai?ioa e iiaeuacaea e oi/ea ?aca?ocee.
.
.
Oaeouee ?aaeeon yeeeina
.
iieo/ei:
.
Iii?iuie oi/eaie yoiai o/anoea o?aaeoi?ee yaeythony: oi/ea A n
eii?aeeiaoaie x1, y1; oi/ea I n eii?aeeiaoaie x2, y2 e oi/ea A n
eii?aeeiaoaie x3, y3.
/oi nouanoaaiii iaeaa/aao ?aoaiea o?aaiaiee, naycaiiuo n ii?aaeaeaieai
oi/ae ia?aoiaea i?yiie io?acie – aeoaa nii?yaeaiey e aeoaa nii?yaeaiey –
yeeein. ?aaeeon R aeoae nii?yaeaiey aeieaeai auoue iacia/eoaeueii
aieueoa oaoiieiae/aneiai /oiau eiiiaine?iaaoue iaaiciiaeiinoue
iaiiaaiiiai eciaiaiey ?aaeeona iiai?ioa naiinaaea.
I?e ?acai?ioa naiinaaea nenoaia i?eaioaoeee aeieaeia ?aaioaoue eae
neaaeyuay e eniieueciaaoue a ea/anoaa caaeathuaai ia?aiao?a oaie
?acai?ioa ia caaeiee oiae (?, eioi?ue aeey aeaiiie ?aca?oci/iie
ieiuaaeee anoue aaee/eia iinoiyiiay.
Iaiin?aaenoaaiii ia?aae o/anoeii niaiu iai?aaeaiey aeaeaeaiey naiinaae
aeieaeai aeaeaaoueny ii i?yiie. I?ia?aiia aeieaeia ca?aiaa au/eneeoue
oi/ee ia?aoiaea i?yiay – nii?yaathuay ie?oaeiinoue (A) e nii?yaathuay
ie?oaeiinoue – yeeein (A, oi/ea niaiu iai?aaeaiey), e ii aeinoeaeaiee
oeacaiiuo oi/ae (n o/?oii iia?aoiinoe) niioaaonoaothuei ia?acii iaiyoue
caaeathuea aicaeaenoaey.
Oi/ee nii?yaeaiey n oi/ee c?aiey aiaeeoe/aneie aaiiao?ee aeieaeiu auoue
iaeaeaiu ec oneiaee:
ie?oaeiinoue aeieaeia eiaoue n i?yiie iauoth oi/eo;
i?iecaiaeiua i?yiie e ie?oaeiinoe a yoie oi/ea aeieaeiu auoue ?aiu;
ie?oaeiinoue e yeeein aeieaeiu eiaoue iauoth oi/eo;
i?iecaiaeiua ie?oaeiinoe e yeeeina a yoie oi/ea aeieaeiu auoue ?aaiu.
?aaeeon (R) aeoae nii?yaeaiey aeieaeai auoue iacia/eoaeueii aieueoa
oaoiieiae/aneiai /oiau eiiiaine?iaaoue iaaiciiaeiinoue iaiiaaiiiai
eciaiaiey ?aaeeona iiai?ioa naiinaaea.
Aaiiao?e/aneea iniaaiiinoe ieaie?iaaiey ?acai?ioa e iiaeuacaea naiinaaea
e ianoo ?aca?ocee ecia?aaeaiu ia ?enoiea 3.8 e ia ieaeaoa
AeI.98.YIO.514.006.
I?eaaae?iiua ia ?enoiea 3.8 aaee/eiu iiaeii ii?aaeaeeoue ii oi?ioeai
3.11 -3.20:
(3.11);
(3.12);
A=(a+R)2+k*(b+R)2 (3.13);
B=2*A1*(a+R)2-2*k*A2*(b+R)2 (3.14);
C=(a+R)2*( A12-(b+R)2 )+ A2*(b+R)2 (3.15);
(3.16);
X2=X1-A1 (3.17);
Y2=k*X1-A2 (3.18);
(3.19);
) (3.20);
A oi?ioeao 3.13 – 3.22 aaaaeaiu i?iiaaeooi/iua aaee/eiu (A, A1, A2, A,
N), iaeaa/athuea i?ia?aiiioth ?aaeecaoeeth au/eneaiee.
?ac?aaioaiiue aeai?eoi aeieaeai caioneaoueny iaeiie?aoii i?e i?iacaea
naiinaaeii oi/ee n aanoeennie X=b+2*R. A oiaea au/eneaiee, eioi?ua
aeieaeiu i?iecaiaeeoueny a ii?yaeea iiia?ia oi?ioe, aoaeoo iieo/aiu
eii?aeeiaou oi/ae (X1, Y1) e (X3, Y3). Aeai?eoi iicaieyao ?aaeeciaaoue
aaoiiaoe/aneia ieaie?iaaiea o/anoea niaiu iai?aaeaiey aeaeaeaiey ia
ai?oiaie YAI nenoaiu aaoiaiaeaeaiey ea?uea?iiai naiinaaea.
Ioiineoaeueiay i?inoioa oi?ioe iicaieeo inouanoaeyoue au/eneaiey ca
ieieiaeueiia a?aiy.
Ieaie?iaaiea auacaea naiinaaea
ec ciiu ?aca?ocee.
Ieaie?iaaiea o?aaeoi?ee auacaea naiinaaea ec ciiu ?aca?ocee ioee/aaony
io ieaie?iaaiey iiaeuacaea e ianoo ?aca?ocee oieueei ionoonoaeai o/anoea
niaiu iai?aaeaiey aeaeaeaiey. Ieaie?iaaiea o?aaeoi?ee oaeaea aeieaeii
ninoiyoue ec ia?ae/iiai e aoi?e/iiai.
Neaaeoao ioiaoeoue, /oi o?aaeoi?ey aeaeaeaiey aeieaeia auoue i?eaeaoa e
noi?iia, i?ioeaiiieiaeiie io oie ia eioi?ie ?aniieiaeaiu ianoa ?aca?ocee
aeey oiai, /oiau ia iaoaoue iai?a?ai naiinaaeia, eioi?ui au? i?aaenoieo
?aca?oceoueny. Aeey aeai?eoia ia?ae/iiai ieaie?iaaiey (i 3.1) yoi
aueeaaaony eeoue ai aaaaeaiee aeiiieieoaeueiuo e?eoa?eaa ioeaiee.
Naeaaeeaaiea iiai?ioia (aoi?e/iia ieaie?iaaiea) aeieaeii auiieiyony ii
aiaeiae/iui (i. 3.2) oi?ioeai.
A nayce ni cia/eoaeueiui eciaiaieai iinea ?aca?ocee
aeeiaie/aneeo naienoa naiinaaea, aeaiiua aeey ?an/?oa caaeaiee ia
onei?aiea, oi?iiaeaiea e iiai?io aeieaeiu auoue ecia?aiu e ?ann/eoaiu
caiiai. I?ia?aiia ieaie?iaaiey o?aaeoi?ee aeieaeia auoue ia?aaeaia
eioi?iaoeey i caaeneiinoe oi?iiciiai iooe io nei?inoe e ?aaeeona
iiai?ioa io nei?inoe.
Eioi?iaoeey i auacaea ec ciiu iai?a?ia iiaeao auoue ia?aaeaia io AeYAI
eee ca?aiaa caeiaeaia a iaiyoue eae e ea?oa ianoiinoe.
Ii?aaeaeaiea oaeoueo eii?aeeiao e i?eaioaoeee naiinaaea.
A nayce n iaaiciiaeiinoueth oi/ii ecia?youe iaiiaaiiia iieiaeaiea
aaoiiiaeey, a oaeaea aunieie /oanoaeoaeueiinoueth e iiiaoai nenoaiu
?aaeeiiaaeaaoeee ea?uea?iiai naiinaaea, iaiaoiaeeii iaania/eoue
i?ia?aiiiia aeoaee?iaaiea ii?aaeaeaiey ia?aiao?ia aai iieiaeaiey ia
ianoiinoe (eii?aeeiaou e oaie iiai?ioa ioiineoaeueii iaiiaeaeaeiie
nenoaiu eii?aeeiao ?aai/ae ieiuaaeee). Oeacaiiua ia?aiao?u iniaaiii
aaaeiu ai a?aiy ieaie?iaaiey o?aaeoi?ee e auiieiaiey iiai?ioia, a oaeaea
i?e auaea/a eiiaiae ia niaio iai?aaeaiey aeaeaeaiey, i?e iaia?oaeaiee
auacaea naiinaaea a oi/eo n caaeaiiuie eii?aeeiaoaie i?e ieaie?iaaiee
iiaeuacaea e oi/ea ?aca?ocee.
Aeey oniaoiiai ooieoeeiie?iaaiey aeai?eoia o?aaoaony ii?aaeaeyoue
iaiiaaiiia cia/aiea ?aaeeona iiai?ioa. ?aaeueiue ?aaeeon iiai?ioa
iicaieytho ii?aaeaeeoue aeao/eee iiai?ioa eie?n ia caaeaiiue oaie,
?aaioathuea ia eaaeaeii eieana iacaaeneii ae?oa io ae?oaa. Anee iaaeaeo
eiioeuenaie aeao/eea, auaeaaaaiuie ei iinea iiai?ioa eieana ia
yeaiaioa?iue oaie, iaeaieeaaoue eiioeuenu aunieie /anoiou, oi ii i?inoui
oi?ioeai iiaeii ii?aaeaeeoue ?aaeeon iiai?ioa (oi?ioea (3.21)):
(3.21).
A oi?ioea: E1 – eiee/anoai eiioeuenia, i?eoaaeoeo iaaeaeo neaiaeaie io
aeao/eea iiai?ioa io caaeiaai eieana, aeeaeiaai e oeaio?o iiai?ioa, N –
oe?eia eieae, E2 – eiee/anoai eiioeuenia, i?eoaaeoeo iaaeaeo neaiaeaie
aeao/eea iiai?ioa io caaeiaai eieana, aeaeueiaai io oeaio?a iiai?ioa.
Auaa?ai /anoioo eiioeuenia io aeao/eea ii neaaeothuei niia?aaeaieyi.
Aeai?eoi ieaie?iaaiey o?aaeoi?ee aeieaeai caioneaoueny iinea i?iacaea
naiinaaeii iaeiie aeene?aou. Aeeeia iaeiie aeene?aou 1,25 i,
iaeaieueoay nei?inoue aeaeaeaiey naiinaaea 15 ei//, iieo/ei, a?aiy iinea
eioi?iai aeaiiua i iieiaeaiee naiinaaea aeieaeiu auoue aioiau:
t=1.25(i)/(15000(ei//)/3600(n//))=0.3 n. O/eouaay niaoeeoeeo a?oiiiaie
?aaiou aeao/eeia oiaiueoei a?aiy au? a 3 ?aca (caian a?aiaie ia ?an/?ou)
e iieo/ei t=0.1 n. Ii?aaeaeei, ia eaeie oaie (() iiaa?i?ony ca yoi a?aiy
eieani naiinaaea (e oaa oaeiaie naoee ia aeao/eea):
(=0,1(n)*4,167(i/n)/3(i)=0,1389 ?aae=7,950 , ie?oaeei iieo/aiiia
cia/aiea aei aeeaeaeoaai /enea ia eioi?ia 360 aeaeeony aac inoaoea e
iieo/ei 80 (iiein ia aeao/eea aeieaeii auoue 45). Anee i?eiaieoue
ioeueoeieeeaoi? eee iiauoathuoth oeaiioth ia?aaea/o, oi aaaa?eou
aeao/eea e eiee/anoai aeene?ao ia i?i oiaiueoeony a i (ia?aaeaoi/iia
ioiioaiea ia?aaea/e) ?ac.
Ia ?enoiea 3.9 i?eaaaeaiu aaee/eiu, eioi?ua ii?aaeaeythony ii
?ac?aaioaiiiio aeai?eoio: ( – oaie, ia eioi?ue iiaa?i?ony inue caaeieo
eie?n aaoiiiaeey; dS – ia?aiauaiea aaoiiiaeey ia yeaiaioa?iii o/anoea
iiai?ioa; R1 e R2 – ?aaeeonu ie?oaeiinoae, iienuaaaiuo caaeieie
eie?naie; ( – oaie iaeeiia aaeoi?a ia?aiauaiey e i?aaeuaeouae
i?eaioaoeee aaoiiiaeey (?aaai iieiaeia (). ?aaeeon iiai?ioa
oeaio?aeueiie oi/ee ine a?auaiey caaeieo eie?n naiinaaea iiaeii
ii?aaeaeeoue ii oi?ioea (3.22): R=R1+C/2 (3.22);
Ii?aaeaeaiea oaeouaai iieiaeaiey aaoiiiaeey (anee ecaanoii i?aaeuaeouaa)
auiieiyaony neaaeothuei ia?acii (ii?aaeaeaiea i?eaioaoeee ni. ?en
3.10.):
Iaoiaeei oaeu ( (oaie ia eioi?ue eciaieeanue i?eaioaoeey naiinaaea) e (
(oaie aaeoi?a yeaiaioa?iiai ia?aiauaiey a nenoaia eii?aeeiao, naycaiiie
n naiinaaeii).
(3.23),
, aaea b – aaca naiinaaea, ( – oaie iiai?ioa ia?aaeieo eie?n, iu
iiaeai au/eneeoue oaeouaa cia/aiea ( e niiinoaaeoue n einaaiii
ecia?yiiui.
(=(/2 (3.24);
Ii?aaeaeyai dS (aeeeia aaeoi?a yeaiaioa?iiai ia?aiauaiey):
dS=2*R*sin(() (3.25);
Ii?aaeaeyai eiyooeoeeaio noeaieaiey:
4) Ooi/iyai dS n o/?oii eiyooeoeeaioa noeaieaiey:
dS’=dS*e (3.27);
Ii?aaeaeyai i?e?auaiey eii?aeeiao a iaiiaeaeaeiie nenoaia:
dx=dS’*cos((+() (3.28);
Ii?aaeaeyai iiaoth i?eaioaoeeth aaoiiiaeey a iaiiaeaeaeiie nenoaia
eii?aeeiao:
(‘=(+( (3.30).
A oi?ioeao 3.28 – 3.30: (‘- i/a?aaeiie oaie i?eaioaoeee naiinaaea a
iaiiaeaeaeiie nenoaia eii?aeeiao; ( – i?aaeuaeouee oaie i?eaioaoeee
naiinaaea a iaiiaeaeaeiie nenoaia eii?aeeiao.
I?eaaae?iiua oi?ioeu aeinoaoi/ii neiaeiu aeey ?aaeecaoeee ia ycuea
i?ia?aiie?iaaiey ieceiai o?iaiy (aeaaea n i?eiaiaieai iaoaiaoe/aneiai
nii?ioeanni?a), iiyoiio aeaeaoaeueii aeaiiue aeai?eoi ?aaeeciaaoue ia
ycueao aunieiai o?iaiy.
Iaianaiea ia ei?oo eii?aeeiao naiinaaea e i?eaycea e iai?aaeaieth
i?iecaiaeeony neaaeothuei ia?acii:
ia ea?oa eae caieiaaiue a aeaiiue iiiaio a?aiaie oeacuaaaony oaeie
eaaae?ao ni noi?iiie a iaeio aeene?aoo, ia eioi?ii iaoiaeeony oeaio?
caaeiae ine naiinaaea
iiia? iai?aaeaiey i?eaioaoeee (n aeene?aoiinoueth 450) auae?aaony oaeie,
e eaeiio oaeouay i?eaioaoeey naiinaaea aeeaea.
Aeaiiua au/eneaiey iiaeii auiieieoue eeoue ii aioiaiinoe anao aeaiiuo
(E) io aeao/eeia, iiyoiio anoue niune iaeaieeaaoue eo a aooa?iie noaia
(niaoeeaeece?iaaiiii eiio?ieea?a, anoaaeyaiii a neiou ai?oiaie YAI), a
ii i?eoiaeo aeaiiuo io /aou??o eie?n iineaoue neaiae i?a?uaaiea a
au/eneeoaeueioth nenoaio. Ae?aeaa?o, ia?aaaouaathuaio cai?in iaiaoiaeeii
n/eoaoue aeaiiua ec yoie aooa?iie noaiu e ii iei i?iecaanoe au/eneaiey.
?acoeueoaou ii?aaeaeaiey iieiaeaiey ii n/eneaieth neaaeoao inoaaeyoue a
niaoeeaeueii auaeaeaiiie iaaei?ia?aiiiie iaeanoe nayce, eeai
inouanoaeyoue auaea/o iineaaeieo aioiauo aeaiiuo ii cai?ino i?ia?aii
/a?ac auciau i?ia?aiiiuo i?a?uaaiee.
?en. 3.1. I?eia?iue aeae iiai?ioa ia ea?oa.
e= (ie1 *R1/( R12+b2 *(ce1) (3.26);
dy=dS’*sin((+()= (dS’)2 -(dx)2 (3.29);
(i
(i+1
X
Y
X’
Y’
dS
?en.3.2 Ii?aaeaeaiea iiaie i?eaioaoeee naiinaaea
(
dS
?en. 3.1. Aaee/eiu, ii?aaeaeyaiua ii aeai?eoio.
N
R1
R2
(
(
1 – Naiinaaeu;
2 – a?aieoea ieiuaaeee;
3 – o?aaeoi?ey;
4 – nii?yaaaiay i?yiay o?aae-oi?ee;
5 – yeeein;
6 – i?yiay ia?aae ?aca?oceie;
7 – i?aiyonoaea.
I
A
A
?en. 2.8 Iai?a?u ia ieiuaaeea ?aca?ocee e eeethno?aoeey ?aaiou
aeai?eoiia ieaie?iaaiey o?aaeoi?ee.
7
Rmin
1
2
3
4
5
6
X
Y
X2,Y2
X1,Y1
X3,Y3
(
a
b
(’
X
(
(
1
2
3
a)
2
(’
1
3
(
(
a)
(
3
2
1
a)
450
(
(’
O
(
O
(’
450
(
3
2
1
a)
?en. 2.7. Ei??aeoeey eioi?iaoeee i i?aaenoiyuai iiai?ioa.
?en. 2.6. I?eia? ?4 naeaaeeaaiey iiai?ioa. 1 – o?aaeoi?ey aei
naeaaeeaaiey;
2 – o?aaeoi?ey iinea naeaaeeaaiey.
1
2
(1
l1
t
(2
(3
(4
l2
(5
t
u
v
l
(
?en. 2.5. I?eia? ?3 naeaaeeaaiey iiai?ioa. 1 – o?aaeoi?ey aei
naeaaeeaaiey;
2 – o?aaeoi?ey iinea naeaaeeaaiey.
R
R
?en. 2.4. I?eia? ?2 naeaaeeaaiey iiai?ioa. 1 – o?aaeoi?ey aei
naeaaeeaaiey;
2 – o?aaeoi?ey iinea naeaaeeaaiey.
1
2
(
u
v
l
t
1
2
(1
(2
u
v
l
R
R
?en. 2.3. I?eia? ?1 naeaaeeaaiey iiai?ioa. 1 – o?aaeoi?ey aei
naeaaeeaaiey;
2 – o?aaeoi?ey iinea naeaaeeaaiey.
r1
r2
(i
(i+1
X
Y
X’
Y’
dS
?en.3.2 Ii?aaeaeaiea iiaie i?eaioaoeee naiinaaea
(
(’
X
(
(
1
2
3
a)
2
(’
1
3
(
(
a)
(
3
2
1
a)
450
(
(’
O
(
O
(’
450
(
3
2
1
a)
?en. 2.7. Ei??aeoeey eioi?iaoeee i i?aaenoiyuai iiai?ioa.
?en. 2.1. I?eia?iue aeae iiai?ioa ia ea?oa.
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