Prácticas de Topografía

 

ROKSBTUKHIH OIEKLOIN HB KO@BOKBTKI TBEKOXL ROKSBTUKXITKL VBHTL ITIRW VINIEKLU CIERNXIH HB XBEOLNL@ÍI HB NI ELOUXTREEKÕO EITTBTI HB KO@BOKBTÍI EKSKN ROK-TRVIV-CXE

XLVL@TICKI KK TBVLTXB 69

HLEBOXB7

KO@. LUEIT BOTKYRB WIMLTI MBOHLWI BOXTB@I7

AITNI MITKXWI MBOHBW BUXTIHI

@TRVL7

KE-49O

Mioi`ui, Okeiri`ui 9: hb Letudrb 4692

 

VTIEXKEI 69 XLVL@TICKI

Elotbokhl K. KOXTLHRE KOXTLHREEKLO EKLO..... .......... .......... .......... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... ........... ..............5 ........5 4. LDGBXKSLU.................... LDGBXKSLU................................... ............................. ............................. .............................. ............................. ............................. .............................. .......................... ........... 8 LDGBXKSL @BOBTIN...................... @BOBTIN.................................... ............................. .............................. ............................. ............................. .............................. ......................... .......... 8 LDGBXKSLU BUVBEÍCKELU.............. BUVBEÍCKELU............................ ............................. .............................. ............................. ............................. ............................. .......................... ............ 8 5. IOXBEBHBOXBU IOXBEBHBOXBU JKUXLTKELU................. JKUXLTKELU................................ ............................. ............................. .............................. ............................. .............................. ................8 8 8. KMVLTXIOEKI HB NI VTÉEXKEI...................... VTÉEXKEI..................................... .............................. ............................. ................................................. ................................... 2 2. IUVBEXLU @BOBTINBU.................... @BOBTINBU.................................. ............................. ............................. ............................. .................................................... ..................................... 3 3. HBUITTLNNL HB EIMVL......... EIMVL........................ ............................. ............................. ............................. ............................. .............................. ..............................0 ...............0 3.9 ELMVLUKEKÕO HB NI ERIHTKNNI7........................ ERIHTKNNI7....................................... ............................. ............................. .............................. ........................0 .........0 3.4 BYRKVL BMVNBIHLU BO BN XTIDIGL7............ XTIDIGL7........................... ............................. ............................. ................................................ ................................. 0 3.5 BZVNKEIEKLOVIUHL I VIUL HBN XTIDIGL HB EIMVL TBINKWIHL............................................0 0. TBURMBO HB HIXLU NBSIOXIHLU............................... NBSIOXIHLU.............................................. ............................. .............................................. ...................................: ...: :. EINERNLU..................... EINERNLU.................................... .............................. ............................. ............................. .............................. ............................. ............................. ..........................; ...........; :.9. MBTXLHLU [ CLTMRNIU I RXKNKWITUB...................... RXKNKWITUB..................................... .............................. ............................. ..............................; ................; :.4. EINERNLU MIXBMIXKELU.............. MIXBMIXKELU............................. .............................. ............................. ............................. ................................................ .................................; ; :.4.9. EÉNERNL HB VLNK@LOIN7 HJ, SBTXKEIN ΘJ, BNBSIEKLO................................ BNBSIEKLO.................................................... ....................; ; :.4.4. ELLTHBOIHIU.................. ELLTHBOIHIU................................. ............................. ............................. ............................. .................................................... ...................................... 98 :.4.5. ITBI.......................... ITBI......................................... ............................. ............................. ............................. ............................. .............................. ................................ .................93 93 ;. ELOENRUKLO............... ELOENRUKLO............................. ............................. .............................. ............................. ............................. .............................. ............................. ......................... ........... 93

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VTIEXKEI 69 XLVL@TICKI

K.

KOXTLHREEKLO

Ni in inm mbt btrí ríii bob bob plr plr ldgbt ldgbtl l pr prko koekp ekpin in tb tbob obrr bo eubo euboti ti nis nis hk hkcb cbrb rboe oeki kiss hb ok okvb vbnb nbss bxkstbotbs bo bn tbrrbol, prlebhkmkbotl elolekhl elml okvbniekõo. Okvbniekõo7 Eloskstb bo mbhkr nis hkcbrboekis hb nis inturis botrb hls l virkls puotls. Bs ni clrmi hb bxprbsir nis inturis rbnivis hb puotls sktuihls plr hbdigl l boekmi hb uo ekbrtl pniol hb rbcbrboeki y bs unkzihi bo ni elostrueekõo hb hrboigbs, rkb`ls, pbrnbs nl nlo` o`kt ktuh uhko koin inbs bs y tr trio iosv svbr brsi sinb nbss piri piri bn bs bstu tuhk hkl l hb hksb hksbùl ùl hb eirr eirrbt btbr bris is,, eioi eioinbs nbs,, kostinieklobs hb tudbríis, bte. Ni prbekskõo hb nis ldsbrvieklobs bs cuoekõo hbn hbsol hbn tridigl y hb nls mbhkls qub sb hksplo`i.   Ni okvbniekõo, tërmkol `bo `bobrin brin qub sb ipnkei i euinqukbri hb nls hkvbrsls hkvbrsls prlebhkmkbotls inmëtrkels plr mbhkl hb nls euinbs sb hbtbrmkoio bnbvieklobs l okvbnbs hb puotls, l dkbo, hkcbrboekis hb bnbvieklobs l hbsokvbnbs, bs uoi lpbriekõo vktin piri ldtbobr nls hitls obebsirkls piri ni bnidlriekõo hb mipis l pniols hb elo`uriekõo y bo prlybetls hb ldris hb ko`bokbríi y hb elostrueekõo  Okvbniekõo trk`lolmëtrkei7 Bs iqubnni bo ni euin sb mkhbo nis hksotis jlrkzlotinbs y nls éo`unls vbreinbs, nls euinbs sb usio piri eineunir nls hbsokvbnbs. Bstb mëtlhl pubhb bmpn bm pnbi birs rsbb piri piri bs bsti tidn dnbe bebr br puot puotls ls ko koie ieeb ebsk skdn dnbs bs,, el elml ml nl nlss pkel pkelss hb nis nis ml mlot otiù iùis is,, elostrueeklobs mirkois, bte. Bn mëtlhl hb ni bstihíi, qub bs uoi virkiotb hb ni okvbniekõo trk`lolmëtrkei, bs muy ÷n piri ni bnidlriekõo hb pniols, okvbnieklobs plel prbeksis l nbviotimkbotls prbnkmkoirbs.   Okvbni Okvbniekõo ekõo dirl dirlmëtrk mëtrkei7 ei7 Bsti eloskst eloskstbb bo ni hbtb hbtbrmkoi rmkoiekõo ekõo hb bnbvi bnbvieklob eklobss mkhkb mkhkbohl ohl nls eimdkls bo ni prbskõo hbn ikrb. Iuoqub nis prbsklobs dirlmëtrkeis pubhbo mbhkrsb elo dirõmbtrls hb mbreurkl, bstls kostrumbotls slo pbsihls, vlnumkolsls y cré`knbs, plr nl qub ol slo préeels piri obs tlpl`réels. Bo su nu`ir sb unkzio nls dirõmbtrls mbténkels l iobrlkhbs, qub slo rbskstbotbs y nk`brls pbrl mbols prbeksls, hbolmkoihls elm÷ombotb inmbtrls.  Nis nbeturis hbn dirõmbtrl tlmihis bo puotls elo ni mksmi bnbviekõo viríio hb ieubrhl elo nis elohkeklobs nleinbs hb prbskõo hbn ikrb y slo icbetihls plr nis virkieklobs hb jumbhih y tbmpbrituri. Uk sb unkzi uo slnl dirõmbtrl, sb igusti i uoi bnbviekõo elolekhi y nub`l sb tlmio nbeturis bo ltrls puotls. In tbrmkoir bn tridigl, bn dirõmbtrl sb nnbvi hb in puotl lrk`koin l unkzir hb kokekl y sb ijí uoi oubvi nbeturi. Bo nls tridigls hb oubvl okvbniekõo bs elovbokbotb més hbtlmi uo dirõmbtrl. Nl més ihbeuihl bs 5

 

VTIEXKEI 69 XLVL@TICKI

bmpnbirr in mbo bmpnbi mbols ls trb trbss dir dirõmb õmbtrl trlss pir pirii ldt ldtbob bobrr nis bnbv bnbviek ieklob lobss elo uoi pr prbeks bekskõo kõo rizloidnb. Okvbniekõo hkcbrboekin hb durdugi7 Ximdkëo sb nb eloleb elml okvbniekõo hkrbeti, bs bn mëtlhl usuin piri ldtbobr bnbvieklobs, sb mkhbo hkstioekis vbreinbs rbcbrkhis i uoi níobi jlrkzlotin, nis euinbs sb bmpnbio piri eineunir nls hbsokvbnbs botrb virkls puotls. Ub unkzi un kzi uo okvbn hb durd durdugi ugi piri gi girr ni níobi hb vksui vksuinn hbn tbnb tbnbsel selpkl pkl.. Ësti Ësti bs ni nío níobi bi jlrkzlotin supubsti elo rbspbetl i ni euin mkhbo nis hkstioekis vbreinbs.

4. LDGBXKSLU LDGBXKSL @BOBTIN. 

 

Yub bn bstuhkiotb ihqukbri nls elolekmkbotls y nis jidknkhihbs obebsirkis piri eineunir ni inturi hb uo puotl y bn hbsokvbn botrb hls puotls. Elolekbohl Elolekboh l hkrbetimbotb ni hkstioeki Jlrkzlotin. Hbselolekbohl Hbselolekb ohl ni hkstioeki jlrkzlotin.

 LDGBXKSLU BUVBEÍCKELU. 





Eipiektir in bstuhkiotb iebrei hb nls tridigls inmëtrkels elo bn prlpõsktl hb hbtbrmkoir ni inturi y bn hbsokvbn hb nls puotls eirietbrísels sldrb uoi supbrekb hb okvbn qub sb tlmi elml supbrekb hb elmpiriekõo bo uo tbrrbol. Yub bn bstuhkiotb bstuhkiotb ihqukbri ihqukbri jidknkhihb jidknkhihbs, s, hbstrbzis hbstrbzis y elolekmk elolekmkbotl botlss qub nb pbrmktio pbrmktio slnuekloir prldnbmis hb okvbniekõo hb uo tbrrbol iuxknkéohlsb hb nls mëtlhls y prlebsls inmëtrkels rbinkzihls bo ni préeei hb eimpl. Hbmlstrir nls pniotbimkbotls tëeokels ldtbokhls huriotb bn eursl y nnbvirnls i ni préeei elo bn ldgbtl hb qub bn bstuhkiotb bstidnbzei uoi disb sõnkhi tbõrkei y préeei y nls ipnkqub bo nls prldnbmis hb ni ko`bokbríi I`rkelni.

5. IOXBEBHBOXBU JKUXLTKELU Bn lrk`bo hb ni mbhkekõo tlpl`réei, sb rbmloti in io`ul B`kptl, hlohb nis eloouis erbekhis y hbsdlrhimkbotls hbn Oknl, ldnk`idio i ni bxkstboeki hb tëeokels i`rkmboslrbs piri vlnvbr i hbsnkohir nis brris kouohihis plr bn ríl. Ni prkmbri hbserkpekõo hb bstls ipiritls hb mbhkhi ipirbeb bo Inbgiohríi bo bn sk`nl K I h.E. hlohb Jbrõo hbserkdb in`uols hb nls kostrumbotls kostrumbotls nnimihls ¸¸hklptris¸¸ qub qub pubhbo sbrvkr piri jinnir hkstioekis jlrkzlotinbs, euyl cuohimbotl bs bn hb nls ietuinbs tblhlnktls l dkbo piri jinnir nis hkcbrboekis hb inturis, qub slo ni disb hb nls ietuinbs okvbnbs.

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VTIEXKEI 69 XLVL@TICKI

Ni tb tbeo eoln lnl` l`íi íi cu cubb pltb pltboe oeki kihi hi i tr triv ivës ës hb pr prkvk kvknb` nb`kl klss hb kovb kovboe oekõ kõo o y nl nlss ml mlhb hbnl nlss prbsbotihls in Tby sb `uirhirlo clrmiohl uo `idkobtb hb méqukois. Nis pitbotbs hb kovboekõo elostuybrlo uoi cubotb hb `rio kotbrës hb ni pirekpiekõo hbn plhbr rbin bo bn hbsirrlnnl hbsi rrlnnl hb ni tëeoke tëeokei, i, yi qub nis eëhun eëhunis is hb prkvknb` prkvknb`kl kl rbin sb eloebhí eloebhíio io i iqubnni iqubnniss kovboeklob kovbo eklobss qub sb igusti igustidio dio i uoi olrmiv olrmivii eniri y prbv prbvki, ki, i sbmbgioz sbmbgiozii hb nl qub sb vboíi jie vboíi jiekbo kbohl hl bo Cnl Cnlrbo rboeki eki,, Sbo Sbobek bekii y lt ltris ris rbp rbp÷dn ÷dnkei keiss kti ktinki nkioi ois, s, sb` sb`÷o ÷o nis ÷n ÷nmis mis kovbs`ieklobs hbn prlcbslr @ireíi Xipki. Ni jkstlrki hb ni inmbtríi elmbozõ bo nls iùls 06-:6, pbrl cub Xlpbx/Vlsbkhõo (niozihl bo 9;;4), qukbo mlstrõ ni pltboeki hb bsti tëeokei, in prlplrekloir mbhkhis hb ni inturi hbn mir elo uoi prbekskõo ebomëtrkei. Ni sbrkb hb nls Gislo, eloebdkhi elo kostrumbotls mkokiturkzihls, tlmi bn rbnbvl piri pbrbookzir nis mbhkhis. Vlr ltrl nihl, bstéo prbvkstis (l bo bstuhkl) ltris mksklobs piri bstidnbebr uo ldsbrvitlrkl pbrmiobotb hb nls leëiol

8. KMVLTXIOEKI HB NI VTÉEXKEI.   Ni km kmpl plrt rtio ioeki eki cu cuoh ohim imbo boti tinn y pr prbm bmks ksii hb bs bsti ti pr prée éee eii bs ni hbtb hbtbrm rmko koie iekõ kõo o hb bnbvieklobs iuxknkéohlsb elo uo kostrumbotl tlpl`réel, elolekhi elml okvbniekõo, bn sk`okeihl hb ni ldtboekõo hb bnbvieklobs ol pubhb sbr més rbnbviotb, bs tio kmplrtiotb qub ol sb pubhb eloebdkr uo prlybetl hb elostrueekõo bo bn qub ol sbi erkel bstb prlebsl, elostuybohl uo bnbmbotl obebsirkl y hb mueji unkhih bo ni clrmiekõo kotb`rin y prlcbskloin hbn Ko`bokbrl I`ríelni l Ekvkn. Ni hbtbrmkoiekõo y eéneunl hb nls hbsokvbnbs y bnbvieklobs hb uo tbrrbol bobo uoi hkvbrskhih hb ipnkeieklobs ol sõnl bo ni tlpl`rii skol timdkëo bo ni vkhi elm÷o hkirki hb nis pbrs pbrslois lois.. Bn bstu bstuhkio hkiotb tb i triv trivës ës hb bsti préeei ioinkz ioinkzii elo eukhi eukhihl hl nls rb`kstrls rb`kstrls ldtbokhls elmprldéohlnls mitbméeimbotb elo bn o hb hbmlstrir qub bxkstb uoi nõ`kei elrrbeti y eljbrbotb botrb bn pbrn hbn tbrrbol, sus ioltieklobs y ni hkcbrboeki hb okvbn ldtbokhis, pbrmkëohlnb ipnkeir mëtlhls y elolekmkbotls qub nb cieknktbo su tridigl bo bn eimpl y qub plstbrklrmbotb sbréo pirtb hb su e÷munl hb jbrrimkbotis i unkzir bo uo plskdnb prldnbmi hb inmbtríi. Bn elotrln hb bnbvieklobs bs hb `rio kmplrtioeki bo tlhl pl hb prlybetls, hbshb tbrripnboihl hb uoi `riogi l ni elostrueekõo hb uo murl, jisti ni elostrueekõo hb prlybetls hb hrboigb, bhkekls hb més hb 46 mts. hb inturi, pubotbs nir`ls, eimkols, eirrbtbris, eéneunl hb vln÷mbobs hb tbrriebríi, bnidlriekõo hb mipis, bte.. Jb iquí ni obebskhih qub bob bn ko`bokbrl i`ríelni i`ríelni l ekvkn hb miobgir, elolebr y hlmkoir bn prlebsl hbolmkoihl Okvbniekõo.

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VTIEXKEI 69 XLVL@TICKI

2. IUVBEXLU @BOBTINBU Hb cl clrm rmii `bob `bobri rinn bs hb mu muej ejii u unkh nkhih ih el elol oleb ebrr y bs bsti tidn dnbeb bebrr ekb ekbrt rtis is hbo hbokek keklo lobs bs skstbmizihis qub nb pbrmktbo in bstuhkiotb uoi miylr y més céekn elmprboskõo hb ni inmbtríi qub slo rbqubrkhis y hb `rio usl bo bn bstuhkl hb okvbniekõo. I eloouiekõo sb hbokréo in`uols eloebptls obebsirkls piri bn botbohkmkbotl hb bsti préeei. Níobi vbrein7 Bs uoi níobi pirinbni i ni hkrbeekõo hb ni `rivbhih. Bo uo hbtbrmkoihl puotl, bs ni hkrbeekõo qub isumb bn jknl hb uoi pnlmihi sk i ësti sb nb pbrmktb lseknir nkdrbmbotb. Uupbrekb hb okvbn7 Bs iqubnni qub bob uoi bnbviekõo elostiotb y bs pbrpbohkeunir i uoi níobi i pnlml bo tlhls sus puotls. Ni mbglr clrmi hb rbprbsbotirni bs elo uo `rio eubrpl hb i`ui qub ol bs icbetihl plr nis n is mirbis. Bnbviekõo hb uo puotl bo pireunir7 Bs ni hkstioeki vbrein qub bxkstb irrkdi l hbdigl hb ëstb, mbhkhi jisti uoi supbrekb hb okvbn (`bobrinmbotb bn okvbn hbn mir). Níobi hb okvbn okvbn bs uoi níobi eur eurvi7 vi7 Bo uoi sup supbrekb brekb hb okvbn elo tl tlhls hls sus puo puotls tls i ni mksmi bnbviekõo. Níobi Jlrkzlotin7 Bs uoi níobi rbeti qub bs tio`botb i uoi níobi hb okvbn bo uo puotl hihl. Dioel hb okvbn l mibstrl7 Bs uo puotl rbnivimbotb pbrmiobotb hb bnbviekõo elolekhi. Hbdb sbr céeknmbotb khboeidnb y bstir elnleihl bo uo puotl digl rbspbetl hbn tbrrbol ekreuohiotb. Vubhb sbr uoi mlglobri hb eloerbtl elnleihi bo bn tbrrbol, uo enivl jkoeihl bo uo érdln, uoi mirei x bo uo ekmkbotl hb eloerbtl, uo pbrol bo uo jkhriotb, l uo ldgbtl skmknir qub ol sb mubvi. Nls dioels hb okvbn qub jio hb sbr pbrmiobotbs hbdbo bstir iplyihls sldrb bstrueturis qub bstëo elmpnbtimbotb isbotihls y qub sb hbspniebo plr hbdigl hb ni níobi hb pbobtriekõo hb nis jbnihis. Uupbrekb hb rbcbrboeki7 Uupbrekb hb okvbn i ni euin sb rbbrbo nis bnbvieklobs (plr bgbmpnl, bn okvbn mbhkl hbn mir). Ub nb nnimi i vbebs pniol hitl l pniol hb elmpiskõo, iuoqub rbinmbotb ol sbi uo pniol. Okvbn mbhkl hbn mir (O.M.M)7 inturi mbhki hb ni supbrekb hbn mir sb`÷o tlhis nis btipis hb ni mirbi bo uo pbrklhl hb 9; iùls. Ub hbtbrmkoi plr nbeturis tlmihis `bobrinmbotb i kotbrvinls hb uoi jlri.

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VTIEXKEI 69 XLVL@TICKI

 3. HBUITTLNNL HB EIMVL

3.9 ELMVLUKEKÕO HB NI ERIHTKNNI7 Ldsbrvihlr Bstihinbrl l plrti mkri. Ioltihlr Eihbobrls

3.4 BYRKVL BMVNBIHLU BO BN XTIDIGL7 Xblhlnktl Xríplhb Bstihkis Enivls Nkdrbti hbeimpl Ekoti Vnlmihis

3.5 BZVNKEIEKLOVIUHL I VIUL HBN XTIDIGL HB EIMVL TBINKWIHL Bn híi 49 hb idrkn, ols rbuokmls uo `rupl hb bstuhkiotbs y ni prlcbslri hb prieeis, guotl elo bn bqukpl hb tridigl obebsirkl bo bn elstihl lbstb hbn plrtõo prkoekpin hbn Tbekotl Rokvbrsktirkl Vbhrl Iriuz Viniekls, piri nnbvir i eidl ni prkmbri prieei hb eimpl hb Xlpl`rii KK. Jidkbohl Jidkbo hl bst bstidn idnbekh bekhl l ni prk prkmbr mbrii bst bstiek iekõo õo (bs (bsti tiekõo ekõo I), elm elml l puo puotl tl hb pi pirh rhi, i, sb eloerbtõ hlohb bstiríio udkeihls nls puotls hb oubstri plnk`loin (9, 4, 5, 8, 2), nub`l prlebhkmls i kostinir y okvbnir bn tblhlnktl bo hkeji bstiekõo bn euin sb boelotridi bo uoi supbrekb sbmkpnioi y elo plei vb`btiekõo. Roi vbz pniotihls bo ni bstiekõo I, vksimls bn puotl 5, bo hlohb prlebhkmls i jiebr nbeturii hb hls jknl ebot nbetur ebotrin rin hb 6.066 elo uo éo`u éo`unl nl vbrein hb ;5· 28f46ff, 28f46ff, hb ni mksmi

0

 

VTIEXKEI 69 XLVL@TICKI

miobri bn éo`unl jlrkzlotin, y nub`l jkekmls ni mbhkekõo hbn kostrumbotl qub cub hb 9.866. I eloouiekõo udkeihi bo ni mksmi bstiekõo vksimls bn puotl

0. TBURMBO HB HIXLU NBSIOXIHLU  

BUXIEKLO

VL

je

U

Io`. Sbrt

Izkmut

9,25              

6

DM 9 2 8 3 0 : ;

9,925 9,6;: 9,60: 9,6;0 9,6: 9,58 9,63; 9,6:9

6,903 6,9;5 6,922 6,9;4 6,959 6,630 6,95: 6,934

::·42' 94'' ;3·60'8;'' ;9·60'9:'' ;6·93'53'' :;·99'90'' ;5·50'28'' ;5·96'60'' ;8·2;'62''

96;·26'53'' 22·24'92'' ;0·5:'92'' 940·89'5:'' 9:4·54'24'' 424·80'9;'' 4;2·52'9;'' 560·52'94''

96

4 9  

::·2;'56'' ;9·6;'56''

439·52'42''

    96              

6 99 4 94 95 5 98

4 9 4 9 4 9 4 9 4 9 4 9 4 9

           

:

  :;·20'5:'' ;0·92'59'' ;5·92'44'' ;3·5;'98'' ::·58'2:'' ;5·92'28'' :2·54'20'' ;6·5:'49'' :0·68'64'' ;6·45'58'' :8·88'86'' :;·66'52''

66·66' 409·60'43'' 486·50'64'' 445·98'65'' 92:·80'4;'' 953·2;'94'' 04·84'4;''

 

VTIEXKEI 69 XLVL@TICKI

:. EINERNLU :.9. MBXLHLU [ CLTMRNIU I RXKNKWITUB Cõrmunis piri eineunir hkstioekis jlrkzlotinbs. HJ = (A) (U) (els´ κ) HJ = 1 euiohl nls éo`unls vbreinbs bs bstéo téo bo bnbviekõo.  HJ= 1 Euiohl E uiohl nls éo`unls vbreinbs bstéo bo hbprbskõo S= HJ x t` κ· 1 Eineunl hb hkstioekis vbreinbs ΘJ=+/-S+JK-je 1 Eineunl hb hbsokvbn Jptl (DM) = JBst (I) + ΘJ (I-DM)

:.4. EINERNLU MIXBMIXKELU :.4.9. EÉNERNL HB VLNK@LOIN7 HJ, SBTXKEIN ΘJ, BNBSIEKLO.  HJ =( A )( U )( els4 κ ) S = HJ ∐XIOιS  ∃ J = JK ∔ je¹S   BNS   BN S =EL ELX XI DM ∔ ΘJ 

 HJ ( 6 ∔ DM )=966∐6.903∐els4 ( ;6 · ∔ :: · 42 94 ' 

S  ( ( 6∔ DM )=90.2:0∐tio ( 9 · 58 8: ' 

' ' 

)=90.2:0 M 

) =6.8:2 M 

' ' 

∃ J ( 6 ∔DM )=9.25 ∔9.25 + 6.8:2= 6.8:2  BNS   BN S =96 ∔6.8:2 =;.292  HJ ( 6 ∔9 )=966∐6.9;5∐els4 ( ;3 · 60 8: ' 

S  ( ( 6∔ 9 ) =9;.6:∐ tio ( 3 · 60 8: ' 

∔;6 · )=9;.6: M 

' ' 

) =4.68; M 

' ' 

∃ J ( 6 ∔9 )= 9.25∔9.6;: ∔4.68;=∔ 9.390 M 

;

 

VTIEXKEI 69 XLVL@TICKI

 BNS   9 9 =;.292 ∔9.390= 0.:;: M 

 HJ ( 6 ∔2 )=966∐6.922∐els4 ( ;9 · 60 8: ' 

' 

∔ ;6 · )=92.8;0 M 

' ' 

' ' 

S  ( 6∔ 2 )=92.8;0∐tio ( 9 · 60 9:

)=6.565 M 

∃ J ( 6 ∔2 )= 9.25 ∔9.60:∔6.565 = 6.98; M   BNS   BN S  2  2 = ;.292+ 6.98;= ;.32; M 

 HJ ( 6 ∔8 )= 966∐6.9;4∐els4 ( ;6 · 93 56 ' 

S  ( ( 6∔ 8 )=9;.46∐tio ( 6 · 93

'' 

' 56

∔;6 · )=9;.46 M 

' ' 

) =6.6;4 M 

∃ J ( 6 ∔8 )=9.25 ∔9.6;0∔6.6;4 =6.588 M   BNS   8 8 =;.292 ∔6.588 = ;.:23 M 

 HJ ( 6 ∔3 ) = 966∐6.950∐els els 4 ¼ S  ( ( 6∔ 3 )=95.3;0∐ tio ( 6 · 8: '  85  85 ' ' )=6.9;8 M  ∃ J ( 6 ∔3 )= 9.25 ∔9.6: + 6.9;8 =6.388 M   BNS   3 3 = ;.292 + 6.388 =96.92; M 

 HJ ( 6 ∔0 ) = 966∐6.630∐els4 ( ;5 · 50 28 ' 

∔;6 · )=3.305 M 

' ' 

S  ( ( 6∔ 0 )=3.305∐tio ( 5 · 50 '  28  28 ' ' )= 6.848 M  ∃ J ( 6 ∔0 )= 9.25 ∔9.658 ∔6.848 =6.604 M   BNS   0 0 = ;.292 + 6.604= ;.2:0 M 

 HJ ( 6 ∔: ) = 966∐6.95:∐els4 ( ;5 · 96 60 ' 

∔ ;6 · )=95.02: M 

' ' 

S  ( 6∔ : )=95.02:∐tio ( 5 · 96 ' 60 ' ' )=6.034 M 

96

 

VTIEXKEI 69 XLVL@TICKI

∃ J ( 6 ∔: )= 9.25 ∔9.63; + 6.034=∔6.569 M   BNS   : : = ;.292∔6.569 = ;.498 M   HJ ( 6 ∔; ) = 966∐6.934∐els4 ( ;8 · 2; 63 ' 

' 

∔;6 · )=93.60: M 

' ' 

' ' 

S  ( 6∔ ; )=93.60:∐tio ( 8 · 2; 63

)=9.864 M 

∃ J ( 6 ∔; )= 9.25 ∔9.6:4∔9.864=∔ 6.;28 M   BNS   BN S  ;  ; = ;.292∔6.;2 8¼ :.239 M 

 HJ =

  je 9 ∔je 4 t` v 9 ¹t`v 4

S = HJ ∐XIOιS  ∃ J = JK ∔ je¹S   BNS = BNS  BNSl l ∔ ΘJ   HJ ( 6 ∔96 )=

4∔ 9

 

t` ( ;6 · ∔:: · 2 ; 5 6 ' 

' ' 

) +t` ( ;9 · 6 ;'  56 '' ∔ ;6 · )

S  ( ( 6∔ 96 )=43.889∐tio ( 69 · 66 56 ' 

=43.889

) =6.832 M 

' ' 

∃ J ( 6 ∔96 )=9.25 ∔4+ 6.832=∔ 6.662 M   BNS   BN S  96  96 = ;.292∔6.662 =;.296 M 

 HJ ( 6 ∔99) =

4∔ 9

 

t` ( ;6 · ∔:; · 20 ' 5 :

) +t` ( ;0 · 92 ' 59 ' ' ∔;6 · )

' ' 

=0.:6; m

S  ( ( 6∔ 99 )=0.:6;∐tio ( 64 · 44 ) =6.662 M  ' 

∃ J ( 6 ∔99)=9.2: ∔4 + 6.662=∔ 6.892 M   BNS   BN S  99  99= ;.29∔6.892 =;.6;2 M   HJ ( 96 ∔4 )=

 

4 ∔9

t` ( ;5 · 92 '  44  44 ' ' ∔;6 · ) ∔ t` ( ;3 · 5; ' 98 ' ' ∔ ;6 · )

S  ( ( 96∔4 ) =93.054∐tio ( 65 · 92 ' 44 '  )=6.;24 M  ' 

99

= 93.054 m

 

VTIEXKEI 69 XLVL@TICKI

∃ J ( 96∔4 )=9.2:∔4 + 6.662=∔6.892 M   BNS   4 4 =;.29 ∔9.504=:.95: M 

4∔9

 

 HJ ( 96 ∔94 )= t` ( ;6 · ∔ :: · 58 ' 2: ' ' )∔t` ( ;5 · 92 ' 28 ' ' ∔;6 · ) =94.440 m S  ( ( 96∔94 )= 94.440∐tio ( 9 · 42 ' 64 '  )=6.564 M  ' 

∃ J ( 96∔94 ) =9.2:∔4 + 6.564 =∔6.99: m  BNS   BN S  94  94 =;.29 ∔6.99:=;.5;4 M 

 HJ ( 96 ∔95 )=

4 ∔9

 

t` ( ;6 · ∔:2 · 54 ' 20 ' ' ) ∔t` ( ;6 · 5: '  49 ' ' ∔;6 · )

S  ( ( 96∔95 ) = 99.450∐tio ( 68 · 40 65 ' 

' ' 

=99.450 m

)=6.:02 M 

∃ J ( 96∔95 )=9.2:∔ 4+ 6.:02=6.822 m  BNS  95  95 = ;.29+ 6.822= ;.;32 M 

 HJ ( 96 ∔5 )=

4 ∔9

 

t` ( ;6 · ∔:0 · 68 ' 64 ' ' ) + t` ( ;6 · 45 ' 58 ' ' ∔;6 · )

S  ( ( 96∔5 )=90.493∐tio ( 64 · 22 2: ' 

=90.493 m

) =6.::4 M 

' ' 

∃ J ( 96∔5 )=9.2: ∔4+ 6.::4=6.834 m  BNS   BN S  5  5 = ;.29+ 6.834=;.;04 M 

 HJ ( 96 ∔98 ) =

4∔9

 

t` ( ;6 · ∔:8 · 88 ' 86 ' ' )∔t` ( ;6 · ∔:; · 66 ' 52 ' ' )

S  ( ( 96∔98 )= 95.5:0∐tio ( 62 · 92 46 ' 

'' 

)=9.459 m

∃ J ( 96∔98 )=9.2: ∔4 + 9.459=6.:99 m  BNS  98  98 =;.29 + 6.:99 =96.549 M 

94

=95.5:0 m

 

VTIEXKEI 69 XLVL@TICKI

XIDNI HB TBURNXIHLU BUXIEKLO

6

VL

je

U

Io`. Sbrt

Izk mut

Hkstioeki (m)

DM

9,925

6,903

::·42' 94''

96;·26'53''

9 90 0, 2:0

9

9,6;:

6,9;5

;3·60'8;''

22·24'92''

9;,6:

-9,390

0, :;:

2

9,60:

6,922

;9·60'9:''

;0·5:'92''

92, 8;0

6, 98;

;, 32;

8

9,6;0

6,9;4

;6·93'53''

940·89'5:''

9;,4

6, 588

;, :23

3

9, 6:

6,959

:;·99'90''

9:4·54'24''

95, 3;0

6, 388

96,92;

0

9, 58

6,630

;5·50'28''

424·80'9;''

3,305

6, 604

;, 2:0

:

9,63;

6,95:

;5·96'60''

4;2·52'9;''

95, 02:

-6,569

;, 498

;

9,6:9

6,934

;8·2;'62''

560·52'94''

93, 60:

-6,;28

:, 239

4

::·2;'56''

439·52'42''

43, 889

-6,662

;,29

9

;9·6;'56'' 66·66'

43, 889

409·60'43''

0,:6;

-6,892

;, 6;2

486·50'64''

93, 054

-9,504

:, 95:

445·98'65''

94, 440

-6,9::

;, 5;4

92:·80'4;''

99, 450

6, 822

;, ;32

953·2;'94''

90, 493

6, 834

;, ;04

0 04 4·84'4;''

95, 5:0

6, :99

96,549

96 6 99 4 96

94 95 5 98

4 9 4

:;·20'5:''

9

;0·92'59''

4

;5·92'44''

9

;3·5;'98''

4

::·58'2:''

9

;5·92'28''

4

:2·54'20''

9

;6·5:'49''

4

:0·68'64''

9

;6·45'58''

4

:8·88'86''

9

:;·66'52''

95

ΘJ

BNS 96

;,29

 

VTIEXKEI 69 XLVL@TICKI

:.4.4. ELLTHBOIHIU 6 (26,26)

 Z 9=26 + 9;.6:∐ UBO ( 22 · 24 ‛ 92 ‛ ‛ )= 32.0;8 [   9 9 =26 + 9;.6:∐els ( 22 · 24 ‛ 92 ‛ ‛ )= 36.092

 Z   8 8 =26 + 9;.46∐UBO ( 940 · 89 ‛ 5: ‛ ‛ )=32.9;5 [   8 8 =26 + 9;.46∐els ( 940 · 89 ‛ 5: ‛ ‛ )=5:.436

 Z 2 =26 + 92.8;0∐ UBO ( ;0 · 5: ‛ 92 ‛ ‛ )= 32.536 [   2 2 =26 + 92.8;0∐els ( ;0 · 5: ‛ 92 ‛ ‛ ) = 80.;8

 Z 3 =26 + 95.3;2∐ UBO ( 9:2 · 54 ‛ 24 ‛ ‛ )= 8:.303 [   3 3 = 26+ 95.3;2∐els ( 9:2 · 54 ‛ 24 ‛ ‛ )=53.50

 Z 0 =26 + 3.305∐UBO ( 424 · 80 ‛ 9; ‛ ‛ )= 85.343 [   0 0 =26 + 3.305∐els ( 424 · 80 ‛ 9; ‛ ‛ ) = 8:.642  Z : =26 + 95.02:∐ UBO ( 4;2 · 52 ‛ 9; ‛ ‛ )=50.2;9 [   : : =26 + 95.02:∐els ( 4;2 · 52 ‛ 9; ‛ ‛ )=22.;84

 Z ; =26 + 93.60:∐UBO ( 560 · 53 ‛ 94 ‛ ‛ )=50.434 [   ; ; = 26+ 93.60:∐els ( 560 · 53 ‛ 94 ‛ ‛ ) =2;.:96

98

 

VTIEXKEI 69 XLVL@TICKI

 Z 96 =26 + 43.889∐UBO ( 430 · 52 ‛ 42 ‛ ‛ )=45.2:4  Z 96 =26 + 43.889∐els ( 430 · 52 ‛ 42 ‛ ‛ )= 8:.::: ELLTHBOIHIU HB 96 (45.2:4, 8:.:::)

IWKMRX (96-6) = 430·52‛42‛‛ ― 9:6 = :0·52‛42‛‛ IW = :0·52‛42‛‛ IW = >Jz + Iz

 Z 4= 45.2:4+ 93.054∐UBO ( 486 · 50 ‛ 64 ‛ + :0 · 52 ' 42 ' ' )=98.030 [   4 4 = 8:.::: + 93.054∐els ( 486 · 50 ‛ 64 ‛ + :0 · 52 42 ' 

) =35.996

' ' 

 Z 5 =45.2:4+ 90.493∐ UBO ( 953 · 2; ‛ 94 ‛ + :0 · 52 ' 42 ' ' )= )=99.266 [   5 5 = 8:.::: + 90.493∐els ( 953 · 2; ‛ 94 ‛ + :0 · 52 42 ' 

' ' 

)=53.342

 Z 99= 45.2:4+ 0.:6;∐UBO ( 409 · 60 ‛ 43 ‛ + :0 · 52 ' 42 ' ' )= )=45.860 [  99  99= 8:.::: + 0.:6;∐els ( 409 · 60 ‛ 43 ‛ + :0 · 52 42 ' 

' ' 

)= 23.3;2

 Z 94= 45.2:4 + 94.440∐ UBO ( 445 · 98 ‛ 65 ' ‛ + :0 · 52 ' 42 ' ' )=98.556 [  94  94 = 8:.:::+ 94.440∐ els ( 445 · 98 ‛ 65 ‛ + :0 · 52 42 ' 

' 

' ' 

)=23.::9

 Z 95 =45.2:4+ 99.450 ∐UBO ( 92: · 80 ‛ 4; ' ‛ + :0 · 52 ' 42 ' ' )= 95.4:3 [  95  95 = 8:.::: + 99.450∐els ( 92: · 80 ‛ 4; ‛ + :0 · 52 42 ' 

' 

) =88.5:3

' ' 

 Z 98 =45.2:4 + 95.5:0∐UBO ( 04 · 84 ‛ 4; ' ‛ +:0 · 52 ' 42 ' ' )=4:.6;2 [  98  98 = 8:.::: + 95.5:0∐els ( 04 · 84 ‛ 4; ' ‛ + :0 · 52 ' 42 ' ' )= 53.4:2

92

 

VTIEXKEI 69 XLVL@TICKI

:.4.5. ITBI Z9 = 32.0;

[9= 36.06

Z4= 98.030 Z5= 99.266

[4=35.996 [5= 53.342

Z8= 32.9; Z9=32.0;

[8=5:.436 [9=36.06

 I pln =

 I pln =

 I pln =

∙  Z[ ∔∙ [Z  4

;,6:;.:09∔3,243.:59 4

4,235.68 4

 4 =9,4:9.24 M  4

;. ELOENRUKLO In jidbr oinkzihl bn prbsbotb koclrmb, plhbmls hirols euboti hb ni `rio kmplrtioeki qub plsbb ni okvbniekõo trk`lolmëtrkei ipnkeihi i nls prlybetls hb ko`bokbríi k o`bokbríi ekvkn.

Vubstl qub eihi mbhkekõo, eihi hbtinnb y bn rbspbevl eéneunl hb nls puotls hb ni plnk`loin nbviotihi cubrlo rbinkzihls y rbvksihl eukhihlsimbotb, y bn mir`bo hb brrlr bo ni préeei bs míokml.

93

 

VTIEXKEI 69 XLVL@TICKI

Hb k`uin clrmi eumpnkmls elo nls ldgbvls pniotbihls in prkoekpkl hb bstb koclrmb, drkohéohl drkoh éohlols ols oubvl oubvlss elolek elolekmkbotl mkbotlss piri slnueklo slnuekloir ir prld prldnbmis nbmis hb okvbni okvbniekõo ekõo bo uo tbrrbol.

90