diseño de intalaciones mineras

8/3/2019 Diseño de intalaciones mineras

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Hnclre

fnehectl

s.e. fl B._.

Hnce li rey`

Fnslõ` fl ncsteiebn`cls

hnclres

M`czåilz Emunier Fecnli Hertèc



Nctr`fubbnòc

Fet`s mlclreils fli lstef` fl puljie

Oeuce

Oi`re

Lstretnmreoèe

Ml`i`mèe lstrubturei

@r`mreoèe

Dnfr`mreoèeBinhe

Ml`i`mèe lb`còhnbe

Fet`s fli pr`ylbt`

? H¶s pere hnce

\jnbebnòc fli pr`ylbt`

Fet`s tîbcnb`s y båibui`s

_lctniebnòc

? H¶s pere vlctniebnòc

Bectnfef fl plrs`cei

Bectnfef fl enrl rlqulrnf`

Fnemrehe fl ie hnce

Ècfnbl



Enrl b`hprnhnf`

Hequncerne e utninzer

Fet`s mlclreils fl ie hequncerne

Båibui` fl bectnfef enrl b`hprnhnf` e utninzer

Rlilbbnòc fli b`hprls`r

Beibui` lstnhef` fl ie cevl ncfustrnei pere b`hprls`rls.

Fnslõ` fl ie erhefure.

Jnjin`mreoèe y Zlolrlcbnes



Li prlslctl pr`ylbt` hnclr` fe uce plrsplbtnve fl i`s

trejea`s y iej`rls qul sl iilvec e bej` lc li trejea` hnclr`,sl fe uce flsbrnpbnòc fli lct`rc` qul r`fle ei pr`ylbt` yequl ls fl suhe nhp`rtecbne tlclr lc bulcte i`s p`snjilsnhpebt`s e ie s`bnlfef, hlfn` ehjnlctl y ie lb`còhne fliiumer. I` ectlrn`rhlctl hlcbn`cef` bejl lc uc s`i`

pr`pòsnt` iilver e bej` uce lxpi`tebnòc fl i`s rlburs`shnclreils lc li lstef` fl puljie fl ie hla`r heclre p`snjilb`c rlsp`csejninfef s`bnei y hlfn`ehjnlctei.

Nctr`fubbnòc



Rlr uce lhprlse ièflr lc ie lxtrebbnòc fl hlteils

prlbn`s`s lc li peès.Zleinzer ebtnvnfefls fl blrtnonbebnòc lc i`s pr`bls`s

fl lxpi`tebnòc slmure y hecla` fl rlsnfu`splinmr`s`s.

Rlr lhprlse b`c blrtnonbebnòc fl beinfef fl suspr`fubt`s.

@jaltnv`s



Wuljie `bupe ie :5ª p`snbnòc lctrl ies 2: lctnfeflsolflretnves hlxnbeces p`r su suplronbnl fl

26,:<5.77 kniòhltr`s buefref`s. Inhnte ei c`rtlb`c li lstef` fl Dnfeim`; ei lstl, b`c li lstef` fl_lrebruz; ei sur, b`c @exebe y Mulrrlr`; y ei

p`cnlctl b`c i`s lstef`s fl H`rli`s, Hîxnb`,

Viexbeie l Dnfeim`. Ie hey`r pertl fli tlrrnt`rn` p`jiec` sl lcbulctre lc li lal Cl`v`ibåcnb`. Libinhe ls b`ctrestectl, y ve fli orè` fl ies eitesh`cteões ei båinf` slhnflsîrtnb` fl ie Hnxtlbe.

FEV@R MLCLZEILR FLI LRVEF@ FLW\LJIE



http://es.wikipedia.org/wiki/Archivo:Puebla_en_M%C3%A9xico.svg



OE\CE

Li b`cauct` fl ecnheils qul vnvlc lc uc fltlrhncef` iumer. Ru oeuce slb`hp`cl fl i`s snmunlctls ecnheils berebtlrèstnb`s fl ie rlmnòc1Hehèolr`s (b`y`tls, z`rres, z`rrnii`s, hepebdls, tiebuebdls); Z`lf`rls(b`cla`s, erfniies, retes, inljrls); Zlptnils (slrpnlctls fl besbejli,b`reinii`s, ret`clres, iemertnaes, lsb`rpn`cls); Ecnheils f`hîstnb`s(plrr`s, met`s, vebes, bejeii`s, esc`s, pulrb`s, evls fl b`rrei, bdnv`s,

`vlaes); Ncslbt`s (h`sbes, cnmues, zecbuf`s, puimes).



OI@ZE

Ie oi`re fl uce rlmnòc sl berebtlrnze p`r su ejucfectl ` p`be vlmltebnòc,y sl hecnonlste fl ebulrf` e ie tlhplreture y duhlfef fli suli`; ierlmnòc bulcte b`c uce vlmltebnòc qul c` ls huy lxujlrectl, plr`tehp`b` requètnbe, snc lhjerm` lcb`ctreh`s mrec vernlfef fl årj`ilsb`h` s`c1 Li hlzquntl, li pnrui, nz`tls, c`peils, het`rreils, pnl flliloectl, x`b`c`ztil, li bezeduetl, jnzcemes, hemulyls, bebtus y eioeioe;eflhås bulcte b`c, oi`rls fl `rcet` b`h` mlrecn`s, jumecvnines, bievlr`s,

r`ses y `tres.



Ie cetureilzeml`iòmnbe fli tlrrnt`rn` p`jiec` ls vernefe y jestectl b`hpilae,lsplbneihlctl lc su

p`rbnòc sur, f`cfl sllcbulctrec tlrrlc`shltehòronb`s b`c

lfefls fliWrlbåhjrnb`,Weil`z`nb` y

Hls`z`nb`, i`s bueilssl deiiec yuxtepulst`sy inhntef`s p`r mrecfls

z`ces fl oeiie.



LRVZEVNMZEONE

Wrlbåhjrnb`

Lc ie pertl surlstl fli lstef` eoi`rec plqulõ`s bulrp`s fl r`beshltehòronbes fl lfef mrlcvniinece, plrtlclbnlctls e ie pertl håsslptlctrn`cei fli tlrrlc` hltehòronb` b`c`bnf` b`h` B`hpila`@exequlõ`, li buei eperlbl rlprlslctef` bert`mråonbehlctl b`c iebievl WL (Mc). Lstes r`bes s`c ies hås ectnmues fl ie lctnfef, b`c

>77-5577 hnii`cls fl eõ`s, qul ies sntñec lc li Wr`tlr`z`nb`Hlfn`. R`c r`bes hltehòronbes fl eit` mref`, fl ies oebnls flmrecuinte y econj`inte, b`cstntunfes p`r mclns, bderc`knte,ec`rt`snte y plmhetnte. Eoi`rec, lc li hucnbnpn` fl Beitlplb, lco`rhe fl vlcteces ml`iòmnbes fl p`be lxtlcsnòc.



Weil`z`nb`

Lc ie hey`r pertl fli lxtrlh` sur`lstl fli lstef`, lc uce z`celcherbefe epr`xnhefehlctl, p`r ies i`beinfefls fl Bdneutie, Nzñberfl Heteh`r`s, Duldultiåc, Recte Ncîs y Eduetlhpec, eoi`rec r`beshltehòronbes fli B`hpila` Ebetiåc, fli Weil`z`nb` Ncolrn`r, b`c håsfl 2<7 hnii`cls fl eõ`s fl ectnmùlfef. Li B`hpila` Ebetiåc ls fl uceint`i`mèe vernefe y lstå nctlmref` p`r cuhlr`ses o`rhebn`cls fnvnfnfeslc f`s sujmrup`s1 Wltieibncm` y Ebetlb`.Li Weil`z`nb` Ruplrn`r (Wlcsnivåcnb`) lstå rlprlslctef` p`ro`rhebn`cls c` hlteh`ro`slefes nctlmrefes p`r f`s slbulcbnesslfnhlcternes, plrtlclbnlctls e ie o`rhebnòc Hetzntzn, qul flsbecsecfnsb`rfectlhlctl s`jrl ies r`bes fli B`hpila` Ebetiåc.



Hls`z`nb`

Ies r`bes hls`z`nbes hås ectnmues flctr` fli lstef`, plrtlclblc ei

plrè`f` Vrnåsnb` y lståc rlprlslctefes p`r uce p`tlctl slbulcbne flslfnhlct`s b`ctnclcteils (ilbd`s r`a`s) plrtlclbnlctls e ieo`rhebnòc Dunzebdei. Ie slbulcbne b`cste fl erlcnsbe,b`cmi`hlref` y eimuces bepes fl iutnte erlc`se VZ (er-bm), qulo`rhec lstret`s hesnv`s y flimef`s y sujyeblc lc fnsb`rfecbne

ecmuier e i`s flpòsnt`s fli Auråsnb` Ncolrn`r. Rl i`beinze ei `lstl flDueubdncecm`, e i` ierm` fl uce mrec lstrubture fl pilmehnlct`b`c `rnlctebnòc c`r`lstl-surlstl b`c`bnfe b`h` li Ectnbinc`rn` flDueyeb`b`tie, lc ie Rnlrre Hefrl @rnlctei.



Blc`z`nb`

Lc ie pertl c`rtl fli lstef`, ies r`bes slfnhlcternes fli

Blc`z`nb` s`c t`fes fl tnp` biåstnb`. Oulr`c flp`sntefes flheclre pr`mrefectl lc orecaes pereilies e ie b`ste fli M`io` flHîxnb`; fl tei o`rhe qul eoi`rec flpòsnt`s fli Weil`blc`,L`blc` y @inm`blc`1 Fli prnhlr`, i` rlprlslcte ie ucnfefVpei(iu-er), qul lstå o`rhefe p`r uce nctlrlstretnonbebnòc fl iutnte

y erlcnsbe (slbulcbne tnp` oiysbd), qul prlslctec duliies fl pnstesfl `rmecnsh`s; s`jrlyebl lc b`cb`rfecbne e ies ucnfefls flbeinze y iutnte fli Brltåbnb` Ruplrn`r. Wlrtlclblc e ie o`rhebnòcBdnb`ctlplb y sl sntñec lctrl ies pertls jeaes fl ie Rnlrre Hefrl@rnlctei y ie Wiecnbnl B`stlre fli M`io` C`rtl, lc i`s lxtrlh`sc`rtl y surlstl fl ie lctnfef.



Buetlrcern`

I`s flrrehls jesåitnb`s fli Buetlrcern`, U(Nmlj), o`rhec

pertl fli vìbecnsh` jåsnb` qul fn` `rnmlc e ie b`conmurebnòctèpnbe fli Lal Cl`vìbåcnb`. Vnlclc uce lxtlcsnòc ehpine,lsplbneihlctl flsfl ie z`ce blctr``bbnflctei deste ie pertlblctr``rnlctei fli lstef`; lc f`cfl b`cstntuylc cuhlr`s`seperet`s vìbåcnb`s, flpòsnt`s pnr`biåstnb`s y flrrehls. Lc ie

berte mlìòmnbe, lste ucnfef ncbiuyl r`bes iåvnbes jesåitnbes flvernefe tlxture, flpòsnt`s fl hetlrnei pnr`biåstnb` fl teheõ`fl "iepniin", mrec bectnfef fl blcnze once y lsb`rne; esè b`h`

ji`quls y "j`hjes" fl fnolrlctl teheõ`, qul sl lcbulctreclsbesehlctl b`csìnfef`s y i`beihlctl lstretnonbef`s.



ML@I@MNE LRVZ\BV\ZEI

Debne ie pertl c`rtl fli lstef`, ies lstrubtures sl hecnonlstec lc

ectnbinceils y sncbinceils -rlb`stef`s debne li c`rlstl-. I`s pinlmulso`rhec pertl fli ectnbinc`rn` fl Dueyeb`b`tie, qul ls uce mrechlmelstrubture qul sl lxtnlcfl flsfl i`s lstef`s vlbnc`s flDnfeim` y _lrebruz, b`c uce `rnlctebnòc c`r`lstl-surlstl y rlhetelc Wuljie ei nctlrslbtersl b`c li Lal Cl`vìbåcnb`.

I`s bulrp`s nctrusnv`s qul eolbtec ie slbulcbne fli Hls`z`nbòulr`c ncylbtef`s furectl li plrè`f` hås ebtnv` fl ie oesl`r`mîcnbe ierehèfnbe qul tuv` iumer flsfl oncls fli Brltåbnb` destehlfnef`s fl ie lre tlrbnerne. Ies oeiies y orebtures fl tnp` c`rhei sles`bnec b`c ies oesls cl`tlbtòcnbes, y eolbtec tect` e ies r`bes fliHls`z`nb`, b`h` e ies fli Vlrbnern`, qul sl lxtnlcflc debne ieWiecnbnl B`stlre fli Mìo` C`rtl, pr`pnbnecf` li esplbt`lsbei`cef` fl ie iiecure.



@Z@MZEONE

Ie b`hucnfef sllcbulctre r`flefe p`r

eimuc`s blrr`s b`h`s`c1 Ei C`rtl li blrr`Muefeiupl, ei C`r`lstl-li B`eyube, V`ceaèe,V`cbdntzl, Ie Bulste y

Viebuetzncm`.



DNFZ@MZEONE

Lc buect` e ie Dnfr`mreoèe slfnbl ie lxnstlcbne fl uc rè`

sujtlrråcl` iiehef` rè` V`ct`,lstes emues pr`vnlclc fli Wnb`fl @rnzeje y iilmec deste iebnufef fl Vlduebåc pesecf`

p`r i`s perquls Auårlz lDnfeim`. Vehjnîc ieb`hucnfef bulcte b`c p`z`s flemue, ye qul ie hey`rèe fl ie

p`jiebnòc ie utninze pere

prlperer sus einhlct`s. \c fet`nhp`rtectl ls qulBueyubetlplb suhncnstre lcmrec pertl li emue qul b`csuhlie p`jiebnòc fl ie bnufef fl

Vlduebåc.



BINHE

LI binhe, ls li b`cauct`fl b`cfnbn`clseth`soîrnbe qul lxnstlclc uce rlmnòc,Bueyubetlplb, lsteeslctef` lc uce z`cepiece b`c lilvebn`cls

p`b` eites, lc li buei slrlprlslctec f`s tnp`s flbinhe tlhpief` y slhn-slb` b`c p`bes iiuvnes eieõ`, lste p`jiebnòc

bulcte b`c uc binhetlhpief` y b`c ucetlhplreture fl 27· B. Lisujsuli` ls huyerbnii`s` y suhehlctlfur` lc eimuc`s iumerlsy jiecf` lc `tr`s.



ML@I@MNE LB@C@HNBE

Lc ie lctnfef, dey uce herbefe fnolrlcbne lc buect` e i`s rlburs`shnclreils, ye qul prlf`hncec ies z`ces lc f`cfl sl lxpi`technclreils c` hltåinb`s y s`c lsbes`s i`s eoi`rehnlct`s `hecnolstebn cls fl yebnhnlct`s hltåinb`s.Fl tei o`rhe qul ie pr`fubbnòc fl hnclreils c` hltåinb`s ls jestectlsnmcnonbetnve, p`r lalhpi` Wuljie de snf` li ñcnb` lstef` pr`fubt`r flhemclsnte e cnvli cebn`cei furectl li plrè`f` 5>4<-5>>6; fl nmueio`rhe `bupe li prnhlr iumer lc ie lxtrebbnòc fl oliflspet`, plrinte yteib`. Lc buect` e i`s hlteils, ls fl p`be nhp`rtecbne y e cnvlicebn`cei b`ctrnjuyl lc i`s ñitnh`s eõ`s b`c p`b` hås fli 5%. I`s

prncbnpeils hlteils qul sl jlclonbnec s`c `r`, piete, b`jrl y pi`h`.



I`beinzebnòc fl ie hnce

Dlr`nbe Wuljie fl Qerem`ze, tehjnîc b`c`bnfeb`h` Wuljie fl i`s Åcmlils, ls uc hucnbnpn` ybepntei fli lstef` fl Wuljie, Hîxnb`. Wuljie ls iebuerte bnufef hås mrecfl fl Hîxnb`, flspuîs flie Bnufef fl Hîxnb`, Muefeieaere y H`ctlrrly; y e

ie vlz ie buerte årle hltr`p`intece hås mrecfl flHîxnb`. Vnlcl uce eitntuf fl :56= hsch, b`cb``rflcefes fl 5>·7:›62′ C y >4·55›<5′@

FEV@R FLI WZ@^LBV@



B``rflcefes1 5>·6=':>.25"C y >=·24'25.7?"]

Lilvebnòc1 :677 hsch

E uce fnstecbne fl ie bnufef fl Qerem`ze fl :==? h



Li årle t`tei fl ie hnce ls fl :=.6257? kh: qul ls

lqunveilctl e :,=62.57? dlbtårles.



B`h` p`flh`s `jslrver lc li hepe fl p`tlcbnei ml`iòmnb` fl ierlpujinbe hlxnbece tlclh`s sntuef` e puljie lc uc årle b`c

hnclreinzebn`cls fl Eu-Em-Bu y p`snjilhlctl Qc-Wj.



FEV@R VÎBCNB@R FLI WZ@^LBV@

O`rhe mlclrei fli yebnhnlct`1

Bulrp` tejuier, lspls`r fl ecm`st` e nctlrhlfn`, lbdef` flvlrtnbei e bnlrte ncbincebnòc hey`r e <7·, fnstrnjubnòc fl ily flucno`rhl e mrefuei, ily pr`hlfn` fl 57 m/t`c fl @r` y 277 m/t`cfl Wiete. Flcsnfef fli hnclrei :.4 t`c/h2, flcsnfef fl r`belcbea`cectl :.? t`c/h2

Berebtlrèstnbes tejie fli jea`1Zlsnstlcbne fl ie r`be fl h`flrefe e oulrtl, lspebnehnlct` lctrl

orebtures blrrefe, rliilc` fl sèinbl lc orebtures lc eimuces pertls.Berebtlrèstnbes tejie fli eit`1Zlsnstlcbne fl ie r`be h`flrefe, lspebnehnlct` lctrl orebtures

p`b` ejnlrt` hlc`r e : hh, rliilc` fl beibnte y sèinbl.



ECEINRNR ?H¶R WEZE HNCE HEC@ FL @JZE

Fnrlbtnv`s Mlrlcbne Ruplrnctlcflcbne Alol fl Hnce Ruplrvnsnòc

Ml`i`mèe V`p`mreoèe Hnce Rlmurnfef Hectlcnhnlct` (Hlbåcnb`s, Liîbtrnb`s, _lctniebnòc)

J.F.F Buefrniies fl Vrejeaef`rls (Hulstrlr`s, Rlrvnbn`s, W`iv`rnc,Wlro`rnstes)

@plref`rls fl Lqunp` y Hequncerne Buefrniie fl Wrnhlr`s Euxnin`s

Inhpnlze



HLV@F@ (B`rtl y Zliilc`)

ZehpeBrublr`sB`ctre p`z`sOrlctl

B`ctreolctlJerrlcebnòcVnr`R`bevòcHeiebetlHectl`Br`c`mrehe fl Ebtnvnfefls e Zleinzer



HEU\NCEZNE ^ LU\NW@

Rb``ptreh Mòcf`ies F`jil trebbnòc Håqunce fl pnlrce Auhj` _lctnief`rls

Vrebt`r Behn`cls fl Jea` Wlroni Håqunce fl R`ifer Håqunce fl Lxpi`rebnòc

B`hprls`rls J`hjes MWR Lstebnòc t`tei



HEVLZNEI

Hecmulres

Lxpi`snv`s Heflre Emue Bulrfes Vuj`s pere Jerrlcebnòc

V`rcnii`s, Vulrbes y Z`cfeces Jr`bes Vujlrèe pere vlctniebnòc y emue Lhpequls

Iiectes Iujrnbectls

B`hjustnjils Jerres Ecbies Iievls Hecmes

Lsbeilres Blrbdes



HLFNBN@CLR

V`clieal V`tei V`c/Fèe Fòierls/V`cliefe Fòierls/Hltr` inclei Kni`hltreal fli Lqunp`

D`res Vrejeaefes fli Lqunp` @plrebnòc fli Lqunp` Hectlcnhnlct` Wrlvlctnv` fli lqunp` y

hequncerne

Evecbl lc ies @jres lc Flserr`ii` Vnlhp`s lc @jres lc Flserr`ii` Lstef` fl i`s Lqunp`s y Hequncerne



HLFN@ EHJNLCVL

Iumerls Rlmur`s pere Vrejeaer Lqunp` fl Wr`tlbbnòc Wlrs`cei _lctniebnòc flctr` fl ie Hnce Flsbecs`s Zlsplt` iej`rei B`hucnbebnòc Reiuf fli plrs`cei



_lctniebnòc

Lc ie ebtueinfef ls flsuhe nhp`rtecbne qult`fes equliies iej`rlshnclres tlcmec uceeflbuefe vlctniebnòc, libåibui` fl uc julcsnstlhe fl vlctniebnòcrlplrbutl lc i`s b`st`s

lclrmîtnb`s y lc iesb`cfnbn`cls iej`reils fli`s trejeaef`rls, p`r lii`ie nhp`rtecbne.



HEC@ FL @JZE

Wieclebnòc (pr`ylbtnste)

Ruplrvns`r

Wiectniie fl `jrlr`s

?H„R WEZE _LCVNIEBN@C

HÎV@F@R

Wiec`s pere ie ncsteiebnòc fli vlctnief`r y/` lxtrebt`r Hecuei pere li lcsehjieal fl ies pnlzes fli vlctnief`r y/` lxtrebt`r

Båibui`s fli Zlqulrnhnlct` fl enrl pere ie vlctniebnòc

Wr`mrehe fl hectlcnhnlct` e i`s vlctnief`rls y/` lxtrebt`rls



HLFNBN@CLR

Zlvnser Mest` fl enrl lc ies fnolrlctls `jres

Zlvnser li oucbn`cehnlct` fl i`s vlctnief`rls y lxtrebt`rls

Zlvnser ie vli`bnfef fli enrl

Zlvnser ie rlbnrbuiebnòc fli enrl flctr` fl ie hnce

HEU\NCEZNE ^ LU\NW@

Mrñe

Hequnce fl R`ifer



HEVLZNEI

Hecmes

Iievls Wnczes Mecbd`s V`cnii`s

Vulrbes Beflces

HLFN@ EHJNLCVL

Iumerls slmur`s pere trejeaer

Lqunp` fl Wr`tlbbnòc Wlrs`cei(LWW)

Iumerls b`c li suonbnlctl enrl



Hequncerne

Behnòc ertnbuief` EF27

Ie Rb``ptreh RV =

Auhj` 5? ot

Vrebt`r

Allp 6x6 ? bnincfr`s

fnlsli

Hequncerne e utninzer qul rlqunlrevlctniebnòc



Behnòc ertnbuief` EF27



Ie Rb``ptreh RV = fl Eties B`pb`

Ls uce peie r`juste b`cbljnfe pere ies epinbebn`cls hås lxnmlctls, su

plqulõ` teheõ` b`hjncef` b`c li eit` rlcfnhnlct` s`c ie bievl pere`jtlclr ie hey`r pr`fubtnvnfef.Ie RV= tnlcl uce bepebnfef fl berme fl ?,4 t`cliefes, fnrlbbnòcertnbuiefe y lal treslr` `sbniectl. Ls einhlctefe p`r uce b`hjustnòcinhpne, h`t`r 5>2 B_ ?,= intr`s Buhhncs Vnlr 2 y bulcte b`c

prlstebn`cls fl b`ctr`i fl trebbnòc pere `jtlclr uc hey`rrlcfnhnlct` fl berme y hla`rer ie vnfe ñtni fl i`s cluhåtnb`s. Lisnstlhe dnfråuinb` slcsnjil fl berme euhlcte ie trebbnòc y lb`c`hnzeli b`hjustnjil.



Fet`s tîbcnb`s RV=

Zlb`hlcfebn`cls ecbd` fl ie ebuhuiebnòc fl 2,5 hBepebnfef fl berme ?.477 kmBepebnfef fli bez` 2,5 h2

Oulrze fl errecqul hlbåcnbe 55,=<7 kmOulrze fl errecqul dnfråuinbe 52,2<7 kmWls` `plretnv` fli vldèbui` 5>.277 km

I`cmntuf 4.?:7 hEiture, tlaefnii`/bejnce :.5?7 h

Eiture håxnhe fli bez`, håx. 6.=57 hEcbdure, :.5:7 hh fl vldèbui`s

C`rhe h t`r fnlsli Buhhncs b`c h`t`r fnlsli fl URJ?.=

LWE Vnlr 2/L\ Rteml NNNEW`tlcbne e :.:77 rph 566 k]/5>2dp

Fnhlcsn`cls fl i`s cluhåtnb`s 5=,< Z:< F: T-Hnce



Vrebt`r HO:4< Hessly Olrmus`c

I`s trebt`rls s`c utninzef`s

lc eimuces hnces pere litrecsp`rtl fl plrs`cei ytrecsp`rtl fl hetlrneilsb`h` hequnces fl pnlrce,rloebbn`cls, lxpi`snv`s,

hecla` fl lsbrlpes, lctrl`tr`s.



Lsbrlpe

Ie lsbrlpe ls uc ncstruhlct`fl trejea` fl mrec utninfef pere li h`vnhnlct` fl tnlrre, pere ie dlbdure fl j`rf`s,lhperlaer y rlperer behnc`s,rliilcer tlrrlc`s, ltb.

Ru oulrtl bdesns fl iehnce2/5?" il merectnze uce iermevnfe ñtni lc su behp`. Rl pulfl utninzer p`r bueiqunlrtrebt`r b`c uce

p`tlcbne hècnhe fl ?7 D.W.



6 Rb``ptreh RV = fl Eties B`pb`

Bepebnfef 8 2.5 h2 x >7 % fl iilcef` 8 :.4 h2 lolbtnv`s

V`tei fl h2 p`r fèe1 2777 t`cliefes / :.4 t`c/h2 8 57=5.< h2Flcsnfef fli hnclrei 1 :.4 t`c/h2W`rblcteal fl ejucfehnlct`1 27%

I`s h2 p`r fèe sl il suhe li 27% p`r ejucfehnlct`.

H2 t`teils 8 57=5.< h2 x 5.2 8 52>2 h2 p`r fèe.

Rl fnvnfl lc i`s 2 turc`s pere `jtlclr li t`clieal p`r turc`1 52>2 / 2

8 6?< h2 p`r turc`.

6?< h2 / :.4 h2 p`r bubderefe / 6 Rb``ptreh 8 6: bubderefes p`rRb``ptreh p`r turc` b`c < d`res lolbtnves.

Båibui` fl bepebnfef p`r lqunp`

Lqunp` Auhj` fl 6 4=?4 h



Lqunp` Hequnce fl pnlrce fl :.6246 h

Fnhlcsn`cls fl ie orlctl 2 x 2 h

>:% fl Zlbuplrebnòc (lonbnlcbne)

_ìuhlc p`r orlctl 8 2 x 2 x :.6246 x 7.>:

_ìuhlc p`r fnsper` lc orlctl 8 :7.: h2

Lqunp` Auhj` fl 6.4=?4 h

Fnhlcsn`cls fl ebbls` e s`bevòc

y jres fl flserrìi` 6 x 6.< h

>:% fl Zlbuplrebnòc (lonbnlcbne)

_ìuhlc p`r orlctl 8 6 x 6.< x

6.4=?4 x 7.>:

_ìuhlc p`r fnsper` fl evecbl fl

`jre 8 47.=? h2

Flcsnfef fl ie Z`be Lcbea`cectl1 :.?

Flcsnfef fli Hnclrei Eu-Em1 :.4

V`clieal jtlcnf` fl hnclrei p`r vìefure 8 :7.: h2 x :.4

<?.<? t`cliefes p`r fnsper`



Cuhlr` fl fnsper`s p`r fèe12777 t`cliefes p`r fèe / <?.<? t`cliefes p`r fnsper`

# fnsper`s 8 <2.7657 8 <6 fnsper`s ei fèe

Ed`re sl `jtlcfrå li cuhlr` fl orlctls fl ie hnce.<6 fnsper`s / 2 turc`s 8 54 orlctls

Cuhlr` fl orlctls y hequnces fl pnlrce1

Rup`cnlcf` qul sl tnlcl uce lonbnlcbne fli >7% lc pieclebnòcslrne1

54 orlctls / >7% 8 :7 orlctls

Rl rlqulrnråc :7 hequnces fl pnlrce pere plro`rebnòc,fnsp`cnjninfef p`r `plrebnòc >:% epr`xnhefehlctl.

:7 hequnces / >:% 8 :: hequnces fl pnlrce.



Bectnfef fl plrs`cei 1

:: Wlro`ref`rls , :: eyufectls pere befe hequnce fl pnlrce p`rturc`.>2% fl esnstlcbne fli plrs`cei.Ei slr lc perlae fl trejea` sl sebere li t`tei fl plrs`cei lc jesl e

befe hequnce fl pnlrce.

Bectnfef fl plrs`cei 8 ::/>2% 8 :6 plro`rnstes.W`r b`csnmunlctl s`c :6 eyufectls fl plro`rnste.

«C@VE1 Ie bectnfef fl hequnces fl pnlrce beibuiefe sl utninzerelc ie slbbnòc fl enrl b`hprnhnf`.»



Zlqulrnhnlct` fl vlctniebnòc «Derthec»

Hequncerne

Hequncerne Bectnfef Dp H2/hnc V`tei H2/hnc

Mòcf`ie :7 2== 2 ::,?:7

Auhj` : :77 2 5,:77

Vrebt`r 2 47 2 =:7 Allp ? :7: 2 5,:5<

Rb``ptreh 6 5>2 2 :,25?

V@VEI :4,7=5 h2/hnc

W i



Wlrs`cei p`r turc`Iej`r Bectnfef

Wlrs`cesh2/hnc fl enrlp`r plrs`ce Dert.

V`tei fl Enrl lch2/hnc

Ruplrvnsnòc 2 7.? 5.4Wlro`rebnòc 64 7.? :4.4

@plrebnòc 2: 7.? 5>.:

Ml`i`mèe 5< 7.? >

V`p`mreoèe 57 7.? ?

Rlrvnbn`s 4 7.? 6.4

_nsntes 5< 7.? >

V@VEI 5:4 =4.? h2/hnc



Fl 7.77 hsch e 5<77 hsch 2.7 h2/hnc. W`r befe trejeaef`r.

Fl 5<75 hsch e 2777 hsch 6.: h2/hnc. W`r Befe Vrejeaef`r.

Fl 2775 hsch e 6777 hsch <.5 h2/hnc. W`r Befe Vrejeaef`r.

Fl 6775 hsch e + hsch ?.7 h2/hnc. W`r Befe Vrejeaef`r.

Fl 5<75 hsch e 2777 hsch 6.: h2/hnc. W`r Befe Vrejeaef`r. Ie

eiture fl ie bnufef ls fl :677 hsch.

Rlrèe uc t`tei fl 525 x 6.: h2/hnc 8 <<7.: h2/hnc slmñc ielilvebnòc.

BECVNFEF FL ENZL W@Z WLZR@CE RLMÑC EIV\ZE

V t i f n n t f tni nò



V`tei fl rlqulrnhnlct` fl vlctniebnòc

Rlmñc Derthec 8 :4,56>.? h2/hnc

Rlmñc Derthec y eiture 8 :4,?:5.: h2/hnc

\ce hnce sujtlrråcle clblsnte 57 t`cliefes fl enrlorlsb` p`r befe t`cliefe fl hnclrei.

2777 t`c/fèe Rl rlqunlrl 27,777 t`c fl enrl orlsb`.

\ce hnce hlbecnzefe b`c b`rtl y rliilc` b`c lqunp`fnlsli tnlcl uc oiua` fl enrl fl 5: t`cliefes fl enrl p`r

t`cliefe fl hnclrei.

2777 t`c/fèe Rl rlqunlrl 2?,777 t`c fl enrl orlsb`

Rlmñc injr` Derf Z`bk

Rlmñc c`rhe 7:2, ncbns` 5:, epîcfnbl FFet` H2/hnc Dp t`tei V`tei plrs`ces V`tei h2/hnc

Hequnce :.52 57,5?6 :5,?6>.2:

Wlrs`ce 5.< 525 5>?.<

V@VEI :5,46<.4:



I` ectlrn`r c`s fe li rlqulrnhnlct` t`tei fl vlctniebnòc

fl ie hnce1

2<,?2:.65 h2/hnc ò 5,:<4,2<4.24< ot2/hnc

Ed`re sl pese e fer uc bnbi` slcbnii` fl vlctniebnòc y`pbn`cls fl vlctniebnòc y lxtrebbnòc tect` o`rzefesb`h` cetureils.



Berbeze fl eblr` ei berjòc, pnctefe b`c pncturelilbtr`lståtnbe y d`rclefe. Espe fl eiuhncn` ectn-bdnspe.

Ebbn`cef` p`r eb`piehnlct` fnrlbt` e uc h`t`r liîbtrnb`.

_lctnief`r Enr Hestlr

EIM\CER BEZEBVLZNRVNBER1- Fnåhltr` fl espe flsfl 5?" deste :?".

- H`t`rls lc vìteal 5:=/::7_. y ::7/667_.(Espes e pertnr fl :6" sì` p`fråc iilver h`t`rb`c vìteal ::7/667_).- _ìñhlcls fl enrl1 6,:77 deste 54,=:< WBH.Wrlsnòc flsfl 7.:" deste :.<" bìuhce fl emue.



Berbeze fl eblr` ei berjòc, pnctefe b`c pncture lilbtr`lståtnbe y

d`rclefe. Vlhplreture håxnhe fl `plrebnòc1 4<±B (54<±O). Espefl eiuhncn` ectn-bdnspe.

Enr hestlr lxtrebt`r

EIM\CER BEZEBVLZNRVNBER1- Fnehltr` fl espe flsfl 57" deste 64".- H`t`r oulre fli Oiua` fl enrl.- H`t`rls lc vìteal 5:=/::7_. y ::7/667_.- _ìñhlcls fl enrl1 5,56? e 25,677 WBH.Wrlsnòc flsfl 7.:" deste :.<" bìuhce flemue.



I`s b`ctrep`z`s s`c `rnonbn`s qul tnlcflc e ie vlrtnbei b`c li

`jaltnv` fl suhncnstrer enrl orlsb` e ie hnce ` lc `tr` bes` seberli enrl vnbnef`. I`s b`ctrep`z`s e utninzer slråc fl 5h flfnåhltr` y sl deråc i`s clblsern`s pere qul li beufei sle li

pr`pnbn` pere uce julce iej`r, lst`s auct`s b`c ie vlctniebnòco`rzefe y tñcli fl ebbls` slråc i`s suhncnstr`s fl enrl inhpn` eie hnce.

B`ctrep`z` pere vlctniebnòc



Fnemrehe pni`t` fl vlctniebnòc fl ie hnce



Enrl b`hprnhnf`

Li enrl b`hprnhnf` ls uc` fl i`s lilhlct`s hesnhp`rtectls fl ies `plrebn`cls hnclres, c` s`i` lc

ies `plrebn`cls jåsnbes fl plro`rebnòc, snc` euc lcies `plrebn`cls slbucfernes. p`frèeh`s flbnr qul pråbtnbehlctl ls uc

lclrmîtnb` ncfnsplcsejil lc t`f` trejea` bnvninzef`.

I`s h`t`rls cluhåtnb`s pulflc `plrer lcb`cfnbn`cls qul s`c flsoev`rejils pere liîbtrnbes,dnfråuinbes, pes` e pes` y slrv`h`t`rls.



Hequncerne cluhåtnbe e utninzer

Hequncerne Bectnfef B`csuh` fl enrlot2/hnc

B`csuh`h2/hnc

V`teiot2/hnc

Heiebetl : :57 <.>6?< 6:7

Wlro`ref`re :: 5:? 2.<?4 :,==:

J`hje V-4 5< ?7 5.?>> >77

Lspnme 57 576 :.>6< <:7

Orlctlre 57 525 2.=5 ?<<

Rprey Mucs 6 5< 7.6:64 ?7

V@VEI <,2:=

C`tes15h2/hnc 8 2<.25< ot2/hnc.

I`s båibui`s s`c dlbd`s ei cnvli fli her

Eitureh

Eiture ot WrlsnòcJer`hîtrnbe

WrlsnòcEth`soîrnbe

O. prlsnòc e >7 psn O. eiture

:677 =4=< ::.62=< 57.>: 5.:>=5 5.:<>4

H i



Heiebetl



J`hjes wniflc V-4

o f n



Wlro`ref`re 2 nc



5.- Li pnstòc sl lcbulctre ei oncei fl su berrlre fl rltr`bls` y lstå

inst` pere b`hlczer su berrlre fl trejea`. Li enrl, e ie prlsnòc fleinhlctebnòc, iilce ie buiete (5) y pese e trevîs fl ie iuhjrlretreslre fl einhlctebnòc (:) ei bnincfr` (2). Li enrl lhpuae li pnstòcdebne efliectl, b`hlczecf` ie berrlre fl trejea`. Hnlctres, ie

pertl or`ctei fli bnincfr` (<) sl lcbulctre e ie prlsnòc eth`soîrnbe,

ei lster ejnlrte ie iuhjrlre fl lsbepl (?).

Oucbnòc fl ie hequnce fl pnlrce



:.- Li pnstòc (6) b`ctncñe eblilråcf`sl, lhpuaef` p`r ie prlsnòc fl einhlctebnòc, deste qul li j`rfl or`ctei (=) fl iebejlze fl b`ctr`i fli pnstòc bnlrre ie lctrefe fli enrl

b`hprnhnf`. Li enrl b`concef` lc ie pertl treslre fli bnincfr`(2) b`hnlcze e lxpecsn`cersl y b`ctncñe lhpuaecf` debneefliectl ei pnstòc. @jsîrvlsl qul ie bejlze fli pnstòc (6)bnlrre ie iuhjrlre fl lsbepl (?) y li lxtrlh` or`ctei sllcbulctre t`fevèe e ie prlsnòc eth`soîrnbe.

2 Li n on f i f i n ò (2) n ñ



2.- Li enrl b`concef` lc ie pertl treslre fli pnstòc (2) b`ctncñelxpecsn`cåcf`sl deste qul li j`rfl treslr` fl ie bejlze fli

pnstòc b`hnlcze e flsbujrnr ie iuhjrlre fl lsbepl (?).

Zlbuîrflsl qul ie bejlze fl b`ctr`i fli pnstòc (=) de blrref` yeie lctrefe fl enrl b`hprnhnf`, b`c i` buei c` sl heimeste li enrlb`hprnhnf` buecf`sl ejrl ie iuhjrlre fl lsbepl.Lc ie pertl or`ctei fl ie bejlze fli pnstòc de qulfef` etrepef`

enrl qul lsteje e ie prlsnòc eth`soîrnbe (<) y qul ed`re lsb`hprnhnf` deste uce prlsnòc inmlrehlctl suplrn`r e ieeth`soîrnbe.



6.- Li pnstòc b`ctncñe h`vnîcf`sl debne efliectl e beuse fl sunclrbne deste qul mìple ei efeptef`r fl buiete. Lct`cbls li j`rfltreslr` fl ie bejlze fli pnstòc (4) de flsbujnlrt` ie iuhjrlre fl

lsbepl (?) y li enrl fl ie pertl treslre ls lxpuisef` e ie ethòsolre.Hnlctres lst` sublfl, li lxtrlh` treslr` (57) fl ie bejlze flb`ctrì fli pnstòc ejrl ie iuhjrlre or`ctei fl lctrefe fli enrlb`hprnhnf` (<) qul lhpuae li pnstòc debne etrås lc ie berrlre flrltr`bls`. Furectl lste ltepe dey enrl b`hprnhnf` lhpuaecf` ei

pnstòc p`r su pertl or`ctei (<) y tehjnîc lhpuaåcfìl p`r su pertltreslre (57). Ie suplronbnl or`ctei ls hubd` hey`r qul ie treslre(57), p`r i` qul li pnstòc sl flspieze debne etrås.



<.- Li pnstòc sl eblilre debne etrås lc su berrlre fl

rltr`bls`, deste qul ie bejlze fl b`ctr`i bujrl ieiuhjrlre fl lctrefe fl enrl (57), lct`cbls, li enrl fl iez`ce (<) sl lxpecsn`ce y b`ctncñe lhpuaecf` ei pnstòcdebne etrås.



Li pnstòc b`ctncñe eblilråcf`sl debne etrås hnlctres li enrlfl ie pertl or`ctei (<) sl lxpecsn`ce deste qul li j`rfl

or`ctei fl ie bejlze fli pnstòc (55) flsbujrl ie iuhjrlre fllsbepl, li enrl lct`cbls ls etrepef` lc ie pertl p`stlrn`rfli bnincfr` (2) y sl b`hprnhl deste uce prlsnòcinmlrehlctl suplrn`r e ie eth`soîrnbe. @jsîrvlsl qul li

j`rfl or`ctei fl ie bejlze fl b`ctr`i (=) ebeje fl ejrnr ie

iuhjrlre treslre fl einhlctebnòc fl enrl b`hprnhnf`.



Ie berrlre fl rltr`bls` onceinze buecf` ie iuhjrlre treslrefl suhncnstr` fl enrl sl ejrl b`hpiltehlctl, plrhntnlcf`

ie lctrefe fli enrl b`hprnhnf` tres li pnstòc.Lst` pr`fubl uc lolbt` fl eh`rtnmuebnòc qul pr`fubl ie

perefe suevl fli pnstòc, y ei hnsh` tnlhp` sl prlpere pereuce culve berrlre fl trejea`.



Were `plrer ies plro`ref`res sl rlqunlrlenrl b`hprnhnf`, emue y

lc i` p`snjil lclrmèeliîbtrnbe, pere p`flrniuhncer li orlctl fltrejea`.

Ies beõlrèes pere enrl yemue fljlc lster e ucefnstecbne fl 54 h fliorlctl fl plro`rebnòc y iencsteiebnòc fl i`s rnlils

fljl lster deste li t`pl.



Ievef` fli t`pl

ls nhp`rtectl li ievef` fli t`pl

ye qul ectls fl ie plro`rebnòcsl tnlcl qul deblr li herbeal flie orlctl, tehjnîc eyufe enflctnonber p`snjils beèf`s flr`be b`c hey`r biernfef.

Bdlqul fl prlsnòc hec`hîtrnbe

Eyufe e vlr sn sl tnlcl uce b`rrlbte prlsnòc fl enrl, ie buei ls beibuiefe pere ies clblsnfefls fl iehequncerne cluhåtnbe.



Ie rlf fl enrl b`hprnhnf` fljl tlclr trehpes pererltlclr i`s b`cflcsef`s y sòinf`s. Li b`st` p`r pîrfnfes

fli enrl b`hprnhnf` p`r i`s lsbepls fl ie rlf lsb`csnflrejil y sl pulfl eprlbner lc ie snmunlctl tejie.



Wiectn i ies fl jerrlcebnòc



Wiectn i ies fl jerrlcebnòc

@jres fl ebbls` 6 x 6.< Auhj`

Zljeals 2 x 2Hequnce fl pnlrce

Båibui` fl rlqulrnhnlct` t`tei fl b`hprls`r



Båibui` fl rlqulrnhnlct` t`tei fl b`hprls`r

Hequncerne Bectnfef V`teiot2/hnc

Oebt`r p`reitntuf

Oebt`r p`rsnhuiteclnfe

f

V`tei ot2/hnc

Heiebetl : 6:7 6:7

Wlro`ref`re :: :,==: 5.:>=5 5.:2= plro`ref`res

6,6::.<6

J`hje V-4 5< >77 >77

Lspnme < <:7 <:7

Orlctlre < ?<< ?<<

Rprey Mucs 6 ?7 ?7

V@VEI <,2:= ?,>==.<6

Eitureh

Eitureot

WrlsnòcJer`hîtrnbe

WrlsnòcEth`soîrnbe

O. prlsnòc e >7 psn O. eiture

:677 =4=< ::.62=< 57.>: 5.:>=5 5.:<>4

Zlqulrnhnlct` ?,>==.<6 p`r ie plrfnfe fl bepebnfef flib`hprls`r qul ls fl 5.:<>4 fe uc t`tei fl1

4,=>7.27< ot2/hnc



Rl userec 6 b`hprls`rls QZ6<7 fl :??2 BOH

Lsplbnonbebn`cls fli b`hprls`r



p p

Vlcnlcf` uc rlqulrnhnlct` fl 4,=>7.27< ot2/hnc h2/hnc sluserec 6 b`hprls`rls QZ6<7 fl :??2 ot2/hnc

B`c ies snmunlctls berebtlrèstnbes1 H`t`r 6<7 K] p`r plrfnfe fl eiture slrå uc h`t`r fl <??.>

K] Wls`1 ><77 Km Fnhlcsn`cls1

E ‒ 67?7 hhJ ‒ :677 hhB ‒ :5:7 hh

Li oebt`r fl slmurnfef ls li snmunlctl1(:,??2*6)/4,=>7.27< 8 5.:5Lstl ncfnbe uc :5 % fl eh`rtnmuehnlct`.



Fnhlcsnòc fl ie cevl ncfustrnei

Fnhlcsn`cls fli

b`hprls`r1

E ‒ 67?7 hh

J ‒ :677 hh

B ‒ :5:7 hh

E

J

B



Eiture fl ie cevl ncfustrnei ls fl ? h qul ls ie : vlbls ie eiture flib`hprls`r :.6 h hes uc :7 % hes fl eiture pere oebninfef flh`vninfef .

Ies iècles r`aesrlprlslctes 5>67hh fl i`cmntuf.

Ies iècles clmres s`c iei`cmntuf fli b`hprls`r fl67?7 hh.

Ie uitnhe iècle fl slperebnòc slrå fl:777 hh p`r lolbt`s fl fnslõ`.



Li ecbd` fl ie cevl ncfustrnei lste fef` p`r : vlbls liecbd` fli b`hprls`r hes li lspebn` pere i`s b`ct`rc`s flie pulrte y `tres b`ses qul pulfec `bupersl.

? h ` 5>. ?> ot

:? h ` 4<.25 ot

? h ` 5>.?> ot

Fnhlcsnòc fl ie erhefure



Ies fnhlcsn`cls fefes ectlrn`rhlctl sl eausterec e hlfnfes hes austesqulfecf` fl1 :7 ot x :7 ot x >7 ot

>7 ot57 ot

Zliebnòcplreitl

bier` 5/2

27 ot

2=.62·

Erhefuretnp` D`wl



Beibui` fl ie erhefure

_li`bnfef fli vnlct` lcpuljie slmñc li hecuei

fl EHDRE ls fl 4< kh/dqul ls lqunveilctl e <2hniies/d. i` buei fe uceprlsnòc fl 55.:6 ij/otS: .Lst` slmñc ie o`rhuieW87.776 _S:

Were ie berme fl cnlvl lcli lstef` fl puljie sl

tnlcl ietntufls eirlflf`rfl :7· p`r i` bueiuserlh`s ie prlsnòc flberme fl cnlvl hes jeaequl slrne 57 ij/otS:.



Fet`s pere li beibui` fl ie erhefure

Ie slperebnòc lctrlerhefures fli tlbd` ls fl 57ot. ie fnstecbne lctrl vnmultniies

ls fl 5.< otLi rlbujrnhnlct` fli tlbd`ncbiuyl uce bepe fl heflrefl pnc` jiecb` fl 5 nc fllspls`r b`c uc pls` ucntern`fl 2ij/ot:.Ie erhefure tlcfre > peclilsfl 57 ot fl ecbdure lc iebulrfe ncolrn`r.

Vehjnîc tnlcl iehncemeivecnzefe b`rrumefe fl 6x 4 ot fli #54 b`c uc pls`

ucntern` fl :.2: ij/ot:. Ieerhefure sl onae lc hur`s flb`cbrlt` fl 4 nc fl lspls`r.

Ie erhefure slrå fl ejlt`ehlrnbec` f`umies onr.R`p`rtere uce berme fl:<,777 ij.



Ie i`cmntuf fli pecli flerhefure lc ie bulrfesuplrn`r lste fefe p`r

57/(B`s 22.?4).Epr`xnhefehlctl 5:.754 ot.

Beibui` fl bermes lc vnmultniiesy p`incls.

Fnhlcsn`cls fli pecli lsnmuei e 5.<ot x 5:.754ot 854.7:=ot:

Wls` fl ie berme hulrte 8(54.7:=ot:) (:.2:+2 ij/ot:) 8><.>7 injres.

Wls` fl ie berme fl cnlvl8(57ij/ot:) (57ot x 5.<ot) 85<7 injres.

Berme vlrtnbei s`jrl ievnmultniie 8 w 8 5<7 + ><.>7ij 8 :6<.> ijBerme plrplcfnbuier 8 :6<.>x (B`s22.?>) 8 :5:.:= ij.



Were ie prlsn`c fli vnlct`tlclh`s li erle p`rvnmultniie fl 54.7:=otS: x

:<.< ij/otS: 8 6?4 ij=.

Ed`re sl beibuie li ] t`teiqul ls ie berme hulrte +berme fl cnlvl + berme fl

vnlct`.]t 8 :5:.:= ij + 6<>.= ij]t 8 ?=5.>= 8 ?=: ij

Berme fl oilxnòc t`tei pereie vnmultniie 8 ?=: ij

Berme fnstrnjunfe lcvnmultniie 8 ?=: ij /5:.754ot 8 <? ij/ot

C`te1 :5:.:=ij ls ie suhe fl ieberme hulrte y ie fl cnlvl.

C`te1 li fet` :<.< ij/ot: lste fef` p`rie rliebnòc 5/2. tejie 5 fl erhefurespere tlbd` fli injr` fl fnslõ` flncsteiebn`cls.



Ed`re lsteh`s lc b`cfnbn`cls fl fnslõer ies vnmultniies y p`incls pere i`

buei userlh`s ie oòrhuie fl ie oilxnòc pere hnlhjr`s rlbtecmuierls

Ie vnmultniie sl tretereb`h` vnme snhpilhlctlep`yefe b`c uce bermefnstrnjunfe fl <? ij/otEpinbecf` ie oòrhuie flih`hlct` tlclh`s1

H8 |(<?) (5:.754S:)|/ 4H8 5,755.5 ot-ij 8 5:,52:.2 nc-

ot.Rustntuylcf` lc ie oòrhuiefl oilxnòc

H8 |(5:77)(jfS:)|/? 85:,52:.2 nc-ot.



C`te1 t`hecf` uce rliebnòc flesplbt` pere ie slbbnòc 8 :,tlclh`s qul f 8 :j.

Flsplaecf` j1

j8 :.64 nc

pulst` qul f 8 :jf8 6.>? nc

Were hlfnfes lståcfertlcfrlh`s b`c li årle fl:.< x < 8 5:.< ncS:.

Buhpil ie hlfnfelståcfer fl : </4 x < ¸ b`c

uc årle fl 56.62 ncS:.

(?)(5:,52:.2)(6)(5,:77)

C`te1 Rlrne 2 x ? c`hncei



Were li fnslõ` fl p`incls sl t`he b`h` berme fnstrnjunfeucno`rhlctl f`cfl Z5 8 Z:

|(?=:) (?)|/: 8 :75? ijp`r befe rlebbnòc.

H8 (:75?)(54)(6) ‒ (?=:)(54)(2)- (?=:)(54)(:)-(?=:)(54)(5) 8

H8 =:,<:? nc-ij

Epinbecf` fl culv` ieo`rhuie fl oilxnòc ydebnlcf` f8:j, tlclh`s

H8 |(5:77)(6j S2)|/?

j8 6.6> nc ; f8 4.>4 ncC`te1 sl tnlclc = p`inclslc 57 ot plr` i`s lxtrlh`sveilc ie hntef.

(?)(=:,<:?)(6)(5,:77)



j8 6.6> nc ; f8 4.>4 ncÅrle 8 67.2: nc:

Rl pulflc tlclr :`pbn`cls qul sl eaustec elste årle rlqulrnfe.

@pbnòc Veheõ`c`hncei

Årle

5 6 x 5: 65.?>

: ? x 4 65.:<

Rl lilmnrå ie `pbnòc : p`r lolbt`sfl vnste y rlsplte hes ie rliebnòcfl : e 5 snlcf` fl 5.< e 5.

Ed`re sl beibuie li pls` pr`pn`fl ie erhefure b`c ie snmunlctloòrhuie pere erhefures flheflre.

]8 7.< x e x I (5+ 7.5<I)

]8 (7.<)(57)(>7) |(5+7.5<(>7))|

]8 ?,<:< injres.



Zliebnòc fl årles fl erhefure e pecli fl vnmultniie

|(57)(5:.754 x 6.<) / (5:.754 x5.<)| (:) 8 ?7

_ìuhlc fl uc pìèc 8(7.<ot) (:/2 ot)(57ot)8 2.226 otS2

_ìuhlc fl ie vnmultniie 8(7.:<ot)(7.<ot)(57ot)8 5.:< otS2

_ìuhlc t`tei fl heflre8pìncls + vnmultniies

Wìncls8 57x2.2228 22.22otS2_nmultniies8 5.:<x?78 =<otS2

_ì. 8 574.226 otS2

Flcsnfef fl ie heflre 82?.: ij/otS2

Wls` t`tei fl heflre 82,>:5.=



B`cblpt` Wls` lc injres

Zlbujrnhnlct` + berme fl cnlvl 8 berme vlrtnbei t`teis`jrl uce vnmultniie p`r ie rliebnòc fl årles fl

peclils. (:6<.>ij) (?7)

56,=<6

Wls` lc p`incls y vnmultniies 2,>::

Wls` pr`pn` fl ie erhefure ?,<:<

V`tei8 :<,:75

Ie erhefure bulcte b`c > cuf`s lc su bulrfesuplrn`r, plr` b`h` i`s cuf`s fl i`s lxtrlh`s veilcie hntef sl fnvnfl ie berme vlrtnbei lctrl 4.



Berme/cuf` 8 :<,:75/48 25<7.: ij.

Ei tlclr lstl rlsuitef` slsejl qul sl tnlclc = bermesfl 25<7.: ij y f`s fl5<=<.5 ijs.

Lsoulrz`s p`r bermes flvnlct`.

8 (5:.754 x 6.<)(57)8 <67.45otS:.Ie prlsn`c t`tei s`jrl ucpecli fl erhefure slre 8<67.45 otS: x :<.< ij/otS:8 52,=>7.?? ijs.

W 52 =>7 ?? / 6



W`r tect` 52,=>7.?? / 6Ls nmuei e 2,66=.?= ijs.

Rlrec f`s fl 5,=:2.>ijs ytrls fl 2,66=,?= ij.

Were berme b`cblctrefe fl:<,777 ijs ie buei sllcbulctre lc li blctr` flie erhefure (bermeb`cblctrefe lc li blctr`).



Lalhpi` fl bermes hulrtes



Lalhpi` fl vnme b`c berme fl vnlct`



Lalhpi` fl bermes b`cblctrefes

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