Libro Tacaná Química II 2º. Semestre 10

Suà`lfc LL Jrupd [cfcnã - LJBY Vbjunkd sb`bstrb

33

Suà`lfc LL Jrupd [cfcnã - LJBY Vbjunkd sb`bstrb

33

Suà`lfc LL

Vbjunkd sb`bstrb Jrupd [cfcnã 33

© Lnstltutd Juctb`cgtbfd kb Bkufcflön Yckldoönlfc, LJBY. Bs unc dirc prdkuflkc pdr bg Kbpcrtc`bntd kb Ybkcfflön y Klsbód, pcrc bg Lnstltutd Juctb`cgtbfd kb Bkufcflön Yckldoönlfc, LJBY. 33 cvbnlkc 35-;2, Flukck Nubvc, zdnc 9 Flukck kb Juctb`cgc. XIU= 9;39 ???? Ocx= 9;39 ?:8; Fdrrbd bgbftrönlfd= ljbrHljbr.bku.jt Xãjlnc wbi= www.ljbr.bku.jt L`prbslön 983? L`prbsd bn LJBY tcggbrbs jrãfds

Fökljd= 333339?989 LVIN <:5<<9<58;?96

Ybsbrvckds tdkds gds kbrbfeds. Subkc rljurdsc`bntb prdelilkc gc rbprdkufflön tdtcg d pcrflcg kb bstb `ctbrlcg bkufctlvd, pdr fucgqulbr `bkld d prdfbkl`lbntd, sln gc cutdrlzcflön kbg Lnstltutd Juctb`cgtbfd kb Bkufcflön Yckldoönlfc, LJBY. Vbjýn crtàfugd ;9 kb gc Fdnstltuflön Xdgàtlfc kb Juctb`cgc qub sb rbbrb c gc cutdràc.

Ànklfb ............................................................................................................................................................... Ànklfb

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Vb`cnc 35

Bg bngcfb quà`lfd...................................................................................................................................

3

¡Xcrc fd`bnzcr! Gc rbjgc kbg dftbtd .....................................................................................................................

6

Bg ùnkd kb gc quà`lfc 3. ´Suì bs un bngcfb quà`lfd4 ....................................................................................................................... 2 9. [lpds kb bngcfb quà`lfd .............................................................................................................................. ? 9.3 Bngcfb lönlfd d bgbftrdvcgbntb ......................................................................................................... ? 9.9 Bngcfb fdvcgbntb ................................................................................................................................... : 9.6 Bngcfb `btãglfd ..................................................................................................................................... 5 Ybsu`bn .......................................................................................................................................................................... < Cutdfdntrdg ................................................................................................................................................................... 38 ¡C gc flbnflc pdr gc bxpbrlbnflc! ¡Vb elzd gc guz! ........................................................................................... 36

Vb`cnc 3<

Oörùgcs quà`lfcs...............................................................................................................................

32

¡Xcrc fd`bnzcr! Bg ný`brd kb vcgbnflc. Gc fcrjc bgìftrlfc ........................................................................ Bg ùnkd kb gc quà`lfc 3. Oörùgc quà`lfc .............................................................................................................................................. 9. Fgcslfcflön kb oörùgcs quà`lfcs .......................................................................................................... 9.3 Oörùgc b`pàrlfc .................................................................................................................................. 9.9 Oörùgc `dgbfugcr ............................................................................................................................... Ybsu`bn .......................................................................................................................................................................... Cutdfdntrdg ................................................................................................................................................................... ¡C gc flbnflc pdr gc bxpbrlbnflc! Bgcidrb un kbsdkdrcntb fcsbrd ............................................................

3: 3< 98 98 96 92 9? 9<

Vb`cnc 98

Ounflön quà`lfc.......................................................................................................................................

63

¡Xcrc fd`bnzcr! Fd`pubstds ilncrlds, tbrncrlds y fuctbrncrlds ¡Kb kds, kb trbs, kb fuctrd!......... 66 Bg ùnkd kb gc quà`lfc 3. Fd`pubstds lndrjãnlfds y sus ounfldnbs quà`lfcs .......................................................................... 62 3.3 Ounflön öxlkd ........................................................................................................................................ 62

Suà`lfc LL ∙ Ànklfb

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3.9 Ounflön ãflkd .........................................................................................................................................

6:

3.6 Ounflön icsb ..........................................................................................................................................

65

3.; Ounflön scg ..............................................................................................................................................

65

Ybsu`bn ..........................................................................................................................................................................

;8

Cutdfdntrdg ...................................................................................................................................................................

;3

¡C gc flbnflc pdr gc bxpbrlbnflc ! ¡Ocirlqub tlntc lnvlsligb! ........................................................................

;6

Vb`cnc 93

Nd`bnfgcturc L

.........................................................................................................................................

¡Xcrc fd`bnzcr! Bg gbnjucmb kb gc `ýslfc ..........................................................................................................

;2 ;:

Bg ùnkd kb gc quà`lfc

3. Nd`bnfgcturc quà`lfc ................................................................................................................................. 3.3 Vlstb`c bstbquld`ìtrlfd ...................................................................................................................

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c. Xrbmds nu`ìrlfds .......................................................................................................................

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i. Ndìrb jbnìrlfd ..........................................................................................................................

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f. Ndìrb bspbfàfd ...................................................................................................................... 3.9 Vlstb`c Vtdfa .........................................................................................................................................

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Ybsu`bn ..........................................................................................................................................................................

2;

Lnvbstljub bn gc rbk ...................................................................................................................................................

2;

Cutdfdntrdg ...................................................................................................................................................................

22

¡C gc flbnflc pdr gc bxpbrlbnflc! Bgcidrb unc tcigc kb vcgbnflcs ùrcg ............................................... [cigc kb vcgbnflcs ...................................................................................................................................................

2< ?3

Vb`cnc 99

Nd`bnfgcturc LL= Öxlkds

..........................................................................................................

¡Xcrc fd`bnzcr! Dxàjbnd, fd`pdnbntb bsbnflcg kb nubstrd pgcnbtc......................................................

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3. Gds öxlkds .......................................................................................................................................................... 3.3 Nd`bnfgcturc kb gds öxlkds ............................................................................................................

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c. Nd`bnfgcturc bn bg slstb`c bstbquld`ìtrlfd ..................................................................

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i. Nd`bnfgcturc bn bg slstb`c Vtdfa ........................................................................................

:9

Ybsu`bn ..........................................................................................................................................................................

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:;

Cutdfdntrdg ...................................................................................................................................................................

:2

¡C gc flbnflc pdr gc bxpbrlbnflc! ¡Rnc trc`pc bfdgöjlfc! ..........................................................................

:5

LL

LJBY ∙ [cfcnã

Vb`cnc 96

Ybpcsd= sb`cncs 3 5‖ 99

.......................................................................................................

53

3. ´Suì bs un bngcfb quà`lfd4 .......................................................................................................................

56

9. Oörùgc quà`lfc ..............................................................................................................................................

52

6. Fd`pubstds lndrjãnlfds y sus ounfldnbs quà`lfcs ..........................................................................

55

;. Nd`bnfgcturc quà`lfc .................................................................................................................................

<3

2. Gds öxlkds ..........................................................................................................................................................

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Vb`cnc 9;

Nd`bnfgcturc LLL= Ãflkds

.........................................................................................................

¡Xcrc fd`bnzcr! Elkröjbnd, bg fdìustligb kbg outurd .................................................................................

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3. Gds ãflkds .......................................................................................................................................................... 3.3 Nd`bnfgcturc kb gds ãflkds ............................................................................................................

383 386

c. Nd`bnfgcturc kb gds elkrãflkds bn bg slstb`c trcklfldncg ..........................................

386

i. Nd`bnfgcturc kb gds ãflkds dxãflkds bn bg slstb`c trcklfldncg ...............................

382


385

Ybsu`bn ..........................................................................................................................................................................

338

Cutdfdntrdg ................................................................................................................................................................... 333 ¡C gc flbnflc pdr gc bxpbrlbnflc! Rn gl`plckdr bfdgöjlfd ............................................................................ 33? Lnvbstljub bn gc rbk ...................................................................................................................................................

33:

Vb`cnc 92 Nd`bnfgcturc L_= Elkröxlkds ..................................................................................

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¡Xcrc fd`bnzcr! Bg elkröxlkd kb `cjnbsld.......................................................................................................

393


3. Gds elkröxlkds d icsbs .................................................................................................................................. 3.3 Nd`bnfgcturc kb gds elkröxlkds ....................................................................................................

396 39;

c. Nd`bnfgcturc bn bg slstb`c Vtdfa ........................................................................................

39;

Ybsu`bn ..........................................................................................................................................................................

39?

Cutdfdntrdg ................................................................................................................................................................... ¡C gc flbnflc pdr gc bxpbrlbnflc! ´Ãflkd d icsb4 Kbpbnkb kbg fdgdr........................................................ Lnvbstljub bn gc rbk ...................................................................................................................................................

39: 369 366

Suà`lfc LL ∙ Ànklfb

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Vb`cnc 9?

Nd`bnfgcturc _= Vcgbs

...............................................................................................................

362

¡Xcrc fd`bnzcr! Gc scg... un ilbn ùy prbflckd .............................................................................................. 36: Bg ùnkd kb gc quà`lfc 3. Gcs scgbs .............................................................................................................................................................. 36< ¡Cntbs kb ndìrcr c gcs scgbs ecgdlkbcs! .............................................................................................. 3;8 3.3 Nd`bnfgcturc kb gcs scgbs ecgdlkbcs ........................................................................................... 3;3 c. Nd`bnfgcturc bn bg slstb`c trcklfldncg kb scgbs ecgdlkbcs odr`ckcs pdr

`btcgbs fdn vcgbnflc mc ........................................................................................................... 3;3 i. Nd`bnfgcturc bn bg slstb`c Vtdfa kb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs fdn vcgbnflc vcrlcigb ................................................................................................................... 3;9 Ybsu`bn .......................................................................................................................................................................... 3;; Cutdfdntrdg ................................................................................................................................................................... 3;2 ¡C gc flbnflc pdr gc bxpbrlbnflc! Vcg, cjuc y cfbltb....................................................................................... 3;:

Vb`cnc 9:

Bg @dg.......................................................................................................................................................................... ¡Xcrc fd`bnzcr! C`ckbd Cvdjckrd.................................................................................................................... Bg ùnkd kb gc quà`lfc 3. @dg= gc `csc kb gcs pcrtàfugcs .................................................................................................................... 3.3 @csc `dgcr ............................................................................................................................................. 9. Ocftdrbs `dgcrbs ............................................................................................................................................. 9.3 Fdnvbrsldnbs kb `dg y `csc ........................................................................................................... 9.9 Fdnvbrsldnbs kb `dg y fcntlkck kb pcrtàfugc s........................................................................ 6. Bg vdgu`bn `dgcr ............................................................................................................................................ Ybsu`bn .......................................................................................................................................................................... Lnvbstljub bn gc rbk ................................................................................................................................................... Cutdfdntrdg ................................................................................................................................................................... ¡C gc flbnflc pdr gc bxpbrlbnflc! Rn jrcn ný`brd... bg ný`brd kb Cvdjckrd.....................................

3;< 323 329 329 32; 32; 32? 325 32< 32< 3?8 3?6

Vb`cnc 95

Ybcffldnbs quà`lfcs....................................................................................................................... ¡Xcrc fd`bnzcr! Gc odtdsàntbsls, unc rbcfflön quà`lfc lnklspbnscigb pcrc gc vlkc ...........................

3?2 3?:

Bg ùnkd kb gc quà`lfc 3. Ybcffldnbs quà`lfcs ...................................................................................................................................... 3?< 9. Bfucfldnbs quà`lfcs ...................................................................................................................................... 3:8 6. Fgcslfcflön kb gcs rbcffldnbs quà`lfcs.............................................................................................. 3:6

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LJBY ∙ [cfcnã

6.3 Ybcffldnbs kb fdìlncflön d sàntbsls ......................................................................................... 3:6 6.9 Ybcffldnbs kb kbsfd`pdslflön ...................................................................................................... 3:; 6.6 Ybcffldnbs kb sustltuflön ................................................................................................................. 3:; Ybsu`bn .......................................................................................................................................................................... 3:? Cutdfdntrdg ................................................................................................................................................................... 3:: ¡C gc flbnflc pdr gc bxpbrlbnflc! Rnc fcnkbgc qub prdkufb cjuc .......................................................... 353

Vb`cnc 9<

Ybpcsd= sb`cnc s 9;‖ 95......................................................................................................... Bg ùnkd kb gc quà`lfc 3. Gds ãflkds .......................................................................................................................................................... 9. Gds elkröxlkds d icsbs .................................................................................................................................. 6. Gcs scgbs .............................................................................................................................................................. ;. @dg= gc `csc kb gcs pcrtàfugcs .................................................................................................................... 2. Ybcffldnbs quà`lfcs ......................................................................................................................................

356

352 35< 3<9 3<2 3<5

Vb`cnc 68

Icgcnfbd kb bfucfldnbs quà`lfcs

.........................................................................

983

¡Xcrc fd`bnzcr! Gc gby kb fdnsbrvcflön kb gc `csc...................................................................................... 986 Bg ùnkd kb gc quà`lfc 3. Bfucfldnbs icgcnfbckcs ............................................................................................................................... 98; Ybsu`bn .......................................................................................................................................................................... 985 Lnvbstljub bn gc rbk ................................................................................................................................................... 985 Cutdfdntrdg ................................................................................................................................................................... 98< ¡C gc flbnflc pdr gc bxpbrlbnflc! @dvl`lbntd `lstbrldsd............................................................................ 936

Vb`cnc 63

Bstbquld`btràc kb gcs rbcffldnbs quà`lfcs

..........................................

932

¡Xcrc fd`bnzcr! Mden Kcgtdn= Bg flbntàolfd qub prdpusd ‗fdntcr‐ gds ãtd`ds....................................... 93: Bg ùnkd kb gc quà`lfc 3. Bstbquld`btràc ................................................................................................................................................. 935 3.3 Fãgfugds `dg ‖ `dg .............................................................................................................................. 935 3.9 Fãgfugds `csc ‖ `csc ......................................................................................................................... 999 Ybsu`bn .......................................................................................................................................................................... 99< Cutdfdntrdg ................................................................................................................................................................... 968 ¡C gc flbnflc pdr gc bxpbrlbnflc! Rn jcs qub cpcjc bg oubjd ................................................................... 969 Lnvbstljub bn gc rbk ................................................................................................................................................... 966 Suà`lfc LL ∙ Ànklfb

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Vb`cnc 69 Vdgufldnbs.....................................................................................................................................................

962

¡Xcrc fd`bnzcr! Gcs `bzfgcs sb pubkbn sbpcrcr .............................................................................................. 96: Bg ùnkd kb gc quà`lfc 3. Vdgufldnbs ........................................................................................................................................................... 96< 3.3 Fgcslfcflön kb gcs sdgufldnbs ........................................................................................................ 9;8 c. Xdr su bstckd kb cjrbjcflön ................................................................................................... 9;8 i. Xdr su fdnfbntrcflön .................................................................................................................. 9;9 9. Fdnfbntrcflön kb unc sdguflön ................................................................................................................. 9;; 9.3 Xdrfbntcmb `csc ‖ `csc (% `/`) ................................................................................................. 9;; 9.9 Xdrfbntcmb vdgu`bn ‖ vdgu`bn (% v/v) ....................................................................................... 9;? Ybsu`bn .......................................................................................................................................................................... 9;5 Cutdfdntrdg ................................................................................................................................................................... ¡C gc flbnflc pdr gc bxpbrlbnflc! ´Vb `bzfgcn d nd sb `bzfgcn4..............................................................

9;< 926

Vb`cnc 66 Fdgdlkbs ...........................................................................................................................................................

922

¡Xcrc fd`bnzcr! Gc `cydnbsc, un fdgdlkb ùy scirdsd ............................................................................... 92: Bg ùnkd kb gc quà`lfc 3. Fdgdlkbs .............................................................................................................................................................. 925 3.3 Fcrcftbràstlfcs kb gds fdgdlkbs ........................................................................................................ 925

3.9 Fd`pdslflön kb gds fdgdlkbs ........................................................................................................... 92< 9. Fgcslfcflön kb gds fdgdlkbs pdr su bstckd kb cjrbjcflön ............................................................ 9?8 Ybsu`bn .......................................................................................................................................................................... 9?3 Cutdfdntrdg ................................................................................................................................................................... 9?9 ¡C gc flbnflc pdr gc bxpbrlbnflc! ´Fdgdlkb d sdguflön4.................................................................................. 9?2 Lnvbstljub bn gc rbk ................................................................................................................................................... 9?2

Vb`cnc 6;

Ybpcsd= sb`cncs 68‖66

.......................................................................................................

9?:

Bg ùnkd kb gc quà`lfc 3. Bfucfldnbs icgcnfbckcs ............................................................................................................................... 9. Bstbquld`btràc ................................................................................................................................................. 6. Vdgufldnbs ..........................................................................................................................................................

9?< 9:6 9:?

;. Fdgdlkbs ...............................................................................................................................................................

9:<

Fgcvbs ............................................................................................................................................................... 956 Iligldjrcoàc ................................................................................................................................................... 636

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LJBY ∙ [cfcnã

35

Bg bngcfb quà`lfd

Suà`lfc LL ∙ Vb`cnc 35

3

Gds gdjrds qub fdnsbjulrã bstc sb`cnc sdn= 

Bxpglfcr fdn sus pcgcircs bg fdnfbptd kb bngcfb quà`lfd.



Lkbntlolfcr fö`d sb odr`c un bngcfb lönlfd, fdvcgbntb y `btãglfd.



Kbsfrlilr gcs prdplbkckbs qub prbsbntcn gds bngcfbs lönlfds, fdvcgbntbs y `btãglfds.



Ybfdndfbr gds bgb`bntds qub lntbrvlbnbn bn gc odr`cflön kb bngcfbs lönlfds, fdvcgbntbs y `btãglfds.



Bmb`pglolfcr fd`pubstds lönlfds, fdvcgbntbs y `btãglfds.



Klobrbnflcr bntrb bngcfb lönlfd y fdvcgbntb.



Bxpbrl`bntcr fdn gcs fcrcftbràstlfcs kb un fd`pubstd lönlfd.



´Suì bnfdntrcrã bstc sb`cnc4

9

¡Xcrc fd`bnzcr!

• Gc rbjgc kbg dftbtd


• ´Suì bs un bngcfb quà`lfd4 • [lpds kb bngcfb quà`lfd

¡C gc flbnflc pdr gc bxpbrlbnflc!

• ¡Vb elzd gc guz!

LJBY ∙ [cfcnã

¡Xcrc fd`bnzcr! Bn nubstrd fursd kb Suà`lfc 3 cprbnkl`ds qub bg nlvbg kb vcgbnflc bs bg nlvbg kb bnbrjàc kdnkb sb uilfcn gds ýgtl`ds bgbftrdnbs kb un ãtd`d. [cìlìn bstuklc`ds qub gds ãtd`ds sb unbn y odr`cn `dgìfugcs d fd`pubstds pcrc sbr nbutrds. Bstds fdnfbptds nds cyukcrãn c bntbnkbr gc rbjgc kbg dftbtd. _bc`ds.

Gc rbjgc kbg dftbtd Bn 3<3?, kbspuìs kb ùfeds códs kb lnvbstljcflön, gds flbntàolfds Zcgtbr Adssbg y Jlgibrt Gbwls fdnfguybrdn qub gds bgb`bntds quà`lfds tlbnkbn c fd`pgbtcr su ýgtl`d nlvbg kb bnbrjàc fdn dfed bgbftrdnbs. Bstc tbnkbnflc iusfc cgfcnzcr unc bstrufturc bgbftrönlfc bstcigb , sl`lgcr c gc kb gds jcsbs ndigbs. Bstc fdnfguslön bs ùnklcg`bntb fdndflkc fd`d gc rbjgc kbg dftbtd y klfb csà= ‗Fucnkd sb odr`c un bngcfb quà`lfd gds ãtd`ds rbflibn, fbkbn d fd`pcrtbn bgbftrdnbs kb tcg odr`c qub gc fcpc `ãs bxtbrnc kb

Zcgtbr Adssbg (3555 - 3<2?) Oàslfd cgb`ãn

fckc ãtd`d fdntbnjc dfed bgbftrdnbs, y csà ckqulbrb gc bstrufturc bgbftrönlfc kbg jcs ndigb `ãs fbrfcnd bn bg slstb`c pbrlöklfd‐.

Xcrc rbflilr, fbkbr d fd`pcrtlr bgbftrdnbs gds ãtd`ds kb gds bgb`bntds kbibn unlrsb fdn dtrds ljucgbs d klobrbntbs. Bscs unldnbs prdkufbn gcs sustcnflcs fd`pubstcs fdn gcs qub nds rbgcfldnc`ds klcrlc`bntb. Xdr bmb`pgd= Jlgibrt Gbwls (35:2 - 3<;?) Oàslfd quà`lfd bstckdunlkbnsb

Rnc `dgìfugc kb cjuc bstã fd`pubstc pdr= Kds ãtd`ds kb elkröjbnd (E), y un ãtd`d kb dxàjbnd (D). Bg ãtd`d kb elkröjbnd tlbnb un sdgd bgbftrön bn su ýgtl`d nlvbg kb bnbrjàc y bg ãtd`d kb dxàjbnd, sbls bgbftrdnbs. Xcrc gdjrcr bg dftbtd, gds kds ãtd`ds kb elkröjbnd sb unbn cg dxàjbnd y cpdrtcn sus bgbftrdnbs. Csà, bn gc `dgìfugc kb

E

D E

Gds jcsbs ndigbs sdn gds bgb`bntds `ãs bstcigbs pdrqub tlbnbn fd`pgbtd su ýgtl`d nlvbg kb bnbrjàc. Vb uilfcn bn gc fdgu`nc 35 kb gc tcigc pbrlöklfc.

cjuc, bg dxàjbnd qubkc fdn dfed bgbftrdnbs bn suc ýgtl`d bnbrjàc y gdjrc unc fdnoljurcflön bgbftrönlfc sl`lgcr gc kbg nlvbg nbön kb (Nb), bg jcs ndigb qub gb qubkc `ãs fbrfc bn gc tcigc pbrlöklfc.


6

‛´\ quì pcsc fdn bg elkröjbnd4 ‛Bg elkröjbnd nd fdnsljub bg dftbtd, pbrd sà fdnsljub tbnbr kds bgbftrdnbs bn su fcpc bxtbrldr y cgfcnzcr bg nlvbg kb vcgbnflc kbg ebgld (Eb), bg jcs ndigb `ãs fbrfcnd c ìg. Gcs unldnbs qub dfurrbn bntrb gds ãtd`ds sb fdndfbn fd`d bngcfbs quà`lfds. Bg tb`c kb bstc sb`cnc.

¡C trcicmcr! Bsfrlic sdirb gcs gànbcs sl bg ãtd`d fu`pgb d nd fu`pgb fdn gc rbjgc kbg dftbtd y bxpglqub pdr quì. [lbnb un bmb`pgd.

Nd fu`pgb gc rbjgc kbg dftbtd pdrqub tlbnb sdgd un bgbftrön bn su

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Gl

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Nb

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LJBY ∙ [cfcnã

Cr

ýgtl`d nlvbg kb bnbrjàc.


3. ´Suì bs un bngcfb quà`lfd4 Gc oubrzc qub gds unb… Fd`d rbfdrkcrã, bn gc [lbrrc ecy ndvbntc y kds bgb`bntds quà`lfds ncturcgbs qub fd`pdnbn tdkd gd qub nds rdkbc. Gc `cydr pcrtb sb prbsbntc bn odr`c kb fd`pubstds3, bs kbflr, bn sustcnflcs odr`ckcs pdr kds d `ãs bgb`bntds

[bnjc c su cgfcnfb gc tcigc pbrlöklfc. Gc nbfbsltcrã.

bn prdpdrfldnbs mcs.kbXdr bmb`pgd, yfd`d ec vlstd, cjuc bs un odr`ckd pdr ãtd`ds elkröjbnd kb dxàjbnd bn bg prdpdrflön kbfd`pubstd 9 c 3. Xbrd… ´Fö`d sb unbn gds ãtd`ds kb gds bgb`bntds pcrc odr`cr fd`pubstds4 ‛Gds ãtd`ds sb unbn pdr `bkld kb bngcfbs quà`lfds. Rn bngcfb quà`lfd bs gc unlön kb ãtd`ds ljucgbs d klstlntds pcrc odr`cr `dgìfugcs. Bsc unlön sb gdjrc pdr gc trcnsobrbnflc tdtcg d pcrflcg kb bgbftrdnbs kb un ãtd`d c dtrd. Ybfubrkb qub gds ãtd`ds sb unbn pcrc gdjrcr unc fdn jurcflön bgbftrönlfc bstcigb. Xdr bmb`pgd= Bg bngcfb bntrb kds ãtd`ds kb elkröjbnd (E) y un ãtd`d kb dxàjbnd (D) prdkufb unc `dgìfugc kb cjuc (E9D).

Bg bngcfb bntrb kds ãtd`ds kb dxàjbnd (D) prdkufb unc `dgìfugc kb dxàjbnd (D9). Bg dxàjbnd qub rbsplrc`ds gd ditbnb`ds kbg clrb bn odr`c kb `dgìfugc.

E

Fdnjurcflön bgbftrönlfc bstcigb= Fdnjurcflön qub gdjrcn gds ãtd`ds fucnkd tlbnbn tdkds gds driltcgbs ggbnds.

D E

D

D

Bmbrflfld 3 Bsfrlic fdn sus pcgcircs quì bs un bngcfb quà`lfd.

3 Ybpcsb bg tb`c —fgcslfcflön kb gc `ctbrlc‐ kb gc

sb`cnc 39 kb gc quà`lfc 3. Suà`lfc LL ∙ Vb`cnc 35

2

9. [lpds kb bngcfb quà`lfd Bn gc sb`cnc 3; bstuklc`ds qub, bn odr`c jbnbrcg, gds bgb`bntds sb fgcslfcn bn `btcgbs y nd `btcgbs. _l`ds qub gds `btcgbs sb fcrcftbrlzcn pdr fbkbr gds bgbftrdnbs kb su ýgtl`d nlvbg kb bnbrjàc kurcntb gcs rbcffldnbs quà`lfcs y qub gds nd `btcgbs sb fcrcftbrlzcn pdr jcncr bgbftrdnbs b lnfdrpdrcrgds c su nlvbg kb vcgbnflc kurcntb gcs rbcffldnbs quà`lfcs. Bstc fcpcflkck kb fbkbr y jcncr bgbftrdnbs kc gujcr c trbs tlpds klobrbntbs kb bngcfb quà`lfd= • Bngcfb lönlfd d bgbftrdvcgbntb • Bngcfb fdvcgbntb • Bngcfb `btãglfd

9.3 Bngcfb lönlfd d bgbftrdvcgbntb @btcg + nd `btcg Éc bsfufeckd bg klfed —gds pdgds dpubstds sb ctrcbn‐4 Xubs bs pbrobftd pcrc bxpglfcr bg bngcfb lönlfd, pdrqub bstb tlpd kb bngcfb sb kc bntrb bgb`bntds fdn fcrjcs bgìftrlfcs dpubstcs. Rn ãtd`d fdn fcrjc bgìftrlfc pdsltlvc (fctlön) sb unb c dtrd qub tlbnb fcrjc bgìftrlfc nbjctlvc (cnlön). Bg bngcfb dfurrb, bntrb cgtc). un `btcg (fdnfbkb bgbftrdnbjctlvlkck icmc) y unlönlfd nd `btcg (fdnjbnbrcg`bntb, bgbftrdnbjctlvlkck Bg `btcg sus bgbftrdnbs cg nd `btcg y csà gds kds gdjrcn unc fdnjurcflön bgbftrönlfc bstcigb, fdn dfed bgbftrdnbs bn bg nlvbg kb vcgbnflc. Bngcfb lönlfd 0 `btcg + nd `btcg Bmb`pgd= Gc scg kb `bsc d fgdrurd kb sdkld (NcFg) sb odr`c fucnkd bg sdkld (Nc) bntrbjc bg bgbftrön kbg ýgtl`d nlvbg kb bnbrjàc cg fgdrd (Fg). Fdn bstc bntrbjc bg ãtd`d kb sdkld ckqulbrb fcrjc pdsltlvc y sb fdnvlbrtb bn bg fctlön Nc + y bg fgdrd ckqulbrb fcrjc nbjctlvc y sb fdnvlbrtb bn bg cnlön Fg ∙. Fckc und qubkc fdn dfed bgbftrdnbs bn su nlvbg kb vcgbnflc y gdjrcn gc bstcilglkck.

Nc

?

LJBY ∙ [cfcnã

+

Fg

Nc+

Fg‖

Fcrcftbràstlfcs kb gds fd`pubstds fdn bngcfbs lönlfds Gds fd`pubstds qub sb odr`cn pdr bngcfbs lönlfds prbsbntcn bstcs fcrcftbràstlfcs= • Vubgbn sbr söglkds frlstcglnds fdn odr`cs rbjugcrbs, fd`d gds fuids kb gc scg fd`ýn, NcFg. • [lbnbn puntds kb ouslön y kb biugglflön bgbvckds. • Vdn iubnds fdnkuftdrbs kb gc bgbftrlflkck, fucnkd sb klsubgvbn bn cjuc. • Vdn fd`pubstds fdn bngcfbs lönlfds= scg fd`ýn (NcFg), irdùrd kb `cjnbsld (@jIr9), sugourd kb pdtcsld (A9V), ydkurd kb fcgfld (FcL9).

Xuntd kb ouslön= [b`pbrcturc c gc fucg gds söglkds pcscn c bstckd gàqulkd. Xuntd kb biugglflön= [b`pbrcturc c gc fucg unc sustcnflc fcìlc kb bstckd gàqulkd c bstckd jcsbdsd.

9.9 Bngcfb fdvcgbntb Nd `btcg + nd `btcg d nd `btcg + elkröjbnd Bn bg bngcfb fdvcgbntb, gds ãtd`ds sb unbn y fd`pcrtbn sus bgbftrdnbs. Bstb tlpd kb bngcfb sb kc bntrb nd `btcgbs y nd `btcgbs b elkröjbnd. Gds bgbftrdnbs sb fd`pcrtbn bn pcrbmcs. Fckc pcrbmc rbprbsbntc un bngcfb. Bngcfb fdvcgbntb

nd `btcg + nd `btcg nd `btcg + elkröjbnd

Xdr bmb`pgd= Gc odr`cflön kb unc `dgìfugc kb elkröjbnd (E 9) c pcrtlr kb kds ãtd`ds kb elkröjbnd bs un bmb`pgd kb bngcfb fdvcgbntb.

E

+

E E9

3 bgbftrön 3 bgbftrön

3 `dgìfugc kb E

9

Fckc ãtd`d kb elkröjbnd tlbnb un bgbftrön bn su nlvbg kb vcgbnflc y gd fd`pcrtb pcrc sbr bstcigb.

Fcrcftbràstlfcs kb gds fd`pubstds fdn bngcfbs fdvcgbntbs Gds fd`pubstds fdn bngcfbs fdvcgbntbs prbsbntcn bstcs fcrcftbràstlfcs= • Gc `cydràc sdn gàqulkds d jcsbs1 cgjunds sdn söglkds igcnkds. • [lbnbn icmds puntds kb ouslön y biugglflön. • Vdn `cgds fdnkuftdrbs kb gc bgbftrlflkck y kbg fcgdr. • Vdn fd`pubstds fdn bngcfbs fdvcgbntbs= bg cjuc (E9D), gc pcrcolnc (F92E29), bg czýfcr (F39E99D33) y bg klöxlkd kb fcridnd (FD9). Suà`lfc LL ∙ Vb`cnc 35

:

9.6 Bngcfb `btãglfd @btcg + @btcg Bg bngcfb `btãglfd sb kc sdgd bntrb `btcgbs. Fd`d rbfdrkcrã, gds `btcgbs tlbnbn bgbftrdnbjctlvlkck icmc y fbkbn sus bgbftrdnbs. Xdr gd tcntd, cg unlrsb kds `btcgbs, gds ãtd`ds nd tlbnbn pdslilglkck kb jcncr bgbftrdnbs. Gc odr`c kb fu`pglr gc rbjgc kb dftbtd bs fd`pcrtlr bgbftrdnbs bntrb ùfeds ãtd`ds. Bn bg bngcfb `btãglfd sb frbc unc nuib kb bgbftrdnbs qub sb ùbvb y bs fd`pcrtlkc pdr tdkds gds nýfgbds kb gds ãtd`ds qub fbkbn bgbftrdnbs cg fdnmuntd. Bg bngcfb sb `cntlbnb pdr gc oubrzc kb ctrcfflön bntrb gcs fcrjcs pdsltlvcs kb gds nýfgbds y gcs fcrjcs nbjctlvcs kb gc nuib kb bgbftrdnbs. nuib kb bgbftrdnbs

Bstb bs un `dkbgd kb `dgìfugc kb cgu`lnld.

Fcrcftbràstlfcs kb gds fd`pubstds fdn bngcfbs `btãglfds Gds fd`pubstds fdn bngcfbs `btãglfds prbsbntcn gcs `ls`cs fcrcftbràstlfcs qub gds `btcgbs. _bc`ds= • Vdn söglkds c tb`pbrcturc cìlbntb, bxfbptd bg `brfurld qub bs gàqulkd. • [lbnbn tb`pbrcturcs kb ouslön y biugglflön ùy bgbvckcs. • Vdn iubnds fdnkuftdrbs kb gc bgbftrlflkck y kbg fcgdr. • Bmb`pgds= `dgìfugcs kb elbrrd, flnf, pgd`d, fdirb y kb tdkds gds bgb`bntds `btãglfds y cgbcfldnbs bntrb `btcgbs= irdnfb, gctön, btf.

Bmbrflfld 9 C.

Ybggbnb bg fuckrd qub fdrrbspdnkb c gc rbspubstc fdrrbftc. [lbnb un bmb`pgd. 8)

Bg gctön bs unc cgbcflön kb fdirb (Fu) y flnf (]n). ´Suì tlpd kb bngcfb sb bstcigbfb bntrb gds `btcgbs qub gd odr`cn4

lönlfd 3)

fdvcgbntb

Bg `btcnd (FE;) bs un jcs odr`ckd pdr fcridnd (F), un nd `btcg, b elkröjbnd (E). ´Suì tlpd kb bngcfb gd odr`c4

lönlfd

5

`btãglfd

LJBY ∙ [cfcnã

fdvcgbntb

`btãglfd

9)

lönlfd 6) lönlfd I.

Bg ogudrurd kb sdkld (NcO), qub sb utlglzc bn tcigbtcs `cstlfcigbs pcrc prbvbnlr gcs fcrlbs, bstã odr`ckd pdr sdkld (Nc), un `btcg, y ogýdr (O), un nd `btcg. ´Suì tlpd kb bngcfb gd odr`c4 fdvcgbntb

`btãglfd

Bg c`dnlcfd (NE6) bs un jcs odr`ckd pdr nltröjbnd (N), un nd `btcg, b elkröjbnd (E). ´Suì tlpd kb bngcfb gd odr`c4 fdvcgbntb

`btãglfd

Oàmbsb bn gcs pcrbmcs kb bgb`bntds y bsfrlic sdirb gc gànbc sl odr`crãn un bngcfb lönlfd, fdvcgbntb d `btãglfd. [lbnb un bmb`pgd. 8) fdirb ‖ elbrrd (Fu ‖ Ob) 3)

fgdrd ‖ fgdrd (Fg ‖ Fg)

9)

pdtcsld ‖ fgdrd (A ‖ Fg)

bngcfb `btãglfd

Ybsu`bn 3.

´Suì bs un bngcfb quà`lfd4 Rn bngcfb quà`lfd bs gc unlön kb ãtd`ds ljucgbs d klstlntds qub pbr`ltb odr`cr `dgìfugcs. Bsc unlön sb gdjrc pdr gc trcnsobrbnflc tdtcg d pcrflcg kb bgbftrdnbs kb un ãtd`d c dtrd. Ecy trbs tlpds kb bngcfb=

3.3 Bngcfb lönlfd `btcg + nd `btcg Bg bngcfb lönlfd sb prdkufb fucnkd gds bgbftrdnbs sb trcnsolbrbn kb un ãtd`d c dtrd. Bstb tlpd kb bngcfb subgb kcrsb bntrb `btcgbs y nd `btcgbs. 3.9 Bngcfb fdvcgbntb nd `btcg + nd `btcg nd `btcg + elkröjbnd Bg bngcfb fdvcgbntb dfurrb fucnkd gds ãtd`ds qub sb unbn fd`pcrtbn gds bgbftrdnbs. Fckc pcr kb bgbftrdnbs qub fd`pcrtbn, odr`cn un bngcfb. Bn jbnbrcg, bstb tlpd kb bngcfb sb prdkufb bntrb bgb`bntds nd `btãglfds d bntrb un nd `btcg y bg elkröjbnd. 3.6 Bngcfb `btãglfd `btcg + `btcg Bg bngcfb `btãglfd sb prdkufb fucnkd gds ãtd`ds bngczckds sdn bgb`bntds `btãglfds. Bn bg bngcfb `btãglfd, gds ãtd`ds fd`pcrtbn gds bgbftrdnbs, pbrd ìstds sb ùbvbn pdr tdkc gc `dgìfugc d pdr tdkd bg fd`pubstd odr`cnkd unc nuib kb bgbftrdnbs. Suà`lfc LL ∙ Vb`cnc 35

<

Cutdfdntrdg Cftlvlkck 3. Ybpcsb gc tbdràc C.

Fd`pgbtb bg `cpc fdnfbptucg kb gds bngcfbs quà`lfds.

bngcfb quà`lfd pubkb sbr=

lönlfd gds bgbftrdnbs=

gdsbgbftrdnbs=

gdsbgbftrdnbs=

sb fd`pcrtbn sb fdìlncn=

sb fdìlncn=

sb prdkufb sdgd bntrb=

bmb`pgd=

pdr bmb`pgd=

`btcgbs bmb`pgd=

I.

Fdnslkbrb gcs lkbcs rbgbvcntbs rbgcfldnckcs fdn gds bngcfbs lönlfds, fdvcgbntbs y `btãglfds y fd`pgbtb gds fuckrds. Vl nbfbsltc `ãs bspcfld, pubkb ecfbrgd bn su fuckbrnd. ´Fö`d sb odr`c un bngcfb lönlfd4

´Fö`d sb odr`c un bngcfb fdvcgbntb4

38

LJBY ∙ [cfcnã

Fcrcftbràstlfcs kb gds fd`pubstds fdn bngcfbs lönlfds=

Fcrcftbràstlfcs kb gds fd`pubstds fdn bngcfbs fdvcgbntbs=

[lpds kb bgb`bntds Bmb`pgd kb un qub subgbn fdìlncrsb= fd`pubstd lönlfd=

[lpds kb bgb`bntds

Bmb`pgd kb un

qub subgbn fdìlncrsb= fd`pubstd fdvcgbntb=

´Fö`d sb odr`c un bngcfb `btãglfd4

Fcrcftbràstlfcs kb gds fd`pubstds fdn bngcfbs `btãglfds=

[lpds kb bgb`bntds qub subgbn fdìlncrsb=

Bmb`pgd kb un fd`pubstd `btãglfd=

Cftlvlkck 9. Xrcftlqub gds bngcfbs C.

Ybggbnb bg fuckrd qub fd`pgbtc fdrrbftc`bntb gds bnunflckds. 3)

9)

6)

Cg fdìlncrsb gds ãtd`ds kb pdtcsld (A), un `btcg, fdn gds ãtd`ds kb ird`d (Ir), un nd `btcg, bntrb bggds sb bstcigbfb un bngcfb=

Cg fdìlncrsb gds ãtd`ds kb dxàjbnd (D), un nd `btcg, fdn gds ãtd`ds kb fgdrd (Fg), un nd `btcg, bntrb bggds sb bstcigbfb un bngcfb=

Cg ecfbr unc cgbcflön kb fdirb (Fu), `btcg, fdn drd (Cu), `btcg, bntrb bggds sb bstcigbfb un bngcfb=

lönlfd `btãglfd fdvcgbntb



I.

F.

´Fuãg sbrã gc fgcsb kb bngcfb quà`lfd `ãs prdicigb qub pubkb bstcigbfbrsb bntrb gds ãtd`ds kb gds sljulbntbs bgb`bntds4 Bsfràicgd. [lbnb un bmb`pgd. 8)

Elbrrd ‖ elbrrd (Ob - Ob)

3)

Fgdrd ‖ `cjnbsld (Fg - @j)

9)

Fcridnd ‖ dxàjbnd (F - D)

bngcfb `btãglfd

Bsfrlic fuãgbs kb gds sljulbntbs fd`pubstds tlbnbn bngcfbs lönlfds y fuãgbs bngcfbs fdvcgbntbs. 3)

Öxlkd kb fcgfld (FcD)

9)

@dgìfugc kb dxàjbnd (D9)

6)

Ogudrurd kb sdkld (NcO) Suà`lfc LL ∙ Vb`cnc 35

33

Cftlvlkck 6. Xcrc rbbxldncr C.

Ybggbnb bg fuckrd kb gc dpflön fdrrbftc pcrc fckc pgcntbc`lbntd. 3)

´Fuãg bs gc fcrcftbràstlfc qub kbstcfc bn un bngcfb lönlfd4 Vb trcnsbrbn bgbftrdnbs Vb fd`pcrtbn bgbftrdnbs

9)

6)

Vb prdkufb bntrb `btcgbs Vb kc bntrb nd `btcgbs

Bg cjuc (E9D) bstã odr`ckc pdr bngcfbs fdvcgbntbs. Xdr bstc fdnklflön, ´fuãg kb gcs sljulbntbs fcrcftbràstlfcs prbsbntc4 Iubn fdnkuftdr kb gc bgbftrlflkck

Bs un söglkd igcnkd

@cg fdnkuftdr kb gc bgbftrlflkck

Cgtd puntd kb ouslön

´Fuãg kb gcs sljulbntbs colr`cfldnbs bs fdrrbftc4 Bn un ãtd`d,gds bgbftrdnbs qub pcrtlflpcn bn un bngcfb sdngds bgbftrdnbs kb vcgbnflc. Gds fd`pubstds odr`ckds pdr bngcfbs fdvcgbntbs sdn iubnds fdnkuftdrbs kb gc bgbftrlflkck. Gds fd`pubstds odr`ckds pdr bngcfbs fdvcgbntbs tlbnbn puntds kb ouslön `ãs cgtds qub gds fd`pubstds odr`ckds pdr bngcfbs lönlfds. Bn un bngcfb fdvcgbntb gds ãtd`ds pcrtlflpcntbs fbkbn sus bgbftrdnbs.

I.

Gbc gcs fcrcftbràstlfcs kb fckc sustcnflc y rbspdnkc c gcs prbjuntcs. Vustcnflc C [lbnb unc tb`pbrcturc kb ouslön ùy icmc. Nd fdnkufb gc bgbftrlflkck bn bstckd söglkd. [c`pdfd gc fdnkufb fucnkd sb bnfubntrc klsubgtc bn cjuc.

Vustcnflc I [lbnb unc tb`pbrcturc kb ouslön bgbvckc. Bs sdguigb bn cjuc. Nd fdnkufb gc bgbftrlflkck bn bstckd söglkd, pbrd sà fucnkd sb bnfubntrc klsubgtc bn cjuc.

Xdr sus fcrcftbràstlfcs, ´quì tlpd kb bngcfb prbsbntc gc sustcnflc C4 ´Lönlfd d fdvcgbntb4

Xdr sus fcrcftbràstlfcs, ´quì tlpd kb bngcfb prbsbntc gc sustcnflc I4 ´Lönlfd d fdvcgbntb4

39

LJBY ∙ [cfcnã


¡Vb elzd gc guz! Bstc sb`cnc cprbnkl`ds qub gds fd`pubstds fdn bngcfbs lönlfds sdn iubnds fdnkuftdrbs kb gc bgbftrlflkck fucnkd sb klsubgvbn bn cjuc. Gc scg bs un fd`pubstd lönlfd. ´Fdnkufb gc bgbftrlflkck4 ¡Fd`pruìibgd!

´Suì nbfbsltc4



? fufecrckcs kb scg Rn orcsfd pbqubód Rnc pcgbtc d un pcgltd kb `ckbrc gl`pld (sbrvlrã fd`d cjltckdr) ° gltrd kb cjuc rbpdsckc d ebrvlkc (pcrc uscrgc kbib kbmcr qub rbpdsb, cg `bnds, unc ndfeb fd`pgbtc d ebrvlrgc) Rn rbflplbntb kb vlkrld fdn fcpcflkck kb cg `bnds ° gltrd Bg flrfultd qub fdnstruyö gc sb`cnc 3; kb quà`lfc 3 gãplz



glirbtc kb fc`pd

  







C3

C9

I

´Suì kbib ecfbr4 Xcsd 3= 3. Fdgdqub gcs ? fufecrckcs kb scg kbntrd kbg orcsfd. 9. Fdnbftb gds bxtrb`ds C9 y I kbg flrfultd c gc scg. 6. Cndtb bn su glirbtc kb fc`pd= ´Bnfbnklö bg odfd4 ´Và d nd4 Mustlolqub su rbspubstc td`cnkd bn fubntc gcs prdplbkckbs kb gds bngcfbs lönlfds. Xcsd 9= ;. [d`b bg ° gltrd kb cjuc rbpdsckc y fdgöqubgd bn bg rbflplbntb jrcnkb kb vlkrld. 2. Cóckc gcs ? fufecrckcs kb scg y cjltb fdn gc pcgbtc. ?. Fucnkd gc scg bstì ilbn klsubgtc, td`b gds bxtrb`ds C9 y I kbg flrfultd y fdnìftbgds fdn bg cjuc. Nd lntrdkuzfc gcs `cnds bn bg cjuc. :. Cndtb bn su glirbtc kb fc`pd= ´Bnfbnklö bg odfd4 ´Và d nd4 Mustlolqub su rbspubstc td`cnkd bn fubntc gcs prdplbkckbs kb gds bngcfbs lönlfds. Suà`lfc LL ∙ Vb`cnc 35

36

Ybvlsb fö`d ec slkd su prdfbsd kb cprbnklzcmb kurcntb bstc sb`cnc. @crqub fdn un febqub

gc fcslggc qub `bmdr lnklqub su rbnkl`lbntd.

gdjrckd

rbjugcr

nd gdjrckd

Cspbftds c bvcgucr 3. 9. 6. Kbspuìs kb ;. bstuklcr... 2. ?. :.

Bxpglfd fdn `ls pcgcircs bg fdnfbptd kb bngcfb quà`lfd. Lkbntlolfd fö`d sb odr`c un bngcfb lönlfd, fdvcgbntb y `btãglfd. Kbsfrlid gcs prdplbkckbs qub prbsbntcn gds bngcfbs lönlfds, fdvcgbntbs y `btãglfds. Ybfdndzfd gds bgb`bntds qub lntbrvlbnbn bn gc odr`cflön kb bngcfbs lönlfds, fdvcgbntbs y `btãglfds. Bmb`pglolfd gds fd`pubstds lönlfds, fdvcgbntbs y `btãglfds. Klobrbnfld bntrb bngcfb lönlfd y fdvcgbntb. Bxpbrl`bntd fdn gcs fcrcftbràstlfcs kb un fd`pubstd lönlfd.

Ndtcs= Bsfrlic cquà sus lnqulbtukbs, kbsfuirl`lbntds d kukcs pcrc fd`pcrtlr bn bg fbntrd kb drlbntcflön.

3;

LJBY ∙ [cfcnã

3<

Oörùgcs quà`lfcs

Suà`lfc LL ∙ Vb`cnc 3<

32


Bxpglfcr fdn sus pcgcircs quì bs unc oörùgc quà`lfc.



Bxtrcbr lnodr`cflön kb unc oörùgc quà`lfc.



Ybfdndfbr gds klstlntds tlpds kb oörùgc quà`lfc.



Fcgfugcr oörùgcs b`pàrlfcs y oörùgcs `dgbfugcrbs.



Cpglfcr unc oörùgc quà`lfc bn gc bgcidrcflön kb kbsdkdrcntb.




3?

¡Xcrc fd`bnzcr!

• Bg ný`brd kb vcgbnflc


• Oörùgc quà`lfc • Fgcslolfcflön kb oörùgcs quà`lfcs


• Kbsdkdrcntb fcsbrd

LJBY ∙ [cfcnã

¡Xcrc fd`bnzcr! Bg ný`brd kb vcgbnflc Gc f crjc bgìftrlfc Cprbnkl`ds qub gds ãtd`ds kb klstlntds bgb`bntds sb unbn pcrc odr`cr fd`pubstds. Bsc unlön sb kc fucnkd fbkbn, cfbptcn d fd`pcrtbn sus bgbftrdnbs. Bstc sb`cnc kcrb`ds un pcsd `ãs cprbnklbnkd bg ný`brd kb vcgbnflc. Bg ný`brd kb vcgbnflc bs un fdnfbptd qub sb rbgcfldnc fdn gc fcntlkck kb bgbftrdnbs qub un ãtd`d pdnb bn mubjd c gc edrc kb odr`cr un fd`pubstd. Vb kbolnb csà= Bg ný`brd kb vcgbnflc bs gc fcrjc bgìftrlfc qub tlbnb un ãtd`d f ucnkd odr`c pcrtb kb un fd`pubstd. Kbpbnkb kb gc fcntlkck kb bgbftrdnbs jcnckds, pbrklkds d fd`pcrtlkds pdr un ãtd`d. Vb rbprbsbntc fdn ný`brds rd`cnds, pbrd ndsdtrds uscrb`ds ný`brds crãiljds pcrc ocflgltcr gc fd`prbnslön. Bg ný`brd kb vcgbnflc pubkb sbr= •

Ný`brd kb vcgbnflc pdsltlvd Bg ný`brd kb dxlkcflön bs pdsltlvd sl bg ãtd`d plbrkb bgbftrdnbs d gds fd`pcrtb fdn un ãtd`d qub gds cfbptb. Xdr bmb`pgd= Bg fcgfld (Fc) tlbnb kds bgbftrdnbs kb vcgbnflc qub tlbnkb c fbkbr pcrc fd`pgbtcr su dftbtd, pdr bsd bn gds fd`pubstds cftýc fdn ný`brd kb vcgbnflc +9 (+LL) ´Fuãntds bgbftrdnbs tlbnb bn tdtcg4

98 b

´Fuãntds bgbftrdnbs kb vcgbnflc tlbnb4

38 b

´Gb sdircn d gb ocgtcn bgbftrdnbs pcrc

Fc+9

fd`pgbtcr bg dftbtd4 ´Fuãntds bgbftrdnbs gb sdircn4

gb sdircn 9b

´Fuãg bs su ný`brd kb vcgbnflc4

+9


3:

•

Ný`brd kb vcgbnflc nbjctlvd Bg ný`brd kb vcgbnflc bs nbjctlvd sl bg ãtd`d jcnc bgbftrdnbs d gds fd`pcrtb fdn un ãtd`d qub gds fbkc. Xdr bmb`pgd= Bg fgdrd (Fg) tlbnb slbtb bgbftrdnbs kb vcgbnflc y tlbnkb c jcncr un bgbftrön pcrc fd`pgbtcr su dftbtd, pdr bsd bn gds fd`pubstds cftýc fdn ný`brd kb vcgbnflc ∙3 (∙L)

´Fuãntds bgbftrdnbs tlbnb bn tdtcg4 ´Fuãntds bgbftrdnbs kb vcgbnflc tlbnb4

3:b :b

´Gb sdircn d gc ocgtcn bgbftrdnbs pcrc

Fg‖

fd`pgbtcr bg dftbtd4

gb ocgtcn

´Fuãntds bgbftrdnbs gb ocgtcn4

3b


∙3

Gds ný`brds kb vcgbnflc bstãn lnfgulkds bn gcs oörùgcs quà`lfcs. Gd lrb`ds cprbnklbnkd pdfd c pdfd.

¡C trcicmcr! Cvbrlj÷b bg ný`brd kb vcgbnflc kbg pdtcsld (A). Xdtcsld (A) ] 0 3<

A

35

LJBY ∙ [cfcnã

c.

´Fuãntds bgbftrdnbs tlbnb bn tdtcg4

i.

´Fuãntds bgbftrdnbs kb vcgbnflc tlbnb4

f.

´Gb sdircn d gb ocgtcn bgbftrdnbs pcrc fd`pgbtcr bg dftbtd4

k.

´Fuãntds bgbftrdnbs gb sdircn4

b.



3. Oörùgc quà`lfc Gcs oörùgcs quà`lfcs nds lnklfcn gds bgb`bntds y gcs fcntlkckbs qub bstãn prbsbntbs bn un fd`pubstd kbtbr`lnckd. Bn jbnbrcg, gc oörùgc quà`lfc sb kbnb fd`d gc rbprbsbntcflön bsfrltc kb gc fd`pdslflön kb unc `dgìfugc d un fd`pubstd `bklcntb sàìdgds quà`lfds. Rnc oörùgc quà`lfc tlbnb kds fd`pdnbntbs iãslfds= 3.

Vàìdgds quà`lfds kb fckc und kb gds bgb`bntds qub odr`cn gc `dgìfugc d bg fd`pubstd.

9.

Vuiànklfbs qub lnklfcn bg ný`brd kb ãtd`ds kb fckc bgb`bntd. Bg suiànklfb 3 sb sdirbbntlbnkb y nd sb bsfrlib. Csà qub fucnkd vbc`ds unc oörùgc sln suiànklfbs, lntbrprbtcrb`ds qub tlbnb un sdgd ãtd`d kbg bgb`bntd qub gd prbfbkb.

Xdr bmb`pgd= Gc oörùgc kbg fgdrurd kb sdkld d scg fd`ýn, NcFg, nds lnklfc qub bsb fd`pubstd bstã odr`ckd pdr= un ãtd`d kb sdkld (Nc)

NcFg

unãtd`dkbfgdrd(

Fg)

Gc oörùgc kbg ãflkd nàtrlfd, END6, nds lnklfc qub bsb fd`pubstd bstã odr`ckd pdr= un ãtd`d kb nltröjbnd (N) un ãtd`d kb elkröjbnd E ()

END6 trbs ãtd`ds kb dxàjbnd (D)

Bmbrflfld 3 Lnklqub quì ãtd`ds y bn quì ný`brd bstãn prbsbntbs bn fckc oörùgc quà`lfc. [lbnb un bmb`pgd. 8)

NE6, c`dnlcfd, odr`ckd pdr= 3 ãtd`d kb nltröjbnd (N), 6 ãtd`ds kb elkröjbnd (E).

3)

D6, dzdnd, odr`ckd pdr=

9) 6)

Cj9D6, öxlkd kb pgctc, odr`ckd pdr= FD9, klöxlkd kb fcridnd, odr`ckd pdr=

;)

FuIr9, irdùrd kb fdirb (LL), odr`ckd pdr=


3<

9. Fgcslolfcflön kb oörùgcs quà`lfcs 9.3 Oörùgc b`pàrlfc Gc `ãs sbnflggc Gc oörùgc b`pàrlfc bs cqubggc qub bxprbsc gc `bndr prdpdrflön, bn ný`brds bntbrds, kb gds ãtd`ds qub odr`cn unc `dgìfugc d un fd`pubstd. Bstc prdpdrflön sb kbtbr`lnc bn odr`c bxpbrl`bntcg c trcvìs kbg cnãglsls kbg fd`pubstd bn un gcidrctdrld quà`lfd. Bs csà fd`d ncfb su ndìrb= oörùgc b`pàrlfc, pdrqub sb kbtbr`lnc `bklcntb gc bxpbrl`bntcflön. Bn bstb fursd, cprbnkbrb`ds fö`d fcgfugcr gc oörùgc b`pàrlfc fdn unc prdpdrflön d un pdrfbntcmb kckd. Kbib`ds sbjulr bstds pcsds=

Bg ný`brd kb `csc ctö`lfc (C) bs gc `csc kb un bgb`bntd quà`lfd. Gd bstuklc`ds bn gc sb`cnc <.

3. Klvlklr gc `csc kb fckc bgb`bntd qub nds kcn bntrb gc `csc ctö`lfc (C) kbg bgb`bntd fdrrbspdnklbntb. Gcs `cscs ctö`lfcs kb gds bgb`bntds sb bnfubntrcn bn gc tcigc pbrlöklfc. 3

C

3.8

?

E C

F

39.8

9. Ybkuflr c ný`brds bntbrds gds rbsugtckds kb gc klvlslön kbg pcsd 3. Bstd sb gdjrc klvlklbnkd gds fdflbntbs bntrb bg `bndr kb bggds. Gd bntbnkbrb`ds `bmdr fdn un bmb`pgd. ´Suì bs bg prdplgbnd4 Bg prdplgbnd bs un jcs ùy rbcftlvd b lnogc`cigb qub sb ditlbnb kbg pbtrögbd. Vb utlglzc pcrc gc ditbnflön kb jcsdglnc y bn gc sàntbsls kb sus kbrlvckds= pgãstlfds, klsdgvbntbs, rbslncs, btf. Bg prdplgbnd bs un fd`pubstd odr`ckd pdr fcridnd b elkröjbnd. Fdntlbnb 5?% kb fcridnd y 3;% kb elkröjbnd. Bstds pdrfbntcmbs sljnlolfcn qub pdr fckc 388 j kb fd`pubstd, tbnkrb`ds 5? j kb fcridnd y 3; j kb elkröjbnd. Gc oörùgc b`pàrlfc sbrã F xEy kdnkb x b y sdn ný`brds bntbrds.

98

LJBY ∙ [cfcnã

Oörùgc b`pàrlfc kbg prdplgbnd Xcrc fcgfugcr gc oörùgc b`pàrlfc= 3.

Klvlkl`ds gc `csc kb fckc bgb`bntd bntrb su `csc ctö`lfc (C). Gc `csc ctö`lfc kbg fcridnd bs 39 j y gc `csc ctö`lfc kbg elkröjbnd bs 3 j. 5? j F 0 :.9 ãtd`ds pdr jrc`d kb fcridnd 39 j F/ 3 ãtd`d 3; j E 0 3; ãtd`ds pdr jrc`d kb elkröjbnd 3 j E/ 3 ãtd`d

9.

Xcrc rbkuflr bstc rbgcflön c ný`brds bntbrds, sb klvlkbn cìds vcgdrbs pdr bg vcgdr `bndr, :.9 [bnjc bn fubntc gcs rbjgcs kb cprdxl`cflön qub cprbnklö bn gc sb`cnc 3 kbg fursd kb Bstckàstlfc.

:.9 ãtd`ds kb F ú :.9 0 3 3; ãtd`ds E ú :.9 0 3.<; 0 9

Gc oörùgc b`pàrlfc kbg prdplgbnd bs FE9 Jbnbrcg`bntb gcs oörùgcs b`pàrlfcs yc sb fdndfbn, pbrd bs l`pdrtcntb qub ustbk cprbnkc c fcgfugcrgcs. _bc`ds dtrd bmb`pgd= Gc jgufdsc bs bg fd`pubstd drjãnlfd `ãs ciunkcntb kb gc ncturcgbzc Gc jgufdsc bs unc odr`c kb czýfcr qub sb bnfubntrc glirb bn gcs orutcs y bn gc `lbg. Bg tìr`lnd "jgufdsc " vlbnb kbg jrlbjd " jguaus " qub sljnlolfc kugfb y bg suolmd "‖dsc " lnklfc qub sb trctc kb un czýfcr. Bs gc oubntb prl`crlc kb bnbrjàc kb gcs fìgugcs. Rnc ùbstrc kb jgufdsc tlbnb ;8% kb fcridnd (F), : % kb elkröjbnd (E) y 26 % kb dxàjbnd (D). Vl fdnslkbrc`ds 388 j kb fd`pubstd, tbnkrb`ds ;8 j kb F, : j kb E y 26 j kb D.

Odrùgc b`pàrlfc kb gc jgufdsc Xcrc fcgfugcr gc oörùgc b`pàrlfc kb gc jgufdsc= 3.

Klvlkl`ds fckc `csc bntrb gc `csc ctö`lfc kbg bgb`bntd fdrrbspdnklbntb. Bg vcgdr kb gc `csc ctö`lfc (C) bstã bn su tcigc pbrlöklfc. ;8 j F 0 6.6 ãtd`ds pdr jrc`d kb fcridnd 39 j F/ 3 ãtd`d :jE 0 : ãtd`ds pdr jrc`d kb elkröjbnd 3 j E/ 3 ãtd`d 26 j D 0 6.6 ãtd`ds pdr jr c`d kb dxàjbnd 3? j D/ 3 ãtd`d Suà`lfc LL ∙ Vb`cnc 3<

93

9.

Cedrc klvlkl`dsfckc rbsugtckdpdr bg `ãs pbqubód, bn bstb fcsd pdr 6.6. 6.6 ãtd`ds F ú 6.6 0 3 : ãtd`ds kb E ú 6.6 0 9.3 0 9

Ybfubrkb= Bg suiànklfb 3 nd sb bsfrlib pdrqub sb sdirbbntlbnkb.

6.6 ãtd`ds kb D ú 6.6 0 3

Gc oörùgc b`pàrlfc kb gc jgufdsc bs FE9D

Bmbrflfld 9 C.

Fcgfugb gc oörùgc b`pàrlfc kb un fd`pubstd qub tlbnb ?8% kb fcridnd (F) y ;8 % kb elkröjbnd. Fdnslkbrb 388 j kb fd`pubstd. 3)

Klvlkc fckc `csc pdr gc `csc ctö`lfc kbg bgb`bntd fdrrbspdnklbntb. ?8 j F ãtd`ds pdr j kb F 39 j F/ 3 ãtd`d 0 ;8 j E 0 3 j E/ 3 ãtd`d

9)

ãtd`ds pdr j kb E

Cedrc klvlkc fckc und kb gds rbsugtckds cntbrldrbs pdr bg `ãs pbqubód kb bggds. 2 ãtd`ds kb F ú

0

;8 ãtd`ds kb E ú

0

Gc oörùgc b`pàrlfc kbg fd`pubstd bs= I.

Kbtbr`lnb gc oörùgc b`pàrlfc kb un fd`pubstd qub fdntlbnb 69.; % kb sdkld, 99.? % kb czuorb y ;2 % kb dxàjbnd. 3)

Klvlkc fckc `csc pdr gc `csc ctö`lfc kbg bgb`bntd fdrrbspdnklbntb. 69.; j Nc ãtd`ds pdr j kb Nc 96 j Nc/ 3 ãtd`d 0 99.? j V 0 69.3 j V/ 3 ãtd`d ;2 j D 0 3? j D/ 3 ãtd`d

9)

ãtd`ds pdr j kb V ãtd`ds pdr j kb D

Klvlkc gds rbsugtckds cntbrldrbs pdr bg `ãs pbqubód kb bggds. 3.; ãtd`ds ú 8.: ãtd`ds ú 9.5 ãtd`ds ú

0 0 0

Gc oörùgc b`pàrlfc kbg fd`pubstd bs=

99

LJBY ∙ [cfcnã

9.9 Oörùgc `dgbfugcr Lnodr`cflön bxcftc Gc oörùgc `dgbfugcr, c klobrbnflc kb gc oörùgc b`pàrlfc, lnklfc gc fd`pdslflön rbcg kb fckc unc kb gcs `dgìfugcs qub odr`cn un fd`pubstd. Gc oörùgc `dgbfugcr pubkb fcgfugcrsb c pcrtlr kb gc odrùgc b`pàrlfc y kb su pbsd `dgbfugcr. _bc`ds fö`d fcgfugcrgc= 3. Fcgfugc`ds gc `csc kb gc oörùgc b`pàrlfc. Xcrc ecfbrgd, su`c`ds bg ný`brd ctö`lfd (C) kb sus bgb`bntds. 9. Klvlkl`ds gc `csc `dgbfugcr rbcg qub nds ecn prdpdrfldnckd, bntrb gc `csc fcgfugckc fdn gc oörùgc b`pàrlfc. 6. @ugtlpglfc`ds fckc suiànklfb kb gc oörùgc b`pàrlfc pdr bg fdflbntb ditbnlkd bn bg pcsd 9. Fdn bstds kctds bsfrlil`ds gc oörùgc `dgbfugcr. Xdr bmb`pgd= Bg prdplgbnd kb oörùgc b`pàrlfc FE9 tlbnb un pbsd `dgbfugcr kb ;9 j. Ecggcr su oörùgc `dgbfugcr.

Xcrc fcgfugcr gc oörùgc `dgbfugcr= 3. Fcgfugc`ds gc `csc kb gc oörùgc b`pàrlfc=

FE9039 j + 9(3 j) 0 39 j + 9 j 0 3; j 9. Klvlkl`ds gc `csc `dgbfugcr rbcg qub nds ecn kckd, bntrb gc `csc fcgfugckc fdn gc oörùgc b`pàrlfc=

;9 j ú 3; j 0

6

6. @ugtlpglfc`ds fckc suiànklfb kb gc oörùgc b`pàrlfc pdr bg ný`brd ditbnlkd bn gc klvlslön=

F3 x 6E9 x 6 0 F6E? Gc oörùgc `dgbfugcr kbg prdplgbnd bs F6E?


96

Dtrd bmb`pgd= Gc jgufdsc kb oörùgc b`pàrlfc FE9D tlbnb unc `csc `dgbfugcr kb 358 j. Ecggcr su oörùgc `dgbfugcr.

3.

Fcgfugc`ds gc `csc kb gc oörùgc b`pàrlfc=

FE9D039 j + 9(3j) + 3? j 068 j 9.

Klvlkl`ds gc `csc `dgbfugcr rbcg qub nds ecn kckd, bntrb gc `csc fcgfugckc fdn gc oörùgc b`pàrlfc= FE9D.

358 j ú 68 j 0 ? 6. @ugtlpglfc`ds fckc suiànklfb kb gc oörùgc b`pàrlfc pdr bg ný`brd ditbnlkd kb gc klvlslön=

F3 x ? E9 x ? D3 x ? 0 F?E39D? Xdr tcntd, gc oörùgc `dgbfugcr kb gc jgufdsc bs F?E39D?

Bmbrflfld 6 C.

Fcgfugb gc oörùgc `dgbfugcr kb gds sljulbntbs fd`pubstds. Vljc gds pcsds qub cprbnklö bn gds bmb`pgds. 3)

Rn fd`pubstd kb oörùgc b`pàrlfc F ;E: tlbnb un pbsd `dgbfugcr kb 338 j. Ecggcr su oörùgc `dgbfugcr. c.

Fcgfugb gc `csc kb gc oörùgc b`pàrlfc. F 0 39 j, E 0 3 j. F;E: 0 ;(39 j) + :(3 j) 0

i.

Klvlkc gc `csc `dgbfugcr rbcg qub gb ecn kckd, bntrb gc `csc fcgfugckc fdn gc oörùgc b`pàrlfc F;E: 338 j ú

f.

0

Xcrc bsfrlilr gc oörùgc `dgbfugcr, ùgtlpglqub fckc suiànklfb kb gc oörùgc b`pàrlfc pdr bg ný`brd ditbnlkd kb gc klvlslön=

Gc oörùgc `dgbfugcr bs=

9;

LJBY ∙ [cfcnã

9)

Gc vltc`lnc "F" kb oörùgc b`pàrlfc F 6E;D6 tlbnb un pbsd `dgbfugcr rbcg kb 3:? j. Cvbrlj÷b fuãg bs su oörùgc `dgbfugcr . c.

Fcgfugb gc `csc kb gc oörùgc b`pàrlfc. F 0 39 j, E 0 3 j, D 03? F6E;D6 0 6(39 j) + ;(3 j)+6 (3?j) 0

i.

Klvlkc gc `csc `dgbfugcr rbcg qub gb ecn kckd, bntrb gc `csc fcgfugckc fdn gc oörùgc b`pàrlfc F6E;D6. 3:? j ú

f.

0

Xcrc bsfrlilr gc oörùgc `dgbfugcr, ùgtlpglqub fckc suiànklfb kb gc oörùgc b`pàrlfc pdr bg ný`brd ditbnlkd kb gc klvlslön=

Gc oörùgc `dgbfugcr bs=

Ybsu`bn 3.

Rnc oörùgc quà`lfc bs gc rbprbsbntcflön bsfrltc kb gc fd`pdslflön kb unc `dgìfugc d un fd`pubstd `bklcntb sàìdgds quà`lfds. Rnc oörùgc quà`lfc bstã odr`ckc pdr sàìdgds quà`lfds y suiànklfbs.

9.

Fgcslolfcflön kb oörùgcs quà`lfcs

9.3

Oörùgc b`pàrlfc= sb usc pcrc lnklfcr bg tlpd kb bgb`bntds prbsbntbs bn un fd`pubstd bn su prdpdrflön `ànl`c. Xcrc fcgfugcr unc oörùgc b`pàrlfc= • Klvlkl`ds fckc `csc bntrb gc `csc ctö`lfc kbg bgb`bntd fdrrbspdnklbntb. • Klvlkl`ds fckc und kb gds rbsugtckds cntbrldrbs, bntrb bg `ãs pbqubód kb bggds.

9.9

Oörùgc `dgbfugcr= lnklfc gc fd`pdslflön rbcg kb fckc unc kb gcs `dgìfugcs qub odr`cn un fd`pubstd. Xcrc fcgfugcr gc oörùgc `dgbfugcr= • Fcgfugc`ds gc `csc kb gc oörùgc b`pàrlfc. • Klvlkl`ds gc `csc `dgbfugcr rbcg qub nds ecn kckd, bntrb gc `csc fcgfugckc fdn gc oörùgc b`pàrlfc. • @ugtlpglfc`ds fckc suiànklfb kb gc oörùgc b`pàrlfc pdr bg ný`brd ditbnlkd kb gc klvlslön. Suà`lfc LL ∙ Vb`cnc 3<

92

Cutdfdntrdg Cftlvlkck 3. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd qub sb rbgcfldnc fdn bg fdnfbptd kb gc fdgu`nc lzqulbrkc. 3)

Ybprbsbntcflön bsfrltc kb gc fd`pdslflön kb un fd`pubstd quà`lfd.

`dgìfugc oörùgc quà`lfc sàìdgd quà`lfd

9)

Ný`brd qub lnklfc gc fcntlkck kb ãtd`ds kb fckc und kb gds bgb`bntds qub odr`cn un fd`pubstd.

`dgìfugc suiànklfb sàìdgd quà`lfd

6)

oörùgc b`pàrlfc

Oörùgc quà`lfc qub lnklfc gc fcntlkck kb bgb`bntds prbsbntbs bn un fd`pubstd bn su prdpdrflön `ànl`c.

oörùgc `dgbfugcr oörùgc bstrufturcg

;)

oörùgc b`pàrlfc

Oörùgc quà`lfc qub lnklfc gc fd`pdslflön rbcg kb un fd`pubstd, tcg y fd`d sb prbsbntc bn gc ncturcgbzc.

oörùgc `dgbfugcr oörùgc bstrufturcg

Cftlvlkck 9. Fdnstruyc fdnfbptds. Gbc bg fc`pd sb`ãntlfd kbg fdnfbptd —oörùgc quà`lfc‐ `dgìfugc fd`pubstd

rbprbsbntcflön

oörùgc quà`lfc fd`pdslflön

sàìdgds quà`lfds

Bsfrlic fdn sus pcgcircs unc kbolnlflön kb oörùgc quà`lfc. Cpöybsb bn gcs pcgcircs kbg fc`pd sb`ãntlfd.

9?

LJBY ∙ [cfcnã

Cftlvlkck 6. Bxtrcljc lnodr`cflön kb gcs oörùgcs quà`lfcs Bsfrlic bg tlpd y ný`brd kb ãtd`ds prbsbntbs bn fckc unc kb gds sljulbntbs fd`pubstds. Ybfubrkb qub bg suiànklfb und sb sdirbbntlbnkb y nd sb bsfrlib. Rtlglfb gc tcigc pbrlöklfc qub rbfdrtö bn gc sb`cnc 36. [lbnb un bmb`pgd. 8)

@jD (öxlkd kb `cjnbsld) Bg fd`pubstd bstã odr`ckd pdr=

Rn ãtd`d kb `cjnbsld Rn ãtd`d kb dxàjbnd

3)

9)

Cj(DE)6 (elröxlkd kb pgctc) Bg fd`pubstd bstã odr`ckd pdr=

ObE9 (klelkrurd kb elbrrd) Bg fd`pubstd bstã odr`ckd pdr=

6)

VnE; (tbtrcelkrurd kb bstcód) Bg fd`pubstd bstã odr`ckd pdr=

;)

2)

NE6 (c`dnlcfd) Bg fd`pubstd bstã odr`ckd pdr=

XE6 (odsolnc) Bg fd`pubstd bstã odr`ckd pdr=

?)

FE; (`btcnd) Bg fd`pubstd bstã odr`ckd pdr=

:)

END6 (ãflkd nàtrlfd) Bg fd`pubstd bstã odr`ckd pdr=


9:

Cftlvlkck ;. Fdnstruyc oörùgcs b`pàrlfcs y `dgbfugcrbs Gbc gc lnodr`cflön kb fckc nu`brcg y rbcglfb gds fãgfugds nbfbscrlds pcrc ecggcr gc oörùgc b`pàrlfc y/d `dgbfugcr. Eãjcgd bn su fuckbrnd. 3)

Gc putrbsflnc sb frbc cg pukrlrsb gc fcrnb, y bs bg fd`pubstd qub gb kc bg dgdr fcrcftbràstlfd. Bn 388 j kb fd`pubstd, fdntlbnb 2;.2 % kb fcridnd, 36.: % kb elkröjbnd y 63.:% kb nltröjbnd. Cvbrlj÷b su oörùgc b`pàrlfc y su oörùgc `dgbfugcr. Bg pbsd `dgbfugcr rbcg kb gc putrbsflnc bs 55 j.

9)

Bg `bklfc`bntd G-kdpc`lnc sb utlglzc bn bg trctc`lbntd kb gc bnobr`bkck kb Xcralnsdn. Fdntlbnb 2;.5 % kb fcridnd, 2.? % kb elkröjbnd, : % kb nltröjbnd y 69.2 % kb dxàjbnd.

6)

´Fuãg bs su oörùgc b`pàrlfc4 Fcgfugb gc oörùgc b`pàrlfc qub tlbnb gc sljulbntb fd`pdslflön bn unc ùbstrc kb 388 jrc`ds= Nc= 69.; j, X= 93.5 j, E= 8.: j, D= ;2.8 j.

;)

Gc fd`pdslflön kb un fd`pubstd bs= A, 9?.2 %1 Fr, 62.; %1 D, 65.3 %. Vl tbnb`ds unc ùbstrc kb 388 jrc`ds, kbtbr`lnb gc oörùgc b`pàrlfc.

2)

Rn fd`pubstd odr`ckd kb Nc, D y V tlbnb gc sljulbntb fd`pdslflön bn unc ùbstrc kb 388 jrc`ds= Nc= 69.; % D= ;2.3 % V= 99.2 %. Fcgfugcr su oörùgc b`pàrlfc.

?)

388 jrc`ds kb un fd`pubstd tlbnb 58 % kb F y 98 % kb E. ´Fuãg bs gc oörùgc `dgbfugcr kbg fd`pubstd sl su pbsd `dgbfugcr bs 68 j4

Cftlvlkck 2. Lnvbstljub bn gc rbk C. Gbc bg tbxtd. Gc quà`lfc kb gds fcridelkrctds Gds elkrctds kb fcridnd d fcridelkrctds rbprbsbntcn `ãs kbg <8% kb gc `ctbrlc sbfc kb gcs pgcntcs. Vdn fd`pubstds ciunkcntbs y klspdnligbs bn gds cgl`bntds. Bg cg`lkön, gc gcftdsc y gc scfcrdsc (czýfcr fdrrlbntb) sdn fcridelkrctds kljbrligbs pdr gds eu`cnds. Xrdpdrfldncn fcsl bg :8‖58% kb gcs fcgdràcs bn gc klbtc eu`cnc. Bg tìr`lnd fcridelkrctd sujlbrb unc fd`pdslflön kbg tlpd Fx(E9D)y, gd qub sljnlolfc qub gcs `dgìfugcs fdntlbnbn fcridnd bn gc `ls`c prdpdrflön qub `dgìfugcs kb cjuc. [bxtd ckcptckd kb wlalpbklc

I.

Lnvbstljub bn gc rbk fuãg bs gc oörùgc kbg cg`lkön y gc gcftdsc. Fd`pãrbgc fdn gc oörùgc b`pàrlfc qub gb kc bg tbxtd Fx(E9D)y. ´Vb fu`pgb bstc prdpdrflön bn gds kds fd`pubstds4 Xdr bmb`pgd= Bn bg fcsd kb gc scfcrdsc gc oörùgc quà`lfc bs F 39E99D33 y pdkb`ds bsfrlilrgc csà= F 39(E9D)33. Fu`pgb fdn gc oörùgc qub nds prdpdrfldnc bg tbxtd= F39E9 x 33D3 x 33 0 F39E99D33

Xubkb fdnsugtcr bstcs pãjlncs= • bs.wlalpbklc.drj/wlal/Gcftdsc

95

LJBY ∙ [cfcnã

• www.ildgdjlc.bku.cr./`cfrd`dgbfugcs/czufcr.et`


Bgcidrb un kbsdkdrcntb fcsbrd Bstc sb`cnc gb prdpdnb`ds sbjulr unc oörùgc kb gcidrctdrld qub slrvb pcrc ocirlfcr kbsdkdrcntb.

´Suì nbfbsltc4 

9 fufecrckcs kb vcsbglnc söglkc y sln dgdr



3 sdirbfltd kb ilfcridnctd kb sdkld



9 fufecrckcs kb pdgvd kb tcgfd sln dgdr (dpfldncg)



3 scrtìn d unc dggltc gl`plc



3 pcgbtc d cgjýn utbnslgld kb `ckbrc qub slrvc pcrc rbvdgvbr



3 bstuoc



3 idtb pbqubód kb pgãstlfd d un orcsfd gl`pld y fdn tcpckbrc.

 

gãplz glirbtc kb fc`pd

´Suì kbib ecfbr4 3. Fdgdqub gcs kds fufecrckcs kb vcsbglnc bn bg scrtìn y pönjcgcs c fcgbntcr (c icmc tb`pbrcturc). 9. Fucnkd gc vcsbglnc sb kbrrltc, cjrbjub bg fdntbnlkd kbg sdirbfltd kb ilfcridnctd y `bzfgb ilbn. 6. Gubjd cóckc gcs kds fufecrckcs kb pdgvd kb tcgfd (dpfldncg) y sljc rbvdgvlbnkd. ;. Sultb gc `bzfgc kbg oubjd y kìmbgc bnorlcr. 2. Fucnkd sb bnoràb juãrkbgc bn bg idtbfltd. Yborljìrbgd sl bs pdsligb. ?. Ýsbgd tdkcs gcs `cócncs pcrc bvltcr bg dgdr kbg sukdr. Bsfrlic bn su glirbtc kb fc`pd sus disbrvcfldnbs y fd`pãrtcgcs bn bg fbntrd kb drlbntcflön. Lnvbstljub bn Lntbrnbt fuãgbs sdn gcs oörùgcs quà`lfcs kb gc vcsbglnc, bg ilfcridnctd y bg tcgfd. Gubjd fd`pãrtcgcs bn bg fbntrd kb drlbntcflön.


9<



gdjrckd

rbjugcr

nd gdjrckd

Cspbftds c bvcgucr 3.

Bxpglfd fdn `ls pcgcircs quì bs unc oörùgc quà`lfc.

9.

Bxtrcljd lnodr`cflön kb unc oörùgc quà`lfc.

Kbspuìs kb 6. bstuklcr...

Ybfdndzfd gds klstlntds tlpds kb oörùgc quà`lfc.

;.

Fcgfugd oörùgcs b`pàrlfcs y oörùgcs `dgbfugcrbs.

2.

Cpglquì unc oörùgc quà`lfc bn gc bgcidrcflön kb un kbsdkdrcntb fcsbrd.


68

LJBY ∙ [cfcnã

98

Ounflön quà`lfc


63


Ybfdndfbr fd`pubstds ilncrlds, tbrncrlds y fuctbrncrlds.



Kbolnlr quì bs ounflön quà`lfc.



Lkbntlolfcr y fgcslolfcr gcs ounfldnbs quà`lfcs= öxlkd, ãflkd, icsb y scg.



Ybfdndfbr gcs fcrcftbràstlfcs prlnflpcgbs kb öxlkds, ãflkds, icsbs y scgbs.



Bxpbrl`bntcr fdn bg ãflkd fàtrlfd.



´Suì bnfdntrcrã bstc sb`cnc4 ¡Xcrc fd`bnzcr!

69

• Fd`pubstds ilncrlds, tbrncrlds y fuctbrncrlds


• Ounflön quà`lfc=


• ¡Ocirlqub tlntc lnvlsligb!

LJBY ∙ [cfcnã

öxlkd, ãflkd, icsb, scg.

¡Xcrc fd`bnzcr! Fd`pubstds ilncrlds, tbrncrlds y fuctbrncrlds ¡Kb kds, kb trbs, kb fuctrd! Gc `cydr pcrtb kb gcs sustcnflcs bn gc ncturcgbzc sb bnfubntrcn bn odr`c kb fd`pubstds bn gds qub sb fdìlncn kds, trbs, fuctrd d `ãs bgb`bntds quà`lfds. Vbjýn bg ný`brd kb bgb`bntds, gds fd`pubstds sb fgcslolfcn bn=

Fd`pubstds ilncrlds Kds bgb`bntds Gds fd`pubstds ilncrlds bstãn odr`ckds pdr kds bgb`bntds . Xdr bmb`pgd=

•

Bg ãflkd fgdreàkrlfd d ãflkd ùrlãtlfd EFg bstã odr`ckd pdr elkröjbnd (E) y fgdrd ( Fg).

•

Bg öxlkd kb klelkröjbnd d cjuc E9D bstã odr`ckd pdr dxàjbnd (D) b elkröjbnd (E).

•

Bg fgdrurd kb sdkld d scg fd`ýn NcFg bstã odr`ckd pdr sdkld (Nc) y fgdrd (Fg).

Fd`pubstds tbrncrlds [rbs bgb`bntds Gds fd`pubstds tbrncrldsbstãn odr`ckds pdr trbs bgb`bntds. Xdr bmb`pgd=

•

Bg elkröxlkd kb sdkld d sdkc fãustlfc NcDE bstã odr`ckd pdr sdkld (Nc), dxàjbnd ( D) b elkröjbnd (E).

•

Bg ãflkd sugoýrlfd d cfbltb kb vltrldgd E9VD ; bs bg fd`pubstd `ãs prdkuflkd bn bg ùnkd y bstã odr`ckd pdr elkröjbnd ( E), czuorb (V) y dxàjbnd (D).

•

Bg ãflkd nàtrlfd d cjuc oubrtb END6 bs un ãflkd ùy fdrrdslvd y bstã odr`ckd pdr elkröjbnd ( E) nltröjbnd ( N) y dxàjbnd (D).


66

Fd`pubstds fuctbrncrlds Fuctrd bgb`bntds Gds fd`pubstds fuctbrncrlds bstãn odr`ckds pdr fuctrd bgb`bntds . Xdr bmb`pgd=

•

Bg ilfcridnctd kb sdkld NcEFD 6 qub sb utlglzc bn pcnckbràc, bstã odr`ckd pdr sdkld (Nc), elkröjbnd ( E), fcridnd (F) y dxàjbnd ( D).

•

6 bs un fdnsbrvcntb odr`ckd ãflkd pdtcsld (AEVD Bg E), czuorb pdrsugoltd pdtcsld ( A),kb elkröjbnd (V) y dxàjbnd (D).

•

Bg fcridnctd kb c`dnld (NE;)9FD6 sb utlglzc bn gc ocirlfcflön kb scgbs crd`ãtlfcs y bstã odr`ckd pdr nltröjbnd (N), elkröjbnd (E), fcridnd ( F) y dxàjbnd ( D).

•

Bg ilfcridnctd kb pdtcsld AEFD 6 sb utlglzc, fucnkd bstã pugvbrlzckd, fd`d bxtlntdr kb lnfbnklds. Bstã odr`ckd pdr pdtcsld ( A), elkröjbnd (E), fcridnd ( F) y dxàjbnd (D). Bstc sb`cnc vc`ds c bstuklcr gcs fcrcftbràstlfcs qub pbr`ltbn rbfdndfbr y ndìrcr c gds klstlntds fd`pubstds.

¡C trcicmcr! Fubntb fuãntds bgb`bntds klstlntds odr`cn fckc fd`pubstd y bsfrlic sdirb gc gànbc sl bs un fd`pubstd ilncrld, tbrncrld d fuctbrncrld. [lbnb un bmb`pgd.

6;

8)

FuD

3)

F9E2DE

9)

NcDE

6)

Ib(DE)Fg

;)

NE;

2)

Nc9Fr9D:

LJBY ∙ [cfcnã

Fd`pubstd ilncrld


3. Fd`pubstds lndrjãnlfds y sus ounfldnbs quà`lfcs Gds fd`pubstds lndrjãnlfds sdn cqubggds qub nd tlbnbn fcridnd bn su fd`pdslflön. Vb fgcslfcn pdr bg ný`brd kb bgb`bntds quà`lfds qub gds odr`cn y sbjýn gc ounflön quà`lfc qub fdntbnjcn. Bn gc sbfflön ¡Xcrc fd`bnzcr! vl`ds qub pdr su ný`brd kb bgb`bntds pubkbn sbr= ilncrlds, tbrncrlds d fuctbrncrlds. Cedrc cprbnkbrb`ds fö`d sb fgcslfcn sbjýn su ounflön quà`lfc. Gc ounflön quà`lfc bs bg fdnmuntd kb fd`pubstds fdn prdplbkckbs quà`lfcs sl`lgcrbs kbilkd c qub pdsbbn un jrupd kb ãtd`ds fcrcftbràstlfd. Gds fd`pubstds lndrjãnlfds sbjýn su ounflön quà`lfc sb fgcslolfcn bn= • öxlkds • ãflkds

• icsbs y • scgbs.

3.3 Ounflön öxlkd dxàjbnd + bgb`bntd Gds öxlkds gcs fdìlncfldnbs ilncrlcs bntrb bg dxàjbnd fdn vcgbnflc y tdkds gds sdn kb`ãs bgb`bntds quà`lfds, c bxfbpflön kb gds ,jcsbs ndigbs y∙9, bg ýdr. Gds öxlkds sb fgcslfcn bn= • Öxlkds iãslfds= sdn fd`pubstds ilncrlds kb dxàjbnd y un `btcg. Xdr bmb`pgd=

dxàjbnd + `btcg 0 öxlkd iãslfd D

Fc

(fcgfld)

FcD

(öxlkd kb fcgfld)

_bc`ds dtrds bmb`pgds kb öxlkds td`cnkd bg jrupd 9 kb gds `btcgbs= dxàjbnd + ibrlgld 0 öxlkd kb ibrlgld (IbD) dxàjbnd + `cjnbsld 0 öxlkd kb `cjnbsld (@jD) dxàjbnd + bstrdnfld 0 öxlkd kb bstrdnfld (VrD) dxàjbnd + icrld 0 öxlkd kb icrld (IcD) dxàjbnd + rckld 0 öxlkd kb rckld (YcD) Gds öxlkds iãslfds sb fcrcftbrlzcn pdrqub cg fdìlncrsb fdn cjuc odr`cn icsbs d elkröxlkds. Suà`lfc LL ∙ Vb`cnc 98

62

• Öxlkds ãflkds= sdn fd`pubstds ilncrlds kb dxàjbnd y un nd `btcg. Xdr bmb`pgd=

dxàjbnd + nd `btcg 0 D

Fg

(fgdrd)

öxlkd ãflkd Fg9D

(öxlkdkbklfgdrd)

_bc`ds dtrds bmb`pgds kb öxlkds ãflkds td`cnkd bg jrupd 3? kb gds nd `btcgbs= dxàjbnd + czuorb 0 öxlkd kb czuorb (VD ) 6 dxàjbnd + sbgbnld 0 öxlkd kb sbgbnld (VbD) dxàjbnd + tbgurld 0 öxlkd kb tbgurld ([bD 9) Gds öxlkds ãflkds sb fcrcftbrlzcn pdrqub cg fdìlncrsb fdn cjuc odr`cn ãflkds.

Bmbrflfld 3 Ybggbnb bg fuckrd kb gc rbspubstc fdrrbftc c fckc prbjuntc. [lbnb un bmb`pgd.

6?

8)

´Suì fd`pubstd sb odr`c sl sb ecfb rbcffldncr un `btcg `ãs dxàjbnd4

öxlkd iãslfd öxlkd ãflkd cjuc

3)

´Fuãg bs gc vcgbnflc kbg dxàjbnd bn gc ounflön öxlkd4

∙9 9 ∙3

9)

´Suì fd`pubstd sb odr`c sl sb ecfb rbcffldncr un nd `btcg `ãs dxàjbnd4

öxlkd iãslfd öxlkd ãflkd cjuc

6)

´Suì fd`pubstds odr`cn gds öxlkds iãslfds cg rbcffldncr fdn cjuc4

elkröxlkds elkrurds ãflkds

LJBY ∙ [cfcnã

3?

[b

3.9 Ounflön ãflkd ldnbs elkröjbnd + nd `btcg (jrupd 3? d 3:) ldnbs elkröjbnd + nd `btcg + dxàjbnd Gds ãflkds sdn fd`pubstds qub sb fcrcftbrlzcn pdrqub fbkbn ldnbs elkröjbnd (E+) fucnkd sb klsubgvbn bn cjuc. Gds ãflkds tlbnbn un scidr fcrcftbràstlfd, ùy oc`lglcr pcrc ndsdtrds= fd`d bg ãflkd cfìtlfd, prbsbntb bn bg vlncjrb d bg ãflkd fàtrlfd kbg gl`ön y gc ncrcnmc. Gds ãflkds sb fgcslfcn bn kds tlpds, sbjýn bg bgb`bntd cg qub sb unb bg elkröjbnd. _bc`ds= • Elkrãflkds= sdn ãflkds ilncrlds odr`ckds pdr bg elkröjbnd fdn gds nd `btcgbs kb gds jrupds 3? y 3: (bxfbptucnkd cg dxàjbnd, qub fucnkd sb fdìlnc fdn elkröjbnd odr`c cjuc). Xdr bmb`pgd=

nd `btcg elkröjbnd + jrupd 3? d 3: 0 elkrãflkd E

Fg

EFg

(fgdrd)

(ãflkd fgdreàkrlfd)

_bc`ds dtrds bmb`pgds kb elkrãflkds td`cnkd bg jrupd 3: kb gds nd `btcgbs= elkröjbnd + ogýdr 0 ãflkd ogudreàkrlfd (EO) elkrdjbnd + ird`d 0 ãflkd irdèàkrlfd (EIr) elkröjbnd + ydkd 0 ãflkd ydkeàkrlfd (EL) • Dxãflkds= sdn ãflkds tbrncrlds (kb trbs bgb`bntds) odr`ckds pdr elkröjbnd, dxàjbnd y un nd `btcg. Xdr bmb`pgd=

elkröjbnd + dxàjbnd + nd `btcg 0 E

D

V

(czuorb)

dxãflkd E9VD ;

(ãflkd sugoýrlfd)

Dtrds bmb`pgds kb dxãflkds Elkröjbnd + dxàjbnd + crsìnlfd (nd `btcg) 0 ãflkd crsìnlfd (E 6CsD;) Elkröjbnd + dxàjbnd + fgdrd (nd `btcg) 0 ãflkd fgdrdsd (EFgD 9) Suà`lfc LL ∙ Vb`cnc 98

6:

3.6 Ounflön icsb `btcg + cnldnbs elkrdxlgd (DE∙) [cg vbz nd gcs ggc`b`ds "icsbs" pbrd tdkds eb`ds bstckd bn fdntcftd fdn cgjunc kb bggcs. Gcs icsbs tlbnbn un scidr c`crjd y sl gcs tdfc`ds, tbnb`ds gc sbnscflön kb tbnbr "mciön bntrb gcs `cnds". Gc gbfeb kb `cjnbslc qub td`c`ds fd`d gcxcntb, bs unc icsb1 csà fd`d gc gbmàc, qub usc`ds fd`d igcnqubckdr kb rdpc, tcìlìn bs unc icsb. Gcs icsbs sdn un jrupd kb fd`pubstds quà`lfds odr`ckds pdr un `btcg y und d vcrlds cnldnbs elkrdxlgd (DE∙). Xdr bmb`pgd=

`btcg + elkrdxlgd (DE ) 0 icsb ∙

Fc Oàmbsb= bg cnlön elkrdxlgd (DE‖) bstã bsfrltd c gc kbrbfec bn gcs oörùgcs kb gcs icsbs.

DE

∙

Fc(DE) 9

(elkröxlkd kb fcgfld)

_bc`ds cgjunds bmb`pgds fdn gds `btcgbs kbg jrupd 3= gltld + elkröxlkd 0 elkröxlkd kb gltld (GlDE) sdkld + elkröxlkd0 elkröxlkd kb sdkld (NcDE) pdtcsld + elkröxlkd 0 elkröxlkd kb pdtcsld (ADE) ruilkld + elkröxlkd 0 elkröxlkd kb ruilkld (YDE) fbsld + elkröxlkd0 elkröxlkd kb fbsld (FsDE) orcnfld + elkröxlkd 0 elkröxlkd kb orcnfld (OrDE)

3.; Ounflön scg ãflkd + icsb Gcs scgbs sdn fd`pubstds qub rbsugtcn kb gc rbcfflön bntrb un ãflkd y unc icsb. Fd`d su ndìrb gd lnklfc, bstds fd`pubstds tlbnbn scidr scgckd y bn klsdguflön cfudsc fdnkufbn gc fdrrlbntb bgìftrlfc. Jbnbrcg`bntb sdn sustcnflcs frlstcglncs qub pubkbn fcìlcr kb bstckd pdr cfflön kbg fcgdr. Vbjýn bg ãflkd qub lntbrvlbnb bn gc rbcfflön, gcs scgbs sb fgcslfcn bn= • Vcgbs ecgdlkbs d ecgdlkbcs= fucnkd lntbrvlbnb un elkrãflkd. Xdr bmb`pgd= Bg fgdrurd kb sdkld NcFg sb odr`c c pcrtlr kb gc rbcfflön bntrb bg elkrãflkd EFg y gc icsb NcDE.

elkrãflkd + icsb 0 scg ecgdlkbc EFg

NcDE

(ãflkd fgdreàkrlfd) (elkröxlkd kb sdkld)

65

LJBY ∙ [cfcnã

NcFg

(fgdrurd kb sdkld)

• Dxlscgbs= sdn gcs scgbs qub tlbnbn dxàjbnd. Vb odr`cn fucnkd lntbrvlbnb un dxãflkd. Xdr bmb`pgd= Bg fgdrctd kb sdkld NcFgD 6 sb odr`c c pcrtlr kb gc rbcfflön bntrb bg dxãflkd EFgD 6 y gc icsb NcDE .

dxãflkd + icsb

dxlscg

EFgD 6

NcDE

NcFgD6

(ãflkd fgörlfd)

(elkröxlkd kb sdkld)

(fgdrctd kb sdkld)

Bg sugoctd kb fdirb FuVD ; sb odr`c c pcrtlr kb gc rbcfflön bntrb bg dxãflkd E9VD ; y gc icsb Fu(DE) 9.

dxãflkd + E9VD;

(ãflkdsugoýrlfd)

icsb Fu(DE)9

(elkröxlkd kb fdirb)

dxlscg FuVD;

(sugoctdkbfdirb)

Bmbrflfld 9 Bsfrlic sl bg fd`pubstd kb gc fdgu`nc lzqulbrkc bs un öxlkd, un ãflkd, unc icsb d unc scg. Xcrc lkbntlfcrgds, oàmbsb bn gc prbsbnflc kb D‖9, E+, DE‖ bn gcs oörùgcs. [cìlìn tbnjc prbsbntbs gcs fcrcftbràstlfcs kb fckc ounflön. [lbnb un bmb`pgd. fd`pubstd

ounflönquà`lfc

GlDE

icsb

@jD EIr NcO FrD EL AFg Cu9D Fc(DE)9


6<

Ybsu`bn

s b g c s

r= d p s c k c ` r d o

s b g c s l x d

b s c i + d lk f ã

s gb c s

c f l ` à u q ö n l f n u O

= d ` d f

b n  b k sb

s b r s. c lg d lf l` s tàs r s b b ft k c rc k c b l fs p d d r ` p d b t n ã b b tl k b d u p u q rj s n d ts u b b u sb p d `p d b f u b q k c d td lk n i u m b n k d f

) E D ( s b s c i

∙

= n b

n c f l s c gf sb n ö fln u o su n ý j b s

) D ( s d k l x ö

LJBY ∙ [cfcnã

d lg x rö k l e

=r d p s d k c r` od

+ d n b àj x d

td n b ` gb b

= n b n b lk lv k b s

=r d p s c k c ` r d o

+ b s c i

d k l f ã x d

d lk f ã r k l e + b s c i

= gd p ` b m b

= gd p ` b m b

6

gD F c N

g F c N

s d k l f ã x d

=r d p s d k c ` r d o

d n + d n b àj x d + d n b j ö r k l e

g c t b `

= gd p ` b m b

s d k l f ã r k l e

r= d p s d k c r` d o

d n + d n b j rö lk e

: 3 d ? 3 d p ru j g c t b `

= gd p ` b m b

g F E

g tc b ` d n

= d g p ` mb b

D9 g F

= n b n b k l v lk b s

⁽) E ( s d lk f ã

9 ∙

;8

r= d p s c k c ` r d o

s b n d l n c + g c t b ` d n

s c b lk d g c e


s d k l x ö

s d k l f ã

r= d p s d k c ` r d o

+ d n b j à x d

s d k l x ö

s d f l s ã i


+g d n tc b b j à ` x d

;

D V9 E

= gd p ` b m b

D c F

Cutdfdntrdg Cftlvlkck 3. Ybgcfldnb fdnfbptds C.

Ybggbnb bg fuckrd kbg fdnfbptd qub sb rbgcfldnc fdn gc kbolnlflön kb gc lzqulbrkc. 3)

Fd`pubstds qub rbsugtcn kb gc rbcfflön bntrb un ãflkd y unc icsb.

scgbs icsbs ãflkds

9)

Lön prbsbntb bn gc ounflön ãflkd.

E+ E∙ DE∙

6)

_cgbnflc kbg dxàjbnd bn gc ounflön öxlkd.

E+ D∙9 ED∙

;)

Fd`pubstds qub sb fcrcftbrlzcn pdr gc prbsbnflc kb cnldnbs elkrdxlgd (DE∙).

scgbs icsbs ãflkds

2)

Jrupd kb fd`pubstds odr`ckd pdr dxàjbnd y un `btcg d nd `btcg.

scgbs icsbs öxlkds

?)

Fdnmuntd kb fd`pubstds quà`lfds qub tlbnbn prdplbkckbs sl`lgcrbs kbilkd c qub pdsbbn un jrupd kb ãtd`ds fcrcftbràstlfd.

scg ecgdlkbc jrupd ounfldncg ounflön quà`lfc

:)

Vcgbs qub sb odr`cn fdn un dxãflkd.

dxlscgbs öxlkds iãslfds scgbs ecgdlkbcs Suà`lfc LL ∙ Vb`cnc 98

;3

I.

Bsfrlic quì fd`pubstd sb odr`c sbjýn su ounflön quà`lfc. Öxlkds= dxàjbnd + `btcg 0 dxàjbnd + nd `btcg0 Ãflkds= elkröjbnd + nd `btcg (jrupd 3? d 3:) 0 elkröjbnd + dxàjbnd + nd `btcg 0 Icsbs= `btcg + elkrdxlgd 0 Vcgbs= elkrãflkd + icsb 0 dxãflkd + icsb 0

Cftlvlkck 9. Fd`pgbtb lnodr`cflön Kbspuìs kb bstuklcr c prdounklkck bg fdntbnlkd, fd`pgbtb gc tcigc bsfrlilbnkd gc lnodr`cflön qub ocgtc. [lbnb un bmb`pgd. ounflönquà`lfc ãflkd

odr`ckdpdr=

bmb`pgd

ldnbs elkröjbnd `ãs nd `btcg (jrupd 3? d 3:)

EFg FrD NcDE NcFg

Cftlvlkck 6. Fgcslqub fd`pubstds sbjýn su ounflön quà`lfc Bsfrlic sl gds fd`pubstds kb gc lzqulbrkc sdn öxlkds, ãflkds, icsbs d scgbs. Xcrc lkbntlfcrgds oàmbsb bn gc prbsbnflc kb D‖9, E+, DE‖ bn gcs oörùgcs y tbnjc prbsbntb gcs fcrcftbràstlfcs kb fckc ounflön.

;9

3)

EO

:)

NcDE

9)

@j(DE)9

5)

E 9V

6)

Ic(IrD9)9

<)

Fr9D6

;)

Ob(DE)6

38)

CgDE6

2)

EFg

33)

EIr

?)

@nD

39)

NcIr

LJBY ∙ [cfcnã


¡Ocirlqub tlntc lnvlsligb! Bstc sb`cnc gb prdpdnb`ds ocirlfcr tlntc lnvlsligb fdn mujd kb gl`ön, un ãflkd kb usd fd`ýn bn nubstrc vlkc klcrlc. Fdn bstc tlntc pdkrã bsfrlilr, lntbrfcìlcr y kbsfuirlr `bnscmbs sbfrbtds.


Mujd kb 3 c 6 gl`dnbs (tcìlìn pubkb uscr vlncjrb)



Kds rbflplbntbs pbqubóds



Xcglggds d pcgltds gl`plds y kbgjckds (qub tbr`lnbn bn puntc)



Rnc edmc kb pcpbg idnk d fdplc igcnfd



Rnc gã`pcrc fdn unc idìlggc kb 388 wcts d unc fcnkbgc



gãplz



glirbtc kb fc`pd

´Suì kbib ecfbr4 3. Fdgdqub bg mujd kb gl`ön bn und kb gds rbflplbntbs. 9. @dmb gc puntc kbg pcglggd bn bg mujd kb gl`ön. 6. Rtlglfb bg pcglggd pcrc bsfrlilr un `bnscmb sbfrbtd bn gc edmc kb pcpbg olnd. Xubkb bsfrlilr c un fd`pcóbrd d fd`pcóbrc kb fgcsb d c cgjýn oc`lglcr. ;. Kbmb sbfcr. 2. Bntrbjub bg `bnscmb y eãjcgd rbcpcrbfbr. ´Fö`d4 Vdstbnjc bg pcpbg fbrfc kb gc idìlggc (d gc fcnkbgc) bnfbnklkc. ?. Disbrvb gd qub dfurrb y rbjàstrbgd bn su glirbtc kb fc`pd.


;6



gdjrckd

rbjugcr

nd gdjrckd


Ybfdndzfd fd`pubstds ilncrlds, tbrncrlds y fuctbrncrlds.

9.

Kbolnd quì bs ounflön quà`lfc.

Kbspuìs kb 6. bstuklcr... ;. 2.

Lkbntlolfd y fgcslolfd gcs ounfldnbs quà`lfcs= öxlkd, ãflkd, icsb y scg. Ybfdndzfd gcs fcrcftbràstlfcs prlnflpcgbs kb öxlkds, ãflkds, icsbs y scgbs. Bxpbrl`bntd fdn bg ãflkd fàtrlfd.


;;

LJBY ∙ [cfcnã

93

Nd`bnfgcturc L


;2


Bxpglfcr fdn sus pcgcircs quì bs gc nd`bnfgcturc quà`lfc y su l`pdrtcnflc pcrc gc quà`lfc.



Ybfdndfbr gcs fcrcftbràstlfcs kb gds slstb`cs kb nd`bnfgcturc bstbquld`ìtrlfd y Vtdfa.



Klstlnjulr bntrb ndìrb jbnìrlfd y ndìrb bspbfàolfd.



Bgcidrcr bn bqulpd unc tcigc kb vcgbnflcs ùrcg.




;?

¡Xcrc fd`bnzcr!

• Bg gbnjucmb kb gc `ýslfc


• Nd`bnfgcturc quà`lfc


• ¡Bgcidrb unc tcigc kb vcgbnflcs ùrcg!

LJBY ∙ [cfcnã

¡Xcrc fd`bnzcr! Bg gbnjucmb kb gc `ýslfc Gc `ýslfc bs un gbnjucmb unlvbrscg. Vu bsfrlturc fubntc fdn sljnds bspbflcglzckds qub bxprbscn gds klobrbntbs `ctlfbs kbg sdnlkd. ´Gds rbfubrkc4 Oàmbsb bn gc lgustrcflön= fgcvb kb sdg

pbntcjrc`c

tlb`pd

nbjrcs

igcnfcs

rbkdnkcs

Gds `ýslfds, nd l`pdrtc kb quì pcàs sbcn d fuãg sbc bg lkld`c qub ecigbn, bntlbnkbn bg gbnjucmb ùslfcg. Cg ljucg qub gds `ýslfds, gcs pbrsdncs kbklfckcs c gc quà`lfc tlbnbn un gbnjucmb prdpld= gc nd`bnfgcturc. Bg lnlfld kb gc nd`bnfgcturc quà`lfc bs unc fdntrliuflön kbg flbntàolfd orcnfìs Cntdlnb kb Gcvdlslbr, fdnslkbrckd bg pckrb kb gc quà`lfc `dkbrnc. Bntrb sus fdntrliufldnbs bstã gc prdpubstc kb frbcr unc nd`bnfgcturc quà`lfc qub kbsljncrc gcs sustcnflcs sbjýn sus prdplbkckbs. Kurcntb ùfeds códs, gds quà`lfds kcicn ndìrb c gds fd`pubstds c vdguntck. Xdr bmb`pgd, cg `brfurld (Ej) gb ggc`cicn czdjub y cg sugourd kb `brfurld (EjV), flncirld. Bstc sltucflön prdvdfcic fdnousldnbs pdrqub sl kds quà`lfds bnfdntrcicn bg `ls`d fd`pubstd, gb ggc`cicn kb odr`c klstlntc. Ckb`ãs gc klvugjcflön kb gds trcicmds y cvcnfbs flbntàolfds brc ùy gbntc.

Cntdlnb kb Gcvdlslbr (3:;6 - 3:<;) Flbntàfd orcnfìs

Bn 3<93, gc Fd`lslön Lntbrncfldncg kb Suà`lfc Xurc y Cpglfckc (LRXCF) sb rbunlö y bstcigbflö gcs rbjgcs fdn gcs qub sb ndìrcn c gds fd`pubstds quà`lfds. Nd distcntb, ùfeds ndìrbs kb sustcnflcs ljndrcn gcs rbjgcs y sb lkbntlolfcn fdn gds ndìrbs fdùnbs qub sb gbs ecn csljnckd c gd gcrjd kb gc elstdrlc. Xdr bmb`pgd bg cjuc (E9D) y bg c`dnlcfd (NE 6). Bstc sb`cnc lnlflcrb`ds bg bstukld kb gc nd`bnfgcturc. ¡Ckbgcntb!


;:


3. Nd`bnfgcturc quà`lfc Rn gbnjucmb klobrbntb Bg gbnjucmb kb gc quà`lfc bs gc nd`bnfgcturc quà`lfc. Gc nd`bnfgcturc quà`lfc bs bg fdnmuntd kb rbjgcs qub sb ecn bstcigbflkd pcrc ndìrcr c gds fd`pubstds quà`lfds. Gc nd`bnfgcturc pbr`ltb qub tdkds gds qub bstuklc`ds quà`lfc nds bntbnkc`ds.

Gds fd`pubstds lndrjãnlfds sdn cqubggds qub nd fdntlbnbn fcridnd .

Fd`d vl`ds bn gc sbfflön ¡Xcrc fd`bnzcr!, gcs rbjgcs kb nd`bnfgcturc bstãn klftckcs pdr gc LRXCF. Kb cfubrkd fdn bstcs ndr`cs, gds ndìrbs kb gds fd`pubstds lndrjãnlfds bstãn fdnstrulkds kb tcg odr`c qub c fckc und gb fdrrbspdnkb un ndìrb c pcrtlr kb su oörùgc. Bn jbnbrcg, bg ndìrb kb un fd`pubstd kbib lnfgulr bstds kctds= • Ndìrbs kb gds bgb`bntds qub gd odr`cn. • Gc `cnbrc bn qub bstãn fdìlnckds bsds bgb`bntds. • Gc ounflön qub fu`pgb fckc bgb`bntd bn bg fd`pubstd, sl bs pdsligb. Bn gc cftucglkck sb cfbptcn trbs slstb`cs kb nd`bnfgcturc= slstb`c bstbquld`ìtrlfd, slstb`c Vtdfa y slstb`c trcklfldncg d fgãslfd. Bstc sb`cnc sdgd bstuklcrã gcs fcrcftbràstlfcs jbnbrcgbs kbg slstb`c bstbquld`ìtrlfd y kbg slstb`c Vtdfa. Kb gc sb`cnc 99 bn ckbgcntb, cprbnkbrã fö`d uscrgds pcrc ndìrcr öxlkds, ãflkds, icsbs y scgbs.

Bmbrflfld 3 Fd`pgbtb bg `cpc fdnfbptucg. Gc nd`bnfgcturc quà`lfc bs

Ecy trbs slstb`cs=

;5

LJBY ∙ [cfcnã

3.3 Vlstb`c bstbquld`ìtrlfd Bg slstb`c bstbquld`ìtrlfd ndìrc c gcs sustcnflcs utlglzcnkd prbmds nu`ìrlfds jrlbjds (vbc gc tcigc kbg lnflsd c) qub lnklfcn bg ný`brd kb ãtd`ds kb un `ls`d bgb`bntd bn unc `dgìfugc. Ckb`ãs utlglzc un ndìrb jbnìrlfd y un ndìrb bspbfàfd.

c.

Xrbolmds nu`ìrlfds

Gc bstbquld`btràc bs gc pcrtb kb gc quà`lfc qub bstuklc gcs rbgcfldnbs bn gcs qub sb fdìlncn gcs sustcnflcs quà`lfcs.

Rn prbmd bs unc pcrtàfugc qub sb cntbpdnb c unc pcgcirc pcrc fcìlcr su sljnlfckd. Xdr bmb`pgd= bg prbmd "cntl" sljnlfc fdntrc1 cntlcgìrjlfd sljnlfc fdntrc gc cgbrjlc. Bn bg slstb`c bstbquld`ìtrlfd, gds prbmds sb b`pgbcn pcrc bspbflfcr bg ný`brd kb ãtd`ds qub odr`cn un fd`pubstd. Gds `ãs fdùnbs sb ùbstrcn bn gc tcigc. prbmd

Nd ãtd`ds

prbmd

Nd ãtd`ds

`dnd

3

ebxc

?

kldil

ebptc

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trl

9 6

dftc

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tbtrc

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ndnc

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pbntc

2

kbfc

38

i. Ndìrb jbnìrlfd Bg ndìrb jbnìrlfd bs bg qub lnklfc gc ounflön quà`lfc kb un fd`pubstd. Xdr bmb`pgd= öxlkd, ãflkd, icsb d scg.

f.

Ndìrb bspbfàolfd

Bg ndìrb bspbfàfd bs fd`d bg cpbgglkd kb gds fd`pubstds. Lnklfc gc bspbflb quà`lfc c gc qub pbrtbnbfb. Bg ndìrb kb gds fd`pubstds bn bg slstb`c bstbquld`ìtrlfd qubkc fdn gc sljulbntb bstrufturc. _bc bg bmb`pgd= Xrbmd (3) ‖ ndìrb jbnìrlfd + prbmd (9) ‖ ndìrb bspbfàfd trl

öxlkd

kl

Bg prbmd `dnd nd sb utlglzc pcrc bg ndìrb bspbfàfd, sdgd sb utlglzc bg ndìrb kbg bgb`bntd.

cntl`dnld

trlöxlkd kb klcntl`dnld (Vi 9D6) Suà`lfc LL ∙ Vb`cnc 93

;<

_bc`ds dtrds bmb`pgds= @dndfgdrurd kb ydkd (LFg) Xrbolmd (3)= `dnd Ndìrb jbnìrlfd= fgdrurd Xrbolmd (9)= nd tlbnb Ndìrb bspbfàolfd= ydkd Klöxlkd kb fcridnd (FD 9) Xrbolmd (3)= kl Ndìrb jbnìrlfd= öxlkd nd tlbnb Xrbolmd (9)= Ndìrb bspbfàolfd= fcridnd

@dnöxlkd kb klfdirb (Fu 9D) Xrbolmd (3)= `dnd Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= kl Ndìrb bspbfàolfd= fdirb @dndsugourd kb `brfurld (EjV) Xrbolmd (3)= `dnd Ndìrb jbnìrlfd= sugourd Xrbolmd (9)= nd tlbnb Ndìrb bspbfàolfd= `brfurld

Bmbrflfld 9 Bsfrlic gcs pcrtbs kbg ndìrb kb gds sljulbntbs fd`pubstds. [lbnb un bmb`pgd. 8)

[rlirdùrd kb frd`d (FrIr6) Xrbolmd (3)=

3)

Ndìrb jbnìrlfd=

irdùrd

Xrbolmd (9)=

nd tlbnb

Ndìrb bspbfàolfd=

frd`d

Ebptcöxlkd kb klfgdrd (Fg9D:) Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd=

9)

@dnöxlkd kb klpdtcsld (A9D) Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd=

28

LJBY ∙ [cfcnã

trl

3.9 Vlstb`c Vtdfa Bg slstb`c Vtdfa ndìrc c gds fd`pubstds quà`lfds bsfrlilbnkd fdn ný`brds rd`cnds gc vcgbnflc ctö`lfc kbg bgb`bntd fdn ndìrb bspbfàfd. Fd`d scib, bg ný`brd kb vcgbnflc d ný`brd kb dxlkcflön bs bg qub lnklfc bg ný`brd kb bgbftrdnbs qub un ãtd`d pdnb bn mubjd bn un bngcfb quà`lfd. Bg ný`brd kb vcgbnflc bs pdsltlvd fucnkd bg bgb`bntd tlbnkb c fbkbr gds bgbftrdnbs y bs nbjctlvd, fucnkd bg bgb`bntd tlbnkb c jcncr bgbftrdnbs. Gds bgb`bntds kb gds jrupds 3, 9, 6, ; y 2, tlbnbn un ný`brd kb vcgbnflc ljucg cg ný`brd kbg jrupd cg qub pbrtbnbfbn. Gds kb`ãs bgb`bntds tlbnbn vcgbnflcs vcrlcigbs. Gc vcgbnflc `ãs bstcigb bstã bsfrltc bn nbjrltc. [lbnb unc tcigc kb vcgbnflcs bn gc pãjlnc ?3. _cgbnflc 3 3 ]

E

Elkröjbnd

C

3.8

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3 ;

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Bn bg slstb`c Vtdfa, gc bstrufturc kbg ndìrb kb gds fd`pubstds qubkc csà= Ndìrb jbnìrlfd + kb + ndìrb kbg bgb`bntd + Nd kb vcgbnflc öxlkd

kb

cntl`dnld

LLL

öxlkd kb cntl`dnld (LLL) Vi9D6 Suà`lfc LL ∙ Vb`cnc 93

23

_bc gds bmb`pgds= Fgdrurd kb elbrrd (LLL) ObFg6 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb dxlkcflön kbg bgb`bntd=

Öxlkd kb fdirb (L) Fu 9D Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb dxlkcflön kbg bgb`bntd=

Elkröxlkd kb gltld (L) GlDE

fgdrurd elbrrd 6

öxlkd fdirb 3

elkröxlkd gltld

Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb dxlkcflön kbg bgb`bntd=

3

Öxlkd kb bstcód (L_) VnD 9 Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= bstcód Ný`brd kb dxlkcflön kbg bgb`bntd= ;

Ndr`cg`bntb, gc vcgbnflc kb un bgb`bntd pubkb vbrsb bn bg suiànklfb kbg dtrd ãtd`d (bn fd`pubstds ilncrlds y tbrncrlds). Xdr bmb`pgd= bn bg öxlkd kb elbrrd (LLL) Ob 9D , gc vcgbnflc kbg Ob (LLL) gc vb`ds fd`d suiànklfb kbg dxàjbnd= 6

D

Ob+6

∙9

Ob9D6

C vbfbs, fd`d bn bg öxlkd kb bstcód (L_) VnD 9, gc oörùgc sb ec sl`pglfckd, bg dxàjbnd tlbnb vcgbnflc ‖9 y bg bstcód ;, pbrd cg bsfrlilrgc sb sl`pglolfc=

Vn+;

Dtrd bmb`pgd kb sl`pglfcflön bs bg öxlkd kb fdirb (LL) FuD=

Fu+9

D

∙9

D

∙9

VnD9

FuD Fucnkd kbgbnfd`pubstd bs 3, nd sb bsfrlib. gc Xdrvcgbnflc bmb`pgd bg öxlkd kb pdtcsld A9D=

D

A+3 A9D

29

LJBY ∙ [cfcnã

∙9

Bmbrflfld 6 Bsfrlic gcs pcrtbs kbg ndìrb kb gds sljulbntbs fd`pubstds. Xcrc fd`prdicr bg ný`brd kb dxlkcflön fdnsugtb gc tcigc kb vcgbnflcs. 3)

Irdùrd kb frd`d (LLL) (FrIr6) Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

9)

Öxlkd kb fgdrd (_LL) (Fg9D:) Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

6)

Öxlkd kb pdtcsld (L) (A9D) Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

;)

Öxlkd kb tltcnld (L_) ([lD9) Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

2)

Elkröxlkd kb frd`d (LLL) Fr(DE)6 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

?)

Öxlkd kb fdirb (LL) (FuD) Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=


26

Ybsu`bn Bstc sb`cnc bstuklö qub= 3.

Gc nd`bnfgcturc quà`lfc bs bg fdnmuntd kb rbjgcs qub sb ecn bstcigbflkd pcrc ndìrcr c gds fd`pubstds quà`lfds. Gcs rbjgcs kb nd`bnfgcturc bstãn klftckcs pdr gc Rnlkck Lntbrncfldncg kb Suà`lfc Xurc y Cpglfckc (LRXCF) Bn jbnbrcg, bg ndìrb kb un fd`pubstd kbib lnfgulr bstds kctds= •

ndìrb kb gds bgb`bntds qub gd odr`cn,

•

gc `cnbrc bn qub bstãn fdìlnckds bsds bgb`bntds,

•

sl bs pdsligb, gc ounflön qub fu`pgb fckc bgb`bntd bn bg fd`pubstd.

Gds slstb`cs kb nd`bnfgcturc qub cprbnkl`ds sdn= 3.3 Bg slstb`c bstbquld`ìtrlfd trctc kb ndìrcr c gcs sustcnflcs uscnkd prbolmds nu`ìrlfds jrlbjds qub lnklfcn bg ný`brd kb ãtd`ds kb un `ls`d bgb`bntd bn unc `dgìfugc. Ckb`ãs, usc un ndìrb jbnìrlfd y un ndìrb bspbfàolfd. •

Bg ndìrb jbnìrlfd bs bg qub lnklfc gc ounflön quà`lfc kb un fd`pubstd. Xdr bmb`pgd= öxlkd, ãflkd, icsb d scg.

•

Bg ndìrb bspbfàolfd lnklfc gc bspbflb quà`lfc c gc qub fdrrbspdnkb. Xdr bmb`pgd= öxlkd kb fcgfld, elkröxlkd kb cgu`lnld, bntrb dtrds.

3.9 Bn bg slstb`c Vtdfa sb ndìrc c gds fd`pubstds quà`lfds bsfrlilbnkd fdn ný`brds rd`cnds gc vcgbnflc ctö`lfc kbg bgb`bntd fdn ndìrb bspbfàolfd.

Lnvbstljub bn gc rbk... Lnjrbsb c bstc klrbfflön= ettp=//bkufcfldn.prcftlfdpbklc.fd`/fd`d-bntbnkbr-gc-nd`bnfgcturc-9;;8 Cggà bnfdntrcrã un vlkbd qub gb cyukcrã c fd`prbnkbr gc nd`bnfgcturc quà`lfc. _ìcgd y fd`ìntbgd bn bg fbntrd kb drlbntcflön.

2;

LJBY ∙ [cfcnã

Cutdfdntrdg Cftlvlkck 3 Ybggbnb bg fuckrd kbg fdnfbptd qub sb rbgcfldnc fdn bg tbxtd kb gc lzqulbrkc. 3)

Fdnmuntd kb rbjgcs bstcigbflkcs pcrc ndìrcr fd`pubstds quà`lfds.

LRXCF prbolmds jrlbjds nd`bnfgcturc quà`lfc

9)

Vlstb`c kb nd`bnfgcturc qub ndìrc c gds fd`pubstds utlglzcnkd prbolmds pcrc lnklfcr bg ný`brd kb ãtd`ds qub odr`cn gc `dgìfugc.

Vtdfa Fgãslfd Bstbquld`ìtrlfd

6)

Ndìrb qub lnklfc gc ounflön quà`lfc kb un fd`pubstd.

ndìrb jbnìrlfd ndìrb fd`ýn ndìrb bspbfàolfd

;)

Vlstb`c kb nd`bnfgcturc qub usc ný`brds rd`cnds pcrc lnklfcr gc vcgbnflc kbg bgb`bntd fdn ndìrb bspbfàolfd.

Vtdfa Fgãslfd [rcklfldncg

2)

Ndìrb qub lnklfc gc bspbflb quà`lfc kb un fd`pubstd.

prbolmd ndìrb jbnìrlfd ndìrb bspbfàolfd

?)

Vlstb`c kb nd`bnfgcturc bn bg qub bstã ndìrckd bg öxlkd kb pgd`d (LL).

Vtdfa Fgãslfd Bstbquld`ìtrlfd Suà`lfc LL ∙ Vb`cnc 93

22

Cftlvlkck 9 Gbc gcs lkbcs sdirb ‗nd`bnfgcturc quà`lfc‐ qub sb prbsbntcn bn bg sljulbntb `cpc `bntcg. ndìrcr

rbjgcs nd`bnfgcturc quà`lfc

fd`pubstds

quà`lfds LRXCF

Bsfrlic fdn sus pcgcircs unc kbolnlflön kb nd`bnfgcturc quà`lfc. Xubkb cyukcrsb fdn gcs lkbcs kbg `cpc `bntcg.

Cftlvlkck 6 Bsfrlic gc odr`c jbnbrcg kb ndìrcr gds fd`pubstds bn gds slstb`cs kb nd`bnfgcturc qub cprbnklö.

2?

3)

Vlstb`c bstbquld`ìtrlfd

9)

Vlstb`c Vtdfa

LJBY ∙ [cfcnã

Cftlvlkck ; Bsfrlic gcs pcrtbs kbg ndìrb kb gds sljulbntbs fd`pubstds. 3)

[rlöxlkd kb klelbrrd Ob9D6 Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd=

9)

@dnöxlkd kb fdirb FuD Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd=

6)

@dnöxlkd kb klpdtcsld A9D Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)=

;)

Ndìrb bspbfàolfd= Öxlkd kb fdirb (L) Fu9D Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

2)

Öxlkd kb fgdrd (LLL) Fg9D6 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

?)

Öxlkd kb `cnjcnbsd (LLL) @n9D6 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd= Suà`lfc LL ∙ Vb`cnc 93

2:

Cftlvlkck 2 Gbc gcs pcrtbs kbg ndìrb kb fckc fd`pubstd y bsfràicgd fd`pgbtd. [lbnb un bmb`pgd. 8) • •

3)

ObFg6 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= • Ný`brd kb vcgbnflc kbg bgb`bntd= • Ndìrb bn bg slstb`c Vtdfa=

fgdrurd kb elbrrd (LLL)

ND 9

•

fgdrurd elbrrd 6

;

Xrbolmd 3= tbtrc • Ndìrb jbnìrlfd= öxlkd • Xrbolmd 9= kl • Ndìrb bspbfàolfd= nltröjbnd • Ndìrb bn bg slstb`c bstbquld`ìtrlfd= 9) • • •

X; D ?

Xrbolmd 3= ebxc Ndìrb jbnìrlfd= öxlkd Xrbolmd 9= tbtrc • Ndìrb bspbfàolfd= oösodrd • Ndìrb bn bg slstb`c bstbquld`ìtrlfd=

6) L9D2 Xrbolmd 3= pbntc • Ndìrb jbnìrlfd= öxlkd • Xrbolmd 9= kl • Ndìrb bspbfàolfd= ydkd • Ndìrb bn bg slstb`c bstbquld`ìtrlfd= •

;) • •

2) •

25

•

Xi (DE)9 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= • Ný`brd kb vcgbnflc kbg bgb`bntd= • Ndìrb bn bg slstb`c Vtdfa=

elkröxlkd pgd`d 9

Fu6(CsD;)9 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= • Ný`brd kb vcgbnflc kbg bgb`bntd= • Ndìrb bn bg slstb`c Vtdfa=

LJBY ∙ [cfcnã

crsbnlctd fdirb 9


Bgcidrb unc tcigc kb vcgbnflcs ùrcg Bstc sb`cnc gb prdpdnb`ds bgcidrcr unc tcigc kb vcgbnflcs pcrc bg fbntrd kb drlbntcflön. [rctb kb trcicmcr bn bqulpd fdn sus fd`pcóbrds y fd`pcóbrcs.


333 fuckrds kb fcrtön d fcrtuglnc kb 38 f` kb gcrjd x 38 f` kb cnfed. Gds fuckrds kbibn sbr kb trbs fdgdrbs klstlntds, pcrc rbprbsbntcr gds `btcgbs, gds nd `btcgbs y gds `btcgdlkbs.

        

Gãplz Ybjgc Vcfcpuntcs Idrrckdr Frcydnbs @crfckdr nbjrd Jd`c [lmbrcs Gc tcigc kb vcgbnflcs rbfdrtcigb kbg glird.

´Suì kbib ecfbr4 Bstc cftlvlkck pubkb rbcglzcrgc kb `cnbrc lnklvlkucg, pbrd gd `bmdr bs ecfbrgc bn jrupd. 3. Klstrliuycn bg trcicmd bntrb gds fd`pcóbrds kb fgcsb. Xdr bmb`pgd, und pubkb td`cr gds bgb`bntds kbg 3 cg 68, dtrd kbg 63 cg ?8, btf. Csà sbrã `ãs oãflg. 9. Bn fckc fuckrd kb fcrtuglnc bsfrlicn bg ný`brd ctö`lfd, bg sàìdgd y bg ndìrb kb und kb gds bgb`bntds quà`lfds. 6. Bg kàc kb gc drlbntcflön, cr`bn gc tcigc bn unc kb gcs pcrbkbs kbg scgön kdnkb sb rbýnbn.

¡Cpýntbsb cg rbtd kb gc sb`cnc! •

´Suì gb pcrbfb sl drjcnlzc un rbtd quà`lfd bn bg fbntrd kb drlbntcflön4 Bg kbscoàd fdnslstb bn cprbnkbr, cg `bnds, 68 ndìrbs y sàìdgds kb bgb`bntds quà`lfds pdr sb`cnc (pubkb cprbnkbr ? pdr kàc).

•

Sulbn `ãs bgb`bntds cprbnkc sbrã bg jcnckdr.

´Sulìn cprbnkb `ãs kb cquà c gc sb`cnc 6;4 ¡Cnà`bsb!


2<



gdjrckd

rbjugcr

nd gdjrckd

Cspbftds c bvcgucr 3. 9. Kbspuìs kb bstuklcr...

Bxpglfd fdn `ls pcgcircs quì bs gc nd`bnfgcturc quà`lfc y su l`pdrtcnflc pcrc gc quà`lfc. Ybfdndzfd gcs fcrcftbràstlfcs kb gds slstb`cs kb nd`bnfgcturc bstbquld`ìtrlfd, stdfa y trcklfldncg.

6.

Klstlnjd bntrb ndìrb jbnìrlfd y ndìrb bspbfàolfd.

;.

Bgcidrd unc tcigc pbrlöklfc kb vcgbnflcs ùrcg bn bqulpd.


?8

LJBY ∙ [cfcnã

99

Nd`bnfgcturc LL Öxlkds


?6


Lkbntlolfcr y `b`drlzcr fd`pdnbntbs kb gc oörùgc jbnbrcg kb gds öxlkds `btãglfds y nd `btãglfds.



Lkbntlolfcr fckc bgb`bntd bn gcs oörùgcs kb klstlntds öxlkds iãslfds y öxlkds ãflkds.



Fgcslolfcr öxlkds bn iãslfds d ãflkds sbjýn bg bgb`bntd qub cfd`pcóc cg dxàjbnd.

 

Ndìrcr öxlkds bn bg slstb`c bstbquld`ìtrlfd y Vtdfa. Bxpbrl`bntcr fdn gc prdkufflön kb FD 9 y cprdvbfecrgc pcrc bgcidrcr unc trc`pc bfdgöjlfc.




?;

• Dxàjbnd, fd`pdnbntb bsbnflcg kb nubstrd pgcnbtc


• Gds öxlkds • Nd`bnfgcturc kb gds öxlkds


• ¡Rnc trc`pc bfdgöjlfc!

LJBY ∙ [cfcnã

¡Xcrc fd`bnzcr! Dxàjbnd, fd`pdnbntb bsbnflcg kb nubstrd pgcnbtc sdg

ct`ösobrc

gltdsobrc elkrdsobrc

Bg dxàjbnd ecfb pdsligb gc vlkc bn bg pgcnbtc. Bstb bgb`bntd quà`lfd bstã prbsbntb bn gcs trbs fcpcs kb gc [lbrrc= ct`ösobrc, gltdsobrc b elkrdsobrc.

Dxàjbnd bn bg clrb Bg dxàjbnd sb prbsbntc bn gc ct`ösobrc kb klstlntcs `cnbrcs= •

Fd`d dxàjbnd `dgbfugcr (D 9) qub bs bg jcs qub rbsplrc`ds gds

sbrbs eu`cnds. •

Fd`d dzdnd (D 6), fuyc prbsbnflc

bn gc ct`ösobrc prdtbjb c gc [lbrrc fdntrc gc rcklcflön ugtrcvldgbtc (R_) qub prdvlbnb kbg Vdg. •

Fd`d fd`pubstd ilncrld unlkd c

dtrds bgb`bntds fd`d fcridnd (F), Nltröjbnd (N) y czuorb (V). Xdr bmb`pgd= klöxlkd kb fcridnd(FD 9), `dnöxlkd kb fcridnd (FD), klöxlkd kb nltröjbnd (ND 9), `dnöxlkd kb nltröjbnd (ND) y klöxlkd kb czuorb (VD9).


?2

Dxàjbnd bn gc tlbrrc Bg dxàjbnd sb bnfubntrc bn gc gltdsobrc, prlnflpcg`bntb, unlkd cg slglfld odr`cnkd gds fd`pubstds qub sb ggc`cn slglfctds. Xdr bmb`pgd= klöxlkd kb slglfld (VlD9).

Dxàjbnd bn bg cjuc Bg dxàjbnd sb bnfubntrc bn gc elkrdsobrc odr`cnkd pcrtb kb gcs `dgìfugcs kb cjuc (E9D).

Gds fd`pubstds odr`ckds pdr dxàjbnd y dtrd bgb`bntd sb ggc`cn öxlkds . Bstc sb`cnc cprbnkbrb`ds fö`d ndìrcrgds bn gds slstb`cs kb nd`bnfgcturc bstbquld`ìtrlfd y Vtdfa.

¡C trcicmcr! 3)

´Suì tlpd kb dxàjbnd rbsplrc`ds gds eu`cnds4

9)

´Suì tlpd kb fd`pubstds odr`c bg dxàjbnd bn gc gltdsobrc y gc elkrdsobrc4

6)

Bsfrlic bg ndìrb y gc oörùgc kb flnfd fd`pubstds ilncrlds kbg dxàjbnd qub sb `bnfldncn bn gc gbfturc. • • • • •

??

LJBY ∙ [cfcnã


3. Gds öxlkds Fd`pubstds kbg dxàjbnd Gds öxlkds sdn fd`pubstds fdndflkds pcrc ndsdtrds= gc fcg vlvc, bg clrb qub bxecgc`ds y bg cjuc dxljbnckc qub utlglzc`ds fd`d kbslnobftcntb, sdn bmb`pgds kb bstb jrupd kb fd`pubstds. Bn gc sb`cnc 98 cprbnkl`ds qub gds öxlkds sdn fd`pubstds ilncrlds odr`ckds pdr gc fdìlncflön kbg dxàjbnd (fdn vcgbnflc ∙9) fdn dtrd bgb`bntd. Vb pubkbn odr`cr kds tlpds kb öxlkds sbjýn gc ncturcgbzc kbg bgb`bntd fdn bg qub sb fdìlnb bg dxàjbnd. • Öxlkd iãslfd= fdìlncflön kb dxàjbnd fdn un `btcg.

dxàjbnd +

`btcg

0 öxlkd iãslfd

Gds öxlkds iãslfds sb rbprbsbntcn fdn gc oörùgc jbnbrcg.

@ x Dy

`btcg

dxàjbnd

vcgbnflc ∙9

vcgbnflc

kbg dxàjbnd

kbg `btc g

Bmb`pgds= cgu`lnld (`btcg)

Cg9D6 vcgbnflc ∙9 kbg dxàjbnd

dxàjbnd

sdkld (`btcg)

vcgbnflc +6 kbg cgu`lnld

Nc9D

dxàjbnd

vcgbnflc ∙9 vcgbnflc +3 kbg dxàjbnd kbg sdkld

Ybfubrkb qub fucnkd gc vcgbnflc kbg fd`pubstd bs 3, nd sb bsfrlib.

Bmbrflfld 3 Lkbntlqub fckc bgb`bntd kb gc oörùgc kbg öxlkd iãslfd sljulbntb. [lbnb un bmb`pgd. 8)

fdirb (`btcg)

Fu9D

vcgbnflc ∙9

kbg dxàjbnd

dxàjbnd

3)

@n9D6

vcgbnflc +3 kbg fdirb


?:

• Öxlkd ãflkd= fdìlncflön kb dxàjbnd fdn un nd `btcg.

dxàjbnd + nd `btcg

0 öxlkd ãflkd

Gds öxlkds ãflkds sb rbprbsbntcn fdn bstc oörùgc jbnbrcg=

NxDy

nd `btcg

vcgbnflc ∙9 kbg dxàjbnd

dxàjbnd vcgbnflc kbg nd `btc g

Bmb`pgds=

FD

fcridnd (nd `btcg) Ybfubrkb qub gcs oörùgcs sb pubkbn sl`pglfcr. Bn gc oörùgc FD, cg tbnbr gds kds bgb`bntds (F y D) vcgbnflc 9, sb ecn sl`pglfckd c 3 y bstb nd sb bsfrlib.

vcgbnflc kbg dxàjbnd

nltröjbnd (nd `btcg)

dxàjbnd vcgbnflc kbg fcridnd

N9D6


ydkd (nd `btcg)

L9D2


dxàjbnd

vcgbnflc +6 kbg nltröjbnd

dxàjbnd

vcgbnflc +2 kbg ydkd

Bmbrflfld 9 C.

Lkbntlolqub fckc bgb`bntd kbg öxlkd ãflkd sljulbntb. [lbnb un bmb`pgd. 8)

czuorb (nd `btcg)

vcgbnflc ∙9

kbg dxàjbnd

vcgbnflc +; kbg czuorb

Vb9D6

3)

I.

dxàjbnd

VD9

Kbtbr`lnb sl bg bgb`bntd qub cfd`pcóc cg dxàjbnd bs un `btcg d un nd `btcg y sbjýn bstc lnodr`cflön, fgcslolqub gds öxlkds bn öxlkds iãslfds u öxlkds ãflkds. [lbnb un bmb`pgd. 8)

VlD9

Vl=

nd `btcg

9)

Fg9D6

Fg=

6)

Ob9D6 Ob=

öxlkd ãflkd 3)

?5

Fd9D6 Fd=

LJBY ∙ [cfcnã

3.3 Nd`bnfgcturc kb gds öxlkds Fd`d bstuklö gc sb`cnc cntbrldr, gds fd`pubstds pubkbn ndìrcrsb sbjýn gcs rbjgcs bstcigbflkcs pdr trbs slstb`cs kb nd`bnfgcturc klstlntds= bstbquld`ìtrlfd, Vtdfa y trcklfldncg. Ndsdtrds cprbnkbrb`ds fö`d ndìrcr c gds öxlkds sdgd bn gds kds prl`brds= bstbquld`ìtrlfd y Vtdfa.

c.

Nd`bnfgcturc bn bg slstb`c bstbquld`ìtrlfd

Cntbs kb fd`bnzcr rbfdrkb`ds qub bstb slstb`c usc gds prbmds nu`ìrlfds jrlbjds `dnd, kl, trl, tbtrc, btf., pcrc lnklfcr gc fcntlkck kb ãtd`ds kb fckc bgb`bntdkbprbsbntbs 3.3.3 gc sb`cncbn93.unc `dgìfugc. Xubkb rbpcscrgds bn gc tcigc kbg cpcrtckd Fd`d scib, bg ndìrb kb gds fd`pubstds bn bg slstb`c bstbquld`ìtrlfd rbspdnkb c bstc bstrufturc= Xrbmd (3) ‖ ndìrb jbnìrlfd + kb + prbmd (9) ‖ ndìrb bspbfàfd Bg ndìrb jbnìrlfd kb gds öxlkds bs öxlkd. Bg ndìrb bspbfàfd bs bg kbg `btcg d nd `btcg qub gd cfd`pcóc. Xdr bmb`pgd= Gc fdìlncflön kb dxàjbnd (D9∙) fdn pgctc (Cj+) kc fd`d rbsugtckd Cj9D.

Xcrc ndìrcrgd=

Cj+

D

∙9

Cj9D

3. Bstcigbfb`ds bg prbolmd (3) y bg ndìrb jbnìrlfd kbg fd`pubstd. Gc oörùgc nds lnklfc qub sdgd ecy un ãtd`d kb dxàjbnd, pdr gd tcntd b`pgbc`ds bg prbolmd `dnd y bg ndìrb jbnìrlfd öxlkd. Xrbolmd (3)= `dnd Ndìrb jbnìrlfd= öxlkd

`dnöxlkd

Bg prbmd `dnd sdgd sb b`pgbc pcrc bg ndìrb jbnìrlfd nd pcrc bg ndìrb bspbfàfd.

9. Bstcigbfb`ds bg prbolmd (9) y bg ndìrb bspbfàolfd kbg fd`pubstd. Bg dxàjbnd bstã cfd`pcóckd pdr kds ãtd`ds kb pgctc. Csà qub uscrb`ds bg ndìrb bspbfàolfd pgctc cfd`pcóckd pdr bg prbolmd kl. Xrbolmd (9)= kl Ndìrb bspbfàolfd= pgctc

klpgctc

6. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc= Xrbmd (3) + ndìrb jbnìrlfd + kb + prbmd (9) ‖ ndìrb bspbfàfd `dnd

öxlkd kl @dnöxlkd kb klpgctc (Cj9D)

pgctc


?<

Gbc`ds dtrds bmb`pgds= Ndìrb`ds bg fd`pubstd fdn oörùgc Il9D6 3. Bstcigbfb`ds bg prbolmd (3) y bg ndìrb jbnìrlfd kbg fd`pubstd. Gc oörùgc nds lnklfc qub ecy trbs ãtd`ds kb dxàjbnd. Rscrb`ds bg prbolmd trl y bg ndìrb jbnìrlfd öxlkd. Xrbolmd (3)= trl Ndìrb jbnìrlfd= öxlkd

trlöxlkd

9. Bstcigbfb`ds bg prbolmd (9) y bg ndìrb bspbfàolfd kbg fd`pubstd. _b`ds qub bg dxàjbnd bstã cfd`pcóckd pdr kds ãtd`ds kb ilsùtd. Csà qub uscrb`ds bg ndìrb bspbfàolfdilsùtd cfd`pcóckd pdr bg prbolmdkl. Xrbolmd (9)= kl Ndìrb bspbfàolfd= ilsùtd

klilsùtd

6. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc= Xrbmd (3) + ndìrb jbnìrlfd + kb + prbmd (9) ‖ ndìrb bspbfàfd trl

öxlkd

kl

ilsùtd

[rlöxlkd kb klilsùtd (Il9D6)

Ndìrb`ds bg fd`pubstd fdn oörùgc N9D6 3. Bstcigbfb`ds bg prbolmd (3) y bg ndìrb jbnìrlfd kbg fd`pubstd. Gc oörùgc nds lnklfc qub ecy trbs ãtd`ds kb dxàjbnd. Bntdnfbs uscrb`ds bg prbolmd trl y bg ndìrb jbnìrlfd öxlkd. Xrbolmd (3)= trl Ndìrb jbnìrlfd= öxlkd

trlöxlkd

9. Bstcigbfb`ds bg prbolmd (9) y bg ndìrb bspbfàolfd kbg fd`pubstd. Bg dxàjbnd bstã cfd`pcóckd pdr kds ãtd`ds kbg nd `btcg nltröjbnd. Csà qub bg ndìrb bspbfàolfd bs nltröjbnd cfd`pcóckd pdr bg prbolmd kl. Xrbolmd (9)= kl Ndìrb bspbfàolfd= nltröjbnd

klnltröjbnd

6. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc= Xrbmd (3) + ndìrb jbnìrlfd + kb + prbmd (9) ‖ ndìrb bspbfàfd trl

öxlkd

kl

[rlöxlkd kb klnltröjbnd (N9D6)

:8

LJBY ∙ [cfcnã

nltröjbnd

Bmbrflfld 6 Bsfrlic bg ndìrb kb gds sljulbntbs öxlkds sbjýn bg slstb`c bstbquld`ìtrlfd. Ybfubrkb qub bg prbmd `dnd sdgd sb b`pgbc pcrc bg ndìrb jbnìrlfd. 3)

]nD Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ndìrb kbg fd`pubstd=

9)

A9D Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ndìrb kbg fd`pubstd=

6)

FD 9

Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ndìrb kbg fd`pubstd= ;)

N9D6 Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ndìrb kbg fd`pubstd=


:3

i.

Nd`bnfgcturc bn bg slstb`c Vtdfa

Gc bstrufturc pcrc ndìrcr öxlkds bn bg slstb`c Vtdfa bs gc sljulbntb= Ndìrb jbnìrlfd + kb + ndìrb kbg bgb`bntd + ný`brd kb vcgbnflc Ybfubrkb qub bn bg slstb`c Vtdfa gc vcgbnflc sb bsfrlib fdn ný`brds rd`cnds.

Xcrc cprbnkbr c bsfrlilr bg ndìrb kb gds öxlkds bn bstb slstb`c, uscrb`ds gds `ls`ds bmb`pgds kbg cpcrtckd cntbrldr. Bsfrlic`ds bg ndìrb kbg fd`pubstd Cj9D 3. Bstcigbfb`ds bg ndìrb jbnìrlfd kbg fd`pubstd. Gc oörùgc nds lnklfc qub sb trctc kb un öxlkd. Ndìrb jbnìrlfd= öxlkd

9. Bstcigbfb`ds bg ndìrb kbg bgb`bntd qub cfd`pcóc cg dxàjbnd. Bn bstb fcsd bg dxàjbnd bstã cfd`pcóckd pdr bg bgb`bntd pgctc. Ndìrb kbg bgb`bntd= pgctc

6. Bstcigbfb`ds bg ný`brd kb vcgbnflc kbg `btcg. Gc pgctc tlbnb vcgbnflc (+3). Ný`brd kb vcgbnflc kbg bgb`bntd qub cfd`pcóc cg dxàjbnd= 3

;. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc= Ybfubrkb qub bg ný`brd kb vcgbnflc d ný`brd kb dxlkcflön bs bg qub lnklfc bg ný`brd kb bgbftrdnbs qub un ãtd`d pdnb bn mubjd bn un bngcfb quà`lfd.

Ndìrb jbnìrlfd + kb + ndìrb kbg bgb`bntd + ný`brd kb vcgbnflc öxlkd

kb

pgctc

L

Öxlkd kb pgctc (L) Cj 9D

Cedrc ndìrb`ds bg fd`pubstd kbg sbjunkd bmb`pgd= Il9D6 3. Bstcigbfb`ds bg ndìrb jbnìrlfd kbg fd`pubstd. Ndìrb jbnìrlfd= öxlkd

9. Bstcigbfb`ds bg ndìrb kbg bgb`bntd qub cfd`pcóc cg dxàjbnd. Ndìrb kbg bgb`bntd= ilsùtd

6. Bstcigbfb`ds bg ný`brd kb vcgbnflc kbg `btcg Bg ilsùtd tlbnb gcs vcgbnflcs= ∙6, +6 d +2. Bn bstb fd`pubstd sb prbsbntc fdn vcgbnflc (+6). Gd pubkb vbr bn gc oörùgc. Ybfubrkb gc bstrufturc jbnbrcg @xDy. Ný`brd kb vcgbnflc kbg bgb`bntd qub cfd`pcóc cg dxàjbnd= 6

:9

LJBY ∙ [cfcnã

;. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc= Ndìrb jbnìrlfd + kb + ndìrb kbg bgb`bntd + ný`brd kb vcgbnflc öxlkd

kb

ilsùtd

LLL

Öxlkd kb ilsùtd (LLL) Il 9D6

Bmbrflfld ; Bsfrlic bg ndìrb kb gds sljulbntbs öxlkds sbjýn bg slstb`c Vtdfa. 3)

Ej9D Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd= Ndìrb kbg fd`pubstd=

9)

Fg9D: Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd= Ndìrb kbg fd`pubstd=

6)

Cj9D6 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd= Ndìrb kbg fd`pubstd=

;)

N 9 D; Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd= Ndìrb kbg fd`pubstd=


:6

Ybsu`bn Bstc sb`cnc bstuklö qub= 3.

Gds öxlkds sdn fd`pubstds ilncrlds odr`ckds pdr gc fdìlncflön kbg dxàjbnd (fdn vcgbnflc ‖9) fdn dtrd bgb`bntd. Gds öxlkds pubkbn sbr kb kds tlpds= • Öxlkds iãslfds, fucnkd bg dxàjbnd sb unb c un `btcg. Oörùgc jbnbrcg=

@ x Dy

`btcg


dxàjbnd vcgbnflc kbg `btc g

• Öxlkds ãflkds, fucnkd bg dxàjbnd sb unb c un nd `btcg. Oörùgc jbnbrcg=

nd `btcg

N x Dy


dxàjbnd vcgbnflc kbg nd `btcg

3.3 Xcrc ndìrcr bstds fd`pubstds sb pubkb utlglzcr bg `ìtdkd bstbquld`ìtrlfd y bg `ìtdkd Vtdfa. c.

Bn bg slstb`c bstbquld`ìtrlfd bg ndìrb kb gds öxlkds qubkc fdn bstc bstrufturc= Xrbolmd (3) ‖ ndìrb jbnìrlfd + kb + prbolmd (9) ‖ ndìrb bspbfàolfd

i.

Bn bg slstb`c Vtdfa bg ndìrb kb gds öxlkds qubkc fdn bstc bstrufturc= Ndìrb jbnìrlfd + kb + ndìrb kbg bgb`bntd + ný`brd kb vcgbnflc

Lnvbstljub bn gc rbk... Vl qulbrb prcftlfcr bn gc rbk fö`d ndìrcr öxlkds, gb rbfd`bnkc`ds bstcs klrbffldnbs= ettp=//www.qul`lfcwbi.nbt/.../pcjlncs/dxlkds.et` ettp=//www.cgdnsdodrùgc.fd`/lndrjcnlfc/dcodrùgcsT3.et`

:;

LJBY ∙ [cfcnã

Cutdfdntrdg Cftlvlkck 3. Lkbntlfcr y `b`drlzcr gds fd`pdnbntbs kb gc oörùgc jbnbrcg kb gds öxlkds `btãglfds y nd `btãglfds C.

Bxpglqub quì rbprbsbntc fckc fd`pdnbntb kb gc oörùgc jbnbrcg kb gds öxlkds `btãglfds.

@ x Dy @= D= x= y= I.

Bxpglqub quì rbprbsbntc fckc fd`pdnbntb kb gc oörùgc jbnbrcg kb gds öxlkds nd `btãglfds.

NxDy N= D= x= y=

Cftlvlkck 9. Lkbntlfcr y `b`drlzcr gc bstrufturc jbnbrcg kb gds öxlkds bn bg slstb`c bstbquld`ìtrlfd y Vtdfa C.

Bsfrlic gc bstrufturc jbnbrcg kbg ndìrb kb gds öxlkds bn bg slstb`c bstbquld`ìtrlfd.

I.

Bsfrlic gc bstrufturc jbnbrcg kbg ndìrb kb gds öxlkds bn bg slstb`c Vtdfa.

Cftlvlkck 6. Fgcslfcr öxlkds Kbtbr`lnb sl bgöxlkds bgb`bntd qubucfd`pcóc cg dxàjbnd bs un `btcg d un nd `btcg y fgcslqub gds sljulbntbs öxlkds bn iãslfds öxlkds ãflkds. 3)

XiD9

Xi=

9)

N9D2 N=


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6)

Gl9D

Gl=

:)

IbD

Ib=

;)

Fg9D:

Fg=

5)

FrD

Fr=

2)

Ir9D2

Ir=

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VlD9

Vl=

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I9 D 6

I=

38)

VD9

V=

Cftlvlkck ;. Ndìrcr öxlkds bn bg slstb`c bstbquld`ìtrlfd Bsfrlic bg ndìrb kb gds sljulbntbs öxlkds sbjýn gcs ndr`cs kbg slstb`c bstbquld`ìtrlfd. 3)

XiD9 Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ndìrb kbg fd`pubstd=

9)

Gl9D Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ndìrb kbg fd`pubstd=

6)

FrD Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ndìrb kbg fd`pubstd=

:?

LJBY ∙ [cfcnã

;)

VD9 Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ndìrb kbg fd`pubstd=

2)

IbD Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ndìrb kbg fd`pubstd=

Cftlvlkck 2. Ndìrcr öxlkds bn bg slstb`c Vtdfa Bsfrlic bg ndìrb kb gds sljulbntbs öxlkds sbjýn gcs ndr`cs kbg slstb`c Vtdfa. 3)

I9 D 6 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd= Ndìrb kbg fd`pubstd=

9)

Ir9D2 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd= Ndìrb kbg fd`pubstd=

6)

Fg9D: Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd= Ndìrb kbg fd`pubstd= Suà`lfc LL ∙ Vb`cnc 99

::


¡Rnc trc`pc bfdgöjlfc! Bg klöxlkd kb fcridnd y gds zcnfukds Bg öxlkd kb fcridnd (L_), tcìlìn ggc`ckd klöxlkd kb fcridnd, bs un jcs fuycs `dgìfugcs bstãn fd`pubstcs pdr kds ãtd`ds kb dxàjbnd y und kb fcridnd. Vu oörùgc quà`lfc bs FD9. Bg klöxlkd kb fcridnd sb prdkufb c trcvìs kb gc rbsplrcflön cnl`cg y vbjbtcg y pdr `bkld kb prdfbsds kb obr`bntcflön. Gds zcnfukds nds plfcn pdrqub pbrflibn bg klöxlkd kb fcridnd FD 9 qub bxecgc`ds cg rbsplrcr. Fdn bstc trc`pc bfdgöjlfc gds zcnfukds sb julcrãn ecflc bg lntbrldr kbg bnvcsb ctrcàkds pdr bg FD9 qub prdkufb gc obr`bntcflön kb gc gbvckurc. Gubjd kb pbrfctcrsb qub nd sb trctc kb un fubrpd eu`cnd, qubkcrãn ctrcpckds, lnfcpcfbs kb bnfdntrcr gc scglkc.






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3 vcsd kb cjuc fcglbntb 28 jrc`ds kb czýfcr nbjrc 3 jrc`d kb gbvckurc unc idtbggc kb pgãstlfd kb 9 gltrds gl`plc y sbfc



   

unc idgsc pgãstlfc nbjrc 3 `crfckdr 3 fufelggd colgckd glirbtc kb fc`pd gcplfbrd

´Fö`d bgcidrcr gc trc`pc4 3.

Fdrtb unc idtbggc kb pgãstlfd pcrtbs fd`dbnsbkds ùbstrc bn gc lgustrcflön.

:5

LJBY ∙ [cfcnã

9.

@bzfgb fdn cjuc fcglbntb bg czýfcr y kbmb qub gc `bzfgc nbjrc sb bnoràb.

6.

Cóckc gc gbvckurc y bfeb gc `bzfgc bn gc icsb kb gc idtbggc. Nd ecfb ocgtc `bzfgcrgd. Vb lrã frbcnkd klöxlkd kb fcridnd.

;.

[cpb gc icsb kb gc idtbggc fdn gc pcrtb supbrldr, pbrd fdgöqubgc cg rbvìs, odr`cnkd un bìukd. _bc gc lgustrcflön.

2.

Odrrb gc idtbggc fdn unc idgsc pgãstlfc nbjrc y fdgöqubgc bn unc bsqulnc kb su fcsc. Bn kds sb`cncs pdkrã vbr gc fcntlkck kb `dsqultds qub ùrlbrdn bn gc idtbggc. Ybjlstrb sus rbsugtckds bn gc glirbtc kb fc`pd. Bstb `ìtdkd fcsbrd, sbnflggd y bfdgöjlfd bs kb jrcn utlglkck bn gcs bsfubgcs, mcrklnbs lnocntlgbs, edspltcgbs y fcscs kb oc`lglc. Bs iubnd pcrc tdkds y nd kcóc bg cìlbntb.

Bstb bxpbrl`bntd nds pubkb cyukcr c prbvbnlr bg kbnjub. ´Suì bs bg kbnjub4 Bg kbnjub bs unc bnobr`bkck lnobffldsc fcusckc pdr un vlrus. Vb trcns`ltb c trcvìs kb gc plfckurc kb gc ebìrc kbg zcnfukd Cbkbs cbjyptl. Gcs pbrsdncs lnobftckcs prbsbntcn birb, kdgdr kb fcibzc, ùsfugcr y kb gcs crtlfugcfldnbs. Bg kbnjub bs un prdigb`c frbflbntb kb scguk pýiglfc qub cobftc c `ãs kb 388 pcàsbs bn bg ùnkd, fdn `ãs kb 28 `lggdnbs kb fcsds lnodr`ckds fckc cód, lnfgulkds 288,888 edspltcglzcfldnbs y cgrbkbkdr kb 98,888 ùbrtbs. Gc ýnlfc odr`c kb prbvbnlr gc bnobr`bkck bs `bklcntb bg fdntrdg kbg `dsqultd y sus frlckbrds y gc kbtbfflön rãplkc y tb`prcnc kb gds fcsds. Bg fdntrdg kbg zcnfukd rbqulbrb kbg cpdyd kb gc fdùnlkck. Csà, bn gcs zdncs fdn prbsbnflc kbg vlrus, tdkds pdkb`ds fdgcidrcr pcrc qub sb bgl`lnbn gds frlckbrds rbcglzcnkd bstcs cftlvlkckbs= • Nd cfuùgcr icsurc. • @cntbnbr tcpckds gds kbpösltds kb cg`cfbnc`lbntd kb cjuc. • _cflcr gds bnvcsbs kb cjuc, gcs ggcntcs vlbmcs y dtrds rbflplbntbs qub pubkbn fdntbnbr cjucs bstcnfckcs. • Fdnstrulr trc`pcs bfdgöjlfcs pcrc bgl`lncr bg zcnfukd kbg kbnjub. Bstcs cffldnbs sdn sl`pgbs, nd l`pglfcn jcstds y pubkbn cyukcr cg fdntrdg kbg kbnjub sln utlglzcr prdkuftds quà`lfds. Suà`lfc LL ∙ Vb`cnc 99

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gdjrckd

rbjugcr

nd gdjrckd

Cspbftds c bvcgucr 3. 9. Kbspuìs kb 6. bstuklcr... ;. 2.

Lkbntlolfd y `b`drlzd fd`pdnbntbs kb gc oörùgc jbnbrcg kb gds öxlkds `btãglfds y nd `btãglfds. Lkbntlolfd fckc bgb`bntd bn gcs oörùgcs kb klstlntds öxlkds iãslfds y öxlkds ãflkds. Fgcslolfd öxlkds bn iãslfds d ãflkds sbjýn bg bgb`bntd qub cfd`pcóc cg dxàjbnd. Ndìrd öxlkds bn bg slstb`c bstbquld`ìtrlfd y Vtdfa. Bgcidrd unc trc`pc bfdgöjlfc qub ounfldnc fdn gc prdkufflön kb FD9.


58

LJBY ∙ [cfcnã

96

Ybpcsd Vb`cncs 35-99


53


Ybpcscr gds fdntbnlkds kb gc sb`cnc 35 c gc 99.



Xrbpcrcrsb pcrc gc prl`brc prubic pcrflcg.



Bstl`ckc y bstl`ckd bstuklcntb= Vb cprdxl`c gc prl`brc bvcgucflön. Fdn bg dimbtlvd kb qub ustbk sb prbpcrb ilbn, vc`ds c rbpcscr gds fdntbnlkds kb gcs sb`cncs 35 c gc 99. Bstc sb`cnc tlbnb gds rbsý`bnbs kb gds tb`cs qub eb`ds vlstd y bmbrflflds pcrc qub vcyc bstuklcnkd. Xcrc cprdvbfecr `bmdr bstb rbpcsd gb rbfd`bnkc`ds= • Gbbr fdn ctbnflön fckc rbsu`bn. • Ybsdgvbr gds bmbrflflds kurcntb gc fgcsb rcklcg y kbspuìs kb bggc. • Ybpcscr gcs sb`cncs cntbrldrbs, bn bggcs tlbnb `ãs bxpglfcfldnbs y bmb`pgds. • Bstuklcr un pdqultd tdkds gds kàcs y rbsdgvbr sus kukcs. Xlkc cyukc c sus `cbstrds drlbntckdrbs d cgjýn `lbìrd kb gc fdùnlkck qub fdndzfc gc `ctbrlc.

59

LJBY ∙ [cfcnã


3. ´Suì bs un bngcfb quà`lfd4 Rn bngcfb quà`lfd bs gc unlön kb ãtd`ds ljucgbs d klstlntds qub pbr`ltb odr`cr `dgìfugcs. Bsc unlön sb gdjrc pdr gc trcnsobrbnflc tdtcg d pcrflcg kb bgbftrdnbs kb un ãtd`d c dtrd. Ecy trbs tlpds kb bngcfb= 3.3 Bngcfb lönlfd `btcg + nd `btcg Bg bngcfb lönlfd sb prdkufb fucnkd gds bgbftrdnbs sb trcnsolbrbn kb un ãtd`d c dtrd. Bstb tlpd kb bngcfb subgb kcrsb bntrb `btcgbs y nd `btcgbs. 3.9 Bngcfb fdvcgbntb nd `btcg + nd `btcg nd `btcg + elkröjbnd Bg bngcfb fdvcgbntb dfurrb fucnkd gds ãtd`ds qub sb unbn fd`pcrtbn gds bgbftrdnbs. Fckc pcr kb bgbftrdnbs qub fd`pcrtbn, odr`cn un bngcfb. Bn jbnbrcg, bstb tlpd kb bngcfb sb prdkufb bntrb bgb`bntds nd `btãglfds d bntrb un nd `btcg y bg elkröjbnd. 3.6 Bngcfb `btãglfd `btcg + `btcg Bg bngcfb `btãglfd sb prdkufb fucnkd gds ãtd`ds bngczckds sdn bgb`bntds `btãglfds. Bn bg bngcfb `btãglfd, gds ãtd`ds fd`pcrtbn gds bgbftrdnbs, pbrd ìstds sb ùbvbn pdr tdkc gc cgbcflön odr`cnkd unc nuib kb bgbftrdnbs.

Bmbrflfld 3. Bsfrlic gcs fcrcftbràstlfcs kbg bngcfb qub bmb`pglfcn gds sljulbntbs fd`pubstds 3)

Gc cgbcflön bntrb bg Fu, `btcg y bg ]n, `btcg, prdkufb un bngcfb `btãglfd. ´Suì fcrcftbràstlfcs prbsbntc bstb tlpd kb bngcfb4

9)

Bg czlkc kb sdkld (NcN6) bstã odr`ckd pdr bg Nc qub bs un `btcg y bg N qub bs un nd `btcg, odr`cnkd un bngcfb lönlfd. Bstb tlpd kb bngcfb ´quì fcrcftbràstlfcs prbsbntc4

6)

9 Bg kbpdr fcridnd ) bstãunodr`ckd pdr bg F qub bs fcrcftbràstlfcs un nd `btcg y prbsbntc bg D qub un bs unklöxlkd nd `btcg, gd qub(FD odr`cn bngcfb fdvcgbntb. ´Suì bngcfb kb bstb tlpd4


56

Bmbrflfld 9. Ybfdndzfc bg tlpd kb bngcfb qub sb kc bntrb gds sljulbntbs bgb`bntds Ybggbnb bg fuckrd kb gc rbspubstc fdrrbftc.

5;

3)

Bg iutcnd (F;E38) bstã odr`ckd pdr fcridnd (F), un nd `btcg, y pdr elkröjbnd (E). ´Suì tlpd kb bngcfb odr`c4

fdvcgbntb lönlfd `btãglfd

9)

Bg irdùrd kb oösodrd (XIr6), bstã odr`ckd pdr bg oösodrd (X) qub bs un nd `btcg y bg ird`d (Ir) qub bs un nd `btcg. ´Suì tlpd kb bngcfb odr`c4


6)

Bg fgdrurd kb bstrdnfld (VrFg9), bstã odr`ckd pdr bg bstrdnfld (Vr) qub bs un `btcg y pdr bg fgdrd (Fg) qub bs un nd `btcg. ´Suì tlpd kb bngcfb odr`c4


;)

Gc fb`bntltc (Ob6F) bstã odr`ckc pdr elbrrd (Ob), un `btcg, y pdr fcridnd (F), un nd `btcg. ´Suì tlpd kb bngcfb odr`c4


2)

Gc cgbcflön bntrb `cjnbsld (@j), un `btcg, y flnf (]n), un `btcg, ´quì tlpd kb bngcfb odr`c4


?)

Bg btcnd (F9E?) bstã odr`ckd pdr fcridnd (F), un nd `btcg, b elkröjbnd (E), un nd `btcg. ´Suì tlpd kb bngcfb odr`c4


LJBY ∙ [cfcnã

9. Oörùgc quà`lfc 3.

Rnc oörùgc quà`lfc bs gc rbprbsbntcflön bsfrltc kb gc fd`pdslflön kb unc `dgìfugc d un fd`pubstd `bklcntb sàìdgds quà`lfds. Rnc oörùgc quà`lfc bstã odr`ckc pdr sàìdgds quà`lfds y suiànklfbs.

9.

Fgcslolfcflön kb oörùgcs quà`lfcs

9.3 Oörùgc b`pàrlfc= sb usc pcrc lnklfcr bg tlpd kb bgb`bntds prbsbntbs bn un fd`pubstd bn su prdpdrflön `ànl`c. Xcrc fcgfugcr unc oörùgc b`pàrlfc= • Klvlkl`ds fckc `csc bntrb gc `csc ctö`lfc kbg bgb`bntd fdrrbspdnklbntb. • Klvlkl`ds fckc und kb gds rbsugtckds cntbrldrbs, bntrb bg `ãs pbqubód kb bggds. 9.9 Oörùgc `dgbfugcr= lnklfc gc fd`pdslflön rbcg kb fckc unc kb gcs `dgìfugcs qub odr`cn un fd`pubstd. Xcrc fcgfugcr gc oörùgc `dgbfugcr= • Fcgfugc`ds gc `csc kb gc oörùgc b`pàrlfc. • Klvlkl`ds gc `csc `dgbfugcr rbcg qub nds ecn kckd, bntrb gc `csc fcgfugckc fdn gc oörùgc b`pàrlfc. • @ugtlpglfc`ds fckc suiànklfb kb gc oörùgc b`pàrlfc pdr bg ný`brd ditbnlkd kb gc klvlslön.

Bmbrflfld 6. Bnfubntrb gc oörùgc b`pàrlfc kb gds sljulbntbs fd`pubstds 3)

Fcgfugb gc oörùgc b`pàrlfc kb un fd`pubstd qub tlbnb 55.5<% kb dxàjbnd (D) y 33.33% kb elkröjbnd (E). c. Klvlkc fckc `csc bntrb gc `csc ctö`lfc kbg bgb`bntd fdrrbspdnklbntb. Cprdxl`b sus rbsugtckds c un ný`brd bntbrd. 55.5< j D ãtd`ds pdr j kb D 3? j D / 3 ãtd`d 0 33.33 j E 0 3 j E / 3 ãtd`d i.

Klvlkc gds rbsugtckds cntbrldrbs pdr bg `ãs pbqubód kb bggds. ãtd`ds ú 0 ãtd`ds ú

f.

ãtd`ds pdr j kb E

0



52

9)

Fcgfugb gc oörùgc b`pàrlfc kb un fd`pubstd qub tlbnb ??.?% kb tltcnld ([l) y 66.;% kb dxàjbnd (D) c.

Klvlkc fckc `csc pdr gc `csc ctö`lfc kbg bgb`bntd fdrrbspdnklbntb. ??.? j [l ãtd`ds pdr j kb [l ;:.< j [l / 3 ãtd`d 0 66.; j D 0 3? j D / 3 ãtd`d

i.

ãtd`ds pdr j kb D

Klvlkc gds rbsugtckds cntbrldrbs pdr bg `ãs pbqubód kb bggds. ãtd`ds ú 0 ãtd`ds ú

f.

0


Bmbrflfld ;. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd qub fdrrbspdnkb c gc kbnlflön kb gc lzqulbrkc.

5?

3)

Ybprbsbntcflön bsfrltc kb gc fd`pdslflön kb un fd`pubstd quà`lfd.

`dgìfugc oörùgc quà`lfc sàìdgd quà`lfd

9)

Ný`brd qub lnklfc gc fcntlkck kb ãtd`ds kb fckc und kb gds bgb`bntds qub odr`cn un fd`pubstd.

`dgìfugc suiànklfb sàìdgd quà`lfd

6)

Oörùgc quà`lfc qub lnklfc bg tlpd kb bgb`bntds prbsbntbs bn un fd`pubstd bn su prdpdrflön `ànl`c.

oörùgc b`pàrlfc oörùgc `dgbfugcr oörùgc bstrufturcg

;)

Oörùgc quà`lfc qub lnklfc gc fd`pdslflön rbcg kb un fd`pubstd, tcg y fd`d sb prbsbntc bn gc ncturcgbzc.


2)

Ybsugtckd kb klvlklr gc `csc kb fckc bgb`bntd qub odr`c bg fd`pubstd kbntrd kb gc `csc ctö`lfc fdrrbspdnklbntb y gubjd klvlklr fckc und kb gds rbsugtckds cntbrldrbs, bntrb bg `ãs pbqubód kb bggds.


LJBY ∙ [cfcnã

Bmbrflfld 2. Bxtrcljc lnodr`cflön kb gcs oörùgcs quà`lfcs Bsfrlic bg tlpd y ný`brd kb ãtd`ds prbsbntbs bn fckc und kb gds sljulbntbs fd`pubstds. 3)

A9D Bg fd`pubstd bstã odr`ckd pdr=

9)

FuDE Bg fd`pubstd bstã odr`ckd pdr=

6)

Nl9D6 Bg fd`pubstd bstã odr`ckd pdr=

;)

EjDE Bg fd`pubstd bstã odr`ckd pdr=

2)

CjFg Bg fd`pubstd bstã odr`ckd pdr=

Bmbrflfld ?. Fcgfugcr gc oörùgc `dgbfugcr 3)

Rn fd`pubstd kb oörùgc b`pàrlfc F9E2 tlbnb un pbsd `dgbfugcr kb 25.9 jrc`ds. Fcgfugb su oörùgc `dgbfugcr. Cprdxl`b sus rbsugtckds c ný`brds bntbrds. c.

Fcgfugb gc `csc kb gc oörùgc b`pàrlfc. F9E2= 9 (39 j) + 2 (3 j) 0

i.

Klvlkc gc `csc `dgbfugcr rbcg qub gb ecn kckd, bntrb gc `csc fcgfugckc fdn gc oörùgc b`pàrlfc.

25.9 j ú f.

0

cprdxl`ckc`bntb

Xcrc bsfrlilr gc oörùgc `dgbfugcr, ùgtlpglqub fckc suiànklfb kb gc oörùgc b`pàrlfc pdr bg ný`brd ditbnlkd kb gc klvlslön= F9 x 9E 2 x 9 Gc oörùgc `dgbfugcr bs= Suà`lfc LL ∙ Vb`cnc 96

5:

s c f l ` à u q s b n d l f n u o s u s y s d f l n ã j r d n l s d t s b u p ` d F . 6

55

LJBY ∙ [cfcnã

s gb c s


s gb c s l x d

b s c i + d lk f ã

b s g c s

n c f o l s c g f sb s d f l n ã j r d n l s td s b u p ` d f s d G

) E D ( s b s c i

∙

c f l ` à u q n ö l f n u o u s n ý j b s

n b

=r d p s c k c ` r od

s b n ld n c + g tc b `

d gl x ö r k l e

) (D s d k l x ö


+ d n b àj x d

d t n b ` b g b

= n b n b k l v l k b s

=r d p s c k c r` d o

+ b s c i

d lk f ã x d

d k l f ã r lk e + b s c i

s d k l f ã x d

r= d p s d k c r` od

d n + d n b àj x d + d n b j ö r lk e

s d k l f ã r k l e

=r d p s d k c ` r od

d n + d n b j ö r lk e

= n b n b k l lv k b s

)⁽ E ( s d lk f ã

9 ∙

s c b k l gd c e

=r d p s c k c r` d o

g tc b `

= d g p ` mb b

= d g p ` b m b

= d g p ` mb b

6

gD F c N

g F c N

;

D V9 E

: 3 d ? 3 d p u r j g c t b `

=g d p ` mb b

g F E

s d k l x ö

s d k l f ã

r= d p s d k c ` r od

+ d n b àj x d

g c t b ` d n

= gd p ` b m b

D9 g F

s d k l x ö

s d f l s ã i

=r d p s d k c ` r od

+ d n b àj x d

g tc b `

= d g p ` mb b

D c F

Bmbrflfld :. Ybgcfldnb fdnfbptds Bsfrlic sdirb gc gànbc bg fdnfbptd qub fdrrbspdnkb c fckc kbnlflön kb gc lzqulbrkc. 3)

Fdnmuntd kb prdplbkckbs sb`bmcntbs bntrb fd`pubstds quà`lfds sl`lgcrbs.

9)

Fd`pubstd qub tlbnb bn su oörùgc bg bgb`bntd E+.

6)

Fd`pubstd odr`ckd pdr un `btcg `ãs DE‖.

;)

Fd`pubstd un nd `btcg.odr`ckd pdr bg cnlön D fdn un `btcg d

2)

Fd`pubstd qub rbsugtc kb gc rbcfflön bntrb un ãflkd y unc icsb.

‖9

Bmbrflfld 5. Ybfdndzfc ounfldnbs quà`lfcs Fd`pgbtb gc tcigc bsfrlilbnkd sl bg fd`pubstd kckd bs un öxlkd, un ãflkd, unc icsb d unc scg. [lbnb kds bmb`pgds. fd`pubstd

ounflön quà`lfc

fd`pubstd

Ob(DE)6

icsb

EL

Cu9D

AFg

EFg

Il9D2

NcO

Fr(DE)9

A 9D

E9VD;

ounflön quà`lfc

scg

Bmbrflfld <. Fd`pgbtb lnodr`cflön Fd`pgbtb gc tcigc bsfrlilbnkd un bmb`pgd kb gc ounflön quà`lfc qub sb gb kc d lkbntlfcnkd c quì ounflön quà`lfc fdrrbspdnkb bg bmb`pgd kckd. ounflön quà`lfc

bmb`pgd

ãflkd Fr9D6 scg GlDE


5<

Bmbrflfld 38. Fgcslqub fd`pubstds Lnklqub sl gds sljulbntbs fd`pubstds sdn ilncrlds, tbrncrlds d fuctbrncrlds. Vl nd rbfubrkc gds fdnfbptds, fdnsugtb gcs pãjlncs 66 y 6; kb su glird. 3)

AFgD6

9)

XFg6

6)

NcFgD6

;)

VnFg

2)

VlD9

?)

AEFD6

:)

F:E3?

5)

NcEFD6

9

Bmbrflfld 33 Fd`pgbtb gc tcigc. Bsfrlic gc ounflön quà`lfc, quì bgb`bntds odr`cn, quì fd`pubstd sb odr`c y un bmb`pgd kb fckc und, sbjýn sbc bg fcsd. ounflönquà`lfc

odr`ckdpdr

icsb ãflkd

`btcg+elkrdxlgd

fd`pubstdodr`ckd icsb elkrãflkd

bmb`pgd Fc(DE)

9

elkröjbnd + nd `btcg + dxàjbnd scg

elkrãflkd+icsb dxlscg

öxlkd

dxlkd iãslfd dxàjbnd + nd `btcg CjND6 AIr E6XD; EO FD9 @jD

<8

LJBY ∙ [cfcnã

;. Nd`bnfgcturc quà`lfc 3.

Gc nd`bnfgcturc quà`lfc bs bg fdnmuntd kb rbjgcs qub sb ecn bstcigbflkd pcrc ndìrcr c gds fd`pubstds quà`lfds. Gcs rbjgcs kb nd`bnfgcturc bstãn klftckcs pdr gc Rnlkck Lntbrncfldncg kb Suà`lfc Xurc y Cpglfckc (LRXCF) Bn jbnbrcg, bg ndìrb kb un fd`pubstd kbib lnfgulr bstds kctds= • ndìrb kb gds bgb`bntds qub gd odr`cn, • gc `cnbrc bn qub bstãn fdìlnckds bsds bgb`bntds, • sl bs pdsligb, gc ounflön qub fu`pgb fckc bgb`bntd bn bg fd`pubstd. Gds slstb`cs kb nd`bnfgcturc qub cprbnkl`ds sdn=

3.3 Bg slstb`c bstbquld`ìtrlfd ndìrc c gcs sustcnflcs uscnkd prbolmds nu`ìrlfds qub lnklfcn bg ný`brd kb ãtd`ds kb un `ls`d bgb`bntd bn unc `dgìfugc. Ckb`ãs, usc un ndìrb jbnìrlfd y un ndìrb bspbfàolfd. • Bg ndìrb jbnìrlfd bs bg qub lnklfc gc ounflön quà`lfc kb un fd`pubstd. Xdr bmb`pgd= öxlkd, ãflkd, icsb d scg. • Bg ndìrb bspbfàolfd lnklfc gc bspbflb quà`lfc c gc qub fdrrbspdnkb. Xdr bmb`pgd= öxlkd kb fcgfld, elkröxlkd kb cgu`lnld, bntrb dtrds. 3.9 Bn bg slstb`c Vtdfa gds fd`pubstds quà`lfds sb ndìrcn bsfrlilbnkd fdn ný`brds rd`cnds gc vcgbnflc ctö`lfc kbg bgb`bntd fdn ndìrb bspbfàolfd.

Bmbrflfld 39. Ybfdndzfc gcs pcrtbs kbg ndìrb kb gds fd`pubstds Bsfrlic gcs pcrtbs kbg ndìrb kb gds sljulbntbs fd`pubstds. Ob9V6 Vlstb`cbstbquld`ìtrlfd trlsugourd kb klelbrrd prbmd (3)= ndìrbjbnìrlfd= prbmd (9)= ndìrb bspbfàfd=

Vlstb`cVtdfa sugourd kb elbrrd (LLL) ndìrb jbnìrlfd= ndìrbkbgbgb`bntd= ný`brd kb vcgbnflc kbg bgb`bntd=


<3

Bmbrflfld 36. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd kbg fdnfbptd qub fdrrbspdnkb c fckc kbnlflön. Ybjgcs bstcigbflkcs pdr gc pubstds quà`lfds.

9)

Vlstb`c kb nd`bnfgcturc qub ndìrc c gds fd`pubstds utlglzcnkd prbolmds nu`ìrlfds pcrc lnklfcr gc fcntlkck kb ãtd`ds prbsbntbs bn gc `dgìfugc.

Vtdfa fgãslfd bstbquld`ìtrlfd

6)

Ndìrb qub lnklfc gc ounflön quà`lfc kb un fd`pubstd.

ndìrb fd`ýn ndìrb jbnìrlfd ndìrb bspbfàolfd

;)

Vlstb`c kb nd`bnfgcturc qub b`pgbc ný`brds rd`cnds pcrc lnklfcr gc vcgbnflc kbg bgb`bntd fdn ndìrb bspbfàolfd.

Vtdfa fgãslfd trcklfldncg

2)

Ndìrb qub lnklfc gc bspbflb quà`lfc kb un fd`pubstd.

prbolmd ndìrb jbnìrlfd

LRXCF

pcrc ndìrcr fd`-

ctd`lflkck suolmds jrlbjds nd`bnfgcturc quà`lfc

3)

ndìrb bspbfàolfd ?)

Vlstb`c bn bg qub bstã ndìrckd bg fd`pubstd öxlkd kb fdicgtd (LLL).

Vtdfa bstbquld`ìtrlfd fgãslfd

Bmbrflfld 3; Bsfrlic gc odr`c jbnbrcg kbg ndìrb kb gds fd`pubstds bn fckc slstb`c kb nd`bnfgcturc.

<9

3)

Vlstb`c bstbquld`ìtrlfd

9)

Vlstb`c Vtdfa

LJBY ∙ [cfcnã

2. Gds öxlkds Bstc sb`cnc bstuklö qub= 3.

Gds öxlkds sdn fd`pubstds ilncrlds odr`ckds pdr gc fdìlncflön kbg dxàjbnd (fdn vcgbnflc ‖9) fdn dtrd bgb`bntd. Gds öxlkds pubkbn sbr kb kds tlpds= • Öxlkds iãslfds, fucnkd bg dxàjbnd sb unb c un `btcg. Oörùgc jbnbrcg=

`btcg

dxàjbnd

@ x Dy vcgbnflc ∙9 kbg dxàjbnd

vcgbnflc kbg `btcg

• Öxlkds ãflkds, fucnkd bg dxàjbnd sb unb c un nd `btcg. Oörùgc jbnbrcg=

N x Dy

nd `btcg


dxàjbnd vcgbnflc kbg nd `btcg

3.3 Xcrc ndìrcr bstds fd`pubstds sb pubkb utlglzcr bg slstb`c bstbquld`ìtrlfd d bg slstb`c Vtdfa. c.

Bn bg slstb`c bstbquld`ìtrlfd bg ndìrb kb gds öxlkds qubkc fdn bstc bstrufturc= Xrbolmd (3) ‖ ndìrb jbnìrlfd + kb + prbolmd (9) ‖ ndìrb bspbfàolfd

i.

Bn bg slstb`c Vtdfa bg ndìrb kb gds öxlkds qubkc fdn bstc bstrufturc= Ndìrb jbnìrlfd + kb + ndìrb kbg bgb`bntd + ný`brd kb vcgbnflc

Bmbrflfld 32. Lkbntlqub bgb`bntds kb un öxlkd iãslfd bn gc oörùgc Lkbntlqub fckc bgb`bntd kb gc oörùgc kbg sljulbntb öxlkd iãslfd. [lbnb un bmb`pgd. 8)

elbrrd (`btcg) vcgbnflc ∙9

kbg dxàjbnd 3)

Ob9D6

dxàjbnd vcgbnflc +6 kbg elbrrd

NL9D6


<6

Bmbrflfld 3?. Ybfdndzfc gcs pcrtbs kbg ndìrb kb gds fd`pubstds Bsfrlic gcs pcrtbs kbg ndìrb kb gds sljulbntbs fd`pubstds. 3)

[rlöxlkd kb klnltröjbnd N9D6 Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)=

9)

Ndìrb bspbfàolfd= @dnöxlkd kb `cjnbsld @jD Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd=

6)

Öxlkd kb pgctc (L) Cj9D Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

;)

Elkröxlkd kb fdirb (L) FuDE Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

2)

Öxlkd kb vcnckld (_) _9D2 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

?)

Öxlkd kb slglfld (L_) VlD9 Ndìrb jbnìrlfd= Ndìrb kbg bgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

<;

LJBY ∙ [cfcnã

Bmbrflfld 3:. Ybfdndzfc gcs pcrtbs kbg ndìrb kb gds öxlkds Fd`pgbtb bg fuckrd bsfrlilbnkd gcs pcrtbs kbg ndìrb kbg sljulbntb öxlkd. [lbnb un bmb`pgd. Nc9D Vlstb`cbstbquld`ìtrlfd

Vlstb`cVtdfa

@dnöxlkd kb klsdkld

Öxlkd kb sdkld (L)

Xrbmd (3)=

`dnd‖

Ndìrb jbnìrlfd=

Ndìrb jbnìrlfd= Xrbmd (9)=

öxlkd kl‖

Ndìrb kbg bgb`bntd= sdkld Ný`brd kb vcgbnflc kbg bgb`bntd=

Ndìrb bspbfàfd= sdkld

öxlkd

3

@nD6 Vlstb`cbstbquld`ìtrlfd [rlöxlkd kb `cnjcnbsd Xrbmd (3)= Ndìrbjbnìrlfd= Xrbmd (9)= Ndìrb bspbfàfd=

Vlstb`cVtdfa Öxlkd kb `cnjcnbsd (_L) Ndìrb jbnìrlfd= Ndìrbkbgbgb`bntd= Ný`brd kb vcgbnflc kbg bgb`bntd=

Bmbrflfld 35. Bsfrlic bg ndìrb kb klstlntds öxlkds Bsfrlic bg ndìrb kb gds sljulbntbs öxlkds sbjýn gcs rbjgcs kb gds slstb`cs bstbquld`ìtrlfd y Vtdfa. 3)

VD9 Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ný`brd kb vcgbnflc kbg bgb`bntd= Bg ndìrb kbg fd`pubstd bs= Vlstb`c bstbquld`ìtrlfd= Vlstb`c Vtdfa=


<2

9)

ND Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ný`brd kb vcgbnflc kbg bgb`bntd= Bg ndìrb kbg fd`pubstd bs= Vlstb`c bstbquld`ìtrlfd= Vlstb`c Vtdfa=

6)

FD9 Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ný`brd kb vcgbnflc kbg bgb`bntd= Bg ndìrb kbg fd`pubstd bs= Vlstb`c bstbquld`ìtrlfd= Vlstb`c Vtdfa=

;)

X9 D 2 Xrbolmd (3)= Ndìrb jbnìrlfd= Xrbolmd (9)= Ndìrb bspbfàolfd= Ný`brd kb vcgbnflc kbg bgb`bntd= Bg ndìrb kbg fd`pubstd bs= Vlstb`c bstbquld`ìtrlfd= Vlstb`c Vtdfa=

LJBY ∙ [cfcnã

9;

Nd`bnfgcturc LLL Ãflkds

Suà`lfc LL ∙ Vb`cnc 9;

<:


Fdndfbr gds ibnbolflds qub cpdrtcràc cg cìlbntb bg usd kbg elkröjbnd fd`d oubntb kb bnbrjàc.



Lkbntlolfcr y `b`drlzcr fd`pdnbntbs kb gc oörùgc jbnbrcg kb gds ãflkds.



Lkbntlolfcr fckc bgb`bntd bn gcs oörùgcs kb klstlntds elkrãflkds y dxãflkds.

 

Fgcslolfcr ãflkds bn elkrãflkds u dxãflkds. Ndìrcr prbolmds y suolmds qub b`pgbcn gds nd `btcgbs bn gc odr`cflön kb ãflkds dxãflkds.



Kbtbr`lncr gc vcgbnflc kb un nd `btcg bn un ãflkd dxãflkd.



Ndìrcr ãflkds bn bg slstb`c trcklfldncg.



Bxpbrl`bntcr fdn bg ãflkd kbg vlncjrb.




<5

¡Xcrc fd`bnzcr!

• Elkröjbnd, bg fdìustligb kbg outurd


• Gds ãflkds • Nd`bnfgcturc kb gds elkrãflkds • Nd`bnfgcturc kb gds ãflkds dxãflkds


• Rn gl`plckdr bfdgöjlfd

LJBY ∙ [cfcnã

¡Xcrc fd`bnzcr! Elkröjbnd, bg fdìustligb kbg outu rd Edy kàc bg usd kb fdìustligbs oöslgbs, fd`d bg pbtrögbd, supdnb cjdtcr gds rbfursds ncturcgbs y prdkuflr fdntc`lncflön ct`dsoìrlfc. @ufeds flbntàolfds bn tdkd bg ùnkd trcicmcn pcrc cu`bntcr gcs oubntbs kb bnbrjàcs rbndvcigbs b l`pugscr bg elkröjbnd fd`d slstb`c bnbrjìtlfd kbg outurd.

3

E

3

3 bgbftrön

Elkröjbnd 3.8

3 prdtön

Fdnoljurcflön bgbftrönlfc kbg elkröjbnd

Bg elkröjbnd bs bg ãtd`d `ãs gljbrd y sl`pgb kb tdkds gds bgb`bntds kbg slstb`c pbrlöklfd. Vu ný`brd ctö`lfd bs 3. Oub kbsfuilbrtd bn 3::? pdr bg quà`lfd y oàslfd lnjgìs Ebnry Fcvbnklse qulbn gd icutlzö fd`d ‗clrb lnogc`cigb‐. Bg elkröjbnd bs bg bgb`bntd `ãs ciunkcntb bn bg unlvbrsd. bnbrjàc klrbftc`bntb, pbrd sà sb pubkb ditbnbr bnbrjàc Nd kb prdkufb ìg. B`pgbcr bg elkröjbnd fd`d fdìustligb cpdrtcràc=

Ebnry Fcvbnklse (3:63 ‖ 3538) Suà`lfd y oàslfd lnjgìs

• Vu`lnlstrd kb bnbrjàc c icmd fdstd. • Rn slstb`c kb prdkufflön kb bnbrjàc gl`pld y slgbnfldsd. • Vu fdìustlön sdgc`bntb prdkufb fcgdr y vcpdr kb cjuc. • Xrbvbnflön kbg cu`bntd kbg fcgbntc`lbntd jgdicg. • Bnbrjàc cg cgfcnfb kb tdkds. Bg elkröjbnd sb ditlbnb prlnflpcg`bntb

kbg cjuc. Bstc bs ùy ciunkcntb y pubkb sbr utlglzckc tcntd bn pcàsbs bnbrjìtlfc`bntb pdirbs fd`d bn gds rlfds. • @cydr rbnkl`lbntd. • Cg`cfbnc`lbntd y trcnspdrtb sbjur ds sln rlbsjds

kb kcód cìlbntcg.


<<

Bn gc cftucglkck bg elkröjbnd sb utlglzc fd`d fdìustligb kb fdebtbs bspcflcgbs y bn ‗plgcs kb fdìustligb‐, unc bspbflb kb ictbràcs pcrc fcrrd qub sb b`pgbcn pcrc jbnbrcr bgbftrlflkck. Bg elkröjbnd odr`c pcrtb kb un ný`brd ùy jrcnkb kb fd`pubstds. Bsds fd`pubstds lnfguybn bg cjuc, gds ãflkds, gcs icsbs, gc `cydr pcrtb kb gds fd`pubstds drjãnlfds y ùfeds `lnbrcgbs. [bxtd td`ckd y ckcptckd kb www.tbfndflbnflc.bs

Ybfubrkb qub bn gc sb`cnc 98 cprbnkl`ds qub gds ãflkds sdn fd`pubstds qub sb odr`cn fucnkd sb unb bg elkröjbnd fdn nd `btcgbs. Bstc sb`cnc gds bstuklcrb`ds y cprbnkbrb`ds c ndìrcrgds fdrrbftc`bntb.

¡C trcicmcr!

388

3)

´Fuãg bs bg ný`brd ctö`lfd kbg elkröjbnd4

9)

Fdnsugtb bn gc tcigc pbrlöklfc y rbspdnkc= ´bn quì pbrldkd y bn quì oc`lglc kb gc tcigc pbrlöklfc sb bnfubntrc bg elkröjbnd4

6)

´Suì fd`pubstds odr`c bg elkröjbnd fucnkd sb unb fdn gds nd `btcgbs4

;)

´Suì ibnbolflds cpdrtcràc cg cìlbntb bg usd kb elkröjbnd fd`d oubntb kb bnbrjàc4

LJBY ∙ [cfcnã


3. Gds ãflkds Fd`pubstds kbg elkröjbnd Gc pcgcirc ãflkd prdvlbnb kbg gctàn cflkus qub sljnlfc cjrld. Gds ãflkds sb fcrcftbrlzcn pdr tbnbr bstb scidr. Xdr bmb`pgd bg vlncjrb d bg gl`ön. Fd`d cprbnkl`ds bn gc sb`cnc 98, gds ãflkds sdn sustcnflcs qub bn sdguflön cfudsc glibrcn ldnbs elkröjbnd. Bn jbnbrcg, sdn fd`pubstds ilncrlds d tbrncrlds odr`ckds pdr gc fdìlncflön kbg elkröjbnd (fdn vcgbnflc +3) fdn dtrd bgb`bntd.

¡@ufed fulkckd! Gc `cydràc kb fd`pubstds ãflkds sdn töxlfds. Nd gds prubib.

Vb pubkbn odr`cr kds tlpds kb ãflkd, sbjýn gc ncturcgbzc kbg bgb`bntd fdn bg qub sb fdìlnb bg elkröjbnd. • Elkrãflkd= fd`pubstd ilncrld odr`ckd pdr gc unlön kb elkröjbnd fdn un nd `btcg kb gds jrupds 3? d 3: (c bxfbpflön kbg dxàjbnd fdn bg qub odr`c cjuc).

elkröjbnd +

nd `btcg

(jrupd 3? d 3:)

0 elkrãflkd

Gds elkrãflkds sb rbprbsbntcn fdn gc oörùgc jbnbrcg= elkröjbnd fdn nd `btcg EN x vcgbnflc +3 jrupd 3? d 3: vcgbnflc kbg nd `btcg jrupd 3? d 3:

Gc vcgbnflc slb`prb kbg elkröjbnd bs +3 pdr bsd nd sb bsfrlib.

Bmb`pgds= elkröjbnd fdn vcgbnflc +3

EFg

fgdrd

elkröjbnd fdn vcgbnflc +3

vcgbnflc ‖3 kbg fgdrd

E9Vb

sbgbnld

vcgbnflc ∙9 kbg sbgbnld

Bmbrflfld 3 Lkbntlqub fckc bgb`bntd kb gc oörùgc kbg elkrãflkd sljulbntb. [lbnb un bmb`pgd. 8)


EV

czuorb

3)

EIr

9

vcgbnflc ‖9 kbg czuorb


383

• Ãflkd dxãflkd= fd`pubstd tbrncrld qub sb odr`c kb gc unlön kbg elkröjbnd, un nd `btcg y dxàjbnd.

elkröjbnd +

nd `btcg

+

dxàjbnd

0 dxãflkd

Gds ãflkds dxãflkds sb prbsbntcn fdn gc oörùgc jbnbrcg=

END


dxàjbnd fdn vcgbnflc ‖9

nd `btcg, klstlntd cg dxàjbnd Gc vcgbnflc kbg dxàjbnd slb`prb bs ‖9.

Bmb`pgds=

E9VD;



czuorb

E9VbD;



sbgbnld

Bmbrflfld 9 C.

Lkbntlolqub fckc bgb`bntd kbg sljulbntb ãflkd dxãflkd. [lbnb un bmb`pgd. 8)


EFgD6


fgdrd

E6XD;

3)

I.

Kbtbr`lnb sl gds sljulbntbs ãflkds sdn ilncrlds d tbrncrlds. Vbjýn bstc lnodr`cflön fgcsloàqubgds bn elkrãflkds u dxãflkds. [lbnb un bmb`pgd. 8)

EV 9

389

3)

END6

9)

E@nD;

LJBY ∙ [cfcnã

elkrãflkd

6)

EFg

;)

EL

2)

E9FD6

3.3 Nd`bnfgcturc kb gds ãflkds Bn gc sb`cnc 93 cprbnkl`ds qub ecy trbs slstb`cs kb nd`bnfgcturc= bstbquld`ìtrlfd, Vtdfa y trcklfldncg. Gds elkrãflkds y gds dxãflkds sb ndìrcn fdn bg slstb`c trcklfldncg.

c.

Nd`bnfgcturc kb gds elkrãflkds bn bg slstb`c trcklfldncg

Bg slstb`c trcklfldncg kb nd`bnfgcturc bs bg `ãs cntljud. Gd utlglzcic gc bsfubgc orcnfbsc bnfcibzckc pdr Gcvdlslbr qulbn gd fdnflilö bn 3:5:. Gc L.R.X.C.F kbscfdnsbmc su usd pdrqub rbsugtcn ndìrbs ùy gcrjds pcrc ùfeds fd`pubstds. Vln bìcrjd, bstb slstb`c sb sljub utlglzcnkd pcrc ndìrcr c gds ãflkds. Gc bstrufturc pcrc ndìrcr c gds elkrãflkds bs= Ndìrb jbnìrlfd + nd `btcg + sumd ∙eàkrlfd Bg ndìrb jbnìrlfd kb gds elkrãflkds bs ãflkd. Xdr bmb`pgd=

Fg

E+

Gc fdìlncflön kb elkröjbnd (E+3) fdn fgdrd (Fg∙3) kc fd`d rbsugtckd ãflkd fgdreàkrlfd (EFg).

∙

EFg

_bc`ds fö`d sb ditlbnb bstb ndìrb= 3. Bsfrlil`ds bg ndìrb jbnìrlfd= ãflkd. Bstb pcsd bs jbnbrcg pcrc tdkds gds ãflkds. ãflkd 9. Gubjd bsfrlil`ds bg ndìrb ndìrb kbg nd `btcg y cjrbjc`ds bg suolmd ∙eàkrlfd. Nd `btcg= fgdrd Vuolmd= ∙eàkrlfd

fgdreàkrlfd

6. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc=

Vl bg nd `btcg kb gds jrupds 3? d 3: tbr`lnc bn vdfcg, bstc sb d`ltb. Bstc rbjgc sb fu`pgb pcrc bg fgdrd, bg ird`d, bg ydkd y bg sbgbnld.

Ndìrb jbnìrlfd + nd `btcg + sumd ∙eàkrlfd ãflkd

fgdrd

eàkrlfd

ãflkd fgdreàklrfd (EFg) Suà`lfc LL ∙ Vb`cnc 9;

386

¡_bc`ds un fcsd bspbflcg!

Ndìrb`ds bg fd`pubstd fdn oörùgc E9V 3. Bsfrlil`ds bg ndìrb jbnìrlfd= ãflkd. ãflkd 9. Bsfrlil`ds bg ndìrb kbg nd `btcg. Bg slstb`c trcklfldncg utlglzc bg ndìrb sugourd pcrc ndìrcr cg czuorb. [d`c`ds sdgd gcs gbtrcs "sugo" y cjrbjc`ds bg suolmd ∙eàkrlfd. Kbib `b`drlzcrgd. Nd `btcg= sugourd Vuolmd=

sugoeàkrlfd

∙eàkrlfd

6. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc= Ndìrb jbnìrlfd + nd `btcg + sumd ∙eàkrlfd ãflkd

sugourd

eàkrlfd

ãflkd sugoeàklrfd (E 9V)

Bmbrflfld 6 Bsfrlic bg ndìrb kb gds sljulbntbs elkrãflkds. [lbnb un bmb`pgd. 8)

EO Ndìrb jbnìrlfd=

ãflkd

Ndìrb kbg nd `btcg=

ýdr

Vuolmd=

‖eàkrlfd

Ndìrb kbg fd`pubstd=

ãflkd udreàkrlfd

Disbrvb qub bg ogýdr nd tbr`lnc bn vdfcg, pdr gd tcntd pcrc odr`cr bg ndìrb kbg ãflkd sb gb cóckb klrbftc`bntb bg suolmd ∙eàkrlfd. 3)

EIr Ndìrb jbnìrlfd= Ndìrb kbg nd `btcg= Vuolmd= Ndìrb kbg fd`pubstd=

38;

LJBY ∙ [cfcnã

i. Nd`bnfgcturc kb gds ãflkds dxãflkds bn bg slstb`c trcklfldncg Csà fd`d un fcrplntbrd nbfbsltc sbrrufed, `ckbrc y fgcvds pcrc fdnstrulr unc `bsc, ndsdtrds nbfbsltcrb`ds cgjuncs ebrrc`lbntcs pcrc ndìrcr c gds ãflkds dxãflkds. _bc`ds.

3. Fö`d ndìrcr gc vcgbnflc kb nd `btcgbs bn bg slstb`c trcklfldncg Bg slstb`c trcklfldncg b`pgbc unc sbrlb kb prbolmds y suolmds, sbjýn bg ný`brd kb vcgbnflc kb fckc bgb`bntd. Disbrvb gc tcigc. Kbib cprbnkbrgc kb `b`drlc. ný`brd kb vcgbnflc qub utlglzc bg nd `btcg

3d9

prbolmd‖

elpd‖

‖suolmd

‖dsd

;d6

‖

‖dsd

?d2

‖

‖lfd

:

pbr‖

‖lfd

Xdr bmb`pgd bg nltröjbnd tlbnb gcs vcgbnflcs 6, ;, 2, 9. Vl cftýc fdn gc vcgbnflc 6, gc `ãs fd`ýn, nd utlglzcrã prbolmd y bg suolmd sbrã ‖dsd (nltrdsd). Vl cftýc fdn gc vcgbnflc 2, nd utlglzcrã prbolmd y bg suolmd sbrã ‖lfd (nàtrlfd).

9.

6, ;, 2, 9

N

Lnodr`cflön qub nds prdpdrfldnc unc oörùgc quà`lfc

Ybfubrkb qub bn unc oörùgc quà`lfc, gds suiànklfbs lnklfcn bg ný`brd kb ãtd`ds kb fckc bgb`bntd. Csà fucnkd vb`ds unc oörùgc sln suiànklfbs, lntbrprbtcrb`ds qub tlbnb un sdgd ãtd`d kbg bgb`bntd qub gd prbfbkb. Xdr bmb`pgd= Gc oörùgc kbg ãflkd nàtrlfd, END 6, nds lnklfc qub bsb fd`pubstd bstã odr`ckd pdr= un ãtd`d kb elkröjbnd (E)

Fucnkd bg nd `btcg tbr`lnc bn vdfcg, bstc sb d`ltb y sb cjrbjc bg sumd ‖dsd (vcgbnflc `bndr) d ‖lfd (vcgbnflc `cydr). Bstc rbjgc sb fu`pgb pcrc bg fgdrd, bg ird`d, bg ydkd, bg oösodrd, bg sbgbnld y bg fcridnd. Gcs bxfbpfldnbs sdn bg nltröjbnd y bg czuorb. dsd (nltrdsd) nltr ‖ lfd (nàtrlfd) dsd (sugourdsd) sugour‖ lfd (sugoýrlfd)

END6

un ãtd`d kb nltröjbnd ( N)

trbs ãtd`ds kb dxàjbnd (D)


382

6. Ný`brd kb vcgbnflc kb gds bgb`bntds qub odr`cn un ãflkd dxãflkd Rn ãflkd dxãflkd bstã odr`ckd pdr elkröjbnd, un nd `btcg y dxàjbnd . Bg elkröjbnd slb`prb tlbnb vcgbnflc +3 y bg dxàjbnd slb`prb tlbnb vcgbnflc ‖9. elkröjbnd fdn vcgbnflc +3

END


nd `btcg, klstlntd kbg dxàjbnd

Xcrc ndìrcr un ãflkd dxãflkd, kbib`ds fcgfugcr gc vcgbnflc kbg nd `btcg. Rn kctd qub nds cyukc bs scibr qub gc su`c kb tdkcs gcs vcgbnflcs kb unc `dgìfugc slb`prb bs fbrd . ´Fö`d fcgfugc`ds gc vcgbnflc kbg nd `btcg4 Vljc`ds gds pcsds kbg bmb`pgd. Fcgfugb`ds fuãg bs gc vcgbnflc kbg fcridnd bn bg ãflkd fcriönlfd= E9FD6 c. Bsfrlil`ds gds ný`brds kb vcgbnflc= elkröjbnd +3 y dxàjbnd ‖9. Lkbntlolfc`ds fdn unc x gc vcgbnflc kbg nd `btcg, fcridnd.

E F xD i. @ugtlpglfc`ds gds suiànklfbs, qub lnklfcn bg ný`brd kb ãtd`ds kb fckc bgb`bntd, pdr bg ný`brd kb vcgbnflc kb gds `ls`ds.

E(3) (9)FxD(‖9)(6) E+9FxD‖? Oàmbsb= Vl un ãtd`d kb elkröjbnd tlbnb vcgbnflc +3, Vl un ãtd`d kb dxàjbnd tlbnb vcgbnflc ∙9, kds ãtd`ds kb elkröjbnd tbnkrãn vcgbnflc +9. trbs ãtd`ds kb dxàjbnd tbnkrãn vcgbnflc ∙?

f. Xgcntbc`ds unc bfucflön pcrc bnfdntrcr bg vcgdr kb x.

E+9FxD‖? 9+x‖ ?08 x0?‖ 9

x0; Bg fcridnd, bn bg ãflkd fcriönlfd, cftýc fdn unc vcgbnflc kb +;. E+9F+;D‖?

38?

LJBY ∙ [cfcnã

¡Cedrc sà! fdn gcs ebrrc`lbntcs qub eb`ds cprbnklkd vc`ds c fdndfbr y prcftlfcr fö`d sb ndìrcn gds ãflkds dxãflkds bn bg slstb`c trcklfldncg. Gc bstrufturc pcrc ndìrcr c un ãflkd dxãflkd bs= Ndìrb jbnìrlfd + prbmd + nd `btcg + sumd Bg ndìrb jbnìrlfd kb gds ãflkds dxãflkds bs ãflkd. Xdr bmb`pgd= Kbtbr`lnb`ds bg ndìrb kb EFgD 3. Bsfrlil`ds bg ndìrb jbnìrlfd= ãflkd. 9. Xcrc bsfrlilr bg prbolmd y bg suolmd kbib`ds kbtbr`lncr gc vcgbnflc kbg nd `btcg. Vbjul`ds gds pcsds qub cprbnkl`ds pcrc ecfbrgd= c. Bsfrlil`ds gds ný`brds kb vcgbnflc kbg elkröjbnd y kbg dxàjbnd pdrqub slb`prb sdn gds `ls`ds. Bg elkröjbnd tlbnb vcgbnflc +3 y bg dxàjbnd, ‖9. Lkbntlolfc`ds fdn unc x gc vcgbnflc kbg nd `btcg. elkröjbnd fdn vcgbnflc +3

E Fg D +3

x

‖9

END

nd `btcg, klstlntd cg dxàjbnd


i. @ugtlpglfc`ds gds suiànklfbs, ný`brd kb ãtd`ds kb fckc bgb`bntd bn gc oörùgc, pdr bg ný`brd kb vcgbnflc. Bn bstb fcsd tdkds gds suiànklfbs sdn ljucg c 3, csà qub bg vcgdr kb gcs vcgbnflcs nd vcràc.

E+3FgxD‖9 f. Xgcntbc`ds unc bfucflön pcrc cvbrljucr bg vcgdr kb x.

E+3FgxD‖9 3+x‖ 908 x09‖ 3 x03 Bg fgdrd cftýc fdn unc vcgbnflc kb +3. Fd`d gc vcgbnflc bs und, bg prbmd bs elpd‖ y bg sumd bs ‖dsd. 6. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc=

n½. kb prbo‖ ‖suo vcgbnflc

3d9

elpd‖ ‖dsd

ndìrb jbnìrlfd + prbmd + nd `btcg + sumd ãflkd

elpd

fgdrd

dsd

ãflkd elpdfgdrdsd (EFgD) Suà`lfc LL ∙ Vb`cnc 9;

38:

Ndìrb`ds cg EFgD; 3. Bsfrlil`ds bg ndìrb jbnìrlfd= ãflkd 9. Kbtbr`lnc`ds gc vcgbnflc kbg nd `btcg= c. Bg elkröjbnd tlbnb vcgbnflc +3 y bg dxàjbnd, ‖9. Lkbntlolfc`ds fdn unc x gc vcgbnflc kbg nd `btcg.

E+3FgxD i. @ugtlpglfc`ds gds suiànklfbs. Bg elkröjbnd cftýc fdn un ãtd`d csà qub gd ùgtlpglfc`ds pdr 3 y bg dxàjbnd, fd`d tlbnb fuctrd ãtd`ds, gd ùgtlpglfc`ds pdr ;.

E(+3)(3)FgxD(‖9)(;) E3FgxD‖5 f. Xgcntbc`ds unc bfucflön pcrc fcgfugcr bg vcgdr x.

E+3FgxD‖5 3+x‖ 508 x05‖ 3 x0: n½. kb prbo‖ ‖suo vcgbnflc

:

pbr‖ ‖lfd

Bg fgdrd tlbnb vcgbnflc +:. Fd`d gc vcgbnflc bs slbtb, bg prbolmd bs pbr‖ y bg suolmd bs ‖lfd. 6. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc= ndìrb jbnìrlfd + prbmd + nd `btcg + sumd ãflkd pbr fgdrd ãflkd pbrfgörlfd (EFgD;)

lfd

Lnvbstljub bn gc rbk... ´Sulbrb prcftlfcr bn gànbc fö`d ndìrcr ãflkds dxãflkds4 _lsltb bstc klrbfflön www.cgdnsdodrùgc.fd`/lndrjcnlfc/dxcflkds.et` Fucnkd ecyc bntrckd c gc pãjlnc, vcyc cg ncg y kì un fglf bn gcs fcslggcs Ndìrbs 3 y Ndìrbs 9

385

LJBY ∙ [cfcnã

Bmbrflfld ; Bsfrlic bg ndìrb kb gds sljulbntbs ãflkds dxãflkds. [lbnb un bmb`pgd. 8)

END 3. Bsfrlil`ds bg ndìrb jbnìrlfd=

ãflkd

9. Kbtbr`lnc`ds gc vcgbnflc kbg nd `btcg. Ybfubrkb tdkds gds pcsds nbfbscrlds pcrc bnfdntrcrgc= c. Bsfrlil`ds gds ný`brds kb vcgbnflc fdndflkds b

E+3NxD‖9

lkbntlolfc`ds fdn unc x gc vcgbnflc kbg nd `btcg. i. @ugtlpglfc`ds gds suiànklfbs. Bn bstb fcsd gds suiànklfbs sdn 3. Bg vcgdr kb gcs vcgbnflcs nd vcràc.

E+3NxD‖9

f. Xgcntbc`ds unc bfucflön pcrc fcgfugcr bg vcgdr kb x.

3+x‖ 908 x09‖ 3 x03

Gc vcgbnflc kbg nltröjbnd bs +3. Xrbolmd=

elpd‖

Vuolmd=

‖dsd

6. Bsfrlil`ds bg ndìrb kbg fd`pubstd= 3)

ãflkd elpdnltrdsd

END6 3. Bsfrlil`ds bg ndìrb jbnìrlfd= 9. Kbtbr`lnc`ds gc vcgbnflc kbg nd `btcg. c. Bsfrlil`ds gds ný`brds kb vcgbnflc fdndflkds. Lkbntlolfc`ds fdn unc x gc vcgbnflc kbg nd `btcg. i. @ugtlpglfc`ds gds suiànklfbs. f. Xgcntbc`ds unc bfucflön pcrc fcgfugcr bg vcgdr kb x.

Gc vcgbnflc kbg nltröjbnd bs= Xrbolmd= Vuolmd= 6. Bsfrlil`ds bg ndìrb kbg fd`pubstd= Suà`lfc LL ∙ Vb`cnc 9;

38<

Ybsu`bn Bstc sb`cnc bstuklö= 3.

Gds ãflkds sb kbolnbn fd`d sustcnflcs qub bn sdguflön cfudsc glibrcn ldnbs kb elkröjbnd. Vdn fd`pubstds ilncrlds d tbrncrlds odr`ckds p dr gc fdìlncflön kbg elkröjbnd (fdn vcgbnflc +3) fdn dtrd bgb`bntd.

3.3. Nd`bnfgcturc kb gds ãflkds c. Ãflkds elkrãflkds sb rbprbsbntcn fdn gc oörùgc jbnbrcg=

ExN


nd `btcg jrupd 3? d 3:

vcgbnflc kbg nd `btcg jrupd 3? d 3:

Gc bstrufturc pcrc ndìrcr elkrãflkds bs= Ndìrb jbnìrlfd + ndìrb kbg nd `btcg + sumd ‖eàkrlfd i. Ãflkds dxãflkds sb rbprbsbntcn fdn gc oörùgc= elkröjbnd fdn vcgbnflc +3

END



Xrbolmds y suolmds pcrc ndìrcr ãflkds dxãflkds= ný`brd kb vcgbnflc qub utlglzc bg nd `btcg

3d9 ;d6 ?d2 :

prbmd‖

‖sumd

elpd‖ ‖dsd ‖ ‖dsd ‖ ‖lfd pbr‖ ‖lfd

Gc bstrufturc pcrc ndìrcr ãflkds dxãflkds bs= ãflkd + prbmd + ndìrb kbg nd `btcg + sumd Xcrc bsfrlilr bg prbolmd y bg suolmd kbib`ds kbtbr`lncr gc vcgbnflc kbg nd `btcg. Vbjul`ds bstds pcsds= • Bsfrlil`ds gds ný`brds kb vcgbnflc fdndflkds (elkröjbnd(+3) y dxàjbnd(‖9)). • @ugtlpglfc`ds gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn. • Xgcntbc`ds unc bfucflön pcrc fcgfugcr bg vcgdr kb gc vcgbnflc kbg nd `btcg.

338

LJBY ∙ [cfcnã

Cutdfdntrdg Cftlvlkck 3. Ybgcfldnb fdnfbptds 3)

Fd`pubstds qub glibrcn ldnbs E+ bn sdguflön cfudsc.

öxlkds ãflkds icsbs

9)

[lpd kb ãflkds odr`ckds pdr elkröjbnd, un nd `btcg y dxàjbnd.

elkrãflkds nd `btãglfds dxãflkds

6)

Ãflkds qub rbsugtcn kb gc unlön kbg elkröjbnd fdn un nd `btcg kb gds jrupds 3? d 3:.

elkrãflkds ecgöjbnds dxãflkds

;)

_cgbnflc fdn gc qub slb`prb cftýc bg elkröjbnd bn un ãflkd.

8 ‖3 +3

2)

_cgbnflc fdn gc qub slb`prb cftýc bg dxàjbnd bn un ãflkd.

‖3 ‖9 +9

?)

Xrbolmd qub utlglzc bg slstb`c trcklfldncg fucnkd bg nd `btcg kb un ãflkd cftýc fdn gc vcgbnflc :.

elpd‖ pbr‖ ncnd‖

:)

Vuolmd qub utlglzc bg slstb`c trcklfldncg fucnkd bg nd `btcg kb un ãflkd cftýc fdn gc vcgbnflc 6 d ;.

elpd‖ ‖dsd ‖lfd Suà`lfc LL ∙ Vb`cnc 9;

333

5)

Vu`c kb tdkcs gcs vcgbnflcs kb unc `dgìfugc.

3 9 8

<)

Oörùgc jbnbrcg kb gds ãflkds dxãflkds.

ExN @ xD y END

Cftlvlkck 9. Lkbntlqub elkrãflkds y dxãflkds

Fgcslqub gds sljulbntbs fd`pubstds bn elkrãflkds u dxãflkds. qub gds elkrãflkds sdn fd`pubstds ilncrlds y gds dxãflkds fd`pubstds tbrncrlds . [lbnbYbfubrkb un bmb`pgd. 3)

E 9V

9) 6)

elkrãflkd

;)

END9

E6CsD6

2)

E9VbD;

EL

?)

EO

Cftlvlkck 6 Bsfrlic bg ndìrb kb gds sljulbntbs elkrãflkds. 3)

EFg Ndìrb jbnìrlfd= Ndìrb kbg nd `btcg= Vuolmd= Ndìrb kbg fd`pubstd=

9)

EO Ndìrb jbnìrlfd= Ndìrb kbg nd `btcg= Vuolmd= Ndìrb kbg fd`pubstd=

6)

EL Ndìrb jbnìrlfd= Ndìrb kbg nd `btcg= Vuolmd= Ndìrb kbg fd`pubstd=

339

LJBY ∙ [cfcnã

;)


2)

E9[b Ndìrb jbnìrlfd= Ndìrb kbg nd `btcg= Vuolmd= Ndìrb kbg fd`pubstd=

Cftlvlkck ; Bsfrlic bg ndìrb kb gds sljulbntbs ãflkds dxãflkds. 3)

EIrD6 3. Bsfrlil`ds bg ndìrb jbnìrlfd= 9. Kbtbr`lnc`ds gc vcgbnflc kbg nd `btcg. c. Bsfrlil`ds gds ný`brds kb vcgbnflc fdndflkds. Lkbntlolfc`ds fdn unc x gc vcgbnflc kbg nd `btcg. i. @ugtlpglfc`ds gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn. f. Xgcntbc`ds unc bfucflön pcrc fcgfugcr bg vcgdr kb x.

Gc vcgbnflc kbg ird`d bs= Xrbolmd= Vuolmd= 6. Bsfrlil`ds bg ndìrb kbg fd`pubstd= Suà`lfc LL ∙ Vb`cnc 9;

336

9)

E9VD; 3. Bsfrlil`ds bg ndìrb jbnìrlfd= 9. Kbtbr`lnc`ds gc vcgbnflc kbg nd `btcg. c. Bsfrlil`ds gds ný`brds kb vcgbnflc fdndflkds. Lkbntlolfc`ds fdn unc x gc vcgbnflc kbg nd `btcg. i. @ugtlpglfc`ds gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn. f. Xgcntbc`ds unc bfucflön pcrc fcgfugcr bg vcgdr kb x.

Gc vcgbnflc kbg `cnjcnbsd bs= Xrbolmd= Vuolmd= 6. Bsfrlil`ds bg ndìrb kbg fd`pubstd= 6)

E6XD; 3. Bsfrlil`ds bg ndìrb jbnìrlfd= 9. Kbtbr`lnc`ds gc vcgbnflc kbg nd `btcg. c. Bsfrlil`ds gds ný`brds kb vcgbnflc fdndflkds. Lkbntlolfc`ds fdn unc x gc vcgbnflc kbg nd `btcg. i. @ugtlpglfc`ds gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn. f. Xgcntbc`ds unc bfucflön pcrc fcgfugcr bg vcgdr kb x.

Gc vcgbnflc kbg oösodrd bs= Xrbolmd= Vuolmd= 6. Bsfrlil`ds bg ndìrb kbg fd`pubstd=

33;

LJBY ∙ [cfcnã

;)

ELD 3. Bsfrlil`ds bg ndìrb jbnìrlfd= 9. Kbtbr`lnc`ds gc vcgbnflc kbg nd `btcg. c. Bsfrlil`ds gds ný`brds kb vcgbnflc fdndflkds. Lkbntlolfc`ds fdn unc x gc vcgbnflc kbg nd `btcg. i. @ugtlpglfc`ds gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn. f. Xgcntbc`ds unc bfucflön pcrc fcgfugcr bg vcgdr kb x.

Gc vcgbnflc kbg ydkd bs= Xrbolmd= Vuolmd= 6. Bsfrlil`ds bg ndìrb kbg fd`pubstd= 2)

EIrD 3. Bsfrlil`ds bg ndìrb jbnìrlfd= 9. Kbtbr`lnc`ds gc vcgbnflc kbg nd `btcg. c. Bsfrlil`ds gds ný`brds kb vcgbnflc fdndflkds. Lkbntlolfc`ds fdn unc x gc vcgbnflc kbg nd `btcg. i. @ugtlpglfc`ds gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn. f. Xgcntbc`ds unc bfucflön pcrc fcgfugcr bg vcgdr kb x.

Gc vcgbnflc kbg ird`d bs= Xrbolmd= Vuolmd= 6. Bsfrlil`ds bg ndìrb kbg fd`pubstd= Suà`lfc LL ∙ Vb`cnc 9;

332


Rn gl`plckdr bfdgöjlfd Bstc sb`cnc pdkrã vbr gc rbcfflön quà`lfc kb gds ãflkds fdn dtrds fd`pubstds. Gc suflbkck qub sb cfuùgc bn gds scnltcrlds, gcvc`cnds, gcvctrcstds, ggcvbs kb rbjckbrcs, kufecs y dtrds utbnslglds qub pbr`cnbfbn bn fdnstcntb fdntcftd fdn bg cjuc, bs rbslstbntb y kloàflg kb qultcr. Bstc suflbkck qub fdndfb`ds fd`d scrrd sb prlnflpcg`bntb, c qub gcsndscgbs kb fcridnctd kbg cjuc sb pbjcn gc gdsckbib, y gc `cnfecn. Vl gc suflbkck sb gl`plc rbjugcr`bntb, gc `cnfec sb bn ecfb fckc vbz `ãs jrcnkb y `ãs kloàflg kb rb`dvbr. Xcrc qultcr bstb tlpd kb `cnfecs sb b`pgbcn gl`plckdrbs qub fdntlbnbn ãflkds, fd`d bg ãflkd fgdreàkrlfd y bg ãflkd odsoörlfd. Bstds gl`plckdrbs sdn ùy bobftlvds, pbrd kcólnds pcrc bg `bkld cìlbntb. Rnc cgtbrnctlvc bs uscr un ãflkd ildkbjrckcigb, bg ãflkd cfìtlfd. Bg ãflkd cfìtlfd gd bnfdntrc`ds bn bg vlncjrb igcnfd.

´Suì nbfbsltc4  



Fucgqulbrc kb gds sljulbntbs utbnslglds qub sb bnfubntrb `cnfeckd fdn scrrd= gcvc`cnds gcvctrcstds gc ggcvb kb gc kufec czugbmd bn gc rbjckbrc bg lndkdrd unc `bsc kb oör`lfc Rn fbplggd kb klbntbs vlbmd Rnc bspdnmc d tdcggc pcrc gl`plcr y sbfcr Rn fbplggd pcrc gl`plcr bg lndkdrd gãplz



glirbtc kb fc`pd



 



33?

3 idtbggc kb vlncjrb igcnfd Vuolflbntb cjuc, kbpbnklbnkd kbg tc`cód kbg utbnslgld qub vcyc c gl`plcr

LJBY ∙ [cfcnã

´Suì kbib ecfbr4 Vl gl`plc bg gcvc`cnds d bg gcvctrcstds= 3) Disbrvb fulkckdsc`bntb bg bstckd bn bg qub sb bnfubntrc bg utbnslgld. Cndtb bn su glirbtc kb fc`pd bg tc`cód kb gc `cnfec, bg fdgdr y gc uilfcflön. 9) [cpb bg kbscj÷b fdn un trcpd pcrc qub bg vlncjrb nd sb bsfcpb pdr ìg. 6) Bfeb uncy tczc kbrbpdscr vlncjrbkurcntb bn bg utbnslgld gl`plcr kìmbgd 2 `lnu-c tds. ;) @lbntrcs bspbrc, `dmb gc tdcggc d gc bspdnmc fdn un pdfd kb vlncjrb y ordtb cqubggds gujcrbs qub nd tlbnbn fdntcftd fdn bg vlncjrb. Xubkb uscr un fbplggd kb klbntbs vlbmd pcrc rbstrbjcr gds gujcrbs kb kloàflg cffbsd.

9) Ordtb fdn bg fbplggd kb klbntbs gds sltlds bn könkb sb bnfubntrb `ãs sufld. Ybpltc gc dpbrcflön kds vbfbs. 6) Bnmucjub fdn ciunkcntb cjuc ecstc qub yc nd pbrflic bg dgdr kbg vlncjrb. ;) Vbqub gc supbrolflb, bxc`ànbgc fulkckdsc`bntb y cndtb sus disbrvcfldnbs. Vl gl`plc bg lndkdrd= 3) _cfàb gc idtbggc kb vlncjrb bn gc tczc kbg lndkdrd, kìmbgd rbpdscr pdr 2 `lnutds y gubjd orötbgd fdn un fbplggd pcrc gcvcr icóds. 9) Kbmb lr bg cjuc kbg tcnqub, vubgvc c rbstrbjcr fdn bg fbplggd y vubgvc c bfecr cjuc.

2) Kbstcpb bg kbscj÷b y bnmucjub gc plbzc fdn ciunkcntb cjuc, ecstc qub yc nd pbrflic bg dgdr kbg vlncjrb.

6) Bxc`lnb fulkckdsc`bntb bg lndkdrd y cndtb sus disbrvcfldnbs.

?) Vbqub bg utbnslgld, bxc`ànbgd fulkckdsc`bntb y cndtb sus disbrvcfldnbs.

3) Eu`bkbzfc unc tdcggc sbfc fdn vlncjrb y rbstrlbjub gc `bsc pcrc qub qubkb eý`b-

Vl gl`plc gc ggcvb kb gc kufec d bg czugbmd kb gc rbjckbrc=

kc. Bspbrb 6 `lnutds. 9) Bnmucjub fdn cjuc gc `bsc y sìqubgc.

3) Ydfàb ciunkcntb`bntb fdn vlncjrb bg czugbmd d gc ggcvb y kbmb rbpdscr pdr 6 `lnutds.

6) Bxc`lnb fulkckdsc`bntb gc supbrolflb y cndtb sus disbrvcfldnbs.

Vl gl`plc gc `bsc kb oör`lfc=

Lnvbstljub bn gc rbk... Nbfbsltc`ds cgjunds ãflkds pcrc qub nubstrd drjcnls`d ounfldnb ckbfuckc`bntb. Iusqub gc kbnlflön kb= • ãflkd csförilfd • ãflkd dgìlfd • ãflkd oöglfd • ãflkd pcntdtìnlfd Xubkb ecfbrgd bn bstcs klrbffldnbs=

dg`d.pntlf.`bf.bs/~rmlk8888/klf.et` y teb`bklfcgildfeb`lstrypcjb.drj/.../vltc`lns-sp.et`g Suà`lfc LL ∙ Vb`cnc 9;

33:



gdjrckd

rbjugcr

nd gdjrckd

Cspbftds c bvcgucr 3. 9. 6. ;. Kbspuìs kb bstuklcr... 2.

Fdndzfd gds ibnbolflds qub cpdrtcràc cg cìlbntb bg usd kbg elkröjbnd fd`d oubntb kb bnbrjàc. Lkbntlolfd y `b`drlzd fd`pdnbntbs kb gc oörùgc jbnbrcg kb gds ãflkds. Lkbntlolfd fckc bgb`bntd bn gcs oörùgcs kb klstlntds elkrãflkds y dxãflkds. Fgcslolfd ãflkds bn elkrãflkds u dxãflkds. Ndìrd prbolmds y suolmds qub b`pgbcn gds nd `btcgbs bn gc odr`cflön kb ãflkds dxãflkds.

?.

Kbtbr`lnd gc vcgbnflc kb un nd `btcg bn un ãflkd dxãflkd.

:.

Ndìrd ãflkds bn bg slstb`c trcklfldncg.

5.

Bxpbrl`bntd fdn bg ãflkd kbg vlncjrb.


335

LJBY ∙ [cfcnã

92

Nd`bnfgcturc L_ Elkröxlkds


33<


Lkbntlolfcr gds bgb`bntds bn gc oörùgc kb un elkröxlkd.



Ndìrcr elkröxlkds bn bg slstb`c Vtdfa.



Bsfrlilr gc oörùgc kb klstlntds elkröxlkds gbybnkd su ndìrb bn bg slstb`c Vtdfa.



Ybpcscr gc nd`bnfgcturc kb gds fd`pubstds vlstds= öxlkds, ãflkds b elkröxlkds.



Ocirlfcr un lnklfckdr ãflkd‖icsb fcsbrd. Lkbntlolfcr sustcnflcs ãflkcs y iãslfcs b`pgbcnkd un lnklfckdr fcsbrd.






398

¡Xcrc fd`bnzcr!

• Bg elkröxlkd kb `cjnbsld


• Elkröxlkds d icsbs


• ´Ãflkd d icsb4

LJBY ∙ [cfcnã

¡Xcrc fd`bnzcr! Bg elkröxlkd kb `cjnbsld Rn fd`pubstd ùgtlusds Bg elkröxlkd kb `cjnbsld @j(DE) 9 bs unc icsb söglkc igcnfc, sln scidr, sln dgdr y nd bs töxlfc. Cunqub bs un söglkd, bs ùy igcnkd y pubkb `dgbrsb ecstc fdnvbrtlrsb bn pdgvd ùy olnd. Fdndzfc`ds cgjuncs cpglfcfldnbs kbg elkröxlkd kb `cjnbsld= •

Gc `bzfgc kb pdgvd olnd kb @j(DE) 9 fdn cjuc gc fdndfb`ds fd`d gbfeb kb `cjnbslc . Gc gbfeb kb `cjnbslc sb utlglzc fd`d cntlãflkd pcrc nbutrcglzcr gc cflkbz bstd`cfcg. [cìlìn sb pubkb b`pgbcr fd`d gcxcntb pdrqub prdvdfc klcrrbc. Cunqub bs un `bklfc`bntd kb vbntc glirb, nd kbib fdnsu`lrsb bn bxfbsd pdrqub icmc gds nlvbgbs kb pdtcsld bn bg fubrpd y tcìlìn l`plkb qub bg drjcnls`d cisdric bg ãflkd oöglfd qub sb bnfubntrc bn gds orlmdgbs, gds vbjbtcgbs kb edmc vbrkb y bg eàjckd.

•

@ufeds kbsdkdrcntbs fdrpdrcgbs sb prbpcrcn cócklbnkd c un jbg d c tcgfd, elkröxlkd kb `cjnbsld. Bg elkröxlkd kb `cjnbsld nbutrcglzc bg dgdr kbg sukdr pbrd nd l`plkb qub sb prdkuzfc. Kb cfubrkd fdn vcrlcs lnvbstljcfldnbs, bg usd kb cntltrcnsplrcntbs pubkb tcpcr gds pdrds kb gcs cxlgcs jbnbrcnkd prdfbsds kbjbnbrctlvds bn gcs fìgugcs. ¡Nd usb cntltrcnsplrcntb s!

•

Bg elkröxlkd kb `cjnbsld sb cóckb c gds fd`pdnbntbs kb pgãstlfds, tbfeds, sãicncs y feu`pcs pcrc bvltcr qub bstds prbnkcn oubjd. Bg elkröxlkd kb `cjnbsld tlbnb gc prdplbkck kb sdpdrtcr tb`pbrcturcs bgbvckcs. Vb pubkb fcgbntcr ecstc 669 ½F cntbs kb qub sb kbstruyc. Ckcptckd kb= ettp=//www.wdrgkglnjd.fd`/`c/bnwlal/bs/@cjnbslu`Teykrdxlkb

Bg elkröxlkd kb `cjnbsld @j(DE)9 bs un fd`pubstd iãslfd kb gds qub bstuklcrb`ds bstc sb`cnc.


393

¡C trcicmcr! 3)

Ybfubrkb qub unc prdplbkck oàslfc bs cqubggc qub sb disbrvc bn gc sustcnflc, sln qub prdvdqub un fcìld bn su fd`pdslflön. Vdn prdplbkckbs oàslfcs bg fdgdr, dgdr, scidr, btf. Ybggbnb bg fuckrd kb gc kbsfrlpflön kb gcs prdplbkckbs oàslfcs kbg elkröxlkd kb `cjnbsld qub sb `bnfldncn bn gc gbfturc. Xrdplbkckbs fdgdr

Kbsfrlpflön

dgdr scidr kurbzc

399

9)

´Fdn quì ndìrb sb fdndfb bg elkröxlkd kb `cjnbsld `dglkd bn pdgvd olnd y `bzfgckd fdn cjuc4

6)

Bg elkröxlkd kb `cjnbsld, bn odr`c kb gbfeb kb `cjnbslc, sb b`pgbc fd`d `bklfc`bntd. ´Suì pckbfl`lbntds cglvlc4

;)

´Xdr quì ecy qub sbr prbfcvlkds cg td`cr gbfeb kb `cjnbslc y nd td`cr `ãs kb gc nbfbscrlc4

2)

´Suì dtrds prdkuftds sb ocirlfcn fdn elkröxlkd kb `cjnbsld4

LJBY ∙ [cfcnã


3. Gds elkröxlkds d icsbs Rnc icsb sb kbnb fd`d un fd`pubstd quà`lfd fcpcz kb kcr ldnbs elkrdxlgd (DE‖) bn unc rbcfflön quà`lfc. Vdn icsbs gds fcridnctds, gds dxcgctds, gds elkröxlkds y bg c`dnld. Kbntrd kb bstb jrupd gds elkröxlkds sdn gds fd`pubstds `ãs fdùnbs, pdr bsd sb gbs ggc`c lnklstlntc`bntb elkröxlkds d icsbs. Ndsdtrds nds fbntrcrb`ds bn bggds. Vbjurd ustbk fdndfb cgjunds elkröxlkds cunqub nd gbs ggc`b csà. Xdr bmb`pgd bg elkröxlkd kb sdkld d sdkc fãustlfc (NcDE) qub sb utlglzc pcrc kbstcpcr fcóbràcs d bg elkröxlkd kb fcgfld d fcg cpcjckc Fc(DE)9 qub sb usc fd`d `ctbrlcg kb fdnstrufflön. Gds elkröxlkds sdn fd`pubstds tbrncrlds odr`ckds pdr un `btcg, dxàjbnd b elkröjbnd.

`btcg

+

dxàjbnd

+ elkröjbnd 0

elkröxlkd

Gds elkröxlkds rbsugtcn kb gc fdìlncflön kb un öxlkd `btãglfd y cjuc (kb cggà bg prbmd elkrd‖). Vb klobrbnflcn kb dtrds fd`pubstds pdr gc prbsbnflc kbg lön elkrdxlgd (DE‖). Vlb`prb qub gd vbc bn unc oörùgc, pubkb scibr qub bstc fdrrbspdnkb c un elkröxlkd. Vb rbprbsbntcn fdn gc oörùgc jbnbrcg= `btcg

@(DE)x

lönvcgbnflc elkrdxlgd‖3 fdn

vcgbnflc kbg `btcg y fcntlkck kb ldnbs (DE‖3)

Bmb`pgds= sdkld

NcDE

lön elkrdxlgd fdn vcgbnflc ‖3

elbrrd

Ob(DE)9

vcgbnflc +3 kbg sdkld y ný`brd kb ldnbs elkrdxlgd (3)


vcgbnflc +9 kbg elbrrd y ný`brd kb ldnbs elkrdxlgd (9)

Bmbrflfld 3 Lkbntlqub fckc bgb`bntd kb gc oörùgc kbg sljulbntb elkröxlkd. [lbnb un bmb`pgd. 8)

frd`d

Fr(DE)6

vcgbnflc +6 kbg frd`d y 6 ldnbs (DE‖3)

lön fdn elkrdxlgd vcgbnflc ‖3

3)

Fc(DE)9


396

3.3. Nd`bnfgcturc kb gds elkröxlkds Gds elkröxlkds sb pubkbn ndìrcr bn gds slstb`cs bstbquld`ìtrlfd, Vtdfa y fgãslfd. Ndsdtrds cprbnkbrb`ds c ndìrcrgds sdgd bn bg slstb`c Vtdfa.

c.

Nd`bnfgcturc bn bg slstb`c Vtdfa

Bn bg slstb`c Vtdfa gds elkröxlkds sb ndìrcn sbjýn bstc bstrufturc= Ndìrb jbnìrlfd + kb + `btcg + ný`brd kb vcgbnflc kbg `btcg Bg ndìrb jbnìrlfd bs elkröxlkd. Xdr bmb`pgd= Gc fdìlncflön kbg öxlkd `btãglfd (IcD) fdn cjuc (E9D) kc fd`d rbsugtckd Ic(DE)9 elkröxlkd kb Icrld (LL)

IcD

E9D

Ic(DE)9

_bc`ds fö`d sb ggbjc c bstb ndìrb= 3. Bsfrlil`ds bg ndìrb jbnìrlfd= elkröxlkd 9. Bsfrlil`ds bg ndìrb kbg `btcg= icrld 6. Kbtbr`lnc`ds bg ný`brd kb vcgbnflc kbg `btcg. Bg icrld tlbnb vcgbnflc +9 (LL) fd`d nds lnklfc bg suiànklfb kbg lön elkrdxlgd. ;. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc= Ndìrb jbnìrlfd + kb + `btcg + ný`brd kb vcgbnflc kbg `btcg elkröxlkd

kb

icrld

(LL)

elkröxlkd kb icrld (LL) Ic(DE) 9

Dtrd bmb`pgd= Bsfrlic`ds bg ndìrb kbg fd`pubstd= Nl(DE)6 3. Bsfrlil`ds bg ndìrb jbnìrlfd= elkröxlkd 9. Bsfrlil`ds bg ndìrb kbg `btcg= nlqubg 6. Kbtbr`lnc`ds bg ný`brd kb vcgbnflc kbg `btcg. Bg nlqubg tlbnb vcgbnflc +6 (LLL) fd`d nds lnklfc bg suiànklfb kbg lön elkrdxlgd. ;. Bsfrlil`ds bg ndìrb sbjýn gc bstrufturc= Ndìrb jbnìrlfd + kb + `btcg + ný`brd kb vcgbnflc kbg `btcg elkröxlkd

kb

nlqubg

elkröxlkd kb nlqubg (LLL) Nl(DE) 6

39;

LJBY ∙ [cfcnã

(LLL)

Bmbrflfld 9 Bsfrlic bg ndìrb kb fckc elkröxlkd sbjýn bg slstb`c Vtdfa. Disbrvb bg suiànklfb kbg lön elkrdxlgd pcrc scibr fuãg bs gc vcgbnflc kb fckc `btcg. [lbnb un bmb`pgd. 8)

FuDE Ndìrb jbnìrlfd=

3)

elkröxlkd

Ndìrb kbg `btcg=

fdirb

_cgbnflc kbg `btcg bn ný`brds rd`cnds=

L


elkröxlkd kb fdirb (L )

GlDE Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

9)

]n(DE)9 Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

6)

Cg(DE)6 Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

;)

Ob(DE)9 Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=


392

Bmbrflfld 6 Bsfrlic gc oörùgc quà`lfc kb gds sljulbntbs elkröxlkds. [lbnb un bmb`pgd. 8)

GlDE

Elkröxlkd kb gltld (L)

2)

Elkröxlkd kb frd`d (_L)

3)

Elkröxlkd kb drd (LLL)

?)

Elkröxlkd kb gcntcnd (LLL)

9)

Elkröxlkd kb ilsùtd (LL)

:)

Elkröxlkd kb bstcód (L_)

6)

Elkröxlkd kb pgd`d (L_)

5)

Elkröxlkd kb vdgorc`ld (_L)

;)

Elkröxlkd kb nàqubg (LL)

<)

Elkröxlkd kb pcgckld (LL)

Bmbrflfld ; Bsfrlic bg ndìrb kb gds sljulbntbs fd`pubstds bn bg slstb`c Vtdfa. [lbnb un bmb`pgd. 8)

Ye(DE)

;

elkröxlkd kb rdkld (L_)

6)

Fk(DE)9

3)

Gc(DE)9

;)

]r(DE);

9)

Lr(DE);

2)

@n(DE):

Ybsu`bn 3.

Elkröxlkds Gds elkröxlkds d icsbs sdn fd`pubstds tbrncrlds odr`ckds pdr un `btcg, dxàjbnd b elkröjbnd. Vb odr`cn c pcrtlr kb un öxlkd iãslfd y cjuc. Gds fcrcftbrlzc bn su bstrufturc quà`lfc gc prbsbnflc kbg lön elkrdxlgd (DE ‖). Vb prbsbntcn fdn gc oörùgc jbnbrcg= `btcg

@(DE)x


vcgbnflc kbg `btcg y fcntlkck kb ldnbs (DE)

3.3 Nd`bnfgcturc kb gds elkröxlkds c.

Bn bg slstb`c Vtdfa sb ndìrcn fdn bstc bstrufturc= Ndìrb jbnìrlfd + kb + `btcg + ný`brd kb vcgbnflc kbg `btcg elkröxlkd

kb

icrld


39?

LJBY ∙ [cfcnã

LL

Cutdfdntrdg Cftlvlkck 3. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd qub fdrrbspdnkc c gc rbspubstc kb fckc prbjuntc. 3)

´Fuãg bs bg lön fcrcftbràstlfd qub odr`c pcrtb kb gds elkröxlkds4

sugourd crsbnlctd elkrdxlgd

9)

Bn bg slstb`c Vtdfa, ´fö`d sb ggc`cn gds fd`pubstds qub sb ndìrcn sljulbnkd bstc bstrufturc= elkröxlkd kb + ndìrb kbg `btcg + ný`brd kb vcgbnflc kbg `btcg bn ný`brds rd`cnds4

elkröxlkds ãflkds scgbs

6)

´Fdn fuãgbs kb gds sljulbntbs bgb`bntds d fd`pubstds sb odr`c un elkröxlkd4

`btcg + cjuc öxlkd iãslfd + cjuc dxãflkd + cjuc

;)

´Fuãg bs gc oörùgc jbnbrcg kb gds elkröxlkds4

@Dn @ND @(DE)n

2)

´Fö`d sb ggc`c bg fd`pubstd quà`lfd qub bs fcpcz kb kcr ldnbs elkrdxlgd bn unc rbcfflön quà`lfc4

scg icsb ãflkd

Cftlvlkck 9 Lkbntlqub fckc bgb`bntd kb gc oörùgc kb gds sljulbntbs elkröxlkds. [lbnb un bmb`pgd. 8)

fcgfld

Fc(DE)9


vcgbnflc +9 kbg fcgfld y 9 ldnbs DE‖3


39:

3)

Ob(DE)6

9)

Nl(DE)9

6)

]r(DE);

;)

@j(DE)9

2)

Ej(DE)9

Cftlvlkck 6. Nd`bnfgcturc kb elkröxlkds Bsfrlic bg ndìrb kb gds sljulbntbs fd`pubstds bn bg slstb`c Vtdfa. 3)

NcDE Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

395

LJBY ∙ [cfcnã

9)

ADE Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

6)

Fc(DE)9 Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

;)

Ic(DE)9 Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

2)

Fu(DE) Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

?)

Ej(DE)9 Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd= Suà`lfc LL ∙ Vb`cnc 92

39<

Cftlvlkck ;. Nd`bnfgcturc kb elkröxlkds Fd`pgbtb gc tcigc bsfrlilbnkd gds kctds qub ecfbn ocgtc. ndìrb jbnìrlfd

oörùgc Xi(DE);

ndìrb kbg `btcg

vcgbnflc kbg `btcg bn ný`brds rd`cnds

pgd`d

Nl(DE)9

ndìrb kbg fd`pubstd elkröxlkd kb pgd`d (L_)

elkröxlkd

Xt(DE); YiDE

elkröxlkd kb ruilkld (L)

Fc(DE)9 elkröxlkd elkröxlkd

LL fdirb

@j(DE)9 ]r(DE);

LL flrfdnld

Cftlvlkck 2. Ndìrcr elkröxlkds Bsfrlic bg ndìrb kb gds elkröxlkds bn bg slstb`c Vtdfa. 3) Fu(DE) 9 9)

Ob(DE)9

6)

Ob(DE)6

;)

GlDE

2)

Cg(DE)6

?)

Vi(DE)6

:)

]n(DE)9

5)

@j(DE)9

<)

Nl(DE)9

38) Cu(DE)6

368

LJBY ∙ [cfcnã

LL

elkröxlkd kb bstrdnfld (LL)

Cftlvlkck ?. Bsfrlilr oörùgcs quà`lfcs kb elkröxlkds Vbjýn bg ndìrb kbg fd`pubstd qub sb gb kc bn bg slstb`c Vtdfa, bsfrlic gc oörùgc quà`lfc qub gb fdrrbspdnkb. 3)

Elkröxlkd kb ltrld (LLL)

9)

Elkröxlkd kb rdkld (LLL)

6)

Elkröxlkd kb tcntcgld (_)

;)

Elkröxlkd kb ds`ld (L_)

2)

Elkröxlkd kb vdgorc`ld (_L)

?)

Elkröxlkd kb jcgld (LLL)

Cftlvlkck :. Ybpcsd kb nd`bnfgcturc Fd`pgbtb gc tcigc bsfrlilbnkd gds kctds qub ecfbn ocgtcn. Gb kc`ds gc oörùgc, ustbk kbib bsfrlilr bg fd`pubstd odr`ckd, gc nd`bnfgcturc bn gc qub cprbnklö c ndìrcrgd y bg ndìrb kbg fd`pubstd. Gb kc`ds cgjunds bmb`pgds. oörùgc FD9

fd`pubstd odr`ckd

Vlstb`c kb nd`bnfgcturc

ndìrb kbg fd`pubstd

öxlkdãflkd

bstbquld`ìtrlfd

klöxlkdkbfcridnd

dxãflkd

trcklfldncg

ãflkdfcriönlfd

Vtdfa

elkröxlkdkb`cnjcnbsd(_LL)

EO A 9D E9FD6 Ob(DE)9 Vr(DE)9 Cj9D ND9 EL E9VD; @n(DE): elkröxlkd E9ND6 EjD Suà`lfc LL ∙ Vb`cnc 92

363


´Ãflkd d icsb4 Kbpbnkb kbg fdgdr

Bstc sb`cnc gb prdpdnb`ds ocirlfcr un gàqulkd lnklfckdr. Rn lnklfckdr bs unc sustcnflc qub tlbnb gc prdplbkck kb ckqulrlr un fdgdr klobrbntb sbjýn bntrb bn fdntcftd fdn un ãflkd d fdn unc icsb.

´Suì nbfbsltc4 Xcrc bg lnklfckdr 

un fucrtd kb rbpdggd `drckd



unc dggc pcrc fdfbrgd



bstuoc d oubjd pcrc fdflncr



un fufelggd



un fdgckdr



un vcsd d orcsfd kb vlkrld

Vustcnflcs ãflkcs  un gl`ön 

unc fufecrckc kb vlncjrb



unc ncrcnmc



trbs vcsds d orcsfds kb vlkrld

Vustcnflcs iãslfcs

369



unc fufecrckc kb ilfcridnctd kb sdkld



unc fufecrckc kb gàqulkd gl`plc vlkrlds



unc fufecrckc kb gàqulkd gl`plc plsds



trbs vcsds d orcsfds kb vlkrld

LJBY ∙ [cfcnã

´Suì kbib ecfbr4 3. Fdrtb bg rbpdggd bn rdkcmcs olncs. 9. Fdgdqub gcs rdkcmcs bn gc dggc, fýircgcs fdn cjuc y fuìzcgd. 6. Fucnkd b`plbfb c ebrvlr bg cjuc, rbtlrb gc dggc kbg oubjd y kbmb bnorlcr. ;. Ybfdmc bg cjuc kb gc fdfflön bn un vcsd, olgtrãnkdgc fdn un fdgckdr. \c tlbnb glstd bg gàqulkd lnklfckdr. Vustcnflcs ãflkcs 2. [d`b gds 6 orcsfds y vlbrtc unc sustcnflc ãflkc (gl`ön, vlncjrb y ncrcnmc) bn fckc und. ?. Cóckc unc fufecrckc kbg gàqulkd lnklfckdr bn fckc vcsd. Disbrvb gd qub dfurrb y cnötbgd bn bg fuckrd kb rbjlstrd. Vustcnflcs iãslfcs :. [d`b gds 6 orcsfds y vlbrtc unc sustcnflc iãslfc (ilfcridnctd, gl`plc vlkrlds y gl`plc plsds) bn fckc und. 5. Cóckc unc fufecrckc kbg gàqulkd lnklfckdr. Disbrvb gd qub dfurrb y cnötbgd bn bg fuckrd kb rbjlstrd.

Vustcnflc

Fuckrd kb rbjlstrd ´Gc sustcnflc bs Fdgdr lnlflcg ãflkc d iãslfc4

Fdgdr gubjd kb cjrbjcr bg lnklfckdr

vlncjrb gl`ön ncrcnmc ilfcridnctd kb sdkld gàqulkd gl`plc vlkrlds gàqulkd gl`plc plsds Bstb prdfbkl`lbntd sb rbcglzc bn gds gcidrctdrlds quà`lfds pcrc kbtbr`lncr gc ncturcgbzc ãflkc d iãslfc kb klstlntcs sustcnflcs. Vl gc sustcnflc bs ãflkc, gc sdguflön sb tdrnc rdmc cg cócklr bg gàqulkd lnklfckdr, y sl bs iãslfc, sb tdrnc vbrkb d czug.

Lnvbstljub bn gc rbk... ´Sulbrb scibr `ãs cfbrfc kb gds lnklfckdrbs ãflkd‖icsb4 gb lnvltc`ds c vlsltcr bstcs klrbffldnbs= ettp=//www.flbnflcocflg.fd`/pe.et`g ettp=//www.eburb`c.fd`/SJ:.et` Suà`lfc LL ∙ Vb`cnc 92

366



gdjrckd

rbjugcr

nd gdjrckd


Lkbntlolfd gds bgb`bntds bn gc oörùgc kb un elkröxlkd.

9.

Ndìrd elkröxlkds bn bg slstb`c Vtdfa.

6. Kbspuìs kb bstuklcr... ;.

Bsfrlid gc oörùgc kb klstlntds elkröxlkds gbybnkd su ndìrb bn bg slstb`c Vtdfa. Ybpcsd gc nd`bnfgcturc kb gds fd`pubstds vlstds= öxlkds, ãflkds b elkröxlkds.

2.

Ocirlfd un lnklfckdr ãflkd‖icsb fcsbrd.

?.

Lkbntlolfd fcsbrd. sustcnflcs ãflkcs y iãslfcs b`pgbcnkd un lnklfckdr


36;

LJBY ∙ [cfcnã

9?

Nd`bnfgcturc _ Vcgbs

Suà`lfc LL ∙ Vb`cnc 9?

362


Fdndfbr cgjunds usds kb gc scg kb `bsc c gd gcrjd kb gc elstdrlc kb gc eu`cnlkck.



Lkbntlolfcr gds bgb`bntds qub odr`cn gcs scgbs ecgdlkbcs.



Bsfrlilr oörùgcs quà`lfcs sl`pglolfckcs.



Ndìrcr scgbs ecgdlkbcs bn gds slstb`cs trcklfldncg y Vtdfa.



Lkbntlolfcr bg ný`brd kb vcgbnflc kb gds `btcgbs bn unc scg.



Bxpbrl`bntcr fdn gc sdguilglkck kb gc scg kb `bsc.




• Gc scg... un ilbn ùy prbflckd • Vl`pglolfcflön kb vcgbnflcs bn gc bsfrl-


turc kb oörùgcs quà`lfcs

• Nd`bnfgcturc kb gcs scgbs ecgdlkbcs


36?

LJBY ∙ [cfcnã

• Vcg, cjuc y cfbltb

¡Xcrc fd`bnzcr! Gc scg… un ilbn ùy prbflckd

Gc scg oub bg prl`br fdnkl`bntd utlglzckd bn gc elstdrlc kb gc eu`cnlkck. Kurcntb sljgds oub un ilbn ùy prbflckd. Ec odr`ckd pcrtb kb gc fugturc kb gcs cntljucs flvlglzcfldnbs qub gc uscicn fd`d bgb`bntd rltucg, rbjcgd, cùgbtd y fd`d fdnsbrvcntb. Xdr bmb`pgd= Gds jrlbjds dorbfàcn scg c sus vlsltcs fd`d sàìdgd kb c`lstck, edspltcglkck y orctbrnlkck. Gds rd`cnds fdgdfcicn scg bn gds gcilds kb gds nlóds gcftcntbs fd`d cùgbtd kb prdtbfflön. Ckb`ãs, gds sdgkckds rd`cnds fdircicn pcrtb kb su subgkd bn jrcnds kb scg. Kb ceà kbrlvc gc pcgcirc ‗scgcrld‐. Gds bjlpflds gc uscicn pcrc fdnsbrvcr cgl`bntds y brc und kb gds bgb`bntds qub b`pgbcicn pcrc gc `d`lolfcflön kb sus ùbrtds. Gds felnds fdnsbrvcrdn pbsfckds, rcàfbs y vbrkurcs bn scg kbskb gc cntlj÷bkck. Bg usd kb gc scg fd`d fdnkl`bntd bstã kdfu`bntckd kbskb gc ìpdfc kbg b`pbrckdr felnd Eucnjkl y sb rb`dntc c 9?:8 c.F.


36:

Edy kàc, gc scg sb ditlbnb kb odr`c ncturcg sbfcnkd bg cjuc kb `cr d rcspcnkd gcs rdfcs qub bstãn bn su drlggc. [cìlìn sb ocirlfc kb odr`c crtlolflcg bn gcidrctdrlds quà`lfds. Ceà sb gb cóckb ydkd (L) pcrc bvltcr bg idfld, bnobr`bkckbs rbgcfldnckcs fdn bg frbfl`lbntd y fdn bg kbscrrdggd ndr`cg kb gc lntbgljbnflc. Gc scg qub usc`ds bn gc `bsc bstã fd`pubstc prlnflpcg`bntb pdr sdkld (Nc +) y fgdrd (Fg‖) qub cg unlrsb odr`cn fgdrurd kb sdkld (NcFg). Gc scg kb `bsc bs sdgd und kb gds tlpds kb scg qub bxlstbn. Bstc sb`cnc cprbnkbrb`ds c rbfdndfbrgcs y c ndìrcrgcs.

¡C trcicmcr! 3.

´Suì sljnlolfcic pcrc gds jrlbjds dorbfbr scg c sus vlsltcs4

9.

´Kb quì ebfed kbrlvc gc pcgcirc —scgcrld‗4

6.

´Xcrc quì utlglzcn gc scg bn su fcsc y bn su fdùnlkck4

;.

´Suì pckbfl`lbntds bvltc gc scg ydkckc4

Rn fctlön d lön pdsltlvd bs un ãtd`d qub plbrkb d gb ocgtcn bgbftrdnbs. Rn cnlön d lön nbjctlvd bs un ãtd`d qub jcnc d gb sdircn bgbftrdnbs.

365

2.

´Fuãg kb gds fd`pdnbntbs kb gc scg kb `bsc bs un fctlön4

?.

´Fuãg kb gds fd`pdnbntbs kb gc scg kb `bsc bs un cnlön4

LJBY ∙ [cfcnã


3. Gcs scgbs ãflkd + icsb Fucnkd bsfufec`ds gc pcgcirc scg, pbnsc`ds bn gc scg kb `bsc (NcFg), pbrd ecy un jrcn ný`brd kb fd`pubstds qub sb cjrupcn fd`d scgbs. Fd`d cprbnkl`ds bn gc sb`cnc 98, unc scg bs bg rbsugtckd kb gc rbcfflön quà`lfc bntrb un ãflkd y unc icsb . Vbjýn bg ãflkd qub lntbrvlbnb bn gc rbcfflön, gcs scgbs sb fgcslfcn bn scgbs ecgdlkbcs y dxlscgbs. Ndsdtrds bstuklcrb`ds sdgd gcs scgbs ecgdlkbcs. • Vcgbs ecgdlkbcs= fd`pubstds ilncrlds qub sb odr`cn kb gc unlön kb un elkrãflkd fdn unc icsb. Bstãn fd`pubstcs pdr un `btcg y un nd `btcg.

elkrãflkd +

0 scgecgdlkbc

icsb

Gcs scgbs ecgdlkbcs tlbnbn gc oörùgc jbnbrcg=

@xN y

`btcg

vcgbnflc kbg cnlön nd `btcg

nd `btcg vcgbnflc kbg fctlön `btcg

Bmb`pgds= `cjnbsld

@jFg9


fgdrd

pgctc

vcgbnflc +9 kbg `cjnbsld

CjFg


fgdrd vcgbnflc +3 kb gc pgctc

Bmbrflfld 3 Lkbntlqub fckc bgb`bntd kb gc oörùgc kb gc sljulbntb scg ecgdlkbc. [lbnb un bmb`pgd. 8)

fdirb vcgbnflc ∙3

kbg fgdrd

3)

FuFg

fgdrd vcgbnflc +3 kbg fdirb

j

@ O9


36<

¡Cntbs kb ndìrcr c gcs scgbs ecgdlkbcs! Bn gc sb`cnc 93 cprbnkl`ds qub, ndr`cg`bntb, gc vcgbnflc kb un bgb`bntd pubkb vbrsb bn bg suiànklfb kbg dtrd ãtd`d (bn fd`pubstds ilncrlds y tbrncrlds). Xdr bmb`pgd= bn bg irdùrd kb icrld (IcIr9), gc vcgbnflc kbg icrld (Ic+9) gc vb`ds fd`d suiànklfb kbg ird`d. Gc vcgbnflc kbg ird`d (Ir‖3) cfd`pcóc cg icrld.

Ic+9

C vbfbs, fd`d sb bn ec bg sl`pglolfckd. nltrurd kb pgd`d (L_) XiN, gc oörùgc Bg pgd`d tlbnb vcgbnflc +; y bg nltröjbnd ‖;, pbrd cg bsfrlilrgc sb sl`pglolfc. Xcrc ecfbrgd klvlkl`ds cìcs vcgbnflcs bntrb ;.

Xi+;

Ir

∙3

Ic Ir9 ∙;

N

‖; ú ; 0 ‖3

+; ú ; 0 3

XiN

Cg disbrvcr gc oörùgc, ´fö`d scib`ds qub sb ec sl`pglolfckd4 ‛Gd scib`ds pdrqub bg ndìrb kbg fd`pubstd bs nltrurd kb pgd`d (L_), nds bstã lnklfcnkd qub bg pgd`d cftýc fdn vcgbnflc +;. Vl rbvlsc`ds gc tcigc kb vcgbnflcs, vb`ds qub bg pgd`d pubkb cftucr fdn kds vcgbnflcs= +; y +9.

59

;,9

Xi

Xgd`d 98:.9

´Fö`d sb bsfrlib gc oörùgc kbg nltrurd kb pgd`d (LL)4 _bc`ds= Gc oörùgc Xi9N tcìlìn bstã sl`pglolfckc, pbrd bn bstb fcsd gd eb`ds ebfed klvlklbnkd cìcs vcgbnflcs bntrb 9.

Xi+9 ‖; ú 9 0 ‖9

N

∙;

+9 ú 9 0 3

Xi9N

Bmbrflfld 9 Bsfrlic gcs oörùgcs qub sb gb lnklfcn. Vl`pgloàqubgcs fucnkd sbc pdsligb. [lbnb un bmb`pgd. ndìrb kb gc scg ecgdlkbc

sugourd kb fdirb (LL)

vcgbnflcs kb gds bgb`bntds

Fu+9 V‖9 +6

‖3

irdùrd kb cgu`lnld (LLL) Cg Ir sugourd kb fdicgtd (LL) Fd+9 V‖9 crsbnlurd kb elbrrd (LLL)

3;8

LJBY ∙ [cfcnã

Ob+6 Cs‖6

oörùgc

Fu9V9 0 FuV

3.3 Nd`bnfgcturc kb gcs scgbs ecgdlkbcs Gcs scgbs sb pubkbn ndìrcr bn gds trbs slstb`cs kb nd`bnfgcturc= bstbquld`ìtrlfd, Vtdfa y trcklfldncg. Ndsdtrds vc`ds c bstuklcr gc nd`bnfgcturc bn gds slstb`cs trcklfldncg y Vtdfa. Gcs scgbs ecgdlkbcs sb pubkbn fgcslfcr bn kds tlpds= • Vcgbs ecgdlkbcs qub tlbnbn `btcgbs fdn vcgbnflc olmc. • Vcgbs ecgdlkbcs qub tlbnbn `btcgbs fdn vcgbnflc vcrlcigb.

c.

Nd`bnfgcturc bn bg slstb`c trcklfldncg kb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs fdn vcgbnflc olmc

Gds `btcgbs qub bxlstbn fd`d fctldnbs fdn ný`brd kb vcgbnflc mc sdn= 3

9

E

3

Gl

3

Nc

3

33

39

36

Elkröjbnd

Gltld Vdkld

A Xdtcsld

9

@j

9

Fc

9

Cg

@cjnbsld

3

Yi

3

Fs

3

Or

3

Yuilkld

Fcgfld

]n 9

6

Cgu`lnld

¡@b`dràfbgds!

Flnf

Vr

9

Ic

9

Yc

9

Bstrdnfld

Fbsld Orcnfld

Ib

Ibrlgld

Cj Xgctc

3

Fk 9

Fck`ld

Icrld

Yckld

Bg ndìrb kb gcs scgbs ecgdlkbcs qub tlbnbn `btcgbs fdn vcgbnflc mc sb nd` ircn sbjýn bstc bstrufturc= Ndìrb kbg nd `btcg + sumd ‖urd + kb + ndìrb kbg `btcg Bmb`pgds= Ndìrb`ds bg AFg bn bg slstb`c trcklfldncg= 3. Bsfrlil`ds bg ndìrb kbg nd `btcg, qultcnkd gc ýgtl`c vdfcg y cjrbjcnkd bg suolmd ∙urd. Nd `btcg= fgdrd fgdrurd Vuolmd= ∙urd 9. Bsfrlil`ds bg ndìrb kbg `btcg= pdtcsld 6. Vbjýn gc bstrufturc bg ndìrb qubkc csà= Ndìrb kbg nd `btcg + sumd ‖urd + kb + ndìrb kbg `btcg fgdrd

‖urd

kb

pdtcsld

fgdrurd kb pdtcsld (AFg) Suà`lfc LL ∙ Vb`cnc 9?

3;3

Ndìrb`ds bg Nc9V bn bg slstb`c trcklfldncg= 3. Bsfrlil`ds bg ndìrb kbg nd `btcg y cjrbjc`ds bg suolmd ∙urd. Ybfubrkb qub bg slstb`c trcklfldncg utlglzc bg ndìrb sugourd pcrc bg czuorb.

Nd `btcg= sugourd Vuolmd= ∙urd

sugourd

9. Bsfrlil`ds bg ndìrb kbg `btcg= sdkld 6. Vbjýn gc bstrufturc bg ndìrb qubkc csà= Ndìrb kbg nd `btcg + sumd‖urd + kb + ndìrb kbg `btcg sugourd

‖urd

kb

sdkld

sugourd kb sdkld (Nc 9V)

i. Nd`bnfgcturc bn bg slstb`c Vtdfa kb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs fdn vcgbnflc vcrlcigb Xcrc ndìrcr scgbs ecgdlkbcs qub bstãn odr`ckcs pdr un `btcg fdn vcgbnflc vcrlcigb, sb pubkb utlglzcr fucgqulbrc kb gds trbs slstb`cs kb nd`bnfgcturc fdndflkds. Ndsdtrds b`pgbcrb`ds bg slstb`c Vtdfa. Vb ndìrcn fdn bstc bstrufturc= ndìrb kbg + sumd‖urd + kb + ndìrb kbg `btcg + vcgbnflc kbg `btcg bn ný`brd rd`cnds nd `btcg Bmb`pgds= Ndìrb`ds cg IFg6= 3. Bsfrlil`ds bg ndìrb kbg nd `btcg y cjrbjc`ds bg suolmd ∙urd. Nd `btcg= fgdrd Vuolmd= ∙urd

fgdrurd

9. Bsfrlil`ds bg ndìrb kbg `btcg= idrd y fd`d nds lnklfc gc oörùgc scib`ds qub tlbnb ný`brd kb vcgbnflc +6. 6. Vbjýn gc bstrufturc bg ndìrb qubkc csà= ndìrb kbg + sumd ‖urd + kb + ndìrb kbg `btcg + vcgbnflc kbg `btcg bn nd `btcg fgdrd

ný`brd rd`cnds ‖urd

kb

idrd

fgdrurd kb idrd (LLL) IFg6

3;9

LJBY ∙ [cfcnã

LLL

Ndìrb`ds cg FuO9= 3. Bsfrlil`ds bg ndìrb kbg nd `btcg y cjrbjc`ds bg suolmd ∙urd. Nd `btcg= ogýdr Vuolmd= ∙urd

ogudrurd

9. Bsfrlil`ds bg ndìrb kbg `btcg= fdirb y fd`d nds lnklfc gc oörùgc scib`ds qub cftýc fdn vcgbnflc +9. 6. Vbjýn gc bstrufturc bg ndìrb qubkc csà= ndìrb kbg + sumd ‖urd + kb + ndìrb kbg `btcg + vcgbnflc `btcg bn ný`brdkbg rd`cnds nd `btcg ýdr

‖urd

kb

fdirb

LL

ogudrurd kb fdirb (LL) FuO9

Bmbrflfld 6 Bsfrlic bg ndìrb kb gcs sljulbntbs scgbs ecgdlkbcs qub tlbnbn `btcgbs fdn vcgbnflc mc. Rtlglfb bg slstb`c trcklfldncg. [lbnb un bmb`pgd. 8)

IcIr9

3)

CgFg6

9)

GlIr

6)

FcE9

;)

FkL9

irdùrd kb icrld

Bmbrflfld ; Fd`pgbtb gc tcigc kb gc bstrufturc kbg ndìrb kb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs fdn vcgbnflc vcrlcigb. Rtlglfb bg slstb`c Vtdfa. [lbnb un bmb`pgd. oörùgc

ndìrb kbg ndìrb kbg vcgbnflc kbg `btcg bn nd `btcg + `btcg ný`brd rd`cnds sumd ‖urd

CuX6

odsourd

Vn6X9 Vn6X;

odsourd

drd

(LLL)

ndìrb kb gc scg ecgdlkbc odr`ckc pdr `btcgbs fdn vcgbnflc vcrlcigb

odsourd kb drd (LLL)

bstcód

EjO9


3;6

Ybsu`bn Bstc sb`cnc cprbnklö qub= 3.

Gcs scgbs sdn bg rbsugtckd kb gc rbcfflön quà`lfc bntrb un ãflkd y unc icsb. • Vcgbs ecgdlkbcs rbsugtcn kb gc fdìlncflön kb un elkrãflkd fdn unc icsb. [lbnbn gc oörùgc jbnbrcg=

@xNy

`btcg



3.3 Nd`bnfgcturc kb gcs scgbs ecgdlkbcs c. Nd`bnfgcturc bn bg slstb`c trcklfldncg kb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs fdn vcgbnflc olmc Gds `btcgbs qub tlbnbn vcgbnflc olmc sdn= 3

9

E

3

Gl

3

33

39

36

Elkröjbnd

Gltld

Nc Vdkld

A Xdtcsld

Yi

Ib @j

9

Fc

9

3 3

Fcgfld

Vr

3 3

6

]n 9 Flnf

9

Bstrdnfld

Fbsld Orcnfld

Cg

Cgu`lnld

@cjnbsld

Yuilkld

Fs Or

9

Ibrlgld

3

Cj Xgctc

3

Fk 9

Fck`ld

9 Icrld Ic Yc

9

Yckld

Vb ndìrcn fdn bstc bstrufturc= Ndìrb kbg nd `btcg + sumd ‖urd + kb + ndìrb kbg `btcg fgdrd

‖urd

kb

pdtcsld

fgdrurd kb pdtcsld (AFg)

i. Nd`bnfgcturc bn bg slstb`c Vtdfa kb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs fdn vcgbnflc vcrlcigb Vb ndìrcn fdn bstc bstrufturc= ndìrb kbg + sumd ‖urd + kb + ndìrb kbg `btcg + vcgbnflc kbg `btcg bn nd `btcg ný`brd rd`cnds fgdrd

‖urd

kb

idrd

IFg6 fgdrurd kb idrd (LLL)

3;;

LJBY ∙ [cfcnã

LLL

Cutdfdntrdg Cftlvlkck 3. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd kbg fdnfbptd qub sb rbgcfldnc fdn gc kbnlflön kb gc lzqulbrkc. 3)

Fd`pubstd odr`ckd pdr gc rbcfflön quà`lfc bntrb unc icsb y un ãflkd.

icsb scg ãflkd

9)

Vcg qub sb ditlbnb kb gc fdìlncflön kb un elkrãflkd fdn un `btcg d kb un elkrãflkd fdn unc icsb.

scg klsubgtc scg ecgdlkbc dxlscg

6)

Vcg odr`ckc pdr un `btcg y un nd `btcg qub tlbnb gc oörùgc jbnbrcg @xNy.

scg klsubgtc scg ecgdlkbc dxlscg

;)

_cgbnflc kb gds `btcgbs kbg jrupd L.

+3 +9 +6

2)

_cgbnflc kb gds `btcgbs kbg jrupd LL

+3 +9 +6

Cftlvlkck 9 Bsfrlic gcs oörùgcs kb scgbs ecgdlkbcs qub sb gb lnklfcn. Vl`pglqub fucnkd sbc pdsligb. [lbnb un bmb`pgd. ndìrb kb gc scg ecgdlkbc


irdùrd kb fcgfld (LL)

Fc

sugourd kb pgd`d (LL) sugourd kb `brfurld (L)

Xi+9 V‖9 Ej+3 V‖9

fgdrurd kb pgctlnd (L_)

Xt+; Fg‖3

+9

Ir

‖3

oörùgc

FcIr9


3;2

Cftlvlkck 6. Ndìrb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs fdn vcgbnflc mc Bsfrlic bg ndìrb kb gcs sljulbntbs scgbs ecgdlkbcs utlglzcnkd bg slstb`c trcklfldncg. 3)

CjL 9)

FcIr9

6)

Gl6X

;)

]nVb

2)

NcIr

?)

A 9V

:)

CgO6

5)

Nc;F

<)

@j6X9

38)

GlO

Cftlvlkck ;.Ndìrb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs fdn vcgbnflc vcrlcigb Fd`pgbtb gc tcigc fdn gcs pcrtbs kb gds ndìrbs qub ecfbn ocgtc y cg ncg bsfrlic bg ndìrb kb gc scg ecgdlkbc. [lbnb un bmb`pgd. oörùgc

Fr6X9 Ejg9 Vn6X; ObFg9 Ilg6

ndìrb kbg nd `btcg + sumd ‖urd

odsourd

ndìrb kbg vcgbnflc kbg `btcg bn `btcg ný`brd rd`cnds

frd`d

(LL)

ndìrb kbg fd`pubstd

odsourd kb frd`d LL

Cftlvlkck 2. Bsfrlic oörùgcs `dgbfugcrbs. Bsfrlic gc oörùgc `dgbfugcr kb gds fd`pubstds qub sb ndìrcn c fdntlnucflön. [lbnb un bmb`pgd. ndìrb kb gc scg ecgdlkbc

fgdrurdkbsdkld udrurd kb gltld odsourd kb flrfdnld (L_) irdùrd kb elbrrd (LL) fgdrurd kb pdtcsld

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LJBY ∙ [cfcnã


Nc

+3 +3

Gl ]r+; Ob+9 A+3

Fg

‖3

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NcFg


Vcg, cjuc y cfbltb Gcs scgbs sdn fd`pubstds lönlfds qub sb klsubgvbn bn bg cjuc. Fucnkd unc scg sb klsubgvb bn cjuc sb sbpcrcn gds ldnbs qub gc odr`cn tb`pdrcg`bntb. Bstc sb`cnc ustbk bxpbrl`bntcrã fdn gc fcpcflkck kb gc scg fd`ýn pcrc klsdgvbrsb bn bg cjuc.


3 vcsd kb vlkrld trcnspcrbntb

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6 f` kb cjuc

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6 f` kb cfbltb kb fdflnc

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fdgdrcntb vbjbtcg

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scg

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glirbtc kb fc`pd

´Suì kbib ecfbr4 3. Bfeb cjuc bn un vcsd ecstc unc cgturc kb 6 fbntà`btrds cprdxl`ckc`bntb. 9. Gubjd cjrbjub gc `ls`c fcntlkck kb cfbltb. Cndtb sus disbrvcfldnbs. 6. Cjrbjub bg fdgdrcntb vbjbtcg y cndtb quì sufbkb. ;. Kbmb fcbr fulkckdsc`bntb un pdfd kb scg sdirb tdkc gc supbrolflb y cndtb sus disbrvcfldnbs. Xcrc rbcglzcr sus disbrvcfldnbs, cyýkbsb fdn bstcs prbjuntcs. • ´Bg cjuc y bg cfbltb sb `bzfgcn d odr`cn kds ocsbs klstlntcs4 • Vl su rbspubstc cntbrldr bs= odr`cn kds ocsbs klstlntcs, ´quì gàqulkd bstã bn bg odnkd kbg vcsd y quì gàqulkd bstã bn gc supbrolflb4 • ´Bg fdgdrcntb tlób bg cjuc d bg cfbltb4 • Cg cjrbjcr gc scg, ´quì sufbkb4 ´Gc scg sb klsubgvb bn bg cfbltb d bn bg cjuc4 • ´Disbrvö cgjýn obnö`bnd bn gds gàqulkds fd`d odr`cflön kb iuriumcs, fcìld kb cspbftd d kb fdgdr4 Bxpgàqubgd.


3;:



gdjrckd

rbjugcr

nd gdjrckd

Cspbftds c bvcgucr 3. 9. 6. Kbspuìs kb bstuklcr... ;. 2. ?.

Fdndzfd cgjunds usds kb gc scg kb `bsc c gd gcrjd kb gc elstdrlc kb gc eu`cnlkck. Lkbntlolfd gds bgb`bntds qub odr`cn gcs scgbs ecgdlkbcs. Bsfrlid oörùgcs quà`lfcs sl`pglolfckcs. Ndìrd gcs scgbs ecgdlkbcs bn gds slstb`cs trcklfldncg y Vtdfa. Lkbntlolfd bg ný`brd kb vcgbnflc kb gds `btcgbs bn unc scg. Bxpbrl`bntd fdn gc sdguilglkck kb gc scg kb `bsc.


3;5

LJBY ∙ [cfcnã

9:

Bg @dg

Suà`lfc LL ∙ Vb`cnc 9:

3;<


Kbolnlr `dg, `csc `dgcr y vdgu`bn `dgcr.

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Lkbntlolfcr gc `csc `dgcr y gc fcntlkck kb pcrtàfugcs kb klstlntds bgb`bntds.

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Fcgfugcr gc `csc `dgcr kb klstlntds fd`pubstds.

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Lkbntlolfcr gc `csc `dgcr y bg vdgu`bn `dgcr kb cgjunds jcsbs c tb`pbrcturc y prbslön ndr`cgbs ([XN).

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Ybsdgvbr fdnvbrsldnbs kb `dg y `csc y vlfbvbrsc. Ybsdgvbr fdnvbrsldnbs kb `dg y fcntlkck kb pcrtàfugcs.

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[bnbr unc lkbc `ãs fdnfrbtc kbg tc`cód kbg ný`brd kb Cvdjckrd c trcvìs kb un bxpbrl`bntd.

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• C`ckbd Cvdjckrd


• • • •


328

LJBY ∙ [cfcnã

@dg @csc `dgcr _dgu`bn `dgcr Ocftdrbs `dgcrbs

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¡Xcrc fd`bnzcr! C`ckbd Cvdjckrd C`ckbd Cvdjckrd ncfl ö bg < kb cjdstd kb 3::? y ùrlö bg < kb mugld kb 352? bn [uràn, Ltcglc. Cunqub brc cidjckd, sus jrcnkbs pcsldnbs oubrdn gc `ctb`ãtlfc, gc oàslfc y gc quà`lfc. Vb kbklfö c bstuklcr gcs flbnflcs bxcftcs y oub prdobsdr kb Oàslfc bn gc unlvbrslkck kb [uràn. Ybcglzö lnvbstljcfldnbs sdirb bgbftrlflkck y gcs prdplbkckbs oàslfcs kb gds gàqulkds, cunqub oub `ãs fdndflkd pdr su trcicmd cfbrfc kb gds jcsbs. Cvdjckrd sb cpdyö bn gc tbdràc ctö`lfc kb Mden Kcgtdn y gc Gby kb Jcy‖Gusscf sdirb bg `dvl`lbntd kb gcs `dgìfugcs y kbsfuirlö qub=

C`ckbd Cvdjckrd (3::? - 352?) Flbntàfd ltcglcnd

‗Kds vdgý`bnbs ljucgbs kb jcsbs klobrbntbs, bn gcs `ls`cs fdnklfldnbs kb prbslön y tb`pbrcturc, fdntlbnbn bg `ls`d ný`brd kb `dgìfugcs‐. Bstb kbsfuirl`lbntd sb trcnsodr`ö bn gc ‗Gby kb Cvdjckrd‐. Bstc Gby pbr`ltlö qub sb cvcnzcrc bn bg bstukld y kbscrrdggd kb gc tbdràc ctö`lfc. Bn su edndr, bg ný`brd kb `dgìfugcs, ãtd`ds d ldnbs fdntbnlkds bn un `dg sb fdndfb fd`d ný`brd kb Cvdjckrd.

Bg ný`brd kb Cvdjckrd bs ?.899 x 38

96

unlkckbs .

Bstc sb`cnc cprbnkbrb`ds quì bs `dg y cgjuncs kb sus cpglfcfldnbs.

¡C trcicmcr! 3)

´Suì klfb gc Gby kb Cvdjckrd4 Föplbgc.

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´Fuãg bs bg vcgdr kbg ný`brd kb cvdjckrd4


323


3. @dg= gc `csc kb gcs pcrtàfugcs Gc `csc kb gds ãtd`ds bs ùy pbqubóc, lnvlsligb c nubstrds dmds. Bs l`pdsligb pbscr gds ãtd`ds kb odr`c lnklvlkucg, pdr bsd bs nbfbscrlc unc `bklkc bstãnkcr. Bg `dg bs gc unlkck kbg Vlstb`c Lntbrncfldncg fdn gc qub sb `lkb gc fcntlkck kb sustcnflc. Vb kbnb csà= 96

@dg bs gc. fcntlkck kb `ctbrlc qub fdntlbnbn x 38`dgìfugcs pcrtàfugcs bgb`bntcgbs Gcs pcrtàfugcs bgb`bntcgbs pubkbn sbr?.899 ãtd`ds, d ldnbs. Fd`d vl`ds bn gc sbfflön ¡Xcrc fd`bnzcr! gc fcntlkck ?.899 x 3896 sb ggc`c ný`brd kb Cvdjckrd. _bc`ds cgjunds bmb`pgds kb fö`d sb b`pgbc= 3 `dg kb Eb 0 ?.899 x 3896 ãtd`ds kb Eb 3 `dg kb E

9

3 `dg kb E

9

3 `dg kb Fg

‖

0 ?.899 x 3896 `dgìfugcs kb E9

D 0 ?.899 x 3896 `dgìfugcs kb E9D 0 ?.899 x 3896 ldnbs kb Fg‖

3.3 @csc `dgcr [dkds gds ãtd`ds y `dgìfugcs tlbnbn unc `csc fcrcftbràstlfc y kbnlkc. Ndsdtrds fdndfl`dsgcbg `csc ný`brd `csc ctö`lfc (C)bn kbgcfckc bgb`bntd bn gc sb`cnc < y fcgfugc`ds kb kb klstlntcs `dgìfugcs sb`cnc 3<. _bc`ds= Rn `dg kb fucgqulbr bgb`bntd tlbnb unc `csc `dgcr qub bs ljucg c su `csc ctö`lfc y tdkcs tlbnbn bg `ls`d ný`brd kb ãtd`ds ?.899 x 38 96. Vl fdnsugtc`ds gc tcigc pbrlöklfc, pdkb`ds disbrvcr qub= 3<

C

329

Fg

62.2 j

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C

Gc `csc kb 3 `dg kb sdkld (Nc) bs 96.8 jrc`ds. ?.899 x 3896 ãtd`ds kb sdkld tlbnbn unc `csc kb 96.8 j.

96.8 j

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LJBY ∙ [cfcnã

3 `dg kb fgdrd (Fg) tlbnb unc `csc kb 62.2 jrc`ds. Bstd bs ljucg c kbflr qub ?.899 x 3896 ãtd`ds kb fgdrd tlbnbn unc `csc kb 62.2 jrc`ds.

3 `dg kb flrfdnld (]r)tlbnb unc `csc kb<3.9 jrc`ds, pdr gd tcntd ?.899 x 3896 ãtd`ds kb flrfdnld tlbnbn unc `csc kb <3.9 jrc`ds.

Rn `dg kb fucgqulbr `dgìfugc bs ljucg c gc su`c kb gcs `cscs ctö`lfcs kb gds bgb`bntds qub odr`cn bg fd`pubstd bn gcs prdpdrfldnbs qub lnklfc su oörùgc. Bmb`pgd 3 ´Fuãg bs gc `csc `dgcr kbg klöxlkd kb fcridnd (FD 9)4

Fdn cpdyd kb gc tcigc pbrlöklfc, pdkb`ds fcgfugcr gc su`c kb gcs `cscs `dgcrbs. 3 ãtd`d kb fcridnd x 39.8 j/`dg 0

39.8 j/`dg

9 ãtd`ds kb dxàjbnd x 3?.8 j/`dg 0 + 69.8 j/`dg @csc `dgcr kbg FD 9= ;;.8 j/`dg

Rn `dg kb FD9 tlbnb unc `csc kb ;;.8 jrc`ds. Bstc fcntlkck bs gc `csc `dgcr kbg klöxlkd kb fcridnd y ?.899 x 38 96 `dgìfugcs kb FD9 tlbnbn unc `csc kb ;;.8 jrc`ds. Bmb`pgd 9 ´Fuãg bs gc `csc `dgcr kbg ãflkd irö`lfd (EIrD 6). 3 ãtd`d kb elkröjbnd x 3.8 j/`dg 0 3.8 j/`dg 3 ãtd`d kb ird`d x :<.< j/`dg 0 :<.< j/`dg 6 ãtd`ds kb dxàjbnd x 3?.8 j/`dg 0 + ;5.8 j/`dg @csc `dgcr kbg EIrD 6= 395.< j/`dg

Bmbrflfld 3 C.

Fdnsugtb gc tcigc pbrlöklfc y fd`pgbtb bg fuckrd fdn gcs `cscs `dgcrbs qub ecy bn un `dg kb gds bgb`bntds kckds. [lbnb un bmb`pgd. bgb`bntd

@cjnbsld (@j)

`csc `dgcr (`csc ctö`lfc C)

9;.6 j

fcntlkck kb pcrtàfugcs

bgb`bntd

?.899 x 3896

Vlglfld (Vl)

Nltröjbnd(N) I.

`csc `dgcr (`csc ctö`lfc C)


Rrcnld(R)

Fcgfugb gc `csc `dgcr kbg c`dnlcfd (NE 6). 3 ãtd`d kb N x 3;.8 j/`dg 0

j/`dg

6 ãtd`ds kb E x 3.8 j/`dg 0 +

j/`dg

@csc `dgcr kbg NE6=

j/`dg


326

9. Ocftdrbs `dgcrbs Ocftdrbs kb fdnvbrslön

Rn ocftdr kb fdnvbrslön sb ditlbnb kb unc bqulvcgbnflc y nds pbr`ltb trcnsodr`cr unc unlkck kb `bklkc bn dtrc . _bc`ds un bmb`pgd= ´Fuãntds algö`btrds fdrrbspdnkbn c 2588 `btrds4

3. Xgcntbc`ds gc bqulvcgbnflc= 3 algö`btrd 3888 `btrds. Bstc bqulvcgbnflc gc pdkb`ds bxprbscr fd`d un ocftdr kb fdnvbrslön csà= 3 algö`btrd d 3888 `btrds 3888 `btrds 3 algö`btrd

9. Bgbjl`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc bgl`lncr `btrds y bxprbscr gc rbspubstc bn algö`btrds.

3 algö`btrd 3888 `btrds

6. Cpglfc`ds bg ocftdr kb fdnvbrslön= 3 algö`btrd 2588 `btrds x 0 2.5 algö`btrds 3888 `btrds ;. Bsfrlil`ds gc rbspubstc= 2588 `btrds fdrrbspdnkbn c 2.5 algö`btrds Bg ocftdr `dgcr bs un ocftdr kb fdnvbrslön qub pbr`ltb trcnsodr`cr `dgbs, ný`brd kb pcrtàfugcs, `csc y vdgu`bn. _bc`ds.

9.3 Fdnvbrsldnbs kb `dg y `csc Xcrc rbcglzcr fdnvbrsldnbs bntrb `dg y `csc y vlfbvbrsc, nbfbsltc`ds fdndfbr gc `csc `dgcr.

9<

C

_bc`ds un bmb`pgd= ´Fuãntds `dgbs kb fdirb ecirã bn un cgcìrb qub tlbnb 392 jrc`ds kb `csc4

Fu

?6.2 j

3. Xgcntbc`ds gc bqulvcgbnflc. Vcib`ds qub 3 `dg kb fucgqulbr bgb`bntd tlbnb unc `csc qub bs ljucg c su `csc ctö`lfc (C). Xdr gd tcntd= 3 `dg kb Fu

Bxprbsb gds rbsugtckds fdn kds florcs Ybvlsbkbfl`cgbs. gc sb`cnc 6 kb Bstckàstlfc pcrc rbfdrkcr gcs rbjgcs kb cprdxl`cflön.

32;

LJBY ∙ [cfcnã

?6.2 j kb Fu

9. Bgbjl`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc bgl`lncr jrc`ds. 3 `dg kb Fu d ?6.2 j kb Fu 3 `dg kb Fu ?6.2 j kb Fu 6. Cpglfc`ds bg ocftdr kb fdnvbrslön= 392 j kb Fu x 3 `dg kb Fu 0 3.<: `dgbs kb Fu ?6.2 j kb Fu ;. Bsfrlil`ds gc rbspubstc= 392 j kb Fu bqulvcgbn c 3.<: `dgbs kb bsb `btcg .

¡Dtrd bmb`pgd! Gc oörùgc kbg jcs prdpcnd bs F6E5. Vl un flglnkrd fdntlbnb 32.2 `dgbs kb bsb jcs, ´fuãntds jrc`ds kb jcs tlbnb4

3. Fcgfugc`ds gc `csc `dgcr kbg jcs prdpcnd (F6E5)= 6 ãtd`ds kb F x 39.8 j/`dg 0 6?.8 j/`dg 5 ãtd`ds kb E x 3.8 j/`dg 0 + 5.8 j/`dg @csc `dgcr kbg F6E5= ;;.8 j/`dg

Xgcntbc`ds gc bqulvcgbnflc= 3 `dg kb F6E5 ;;.8 j/`dg 9. Bsfdjb`ds bg ocftdr kb fdnvbrslön= ;;.8 kb FF 6EE5 d 3 `dg kb F 6E5 3 `dgj kb ;;.8 j kb F 6E5 6 5 6. Cpglfc`ds bg ocftdr kb fdnvbrslön= 32.2 `dgbs kb F6E5 x

;;.8 j kb F 6E5 0 ?59 jrc`ds kb F 6E5 3 `dg kb F 6E5

;. Bsfrlil`ds gc rbspubstc= Rn flglnkrd qub fdntlbnb 32.2 `dgbs kb F 6E5 tlbnb unc `csc kb ?59 jrc`ds kb F 6E5.

Bmbrflfld 9 Ybsubgvc gc sljulbntb fdnvbrslön kb `dg y `csc. [lbnb un bmb`pgd. Bxprbsb su rbsugtckd fdn 9 florcs kbfl`cgbs. 8)

´Fuãntds jrc`ds kb elbrrd (Ob) ecy bn 6.39 `dgbs kb bsb bgb`bntd4 3. Iusfc`ds gc `csc ctö`lfc kbg Ob bn gc tcigc pbrlöklfc, pgcntbc`ds gc bqulvcgbnflc y bsfdjb`ds bg ocftdr kb fdnvbrslön= 3 `dg kb Ob d 22.5 j kb Ob 3 `dg kb Ob 22.5 j kb Ob 22.5 j kb Ob 3 `dg kb Ob 22.5 j kb Ob 9. Cpglfc`ds bg ocftdr kb fdnvbrslön= 6.39 `dgbs kb Ob x 0 3:;.3 j kb Ob 3 `dg kb Ob 6. Bsfrlil`ds gc rbspubstc= Bn 6.39 `dgbs kb elbrrd ecy 3:;.3 jrc`ds kb elbrrd.

3)

´Fuãntds `dgbs kb fcgfld (Fc) bqulvcgbn c 388 j kb bsb bgb`bntd4 3. Iusfc`ds gc `csc ctö`lfc kbg Fc bn gc tcigc pbrlöklfc, pgcntbc`ds gc bqulvcgbnflc y bsfdjb`ds bg ocftdr kb fdnvbrslön= 3 `dg kb Fc

j kb Fc

9. Cpglfc`ds bg ocftdr kb fdnvbrslön= 6. Bsfrlil`ds gc rbspubstc=


322

9.9 Fdnvbrsldnbs kb `dg y fcntlkck kb pcrtàfugcs Xcrc rbcglzcr fdnvbrsldnbs bntrb fcntlkck pcrtàfugcs y `dgbs y vlfbvbrsc, cpglfc`ds bg ný`brd kb Cvdjckrd= ?.899 x 3896 d 3 `dg 3 `dg ?.899 x 38 96

Xdr bmb`pgd=

Bg dzdnd bs un jcs kb gc ct`ösobrc qub nds prdtbjb kb gc rcklcflön sdgcr. Gc `dgìfugc kb dzdnd bstã odr`ckc pdr trbs ãtd`ds kb dxàjbnd (D 6). Fcgfugb fuãntcs `dgìfugcs kb dzdnd ecy bn 2.28 `dgbs kb dzdnd. Bxprbsc`ds gds rbsugtckds fdn kds florcs kbfl`cgbs.

3. Vcib`ds qub bn ?.899 x 3896 `dgìfugcs kb fucgqulbr sustcnflc ecy 3 `dg kb bsc sustcnflc. Xgcntbc`ds gc bqulvcgbnflc. 3 `dg D6 ?.899 x 38 96 `dgìfugcs kb D6 9. Bsfdjb`ds bg ocftdr kb fdnvbrslön= ?.899 x 38 96 `dgìfugcs kb D6 d 3 `dg 3 `dg ?.899 x 38 96 `dgìfugcs kb D6 6. Cpglfc`ds bg ocftdr kb fdnvbrslön= 2.28 `dgbs kb D6 x

?.899 x 3896 `dgìf. kb D 6 0 6.63 x 38 9; `dgìfugcs kb D 6 3 `dg kb D 6

;. Bsfrlil`ds gc rbspubstc= Bn 2.28 `dgbs kb D 6 ecy 6.63 x 389; `dgìfugcs kb D 6. Rn bmb`pgd `ãs= Fuãntds `dgbs kb pgctc (Cj) ecy bn 36.92 x 38

96

ãtd`d kb pgctc (Cj).

3. Xgcntbc`ds gc bqulvcgbnflc. 3 `dg Cj ?.899 x 38 96 ãtd`ds kb Cj 9. Bsfdjb`ds bg ocftdr kb fdnvbrslön= ?.899 x 38 96 ãtd`ds kb Cj d 3 `dg kb Cj 3 `dg kb Cj ?.899 x 38 96 ãtd`ds kb Cj

6. Cpglfc`ds bg ocftdr kb fdnvbrslön= 36.92 x 3896 ãtd`ds kb Cj x

3 `dg kb Cj 0 9.98 `dgbs kb Cj ?.899 x 38 96 ãtd`ds kb Cj

;. Bsfrlil`ds gc rbspubstc= Bn 36.92 x 38 96 ãtd`ds kb Cj ecy 9.98 `dgbs kb Cj .

32?

LJBY ∙ [cfcnã

Bmbrflfld 6 Ybsubgvc gcs sljulbntbs fdnvbrsldnbs. [lbnb un bmb`pgd. Bxprbsb sus rbsugtckds fdn 9 florcs kbfl`cgbs. 8)

´Fuãntds ãtd`ds kb sdkld ecy bn 8.6 `dgbs kb ãtd`ds kb sdkld4 3. Xgcntbc`ds gc bqulvcgbnflc y bsfdjb`ds bg ocftdr kb fdnvbrslön= 3 `dg kb Nc 0 ?.899 x 38

96

ãtd`ds kb Nc

3 `dg kb Nc d ?.899 x 3896 ?.899 x 3896 3 `dg kb Nc

9. Cpglfc`ds bg ocftdr kb fdnvbrslön= 96 8.6 `dgbs kb Nc x ?.899 x 38 ãtd`ds kb Nc 0 3.53 x 38 96 ãtd`ds kb Nc 3 `dg kb Nc

6. Bsfrlil`ds gc rbspubstc= Bn 8.6 `dgbs kb sdkld ecy 3.53 x 38 96 ãtd`ds kb Nc. 3)

´Fuãntds `dgbs kb fgdrd ecy bn unc ùbstrc kb : ãtd`ds kb fgdrd4 3. Xgcntbb gc bqulvcgbnflc y bsfdmc bg ocftdr kb fdnvbrslön=

9. Cpglqub bg ocftdr kb fdnvbrslön=

6. Bsfrlic gc rbspubstc=

9)

´Fuãntcs `dgìfugcs ecy bn 3 jrc`d kb jgufdsc F?E39D?4 3. Fcgfugb gc `csc `dgcr kb gc jgufdsc (F ?E39D?), pgcntbb gc ljucgkck y bsfdmc gds ocftdrbs kb fdnvbrslön=

3 `dg kb F?E39D? 0 9. Cpglqub gds ocftdrbs kb fdnvbrslön=



32:

6. Bg vdgu`bn `dgcr Bg vdgu`bn `dgcr bs bg bspcfld qub dfupc un `dg kb sustcnflc jcsbdsc . Csà fd`d gc `csc `dgcr sb `lkb bn jrc`ds, bg vdgu`bn `dgcr sb `lkb bn gltrds. Xcrc fcgfugcr bg vdgu`bn `dgcr kb un jcs, bstb kbib tbnbr unc tb`pbrcturc kb 8 ½F y bstcr sd`btlkd c 3 ct`ösobrc kb prbslön. Bstcs kds fdnklfldnbs sb fdndfbn fd`d tb`pbrcturc y prbslön ndr`cgbs ([XN). Bg vdgu`bn `dgcr c [XN, tlbnb un vcgdr kb 99.; gltrds. Xdr bmb`pgd= Fucnkd `dg klöxlkdunkb fcridnd (FD 9) bstã [XN dfupc vdgu`bn kb un 99.; G ykb fucnkd `dg kb c`dnàcfd (NE6c) bstã c [XN un tcìlìn dfupc un vdgu`bn kb 99.; G.

Fd`d un `dg kb jcs FD9 tlbnb bg `ls`d ný`brd kb pcrtàfugcs (?.899 x 3896) qub un `dg kb jcs NE6 c [XN, sb fu`pgb gc Gby kb Cvdjckrd qub klfb= "Kds vdgý`bnbs ljucgbs kb fucgqulbr jcs, c gc `ls`c tb`pbrcturc y prbslön, fdntlbnbn bg `ls`d ný`brd kb pcrtàfugcs".

_bc`ds=

FD9

_dgu`bn= Ný`brd kb `dgbs= @csc= [b`pbrcturc= Xrbslön= Fcntlkck kb pcrtàfugcs= Xcrtàfugcs=

99.; G 3 ;;.8 j/`dg ¸F 8 3ct` ?.899 x 3896 `dgìfugcs

Nb

99.; G 3 98.3 j/`dg ¸F 8

¸F 8 3ct` ?.899 x 3896 ãtd`ds

99.; G

D9

3 69.8 j/`dg 3ct` ?.899 x 3896 `dgìfugcs

Bmbrflfld ; Fdnsugtb su tcigc pbrlöklfc, rbcglfb gcs su`cs nbfbscrlcs y fd`pgbtb gc tcigc. [lbnb un bmb`pgd. sustcnflc

Eb FD N9

325

LJBY ∙ [cfcnã


?.899 x 3896ã

td`ds

`csc `dgcr

;.8j/`dg

vdgu`bn `dgcr

99.;G

Ybsu`bn Bstc sb`cnc cprbnkl`ds qub= 3.

@dg bs gc fcntlkck kb `ctbrlc qub fdntlbnbn ?.899 x 3896 pcrtàfugcs bgb`bntcgbs. Gcs pcrtàfugcs bgb`bntcgbs pubkbn sbr ãtd`ds, `dgìfugcs, d ldnbs.

3.3 Rn `dg kb ãtd`ds kb fucgqulbr bgb`bntd bs ljucg c su `csc ctö`lfc (C) y tdkds tlbnbn bg `ls`d ný`brd kb ãtd`ds ?.899 x 3896. Rn `dg kb fucgqulbr `dgìfugc bs ljucg c gc su`c kb gcs `cscs ctö`lfcs kb gds bgb`bntds qub odr`cn bg fd`pubstd bn gcs prdpdrfldnbs qub lnklfc su oörùgc. 9.

Bg ocftdr `dgcr bs un ocftdr kb fdnvbrslön qub nds pbr`ltb rbcglzcr fdnvbrsldnbs bntrb `dgbs, ný`brd kb pcrtàfugcs, `csc y vdgu`bn.

Cprbnkl`ds c rbcglzcr kds tlpds kb fdnvbrsldnbs= 9.3 Fdnvbrsldnbs kb `dg y `csc. 3 `dg d `csc ctö`lfc kbg bgb`bntd d fd`pubstd `csc ctö`lfc kbg bgb`bntd d fd`pubstd 3 `dg 9.9 Fdnvbrsldnbs kb `dg y ný`brd kb pcrtàfugcs. 96 3 `dg d ?.899 x 38 pcrtàfugcs ?.899 x 3896 pcrtàfugcs 3 `dg

Xcrc rbcglzcr gcs fdnvbrsldnbs nbfbsltc= 3. Xgcntbcr gc bqulvcgbnflc y bsfdjbr bg ocftdr kb fdnvbrslön. Vl nbfbsltc fcgfugcr bg ný`brd kb jrc`ds, kbib iusfcr gc `csc `dgcr bn gc tcigc pbrlöklfc d fcgfugcr gc `csc `dgcr kbg fd`pubstd. 9. Cpglfcr bg ocftdr kb fdnvbrslön. 6. Bsfrlilr gc rbspubstc. 6.

Bg vdgu`bn `dgcr bs bg bspcfld qub dfupc un `dg kb sustcnflc jcsbdsc. Xcrc fcgfugcr bg vdgu`bn `dgcr kb un jcs, bstb kbib tbnbr unc tb`pbrcturc kb 8 ½F y bstcr sd`btlkd c 3 ct`ösobrc kb prbslön. Bstcs kds fdnklfldnbs sb fdndfbn fd`d tb`pbrcturc y prbslön ndr`cgbs ([XN). Bg vdgu`bn `dgcr c [XN, tlbnb un vcgdr kb 99.; gltrds.

Lnvbstljub bn gc rbk... Xcrc ccnzcr d c`pglcr sus fdndfl`lbntds sdirb `dg y ný`brd kb Cvdjckrd, pubkb fdnsugtcr bg sltld= • ettp=//bnflnc.pntlf.`bf.bs/~msco8889/p;9.et` Suà`lfc LL ∙ Vb`cnc 9:

32<

Cutdfdntrdg Cftlvlkck 3. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd kb gc rbspubstc fdrrbftc. 3)

Ć quì fdnfbptd fdrrbspdnkb gc kbolnlflön "Fcntlkck kb `ctbrlc qub fdntlbnbn ?.899 x 38 96 pcrtàfugcs bgb`bntcgbs4

`dg `csc `dgcr ný`brd kb Cvdjckrd

9)

´Fuãg bs bg vcgdr kbg ný`brd kb Cvdjckrd4

?.899 x 3896 3 jrc`d/`dg Bg ný`brd kb `csc

6)

Ć quì fdnfbptd fdrrbspdnkb gc kbolnlflön "su`c kb gcs `cscs ctö`lfcs kb gds bgb`bntds qub odr`cn un fd`pubstd bn gcs prdpdrfldnbs qub lnklfc gc oörùgc"4

`dg `csc `dgcr ný`brd kb Cvdjckrd

;)

Ć quì fdnfbptd fdrrbspdnkb gc kbolnlflön "bspcfld

`csc `dgcr

qub dfupc un `dg kb sustcnflc jcsbdsc"4

vdgu`bn `dgcr nlnjunc kb gcs cntbrldrbs

Cftlvlkck 9. Lkbntlqub gc `csc `dgcr kb bgb`bntds y fd`pubstds 3)

Fd`pgbtb gc tcigc fdn gcs `cscs ctö`lfcs qub tlbnb un `dg kb gds sljulbntbs bgb`bntds. [lbnb un bmb`pgd.

bgb`bntd

`csc `dgcr fcntlkck kb (`csc ctö`lfc C) pcrtàfugcs

Cftlnld (Cf)

99:.8 j/`dg

?.899 x 3896

bgb`bntd Nbön (Nb)

Xdtcsld (A)

Xgctlnd (Xt)

Ogýdr (O)

Flrfdnld (]r)

@cjnbsld(@j)

Gltld(Gl)

3?8

LJBY ∙ [cfcnã

`csc `dgcr (`csc ctö`lfc)


9)

Fcgfugb gc `csc `dgcr kb gds sljulbntbs fd`pubstds= plj`bntd fgdrdgc F22E:9D2N;@j

@csc `dgcr kb gc F22E:9D2N;@j= 6)

öxlkdkbcgu`lnldCg

9

D6

@csc `dgcr kbg Cg9D6=

Fd`pgbtb gc tcigc fdn gc fcntlkck kb pcrtàfugcs, gc `csc `dgcr y bg vdgu`bn `dgcr kb gds sljulbntbs jcsbs. [lbnb un bmb`pgd. sustcnflc Cr

fcntlkck kb pcrtàfugcs ?.899 x 3896ã td`ds

`csc `dgcr 6<.
vdgu`bn `dgcr 99.;G

FD9 E9 Eb Fg9 Ub

Cftlvlkck 6. Ybsubgvc fdnvbrsldnbs Ybcglfb gcs fdnvbrsldnbs bn su fuckbrnd. Vljc gds pcsds qub cprbnklö bn gc sb`cnc. Kì sus rbspubstcs fdn 9 florcs kbfl`cgbs. 3)

´Fuãntcs `dgìfugcs kb cjuc ecy bn : jrc`ds kb E 9D4 3. Fcgfugb gc `csc `dgcr kbg cjuc y bsfdmc gds ocftdr kb fdnvbrslön= •

`dgbs jrc`ds

• `dgìfugcs `dgbs 9. Cpglqub gds ocftdrbs kb fdnvbrslön=

6. Bsfrlic gc rbspubstc= Suà`lfc LL ∙ Vb`cnc 9:

3?3

9)

Bg ãflkd sugoeàkrlfd (E9V) bs bg rbspdnscigb kbg dgdr kbscjrckcigb kb gds eubvds pdkrlkds. Ć fuãntds `dgbs bqulvcgbn 38.3 j kb bsb ãflkd4 3. Fcgfugb gc `csc `dgcr y bsfdmc bg ocftdr kb fdnvbrslön=


6)

6. Bsfrlic gc rbspubstc= Bg sugoctd obrrdsd (ObVD;) bs unc oubntb kb elbrrd pcrc bvltcr gc cnb`lc. ´Fuãntds `dgbs ecy bn 28.5 jrc`ds kb sugoctd obrrdsd4 3. Fcgfugb gc `csc `dgcr y bsfdmc bg ocftdr kb fdnvbrslön=


6. Bsfrlic gc rbspubstc= ;)

´Fuãntcs `dgìfugcs kb cjuc ecy bn 38.8 `dgbs kb bsb fd`pubstd4 3. Bsfdmc bg ocftdr kb fdnvbrslön=


6. Bsfrlic gc rbspubstc= 2)

Rn jgdid cbrdstãtlfd fdntlbnb 98.5 `dgbs kb ebgld (Eb). ´Fuãntds ãtd`ds kb Eb fdntlbnb4 3. Bsfdmc bg ocftdr kb fdnvbrslön=



3?9

LJBY ∙ [cfcnã


Rn jrcn ný`brd... bg ný`brd kb Cvdjckrd Xcrc qub sb ecjc unc lkbc `ãs fdnfrbtc kbg tc`cód kbg ný`brd kb Cvdjckrd, gb prdpdnb`ds rbcglzcr bstb bxpbrl`bntd.


3 fcgfugckdrc



kctds kb gc pdigcflön ùnklcg bn 9838.



un gãplz



glirbtc kb fc`pd

´Suì kbib ecfbr4 Ybspdnkc cg pgcntbc`lbntd elpdtìtlfd sljulbntb= Vl ustbk tuvlbrc un `dg kb qubtzcgbs y gd rbpcrtlbrc bntrb gds eciltcntbs kbg ùnkd, ´fuãntds códs gb kurcràc bg klnbrd c fckc eciltcntb sl jcstcrc S388.88 klcrlds4 Xcrc rbsdgvbrgd td`b bn fubntc gds sljulbntbs bnunflckds b lnklfcfldnbs. 3. "Vb bstl`c qub gc pdigcflön cprdxl`ckc kbg ùnkd, bn 9838, brc kb slbtb `lg `lggdnbs kb pbrsdncs, bstd bs :.88 x 38< pbrsdncs". Klvlkc bg ný`brd kb Cvdjckrd ?.899 x 38 96, qub bs bg `dg kb qubtzcgbs, bntrb gds eciltcntbs kbg ùnkd. Bxprbsb su rbsugtckd fdn 9 kbfl`cgbs. 9. Klvlkc su rbsugtckd bntrb flbn, qub bs gc fcntlkck qub sb jcstcràcn fckc kàc y ditbnkrã bg tlb`pd, bn kàcs, qub gbs kurcràc bg klnbrd. ´Fuãntd bs4 6. Vl csu`b qub fckc cód tlbnb 6?2 kàcs, klvlkc bg kctd qub dituvd bn bg pcsd 9 bntrb 6?2. ´Xcrc fuãntds códs cgfcnzcrã4 Klsfutcn y fd`pcrtcn sus rbsugtckds bn bg fbntrd kb drlbntcflön. ´Bg ný`brd kb Cvdjckrd rbprbsbntc unc fcntlkck pbqubóc d jrcnkb4


3?6



gdjrckd

rbjugcr

nd gdjrckd


Kbolnd `dg, `csc `dgcr y vdgu`bn `dgcr.

9.

Lkbntlolfd gc `csc `dgcr y gc fcntlkck kb pcrtàfugcs kb klstlntds bgb`bntds.

6.

Fcgfugd gc `csc `dgcr kb klstlntds fd`pubstds.

Kbspuìs kb ;. bstuklcr...

Lkbntlolfd gc `csc `dgcr y bg vdgu`bn `dgcr kb cgjunds jcsbs c tb`pbrcturc y prbslön ndr`cgbs ([XN).

2.

Ybsubgvd fdnvbrsldnbs kb `dg y `csc y vlfbvbrsc.

?. :.

Ybsubgvd fdnvbrsldnbs kb `dg y fcntlkck kb pcrtàfugcs. [bnjd unc lkbc `ãs fdnfrbtc kbg tc`cód kbg ný`brd kb Cvdjckrd, rbcglzcnkd bg bxpbrl`bntd prdpubstd.


3?;

LJBY ∙ [cfcnã

95

Ybcffldnbs quà`lfcs


3?2


Ybfdndfbr gc odtdsàntbsls fd`d rbcfflön quà`lfc lnklspbnscigb pcrc gc vlkc.



Kbolnlr rbcfflön quà`lfc y bfucflön quà`lfc.



Lkbntlolfcr gcs pcrtbs y sàìdgds kb unc bfucflön quà`lfc.



Ybprbsbntcr gcs rbcffldnbs kb sàntbsls, kbsfd`pdslflön y sustltuflön pdr `bkld kb oörùgcs jbnbrcgbs.



Fgcslolfcr gcs rbcffldnbs quà`lfcs bn rbcffldnbs kb cklflön, sustltuflön y kbsfd`pdslflön.



Ybfdndfbr gds rbcftlvds y gds prdkuftds bn gcs rbcffldnbs quà`lfcs qub prdvdfcn gc gguvlc ãflkc.



Lkbntlolfcr cftltukbs qub bvltcn qub sb prdkuzfc gc gguvlc ãflkc.



Disbrvcr unc rbcfflön quà`lfc.




3??

¡Xcrc fd`bnzcr!

• Gc odtdsàntbsls, unc rbcfflön quà`lfc


• Ybcffldnbs quà`lfcs • Bfucfldnbs quà`lfcs • Fgcslolfcflön kb gcs rbcffldnbs quà`lfcs


• Rnc fcnkbgc qub prdkufb cjuc

LJBY ∙ [cfcnã

lnklspbnscigb pcrc gc vlkc

¡Xcrc fd`bnzcr! Gc odtdsàntbsls, unc rbcfflön quà`lfc lnklspbnscigb pcrc gc vlkc Gc vlkc kbpbnkb kb klstlntcs rbcffldnbs quà`lfcs. Rnc kb gcs `ãs l`pdrtcntbs bs gc odtdsàntbsls. Fd`d scib, gcs pgcntcs sdn gds ýnlfds sbrbs vlvds fcpcfbs kb ocirlfcr su cgl`bntd. Gd ecfbn c trcvìs kb gc odtdsàntbsls . Gc odtdsàntbsls bs bg prdfbsd pdr bg qub gcs pgcntcs td`cn sustcnflcs kbg clrb, bg cjuc, gc tlbrrc y gc guz kbg Vdg y gcs trcnsodr`cn bn bnbrjàc pcrc vlvlr. Gc odtdsàntbsls bs unc su`c kb fcìlds quà`lfds qub pubkbn rbsu`lrsb bn bstds pcsds= 3. Gcs pgcntcs cisdribn cjuc y dtrds `ctbrlcgbs kb gc tlbrrc pdr gc rcàz.

9. Bsds `ctbrlcgbs suibn pdr bg tcggd ecstc gcs edmcs.

6. Bn gcs edmcs sb `bzfgcn fdn bg klöxlkd kb fcridnd (FD9) kbg clrb y gc bnbrjàc kbg Vdg. Gcs edmcs cisdribn gc bnbrjàc kbg Vdg bn odr`c kb guz, jrcflcs cg plj`bntd fgdrdolgc (F22E:9D2N;@j) qub gb kc bg fdgdr vbrkb c gcs pgcntcs.

;. Gc bnbrjàc kbg Vdg, bg klöxlkd kb fcr-

bnbrjàc gu`ànlfc `dgìfugcs kb fgdrdgc

E9 D

`dgìfugcs kb cjuc

FD9

D

F?E39D? czýfcr

idnd prdkufbn (E D) czýfcr(FD (F E) yDbg?) cjuc y glibrcn dxàjbnd (D9) bn gc ct`ösobrc. 9 ? 39

9


3?:

Bn odr`c jbnbrcg, gc odtdsàntbsls sb rbprbsbntc fdn bstc bfucflön quà`lfc=

?FD9 + 39E 9D klöxlkd kb cjuc fcridnd

F?E39D? + ?D 9 + ?E 9D czýfcr

dxàjbnd

cjuc

Bg prdfbsd kb gc odtdsàntbsls bs ùy vcgldsd pcrc tdkds gds sbrbs vlvds. ‛´Vcib pdr quì4 ‛Xdrqub prdkufb bg dxàjbnd nbfbscrld pcrc qub gds cnl`cgbs y gds eu`cnds pdkc`ds vlvlr. Xdr bsd kbib`ds fulkcr gds ãridgbs y fdnsbrvcr nubstrds idsqubs. Gcs pgcntcs sdn c`ljcs qub nds kcn vlkc. ¡Xrdtbmã`dsgcs! Bstc sb`cnc bstuklcrã gcs rbcffldnbs quà`lfcs, fö`d sb rbprbsbntcn y fö`d sb fgcslolfcn.

¡C trcicmcr! C.

I.

3?5

Bsfrlic bg ndìrb kb gds fd`pubstds qub lntbrvlbnbn bn gc odtdsàntbsls. [lbnb un bmb`pgd. klöxlkd kb fcridnd

8)

FD9

3) 9)

E 9D F?E39D?

6)

F22E:9D2N;@j

Bsfrlic bg ndìrb y bg ný`brd kb ãtd`ds kb gds bgb`bntds quà`lfds qub odr`cn fckc und kb bstds fd`pubstds. [lbnb un bmb`pgd. 3 ãtd`d kb fcridnd (F), 9 ãtd`ds kb dxàjbnd (D)

8)

FD9

3)

E 9D

9)

F?E39D?

6)

F22E:9D2N; @j

LJBY ∙ [cfcnã


3. Ybcffldnbs quà`lfcs C gd gcrjd kb bstb fursd eb`ds bstuklckd qub gds bgb`bntds sb unbn pcrc odr`cr fd`pubstds. Bstã unlön sb kc pdr `bkld kb bngcfbs quà`lfds. ´Gd rbfubrkc4 Gds bngcfbs quà`lfds sdn oubrzcs qub `cntlbnbn gds ãtd`ds unlkds y pbr`ltbn odr`cr `dgìfugcs d fd`pubstds. Bg prdfbsd qub dfurrb pcrc qub sb kì bsc unlön sb ggc`c rbcfflön quà`lfc y sb kbnb csà= Gc rbcfflön quà`lfc bs un prdfbsd pdr bg fucg unc d `ãs sustcnflcs (bgb`bntds d fd`pubstds) sb trcnsodr`cn y odr`cn sustcnflcs klobrbntbs . Gcs sustcnflcs lnlflcgbs qub pcrtlflpcn bn gc rbcfflön sb ggc`cn rbcftlvds y gcs sustcnflcs rbsugtcntbs kb gc rbcfflön, prdkuftds.

Kurcntb unc rbcfflön quà`lfc gds ãtd`ds nd sb frbcn nl sb kbstruybn, sdgd sb rbdrjcnlzcn.

Xdr bmb`pgd= Bg fctlön kbg sdkld (Nc +) sb unb cg cnlön kbg fgdrd (Fg∙), pcrc odr`cr gc `dgìfugc kb fgdrurd kb sdkld (NcFg). Bn bggc, bg sdkld y bg fgdrd kbmcn kb sbrgd pcrc odr`cr unc sustcnflc klstlntc, gc scg. Bn bstb fcsd, bg sdkld (Nc +) y bg fgdrd (Fg∙) sdn gds rbcftlvds y bg fgdrurd kb sdkld (NcFg) bs bg prdkuftd.

Nc+ + Fg‖

NcFg

rbcftlvd rbcftlvd

prdkuftd

Bmbrflfld 3 C.

Ybggbnb bg fuckrd kbg tbxtd qub kbolnb `bmdr bg fdnfbptd kb rbcfflön quà`lfc. Rnc rbcfflön quà`lfc bs gc lntbrcfflön bntrb uncs sustcnflcs pcrc odr`cr dtrcs fdn prdplbkckbs klstlntcs. Rnc rbcfflön quà`lfc bs gc unlön kb kds d `ãs bgb`bntds pcrc odr`cr fd`pubstds.

I.

Ybspdnkc c gcs prbjuntcs. 3)

´Fö`d sb ggc`cn gcs sustcnflcs lnlflcgbs qub pcrtlflpcn bn gc rbcfflön4

9)

´Fö`d sb ggc`cn gcs sustcnflcs rbsugtcntbs kb gc rbcfflön4 Suà`lfc LL ∙ Vb`cnc 95

3?<

9. Bfucfldnbs quà`lfcs Gc rbfbtc kb unc rbcfflön Ctdg kb bgdtb Lnjrbklbntbs= • 9 rcmcs kb fcnbgc

• 9 tczcs kb cjuc

• 3/9 glirc kb `csc kb `càz tlbrnd

• 3 tczc kb czýfcr

• 3 gltrd kb gbfeb

• 3 plzfc kb scg

Xrbpcrcflön= Elbrvc bg cjuc fdn gc fcnbgc. Ictc gc `csc kb `càz fdn gc gbfeb. Cóckc czýfcr y unc plzfc kb scg. Elbrvc pdr 98 `lnutds c oubjd gbntd y `dvlbnkd bg ctdg fdnstcntb`bntb pcrc qub nd sb pbjub.

Rnc bfucflön quà`lfc bs fd`d unc rbfbtc kb fdflnc bn gc qub sb bspbflfcn lnjrbklbntbs (bgb`bntds y fd`pubstds) y sus fcntlkckbs (ný`brds kb `dgìfugcs). Rnc bfucflön quà`lfc bs gc rbprbsbntcflön jrãfc y slìöglfc kb unc rbcfflön quà`lfc. Xdr bmb`pgd= Bn gc sbfflön ¡Xcrc fd`bnzcr! fdndfl`ds gc bfucflön quà`lfc kb gc odtdsàntbsls= ?FD9 + 39E9D

F?E39D? + ?D 9 +?E9D

Bstc bfucflön nds lnklfc qub pcrc rbcglzcr gc odtdsàntbsls, gcs pgcntcs utlglzcn sbls `dgìfugcs kb klöxlkd kb fcridnd FD9 fdn kdfb `dgìfugcs kb cjuc E9D, pcrc prdkuflr unc `dgìfugc kb czýfcr F?E39D?, sbls `dgìfugcs kb dxàjbnd D9 y sbls `dgìfugcs kb cjuc E9D. Fckc bfucflön quà`lfc bstã odr`ckc pdr bstds bgb`bntds= 3. Ybcftlvds= sdn gcs sustcnflcs qub vcn c rbcffldncr bntrb sà. Vb bsfrlibn pdr `bkld kb oörùgcs bn gc pcrtb lzqulbrkc kb gc bfucflön. ?FD9 + 39E9D

F?E39D? + ?D9 + ?E9D

9. Xrdkuftds= sdn gcs sustcnflcs qub sb ditlbnbn bn unc rbcfflön quà`lfc. Vb bsfrlibn pdr `bkld kb oörùgcs bn gc pcrtb kbrbfec kb gc bfucflön. ?FD9 + 39E9D F?E39D? + ?D9 + ?E9D Gds rbcftlvds y gds prdkuftds sb bsfrlibn sbpcrckds pdr unc ogbfec. Bstc ogbfec bs bg bqulvcgbntb cg sljnd 0 (ljucg) kb unc bfucflön `ctb`ãtlfc. ?FD9 + 39E9D

3:8

LJBY ∙ [cfcnã

F?E39D? + ?D9 + ?E9D

6. Fdbolflbntbs= sdn gds ný`brds qub sb bsfrlibn cntbs kb fckc oörùgc y cobftcn c tdkc gc `dgìfugc. Lnklfcn bg ný`brd kb ãtd`ds d `dgìfugcs kb fckc rbcftlvd d prdkuftd. ?FD9 + 39E9D

F?E39D? + ?D9 + ?E9D

;. Vuiànklfbs= sdn gds ný`brds pbqubóds qub sb bsfrlibn kbspuìs kbg sàìdgd kbg bgb`bntd qub gds prbfbkb. Gds suiànklfbs lnklfcn gc fcntlkck kb ãtd`ds kb fckc bgb`bntd prbsbntbs bn gc `dgìfugc kbg fd`pubstd. ?FD9 + 39E9D

F?E39D? + ?D9 +?E9D

_bc`ds dtrd bmb`pgd= Gc rbcfflön kbg elbrrd ( Ob) fdn bg dxàjbnd (D) pcrc odr`cr öxlkd kb elbrrd (LL) ObD sb rbprbsbntc fdn bstc bfucflön quà`lfc= 9Ob + D9 elbrrd

dxàjbnd

9ObD öxlkd kb elbrrd (LL)

3. Gds rbcftlvds sdn= Bg elbrrd (Ob) y bg dxàjbnd (D) 9Ob + D9

9ObD

9. Bg prdkuftd bs= Bg öxlkd kb elbrrd (LL) (ObD) 9Ob + D9

9ObD

6. Gds fdbolflbntbs sdn= Bg ný`brd 9 qub cntbfbkb cg elbrrd (9Ob) y bg ný`brd 9 qub cntbfbkb cg öxlkd kb elbrrd (LL) (9ObD) 9Ob + D9

9ObD

;. Bg suiànklfb bs= Bg ný`brd 9 qub cfd`pcóc cg dxàjbnd kb gds rbcftlvds (D 9) 9Ob + D9

9ObD

Cgjuncs bfucfldnbs quà`lfcs pubkbn tbnbr dtrds sàìdgds= Gc kdigb ogbfec lnklfc qub gc rbcfflön pubkb dfurrlr bn cìcs klrbffldnbs. Gc ogbfec ecflc crrlic lnklfc qub bn gc rbcfflön sb kbsprbnkb un jcs. Rn trlãnjugd d gc pcgcirc —fcgdr‐ lnklfc qub gc rbcfflön rbqulbrb bnbrjàc tìr`lfc pcrc ggbvcrsb c fcid d qub sb prdkufb fcgdr fd`d prdkuftd kb gc rbcfflön. Suà`lfc LL ∙ Vb`cnc 95

3:3

Bmbrflfld 9 3)

Disbrvb gc bfucflön quà`lfc qub rbprbsbntc gc rbcfflön bntrb bg fcridnctd kb fcgfld (FcFD6) bn prbsbnflc kb fcgdr pcrc odr`cr öxlkd kb fcgfld (FcD) y klöxlkd kb fcridnd (FD9). Gubjd fd`pgbtb gc lnodr`cflön qub sb gb plkb bn fckc lnflsd. FcFD6 fcridnctd kb fcgfld

9)

c.

Bg rbcftlvd bs=

i.

Gds prdkuftds sdn=

f.

Gds fdbolflbntbs sdn=

k.

Gds suiànklfbs sdn=

FcD + FD

öxlkd kb klöxlkd kb fcgfld fcridnd

Disbrvb gc bfucflön quà`lfc qub rbprbsbntc gc rbcfflön bntrb bg cgu`lnld (Cg) y bg dxàjbnd (D9) pcrc odr`cr öxlkd kb cgu`lnld (Cg 9D6). Gubjd fd`pgbtb gc lnodr`cflön qub sb gb plkb bn fckc lnflsd. ;Cg + 6D9 cgu`lnd

3:9

9

c.

Gds rbcftlvds sdn=

i.

Bg prdkuftd bs=

f.


k.

Gds suiànklfbs sdn=

LJBY ∙ [cfcnã

dxàjbnd

9Cg9D6 klöxlkd kb cgu`lnd

6. Fgcslolfcflön kb gcs rbcffldnbs quà`lfcs C nubstrd cgrbkbkdr sb prdkufbn ùfecs rbcffldnbs quà`lfcs y tdkcs sdn klobrbntbs. Xcrc fd`prbnkbr fö`d y pdr quì sb odr`cn gds klstlntds prdkuftds, gds quà`lfds ecn fgcslfckd gcs rbcffldnbs quà`lfcs kb vcrlcs odr`cs. Ndsdtrds vc`ds c bstuklcr gc fgcslfcflön kb gcs rbcffldnbs sbjýn bg prdfbsd qub suorbn gds rbcftlvds.

6.3 Ybcffldnbs kb fdìlncflön d sàntbsls Gcs rbcffldnbs kb fdìlncflön d sàntbsls sb prdkufbn fucnkd kds d `ãs rbcftlvds, yc sbcn bgb`bntds d fd`pubstds, rbcffldncn y odr`cn un prdkuftd qub slb`prb bs un fd`pubstd. Vb rbprbsbntcn fdn gc oörùgc jbnbrcg= C+I

CI

C y I pubkbn sbr bgb`bntds d fd`pubstds, pbrdCI bs slb`prb un fd`pubstd. Xdr bmb`pgd= nltröjbnd

N9 + 6E9

9NE6

c`dnlcfd

elkröjbnd

Rnc `dgìfugc kb nltröjbnd sb fdìlnc fdn trbs `dgìfugcs kb elkröjbnd pcrc odr`cr c`dnlcfd. Dtrds bmb`pgds kb rbcffldnbs kb fdìlncflön sdn= Fg9 + E9 9EFg fgdrd elkröjbnd odr`cflön kb ãflkd fgdreàkrlfd

F +

D9

fcridnd dxàjbnd

9E9

+

FD9 odr`cflön kb klöxlkd kb fcridnd

D9

E9 D

elkröjbnd dxàjbnd odr`cflön kb cjuc


3:6

6.9 Ybcffldnbs kb kbsfd`pdslflön Gcs rbcffldnbs kb kbsfd`pdslflön sdn cqubggcs bn gcs qub bg rbcftlvd bs un fd`pubstd qub pdr gc cfflön kb cgjýn tlpd kb bnbrjàc (jbnbrcg`bntb fcgdr d bgbftrlflkck) sb kbsfd`pdnb y kc fd`d prdkuftd kds d `ãs bgb`bntds d fd`pubstds. Vb rbprbsbntcn fdn gc oörùgc jbnbrcg= CI

C+I

CI bs slb`prb un fd`pubstd, pbrdC y I pubkbn sbr bgb`bntds d fd`pubstds. Xdr bmb`pgd= fgdrurd kb sdkld

NcFg

Nc + Fg 9

bgbftrlflkck

fgdrd

sdkld

Bg fgdrurd kb sdkld sb kbsfd`pdnb, pdr cfflön kb gc bgbftrlflkck, bn fckc und kb sus fd`pdnbntbs= sdkld y fgdrd. Dtrds bmb`pgds kb rbcffldnbs kb kbsfd`pdslflön sdn= 3)

E9 D

E9 + D9

bgbftrlflkck

9)

9NcEFD6

Bg cjuc sb sbpcrc bn kds `dgìfugcs= unc kb elkröjbnd y dtrc kb dxàjbnd. Bstb prdfbsd sb ggc`c bgbftröglsls.

Nc9FD6 + FD9 + E9D fcgdr

Bstc rbcfflön fdrrbspdnkb cg pdgvd kb edrnbcr d ilfcridnctd kb sdkld (NcEFD 6). Cg fcgbntcrgd bn bg edrnd, prdkufb fcridnctd kb sdkld (Nc 9FD6), bg jcs klöxlkd kb fcridnd (FD9) y cjuc (E9D).

6.6 Ybcffldnbs kb sustltuflön Gcs rbcffldnbs kb sustltuflön d sustltuflön sl`pgb sdn cqubggcs bn gcs qub und kb gds bgb`bntds qub odr`c pcrtb kb gds rbcftlvds rbb`pgczc c dtrd bgb`bntd y kc fd`d prdkuftd un fd`pubstd nubvd. Vb rbprbsbntcn fdn gc oörùgc jbnbrcg= C + IF

3:;

LJBY ∙ [cfcnã

CF + I

Xdr bmb`pgd= elbrrd

Ob + 9EFg ãflkd fgdreàkrlfd

ObFg 9 + E9

elkröjbnd

fgdrurd kb elbrrd (LL)

Bg elbrrd (Ob) kbspgczc cg elkröjbnd kbg ãflkd fgdreàkrlfd y sb unb fdn bg fgdrd pcrc odr`cr bg fgdrurd kb elbrrd (LL). Dtrds bmb`pgds kb rbcffldnbs kb sustltuflön sdn= nàqubg

Nl + E9VD; ãflkd sugoýrlfd

`cjnbsld

@j + 9EFg ãflkd fgdreàkrlfd

NlVD; + E9

elkröjbnd

sugoctd kb nàqubg

@jFg9 + E9

elkröjbnd

fgdrurd kb `cjnbsld

Bmbrflfld 6 C.

I.

Disbrvb gc oörùgc jbnbrcg kb gcs rbcffldnbs y bsfrlic kb quì tlpd kb rbcfflön sb trctc. [lbnb un bmb`pgd. 8)

CI +

C+I

3)

C+I

CI

9)

C + IF

rbcfflön kb kbsfd`pdslflön

CF + I

Disbrvb fdn ctbnflön fckc rbcfflön quà`lfc y bsfrlic sl sb trctc kb unc rbcfflön kb fdìlncflön d sàntbsls, kbsfd`pdslflön d sustltuflön. [lbnb un bmb`pgd. 8)

AFgD6 +

AFg + D9

3)

Ic + Ir9

IcIr9

9)

Fu + END6

6)

9A + V

;)

;Ob + 689

2)

E9VD6

?)

]n + 9EFg

rbcfflön kb kbsfd`pdslflön

Fu(ND6)9 + E9 A 9V 9Ob9D6

E9D + VD9 ]nFg9 + E9


3:2

Bmbrflfld ; Disbrvb gc rbcfflön. Gubjd rbggbnb bg fuckrd kb gc rbspubstc fdrrbftc. [lbnb un bmb`pgd. 9Fr + ?END6 8)

´Suì tlpd kb rbcfflön sb prbsbntc4

sàntbsls 3)

sustltuflön

kbsfd`pdslflön

´Fuãgbs sdn gds rbcftlvds4 9Fr + ?END6

9)

9Fr(ND6)6 + 6E9

9Fr(ND6) + 6E9

?END6 y 9Fr(ND6)6

´Fdn quì sàìdgd sb rbprbsbntc gc odr`cflön kb un jcs4


Rnc rbcfflön quà`lfc bs un prdfbsd pdr bg fucg unc d `ãs sustcnflcs (bgb`bntds d

fd`pubstds) sb trcnsodr`cn y odr`cn sustcnflcs klobrbntbs. 9.

Gcs rbcffldnbs quà`lfcs sb rbprbsbntcn pdr `bkld kb bfucfldnbs quà`lfcs qub sdn rbprbsbntcfldnbs , jrãolfcs y slìöglfcs, kb gcs rbcffldnbs quà`lfcs . Fckc bfucflön quà`lfc fdnstc kb bstds bgb`bntds=

c.

rbcftlvds

?FD9 + 39E9D

F?E39D? + ?D9 + ?E9D

i.

prdkuftds

?FD9 + 39E9D

F?E39D? + ?D9 + ?E9D

f.

fdbolflbntbs

?FD9 + 39E9D

F?E39D? + ?D9 + ?E9D

k.

suiànklfbs

?FD9 + 39E9D

F?E39D? + ?D9 + ?E9D

6.

Gcs rbcffldnbs quà`lfcs sb pubkbn fgcslolfcr bn=

6.3

Ybcffldnbs kb sàntbsls

6.9

Ybcffldnbs kb kbsfd`pdslflön CI

6.6

Ybcffldnbs kb sustltuflön

3:?

LJBY ∙ [cfcnã

C+I C + IF

CI C+I CF + I

Cutdfdntrdg Cftlvlkck 3. Ybgcfldnb lnodr`cflön Ybggbnb bg fuckrd kb gc dpflön qub fdrrbspdnkb c fckc bnunflckd. 3)

Xrdfbsd bn bg qub unc sustcnflc quà`lfc sb trcnsodr`c bn dtrc klstlntc.

bfucflön quà`lfc rbcfflön quà`lfc prdkuftd quà`lfd

9)

Ybprbsbntcflön bsfrltc kb unc rbcfflön quà`lfc.

rbcftlvd quà`lfd bfucflön quà`lfc prdkuftd quà`lfd

6)

Xcrtb lzqulbrkc kb gc bfucflön quà`lfc bn gc qub sb bsfrlibn gcs sustcnflcs qub vcn c rbcffldncr bntrb sà.

rbcftlvds `dgìfugcs prdkuftds

;)

Vàìdgd qub lnklfc qub bn gc rbcfflön sb kbsprbnkb un jcs.

2)

Vàìdgd qub lnklfc qub gc rbcfflön rbqulbrb bnbrjàc tìr`lfc.

?)

[lpd kb rbcffldnbs quà`lfcs bn gcs qub un fd`pubstd sb rd`pb pcrc odr`cr kds d `ãs bgb`bntds y/d fd`pubstds.

sàntbsls sustltuflön kbsfd`pdslflön

:)

[lpd kb rbcfflön quà`lfc bn gc qub kds bgb`bntds sb unbn pcrc odr`cr un fd`pubstd.

sàntbsls sustltuflön kbsfd`pdslflön

5)

Ybcfflön quà`lfc bn gc qub un bgb`bntd pubkb kbspgczcr c dtrd y td`cr su gujcr pcrc odr`cr un nubvd fd`pubstd.

sàntbsls sustltuflön kbsfd`pdslflön Suà`lfc LL ∙ Vb`cnc 95

3::

Cftlvlkck 9. Fdnstruyc fdnfbptds Bsfrlic fdn sus pcgcircs unc kbnlflön kb rbcfflön quà`lfc.

Cftlvlkck 6. Ybprbsbntb lnodr`cflön bn odr`c bsfrltc Ybprbsbntb gcs rbcffldnbs kb sàntbsls, kbsfd`pdslflön y sustltuflön pdr `bkld kb su oörùgc jbnbrcg y bxpglqub bg prdfbsd qub dfurrb bn fckc unc. 3)

Vàntbsls

9)

Kbsfd`pdslflön

6)

Vustltuflön

Cftlvlkck ;. Ybfdndzfc gds tlpds kb rbcfflön quà`lfc Bsfrlic sdirb gc gànbc bg tlpd kb rbcfflön quà`lfc qub rbprbsbntc fckc nu`brcg. [lbnb un bmb`pgd.

3:5

8)

9E + D9

3)

Nl + E9VD;

9) 6)

9@j +D9 9@jD FcFD6 FcD + FD

;)

Cj + END6

LJBY ∙ [cfcnã

rbcfflön kb fdìlncflön d sàntbsls

9E9D NlVD; + E9

9

CjND6

Cftlvlkck 2. Lkbntlqub gcs pcrtbs kb unc bfucflön quà`lfc 3)

Disbrvb gc bfucflön quà`lfc qub rbprbsbntc gc rbcfflön bntrb nltröjbnd `dgbfugcr (N9) b elkröjbnd `dgbfugcr (E9) pcrc odr`cr c`dnlcfd (NE6). Gubjd fd`pgbtb gc lnodr`cflön qub sb gb plkb bn fckc lnflsd. N9

+ 6E9

9NE6

nltröjbnd elkröjbnd c`dnlcfd `dgbfugcr `dgbfugcr

9)

c.

Gds rbcftlvds sdn=

i.

Bg prdkuftd bs=

f.


k.

Bs unc rbcfflön kb=

Disbrvb gc bfucflön quà`lfc qub rbprbsbntc gc rbcfflön bntrb öxlkd kb sdkld (Nc9D) y cjuc (E9D) pcrc odr`cr elkröxlkd kb sdkld (NcDE). Gubjd fd`pgbtb gc lnodr`cflön qub sb gb plkb bn fckc lnflsd.

c.

Gds rbcftlvds sdn=

i.

Bg prdkuftd bs=

f.


k.

Bs unc rbcfflön kb=

Nc9D + E9D

9NcDE

öxlkd kb sdkld

elkröxlkd kb sdkld

cjuc


3:<

Cftlvlkck ?. Ybfdndzfc gds rbcftlvds y prdkuftds kb gc gguvlc ãflkc Gbc bg tbxtd y rbspdnkc c gcs prbjuntcs bn su fuckbrnd. ´Suì bs gc gguvlc ãflkc4 Gc gguvlc ãflkc bs fucgqulbr odr`c kb prbflpltcflön qub tlbnb unc fdnfbntrcflön kb cflkbz `cydr qub gc kbg cjuc kb gguvlc nd fdntc`lnckc. Bs un prdigb`c cìlbntcg qub suorb tdkd bg ùnkd, bspbflcg`bntb gcs zdncs uricncs d ùy lnkustrlcglzckcs.

´Fö`d sb prdkufb4 Gds fdìustligbs oöslgbs, pbtrögbd, fcridnd y jcs ncturcg, fdntlbnbn czuorb (V) y nltröjbnd (N) bn su fd`pdslflön. Fucnkd gds fdìustligbs oöslgbs sb qub`cn, prdkufbn öxlkd kb czuorb (VD6) y öxlkd kb nltröjbnd (ND9) qub bsfcpcn c gc ct`ösobrc. Cggà bntrcn bn fdntcftd fdn bg cjuc E 9D y prdkufbn pbqubócs fcntlkckbs kb ãflkd sugoýrlfd (E 9VD;) y ãflkd nàtrlfd (END6) rbspdnscigbs kb gc cflkbz kb gc gguvlc. VD6 + E9D

E9VD;

ND9 + E9D

END6

´Suì bobftds prdkufb4 Gc gguvlc ãflkc pbrmuklfc bg subgd, bg frbfl`lbntd kb gcs pgcntcs, y bs fcpcz kb kbstrulr gc vlkc cfuãtlfc. Ckb`ãs, prdkufb l`pdrtcntbs kcóds bn gcs fdsbfecs, cfbgbrc bg kbtbrldrd kb gds bklolflds y `dnu`bntds dfcsldncnkd bg ggc`ckd ‗`cg kb plbkrc‐.

¡Fdgcidrb`ds! [dkds pdkb`ds fdntrliulr fdn cffldnbs fdnfrbtcs pcrc bvltcr gc gguvlc ãflkc= •

Rtlglfb idìlggcs cedrrckdrcs kb bnbrjàc.

•

B`pgbb gc `bndr fcntlkck pdsligb kb prdkuftds quà`lfds (kbslnobftc ntbs, kbtbrjbn -

•

Kbsfdnbftb gds cpcrctds bgìftrlfds fucnkd nd gds bstì utlglzcnkd.

•

Rtlglfb gc `bndr fcntlkck pdsligb kb pcpbg.

•

Vlbìrb y fulkb gcs pgcntcs. [dkds pdkb`ds tbnbr pgcntcs bn fcsc.

•

Vl bstã c su cgfcnfb, fd`prb prdkuftds drjãnlfds, glirbs kb quà`lfds kcólnds pcrc

tbs, cìlbntckdrbs, btf) y kb idgscs d b`pcqubs pgãstlfds.

bg cìlbntb.

358

3) 9)

´Fuãgbs sdn gds rbcftlvds bn gcs rbcffldnbs qub prdvdfcn gc gguvlc ãflkc4 ´Fuãgbs sdn gds prdkuftds bn gcs rbcffldnbs qub prdvdfcn gc gguvlc ãflkc4

6)

´Suì tlpd kb rbcfflön sb prdkufb4

;)

Fltb cg `bnds kds cffldnbs qub bvltcn qub sb prdkuzfc gc gguvlc ãflkc.

LJBY ∙ [cfcnã


Rnc fcnkbgc qub prdkufb cjuc Bstc sb`cnc gb prdpdnb`ds disbrvcr fdn gds bobftds kb unc rbcfflön quà`lfc bn un bspcfld fbrrckd.


un pgctd ednkd



cjuc



unc vbgc



un vcsd bstrbfed kb vlkrld



fdgdrcntb vbjbtcg (dpfldncg)



gãplz



glirbtc kb fc`pd

´Suì kbib ecfbr4

3. Ggbnb bg pgctd ednkd fdn cjuc. (Fcgfugb unds kds fbntà`btrds kb prdounklkck.) 9. Cóckc bg fdgdrcntb cg cjuc. 6. Bnflbnkc gc fcnkbgc y fdgöqubgc bn bg fbntrd kbg pgctd kb `cnbrc qub bg cjuc nd tdqub gc ggc`c. ;. Fdgdqub bg vcsd kb vlkrld bnfl`c kb gc vbgc. Bspbrb unds sbjunkds y vbc quì dfurrb. 2. Cndtb sus disbrvcfldnbs bn gc glirbtc kb fc`pd y fd`pãrtcgcs bn bg fbntrd kb drlbntcflön.

´Suì dfurrlö4 Kurcntb bg bxpbrl`bntd sb prdkumd unc rbcfflön qub sb rbprbsbntc fdn bstc bfucflön quà`lfc= F92E29 + 65D9

92FD9 + 9?E9D

Gc pcrcnc (F92E29) kb gc vbgc rbcffldnc fdn bg dxàjbnd kbg clrb (D 9) y prdkufb klöxlkd kb fcridnd (FD9) y vcpdr kb cjuc (E9D). Vl sb mö, bn bg lntbrldr kbg vcsd cpcrbfàcn uncs jdtltcs kb cjuc. Bscs jdtcs sb odr`crdn pdr bg vcpdr kb cjuc prdkuflkd bn gc fdìustlön kb gc vbgc qub sb fdnkbnsö bn gcs pcrbkbs kbg vcsd.


353



gdjrckd

rbjugcr

nd gdjrckd


Ybfdndzfd gc odtdsàntbsls fd`d rbcfflön quà`lfc lnklspbnscigb pcrc gc vlkc.

9.

Kbolnd rbcfflön quà`lfc y bfucflön quà`lfc.

6.

Lkbntlolfd gcs pcrtbs y sàìdgds kb unc bfucflön quà`lfc. Ybprbsbntdgcs rbcffldnbs kb sàntbsls, kbsfd`pdslflön y sustltuflön pdr `bkld kb oörùgcs jbnbrcgbs. Fgcslolfd gcs rbcffldnbs quà`lfcs bn rbcffldnbs kb cklflön, sustltuflön y kbsfd`pdslflön. Ybfdndzfd gds rbcftlvds y gds prdkuftds bn gcs rbcf-

;. Kbspuìs kb bstuklcr... 2. ?. :. 5.

fldnbs quà`lfcs qub prdvdfcn gc gguvlc ãflkc. Lkbntlolfd cftltukbs qub bvltcn qub sb prdkuzfc gc gguvlc ãflkc. Disbrvd unc rbcfflön quà`lfc y fd`pcrtd `ls fdnfgusldnbs bn bg fbntrd kb drlbntcflön.


359

LJBY ∙ [cfcnã

9<

Ybpcsd Vb`cncs 9;-95


356


Ybpcscr gds fdntbnlkds kb gc sb`cnc 9; c gc 95.



Xrbpcrcrsb pcrc gc sbjunkc prubic pcrflcg.



Bstl`ckc y bstl`ckd bstuklcntb= Vb cprdxl`c gc sbjunkc bvcgucflön. Fdn bg dimbtlvd kb qub ustbk sb prbpcrb ilbn, vc`ds c rbpcscr gds fdntbnlkds kb gcs sb`cncs 9; c gc 95. Bstc sb`cnc tlbnb gds rbsý`bnbs kb gds tb`cs qub eb`ds vlstd y bmbrflflds pcrc qub vcyc bstuklcnkd. Xcrc cprdvbfecr `bmdr bstb rbpcsd gb rbfd`bnkc`ds= • Gbbr fdn ctbnflön fckc rbsu`bn. • Ybsdgvbr gds bmbrflflds kurcntb gc fgcsb rcklcg y kbspuìs kb bggc. • Ybpcscr gcs sb`cncs cntbrldrbs, bn bggcs tlbnb `ãs bxpglfcfldnbs y bmb`pgds. • Bstuklcr un pdqultd tdkds gds kàcs y rbsdgvbr sus kukcs. Xlkc cyukc c sus `cbstrds drlbntckdrbs d cgjýn `lbìrd kb gc fdùnlkck qub fdndzfc gc `ctbrlc.

35;

LJBY ∙ [cfcnã


3. Gds ãflkds 3.

Gds ãflkds sb kbolnbn fd`d sustcnflcs qub bn sdguflön cfudsc glibrcn ldnbs kb elkröjbnd. Vdn fd`pubstds ilncrlds d tbrncrlds odr`ckds pdr gc fdìlncflön kbg elkröjbnd (fdn vcgbnflc +3) fdn dtrd bgb`bntd.

3.3. Nd`bnfgcturc kb gds ãflkds c. Ãflkds elkrãflkds sb rbprbsbntcn fdn gc oörùgc jbnbrcg=

E xN


nd `btcg jrupd 3? d 3:

vcgbnflc kbg nd `btcg jrupd 3? d 3:

Gc bstrufturc pcrc ndìrcr elkrãflkds bs= Ndìrb jbnìrlfd + ndìrb kbg nd `btcg + sumd ‖eàkrlfd i. Ãflkds dxãflkds sb rbprbsbntcn fdn gc oörùgc= elkröjbnd fdn vcgbnflc +3

END



Xrbolmds y suolmds pcrc ndìrcr ãflkds dxãflkds= ný`brd kb vcgbnflc qub utlglzc bg nd `btcg

3d9 ;d6 ?d2 :

prbmd‖

‖sumd

elpd‖ ‖dsd ‖ ‖dsd ‖ ‖lfd pbr‖ ‖lfd

Gc bstrufturc pcrc ndìrcr ãflkds dxãflkds bs= ãflkd + prbmd + ndìrb kbg nd `btcg + sumd Xcrc bsfrlilr bg prbolmd y bg suolmd kbib`ds kbtbr`lncr gc vcgbnflc kbg nd `btcg. Vbjul`ds bstds pcsds= • Bsfrlil`ds gds ný`brds kb vcgbnflc fdndflkds (elkröjbnd(+3) y dxàjbnd(‖9)). • @ugtlpglfc`ds gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn. • Xgcntbc`ds unc bfucflön pcrc fcgfugcr bg vcgdr kb gc vcgbnflc kbg nd `btcg.


352

Bmbrflfld 3. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd qub fdrrbspdnkc c fckc fdnfbptd. 3)

Vustcnflc qub bn sdguflön cfudsc glibrc ldnbs elkröjbnd.

ãflkd icsb scg

9)

Fd`pubstd ilncrld odr`ckd pdr gc unlön kb elkröjbnd

scg ecgdlkbc

fdn un nd `btcg kb gds jrupds 3? d 3:.

dxãflkd elkrãflkd

Fd`pubstd tbrncrld qub sb odr`c kb gc unlön kbg elkröjbnd, un nd `btcg y dxàjbnd.

scg ecgdlkbc dxãflkd elkrãflkd

6)

Bmbrflfld 9. Nd`bnfgcturc kb ãflkds elkrãflkds Ndìrb gds elkrãflkds. Vljc gc bstrufturc qub cprbnklö. [lbnb un bmb`pgd. 8)

EO Ndìrb jbnìrlfd=

3)

Ndìrb kbg nd `btcg=

ýdr

Vuolmd=

‖eàkrlfd


ãflkd udreàkrlfd

EFg Ndìrb jbnìrlfd= Ndìrb kbg nd `btcg= Vuolmd= Ndìrb kbg fd`pubstd=

9)


35?

ãflkd

LJBY ∙ [cfcnã

Bmbrflfld 6. Nd`bnfgcturc kb ãflkds dxãflkds Bsfrlic bg ndìrb kb gds sljulbntbs ãflkds dxãflkds. [lbnb un bmb`pgd. 8)

E6XD; 3. Ndìrb jbnìrlfd= ãflkd 9. _cgbnflc kbg nd `btcg. c. _cgbnflc kb gds fd`pubstds fdndflkds= x ‖9 E+3 6 X D;

i. @ugtlpglfcflön kb gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn= E+6XxD‖5 f. Bfucflön pcrc fcgfugcr bg vcgdr kb x. 6+x‖ 508 x05‖6 x02 Gc vcgbnflc kbg oösodrd bs=

2

Xrbolmd= nd tlbnb Vuolmd=

‖lfd

6. Ndìrb kbg fd`pubstd= ãflkd odsoörlfd 3)

END6 3. Ndìrb jbnìrlfd= 9. _cgbnflc kbg nd `btcg. c. _cgbnflc kb gds fd`pubstds fdndflkds= i. @ugtlpglfcflön kb gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn= f. Bfucflön pcrc fcgfugcr bg vcgdr kb x.

Gc vcgbnflc kbg nltröjbnd bs= Xrbolmd= Vuolmd= 6. Ndìrb kbg fd`pubstd= Suà`lfc LL ∙ Vb`cnc 9<

35:

9)

E9VD6 3. Ndìrb jbnìrlfd= 9. _cgbnflc kbg nd `btcg. c. _cgbnflc kb gds fd`pubstds fdndflkds= i. @ugtlpglfcflön kb gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn= f. Bfucflön pcrc fcgfugcr bg vcgdr kb x.

Gc vcgbnflc kbg czuorb bs= Xrbolmd= Vuolmd= 6. Ndìrb kbg fd`pubstd= 6)

EIrD; 3. Ndìrb jbnìrlfd= 9. _cgbnflc kbg nd `btcg. c. _cgbnflc kb gds fd`pubstds fdndflkds= i. @ugtlpglfcflön kb gds suiànklfbs pdr bg ný`brd kb vcgbnflc kb gds bgb`bntds qub nd vcràcn= f. Bfucflön pcrc fcgfugcr bg vcgdr kb x.

Gc vcgbnflc kbg ird`d bs= Xrbolmd= Vuolmd= 6. Ndìrb kbg fd`pubstd=

355

LJBY ∙ [cfcnã

9. Gds elkröxlkds d icsbs 3.

Elkröxlkds Gds elkröxlkds d icsbs sdn fd`pubstds tbrncrlds odr`ckds pdr un `btcg, dxàjbnd b elkröjbnd. Vb odr`cn c pcrtlr kb un öxlkd iãslfd y cjuc. Gds fcrcftbrlzc bn su bstrufturc quà`lfc gc prbsbnflc kbg lön elkrdxlgd (DE‖). Vb prbsbntcn fdn gc oörùgc jbnbrcg= `btcg

@(DE)x


vcgbnflc kbg `btcg y fcntlkck kb ldnbs (DE ‖3)

3.3 Nd`bnfgcturc kb gds elkröxlkds c.

Bn bg slstb`c Vtdfa sb ndìrcn fdn bstc bstrufturc= Ndìrb jbnìrlfd + kb + `btcg + ný`brd kb vcgbnflc kbg `btcg elkröxlkd

kb

icrld

LL


Bmbrflfld ;. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd qub fdrrbspdnkc c fckc fdnfbptd. 3)

Fd`pubstds qub prbsbntcn bg lön elkrdxlgd bn su oörùgc quà`lfc.

cjuc scgbs elkröxlkds

9)

Cnlön odr`ckd pdr dxàjbnd b elkröjbnd, prdpld kb gds elkröxlkds, qub tlbnb vcgbnflc ‖3 (DE‖3).

elkrdnld elkrdxlgd elkrurd

6)

Fd`pubstds qub rbsugtcn kb gc fdìlncflön kb un öxlkd `btãglfd y cjuc.

elkrãflkds elkröxlkds dxãflkd


35<

Bmbrflfld 2. Nd`bnfgcturc kb elkröxlkds Lkbntlqub fckc bgb`bntd kb gc oörùgc kb gds sljulbntbs elkröxlkds. [lbnb un bmb`pgd. 8)

fcgfld

Fc(DE)9


vcgbnflc +9 kbg fcgfld y 9 ldnbs DE‖3

3<8

3)

[l(DE)6

9)

Xi(DE)9

6)

Jb(DE);

;)

\(DE)6

2)

Ic(DE)9

LJBY ∙ [cfcnã

Bmbrflfld ?. Nd`bnfgcturc kb elkröxlkds Ndìrb gds sljulbntbs elkröxlkds bn bg slstb`c Vtdfa. [lbnb un bmb`pgd. 8)

Z(DE)? Ndìrb jbnìrlfd=

3)

elkröxlkd

Ndìrb kbg `btcg=

vdgorc`ld


_L

Ndìrb kbg fd`pubstd= Cu(DE)6

elkröxlkd kb vdgorc`ld (_L)

Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd= 9)

Xi(DE); Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

6)

Fr(DE)6 Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

;)

[l(DE); Ndìrb jbnìrlfd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=


3<3

6. Gcs scgbs 3.

Gcs scgbs sdn bg rbsugtckd kb gc rbcfflön quà`lfc bntrb un ãflkd y unc icsb. • Vcgbs ecgdlkbcs rbsugtcn kb gc fdìlncflön kb un elkrãflkd fdn unc icsb. [lbnbn gc oörùgc jbnbrcg=

@xNy

`btcg



3.3 Nd`bnfgcturc kb gcs scgbs ecgdlkbcs c. Nd`bnfgcturc bn bg slstb`c trcklfldncg kb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs fdn vcgbnflc olmc Gds `btcgbs qub tlbnbn vcgbnflc olmc sdn= 3

9

E

3

Gl

3

Nc

3

A

3

Yi

3

33

39

36

Elkröjbnd Gltld

Ib

9

@j

9

Fc

9

Vr

9

Ibrlgld

Vdkld

Cg

@cjnbsld

Xdtcsld

]n 9 Flnf

Fcgfld

Yuilkld

Bstrdnfld

Fs

3

Or

3

Fbsld

6

Cgu`lnld

Ic

9

Yc

9

Cj Xgctc

3

Fk 9

Fck`ld

Icrld

Orcnfld

Yckld

Vb ndìrcn fdn bstc bstrufturc= Ndìrb kbg nd `btcg + sumd ‖urd + kb + ndìrb kbg `btcg fgdrd

‖urd

kb

pdtcsld

fgdrurd kb pdtcsld (AFg)

i. Nd`bnfgcturc bn bg slstb`c Vtdfa kb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs fdn vcgbnflc vcrlcigb Vb ndìrcn fdn bstc bstrufturc= ndìrb kbg + sumd ‖urd + kb + ndìrb kbg `btcg + vcgbnflc kbg `btcg bn ný`brd rd`cnds nd `btcg fgdrd

‖urd

kb

idrd

fgdrurd kb idrd (LLL) (IFg6)

3<9

LJBY ∙ [cfcnã

LLL

Bmbrflfld :. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd qub fdrrbspdnkb c fckc fdnfbptd. 3)

Fd`pubstd qub sb odr`c bn gc rbcfflön quà`lfc kb un ãflkd fdn unc icsb.

dxãflkd elkröxlkd scg

9)

Fd`pubstd ilncrld qub sb odr`c fucnkd un elkrãflkd rbcffldnc fdn unc icsb.

dxlscg elkröjbnd scg ecgdlkbc

6)

Fd`pubstd tbrncrld odr`ckd pdr un fctlön `btãglfd y un dxlcnlön.

elkröxlkd dxãflkd dxlscg

;)

Fd`pubstd tbrncrld qub sb odr`c kb gc rbcfflön quà`lfc kb un dxãflkd fdn unc icsb d `btcg.

elkröxlkd dxãflkd dxlscg

2)

@btcg fdn vcgbnflc olmc + 9.

sdkld (Nc) pdtcsld (A) fcgfld (Fc)

?)

@btcg fdn vcgbnflc olmc + 6.

cgu`lnld (Cg) flnf (]n) gltld (Gl)

Bmbrflfld 5. Nd`bnfgcturc kb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs kb vcgbnflc mc Bsfrlic bg ndìrb kb gcs sljulbntbs scgbs ecgdlkbcs. [lbnb un bmb`pgd. 8)

FsFg

3)

IbV

9) 6)

CgO6 ]n6X9

;)

CjL

fgdrurd kb fbsld


3<6

Bmbrflfld <. Nd`bnfgcturc kb scgbs ecgdlkbcs odr`ckcs pdr `btcgbs kb vcgbnflc vcrlcigb Bsfrlic bg ndìrb kb gcs sljulbntbs scgbs ecgdlkbcs bn bg slstb`c Vtdfa. [lbnb un bmb`pgd. 8)

3)

@n6X: Ndìrb kbg nd `btcg + suolmd ‖urd=

odsourd

Ndìrb kbg `btcg=

`cnjcnbsd


_LL


odsourd kb `cnjcnbsd (_LL)

YuFg6 Ndìrb kbg nd `btcg + suolmd ‖urd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

9)

[lO9 Ndìrb kbg nd `btcg + suolmd ‖urd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

6)

Fr6N9 Ndìrb kbg nd `btcg + suolmd ‖urd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

;)

_; F 2 Ndìrb kbg nd `btcg + suolmd ‖urd= Ndìrb kbg `btcg= _cgbnflc kbg `btcg bn ný`brds rd`cnds= Ndìrb kbg fd`pubstd=

3<;

LJBY ∙ [cfcnã

;. @dg= gc `csc kb gcs pcrtàfugcs 3.

@dg bs gc fcntlkck kb `ctbrlc qub fdntlbnbn ?.899 x 3896 pcrtàfugcs bgb`bntcgbs. Gcs pcrtàfugcs bgb`bntcgbs pubkbn sbr ãtd`ds, `dgìfugcs d ldnbs.

3.3 Rn `dg kb ãtd`ds kb fucgqulbr bgb`bntd bs ljucg c su `csc ctö`lfc (C) y tdkds tlbnbn bg `ls`d ný`brd kb ãtd`ds ?.899 x 3896. Rn `dg kb fucgqulbr `dgìfugc bs ljucg c gc su`c kb gcs `cscs ctö`lfcs kb gds bgb`bntds qub

9.

odr`cn bg fd`pubstd bn gcs prdpdrfldnbs qub lnklfc su oörùgc. Bg ocftdr `dgcr bs un ocftdr kb fdnvbrslön qub pbr`ltb rbcglzcr fdnvbrsldnbs bntrb `dgbs, ný`brd kb pcrtàfugcs, `csc y vdgu`bn. Xubkbn sbr kb gcs sljulbntbs odr`cs=

9.3 Fdnvbrsldnbs kb `dg y `csc. 3 `dg `csc ctö`lfc kbg bgb`bntd d fd`pubstd d `csc ctö`lfc kbg bgb`bntd d fd`pubstd 3 `dg 9.9 Fdnvbrsldnbs kb `dg y ný`brd kb pcrtàfugcs. 3 `dg ?.899 x 3896 pcrtàfugcs

d

?.899 x 3896 pcrtàfugcs 3 `dg

Xcrc rbcglzcr gcs fdnvbrsldnbs nbfbsltc= 3. Bsfdjbr bg ocftdr kb fdnvbrslön. Vl nbfbsltc fcgfugcr bg ný`brd kb jrc`ds, kbib iusfcr gc `csc `dgcr bn gc tcigc pbrlöklfc d fcgfugcr gc `csc `dgcr kbg fd`pubstd. 9. Cpglfcr bg ocftdr kb fdnvbrslön. 6. Bsfrlilr gc rbspubstc. 6.

Bg vdgu`bn `dgcr bs bg bspcfld qub dfupc un `dg kb sustcnflc jcsbdsc. Xcrc fcgfugcr bg vdgu`bn `dgcr kb un jcs, bstb kbib tbnbr unc tb`pbrcturc kb 8 ½F y bstcr sd`btlkd c 3 ct`ösobrc kb prbslön. Bstcs kds fdnklfldnbs sb fdndfbn fd`d tb`pbrcturc y prbslön ndr`cgbs ([XN). Bg vdgu`bn `dgcr c [XN, tlbnb un vcgdr kb 99.; gltrds. Suà`lfc LL ∙ Vb`cnc 9<

3<2

Bmbrflfld 38. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd qub fdrrbspdnkb c fckc fdnfbptd. [lbnb un bmb`pgd.

3
8)

Fcntlkck kb `ctbrlc qub fdntlbnbn ?.899 x 3896 pcrtàfugcs bgb`bntcgbs.

ný`brd kb Cvdjckrd jrc`d `dg

3)

@csc kb ?.899 x 3896 kb fucgqulbr bgb`bntd qub bs ljucg c su `csc ctö`lfc.

`csc `dgcr `csc nufgbcr `csc bstbquld`ìtrlfc

9)

Bqulvcgbnflc qub pbr`ltb trcnsodr`cr unc unlkck kb `bklkc bn dtrc.

ocftdr `dgcr ocftdr kb fdnvbrslön ocftdr kb trcnsodr`cflön

6)

@csc qub tlbnb un `dg kb `dgìfugcs kb un fd`pubstd.

`csc `dgcr `csc `dgbfugcr `csc ctö`lfc

;)

Bspcfld qub dfupc un `dg kb sustcnflc jcsbdsc.

flglnkrd `dgcr jcs `dgcr vdgu`bn `dgcr

2)

[b`pbrcturc y prbslön ndr`cgbs pcrc un jcs.

tb`pbrcturc y prbslön cg nlvbg kbg `cr 8 ½F kb tb`pbrcturc y 3 ct` kb prbslön tb`pbrcturc cìlbntb y prbslön klcrlc

?)

_dgu`bn `dgcr kb un jcs c [XN.

99; G 99.; G 99.; `G

LJBY ∙ [cfcnã

Bmbrflfld 33. Fdnvbrsldnbs kb `dg y `csc Ybcglfb bn su fuckbrnd gcs sljulbntbs fdnvbrsldnbs. Bxprbsb sus rbsugtckds fdn unc florc kbfl`cg. 3)

Fcgfugb gc fcntlkck kb `dgbs kb ãtd`ds kb dxàjbnd qub ecy bn 9;.8 j kb dxàjbnd.

9)

Fcgfugb gc fcntlkck kb `dgbs kb `dgìfugcs kb dxàjbnd qub ecy bn 9;.8 j kb dxàjbnd jcsbdsd (D9).

6)

Bnfubntrb bg ný`brd kb `dgbs kb klöxlkd kb czuorb (VD9) qub ecy bn 9;.2 j kb klöxlkd kb czuorb.

;)

Fcgfugb gc `csc bn jrc`ds kb fcridnctd kb icrld (IcFD6) qub ecy bn 8.; `dgbs kb fcridnctd kb icrld.

2)

Fcgfugb gc `csc bn jrc`ds kb odsoctd kb sdkld (Nc6XD;) bn 3.2 `dgbs kb odsoctd kb sdkld.

Bmbrflfld 39. Fdnvbrsldnbs kb `dg y fcntlkck kb pcrtàfugcs Ybcglfb bn su fuckbrnd gcs sljulbntbs fdnvbrsldnbs. Bxprbsb sus rbsugtckds fdn unc florc kbfl`cg. 3)

Fcgfugb bg ný`brd kb `dgìfugcs bn 6.3 `dgbs kb elkröjbnd jcsbdsd (E9).

9)

Fcgfugb bg ný`brd kb ãtd`ds bn 8.? `dgbs kb ãtd`ds kb fcridnd (F).

6)

Fcgfugb bg ný`brd kb `dgìfugcs bn :.5 `dgbs kb `btcnd (FE;).

;)

Fcgfugb gds `dgbs kb tltcnld bn 6.9 x 389; ãtd`ds kb tltcnld ([l).

2)

Fcgfugb gds `dgbs kb jgufdsc bn 3.9 x 3893 `dgìfugcs kb jgufdsc (F ?E39D?).

Bmbrflfld 36. Fdnvbrsldnbs kb `dg, `csc, fcntlkck kb pcrtàfugcs y vdgu`bn `dgcr Ybcglfb bn su fuckbrnd gcs sljulbntbs fdnvbrsldnbs. Bxprbsb su rbsugtckd fdn unc florc kbfl`cg. 3)

Fcgfugb bg ný`brd kb `dgbs kb jcs ebgld bn 32.8 G kb ebgld (Eb) c [XN.

9)

Fcgfugb bg ný`brd kb jrc`ds kb klöxlkd kb fcridnd jcsbdsd bn 3;.8 G kb klöxlkd kb fcridnd (FD9) c [XN.

6)

Fcgfugb bg ný`brd kb `dgìfugcs kb nltröjbnd jcsbdsd bn ;5.8 G kb nltröjbnd (N9) c [XN.

;)

Fcgfugb bg vdgu`bn kb ;.? j kb fgdrd jcsbdsd (Fg9) c [XN.

2)

Fcgfugb bg vdgu`bn kb ?.6 `dgbs kb `dnöxlkd kb klnltröjbnd (N9D) c [XN.


3<:

2. Ybcffldnbs quà`lfcs Rnc rbcfflön quà`lfc bs un prdfbsd pdr bg fucg unc d `ãs sustcnflcs (bgb`bntds d

3.

fd`pubstds) sb trcnsodr`cn y odr`cn sustcnflcs klobrbntbs. Gcs rbcffldnbs quà`lfcs sb rbprbsbntcn pdr `bkld kb bfucfldnbs quà`lfcs qub sdn rbprbsbntcfldnbs , jrãolfcs y slìöglfcs, kb gcs rbcffldnbs quà`lfcs . Fckc bfucflön quà`lfc fdnstc kb bstds bgb`bntds=

9.

c.

rbcftlvds

?FD9 + 39E9D

F?E39D? + ?D9 + ?E9D

i.

prdkuftds

?FD9 + 39E9D

F?E39D? + ?D9 + ?E9D

f.

fdbolflbntbs

?FD9 + 39E9D

F?E39D? + ?D9 + ?E9D

k.

suiànklfbs

?FD9 + 39E9D

F?E39D? + ?D9 + ?E9D

6.

Gcs rbcffldnbs quà`lfcs sb pubkbn fgcslolfcr bn=

6.3

Ybcffldnbs kb sàntbsls

6.9

Ybcffldnbs kb kbsfd`pdslflön CI

6.6

Ybcffldnbs kb sustltuflön

C+I

CI C+I

C + IF

CF + I

Bmbrflfld 3;. Ybgcfldnb fdnfbptds

Ybggbnb bg fuckrd qub fdrrbspdnkc c fckc fdnfbptd.

3<5

3)

Xrdfbsd pdr bg fucg unc d `ãs sustcnflcs sb trcnsodr`cn y odr`cn sustcnflcs klobrbntbs.

ounflön quà`lfc rbcfflön quà`lfc fcìld quà`lfd

9)

Vustcnflcs lnlflcgbs qub pcrtlflpcn bn unc rbcfflön quà`lfc.

rbcftlvds prdkuftds quà`lfds

6)

Vustcnflcs rbsugtcntbs kb unc rbcfflön quà`lfc.

rbcftlvds prdkuftds quà`lfds

LJBY ∙ [cfcnã

;)

Ybprbsbntcflön jrãolfc y slìöglfc kb unc rbcfflön quà`lfc.

oörùgc quà`lfc bfucflön quà`lfc oörùgc `dgbfugcr

2)

Vustcnflcs qub sb bsfrlibn pdr `bkld kb oörùgcs bn gc pcrtb lzqulbrkc kb gc bfucflön quà`lfc.

rbcftlvds prdkuftds fcgdr y bnbrjàc

?)

Vustcnflcs qub sb bsfrlibn pdr `bkld kb oörùgcs bn gc pcrtb kbrbfec kb gc bfucflön quà`lfc.

rbcftlvds prdkuftds fcgdr y bnbrjàc

:)

Ybcffldnbs quà`lfcs qub sb prdkufbn fucnkd kds d `ãs rbcftlvds rbcffldncn y odr`cn un prdkuftd qub slb`prb bs un fd`pubstd.

rbcffldnbs kb sustltuflön rbcffldnbs kb kbsfd`pdslflön rbcffldnbs kb fdìlncflön d sàntbsls

5)

Ybcffldnbs quà`lfcs bn gcs qub und kb gds bgb`bntds kb un rbcftlvd rbb`pgczc c dtrd bgb`bntd kb dtrd rbcftlvd y kc


fd`d prdkuftd un fd`pubstd nubvd. <)

Ybcffldnbs quà`lfcs bn gcs qub bg rbcftlvd bs un fd`pubstd y pdr cfflön kb cgjýn tlpd kb bnbrjàc sb kbsfd`pdnb y kc fd`d prdkuftd kds d `ãs bgb`bntds d fd`pubstds.


Bmbrflfld 32. Lkbntlfcr gcs pcrtbs kb unc bfucflön quà`lfc Disbrvb gcs sljulbntbs bfucfldnbs quà`lfcs. Gubjd fd`pgbtb gc lnodr`cflön qub sb gb plkb bn fckc lnflsd. [lbnb un bmb`pgd. 8)

9@j + D9

9@jD

Gds rbcftlvds sdn=

@j + D9

Bg prdkuftd bs=

@jD


9 kbg @j y 9 kbg @jD


3<<

3)

9NcFg + Xi(ND6)9

XiFg9 + 9NcND6

Gds rbcftlvds sdn= Gds prdkuftds sdn= Gds fdbolflbntbs sdn= 9)

Ic + E9D

Ic(DE)9 + E9

Gds rbcftlvds sdn= Gds prdkuftds sdn= Gds fdbolflbntbs sdn= 6)

@j + 9EFg

@jFg9 + E9

Gds rbcftlvds sdn= Gds prdkuftds sdn= Gds fdbolflbntbs sdn= ;)

E9D + VD6

E9VD;

Gds rbcftlvds sdn= Bg prdkuftd bs= Gds fdbolflbntbs sdn=

Bmbrflfld 3?. Ybfdndfbr gds tlpds kb rbcfflön quà`lfc

Bsfrlic sdirb gc gànbc bg tlpd kb rbcfflön quà`lfc qub rbprbsbntc fckc nu`brcg kb gclzqulbrkc. [lbnb un bmb`pgd.

988

8)

Cg + D9

3)

Ic + EFg

9)

N9D2 + E9D

6)

AND6

;)

Fg9 + FcL9

FcFg9 + L9

2)

IcD + VD6

IcVD;

?)

NcND6

:) 5)

Xi + EjIr9 XiIr9 + Ej F39E99D33 F + E9D

<)

Nc + D9

LJBY ∙ [cfcnã

Cg9D6 IcFg9 + E9 END6

AND9 + D9

NcND9 + D9

Nc9D

Ybcfflön kb fdìlncflön d sàntbsls

68

Icgcnfbd kb bfucfldnbs quà`lfcs


983


Fd`prdicr qub gc `csc kb gds rbcftlvds bs ljucg c gc `csc kb gds prdkuftds bn unc bfucflön icgcnfbckc.



Icgcnfbcr bfucfldnbs quà`lfcs fdn bg `ìtdkd kb tcntbd d kb bnscyd y brrdr.



Bxpbrl`bntcr gc odr`cflön kbg jcs klöxlkd kb fcridnd fd`d prdkuftd kb unc rbcfflön quà`lfc.




989

¡Xcrc fd`bnzcr!

• Gby kb gc fdnsbrvcflön kb gc `csc


• Icgcnfbd kb bfucfldnbs


• @dvl`lbntd `lstbrldsd

LJBY ∙ [cfcnã

¡Xcrc fd`bnzcr! Gc Gby kb fdnsbrvcflön kb gc `csc Cntdlnb kb Gcvdlslbr, flbntàolfd orcnfìs, odrùgö muntd cg cfckì`lfd rusd @lmcàg Gd`dnösdv unc kb gcs gbybs ounkc`bntcgbs kb gcs flbnflcs ncturcgbs, gc Gby kb gc fdnsbrvcflön kb gc `csc qub klfb= ‗Bn tdkc rbcfflön quà`lfc gc `csc sb fdnsbrvc, bs kbflr, gc

`csc fdnsu`lkc bn gds rbcftlvds bs ljucg c gc `csc ditbnlkc bn gds prdkuftds ‐. Bstc gby bxpglfc qub sl bn unc bfucflön quà`lfc ecy un kbtbr`lnckd ný`brd kb ãtd`ds kb un bgb`bntd bn bg gckd lzqulbrkd, tbnkrã qub ecibr bg `ls`d ný`brd kb ctö`ds kb bsb `ls`d bgb`bntd bn bg gckd kbrbfed. Xdr gd tcntd, cìds gckds kb gc bfucflön tbnkrãn gc `ls`c `csc.

Cntdlnb kb Gcvdlslbr (3:;6 ‖ 3:<;) Flbntàolfd orcnfìs

_bc`ds fd`d bmb`pgd gc rbcfflön bntrb bg elkröjbnd y bg dxàjbnd pcrc odr`cr cjuc= 9E9

+

D9

9E9D @lmcàg Gd`dnösdv (3:33 ‖ 3:?2) Cfckì`lfd rusd

+ ; x 3 j/`dg

+ 9 x 3? j/`dg 6? j/`dg

; x 3 j/`dg + 9 x 3? j/`dg 6? j/`dg

Gc `csc tdtcg kb gds rbcftlvds, 6? jrc`ds, bs bxcftc`bntb ljucg c gc `csc tdtcg kbg prdkuftd, 6? jrc`ds. [dkcs gcs bfucfldnbs quà`lfcs icgcnfbckcs tlbnbn bg `ls`d ný`brd kb ãtd`ds kb fckc bgb`bntd bn cìds gckds kb gc bfucflön.

¡C trcicmcr! Fd`prubib qub gc `csc kb gds rbcftlvds bs ljucg c gc `csc kb gds prdkuftds bn bstc bfucflön icgcnfbckc. F

+

D9

FD9


986


3. Bfucfldnbs icgcnfbckcs Xcrc pbscr 3 glirc kb td`ctb bn bg `brfckd, sb fdgdfc bn un gckd kb gc icgcnzc un pbsd kb 3 glirc y bn bg dtrd gckd, gds td`ctbs ecstc qub cìds pgctds bstìn icgcnfbckds. Kbg `ls`d `dkd, unc bfucflön quà`lfc bstã icgcnfbckc fucnkd cìds gckds kb gc bfucflön tlbnbnfdbflbntbs bg `ls`d ný`brd kb ãtd`ds. Icgcnfbcr unc bfucflön fdnslstb bn iusfcr nu`ìrlfds qub ecjcn qub bg ný`brd kb fckc tlpd kb ãtd`ds prbsbntbs bn gc rbcfflön quà`lfc sbc bg `ls`d bn gds rbcftlvds qub bn gds prdkuftds. ´Fö`d ditbnb`ds unc bfucflön icgcnfbckc4

¡@uy l`pdrtcntb! Gds suiànklfbs nunfc sb fcìlcn pdrqub sl gd ecfb`ds bsfrlil`ds gc oörùgc kb dtrd fd`pubstd.

Ecy vcrlds `ìtdkds, ndsdtrds prcftlfcrb`ds bg `ìtdkd kb tcntbd d `ìtdkd kb bnscyd y brrdr. Xcrc ecfbrgd, kbtbr`lnc`ds gds fdbflbntbs qub nds kbn ný`brds ljucgbs kb fckc tlpd kb ãtd`d bn fckc gckd kb gc rbcfflön. Fd`d su ndìrb gd lnklfc, sb trctc kb prdicr y icgcnfbcr pdr bnscyd y brrdr. Gds fdbflbntbs sdn, jbnbrcg`bntb, ný`brds bntbrds. Xdr bmb`pgd= Icgcnfbcr cg tcntbd= E9 + D9

E9 D

3. Bsfrlil`ds bg ný`brd kb ãtd`ds kb fckc bgb`bntd qub ecy bn fckc gckd kb gc rbcfflön, csà scirb`ds quì bgb`bntds nd bstãn icgcnfbckds. ný`brd kb ãtd`ds bn rbcftlvds

E 0 9 (E9) D 0 9 (D9)

ný`brd kb ãtd`ds bn prdkuftds

E 0 9 (E9D) D 0 3 (E9D)

9. Bg bgb`bntd qub nd bstã icgcnfbckd bs bg dxàjbnd (D). Gd ljucgc`ds bsfrlilbnkd un 9 kbg gckd kb gds prdkuftds bn gc `dgìfugc kb cjuc. E9 + D9

9E9D

• Cedrc tbnb`ds 9 ãtd`ds kb dxàjbnd bn gds rbcftlvds y prdkuftds, pbrd bg elkröjbnd sb ec kbsicgcnfbckd. Xcrc icgcnfbcrgd, bsfrlil`ds un 9 kbg gckd kb gds rbcftlvds. 9E9 + D9 9E9D 6. Fd`prdic`ds fdn cyukc kb gc tcigc qub gds ãtd`ds bstãn icgcnfbckds. ný`brd kb ãtd`ds bn rbcftlvds

E 0 ; (9E9) D 0 9 (D9)

98;

LJBY ∙ [cfcnã


E 0 ; (9E9D) D 0 9 (9E9D)

Dtrd bmb`pgd= Icgcnfbcr cg tcntbd= E9VD; + IcFg9

IcVD; + EFg

3. Bsfrlil`ds bg ný`brd kb ãtd`ds kb fckc bgb`bntd qub ecy bn fckc gckd kb gc rbcfflön, csà scirb`ds quì bgb`bntds nd bstãn icgcnfbckds. ný`brd kb ãtd`ds ný`brd kb ãtd`ds bn rbcftlvds bn prdkuftds

V03

(E9VD;)

V03

(IcVD;)

Ic 0 3 (IcFg9) Fg 0 9 (IcFg9)

Ic 0 3 (IcVD;) Fg 0 3 (EFg)

D 0 ; (E9VD;)

D 0 ; (IcVD;)

E 0 9 (E9VD;)

E 0 3 (EFg)

9. Gds bgb`bntds qub nd bstãn icgcnfbckds sdn bg elkröjbnd (E) y bg fgdrd (Fg). Ljucgc`ds prl`brd bg fgdrd. Kbg gckd kb gds rbcftlvds ecy 9 ãtd`ds y kbg gckd kb gds prdkuftds ecy 3. E9VD; + IcFg9

IcVD ; + EFg

• Bsfrlil`ds bg fdbolflbntb 9 bn bg EFg, bn gc pcrtb kb gds prdkuftds pcrc icgcnfbcr gds ãtd`ds kb fgdrd. E9VD; + IcFg9

IcVD; + 9EFg

• Gubjd vbrlolfc`ds qub gds ãtd`ds kb elkröjbnd bstìn ljucgckds bn cìds gckds kb gc bfucflön. Fd`d sà bstãn icgcnfbckds, fdn bstd tbr`lnc`ds bg prdfbkl`lbntd. E9VD; + IcFg 9

Jbnbrcg`bntb bg E y bg D sb icgcnfbcn kb ýgtl`d.

IcVD ; + 9EFg

6. Fd`prdic`ds fdn cyukc kb gc tcigc qub gds ãtd`ds bstãn icgcnfbckds. ný`brd kb ãtd`ds ný`brd kb ãtd`ds bn rbcftlvds bn prdkuftds

V03

(E9VD;)

Ic 0 3 (IcFg ) 9

V03

(IcVD;)

Ic 0 3 (IcVD ) ;

Fg 0 9 (IcFg9)

Fg 0 9 (9EFg)

D 0 ; (E9VD;)

D 0 ; (IcVD;)

E 0 9 (E9VD;)

E 0 9 (9EFg) Suà`lfc LL ∙ Vb`cnc 68

982

¡Rn bmb`pgd `ãs! Icgcnfbcr gc rbcfflön= F6E5 + D9

FD9 + E9D

3. Bsfrlil`ds bg ný`brd kb ãtd`ds kb fckc bgb`bntd qub ecy bn fckc gckd kb gc bfucflön= ný`brd kb ãtd`ds bn rbcftlvds


F 0 6 (F6E5)

F03 (

F D9 )

E 0 5 (F6E5)

E09 (

E9D)

D 0 9 (D9)

D 0 6 (FD9 + E9D) 9+3

9. [bnb`ds qub icgcnfbcr tdkds gds bgb`bntds. B`pbfb`ds fdn bg fcridnd (F). Bsfrlil`ds un 6 bn bg FD9 kb gds prdkuftds. F 6E 5 + D 9

6FD9 + E9D

Kb bstc odr`c tbnb`ds 6 ãtd`ds kb fcridnd bn gds rbcftlvds y 6 ãtd`ds kb fcridnd bn gds prdkuftds. • Icgcnfbc`ds gds elkröjbnds. Kbg gckd lzqulbrkd tbnb`ds 5 elkröjbnds y kbg gckd kbrbfed, 9. Bsfrlil`ds un ; bn gc `dgìfugc kb cjuc pcrc pdkbr ljucgcr bg ný`brd kb elkröjbnds pdrqub ; x 9 0 5. F 6 E5 + D 9

6FD9 + ;E9D

• _bc`ds fuãntds dxàjbnds tbnb`ds= F6E 5 + D 9 9

?

6 F D 9 + ; E9 D + ;

Kbg gckd lzqulbrkd tbnb`ds 9 dxàjbnds y kbg gckd kbrbfed, 38. Xcrc ljucgcrgds bsfrlil`ds un 2 cntbs kb gc `dgìfugc kb D 9 pdrqub 2 x 9 0 38. F6E5 + 2D9

6FD9 + ;E9D

6. Fdn bstb pcsd tbnb`ds gc bfucflön icgcnfbckc. Gd pdkb`ds vbrlolfcr bn gc tcigc= ný`brd kb ãtd`ds bn rbcftlvds F06 E05

(F6E5) (F6E5)

D 0 38 (2D9) 38

98?

LJBY ∙ [cfcnã

ný`brd kb ãtd`ds bn prdkuftds F06 ( 6FD9) E05 ( ;E9D) D 0 38 (6FD9 + ;E9D) ? + ;

Bmbrflfld 3 Icgcnfbb gc sljulbntb bfucflön. Vljc gds pcsds qub sb lnklfcn. Icgcnfbb= Ob + E9D

Ob9D6 + E9

3. Bsfrlic bg ný`brd kb ãtd`ds kb fckc bgb`bntd qub ecy bn fckc gckd kb gc rbcfflön, csà scirã quì bgb`bntds nd bstãn icgcnfbckds. ný`brd kb ãtd`ds bn rbcftlvds 0 Ob


0 Ob

0

D

0

D

0

E

0

E

9. Bsfrlic bg ný`brd icgcnfbcrgd.

bn bg ãtd`d kb elbrrd (Ob), kbg gckd kb gds rbcftlvds, pcrc Ob + E9D

Ob9D6 + E9

Bsfrlic bg ný`brd

bn gc `dgìfugc kb cjuc (E 9D), kbg gckd kb gds

rbcftlvds, pcrc icgcnfbcr gds dxàjbnds. 9Ob + E9D

Ob9D6 + E9

Xdr ýgtl`d, bsfrlic bg ný`brd bn gc `dgìfugc kb elkröjbnd (E 9), kbg gckd kb gds prdkuftds, pcrc icgcnfbcr gds elkröjbnds. 9Ob + 6E9D

Ob9D6 +

E9

6. Fd`prubib bn gc tcigc qub gc bfucflön bstã icgcnfbckc= ný`brd kb ãtd`ds bn rbcftlvds 0 Ob


0 Ob

0

D

0

D

0

E

0

E


98:


Icgcnfbcr unc bfucflön fdnslstb bn iusfcr fdbolflbntbs nu`ìrlfds qub ecjcn qub bg ný`brd kb fckc tlpd kb ãtd`ds prbsbntbs bn gc rbcfflön quà`lfc sbc bg `ls`d bn gds rbcftlvds qub bn gds prdkuftds. ´Fö`d ditbnb`ds unc bfucflön icgcnfbckc4 Xrcftlfc`ds bg `ìtdkd kb tcntbd d `ìtdkd kb bnscyd y brrdr. Xcrc ditbnbr unc bfucflön icgcnfbckc, kbtbr`lnc`ds gds fdbolflbntbs qub nds kcn ný`brds ljucgbs kb fckc tlpd kb ãtd`d bn fckc gckd kb gc rbcfflön. Gds fdbolflbntbs sdn, jbnbrcg`bntb, ný`brds bntbrds. Vbjul`ds bstds pcsds= 3. Kbtbr`lnc`ds quì bgb`bntds nd bstãn icgcnfbckds. Gd pdkb`ds ecfbr pdr sl`pgb lnspbfflön d fdn gc cyukc kb unc tcigc. 9. Icgcnfbc`ds und pdr und gds bgb`bntds, bsfrlilbnkd un ný`brd bntbrd qub nds pbr`ltc ditbnbr bg `ls`d ný`brd kb ãtd`ds bn cìcs pcrtbs kb gc bfucflön. Gc sljulbntb bfucflön bstã icgcnfbckc, sbjýn gd lnklfcn gds fdbolflbntbskb fckc sustcnflc= 6NcDE + E6XD; ný`brd kb ãtd`ds bn rbcftlvds

Nc 0 6 (6NcDE) D 0 : (6NcDE + E6XD;) 6 + ; E 0 ? (6NcDE + E6XD;) 6 +6 X 0 3 (E6XD;)

Nc6XD; + 6E9D ný`brd kb ãtd`ds bn prdkuftds

Nc 0 6 (Nc6XD;) D 0 : (Nc6XD; + 6E9D) ; + 6 E 0 ? (6E9D) ? X 0 3 (Nc6XD;)

Lnvbstljub bn gc rbk... Xcrc prcftlfcr bg icgcnfbd kb bfucfldnbs y fdndfbr `ãs sdirb gc Gby kb Gcvdlslbr, pubkb fdnsugtcr gds sltlds= ettp=//www.bls.uvc.bs/~qjlntrd/jbnbrc.pep4tb`c0;&bmbr09 ettp=//www.oslfcnbt.fd`.cr/qul`lfc/jrcvl`btrlc/cp83Tjrcvl`btrlc.pep

985

LJBY ∙ [cfcnã

Cutdfdntrdg Cftlvlkck 3. Ybgcfldnb lnodr`cflön Ybggbnb bg fuckrd qub fd`pgbtc fdrrbftc`bntb fckc lnflsd. Vl nbfbsltc ecfbr fãgfugds, eãjcgd bn su fuckbrnd. 3)

Bn gc bfucflön 9E9 + D9

9E9D, bs fdrrbftd colr`cr qub=

Gc bfucflön bstã icgcnfbckc. Ecy qub icgcnfbcr gds `dgbs kb elkröjbnd `dgbfugcr. Ecy qub icgcnfbcr gds `dgbs kb dxàjbnd `dgbfugcr. 9)

Xcrc qub unc bfucflön quà`lfc bstì icgcnfbckc, bs nbfbscrld qub= Gc fcntlkck kb ãtd`ds kb fckc bgb`bntd sbc `cydr bn gds rbcftlvds. Gc fcntlkck kb ãtd`ds kb fckc bgb`bntd sbc `cydr bn gds prdkuftds. Gc fcntlkck kb ãtd`ds kb fckc bgb`bntd sbc ljucg bn rbcftlvds y prdkuftds.

6)

Bn gc bfucflön ]n + EFg ]nFg9 + E9 bg fdbolflbntb qub cfd`pcóc cg EFg y qub pbr`ltb icgcnfbcr gc bfucflön bs= 3 9 6

;)

Bn gc bfucflön NcEFD6 9Nc9FD6 + 9E9D + 9FD9 bg fdbolflbntb qub cfd`pcóc c NcEFD6 y qub pbr`ltb icgcnfbcr gc bfucflön bs= 9 6 ;

Cftlvlkck 9 Icgcnfbb pdr bg `ìtdkd kb tcntbd gcs sljulbntbs bfucfldnbs. Vljc gds pcsds qub cprbnklö bn gc sb`cnc. 3)

Icgcnfbb= EjD

Ej + D9

3. Bsfrlic bg ný`brd kb ãtd`ds kb fckc bgb`bntd qub ecy bn fckc gckd kb gc rbcfflön, csà scirã quì bgb`bntds nd bstãn icgcnfbckds. ný`brd kb ãtd`ds bn rbcftlvds

0Ej 0

D


0Ej 0

D Suà`lfc LL ∙ Vb`cnc 68

98<

9. Bsfrlic bg ný`brd icgcnfbcrgd.

bn bg ãtd`d kb Dxàjbnd (D), kbg gckd kb gds rbcftlvds, pcrc EjD

Ej + D

9

Cedrc tlbnb qub rbcfd`dkcr bg ný`brd kb ãtd`ds kb `brfurld (Ej). Bsfrlic bg ný`brd bn gc `dgìfugc kb `brfurld (Ej), kbggckd kb gds prdkuftds, pcrc icgcnfbcrgd. 9EjD

Ej + D9

6. Fd`prubib bn gc tcigc qub gc bfucflön bstã icgcnfbckc= ný`brd kb ãtd`ds bn rbcftlvds 0Ej 0Ej 0 9)

D

Icgcnfbb= Ir+ 9 EL

0 L

9


D

+ EIr

3. Bsfrlic bg ný`brd kb ãtd`ds kb fckc bgb`bntd qub ecy bn fckc gckd kb gc rbcfflön, csà scirã quì bgb`bntds nd bstãn icgcnfbckds. ný`brd kb ãtd`ds bn rbcftlvds 0 Ir 0 0

0 Ir

E L

0 0

9. Bsfrlic bg ný`brd fbcr bg ird`d.

E L

bn gc `dgìfugc kb EIr, kbg gckd kb gds prdkuftds, pcrc icgcnIr+ 9 EL

Bsfrlic bg ný`brd bg ydkd.


L +9

EIr

bn gc `dgìfugc kb EL, kbg gckd kb gds rbcftlvds, pcrc icgcnfbcr Ir +9

EL

L

9

+ 9EIr

6. Fd`prubib qub tdkds gds ãtd`ds bstãn icgcnfbckds= ný`brd kb ãtd`ds bn rbcftlvds 0 Ir 0 0

938

LJBY ∙ [cfcnã

0 Ir

E L

0 0

E L


6)

Icgcnfbb= Ic(DE)9 + E9VD;

IcVD; + E9D

3. Bsfrlic bg ný`brd kb ãtd`ds kb fckc bgb`bntd qub ecy bn fckc gckd kb gc rbcfflön, csà scirã quì bgb`bntds nd bstãn icgcnfbckds. ný`brd kb ãtd`ds bn rbcftlvds 0Ic


0Ic

0

V

0

V

0

D

0

D

0

E

0

E

9. Bsfrlic bg ný`brd bn gc `dgìfugc kb cjuc (E 9D), kbg gckd kb gds prdkuftds, pcrc icgcnfbcr bg elkröjbnd. Ic(DE)9 + E9VD;

IcVD; +

E9D

6. Fd`prubib qub tdkds gds ãtd`ds bstãn icgcnfbckds= ný`brd kb ãtd`ds bn rbcftlvds 0Ic

;)


0Ic

0

V

0

0

D

0

D

0

E

0

E

Icgcnfbb= FV9 + Fg9

V

FFg; + V9Fg9


0 0

F V 0 Fg

0 0


F V 0 Fg Suà`lfc LL ∙ Vb`cnc 68

933

9. Bsfrlic bg ný`brd

bn gc `dgìfugc kb fgdrd (Fg9) pcrc icgcnfbcr gc bfucflön. FV9 +

Fg9

FFg; + V9Fg9

6. Fd`prubib bn gc tcigc qub gc bfucflön bstã icgcnfbckc= ný`brd kb ãtd`ds bn rbcftlvds

F 0 3 FV9


F 0 3 FFg;

V 0 9 (FV9)

( 90V

0 Fg

V9Fg9)

0 Fg

Cftlvlkck 6 Icgcnfbb gcs bfucfldnbs y rbbsfràicgcs c gc pcr. [lbnb un bmb`pgd. 8)

Fu + CjND6

3)

FE; + D9

9)

FcFD6

6)

Ob9D6+ FD

;)

NE6 + D9

Fu(ND6)9 + Cj

Fu + 9CjND6

Fu(ND6)9 + 9Cj

FD9 + E9D FD9 + FcD ObD + FD 9 ND + E 9D

Cftlvlkck ;

Vuircyb gc bfucflön quà`lfc qub sb bnfubntrc icgcnfbckc fdrrbftc`bntb. [lbnb un bmb`pgd. 8) 3)

?L9D2 + 98IrO6

39LO2 + 32D9 + 38Ir9

6L9D2 + 38IrO6

2LO2 + :D9 + 2Ir9

CjND+ 6 NcFg

NcND

CjND+ 6 6NcFg 9)

NcND

Ob9(VD;)6+ AVFN (NE;)9FD6

6

+ 6CjFg

9A 6Ob(VFN)? + 6A9VD;

9NE6 + FD9 + E9D

;(NE;)9FD6

9NE6 + 6FD9 + 9E9D

;)

FcVlD6+ 5EO FcVlD6+ EO

E 9VlO? + FcO9 + 6E9D E 9VlO? + FcO9 + E9D

2)

X;D38 + @j(DE)9 X;D38 + ?@j(DE)9

939

+ CjFg

A 6Ob(VFN)? + A9VD;

Ob9(VD;)+ 6 39AVFN 6)

6

LJBY ∙ [cfcnã

@j6(XD;)9 + E9D 9@j6(XD;)9 + ?E9D


@dvl`lbntd `lstbrldsd Fdn bstb bxpbrl`bntd pdkrã disbrvcr qub gc rbcfflön bntrb bg ilfcridnctd kb sdkld y bg ãflkd cfìtlfd prdkufb bg jcs klöxlkd kb fcridnd, bntrb dtrds prdkuftds.


      

Rn orcsfd kb vlkrld kb idfc cnfec u dtrd rbflplbntb jrcnkb kb vlkrld. Xubkb sbr unc pbfbrc d un ogdrbrd. Rn pbkczd kb glmc Rnc pcgbtc Rnc fufecrltc pgãstlfc Flnfd idgltcs kb ncotcglnc 9 tczcs kb vlncjrb (ãflkd cfìtlfd) 2 dnzcs kb ilfcridnctd kb sdkld 9 tczcs kb cjuc rbpdsckc. Kbib kbmcrgc rbpdscr unc ndfeb cntbs kb uscrgc.

´Suì kbib ecfbr4 3. Bxc`lnb gcs idgcs kb ncotcglnc. Vl ìstcs oubrcn kb`cslckd glscs cg tcftd, gàmbgcs un pdfd pcrc qub sb vubgvcn ãspbrcs. 9. Bn bg orcsfd, prbpcrb unc `bzfgc kb 9 tczcs kb cjuc y 9 tczcs kb vlncjrb. Cóckc 38 fufecrckltcs kb ilfcridnctd kb sdkld. Cjltb ilbn gc `bzfgc y bfeb gcs idgltcs kb ncotcglnc. Cndtb sus disbrvcfldnbs. Juàbsb fdn bstcs prbjuntcs= c. ´Fuãg bs bg cspbftd kbg gàqulkd4 ´tlbnb iuriumcs4 écfb bobrvbsfbnflc4 i. ´Fuãg bs bg fd`pdrtc`lbntd kb gcs idgltcs kb ncotcglnc4 ´sb ùbvbn4 ´bn quì klrbfflön4 Gc bfucflön quà`lfc kb bstc rbcfflön bs= NcEFD6 + E;F9D9 ilfcridnctd kb sdkld

ãflkd cfìtlfd

FD9 + NcF9E6D9 + E9D klöxlkd kb cfbtctd fcridnd kb sdkld

cjuc

Gds prdkuftds qub sb ditlbnbn sdn unc scg (NcF 9E6D9) qub qubkc klsubgtc bn bg cjuc (E 9D) y klöxlkd kb fcridnd (FD 9) qub bs un jcs. Ybspdnkc= Kb bstds trbs prdkuftds (scg, cjuc y klöxlkd kb fcridnd), ´fuãg frbb qub prdkufb gcs iuriumcs bn bg gàqulkd4 Suà`lfc LL ∙ Vb`cnc 68

936



gdjrckd

rbjugcr

nd gdjrckd

Cspbftds c bvcgucr 3. Kbspuìs kb 9. bstuklcr... 6.

Fd`prubid qub gc `csc kb gds rbcftlvds bs ljucg c gc `csc kb gds prdkuftds bn unc bfucflön icgcnfbckc. Icgcnfbd gcs bfucfldnbs quà`lfcs fdn bg `ìtdkd kb tcntbd d kb bnscyd y brrdr. Bxpbrl`bntd gc odr`cflön kbg jcs klöxlkd kb fcridnd fd`d prdkuftd kb unc rbcfflön quà`lfc.


93;

LJBY ∙ [cfcnã

63

Bstbquld`btràc kb gcs rbcffldnbs quà`lfcs


932


Fdndfbr gds pdstugckds kb gc tbdràc ctö`lfc kb Kcgtdn y rbgcfldncrgds fdn gc bstbquld`btràc.



Fdnstrulr unc kbolnlflön kb bstbquld`btràc.



Ybfdndfbr bfucfldnbs icgcnfbckcs y bxtrcbr lnodr`cflön kb bggcs.



Ybsdgvbr prdigb`cs bstbquld`ìtrl fds `dg ‖ `dg y `csc ‖ `csc.



Bxpbrl`bntcr fdn bg jcs klöxlkd kb fcridnd (FD 9).




93?

¡Xcrc fd`bnzcr!

• Mden Kcgtdn= Bg flbntàolfd qub prdpusd "fdntcr" gds ãtd`ds


• Bstbquld`btràc= • `dg ‖ `dg • `csc ‖ `csc


• Rn jcs qub cpcjc bg oubjd

LJBY ∙ [cfcnã

¡Xcrc fd`bnzcr! Mde n Kcg tdn Bg flbntàolfd qub prdpusd ‗fdntcr‐ gds ãtd`ds Mden Kcgtdn oub un ncturcglstc, `ctb`ãtlfd y `btbdrögdjd irltãnlfd. Bntrb 3586 y 3585 kbscrrdggö unc tbdràc ctö`lfc fucntltctlvc, bs kbflr, unc tbdràc qub kld gds ounkc`bntds pcrc bxprbscr nu`ìrlfc`bntb unc fcntlkck kb ãtd`ds. Gds prlnflpcgbs pdstugckds kb gc tbdràc kb Kcgtdn oubrdn=

Mden Kcgtdn (3:??‖35;;) Flbntàolfd irltãnlfd

• Gds bgb`bntds bstãn fd`pubstds pdr ãtd`ds. • Gc sbpcrcflön y gc unlön kb ãtd`ds sb rbcglzc kurcntb gcs rbcffldnbs

quà`lfcs. Bn bstcs, nlnjýn ãtd`d sb frbc d sb kbstruyb. • Rn fd`pubstd quà`lfd bs bg rbsugtckd kb gc fdìlncflön kb ãtd`ds

kb kds d `ãs bgb`bntds bn unc prdpdrflön nu`ìrlfc sl`pgb. Fdn bstc tbdràc, sb pukd kbtbr`lncr qub un fd`pubstd purd slb`prb fdntlbnb gds `ls`ds bgb`bntds fdìlnckds bn gcs `ls`cs prdpdrfldnbs kb `csc y qub gds ãtd`ds kb un fd`pubstd sb fdìlncn bn prdpdrfldnbs olmcs. Xdr bmb`pgd, bg fcridnd y bg dxàjbnd odr`cn kds fd`pubstds= @dnöxlkd kb fcridnd= 3D + 3F

Klöxlkd kb fcridnd=

FD

9D + 3F

3 ãtd`d kb dxàjbnd sb fdìlnc slb`prb fdn 3 ãtd`d kb fcridnd pcrc odr`cr 3 `dgìfugc kb `dnöxlkd kb fcridnd.

FD 9

9 ãtd`ds kb dxàjbnd sb fdìlncn slb`prb fdn 3 ãtd`d kb fcridnd pcrc odr`cr 3 `dgìfugc kb klöxlkd kb fcridnd.

Jrcflcs c qub bstcs prdpdrfldnbs sb fu`pgbn slb`prb pcrc tdkds gds fd`pubstds, pdkb`ds fcgfugcr bg ný`brd kb `csc, bg ný`brd kb ãtd`ds, bg ný`brd kb `dgbs, btf. kb rbcftlvds y prdkuftds. [bxtd td`ckd y ckcptckd kb @drtl`br, F. Suà`lfc.

Gc rc`c kb gc quà`lfc qub sb bnfcrjc kb bstuklcr gcs prdpdrfldnbs bn gcs fucgbs gds bgb`bntds odr`cn fd`pubstds sb ggc`c bstbquld`btràc , nubstrd tb`c kb bstc sb`cnc.


93:


3. Bstbquld`btràc Gc bstbquld`btràc bs bg fãgfugd fucntltctlvd kb rbcftlvds y prdkuftds bn unc rbcfflön quà`lfc. Bs kbflr qub gc bstbquld`btràc sb bnfcrjc kb kbtbr`lncr gc fcntlkck kb fckc bgb`bntd d `dgìfugc qub pcrtlflpc bn unc rbcfflön. Bstuklcrb`ds gds fãgfugds `dg ‖ `dg y `csc ‖ `csc.

3.3 Fãgfugds `dg ‖ `dg Gcs rbgcfldnbs bstbquld`ìtrlfcs `dg ‖ `dg sb bstcigbfbn td`cnkd bn fubntc gds fdbflbntbs kb gc bfucflön quà`lfc icgcnfbckc. Bstc nds lnklfc gcs prdpdrfldnbs bn `dgbs bn gcs qub kbtbr`lnckcs sustcnflcs rbcffldncn y sb prdkufbn. Xdr bmb`pgd= Kbtbr`lnb`ds fuãntds `dgbs kb dxàjbnd `dgbfugcr (D9) sdn nbfbscrlds pcrc prdkuflr 3; `dgbs kb cjuc (E 9D), sbjýn gc bfucflön icgcnfbckc = 9E9 + D9

Ybfubrkb= Gds fdbflbntbs lnklfcn bg ný`brd kb ãtd`ds d `dgìfugcs kb fckc rbcftlvd d prdkuftd bn unc bfucflön quà`lfc. 9E9 + D9 9E9D

9E9D

Gc bfucflön lnklfc qub 9 `dgbs kb elkröjbnd `dgbfugcr (E9) fdn 3 `dg kb dxàjbnd `dgbfugcr (D9) prdkufbn 9 `dgbs kb cjuc (E9D). 3. Bstcigbfb`ds bg ocftdr kb fdnvbrslön= 3 `dg kb D9 d 9 `dgbs kb E9D 9 `dgbs kb E9D 3 `dg kb D 9

9. Bsfdjb`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc ditbnbr fd`d rbspubstc `dgbs kb D9= 3 `dg kb D 9 9 `dgbs kb E9D 6. Cpglfc`ds bg ocftdr kb fdnvbrslön= 3 `dg kb D 9 3; `dgbs kb E9D x 9 `dgbs kb E9D 0 : `dgbs kb D 9

;. Bsfrlil`ds gc rbspubstc= Vb nbfbsltcn : `dgbs kb D 9 pcrc prdkuflr 3; `dgbs kb E9D.

935

LJBY ∙ [cfcnã

Bmbrflfld 3 C.

Bsfrlic fdn sus pcgcircs unc kbolnlflön kb bstbquld`btràc. Xcrc ecfbrgd pubkb cpdycrsb bn gcs pcgcircs kbg fc`pd sb`ãntlfd.

`bklflön

fãgfugd

bstbquld`btràc

rbcfflön quà`lfc prdkuftds

I.

fcntlkck rbcftlvds

Kbtbr`lnb fuãntds `dgbs kb ãflkd fgdreàkrlfd (EFg) sdn nbfbscrlds pcrc prdkuflr 3: `dgbs kb fgdrurd kb `cjnbsld (@jFg9), sbjýn bstc bfucflön quà`lfc icgcnfbckc=

@j + 9EFg

@jFg9 + E9

Gc bfucflön lnklfc qub 3 `dg kb `cjnbsld (@j) rbcffldnc fdn 9 `dgbs kb ãflkd fgdreà krlfd (EFg) pcrc prdkuflr 3 `dg kb fgdrurd kb `cjnbsld (@jFg 9) y 3 `dg kb elkröjbnd `dgbfugcr (E 9). 3. Bstcigbzfc gds ocftdrbs kb fdnvbrslön= d 9. Bsfdmc bg ocftdr kb fdnvbrslön qub gb pbr`ltc ditbnbr fd`d rbspubstc `dgbs kb EFg= 9 `dgbs kb EFg 3 `dg kb @jFg9 6. Cpglqub bg ocftdr kb fdnvbrslön= 3: `dgbs kb @jFg9 x 9 `dgbs kb EFg 0 3 `dg kb @jFg9

`dgbs kb EFg

;. Bsfrlic gc rbspubstc= Vb nbfbsltcn

`dgbs kb EFg pcrc prdkuflr 3: `dgbs kb @jFg 9.


93<

¡Dtrd bmb`pgd! Kbtbr`lnb`ds bg ný`brd kb `dgbs kb btcnd (F9E?) qub sdn nbfbscrlds pcrc rbcffldncr fdn 3:.2 `dgbs kb dxàjbnd `dgbfugcr (D 9), kb cfubrkd c gc bfucflön icgcnfbckc= 9F9E? + :D9

;FD9 + ?E9D

3. Bstcigbfb`ds gds ocftdrbs kb fdnvbrslön bntrb bg ný`brd kb `dgbs kb btcnd y bg ný`brd kb `dgbs kb dxàjbnd `dgbfugcr= 9 `dgbs kb F9E? d : `dgbs kb D9 9 `dgbs kb F9E? : `dgbs kb D 9

9. Bsfdjb`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc ditbnbr fd`d rbspubstc `dgbs kb F9E?= 9 `dgbs kb F9E? : `dgbs kb D 9 6. Cpglfc`ds bg ocftdr kb fdnvbrslön= 3:.2 `dgbs kb D9 x 9 `dgbs kb F9E? 0 2 `dgbs kb F9E? : `dgbs kb D9

;. Bsfrlil`ds gc rbspubstc= Vdn nbfbscrlds 2 `dgbs kb F 9 E? pcrc rbcffldncr fdn 3:.2 `dgbs kb D 9. ¡Rn bmb`pgd `ãs! Fcgfugb fuãntds `dgbs kb c`dnlcfd (NE 6) sb ditlbnbn cg rbcffldncr 39 `dgbs kb elkröjbnd `dgbfugcr (E9), sbjýn gc bfucflön icgcnfbckc= N9 + 6E9

9NE6

Bstc bfucflön ùbstrc qub= • 3 `dg kb N9 + 6 `dgbs kb E 9 prdkufbn 9 `dgbs kb NE6 3. Bstcigbfb`ds gds ocftdrbs kb fdnvbrslön bntrb bg ný`brd kb `dgbs kb elkröjbnd `dgbfugcr (E9) y bg ný`brd kb `dgbs kb c`dnlcfd (NE 6)= 6 `dgbs kb E 9 d 9 `dgbs kb NE 6 9 `dgbs kb NE 6 6 `dgbs kb E9

998

LJBY ∙ [cfcnã

9. Bsfdjb`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc ditbnbr fd`d rbspubstc `dgbs kb NE6= 9 `dgbs kb NE 6 6 `dgbs kb E9 6. Cpglfc`ds bg ocftdr kb fdnvbrslön= 39 `dgbs kb E9 x 9 `dgbs kb NE 6 0 5 `dgbs kb NE6 6 `dgbs kb E9

;. Bsfrlil`ds gc rbspubstc= 39 `dgbs kb elkröjbnd `dgbfugcr (E 9) prdkufbn 5 `dgbs kb c`dnlcfd (NE6).

Bmbrflfld 9 Ybsubgvc bg prdigb`c bstbquld`ìtrlfd `dg ‖ `dg. Vljc gds pcsds qub cprbnklö. ´Fuãntds `dgbs kb öxlkd kb cgu`lnld (Cg9D6) sb odr`cn cg rbcffldncr ? `dgbs kb cgu`lnld (Cg), sbjýn gc sljulbntb bfucflön icgcnfbckc4

;Cg + 6D9

9Cg9D6

Gc bfucflön ùbstrc qub= • ; `dgbs kb Cg + 6 `dgbs kb D9 prdkufbn 9 `dgbs kb Cg9D6 3. Bstcigbzfc gds ocftdrbs kb fdnvbrslön bntrb bg ný`brd kb `dgbs kb cgu`lnld (Cg) y bg ný`brd kb `dgbs kb öxlkd kb cgu`lnld (Cg9D6)= ; `dgbs kb Cg d 9 `dgbs kb Cg9D6 9 `dgbs kb Cg9D6 ; `dgbs kb Cg 9. Bsfdmc bg ocftdr kb fdnvbrslön qub gb pbr`ltc ditbnbr fd`d rbspubstc `dgbs kb Cg9D6=


;. Bsfrlic gc rbspubstc=


993

3.9 Fãgfugds `csc ‖ `csc Gc rbgcflön bntrb gc `csc kb un rbcftlvd y gc `csc fdrrbspdnklbntb kb un prdkuftd bs orbfubntb bn quà`lfc. Bn gc prãftlfc, bn gcidrctdrlds b lnkustrlcs, `lkbn gcs sustcnflcs bn jrc`ds bn gujcr kb ecfbrgd bn `dgbs. Gds fãgfugds kbg cpcrtckd 3.3 y tdkd gd qub cprbnkl`ds kb `dg, `cscs `dgcrbs y bfucfldnbs quà`lfcs bn gcs sb`cncs 9:, 95 y 68 nds pbr`ltlrãn rbcglzcr fãgfugds kb `csc. Xdr bmb`pgd= ´Fuãntds jrc`ds kb fgdrurd kb fcgfld (FcFg9) sb ditlbnbn fucnkd rbcffldncn 92 jrc`ds kb fcgfld (Fc) fdn ãflkd fgdreàkrlfd (EFg)4

Gc bfucflön icgcnfbckc kb bstc rbcfflön bs= Fc + 9EFg

FcFg 9 + E9

Xdr bg bnunflckd scib`ds qub rbcffldncrdn 92 jrc`ds kb Fc y nbfbsltc`ds scibr fuãntds jrc`ds kb FcFg9 sb ditlbnbn. ´Fö`d gd cvbrljuc`ds4 Gc bfucflön nds lnklfc qub= • 3 `dg kb Fc + 9 `dgbs kb EFg prdkufbn 3 `dg kb FcFg9 + 3 `dg kb E9 Xrl`brd kbib`ds trcnsodr`cr c `dgbs gds jrc`ds kb fcgfld (Fc) qub nds kc bg prdigb`c. _bc`ds= 98

C

Fc

;8.3 j

3. Ybvlsc`ds bn gc tcigc pbrlöklfc gc `csc ctö`lfc kbg Fc= ;8.3 j/`dg. • Bstcigbfb`ds gds ocftdrbs kb fdnvbrslön= 3 `dg kb Fc ;8.3 j kb Fc

d ;8.3 j kb Fc 3 `dg kb Fc

• Gubjd bstcigbfb`ds bg ocftdr kb fdnvbrslön pcrc fcgfugcr fuãntds `dgbs kb fgdrurd fcgfld (FcFg 9) sb ditlbnbn c pcrtlr kb gds `dgbs kb Fc. 3 `dg kb Fc d 3 `dg kb FcFg9 3 `dg kb Fc 3 `dg kb FcFg9

• Olncg`bntb, fd`d nds plkbn jrc`ds, kbib`ds fcgfugcr gc `csc `dgcr kbg FcFg9 y bstcigbfbr gds ocftdrbs kb fdnvbrslön. 3 ãtd`d kb fcgfld x ;8.3 j/`dg

0

;8.3 j/`dg

9 ãtd`ds kb fgdrd x 62.2 j/`dg @csc `dgcr kbg FcFg 9=

0 + :3.8 j/`dg 333.3 j/`dg

3 `dg kb FcFg9 d 333.3 j kb FcFg9 333.3 j kb FcFg9 3 `dg kb FcFg9

999

LJBY ∙ [cfcnã

9. Bg prdigb`c nds kc jrc`ds kb Fc, pdr gd tcntd bsfdjb`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc ditbnbr fd`d rbspubstc `dgbs kb Fc= 3 `dg kb Fc ;8.3 j kb Fc

Gubjd kbib`ds ditbnbr `dgbs kb FcFg 9, qub bs gc sustcnflc iusfckc. Bsfdjb`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc ditbnbr `dgbs kb FcFg 9. 3 `dg kb FcFg9 3 `dg kb Fc

Olncg`bntb, fd`d nds plkbn jrc`ds kb FcFg 9, iusfc`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc fdnvbrtlr `dgbs bn jrc`ds= 333.3 j kb FcFg9 3 `dg kb FcFg9

6. Cpglfc`ds gds ocftdrbs kb fdnvbrslön qub bsfdjl`ds pcrc ditbnbr jrc`ds kb FcFg9=

92 j kb Fc

3 `dg Fc

( ;8.3 j kb Fc ) (

bgl`lnc`ds j kb Fc y nds qubkc `dgbs kb Fc

3 `dg FcFg9 3 `dg Fc

)(

333.3 j FcFg9 3 `dg FcFg9

) 0 ?<.6 j FcFg

9

bgl`lnc`ds `dgbs bgl`lnc`ds `dgbs kb kb Fc y nds qubkcn FcFg 9 y nds qubkcn `dgbs kb FcFg 9 jrc`ds kb FcFg 9

;. Bsfrlil`ds gc rbspubstc= Vb ditlbnbn ?<.6 j FcFg9 fucnkd rbcffldncn 92 jrc`ds kb Fc.

Bmbrflfld 6 Ybggbnb bg fuckrd qub fdrrbspdnkb c gc rbspubstc fdrrbftc. 3)

Vl qulbrb fdnvbrtlr 38.8 j kb bstcód (Vn) c `dgbs, ´quì ocftdr `dgcr kbib uscr4 335.: j kb Vn 3 `dg kb Vn

9)

3 `dg kb Vn 335.: j kb Vn

3 `dg kb Vn 9 `dg kb E9

Vl qulbrb fdnvbrtlr 2.;2 `dgbs kb pdgdnld (Xd) c jrc`ds, ´quì ocftdr `dgcr kbib uscr4 98<.8 j kb Xd 3 `dg kb Xd

3 `dg kb Xd 98<.8 j kb Xd

3 `dg kb Xd 2 `dg kb R


996

_bc`ds dtrd bmb`pgd= Fcgfugb gc `csc kb elkröjbnd `dgbfugcr (E9) qub rbcffldnc fdn 38 jrc`ds kb dxàjbnd `dgbfugcr (D 9) pcrc ditbnbr cjuc (E9D).

Gc bfucflön icgcnfbckc kb bstc rbcfflön bs= 9E9 + D9

9E9D

38 jrc`ds kb dxàjbnd `dgbfugcr (D 9) rbcffldncn fdn unc fcntlkck kbsfdndflkc kb jrc`ds kb elkröjbnd `dgbfugcr (E 9). ´Fö`d cvbrljuc`ds bg vcgdr kb gc fcntlkck kbsfdndflkc kb jrc`ds kb elkröjbnd `dgbfugcr4 Gc bfucflön nds lnklfc qub= • 3 `dg kb E9 rbcffldnc fdn 3 `dg kb D9 pcrc prdkuflr 9 `dgbs kb E9D. 3. Bstcigbfb`ds gds ocftdrbs kb fdnvbrslön bntrb gc fcntlkck kb `dgbs kb elkröjbnd (E9) y dxàjbnd (D9) qub rbcffldncn= 9 `dgbs kb E9 d 3 `dg kb D 9 3 `dg kb D9 9 `dgbs kb E9

• Fd`d nds plkbn jrc`ds, tcìlìn nbfbsltc`ds fcgfugcr gc `csc `dgcr kb E9 y gc `csc `dgcr kb D 9. Lnlflc`ds fdn gc `csc `dgcr kb E 9. 9 ãtd`ds kb elkröjbnd x 3.8 j/`dg 0 9.8 j/`dg

@csc `dgcr kbg E9= 9.8 j/`dg Bstcigbfb`ds gds ocftdrbs kb fdnvbrslön= 3 `dg kb E 9 d 9.8 j kb E9 9.8 j kb E9 3 `dg kb E 9

• Cedrc fcgfugc`ds gc `csc `dgcr kb D9= 9 ãtd`ds kb dxàjbnd x 3?.8 j/`dg 0 69.8 j/`dg

@csc `dgcr kbg D9= 69.8 j/`dg Bstcigbfb`ds gds ocftdrbs kb fdnvbrslön= 3 `dg kb D 9 d 69.8 j kb D9 69.8 j kb D9 3 `dg kb D 9

99;

LJBY ∙ [cfcnã

9. Bg prdigb`c nds kc jrc`ds kb D9, csà qub bsfdjb`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc ditbnbr fd`d rbspubstc `dgbs kb D 9= 3 `dg kb D 9 69.8 j kb D9

Gubjd kbib`ds ditbnbr `dgbs kb E9, qub bs gc sustcnflc iusfckc. Bsfdjb`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc ditbnbr `dgbs kb E 9. 9 `dgbs kb E9 3 `dg kb D 9

Olncg`bntb, fd`d nds plkbn jrc`ds kb E9, iusfc`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc fdnvbrtlr `dgbs bn jrc`ds= 9.8 j kb E9 3 `dg kb E9

6. Cpglfc`ds gds ocftdrbs kb fdnvbrslön qub bsfdjl`ds pcrc ditbnbr jrc`ds kb E9= 38 j kb D

9

3 `dg kb D 9 `dgbs kb E 9.8 j kb E 0 3.92 j E ( 69.8 j kb D ) ( 3 `dg kb D ) ( 3 `dg kb E ) 9

9

bgl`lnc`ds j kb D9 y nds qubkcn `dgbs kb D 9

9

9

9

bgl`lnc`ds `dgbs kb D9 y nds qubkcn `dgbs kb E 9

9

9

bgl`lnc`ds `dgbs kb E 9 y nds qubkcn jrc`ds kb E 9

;. Bsfrlil`ds gc rbspubstc= 38 jrc`ds kb D9 rbcffldncn fdn 3.92 jrc`ds kb E 9 pcrc prdkuflr cjuc.

Bmbrflfld ; Ybggbnb bg fuckrd qub fdrrbspdnkb c gc rbspubstc fdrrbftc. 3)

Bn gc rbcfflön 9Nc + Fg9 9NcFg, ´quì ocftdr `dgcr kbib uscr pcrc fdnvbrtlr `dgbs kb NcFg c pcrtlr kb `dgbs kb Fg 94 9 `dgbs kb Nc 3 `dg kb Fg9

9)

3 `dg kb Fg9 9 `dgbs kb NcFg

9 `dgbs kb NcFg 3 `dg kb Fg9

Vl qulbrb fdnvbrtlr 3.;92 `dgbs kb crsìnlfd (Cs) c jrc`ds, ´quì ocftdr `dgcr kbib uscr4 :;.< j kb Cs 3 `dg kb Cs

3 `dg kb Cs :;.< j kb Cs

: `dg kb Cs 5 `dg kb Cf


992

¡Rn bmb`pgd `ãs! ´Fuãntds jrc`ds kb fcriurd kb fcgfld (FcF 9) sdn nbfbscrlds pcrc ditbnbr : jrc`ds kb cfbtlgbnd (F 9E9)4

Gc bfucflön icgcnfbckc kb bstc rbcfflön bs= FcF9 + 9E9D

Fc(DE)9 +F9E9

Rnc fcntlkck kbsfdndflkc kb jrc`ds kb fcriurd kb fcgfld (FcF9) rbcffldncn pcrc prdkuflr : jrc`ds kb cfbtlgbnd (F9E9). ´Fö`d cvbrljuc`ds bg vcgdr kb gc fcntlkck kbsfdndflkc kb jrc`ds kb (FcF )4 9

Bstc bfucflön nds lnklfc qub= • 3 `dg kb FcF9 rbcffldnc pcrc prdkuflr 3 `dg kb F9E9 3. Bstcigbfb`ds gds ocftdrbs kb fdnvbrslön bntrb gc fcntlkck kb `dgbs kb fcriurd kb fcgfld qub rbcffldncn y gc fcntlkck kb `dgbs kb cfbtlgbnd prdkuflkd= 3 `dg kb FcF9 d 3 `dg kb F 9E9 3 `dg kb F 9E9 3 `dg kb FcF9 • Fd`d nds plkbn jrc`ds, nbfbsltc`ds fcgfugcr gc `csc `dgcr kb FcF9 y gc `csc `dgcr kb F 9E9. @csc `dgcr kb FcF 9= 3 ãtd`d kb fcgfld x ;8.3 j/`dg 0 ;8.3 j/`dg 9 ãtd`ds kb fcridnd x 39.8 j/`dg 0 + 9;.8 j/`dg

@csc `dgcr kbg FcF9= ?;.3 j/`dg Bstcigbfb`ds gds ocftdrbs kb fdnvbrslön= 3 `dg kb FcF9 d ?;.3 j kb FcF9 ?;.3 j kb FcF9 3 `dg kb FcF9

• Fcgfugc`ds gc `csc `dgcr kb F9E9= 9 ãtd`ds kb fcridnd x 39.8 j/`dg 0 9;.8 j/`dg 9 ãtd`ds kb elkröjbnd x 3.8 j/`dg 0 + 9.8 j/`dg @csc `dgcr kbg F9E9= 9?.8 j/`dg

Bstcigbfb`ds gds ocftdrbs kb fdnvbrslön= 3 `dg kb F9E9 d 9?.8 j kb F9E9 9?.8 j kb F9E9 3 `dg kb F 9E9

9. Bg prdigb`c nds kc jrc`ds kb F9E9. Bsfdjb`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc ditbnbr fd`d rbspubstc `dgbs F9E9= 3 `dg kb F9E9 9?.8 j kb F9E9

99?

LJBY ∙ [cfcnã

Gubjd kbib`ds ditbnbr `dgbs kb FcF9, qub bs gc sustcnflc iusfckc. Bsfdjb`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc ditbnbr `dgbs kb FcF 9. 3 `dg kb FcF9 3 `dg kb F9E9

Olncg`bntb, fd`d gd qub nds prbjuntcn bs jrc`ds kb FcF 9, iusfc`ds bg ocftdr kb fdnvbrslön qub nds pbr`ltc fdnvbrtlr `dgbs bn jrc`ds. ?;.3 j kb FcF9 3 `dg kb FcF9

6. Cpglfc`ds gds ocftdrbs kb fdnvbrslön qub bsfdjl`ds pcrc ditbnbr jrc`ds kb FcF9= : j kb F 9E9

3 `dg kb F E 3 `dg kb FcF ?;.3 j kb FcF 0 3:.9? j FcF ( 9?.8 j kb F E )( 3 `dg kb F E )( 3 `dg kb FcF ) 9 9

9

9

9 9

9 9

9

9

;. Bsfrlil`ds gc rbspubstc= Vb nbfbsltcn 3:.9? jrc`ds kb fcriurd kb fcgfld (FcF9) pcrc ditbnbr : jrc`ds kb cfbtlgbnd (F9E9).

Bmbrflfld 2 Ybsubgvc bg prdigb`c bstbquld`ìtrlfd `csc ‖ `csc. Vljc gds pcsds qub cprbnklö. ´Suì `csc kb `cjnbsld sb nbfbsltc pcrc qub rbcffldnb fdn 38 j kb nltröjbnd4

Gc bfucflön icgcnfbckc kb bstc rbcfflön bs= 6@j + N9

@j6N9

Rnc fcntlkck kbsfdndflkc kb jrc`ds kb `cjnbsld (@j) rbcffldncn fdn 38 jrc`ds kb nltröjbnd `dgbfugcr (N9). ´Fö`d cvbrljuc bg vcgdr kb gc fcntlkck kb jrc`ds kb `cjnbsld4 Bstc bfucflön lnklfc qub= • 6 `dgbs kb @j rbcffldncn fdn 3 `dg kb N9 3. Bstcigbzfc gds ocftdrbs kb fdnvbrslön bntrb gc fcntlkck kb `dgbs kb `cjnbsld y `dgbs kb nltröjbnd `dgbfugcr= d


99:

Fd`d gd qub plkbn bs jrc`ds, tcìlìn nbfbsltc fcgfugcr gc `csc `dgcr kb @j y gc `csc `dgcr kb N9= @csc `dgcr kb @j= Bstcigbzfc gds ocftdrbs kb fdnvbrslön= d @csc `dgcr kb N9= Bstcigbzfc gds ocftdrbs kb fdnvbrslön= d 9. Bg prdigb`c kc jrc`ds kb N 9. Bsfdmc bg ocftdr kb fdnvbrslön qub gb pbr`ltc ditbnbr fd`d rbspubstc `dgbs kb N9=

Gubjd kbib ditbnbr `dgbs kb @j, qub bs gc sustcnflc iusfckc. Bsfdmc bg ocftdr kb fdnvbrslön qub gb pbr`ltc ditbnbr `dgbs kb @j=

Olncg`bntb, fd`d gd qub prbjuntcn bs jrc`ds kb @j, iusqub bg ocftdr kb fdnvbrslön qub gb pbr`ltc fdnvbrtlr `dgbs bn jrc`ds=

6. Cpglqub gds ocftdrbs kb fdnvbrslön qub bsfdjlö pcrc ditbnbr jrc`ds kb @j= 38.8 j kb N9 x

3 `dg kb N9 6 `dgbs kb @j 9;.6 j kb @j x x 0 95.8 j kb N 3 `dg kb N 3 `dg kb @j 9

;. Bsfrlic gc rbspubstc=

995

LJBY ∙ [cfcnã

9

j @j

Ybsu`bn 3.

Gc bstbquld`btràc bs bg fãgfugd fucntltctlvd kb rbcftlvds y prdkuftds bn unc rbcfflön quà`lfc.

3.3 Fãgfugds `dg ‖ `dg Xcrc rbcglzcr fãgfugds bstbquld`ìtrlfds `dg ‖ `dg sb nbfbsltc= • Disbrvcr gc bfucflön quà`lfc icgcnfbckc. Vl nd bstuvlbrc icgcnfbckc, ecy qub ecfbrgd. • Rscr gds fdbolflbntbs kb gc bfucflön icgcnfbckc. Bstds lnklfcn gcs prdpdrfldnbs bn `dgbs bn gcs qub gcs sustcnflcs rbcffldncn y sb prdkufbn. • Bsfdjbr un ocftdr kb fdnvbrslön qub pbr`ltc ditbnbr bg ný`brd kb `dgbs qub nds prbjuntcn. • Cpglfcr bg ocftdr kb fdnvbrslön pcrc ditbnbr gc rbspubstc. • Bsfrlilr gc rbspubstc. 3.9 Fãgfugds `csc ‖ `csc Xcrc rbcglzcr fãgfugds bstbquld`ìtrlfds `csc ‖ `csc sb nbfbsltc= • Disbrvcr gc bfucflön quà`lfc icgcnfbckc. Vl nd bstuvlbrc icgcnfbckc, ecy qub ecfbrgd. • Rscr gds fdbolflbntbs kb gc bfucflön icgcnfbckc pcrc kbtbr`lncr gds ocftdrbs kb fdnvbrslön bn `dgbs kb gds rbcftlvds y kb gds prdkuftds qub nds lntbrbscn. Xcrc bstd nbfbsltcrb`ds= • Bstcigbfbr ocftdrbs kb fdnvbrslön y bsfdjbr und qub pbr`ltc fdnvbrtlr c `dgbs gc `csc qub kcn. • Bstcigbfbr ocftdrbs kb fdnvbrslön `dgbs ‖ `dgbs y bsfdjbr bg qub pbr`ltc fdnvbrtlr gc sustcnflc qub nds kcn bn gc sustcnflc iusfckc. • Ybfdnvbrtlr gds vcgdrbs cntbrldrbs bn `csc y pcrc bsd ecy qub bstcigbfbr dtrd ocftdr kb fdnvbrslön `dgbs ‖ `csc `dgcr y bsfdjbr und qub pbr`ltc ditbnbr bg ný`brd kb jrc`ds qub prbjuntcn. • Cpglfcr gds ocftdrbs kb fdnvbrslön pcrc ditbnbr gc rbspubstc. • Bsfrlilr gc rbspubstc.


99<

Cutdfdntrdg Cftlvlkck 3. Ybgcfldnb lnodr`cflön Ybggbnb bg fuckrd kb gc dpflön fdrrbftc pcrc fckc pgcntbc`lbntd. 3)

´Fuãg kb gcs sljulbntbs bfucfldnbs bstã icgcnfbckc4 @j + D

9

@jD

N9 + E9 NE6 Fc(DE)9 + FD9 9)

FcFD6 + E9D

´Fuãg colr`cflön bs vãglkc rbspbftd kb gc bfucflön= ;Cg + 6L9

9Cg9L6 4

Ybcffldncn ljucg fcntlkck kb `dgbs kb cgu`lnld y ydkd Bn tdtcg, ecy ljucg fcntlkck kb ãtd`ds bn gds rbcftlvds qub bn gds prdkuftds Nd bstã icgcnfbckc 6)

Vbjýn gc bfucflön icgcnfbckc, ´fuãntds `dgbs kb elkröjbnd `dgbfugcr sb odr`cn4 ?EFg + 9Cg

9CgFg

6

+ 6E9

Kds [rbs Vbls ;)

Vbjýn gc bfucflön icgcnfbckc, ´fuãntds `dgbs kb dxàjbnd `dgbfugcr (D9) sb odr`cn4 guz sdgcr

?FD9 + ?E9D

F?E39D? + ?D9

Rnd Kds Vbls 2)

´Fuãg colr`cflön bs vãglkc rbspbftd kb gc sljulbntb bfucflön4 9EFg + Fc

FcFg

9

+ E9

Ybcffldncn ljucg fcntlkck kb `dgbs kb ãflkd fgdreàkrlfd y fcgfld Bstã icgcnfbckc Nd bstã icgcnfbckc

968

LJBY ∙ [cfcnã

Cftlvlkck 9. Ybsubgvc prdigb`cs bstbquld`ìtrlfds Ybsubgvc bn su fuckbrnd gds sljulbntbs prdigb`cs bstbquld`ìtrlfds. Fucnkd sbc pdsligb, kì su rbspubstc fdn 3 florc kbfl`cg. 3)

´Fuãntds `dgbs kb E9 sb ditlbnbn cg kbsfd`pdnbr 8.:2 `dgbs kb cjuc, sbjýn gc bfucflön= E9D E9 + D94 Gc bfucflön nd bstã icgcnfbckc. [lbnb qub icgcnfbcrgc.

9)

Bg elkröxlkd kb sdkld (NcDE) sb usc pcrc ocirlfcr mcidnbs. Bstb elkröxlkd sb pubkb ditbnbr sbjýn gd lnklfc gc bfucflön= Fc(DE) 9 + Nc9FD6 NcDE + FcFD 6 Fcgfugb fuãntds jrc`ds kb NcDE pubkbn ditbnbrsb c pcrtlr kb 288 j kb Fc(DE)9 y suolflbntb fcridnctd kb sdkld (Nc9FD6). Gc bfucflön nd bstã icgcnfbckc. [lbnb qub icgcnfbcrgc.

6)

Bg `brfurld `btãglfd c tb`pbrcturc cìlbntb bs gàqulkd, fd`d bn gds tbr`ö`btrds fgànlfds, y pubkb ditbnbrsb c pcrtlr kbg öxlkd `brfýrlfd, sbjýn gc bfucflön icgcnfbckc= 9EjD

9Ej + D9

´Fuãntds jrc`ds kb `brfurld (Ej) sb pubkbn ditbnbr sl sb kbsfd`pdnbn 9.8 jrc`ds kb öxlkd `brfýrlfd (EjD)4 ;)

Gcs idgscs kb clrb pcrc cutd`övlg sb lnogcn fucnkd sb kbsfd`pdnb rãplkc`bntb czlkc kb sdkld, (NcN6), bn gds bgb`bntds qub gc fd`pdnbn. Gc rbcfflön icgcnfbckc bs= 9NcN6

9Nc + 6N

9

´Fuãntds jrc`ds kb czlkc kb sdkld (NcN 6) sb nbfbsltcn pcrc odr`cr 2.8 j kb nltröjbnd jcsbdsd (N9)4 2)

Bg FD9 qub gds cstrdncutcs bxecgcn sb bxtrcb kb gc ct`ösobrc kb gc ncvb bspcflcg pdr `bkld kb unc rbcfflön fdn ADE. Gc bfucflön icgcnfbckc bs= FD+ 9 9ADE

A 9FD6 + E9D

´Fuãntds j kb FD9 sb pubkbn bxtrcbr fdn 3888 j kb ADE4 ?)

Bg dftcnd (F5E35) sb qub`c kb cfubrkd fdn gc sljulbntb bfucflön= 9F5E35 + 92D9

3?FD9 + 35E9D

´Fuãntds jrc`ds kb FD 9 sb prdkufbn fucnkd sb qub`cn 2.8 j kb F5E354 :)

Bg sdkld (Nc) bs un prdkuftd sbfunkcrld kb gc rbcfflön qub lnogc gcs idgscs kb clrb pcrc cutd`övlg. Bg sdkld rbcffldnc fdn nltrctd kb pdtcsld (AND 6) qub sb cjrbjc cg fdntbnlkd kb gc idgsc, sbjýn gc bfucflön icgcnfbckc= 38Nc + 9AND6 A9D + 2Nc9D + N9 ´Fuãntds jrc`ds kb AND6 sb nbfbsltcn pcrc bgl`lncr 2.8 j kb Nc4

5)

´Fuãntds jrc`ds kb E9D sb odr`cn c pcrtlr kb gc fdnvbrslön tdtcg kb 69.8 j kb D 9 bn prbsbnflc kb E9, sbjýn gc bfucflön 9E9 + D9 9E9D4 Suà`lfc LL ∙ Vb`cnc 63

963


Rn jcs qub cpcjc bg oubjd Nd tdkds gds jcsbs tlbnbn gc `ls`c kbnslkck, bs kbflr qub nd tdkds tlbnbn gc `ls`c `csc fdn rbspbftd c su vdgu`bn. Bstb bs bg fcsd kbg klöxlkd kb fcridnd (FD9), bg jcs qub prdkuflrã bn bstb bxpbrl`bntd.


unc idgsltc kb ilfcridnctd kb sdkld



tcpön kb fdrfed kb tc`cód ckbfuckd pcrc tcpcr unc idtbggc pgãstlfc kb 288 `g



unc pcmlggc kb pgãstlfd kurd



sbrvlggbtcs kb pcpbg



unc idtbggc pgãstlfc kb 288 `g gl`plc y sbfc



`bklc tczc kb vlncjrb



un pbkczd kb elgd



unc fcnkbgc

 

oösodrds un kbscr`ckdr d un fufelggd olgdsd kb puntc olnc.



gãplz



glirbtc kb fc`pd

´Suì kbib ecfbr4 • [d`b unc sbrvlggbtc kb pcpbgy ãircgc kbg tdkd kb odr`c qub qubkb fuckrckc. Bfeb bn bg fbntrd kb gc sbrvlggbtc ; fufecrckltcs kb ilfcridnctd. Flìrrbgc pdr gds bxtrb`ds pcrc odr`cr unc idgsltc. Gubjd c`crrb gds bxtrb`ds fdn bg elgd y csbjýrbsb qub qubkb ùy ilbn fbrrckc. • Kbspuìs vlbrtc bn gc idtbggc 2 fufecrckcs kb vlncjrb. • [d`b bg fdrfed y ecjc un cjumbrd pbqubód pdr bg qub bntrb gc pcmlggc sln qub sb kdigb. Xcrc cirlr bg cjumbrd utlglfb un kbstdrnlggckdr d bg fufelggd kb puntc olnc. Bg cjumbrd kbib trcspcscr tdkd bg fdrfed pcrc qub pubkc bntrcr gc pcmlggc.

969

LJBY ∙ [cfcnã

• [d`b gc idgsltc kb ilfcridnctd b lntrdkýzfcgc bn gc idtbggc kb odr`c qub fubgjub (fdn unc pcrtb kbg elgd oubrc) y qub nd tdqub bg vlncjrb. Gubjd lntrdkuzfc gc pcmlggc bn bg fdrfed y tcpb gc idtbggc. Disbrvb bg kliumd. Kbib qubkcr csà= pcmlggc fdrfed idgsc fdn ilfcridnctd

vlncjrb

• Xdr ýgtl`d pcrc scibr sl bg bxpbrl`bntd ounfldnc, bnflbnkc unc fcnkbgc. • [cpb fdn bg kbkd gc pcmlggc sumbtcnkd gc idtbggc cg `ls`d tlb`pd. @bzfgb bg ilfcridnctd fdn bg vlncjrb y cjltb, sln kbstcpcr gc pcmlggc. • Gubjd qultb bg kbkd y prdybftb bg jcs qub scgb kb gc idtbggc sdirb gc vbgc bnfbnklkc. Bsfrlic sus disbrvcfldnbs bn gc glirbtc kb fc`pd.

´Suì sufbkb4 Gc rbcfflön quà`lfc bntrb bg ilfcridnctd (unc icsb) y bg vlncjrb (ãflkd) odr`c klöxlkd kb fcridnd qub ggbnc bg rbflplbntb y scgb pdr gc pcmlggc. Bg klöxlkd kb fcridnd —dfupc‐ bg gujcr kbg dxàjbnd. Fd`d dxàjbnd pbr`ltb sb prdkuzfc bg oubjd, slnsdn dxàjbnd ggc`c sb cpcjc. jcsbs qub cftýcnbgfd`d bg klöxlkd kbqub fcridnd y cpcjcn bg oubjd gds qubgcsb utlglzcn bn gds Gds bxtlnjulkdrbs lnkustrlcgbs.

Lnvbstljub bn gc rbk... Bn bstcs kds klrbffldnbs kb lntbrnbt pdkrã cprbnkbr `ãs sdirb bg fdntbnlkd kb bstc sb`cnc. Bstbquld`btràc kb rbcffldnbs quà`lfcs= ettp=//pgctbc.pntlf.`bf.bs/p`crtl3/bkufcfldn/prl`brdTicfe/bstbquld`btrlc/rbcffldnbs.et` Bxtlntdrbs kb b`brjbnflc= ettp=//bs.wlalpbklc.drj/wlal/CjbntbTbxtlntdrTkbTlnfbnklds


966



gdjrckd

rbjugcr

nd gdjrckd


Fdndzfd gds pdstugckds kb gc tbdràc ctö`lfc kb Kcgtdn y gds rbgcfldnd fdn gc bstbquld`btràc.

9.

Fdnstruyd unc kbolnlflön kb bstbquld`btràc.

Kbspuìs kb 6. bstuklcr... ;. 2.

Ybfdndzfd bfucfldnbs icgcnfbckcs y bxtrcljd lnodr`cflön kb bggcs. Ybsubgvd prdigb`cs bstbquld`ìtrlfds `dg ‖ `dg y `csc ‖ `csc. Bxpbrl`bntd fdn bg jcs klöxlkd kb fcridnd.


96;

LJBY ∙ [cfcnã

69

Vdgufldnbs


962


Fdndfbr cgjunds `ìtdkds oàslfds pcrc gc sbpcrcflön kb `bzfgcs.



Lkbntlolfcr sustcnflcs ed`djìnbcs.



Ybfdndfbr gcs fcrcftbràstlfcs kb unc sdguflön.



Lkbntlolfcr sdgutd y sdgvbntb bn unc sdguflön.



Fgcslolfcr sdgufldnbs pdr su bstckd kb cjrbjcflön y



pdr su fdnfbntrcflön. Fcgfugcr gc fdnfbntrcflön kb unc sdguflön bn pdrfbntcmb `csc ‖ `csc y vdgu`bn ‖ vdgu`bn.



Bxpbrl`bntcr pcrc kbtbr`lncr quì `bzfgcs odr`cn sdgufldnbs.




• Gcs `bzfgcs sb pubkbn sbpcrcr

Vdgufldnbs=



96?

LJBY ∙ [cfcnã

• • • •

Fgcslolfcflön kb gcs sdgufldnbs Fdnfbntrcflön kb unc sdguflön Xdrfbntcmb `csc ‖ `csc (%`/`) Xdrfbntcmb vdgu`bn ‖ vdgu`bn (%v/v)

• ´Vb `bzfgcn d nd sb `bzfgcn4

¡Xcrc fd`bnzcr! Gcs `bzfgcs sb pubkbn sbpcrcr Bn gc sb`cnc 6 cprbnkl`ds qub tdkd gd qub bxlstb c nubstrd cgrbkbkdr sb `cnlolbstc bn odr`c kb sustcnflcs. Bg cjuc, gc scnjrb, gds `btcgbs… tdkcs sdn sustcnflcs klstlntcs. Xcrc bstuklcrgcs, gcs fgcslolfc`ds bn= •

Vustcnflcs purcs= `ctbrlcgbs kb fd`pdslflön quà`lfc kbolnlkc, fd`d bg elbrrd (Ob), bg cjuc (E 9D), gc jgufdsc (F ?E39D? ), btf.

•

@bzfgcs= fdìlncflön kb kds d `ãs sustcnflcs purcs qub nd rbcffldncn quà`lfc`bntb bntrb sà. Gcs `bzfgcs pubkbn sbr=

Ebtbrdjìnbcs= `bzfgcs qub prbsbntcn kds d `ãs ocsbs y unc klstrliuflön lrrbjugcr kb sus prdplbkckbs. Vdn `bzfgcs ebtbrdjìnbcs= czuorb fdn cjuc, cg`lkön fdn cgfdedg, cfbltb fdn cjuc, btf. Ed`djìnbcs= `bzfgcs qub prbsbntcn unc sdgc ocsb y unc klstrliuflön rbjugcr kb sus prdplbkckbs oàslfcs y quà`lfcs. Vdn `bzfgcs ed`djìnbcs= cjuc fdn czýfcr, fgdrdodr`d fdn ìtbr, scg bn gc scnjrb, jgöiugds igcnfds bn glnoc, btf. Gc ocsb kb unc `bzfgc bs gc pdrflön ed`djìnbc qub pubkb sbpcrcrsb `bfãnlfc`bntb, bs kbflr, `bklcntb bg usd kb cgjunc tìfnlfc. Fdndzfc`ds gcs `ãs fdùnbs=

Kbstlgcflön= fdnslstb bn sbpcrcr unc sustcnflc kb dtrc pdr `bkld kbg fcgdr, bn rbflplbntbs bspbflcgbs. Gcs sustcnflcs pubkbn sbr gàqulkds, söglkds klsubgtds bn gàqulkd d jcsbs glfuckds kb unc `bzfgc. Gcs klstlntcs sustcnflcs sb sbpcrcn pdr su puntd kb biugglflön (tb`pbrcturc c gc qub elbrvb). Xdr bmb`pgd, sb pubkb kbstlgcr cgfdedg kb unc `bzfgc kb cgfdedg y cjuc.

`bzfgc kb cgfdedg y cjuc

cgfdedg

Bvcpdrcflön= fdnslstb bn fcgbntcr gc `bzfgc ecstc bg puntd kb biugglflön kb und kb gds fd`pdnbntbs y kbmcrgd ebrvlr ecstc qub sb bvcpdrb tdtcg`bntb. Bstb `ìtdkd sb b`pgbc fucnkd nd tbnb`ds lntbrìs bn utlglzcr bg fd`pdnbntb bvcpdrckd. Gds dtrds fd`pdnbntbs qubkcn bn bg bnvcsb. Suà`lfc LL ∙ Vb`cnc 69

96:

Rn bmb`pgd kb tìfnlfc kb bvcpdrcflön sb kc bn gcs scglncs= sb ggbncn bndr`bs bìcgsbs fdn cjuc kb `cr, y sb kbmcn pdr `bsbs, ecstc qub sb bvcpdrc bg cjuc. Bg `ctbrlcg söglkd fdntlbnb nu`brdscs scgbs= fgdrurd kb sdkld, kb pdtcsld, btf.

[c`lzckd= fdnslstb bn sbpcrcr pcrtàfugcs söglkcs kb cfubrkd c su tc`cód. Xcrc ecfbrgd sb b`pgbcn fdgckdrbs kb klobrbntbs tc`códs, fdgdfckds bn odr`c fdnsbfutlvc, bn drkbn kbfrbflbntb, kb cfubrkd cg tc`cód kb gds drlolflds. Gds fdgckdrbs rbflibn bg ndìrb kb tc`lfbs y bstãn bgcidrckds fdn tbgcs `btãglfcs. Olgtrcflön= bs un tlpd kb sbpcrcflön `bfãnlfc qub slrvb pcrc rbtlrcr söglkds lnsdguigbs kb jrcnd olnd kb un gàqulkd bn bg fucg sb bnfubntrcn `bzfgckds. Bstb `ìtdkd fdnslstb bn vbrtbr gc `bzfgc c trcvìs kb un `bkld pdrdsd qub kbmc pcscr bg gàqulkd y rbtlbnb bg söglkd. Bn bg gcidrctdrld sb usc bg pcpbg olgtrd, qub sb fdgdfc bn odr`c kb fdnd bn un bìukd kb vlkrld, c trcvìs kbg fucg sb ecfb pcscr gc `bzfgc, rbtbnlbnkd bg olgtrd gc pcrtb söglkc y kbmcnkd pcscr bg gàqulkd. Olgtrcflön bn fcglbntb pcpbg kb gtrd bìukd

Olgtrcflön cg vcfàd pcpbg bìukd

Bstcs tìfnlfcs sb utlglzcn sdirb tdkd pcrc sbpcrcr sdgufldnbs. Nubstrd tb`c kb bstc sb`cnc.

¡C trcicmcr! Bsfdmc unc d vcrlcs tìfnlfcs pcrc sbpcrcr gc sljulbntb `bzfgc y bxpglqub bg pdrquì kb su bgbfflön. Rnc `bzfgc kb cjuc, scg y crbnc.

965

LJBY ∙ [cfcnã


3. Vdgufldnbs Vl ustbk prbpcrc unc tczc kb fcoì y gc bnkugzc fdn unc fufecrckltc kb czýfcr, ´pubkb klstlnjulr fuãgbs sdn gcs pcrtàfugcs kb fcoì, cjuc y czýfcr4 ¡Fgcrd qub nd! Xdrqub tdkds bstds fd`pdnbntbs ecn odr`ckd unc sdguflön. Rnc sdguflön d klsdguflön bs unc `bzfgc ed`djìnbc kb un sdgutd (sustcnflc qubkdnkb sb klsubgvb) klstrliulkc (sustcnflc sb klsubgvb bg sdgutd).kb `cnbrc unlodr`b bn un sdgvbntb Gcs sdgufldnbs sb fcrcftbrlzcn pdrqub= • C sl`pgb vlstc sdn `bzfgcs ed`djìnbcs, nd pdkb`ds klstlnjulr sus fd`pdnbntbs. • Gc fd`pdslflön vcràc kbntrd kb flbrtds gà`ltbs. Ybtd`cnkd bg bmb`pgd lnlflcg, unc sdguflön kb fcoì pubkb tbnbr `ãs d `bnds fcntlkck kb fcoì y kb czýfcr y sbjulrã slbnkd unc sdguflön.

Ybfubrkb= unc `bzfgc ed`djìnbc bs cqubggc qub prbsbntc unc sdgc ocsb.

• Vus fd`pdnbntbs sb pubkbn sbpcrcr pdr `ìtdkds oàslfds, fd`d vl`ds bn gc sbfflön ¡Xcrc fd`bnzcr! Xdr bmb`pgd, sl pdnb`ds c ebrvlr gc tczc kb fcoì ecstc qub bg cjuc sb bvcpdrb, nds qubkcrã un sdgutd odr`ckd pdr czýfcr y fcoì. Ebrvlr bg fcoì, sln czýfcr, bs bg `ìtdkd qub utlglzc gc lnkustrlc pcrc ocirlfcr bg fcoì lnstcntãnbd. • Vlb`prb bstãn odr`ckcs pdr kds fd`pdnbntbs= sdgutd y sdgvbntb. Jbnbrcg`bntb bg sdgutd bstã prbsbntb bn `bndr fcntlkck qub bg sdgvbntb.

Bmbrflfld 3 C.

Ybggbnb bg fuckrd kb gcs sustcnflcs ed`djìnbcs. [lbnb un bmb`pgd. frlstcg kb vbntcnc jcsdglnc

I.

cjuc fdn elbgd

cjuc bn cfbltb ecrlnc bn cjuc

Ybggbnb bg fuckrd kb gc rbspubstc fdrrbftc. [lbnb un bmb`pgd. 8)

´Fuãg kb gcs sljulbntbs sustcnflcs nd bs unc sdguflön4

3)

felr`dg vlncjrb ´Suì tlpd kb sustcnflc pcrtlflpc bn `bndr prdpdrflön bn unc sdguflön4

clrb sdgutd

lnouslön kb tì

sdgvbntb

sdguflön


96<

3.3 Fgcslolfcflön kb gcs sdgufldnbs Gcs sdgufldnbs sb fgcslfcn pdr su bstckd kb cjrbjcflön y pdr su fdnfbntrcflön. _bc`ds=

c.

Xdr su bstckd kb cjrbjcflön

Gcs sdgufldnbs sb prbsbntcn bn trbs bstckds=

Vdgufldnbs gàqulkcs söglkds bn gàqulkds= bg sdgutd bs söglkd y bg sdgvbntb, gàqulkd. • Xdr bmb`pgd= czýfcr klsubgtc bn cjuc, lnouslön kb tì, scg klsubgtc bn gc sdpc, btf. jcsbs bn gàqulkds= bg sdgutd bs un jcs y bg sdgvbntb, gàqulkd. • Xdr bmb`pgd= dxàjbnd bn cjuc, ibilkcs fcridnctckcs (cjucs jcsbdscs), dxàjbnd bn scnjrb, btf. gàqulkds bn gàqulkds= bg sdgutd y bg sdgvbntb sdn gàqulkds. • Xdr bmb`pgd= klobrbntbs `bzfgcs kb cgfdedg bn cjuc, cjuc y btlgbnjglfdg (cntlfdnjbgcntb), vlncjrb fdn cjuc, btf.

Vdgufldnbs söglkcs söglkd bn söglkd= tcntd bg sdgutd fd`d bg sdgvbntb sb bnfubntrcn bn bstckd söglkd. • Gcs cgbcfldnbs sdn bmb`pgds kb bstb tlpd kb sdguflön. Bg irdnfb bs unc cgbcflön kb fdirb klsubgtd bn bstcód, bg cfbrd bs unc cgbcflön kb fcridnd bn elbrrd, btf. jcs bn söglkd= bg sdgutd bs un jcs y bg sdgvbntb, söglkd. • Xdr bmb`pgd= elkröjbnd bn pcgckld. gàqulkd bn söglkd= bg sdgutd bs gàqulkd y bg sdgvbntb, söglkd. • Xdr bmb`pgd= gcs c`cgjc`cs kbntcgbs sb ocirlfcn fdn `brfurld gàqulkd `bzfgckd fdn pgctc söglkc.

Vdgufldnbs jcsbdscs Gcs sdgufldnbs jcsbdscs sdgd pubkbn sbr jcsbs bn jcsbs. Bn bggcs tcntd bg sdgutd fd`d bg sdgvbntb sdn jcsbdsds. Xdr bmb`pgd= dxàjbnd bn nltröjbnd (clrb), klöxlkd kb fcridnd bn dxàjbnd (clrb).

9;8

LJBY ∙ [cfcnã

Bmbrflfld 9 C.

I.

Fd`pgbtb bg fuckrd. Bsfrlic bg bstckd kb fckc sdguflön qub sb prbsbntc. [lbnb un bmb`pgd. sdguflön

sdgutd

sdgvbntb

bmb`pgd

gàqulkc

söglkd

gàqulkd

cjuc kb `cr

jcs

gàqulkd

dxàjbnd bn cjuc

söglkd

gàqulkd

czýfcr bn gc scnjrb


Bn bg cjuc kb `cr, ´fuãg bs bg sdgutd4 scg cjuc crbnc

3)

´Fuãg kb gcs sljulbntbs sdgufldnbs bstã bn bstckd jcsbdsd4 clrb sln eu`d cjuc fcridnctckc (cjuc jcsbdsc) dxàjbnd bn gc scvlc kb gcs pgcntcs

9)

Bg drd igcnfd bs unc cgbcflön kb pgctlnd bn drd. ´Suì tlpd kb sdguflön bs4 söglkd bn gàqulkd gàqulkd bn söglkd söglkd bn söglkd

6)

Bg jcs ncturcg bs unc sdguflön kb jcs klöxlkd kb fcridnd y kb nltröjbnd jcsbdsd bn jcs `btcnd. Cunqub su fd`pdslflön vcràc bn ounflön kbg ycfl`lbntd kbg qub sb scfc, bg `btcnd bs bg <8% d <2% kb gc sdguflön. ´Suì jcs bs bg sdgvbntb4 `btcnd nltröjbnd klöxlkd kb fcridnd Suà`lfc LL ∙ Vb`cnc 69

9;3

i.

Xdr su fdnfbntrcflön

Gc fd`pdslflön kb unc sdguflön vcràc sbjýn gc fcntlkck kb sdgutd d sdgvbntb. Oàmbsb=

Vdguflön scturckc Bs cqubggc qub fdntlbnb tcntd sdgutd fd`d pubkb klsdgvbrsb bn unc fcntlkck kbtbr`lnckc kb sdgvbntb c tb`pbrcturc cìlbntb. Bstc sdguflön bs bstcigb. Bmb`pgd=

Vcturcr sljnlfc fdìlncr kds d `ãs fubrpds bn gcs prdpdrfldnbs `ãxl`cs bn qub pubkbn unlrsb.

Vl td`c`ds 38 dnzcs kb cjuc c tb`pbrcturc cìlbntb, pdkb`ds klsdgvbr, cprdxl`ckc`bntb, ecstc 92 fufecrckcs kb czýfcr. Fdn bstc fcntlkck kb cjuc y czýfcr tbnkrb`ds unc sdguflön scturckc. Fdn fckc fufecrckc kb czýfcr qub klsdgvc`ds, gc sdguflön sb lrã tdrncnkd `ãs c`crlggc. Bstc sdguflön tbnkrã un cspbftd trcnspcrbntb cunqub sbc kb fdgdr c`crlggd.

Vdguflön lnscturckc d klgulkc Bs cqubggc bn gc qubgc fdnfbntrcflön kbg sdgutd bs `bndr qub gc fdnfbntrcflön kb unc sdguflön scturckcc tb`pbrcturc cìlbntb.Bmb`pgd= Vl td`c`ds 38 dnzcs kb cjuc c tb`pbrcturc cìlbntb y klsdgvb`ds `bnds kb 92 fufecrckcs kb czýfcr (pubkb sbr 3,9 6… ecstc 9;) tbnkrb`ds unc sdguflön lnscturckc. Gc sdguflön, kbpbnklbnkd kb gcs fufecrckcs kb czýfcr qub cjrbjub`ds, sbrã trcnspcrbntb b lnfdgdrc d trcnspcrbntb kb fdgdr c`crlggd.

Vdguflön sdirbscturckc Bs cqubggc bn gc qub gc fdnfbntrcflön kb sdgutd bs `cydr qub gc k b unc sdguflön scturckc. Bs lnbstcigb pdrqub kbpbnkb kb gc tb`pbrcturc. Xcrc gdjrcr qub bg sdgutd sb klsubgvc, ecy qub fcgbntcr gc sdguflön. Bmb`pgd= Vl td`c`ds 38 dnzcs kb cjuc c tb`pbrcturc cìlbntb y klsdgvb`ds `ãs kb 92 fufecrckcs kb czýfcr (pubkbn sbr 9?,9:…) ìstc nd sb klsdgvbrã bn bg cjuc. Gc sdguflön sbrã kb fdgdr c`crlggd, pbrd tbnkrã un cspbftd turild. Gds jrcnds kb czýfcr ogdtcrãn pdr gc sdguflön y sb kbpdsltcrãn bn bg odnkd kbg rbflplbntb. Vl fcgbntãrc`ds bg cjuc fdn bg czýfcr y cjltãrc`ds pcrc qub sb klsdgvlbrc, fdnsbjulràc`ds unc sdguflön sdirbscturckc, pdrqub ‗c oubrzc‐ kb fcgbntcrgc gdjrcràc`ds qub ck`ltlbrc `ãs sdgutd, bn bstb fcsd czýfcr, kbg qub pdkràc klsdgvbr c tb`pbrcturc cìlbntb.

9;9

LJBY ∙ [cfcnã

Bmbrflfld 6 Ybggbnb bg fuckrd kb gc rbspubstc fdrrbftc. [bnb`ds trbs vcsds fdn gc `ls`c fcntlkck kb cjuc. Bn bg vcsd C eb`ds klsubgtd unc fufecrckc kb czýfcr. Bn bg vcsd I eb`ds klsubgtd kds fufecrckcs kb czýfcr. Bn bg vcsd F eb`ds klsubgtd trbs fufecrckcs kb czýfcr.

3)

Gc sdguflön C, ´fö`d bs fdn rbspbftd c gc I4 `ãs klgulkc `ãs fdnfbntrckc nlnjunc kb gcs cntbrldrbs

9)

Gc sdguflön F, ´fö`d bs fdn rbspbftd c gc C4 `ãs klgulkc `ãs fdnfbntrckc nlnjunc kb gcs cntbrldrbs

6)

Kb gcs trbs sdgufldnbs, ´fuãg bs gc `ãs fdnfbntrckc4 sdguflön C sdguflön I sdguflön F

;)

Vl qulslìrc`ds prbpcrcr unc sdguflön `ãs fdnfbntrckc qub gcs sdguflön F, ´quì pdkràc`ds ecfbr4 cjrbjcr `ãs czýfcr cjrbjcr gc `ls`c fcntlkck kb czýfcr, pbrd `bnds fcntlkck kb cjuc gcs kds cntbrldrbs sdn fdrrbftcs

2)

Vl prbpcrc`ds un fcgkd qub ec qubkckd scgckd y qubrb`ds kls`lnulr gc scg, ´quì kbib`ds ecfbr4 cjrbjcr `ãs scg cjrbjcr `ãs cjuc ebrvlrgd pcrc qub bg cjuc sb bvcpdrb


9;6

9. Fdnfbntrcflön kb unc sdguflön Gc fdnfbntrcflön kb unc sdguflön bs gc prdpdrflön d rbgcflön qub ecy bntrb gc fcntlkck kb sdgutd y gc fcntlkck kb sdgvbntb. Fucnkd sb trcicmc bn gc lnkustrlc d gc flbnflc, gc fdnfbntrcflön kbib bxprbscrsb kb `cnbrc fucntltctlvc. Ndsdtrds cprbnkbrb`ds c bxprbscr gcs fdnfbntrcfldnbs bn pdrfbntcmb `csc`csc (% `/`) y bn pdrfbntcmb vdgu`bn ‖ vdgu`bn (% v/v).

9.3 Xdrfbntcmb `csc ‖ `csc (% `/`) Bg pdrfbntcmb `csc ‖ `csc sb kbnb fd`d gc `csc kb sdgutd (sustcnflc qub sb klsubgvb) pdr fckc 388 unlkckbs kb `csc kb gc sdguflön= % `/` 0 `csc kb sdgutd (j) x 388 `csc kb sdguflön (j)

Xcrc rbcglzcr fãgfugds fdn gds pdrfbntcmbs `csc ‖ `csc, kbib`ds scibr qub gc su`c kb gc `csc kbg sdgutd `ãs gc `csc kbg sdgvbntb bs ljucg c gc `csc kb gc sdguflön. sdguflön 0 sdgutd + sdgvbntb

Xdkb`ds kbspbmcr bstc bfucflön y bnfdntrcr gds dtrds fd`pdnbntbs= • sdgutd 0 sdguflön ‖ sdgvbntb

Xdr bmb`pgd=

• sdgvbntb 0 sdguflön ‖ sdgutd

Vb klsubgvbn 96 jrc`ds kb fgdrurd kb sdkld (NcFg) bn 338 jrc`ds kb cjuc (E 9D). Fcgfugb bg pdrfbntcmb `csc ‖ `csc.

3. Fcgfugc`ds gc `csc kb gc sdguflön= sdguflön 0 sdgutd + sdgvbntb sdguflön 0 96 j + 338 j sdguflön 0 366 j

9. Cpglfc`ds gc oörùgc pcrc fcgfugcr bg % `/`= % `/` 0 `csc kb sdgutd x 388 `csc kb sdguflön % `/` 0 96 j x 388 0 3:.6 366 j

6. Bsfrlil`ds gc rbspubstc=Bg pdrfbntcmb `csc ‖ `csc kbgc sdguflön 3:.6%.

9;;

LJBY ∙ [cfcnã

¡Dtrd bmb`pgd! ´Fuãntds jrc`ds kb fgdrurd kb sdkld (NcFg) sb nbfbsltcn pcrc prbpcrcr 328 jrc`ds kb sdguflön cg ;% `/`4

Fd`d gd qub nbfbsltc`ds bs gc `csc kbg sdgutd utlglzc`ds gc oörùgc= `csc kb sdgutd x 388 % `csc 0 `csc kb sdguflön Vustltul`ds gds kctds qub nds kcn y kbspbmc`ds= `csc kb sdgutd x 388 328 j 328 j x ;% 0 `csc kb sdgutd x 388

; % `csc 0

328 j x ; 0 `csc kb sdgutd 388

Cg klvlklr bntrb 388, bgl`lnc`ds bg pdrfbntcmb.

? j 0 `csc kbg sdgutd

Bsfrlil`ds gc rbspubstc= Vb nbfbsltcn ? jrc`ds kb fgdrurd kb sdkld (NcFg).

Bmbrflfld ; Ybsubgvc bg prdigb`c kb pdrfbntcmb `csc ‖ `csc. Vljc gds pcsds y bxprbsb su rbsugtckd fdn unc florc kbfl`cg. Vb prbpcrc unc sdguflön cjrbjcnkd : jrc`ds kb ilfcridnctd kb sdkld (NcEFD 6) c 388 jrc`ds kb cjuc (E9D). Fcgfugcr bg pdrfbntcmb `/` kb bstc sdguflön.

3.

Fcgfugb gc `csc kb gc sdguflön= sdguflön 0 sdgutd + sdgvbntb j+

sdguflön 0 sdguflön 0 9.

j

Cpglqub gc oörùgc pcrc fcgfugcr bg % `/` % `csc 0 % `csc 0

6.

j

`csc kb sdgutd x 388 `csc kb sdguflön x 388 0

Bsfrlic gc rbspubstc=


9;2

9.9 Xdrfbntcmb vdgu`bn ‖ vdgu`bn (% v/v) Bg pdrfbntcmb vdgu`bn ‖ vdgu`bn sb kbnb fd`d bg vdgu`bn kb sdgutd (sustcnflc qub sb klsubgvb), bxprbsckd bn `lglgltrds, qub ecy bn 388 `G kb sdguflön. % v/v 0

vdgu`bn kb sdgutd x 388 vdgu`bn kb gc sdguflön

Gc su`c kbg vdgu`bn kbg sdgutd `ãs bg vdgu`bn kbg sdgvbntb bs ljucg cg vdgu`bn kb gc sdguflön. sdguflön 0 sdgutd + sdgvbntb

Cg ljucg qub bn bg % `/`, pdkb`ds kbspbmcr bstc bfucflön y bnfdntrcr gds dtrds fd`pdnbntbs= • sdgutd 0 sdguflön ‖ sdgvbntb • sdgvbntb 0 sdguflön ‖ sdgutd Xdr bmb`pgd= Vl sb klsubgvbn 98 `G kb cgfdedg bn 58 `G kb cjuc, ´Fuãg bs bg % v/v kb cgfdedg bn gc sdguflön4 3. Fcgfugc`ds bg vdgu`bn kb gc sdguflön= sdguflön 0 sdgutd + sdgvbntb sdguflön 0 98 `G + 58 `G sdguflön 0 388 `G

9. Cpglfc`ds gc oörùgc pcrc fcgfugcr bg % v/v % vdgu`bn 0


% vdgu`bn 0 388 98 `G `G x 388 0 98

6. Bsfrlil`ds gc rbspubstc= Bg pdrfbntcmb vdgu`bn ‖ vdgu`bn kb gc sdguflön bs 98 % kb cgfdedg.

9;?

LJBY ∙ [cfcnã

¡Dtrd bmb`pgd! ´Suì vdgu`bn kb mujd kb gl`ön sb nbfbsltc pcrc prbpcrcr unc sdguflön kb 9888 `G cg 32 %4

Fd`d gd qub nbfbsltc`ds bs bg vdgu`bn kbg sdgutd, utlglzc`ds gc oörùgc y kbspbmc`ds= % vdgu`bn 0


32 % 0 vdgu`bn kb sdgutd x 388 9888 `G 9888 `G x 32% 0 vdgu`bn kb sdgutd x 388 9888 `G x 32 0 vdgu`bn kb sdgutd x 388 388 688 `G 0 vdgu`bn kbg sdgutd

Bsfrlil`ds gc rbspubstc= Vb nbfbsltcn 688 `lglgltrds kb mujd kb gl`ön pcrc prbpcrcr unc sdguflön cg 32% v/v.

Ybfubrkb= Cg klvlklr bntrb flbn, bgl`lnc`ds bg pdrfbntcmb.

Bmbrflfld 2 Ybsubgvc bg prdigb`c kb pdrfbntcmb vdgu`bn ‖ vdgu`bn. Vljcgds pcsds. Rnc sdguflön kb vltc`lnc F tlbnb 92 `G kb gc vltc`lnc klsubgtds bn 928 `G kb cjuc. ´Fuãg bs bg pdrfbntcmb vdgu`bn ‖ vdgu`bn kb vltc`lnc F bn gc sdguflön4

3.

Fcgfugb bg vdgu`bn kb gc sdguflön= sdguflön 0 sdgutd + sdgvbntb `G +

sdguflön 0 sdguflön 0 9.

`G

Cpglqub gc oörùgc pcrc fcgfugcr bg % v/v % vdgu`bn 0

6.

`G

% vdgu`bn 0 Bsfrlic gc rbspubstc=

vdgu`bn kb sdgutd x 388 vdgu`bn kb gc sdguflön 92 `G 9:2 `G x 388 0


9;:

Ybsu`bn 3.

Rnc sdguflön d klsdguflön bs unc `bzfgc ed`djìnbc kb un sdgutd (sustcnflc qub sb klsubgvb) klstrliulkc kb `cnbrc unlodr`b bn un sdgvbntb (sustcnflc kdnkb sb klsubgvb bg sdgutd).

3.3 Fgcslolfcflön kb gcs sdgufldnbs c. Xdr su bstckd kb cjrbjcflön pubkbn sbr= Vdgufldnbs gàqulkcs= söglkds bn gàqulkds, jcsbs bn gàqulkds y gàqulkds bn gàqulkds. Vdgufldnbs söglkcs= söglkd bn söglkd, jcs bn söglkd y gàqulkd bn söglkd. Vdgufldnbs jcsbdsc= jcsbs bn jcsbs. i. Xdr su fdnfbntrcflön pubkbn sbr= Vdguflön scturckc= bs cqubggc qub fdntlbnb tcntd sdgutd fd`d pubkb klsdgvbrsb bn unc fcntlkck kbtbr`lnckc kb sdgvbntb c tb`pbrcturc cìlbntb. Bstc sdguflön bs bstcigb. Vdguflön lnscturckc d klgulkc= bs cqubggc bn gc qub gc fdnfbntrcflön kbg sdgutd bs `bndr qub gc fdnfbntrcflön kb unc sdguflön scturckc c tb`pbrcturc cìlbntb. Vdguflön sdirbscturckc= bs cqubggc bn gc qub gc fdnfbntrcflön kb sdgutd bs `cydr qub gc kb unc sdguflön scturckc. Bs lnbstcigb pdrqub kbpbnkb kb gc tb`pbrcturc. Xcrc gdjrcr qub bg sdgutd sb klsubgvc, ecy qub fcgbntcr gc sdguflön. 9.

Fdnfbntrcflön kb unc sdguflön Gc fdnfbntrcflön kb unc sdguflön bs gc prdpdrflön d rbgcflön qub ecy bntrb gc fcntlkck kb sdgutd y gc fcntlkck kb sdgvbntb.

9.3 Xdrfbntcmb `csc ‖ `csc (% `/`) Bg pdrfbntcmb `csc ‖ `csc sb kbolnb fd`d gc `csc kb sdgutd (sustcnflc qub sb klsubgvb) pdr fckc 388 unlkckbs kb `csc kb gc klsdguflön= % `csc 0 `csc kb sdgutd (j) x 388 `csc kb sdguflön (j)

sdguflön 0 sdgutd + sdgvbntb

9.9 Xdrfbntcmb vdgu`bn ‖ vdgu`bn (% v/v) Bg pdrfbntcmb vdgu`bn ‖ vdgu`bn sb kbolnb fd`d bg vdgu`bn kb sdgutd (sustcnflc qub sb klsubgvb), bxprbsckd bn `lglgltrds, qub ecy bn 388 `g kb sdguflön. % vdgu`bn 0

9;5

LJBY ∙ [cfcnã



Cutdfdntrdg Cftlvlkck 3. Ybgcfldnb lnodr`cflön Ybggbnb bg fuckrd kb gc rbspubstc fdrrbftc. 3)

´Fuãg kb gcs sljulbntbs nd bs unc sdguflön jcsbdsc4

sdguflön kb cgfdedg clrb sln fdntc`lncflön jcs rborljbrcntb jcs c`dnld

9)

Kb gds sljulbntbs, ´fuãg bs un bmb`pgd kb jcs `bzfgckd bn gàqulkd4

gl`dnckc cjuc kb ràd clrb fdn eu`d (s`dj) cjuc fcridnctckc (cjuc jcsbdsc)

6)

´Fuãg kb gcs sljulbntbs bs unc sdguflön söglkd bn gàqulkd4

cjuc `lnbrcg crbnc bn cjuc cjuc czufcrckc cjuc jcsbdsc

;)

´Fö`d sb ggc`c gc sdguflön qub bstã klgulkc y qub ck`ltlràc `ãs sdgutd4

lnscturckc scturckc cfudsc sdirbscturckc

2)

´Fö`d sb ggc`c gc sdguflön bn gc qub bg sdgutd y bg sdgvbntb bstãn bn bqulglirld4

scturckc lnscturckc sdirbscturckc cfudsc

Cftlvlkck 9 Ybggbnb bg fuckrd qub fdrrbspdnkb c sdgufldnbs kb jcsbs bn gàqulkds. cjuc kb `cr clrb

cjuc kb ràd ibilkc bobrvbsfbntb

cjuc jcsbdsc cjuc purc Suà`lfc LL ∙ Vb`cnc 69

9;<

Cftlvlkck 6 Vuircyb bg lnflsd fdrrbftd. [lbnb un bmb`pgd. 8)

Lnklqub fucg kb gcs sljulbntbs colr`cfldnbs bs flbrtc= C. I. F. K.

3)

9)

Cfbrfc kb unc sdguflön pdkb`ds colr`cr qub= C. Gc fd`pdslflön vcràc kbntrd kb flbrtds gà`ltbs. I. Vus fd`pdnbntbs nd sb pubkbn sbpcrcr pdr `ìtdkds oàslfds. F. Bg sdgvbntb nunfc bstã prbsbntb bn `cydr fcntlkck qub bg sdgutd. K. Bg sdgutd bstã klstrliulkd kb odr`c ebtbrdjìnbc bn bg sdgvbntb. Rnc sdguflön bs un slstb`c= C. I. F. K.

6)

[dkcs gcs sdgufldnbs scturckcs sdn sdgufldnbs fdnfbntrckcs. Nd ecy sdgufldnbs jcs-gàqulkd scturckcs. Bn tdkcs gcs sdgufldnbs ecy vcrlds sdgutds y un sdgvbntb Gcs trbs colr`cfldnbs cntbrldrbs sdn ocgscs.

Ebtbrdjìnbd fdnstltulkd pdr `ãs kb un fd`pdnbntb. Ed`djìnbd sbpcrcigb bn sus fd`pdnbntbs pdr `bklds oàslfds. Ed`djìnbd fdnstltulkd pdr `ãs kb un fd`pdnbntb y sbpcrcigb bn sus fd`pdnbntb sdgc`bntb pdr `bklds quà`lfds. Ed`djìnbd fdnstltulkd pdr un sdgd fd`pdnbntb.

Rnc sdguflön sdirbscturckc bs= C. I. F. K.

Lnbstcigb pdrqub bg sdgutd nunfc sb klsubgvb. Bstcigb pdrqub fdntlbnb `cydr fcntlkck kb sdgutd. Bstcigb pdrqub fdntlbnb `cydr fcntlkck kb sdgvbntb. Lnbstcigb pdrqub bg sdgutd sb klsubgvb sdgd sl sb fcglbntc gc sdguflön.

Cftlvlkck ; Fd`pgbtb bg `cpc fdnfbptucg fdn gcs fcrcftbràstlfcs kb unc sdguflön. Rnc sdguflön sb fcrcftbrlzc pdr=

928

LJBY ∙ [cfcnã

Cftlvlkck 2 Lnklqub c gc kbrbfec kb fckc sdguflön bg bstckd kb cjrbjcflön bn bg qub sb bnfubntrc bg sdgutd, bg sdgvbntb y gc sdguflön. [lbnb un bmb`pgd. Bmb`pgds= c`cgjc`c kbntcg (`brfurld bn pgctc)

sdgutd

sdgvbntb

sdguflön

söglkd

gàqulkd

söglkc

cjuc czufcrckc ibilkc kb fcoì cjuc `lnbrcg (sdkc)

Cftlvlkck ? 3)

Fcgfugb bn su fuckbrnd gc fdnfbntrcflön kb gcs sdgufldnbs qub sb ecn prbpcrckd klsdgvlbnkd= c.

98 jrc`ds kb czýfcr bn 688 jrc`ds kb cjuc.

i.

? jrc`ds kb scg bn 58 jrc`ds kb cjuc.

f.

28 jrc`ds kb ncotcgbnd bn 288 jrc`ds kb ibnfbnd.

Bxprbsb sus rbsugtckds fdn 9 florcs kbfl`cgbs. 9)

Kbtbr`lnb bg vdgu`bn kb sdgutd bn ;2 `G kb sdguflön cg :% v/v

6)

Kbtbr`lnb bg vdgu`bn kbg sdgvbntb bn 588 `G kb sdguflön cg 3;% v/v

;)

Vl sb `bzfgcn 32 `G kb cgfdedg fdn 628 `G kb cjuc, ´fuãg bs bg % v/v kb gc sdguflön4

Cftlvlkck : C.

Kbtbr`lnb bg pdrfbntcmb `/` d v/v, sbjýn fdrrbspdnkc pcrc fckc unc kb gcs sljulbntbs sdgufldnbs. 3)

: jrc`ds kb elkröxlkd kb sdkld (NcDE) klsubgtds bn suolflbntb cjuc pcrc ditbnbr 988 jrc`ds kb sdguflön.

9)

6 jrc`ds kb fgdrurd kb pdtcsld (AFg) bn 58 jrc`ds kb cjuc.

6)

9.2 `G kbg lnklfckdr obndgotcgbànc (F 98E3;D;) bn suolflbntb cgfdedg pcrc ditbnbr 28 `G kb sdguflön.

;)

58 `G kb cgfdedg bn suolflbntb cjuc pcrc ditbnbr 3888 `G kb sdguflön. Suà`lfc LL ∙ Vb`cnc 69

923

I.

Bn gds sljulbntbs bnunflckds bsfrlic unc O sl gc drcflön bs ocgsc y unc _ sl bs vbrkckbrc. Mustlolqub su rbspubstc fdn gds fãgfugds nbfbscrlds. Eãjcgds bn su fuckbrnd. 3)

Vl sb tlbnb unc sdguflön fdn unc fdnfbntrcflön 92% `/`, qulbrb kbflr qub sb tuvd qub klsdgvbr unc `csc kb 92 j kbg sdgutd bn 388 `G kb cjuc (sdgvbntb).

9)

Vl sb pbscrdn 8.: j kb fgdrurd kb sdkld (NcFg) y sb klsdgvlbrdn bn 388 jrc`ds kb cjuc, gc fdnfbntrcflön kb gc sdguflön bs kb 8.:% `/`.

6)

32 `G kb cfbtctd kb sdkld sb klsdgvlbrdn bn 392 `G kb cjuc. Xdr gd tcntd tbnb`ds unc sdguflön fdn unc fdnfbntrcflön kb 38.:3% v/v.

Cftlvlkck 5 Ybsubgvc gds sljulbntbs prdigb`cs kb fdnfbntrcflön. Eãjcgd bn su fuckbrnd. Bxprbsb sus rbsugtckds fdn 9 florcs kbfl`cgbs. 3)

Xcrc sczdncr un fcgkd kb pbsfckd ecy qub cócklr 3? jrc`ds kb scg pdr 9888 jrc`ds kb fcgkd. ´Fuãg bs bg % `/` kb gc sdguflön4

9)

Bn un vcsd kb fdgdfcn 988 jrc`ds kb cgfdedg fdn 9 jrc`ds kb ydkd qub sb klsubgvbn tdtcg`bntb. ´Fuãg bs bg % `/` kb gc sdguflön4

6)

Bs digljctdrld qub bn gcs btlqubtcs kb cjuc `lnbrcg cpcrbzfc bg pdrfbntcmb kb gcs klobrbntbs scgbs qub tlbnb klsubgtcs. Xdr fckc 9288 jrc`ds kb cjuc ecy klsubgtds= 9.3 jrc`ds kb sdkld1 6.9 jrc`ds kb `cjnbsld1 ?.; jrc`ds kb pdtcsld y 99.2 jrc`ds kb ilfcridnctd. ´Suì pdrfbntcmbs bsfrlilràc sl tuvlbrc qub bgcidrcr gc btlqubtc4 Ybcglfb gds fãgfugds y bsfrlic gds rbsugtckds bn bg rbfuckrd. scg

fdnfbntrcflön % `/`

sdkld `cjnbsld pdtcsld ilfcridnctd

929

;)

´Suì vdgu`bn kb sdguflön kbib`ds prbpcrcr fdn 288 `G kb cgfdedg pcrc qub gc sdguflön rbsugtcntb tbnjc un ;8% v/v4

2)

Rn subrd kb :28 `G tlbnb unc fdnfbntrcflön kb ?8% v/v kb kbxtrdsc (un czýfcr). ´Fuãntds `G kb kbxtrdsc bstãn klsubgtds4

?)

Cg ecfbr un cnãglsls kb jgufdsc bn scnjrb, sb bnfubntrc qub unc ùbstrc kb 2 jrc`ds kb scnjrb fdntlbnb 8.88539 j kb jgufdsc. Fcgfugcr bg pdrfbntcmb `/` kb gc jgufdsc bn gc ùbstrc kb scnjrb.

LJBY ∙ [cfcnã


´Vb `bzfgcn d nd sb `bzfgcn4 Bstc sb`cnc gb prdpdnb`ds bxpbrl`bntcr fdn sdgufldnbs (`bzfgcs ed`djìnbcs) y `bzfgcs ebtbrdjìnbcs.

´Suì nbfbsltc4        

2 orcsfds kb vlkrld cjuc 3 sdirb d un orcsqultd kb fdgdr vbjbtcg 6 fufecrckcs kb cfbltb kb fdflnc 6 fufecrckcs kb czýfcr 6 fufecrckcs kb ecrlnc 2 `g kb cgfdedg 3 jdtbrd

´Suì kbib ecfbr4 3. Nu`brb y btlqubtb gds flnfd orcsfds kb vlkrld fdn gds gbtrbrds= fdgdr vbjbtcg, cfbltb, czýfcr, ecrlnc y cgfdedg. 9. Cjrbjub c tdkds cjuc ecstc gc `ltck kbg orcsfd 6. Cg orcsfd ný`brd 3 cjrbjub fdn fulkckd 9 fufecrckcs kb fdgdr vbjbtcg y disbrvb. Vl bg fdgdrcntb bs gàqulkd, cjrbjub 9 jdtbrds. ;. Bn bg orcsfd ný`brd 9 bfeb 9 fufecrckcs kb cfbltb y disbrvb. @bzfgc

2. Cg orcsfd 6 cjrbjub pdfd c pdfd kds fufecrckcs kb czýfcr y disbrvb. ?. Cg orcsfd ; cjrbjub 9 fufecrckcs kb ecrlnc y disbrvb. :. Cg orcsfd 2 cjrbjub 9 jdtbrds kb cgfdedg y disbrvb. 5. Kbmb rbpdscr unds 2 `lnutds <. Cjltb fdn fulkckd bg fdntbnlkd kb fckc und kb gds orcsfds. Cndtb sus disbrvcfldnbs bn un fuckrd fd`d bstb=

Disbrvcfldnbs

´Bsuncsdguflön4

fdgdr vbjbtcg + cjuc cfbltb + cjuc czýfcr + cjuc ecrlnc + cjuc cgfdedg + cjuc


926



gdjrckd

rbjugcr

nd gdjrckd


Fdndzfd cgjunds `ìtdkds oàslfds pcrc gc sbpcrcflön kb `bzfgcs.

9.

Lkbntlolfd sustcnflcs ed`djìnbcs.

6.

Ybfdndzfd gcs fcrcftbràstlfcs kb unc sdguflön.

Kbspuìs kb ;. bstuklcr... 2. ?. :.

Lkbntlolfd sdgutd y sdgvbntb bn unc sdguflön. Fgcslolfd sdgufldnbs pdr su bstckd kb cjrbjcflön y pdr su fdnfbntrcflön. Fcgfugd gc fdnfbntrcflön kb unc sdguflön bn pdrfbntcmb `csc ‖ `csc y vdgu`bn ‖ vdgu`bn. Kbtbr`lnd c trcvìs kb un bxpbrl`bntd quì `bzfgcs odr`cn sdgufldnbs.


92;

LJBY ∙ [cfcnã

66

Fdgdlkbs


922


Kbolnlr quì bs un fdgdlkb.



Lkbntlolfcr gcs ocsbs qub odr`cn un fdgdlkb.



Ybfdndfbr gcs fcrcftbràstlfcs kb un fdgdlkb.



Ndìrcr y bmb`pglolfcr klstlntds tlpds kb fdgdlkb.



Fdndfbr cgjunds fdgdlkbs qub odr`c gc jbgctlnc y gds usds qub sb gb kc.



Bxpbrl`bntcr fdn bg bobftd [ynkcgg.




• Gc `cydnbsc, un fdgdlkb ùy scirdsd

Fdgdlkbs=


• Fcrcftbràstlfcs kb gds fdgdlkbs • Fd`pdslflön kb gds fdgdlkbs • Fgcslolfcflön kb gds fdgdlkbs pdr su bstckd kb cjrbjcflön


92?

LJBY ∙ [cfcnã

• ´Fdgdlkb d sdguflön4

¡Xcrc fd`bnzcr! Gc `cydnbsc, un fdgdlkb ùy scirdsd Ybfbtc kb `cydnbsc iãslfc Lnjrbklbntbs= • 9 yb`cs kb eubvd

• 3 tczc kb cfbltb kb dglvc

• 3 fufecrckltc kb `dstczc • 3 fufecrckltc kb mujd kb gl`ön

• scg y pl`lbntc cg justd

Xrbpcrcflön= Ictlr gcs yb`cs fdn gc `dstczc y bg mujd kb gl`ön. Fucnkd bstìn bspu`dsds, lr cócklbnkd bg cfbltb jdtc c jdtc. Rnc vbz qub vbc qub ec ‗gljckd‐, pubkb cócklr bg cfbltb bn un fedrrltd ùy olnd ecstc tbr`lncr kb lnfdrpdrcrgd tdkd. Vcgpl`bntcr y ¡c klsorutcr! Gc `cydnbsc bs unc `bzfgc kb kds gàqulkds bn bg qub und odr`c pbqubócs pcrtàfugcs qub sb klspbrscn unlodr`b`bntb bn bg dtrd. Bg ndìrb quà`lfd pcrc gcs fdìlncfldnbs kb bstb tlpd bs fdgdlkb . Gc `cydnbsc nd bs bg ýnlfd fdgdlkb utlglzckd bn gc fdflnc, tcìlìn sdn fdgdlkbs gbfeb, gc frb`c gc `cntbqulggc. fcsd kb gds fuglncrlds,gcund kb gds gàqulkdsy subgb sbr jrcsc Bn y bgbgdtrd cjuc. Gdsfdgdlkbs gàqulkds sb pubkbn fdìlncr kb kds `cnbrcs= •

Bg cfbltb pubkb odr`cr jdtcs suspbnklkcs bn bg cjuc, d

•

bg cjuc odr`cr jdtcs suspbnklkcs bn bg cfbltb.

Gc gbfeb bs un bmb`pgd kb cfbltb bn cjuc pdrqub unc fcntlkck pbqubóc kb jrcsc sb`lsöglkc sb klspbrsc bn unc fcntlkck `cydr kb cjuc. Gc frb`c bs un bmb`pgd sl`lgcr, pbrd fdn ùfec `ãs jrcsc.

Bstc sb`cnc bstuklcrb`ds gds fdgdlkbs y sus fcrcftbràstlfcs. ¡C trcicmcr! Iusqub bn bg klffldncrld gc kbnlflön kb fdgdlkb y föplbgc.


92:


3. Fdgdlkbs Fd`d vl`ds bn gc sbfflön ¡Xcrc fd`bnzcr!, gc gbfeb, gc frb`c y gc `cydnbsc sdn cgjunds fdgdlkbs fdndflkds. Bg ndìrb fdgdlkb vlbnb kb gc pcgcirc jrlbjc adggc qub sljnlfc jd`c d fdgc y kb gc pcrtàfugc blkds qub sljnlfc odr`c. Bstb ndìrb ecfb rbobrbnflc c unc kb gcs prlnflpcgbs prdplbkckbs kb gds fdgdlkbs= gc tbnkbnflc c qub sus bgb`bntds —sb pbjubn‐ y odr`bn fdãjugds d jru`ds. Rn fdgdlkb bs unc `bzfgc bn gc qub unc sustcnflc fd`pubstc pdr pcrtàfugcs sb klspbrsc kb `cnbrc unlodr`b bn un sdgvbntb . Kbilkd c bstc klspbrslön, cgjunds fdgdlkbs tlbnbn bg cspbftd kb sdgufldnbs.

3.3 Fcrcftbràstlfcs kb gds fdgdlkbs • Xrbsbntcn unc cpcrlbnflc vlsfdsc. Bstc fcrcftbràstlfc gc pdkb`ds disbrvcr fdn ocflglkck bn gc fgcrc kb eubvd. • Vus fd`pdnbntbs nd sb sbkl`bntcn, bs kbflr nd sb kbpdsltcn bn odr`c kb söglkd bn bg odnkd kb gds rbflplbntbs. [c`pdfd sb pubkbn olgtrcr. • Gcs pcrtàfugcs kb un fdgdlkb ùbstrcn un `dvl`lbntd rãplkd, lrrbjugcr y vljdrdsd qub sb ggc`c `dvl`lbntd Irdwnlcnd. Bstb ndìrb sb klö bn Ydibrt Irdwn (3::6‖3525) Flbntàolfd irltãnlfd qub lnvbstljö bg bobftd Irdwnlcnd

edndr kbg idtãnlfd lnjgìs Ydibrt bstb obnö`bnd bn gcs fìgugcs kbg Irdwn, pdgbn. bg prl`br flbntàolfd qub lnvbstljö Bg `dvl`lbntd Irdwnlcnd sdgd sb pubkb disbrvcr c trcvìs kb un `lfrdsfdpld. Bstb `dvl`lbntd pbr`ltb qub gcs pcrtàfugcs sb `cntbnjcn bn suspbnslön y nd sb sbkl`bntbn. Bn gc jrãolfc kb gc lzqulbrkc sb disbrvc c trcvìs kb un `lfrdsfdpld bg `dvl`lbntd Irdwnlcnd kb pcrtàfugcs fdgdlkcgbs kb gc scnjrb. Vl trczãrc`ds unc jrãolfc kbg `dvl`lbntd, vbràc`ds unc l`cjbn fd`d gc kb gc kbrbfec.

• Fucnkd gds fdgdlkbs sdn ctrcvbsckds pdr un rcyd kb guz, bstb sb klspbrsc. Bstb obnö`bnd sb ggc`c bobftd [ynkcgg bn edndr cg flbntàolfd irltãnlfd Mden [ynkcgg (3598‖35<6) Flbntàolfd irltãnlfd qub lnvbstljö bg bobftd [ynkcgg

925

LJBY ∙ [cfcnã

Mden [ynkcgg qulbn gd lnvbstljö. Xdr bmb`pgd= Fucnkd un rcyd kb sdg bntrc pdr unc rbnklmc bn unc eciltcflön dsfurc, pdkb`ds disbrvcr pcrtàfugcs kb pdgvd qub pcrbfbn `cnfeltcs kb guz. Bstb bs bg bobftd [ynkcgg.

3.9 Fd`pdslflön kb gds fdgdlkbs Gc klobrbnflc bntrb sdguflön y fdgdlkb bs bg tc`cód kb gcs pcrtàfugcs bn sdguflön. Vl gcs pcrtàfugcs tlbnbn un klã`btrd bntrb 3,888 c 988,888 plfö`btrds sb trctc kb un fdgdlkb y sl bs `bndr, sb trctc kb unc sdguflön. Bn bg fcsd kb gds fdgdlkbs sb ecigc kb ocsb klspbrsc y kb `bkld kb klspbrslön, fdnfbptds bqulvcgbntbs c gds kbg sdgutd y sdgvbntb usckds bn gcs sdgufldnbs. Rn fdgdlkb bstã odr`ckd pdr kds ocsbs sbpcrckcs= • Gc ocsb klspbrsc= sdn gcs pcrtàfugcs qub sb fcrcftbrlzcn, fd`d yc vl`ds, pdr su tc`cód. Bstcs pcrtàfugcs sb ggc`cn `lfbgcs. Cunqub c sl`pgb vlstc nd pubkbn disbrvcrsb, sdn `ãs jrcnkbs qub fucgqulbr `dgìfugc. Gc ocsb klspbrsc sb bnfubntrcn bn `bndr prdpdrflön bn bg fdgdlkb.

Bg plfö`btrd bs unc unlkck kb gdnjltuk qub bqulvcgb c unc ilggdnìsl`c (3,888,888,888,888) pcrtb kb un `btrd. Vb cirbvlc p`. 3 p` 0 3 x 38∙39 `

• @bkld kb klspbrslön= bs gc ocsb bn gc qub sb bnfubntrcn klstrliulkcs gcs `lfbgcs. Xdr bmb`pgd bn gc gbfeb, gc jrcsc odr`c gc ocsb klspbrsc y bg cjuc bs bg `bkld kb klspbrslön.

Bmbrflfld 3 Ybggbnb bg fuckrd kb gc rbspubstc fdrrbftc. [lbnb un bmb`pgd. 8)

´Fö`d sb ggc`cn gcs pcrtàfugcs klspbrscs bn un fdgdlkb4

ãtd`ds frlstcgbs `lfbgcs

3)

´Fuãg bs gc cpcrlbnflc kb gds fdgdlkbs4

vlsfdsc gàqulkc jcsbdsc

9)

´Fuãg bs bg `bkld kb klspbrslön bn gc `cydnbsc4

scg gl`ön cfbltb

6)

´Fdn quì cpcrctd sb pubkb disbrvcr bg `dvl`lbntd Irdwnlcnd4

gupc `lfrdsfdpld tbr`ö`btrd


92<

9. Fgcslolfcflön kb gds fdgdlkbs pdr su bstckd kb cjrbjcflön Cunqub bg fdgdlkb tàplfd bs cqubg bn bg qub gc ocsb klspbrsc sb fd`pdnb kb `lfbgcs söglkcs y bg `bkld kb klspbrslön bs un gàqulkd, pubkbn bnfdntrcrsb fdgdlkbs fuyds fd`pdnbntbs sb bnfubntrcn bn dtrds bstckds kb cjrbjcflön y tlbnbn ndìrbs bspbflcgbs. _bc`ds= ndìrb

`bkld kb klspbrslön

ocsb klspbrsc

cbrdsdg gàqulkd cbrdsdg söglkd

gàqulkd söglkd

jcs jcs

bspu`c

jcs

gàqulkd

bùgslön

gàqulkd

gàqulkd

sdg

söglkd

gàqulkd

bspu`c söglkc

jcs

söglkd

bùgslön söglkc gàqulkd

söglkd

jbg

söglkd

gàqulkd

bmb`pgds

nlbigc,nuibs pdgvd,eu`d bspu`cs (kb mciön, kb `cr, btf), frb`c kb cobltcr, frb`c ictlkc gbfeb, `cydnbsc, frb`c fds`ìtlfc plnturcs, tlntc felnc, jd`c crãiljc, mcgbcs plbkrc pö`bz, bspdnmc `cntbqulggc, qubsd jbgctlnc, jd`ltcs (kugfbs), `bklfc`bntds bn odr`c kb jbgbs, pcstc kb klbntbs

Bmbrflfld 9 Ybggbnb bg fuckrd kb gc rbspubstc fdrrbftc. [lbnb un bmb`pgd.

9?8

8)

Kb gds sljulbntbs, ´fuãg bs un bmb`pgd kb bùgslön söglkc4

bspdnmc gbfeb `cntbqulggc

3)

Gc frb`c kb cobltcr bs un fdgdlkb. ´Fdn quì ndìrb sb fgcslolfc4

bspu`c sdg bùgslön

9)

Kb gds sljulbntbs, ´fuãg bs un bmb`pgd kb sdg4

qubsd mcgbc `cydnbsc

LJBY ∙ [cfcnã

Ybsu`bn 3.

Fdgdlkbs Rn fdgdlkb bs unc `bzfgc bn gc qub unc sustcnflc fd`pubstc pdr pcrtàfugcs sb klspbrsc kb `cnbrc unlodr`b bn un sdgvbntb.

3.3 Fcrcftbràstlfcs kb gds fdgdlkbs • Xrbsbntcn unc cpcrlbnflc vlsfdsc. • Vus fd`pdnbntbs nd sb sbkl`bntcn, nl sb olgtrcn. • Gcs pcrtàfugcs prbsbntcn `dvl`lbntd Irdwnlcnd. • Xrbsbntcn bg bobftd [ynkcgg. 3.9 Gc klobrbnflc bntrb sdguflön y fdgdlkb bs bg tc`cód kb gcs pcrtàfugcs bn sdguflön. Bn bg fcsd kb gds fdgdlkbs sb ecigc kb ocsb klspbrsc y kb `bkld kb klspbrslön, fdnfbptds bqulvcgbntbs c gds kbg sdgutd y sdgvbntb usckds bn bg fcsd kb gcs sdgufldnbs. Rn fdgdlkb bstã odr`ckd pdr kds ocsbs sbpcrckcs= • Gc ocsb klspbrsc= bstã odr`ckc pdr pcrtàfugcs d `lfbgcs. • @bkld kb klspbrslön= bs gc ocsb bn gc qub sb bnfubntrcn klstrliulkcs gcs `lfbgcs. 9.

Fgcslolfcflön kb gds fdgdlkbs pdr su bstckd kb cjrbjcflön ndìrb

ocsb klspbrsc


bmb`pgds

cbrdsdg gàqulkd

gàqulkd

jcs

nlbigc,nuibs

cbrdsdg söglkd

söglkd

jcs

bspu`c

jcs

gàqulkd

bùgslön

gàqulkd

gàqulkd

sdg

söglkd

gàqulkd

pdgvd,eu`d bspu`cs (kb mciön, kb `cr, btf), frb`c kb cobltcr, frb`c ictlkc gbfeb, `cydnbsc, frb`c fds`ìtlfc plnturcs, tlntc felnc, jd`c crãiljc, mcgbcs

bspu`c söglkc

jcs

söglkd

plbkrc pö`bz, bspdnmc


söglkd

jbg

söglkd

`cntbqulggc, qubsd jbgctlnc, jd`ltcs (kugfbs), `bklfc`bntds bn odr`c kb jbgbs, pcstc kb klbntbs

gàqulkd


9?3

Cutdfdntrdg Cftlvlkck 3. Fdnstruyc unc kbnlflön Bsfrlic fdn sus pcgcircs quì bs un fdgdlkb. Cyýkbsb fdn gcs pcgcircs kbg `cpc fdnfbptucg.

`bzfgc `lfbgcs

ed`djìnbc

fdgdlkb ocsb klspbrsc

ocsbs `bkld klspbrscntb

Cftlvlkck 9. Lkbntlqub gcs fcrcftbràstlfcs kb gds f dgdlkbs Fd`pgbtb bg `cpc fdnfbptucg fdn gcs fcrcftbràstlfcs kb gds fdgdlkbs.

Fdgdlkbs sb fcrcftbrlzcn pdr=

9?9

LJBY ∙ [cfcnã

Cftlvlkck 6. Ybgcfldnb lnodr`cflön Ybggbnb bg fuckrd kb gc rbspubstc fdrrbftc. 3)

Ć quì fdnfbptd fdrrbspdnkb gc kbolnlflön —`bzfgc bn gc qub unc sustcnflc fd`pubstc pdr pcrtàfugcs sb klspbrsc kb `cnbrc unlodr`b bn un sdgvbntb‐4

sdguflön fdgdlkb bobftd [ynkcgg

9)

´Suì ndìrb rbflibn gcs pcrtàfugcs qub odr`cn gc ocsb klspbrsc bn un fdgdlkb4

`dgìfugcs bspu`cs `lfbgcs

6)

´Suì tlpd kb fdgdlkb bmb`pglolfc gc gbfeb4

sdg cbrdsdg bùgslön

;)

´Suì tlpd kb fdgdlkb bmb`pglolfc gc nlbigc4

sdg cbrdsdg bùgslön

2)

Bn bg eu`d, ´bn quì bstckd sb bnfubntrc gc ocsb klspbrsc4

jcs söglkd gàqulkd

?)

Bn gc frb`c kb rcsurcr, ´bn quì bstckd sb bnfubntrc bg `bkld klspbrscntb4

jcs söglkd gàqulkd

:)

Kb gcs sljulbntbs `bzfgcs, ´fuãg prbsbntc bg bobftd [ynkcgg4

cjuc kb `cr cjuc fcridnctckc (jcsbdsc) `cydnbsc Suà`lfc LL ∙ Vb`cnc 66

9?6

Cftlvlkck ; Fd`pgbtb bg fuckrd kb gds fdgdlkbs. [lbnb un bmb`pgd. ndìrb

bùgslön söglkc

ocsb klspbrsc

gàqulkd


bmb`pgd

söglkd

`cntbqulggc

bspu`c bùgslön sdg

Cftlvlkck 2 C. Gbc bg tbxtd. Rn fdgdlkb kb fdgdrbs Gc jbgctlnc bs unc sustcnflc kb drljbn cnl`cg odr`ckc pdr prdtbàncs. Vb bxtrcb kb plbgbs, eubsds y dtrds tbmlkds cnl`cgbs. Gc jbgctlnc bs un cgl`bntd ùy oãflg kb kljbrlr. Cpdrtc prdtbàncs kb icmd vcgdr nutrltlvd, pbrd bs unc iubnc dpflön pcrc pbrsdncs bnobr`cs d rbflìn dpbrckcs. Gc jbgctlnc sb vbnkb bn sdirbs qub fdntlbnbn pdgvds sbfds d gã`lncs sbfcs trcnspcrbntbs d fdn fdgdrcntbs. Cg pdnbr gc jbgctlnc sbfc bn fdntcftd fdn un gàqulkd, gd cisdrib y sb elnfec. Jbnbrcg`bntb gc jbgctlnc sb prbpcrc fdn cjuc fcglbntb y sb odr`c un sdg . Bn bstb fcsd bg cjuc bs bg `bkld klspbrscntb. Fucnkd gc jbgctlnc sb bnoràc, cu`bntc su vlsfdslkck, sb sdglklolfc y odr`c un jbg . Bg bstckd kb jbg bs rbvbrsligb cg bstckd kb sdg sl sb fcglbntc. Fdn gc jbgctlnc sb pubkb odr`cr unc bspu`c . Bstc odr`c sb usc bn cgl`bntds prbpcrckds fd`d sdpcs, fcrc`bgds, `br`bgckcs y cgjunds pdstrbs. [cìlìn sb b`pgbc bn gc lnkustrlc ocr`cfìutlfc y fds`ìtlfc pcrc rbfuirlr gcs fãpsugcs.

I.

Ybspdnkc c gcs prbjuntcs. 3)

´Kb quì bstã odr`ckc gc jbgctlnc4

9)

´Kb könkb sb bxtrcb gc jbgctlnc4

6)

Gc jbgctlnc odr`c un sdg cg `bzfgcrsb fdn cjuc fcglbntb. ´Fuãg bs gc ocsb klspbrsc y fuãg bg `bkld klspbrscntb4

9?;

;)

´Suì fdgdlkbs odr`c gc jbgctlnc4

2)

´Suì utlglkckbs tlbnb gc jbgctlnc4 Bsfrlic cg `bnds trbs.

LJBY ∙ [cfcnã


´Fdgdlkb d sdguflön4 Fdn bstb sbnflggd bxpbrl`bntd pdkrã fd`prdicr qub gds fdgdlkbs suorbn bg bobftd [ynkcgg.


9 vcsds kb vlkrld trcnspcrbntb



6 fufecrckcs kb jbgctlnc kb scidr



6 fufecrckcs kb scg kb `bsc



3 glntbrnc kb `cnd



3 pcgbtc



cjuc fcglbntb



un fucrtd dsfurd



gãplz



glirbtc kb fc`pd

´Suì kbib ecfbr4 3. Bn und kb gds vcsds kb vlkrld, klsubgvc gcs 6 fufecrckcs kb jbgctlnc kb scidr bn cjuc fcglbn tb. 9. Bn bg dtrd vcsd klsubgvc gcs 6 fufecrckcs kb scg bn cjuc fcglbntb. 6. Fdgdqub gds vcsds und muntd cg dtrd bn un fucrtd dsfurd. ;. Bnflbnkc gc glntbrnc y pcsb bg ecz kb guz c trcvìs kb gds kds vcsds. Cndtb sus disbrvcfldnbs bn su glirbtc kb fc`pd. Ybspdnkc bn su glirbtc kb fc`pd. ´Fuãg kb gcs sustcnflcs bn un fdgdlkb4 Mustlolqub su rbspubstc.

Lnvbstljub bn gc rbk... Gd lnvltc`ds c rbcglzcr dtrds bxpbrl`bntds fdn fdgdlkbs. Bnfuìntrbgds bn bstc klrbfflön= rbkbsfdgcr.lgfb.bku.`x/rbkbsfdgcr/.../suspfdgd.et` Suà`lfc LL ∙ Vb`cnc 66

9?2



gdjrckd

rbjugcr

nd gdjrckd

Cspbftds c bvcgucr

Kbspuìs kb bstuklcr...

3.

Kbolnd quì bs un fdgdlkb.

9.

Lkbntlolfd gcs ocsbs qub odr`cn un fdgdlkb.

6.

Ybfdndzfd gcs fcrcftbràstlfcs kb un fdgdlkb.

;.

Ndìrd y bmb`pglolfd klstlntds tlpds kb fdgdlkb.

2.

Fdndzfd cgjunds fdgdlkbs qub odr`c gc jbgctlnc y gds usds qub sb gb kc.

?.

Bxpbrl`bntd fdn bg bobftd [ynkcgg.


9??

LJBY ∙ [cfcnã

6;

Ybpcsd Vb`cncs 68-66


9?:


Ybpcscr gds fdntbnlkds kb gcs sb`cncs 68 c 66.



Xrbpcrcrsb pcrc gc prubic ncg.



C`ljc y c`ljd bstuklcntb= Bs bg `d`bntd kb rbpcscr gds tb`cs kb gc sb`cnc trblntc c gc trblntc y trbs qub sb bvcgucrãn bn gc prubic ncg. Gb sujbrl`ds= • Iusqub un gujcr trcnqulgd pcrc bstuklcr, bvltb lntbrrupfldnbs pcrc qub pubkc fdnfbntrcrsb. • Gbc gds rbsý`bnbs kb fckc sb`cnc. Vuircyb d cndtb gcs lkbcs `ãs l`pdrtcntbs. • Bsfufeb gc fgcsb rcklcg y rbsubgvc gds bmbrflflds qub gb prdpdnbn sus `cbstrds gdfutdrbs. • Fd`prubib qub ec rbcglzckd fdrrbftc`bntb gds cutdfdntrdgbs kb fckc sb`cnc. Vl tlbnb kukcs, cnötbgcs. • Bstuklb un pdqultd fckc kàc. Ecjc un pgcn kb gds kàcs qub gb qubkcn ecstc bg kàc kb gc prubic y kdslolqub gds fdntbnlkds. Cg rbcglzcr su pgcn, rbfubrkb cqubggds tb`cs qub gb rbsugtcrdn `ãs kloàflgbs y kbkàqubgbs `ãs tlb`pd. ¡C bstuklcr fdn jcncs!

9?5

LJBY ∙ [cfcnã


3. Bfucfldnbs icgcnfbckcs 3.

Icgcnfbcr unc bfucflön fdnslstb bn iusfcr fdbolflbntbs nu`ìrlfds qub ecjcn qub bg ný`brd kb fckc tlpd kb ãtd`ds prbsbntbs bn gc rbcfflön quà`lfc sbc bg `ls`d bn gds rbcftlvds qub bn gds prdkuftds. ´Fö`d ditbnb`ds unc bfucflön icgcnfbckc4 Xrcftlfc`ds bg `ìtdkd kb tcntbd d `ìtdkd kb bnscyd y brrdr. Xcrc ditbnbr unc bfucflön icgcnfbckc, kbtbr`lnc`ds gds fdbolflbntbs qub nds kcn ný`brds ljucgbs kb fckc tlpd kb ãtd`d bn fckc gckd kb gc rbcfflön. Gds fdbolflbntbs sdn, jbnbrcg`bntb, ný`brds bntbrds. Vbjul`ds bstds pcsds= 3. Kbtbr`lnc`ds quì bgb`bntds nd bstãn icgcnfbckds. Gd pdkb`ds ecfbr pdr sl`pgb lnspbfflön d fdn gc cyukc kb unc tcigc. 9. Icgcnfbc`ds und pdr und gds bgb`bntds, bsfrlilbnkd un ný`brd bntbrd qub nds pbr`ltc ditbnbr bg `ls`d ný`brd kb ãtd`ds bn cìcs pcrtbs kb gc bfucflön. Gc sljulbntb bfucflön bstã icgcnfbckc, sbjýn gd lnklfcn gds fdbolflbntbs kb fckc sustcnflc= 6NcDE + E6XD; ný`brd kb ãtd`ds bn rbcftlvds

Nc 0 6 (6NcDE) D 0 : (6NcDE + E6XD;) 6 + ; E 0 ? (6NcDE + E6XD;) 6 +6 X 0 3 (E6XD;)

Nc6XD; + 6E9D ný`brd kb ãtd`ds bn prdkuftds

Nc 0 6 (Nc6XD;) D 0 : (Nc6XD; + 6E9D) ; + 6 E 0 ? (6E9D) ? X 0 3 (Nc6XD;)

Bmbrflfld 3. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd kb gc rbspubstc fdrrbftc. [lbnb un bmb`pgd. 8)

Bn gc bfucflön= 9A + 9E9D ADE + E9 ´Fuãg bs bg fdbolflbntb qub cfd`pcóc cg ADE y qub pbr`ltb icgcnfbcr gc bfucflön4 3 9 6 Suà`lfc LL ∙ Vb`cnc 6;

9?<

3)

Bn gc bfucflön= E9 + Fg9 EFg ´Fuãg bs bg fdbolflbntb qub cfd`pcóc cg EFg y qub pbr`ltb icgcnfbcr gc bfucflön4 3 9 6

9)

Bn gc bfucflön= 9NcIr + Fg9 NcFg + Ir 9 ´Fuãg bs bg fdbolflbntb qub cfd`pcóc cg NcFg y qub pbr`ltb icgcnfbcr gc bfucflön4 3 9 6

6)

Bn gc bfucflön= ObFg6 + 6NE;DE Ob(DE)6 + NE;Fg ´Fuãg bs bg fdbolflbntb qub cfd`pcóc cg NE ;Fg y qub pbr`ltb icgcnfbcr gc bfucflön4 9 6 ;

;)

Bn gc bfucflön= 9Fr + END6 9Fr(ND6)6 + 6E9 ´Fuãg bs bg fdbolflbntb qub cfd`pcóc cg END 6 y qub pbr`ltb icgcnfbcr gc bfucflön4 ; ? 38

2)

Bn gc bfucflön= F6E5 + D9 6FD9 + ;E9D ´Fuãg bs bg fdbolflbntb qub cfd`pcóc cg D 9 y qub pbr`ltb icgcnfbcr gc bfucflön4 6 ; 2

?)

Bn gc bfucflön= Fc(DE)9 + E9VD; FcVD; + 9E9D ´Fuãg kb gcs sljulbntbs colr`cfldnbs bs fdrrbftc4 Gc bfucflön bstã icgcnfbckc. Ecy qub icgcnfbcr gds `dgbs kb czuorb. Ecy qub icgcnfbcr gds `dgbs kb elkröjbnd.

9:8

LJBY ∙ [cfcnã

Bmbrflfld 9 Icgcnfbb pdr bg `ìtdkd kb tcntbd gcs sljulbntbs bfucfldnbs. Vljc gds pcsds qub cprbnklö bn gc sb`cnc 68. [lbnb un bmb`pgd. 8)

Icgcnfbb= E9VD; + Fc6(XD;)9

FcVD; + E6XD;



Fc 0 6 (Fc6(XD; )9 )

Fc 0 3 (FcVD; )

X09

(Fc6(XD; )9 )

X 0 3 (E6XD; )

V03

(E9VD; )

V 0 3 (Fc VD; )

D 0 39 (E 9VD; + Fc6(XD; )9 ) D 0 5 (FcV D; + E6XD; ) E 0 9 (E9VD; )

E 0 6 (E6XD; )

9. Bsfrlic bg ný`brd 6 bn gc `dgìfugc kb FcVD; pcrc icgcnfbcr bg fcgfld y bg ný`brd 9 bn gc `dgìfugc kb E 6XD;, pcrc icgcnfbcr bg oösodrd. E9VD; + Fc6(XD;)9

6FcVD; + 9E6XD;

Bsfrlic bg ný`brd 6 bn gc `dgìfugc kb E9VD; pcrc icgcnfbcr bg czuorb, dxàjbnd b elkröjbnd. 6E9VD; + Fc6(XD; )9

6FcVD; + 9E6XD;

6. Fd`prubib qub tdkds gds ãtd`ds bstãn icgcnfbckds= ný`brd kb ãtd`ds bn rbcftlvds


Fc 0 6 (Fc6(XD; )9 )

Fc 0 6 (6FcVD; )

X09

X09

(9E6XD; )

V06

(6FcVD; )

(Fc6(XD; )9 )

V 0 6 (6E 9VD; )

D 0 98 (6E9VD; + Fc6(XD; )9 ) D 0 98 (6FcVD; + 9E6XD; ) E 0 ? (6E9VD; )

E 0 ? (9E6XD; )


9:3

3)

Icgcnfbb=

END6

N9D2 + E9D

3. Bsfrlic bg ný`brd kb ãtd`ds kb fckc bgb`bntd bn fckc gckd kb gc rbcfflön, csà scirã qub bgb`bntds nd bstãn icgcnfbckds. ný`brd kb ãtd`ds bn rbcftlvds

0 0 0

N D E

0 0 0

9. Bsfrlic bg ný`brd elkröjbnd y dxàjbnd.


N D E

bn gc `dgìfugc kb END6, pcrc icgcnfbcr bg nltröjbnd, END6

N9D2 + E9D

6. Fd`prubib qub tdkds gds ãtd`ds bstãn icgcnfbckds= ný`brd kb ãtd`ds bn rbcftlvds

0 0 0 9)

N D E

0 0 0

Icgcnfbb= @j + EFg


N D E

@jFg9 + E9

3. Bsfrlic bg ný`brd kb ãtd`ds kb fckc bgb`bntd bn fckc gckd kb gc rbcfflön, csà scirã qub bgb`bntds nd bstãn icgcnfbckds. ný`brd kb ãtd`ds bn rbcftlvds

0@j 0 Fg 0 E

0@j 0 Fg E

0

9. Bsfrlic bg ný`brd


bn gc `dgìfugc kb EFg, pcrc icgcnfbcr bg fgdrd y bg elkröjbnd. @j +

EFg

@jFg9 + E9

6. Fd`prubib qub tdkds gds ãtd`ds bstãn icgcnfbckds=

0@j 0 Fg 0 E

9:9

LJBY ∙ [cfcnã

ný`brd kb ãtd`ds

ný`brd kb ãtd`ds

bn rbcftlvds

bn prdkuftds

0

0@j 0 Fg E

9. Bstbquld`btràc 3.

Gc bstbquld`btràc bs bg fãgfugd fucntltctlvd kb rbcftlvds y prdkuftds bn unc rbcfflön quà`lfc.

3.3 Fãgfugds `dg ‖ `dg Xcrc rbcglzcr fãgfugds bstbquld`ìtrlfds `dg ‖ `dg sb nbfbsltc= • Disbrvcr gc bfucflön quà`lfc icgcnfbckc. Vl nd bstuvlbrc icgcnfbckc, ecy qub ecfbrgd. • Rscr gds fdbolflbntbs kb gc bfucflön icgcnfbckc. Bstds lnklfcn gcs prdpdrfldnbs bn `dgbs bn gcs qub gcs sustcnflcs rbcffldncn y sb prdkufbn. • Bsfdjbr un ocftdr kb fdnvbrslön qub pbr`ltc ditbnbr bg ný`brd kb `dgbs qub nds prbjuntcn. • Cpglfcr bg ocftdr kb fdnvbrslön pcrc ditbnbr gc rbspubstc. • Bsfrlilr gc rbspubstc. 3.9 Fãgfugds `csc ‖ `csc Xcrc rbcglzcr fãgfugds bstbquld`ìtrlfds `csc ‖ `csc sb nbfbsltc= • Disbrvcr gc bfucflön quà`lfc icgcnfbckc. Vl nd bstuvlbrc icgcnfbckc, ecy qub ecfbrgd. • Rscr gds fdbolflbntbs kb gc bfucflön icgcnfbckc pcrc kbtbr`lncr gds ocftdrbs kb fdnvbrslön bn `dgbs kb gds rbcftlvds y kb gds prdkuftds qub nds lntbrbscn. Xcrc bstd nbfbsltcrb`ds= • Bstcigbfbr ocftdrbs kb fdnvbrslön y bsfdjbr und qub pbr`ltc fdnvbrtlr c `dgbs gc `csc qub kcn. • Bstcigbfbr ocftdrbs kb fdnvbrslön `dgbs ‖ `dgbs y bsfdjbr bg qub pbr`ltc fdnvbrtlr gc sustcnflc qub nds kcn bn gc sustcnflc iusfckc. • Ybfdnvbrtlr gds vcgdrbs cntbrldrbs bn `csc y pcrc bsd ecy qub bstcigbfbr dtrd ocftdr kb fdnvbrslön `dgbs ‖ `csc `dgcr y bsfdjbr und qub pbr`ltc ditbnbr bg ný`brd kb jrc`ds qub prbjuntcn. • Cpglfcr gds ocftdrbs kb fdnvbrslön pcrc ditbnbr gc rbspubstc. • Bsfrlilr gc rbspubstc. Suà`lfc LL ∙ Vb`cnc 6;

9:6

Bmbrflfld 6. Ybgcfldnb fdnfbptds Ybggbnb bg fuckrd qub fdrrbspdnkb cg ocftdr kb fdnvbrslön ckbfuckd pcrc fckc und kb gds fcsds. [lbnb un bmb`pgd. 8)

Vl kbsbc scibr fuãntds ãtd`ds kb nbön (Nb) ecy bn 3.9 `dgbs kb nbön (Nb), ´quì ocftdr kb fdnvbrslön kbib uscr4 98.3 j kb Nb 3.8 `dg kb Nb

3)

3.8 `dg kb Nb ?.899 x 3896 ãtd`ds kb Nb

´Suì ocftdr kb fdnvbrslön ecy qub uscr pcrc fdnvbrtlr 288 j kb pgd`d (Xi) c `dgbs kb pgd`d (Xi)4 3 `dg kb Xi 98:.9 j kb Xi

9)

98:.9 j kb Xi 3 `dg kb Xi

3 `dg kb Ic 36:.6 j kb Ic

36:.6 j kb Ic 3 `dg kb Ic

´Suì ocftdr kb fdnvbrslön nbfbsltc pcrc bnfdntrcr bg vdgu`bn `dgcr kb 8.<: `dgbs kb fgdrd `dgbfugcr (Fg9)4 3 `dg kb Fg9 99.; G kb Fg9

;)

3 `dg kb Xi 9 `dg kb E +

´Suì ocftdr kb fdnvbrslön nbfbsltc pcrc fdnvbrtlr 8.:9 `dgbs kb icrld (Ic) bn jrc`ds kb icrld (Ic)4 3 `dg kb Ic ?.899 x 3896 ãtd`ds kb Ic

6)

?.899 x 3896 ãtd`ds kb Nb 3.8 `dg kb Nb

3 `dg kb Fg9 :3.8 j kb Fg9

99.; G kb Fg9 3 `dg kb Fg9

Bn gc bfucflön quà`lfc= Nc9Fr9D:+ 9AFg

9NcFg + A 9Fr9D:

´Suì ocftdr kb fdnvbrslön kbib utlglzcr pcrc ditbnbr `dgbs kb fgdrurd kb sdkld (NcFg) c pcrtlr kb `dgbs kb klfrd`ctd kb sdkld (Nc 9Fr9D:)4 9 `dgbs kb NcFg 9 `dgbs kb AFg

2)

3 `dg kb Nc9Fr9D: 9 `dgbs kb NcFg

9 `dgbs kb NcFg 3 `dg kb Nc9Fr9D:

´Suì ocftdr kb fdnvbrslön kbib uscr pcrc fdnvbrtlr 3;.<5 x 389? `dgìfugcs kb F?8 bn `dgbs kb F?84 3 `dg kb F?8 ?.899 x 3896 `dgìf. kb F?8

9:;

LJBY ∙ [cfcnã

?.899 x 3896 `dgìf. kb F?8 3 `dg kb F?8

3 `dg kb F?8 3;.<5 x 389? `dgìf. kb F?8

Bmbrflfld ; Ybcglfb gcs fdnvbrsldnbs bn su fuckbrnd. 3)

Bg cgfdedg btàglfd (F9E2DE) sb qub`c kb cfubrkd fdn gc bfucflön icgcnfbckc= F9E2DE + 6D9

9FD9+ 6E9D

´Fuãntds `dgbs kb klöxlkd kb fcridnd (FD 9) sb prdkufbn fucnkd sb qub`cn 6.8 `dgbs kb cgfdedg btàglfd (F9E2DE) kb bstc `cnbrc4 9)

Bg dftcnd (F5E35) sb qub`c kb cfubrkd fdn gc bfucflön icgcnfbckc= 9F5E35 + 92D9

3?FD9 + 35E9D

´Fuãntds jrc`ds kb klöxlkd kb fcridnd (FD 9) sb prdkufbn fucnkd sb qub`cn 2.8 j kb dftcnd (F5E35)4 6)

´Suì `csc kb `cjnbsld (@j) sb nbfbsltc pcrc qub rbcffldnb fdn <.6 j kb nltröjbnd (N)4 Gc bfucflön nd icgcnfbckc kb bstc rbcfflön bs= @j + N

9

@j6N9

Bg prl`br pcsd bs icgcnfbcr gc bfucflön. ;)

Vl 6.8 `dgbs kb klöxlkd kb czuorb (VD9) jcsbdsd rbcffldncn fdn dxàjbnd (D 9) pcrc prdkuflr trlöxlkd kb czuorb (VD6), ´fuãntds jrc`ds kb dxàjbnd sb nbfbsltcn4 Gc bfucflön nd icgcnfbckc bs= VD9 + D9

2)

VD6

´Fuãntds jrc`ds kb öxlkd kb elbrrd (LLL), (Ob9D6), sb pubkbn prdkuflr c pcrtlr kb 9.2 j kb dxàjbnd (D9) qub rbcffldncn fdn elbrrd söglkd (Ob)4 Gc bfucflön nd icgcnfbckc bs= Ob + D9

Ob9D6

?)

´Fuãntds jrc`ds kb cjuc (E9D) sb odr`cn c pcrtlr kb gc fdnvbrslön tdtcg kb 69.8 j kb dxàjbnd jcsbdsd (D9) bn prbsbnflc kb elkröjbnd jcsbdsd (E9), sbjýn gc bfucflön icgcnfbckc 9E9 + D9 9E9D4

:)

Gc obr`bntcflön kb jgufdsc (F?E39D?) prdkufb cgfdedg btàglfd, (F9E2DE) y klöxlkd kb fcridnd (FD9). Gc bfucflön icgcnfbckc bs= F?E39D?

9F9E2DE + 9FD9

´Fuãntds jrc`ds kb cgfdedg btàglfd sb pubkbn prdkuflr c pcrtlr kb 38.8 j kb jgufdsc4


9:2

6. Vdgufldnbs 3.

Rnc sdguflön d klsdguflön bs unc `bzfgc ed`djìnbc kb un sdgutd (sustcnflc qub sb klsubgvb) klstrliulkc kb `cnbrc unlodr`b bn un sdgvbntb (sustcnflc kdnkb sb klsubgvb bg sdgutd).

3.3 Fgcslolfcflön kb gcs sdgufldnbs c. Xdr su bstckd kb cjrbjcflön pubkbn sbr= Vdgufldnbs gàqulkcs= söglkds bn gàqulkds, jcsbs bn gàqulkds y gàqulkds bn gàqulkds. Vdgufldnbs söglkcs= söglkd bn söglkd, jcs bn söglkd y gàqulkd bn söglkd. Vdgufldnbs jcsbdsc= jcsbs bn jcsbs. i. Xdr su fdnfbntrcflön pubkbn sbr= Vdguflön scturckc= bs cqubggc qub fdntlbnb tcntd sdgutd fd`d pubkb klsdgvbrsb bn unc fcntlkck kbtbr`lnckc kb sdgvbntb c tb`pbrcturc cìlbntb. Bstc sdguflön bs bstcigb. Vdguflön lnscturckc d klgulkc= bs cqubggc bn gc qub gc fdnfbntrcflön kbg sdgutd bs `bndr qub gc fdnfbntrcflön kb unc sdguflön scturckc c tb`pbrcturc cìlbntb. Vdguflön sdirbscturckc= bs cqubggc bn gc qub gc fdnfbntrcflön kb sdgutd bs `cydr qub gc kb unc sdguflön scturckc. Bs lnbstcigb pdrqub kbpbnkb kb gc tb`pbrcturc. Xcrc gdjrcr qub bg sdgutd sb klsubgvc, ecy qub fcgbntcr gc sdguflön. 9.

Fdnfbntrcflön kb unc sdguflön Gc fdnfbntrcflön kb unc sdguflön bs gc prdpdrflön d rbgcflön qub ecy bntrb gc fcntlkck kb sdgutd y gc fcntlkck kb sdgvbntb.

9.3 Xdrfbntcmb `csc ‖ `csc (% `/`) Bg pdrfbntcmb `csc ‖ `csc sb kbolnb fd`d gc `csc kb sdgutd (sustcnflc qub sb klsubgvb) pdr fckc 388 unlkckbs kb `csc kb gc klsdguflön= % `csc 0 `csc kb sdgutd (j) x 388 `csc kb sdguflön (j)


9.9 Xdrfbntcmb vdgu`bn ‖ vdgu`bn (% v/v) Bg pdrfbntcmb vdgu`bn ‖ vdgu`bn sb kbolnb fd`d bg vdgu`bn kb sdgutd (sustcnflc qub sb klsubgvb), bxprbsckd bn `lglgltrds, qub ecy bn 388 `g kb sdguflön. % vdgu`bn 0

9:?

LJBY ∙ [cfcnã



Bmbrflfld 2 C.


´Suì tlpd kb sustcnflc pcrtlflpc bn `cydr prdpdrflön bn unc sdguflön4

sdgutd sdgvbntb sdguflön

3)

Bn bg cjuc czufcrckc, ´fuãg bs bg sdgutd4

dxàjbnd czýfcr cjuc

I.

9)

´Fuãg kb gcs sljulbntbs sdgufldnbs bstã bn bstckd gàqulkd4

clrb kb gc ct`ösobrc dxàjbnd bn cjuc cfbrd

6)

´Fö`d sb ggc`c gc sdguflön bn gc qub bg sdgutd y bg sdgvbntb bstãn bn bqulglirld4

scturckc lnscturckc sdirbscturckc

Fd`pgbtb gc tcigc pcrc fgcslolfcr gcs sdgufldnbs y sus fd`pdnbntbs sbjýn su bstckd kb cjrbjcflön. [lbnb un bmb`pgd. sdguflön

cjuc dxljbnckc `bklflncg subrd drcg

kb gcbstckd sdguflön

gàqulkd

sdgutd

pbröxlkd kb elkröjbnd (E9D9 ) scg fd`ýn (NcFg) y czýfcr (F39E99D33)

bstckd sdgutdkbg

gàqulkd

sdgvbntb

cjuc

gàqulkd

cjuc

dxàjbnd `bklflncg

dxàjbnd (D9)

nltröjbnd (N9)

cgfdedg kb ocr`cflc

cgfdedg (FE6FE9DE)

cjuc

cjuc kb `cr

scg fd`ýn (NcFg)

cjuc nltröjbnd (N9)

cjuc jcsbdsc d

dxàjbnd (D9) y klöxlkd kb fcridnd (FD9) klöxlkd kb fcridnd

fcridnctckc c`cgjc`c kbntcg

(FD9) `brfurld `btãglfd (Ej)

pgctc (Cj)

nlfrd`d

nàqubg(Nl)

frd`d(Fr)

ct`ösobrc

bstckd kbg sdgvbntb

cjuc


9::

Bmbrflfld ? Ybsubgvc gds prdigb`cs kb % `csc ‖ `csc y % vdgu`bn ‖ vdgu`bn bn su fuckbrnd. 3)

´Fuãg bs bg pdrfbntcmb ` ‖ ` kb unc sdguflön kb 28 j kb `csc tdtcg, bn gc qub sb ecn klsubgtd 38.8 j kb sugoctd kb fdirb (FuVD;)4

9)

Kbib prbpcrcr 928 j kb sdguflön kb scg bn cjuc, fdn unc fdnfbntrcflön kb 2 % `/`. ´Suì fcntlkck kb scg kbib klsdgvbr bn bg cjuc4

6)

Gc jgufdsc, und kb gds fd`pdnbntbs kbg czýfcr, bs unc sustcnflc söglkc sdguigb bn cjuc. Gc sdguflön kb jgufdsc bn cjuc (subrd jgufdsckd) sb usc pcrc cgl`bntcr c gds bnobr`ds fucnkd nd pubkbn fd`br. Bn gc btlqubtc kb unc idtbggc kb subrd kb 288 j cpcrbfb= —Vdguflön kb jgufdsc bn cjuc, fdnfbntrcflön 22 % `/`‐. c. ´Fuãg bs bg sdgvbntb y fuãg bg sdgutd bn gc sdguflön4 i. Xdnb`ds bn un pgctd 28 j kb subrd. Vl kbmc`ds qub sb bvcpdrb bg cjuc, ´quì fcntlkck kb jgufdsc qubkcrã bn bg pgctd4

;)

Vb ec prbpcrckd unc sdguflön kb fgdrurd kb fdirb (FuFg9) bn cjuc (E9D), klsdgvlbnkd 39 j kb fgdrurd kb fdirb bn <5 j kb cjuc. Fcgfugb gc fdnfbntrcflön bn % `/` kb gc sdguflön.

2)

´Fuãg bs bg pdrfbntcmb vdgu`bn ‖ vdgu`bn kb unc sdguflön qub fdntlbnb 28 `G kb cgfdedg y 3;8 `G kb cjuc4

?)

Bg cjuc dxljbnckc cg 6% v/v bs un cntlsìptlfd kb usd jbnbrcg. Bs unc sdguflön kb pbröxlkd kb elkröjbnd (E9D9) bn cjuc. Vl un rbflplbntb tlbnb 92 `G kb sdguflön, ´fuãntds `lglgltrds kb pbröxlkd kb elkröjbnd fdntlbnb4

:)

Vb usc unc `bzfgc kb 9 gltrds kb btlgbnjglfdg (rborljbrcntb) y ; jcgdnbs (98 gltrds) kb cjuc pcrc ggbncr bg rcklckdr kb un fcrrd. ´Fuãg bs bg % v/v kb gc sdguflön4

5)

Gcs cgbcfldnbs `btãglfcs sdn sdgufldnbs bn gcs qub gds fd`pdnbntbs bstãn bn bstckd söglkd. Xcrc `bklr gc fdnfbntrcflön kb drd bn unc cgbcflön (bg rbstd subgb sbr pgctc) sb usc unc unlkck ggc`ckc qulgctb. Rnc fdnfbntrcflön kb 3 qulgctb bs kb 3/9; kbg tdtcg, bs kbflr, kb fckc 9; j kb cgbcflön, 3 j bs kb drd purd. c. ´Suì % bn `csc fdrrbspdnkb c unc cgbcflön kb 3 qulgctb4 i. ´Suì % bn `csc tbnkrã unc cgbcflön kb 35 qulgctbs4 f. ´Suì fcntlkck kb drd purd pdsbb un glnjdtb kb drd kb 35 qulgctbs kb ; aj kb `csc4 Ybfubrkb qub 3 aj fdntlbnb 3888 j.

9:5

LJBY ∙ [cfcnã

;. Fdgdlkbs 3.

Fdgdlkbs Rn fdgdlkb bs unc `bzfgc bn gc qub unc sustcnflc fd`pubstc pdr pcrtàfugcs sb klspbrsc kb `cnbrc unlodr`b bn un sdgvbntb.

3.3 Fcrcftbràstlfcs kb gds fdgdlkbs • Xrbsbntcn unc cpcrlbnflc vlsfdsc. • Vus fd`pdnbntbs nd sb sbkl`bntcn, nl sb olgtrcn. • Gcs pcrtàfugcs prbsbntcn `dvl`lbntd Irdwnlcnd. • Xrbsbntcn bg bobftd [ynkcgg. 3.9 Gc klobrbnflc bntrb sdguflön y fdgdlkb bs bg tc`cód kb gcs pcrtàfugcs bn sdguflön. Bn bg fcsd kb gds fdgdlkbs sb ecigc kb ocsb klspbrsc y kb `bkld kb klspbrslön, fdnfbptds bqulvcgbntbs c gds kbg sdgutd y sdgvbntb usckds bn gcs sdgufldnbs. Rn fdgdlkb bstã odr`ckd pdr kds ocsbs sbpcrckcs= • Gc ocsb klspbrsc= bstã odr`ckc pdr pcrtàfugcs d `lfbgcs. • @bkld kb klspbrslön= bs gc ocsb bn gc qub sb bnfubntrcn klstrliulkcs gcs `lfbgcs. 9.

Fgcslolfcflön kb gds fdgdlkbs pdr su bstckd kb cjrbjcflön ndìrb

ocsb klspbrsc


bmb`pgds

cbrdsdg gàqulkd

gàqulkd

jcs

nlbigc,nuibs

cbrdsdg söglkd

söglkd

jcs

bspu`c

jcs

gàqulkd

bùgslön

gàqulkd

gàqulkd

sdg

söglkd

gàqulkd

pdgvd,eu`d bspu`cs (kb mciön, kb `cr, btf), frb`c kb cobltcr, frb`c ictlkc gbfeb, `cydnbsc, frb`c fds`ìtlfc plnturcs, tlntc felnc, jd`c crãiljc, mcgbcs

bspu`c söglkc

jcs

söglkd

plbkrc pö`bz, bspdnmc


söglkd

`cntbqulggc, qubsd

jbg

söglkd

jbgctlnc, jd`ltcs (kugfbs), `bklfc`bntds bn odr`c kb jbgbs, pcstc kb klbntbs

gàqulkd


9:<

Bmbrflfld : Fd`pgbtcr gc tcigc fdn gc lnodr`cflön qub ecfb ocgtc. [lbnb un bmb`pgd. ocsb klspbrsc

mciön

bstckd kb cjrbjcflön

söglkd


cjuc

cjuc

clrb

plj`bntd

sdgvbntb`lnbrcg

vbnbnd

jcs prbslön c

cjuc

cfbltb vbjbtcg

clrb

pgãstlfd

pdgvd kb fcridnd

clrb


ndìrb kbg fdgdlkb

gàqulkd

sdg

sustcnflc rbsugtcntb

cjucfdnmciön nlbigc plnturckbcfbltb lnsbftlflkc `crjcrlnc bspdnmc eu`d

Bmbrflfld 5 Kb fckc unc kb gcs dpfldnbs `crqub bg fuckrd kb gc qub `ãs sb cfbrqub c gc kbnlflön kbg fdnfbptd kbsfrltd. 3)

Fdgdlkb Bs unc `bzfgc ed`djìnbc kb kds sustcnflcs qub nd sb `bzfgcn. Bs unc `bzfgc bn gc qub unc sustcnflc fd`pubstc pdr pcrtàfugcs sb klspbrsc kb `cnbrc unlodr`b bn un sdgvbntb.

9)

Bs unc sdguflön ebtbrdjìnbc. Bobftd [ynkcgg Obnö`bnd qub sb prdkufb fucnkd gds fdgdlkbs sdn ctrcvbsckds pdr un rcyd kb guz y bstb sb klspbrsc. Obnö`bnd qub sb prdkufb bn gcs eciltcfldnbs dsfurcs kdnkb sb vb fö`d bntrcn gds rcyds kb guz. Obnö`bnd qub kbsfrlib bg `dvl`lbntd kb gcs `lfbgcs.

6)

@dvl`lbntd Irdwnlcnd @dvl`lbntd kb Irdwn. @dvl`lbntd qub sb prdkufb fucnkd sb cjltc un fdgdlkb. @dvl`lbntd rãplkd, lrrbjugcr y vljdrdsd kb gcs pcrtàfugcs qub odr`cn un fdgdlkb.

;)

Ocsb klspbrsc Vdn gcs pcrtàfugcs qub sb bnfubntrcn suspbnklkcs odr`cnkd un fdgdlkb y sb ggc`cn `lfbgcs. Bs gc jrcsc gãftbc bn cjuc pcrc odr`cr gbfeb. Bs gc ocsb qub nd sb bnfubntrc bn un fdgdlkb.

958

LJBY ∙ [cfcnã

Xcrc tbr`lncr nubstrd fursd kb Suà`lfc... Gd lnvltc`ds c rbbxldncr fdn unc pbqubóc elstdrlc.

_lrjlnlc, tcn glstc fd`d bg prdobsdr Dic`c Vl bn nubstrds pcàsbs nd bxlstlbrc bg cils`d kb gc kbsljucgkck qub pckbfb`ds, _lrjlnlc tbnkràc un kdftdrckd bn gc `bmdr unlvbrslkck kbg ùnkd, pdrqub bs glstc fd`d bg prdobsdr Dic`c. Vb gb vb kbskb gc prl`brc vbz qub und ecigc fdn bggc. Vögd bstuklö ecstc fucrtd kb prl`crlc, pbrd nd pcrbfb frbàigb pdrqub, `lbntrcs kbsicrctc gds nukds qub kbmc gc tbnslön bn unc bspcgkc, kbs`bnuzc gc rbcglkck fd`d qulbn ecfb un kbselgckd d unc tbsls kdftdrcg. \ gc muzjc, gc bnorbntc, gc kljlbrb fdn unc sbnflggbz pcs`dsc. Bs l`pgcfcigb y kbsfdndfb gc plbkck jrctultc. Bs ùy iubnc gbftdrc. Gd qub gb vcyc rbjcgcnkd su fglbntbgc sb gd ibib. \ kb tdkd bntlbnkb, pdrqub csà fd`d scib fdntcr elstdrlcs, scib dàrgcs. [bxtd td`ckd y ckcptckd kb ‗Kdftdrckd bn elstdrlcs‐. Ãnjbgbs @cstrbttc

Cg ljucg qub _lrjlnlc, ùfecs ùmbrbs y edìrbs, glstds fd`d bg —prdobsdr Dic`c‐, nd kbscrrdggcn tdkd su pdtbnflcg pdrqub nd ecn tbnlkd dpdrtunlkck kb bstuklcr. Rstbk tbr`lncrã bg icfelggbrctd ùy prdntd y tbnkrã gc pdslilglkck kb fdntlnucr sus bstuklds bn gc unlvbrslkck d bn unc lnstltuflön qub gd prbpcrb fd`d tìfnlfd. Gc ggcvb pcrc cirlr bstc pubrtc kb dpdrtunlkckbs bstã ocirlfckc fdn su bsoubrzd y su kbklfcflön, pbrd tcìlìn fdn gc jbnbrdslkck kb gcs `cbstrcs y `cbstrds drlbntckdrbs vdguntcrlds qub gd ecn cfd`pcóckd.

´Sulbrb irlnkcr dpdrtunlkckbs c dtrcs pbrsdncs kb su fdùnlkck4 Gd lnvltc`ds c qub sb unc cg vdguntcrlckd bn bkufcflön kbg LJBY. Irlnkcr su tlb`pd fdn rbspdnscilglkck y jbnbrdslkck fd`d `cbstrd drlbntckdr vdguntcrld pubkb kls`lnulr bg cils`d kb gc kbsljucgkck. ´Vb fd`prd`btb4 \d= `b fd`prd`btd c sbr `cbstrd drlbntckdr vdguntcrld kurcntb bg flfgd

.

olr`c c

gc gc eubg ¡Bstc bs drczön kb un f y sdglkcrld! lk d jrckbf


953



gdjrckd

rbjugcr

nd gdjrckd

Cspbftds c bvcgucr Kbspuìs kb bstuklcr...

3.

Kd`lnd gds fdntbnlkds kb gc sb`cnc 68 c 66.

9.

@b slbntd prbpcrckd pcrc gc prubic olncg kb Suà`lfc.

Bn bg `d`bntd kb gc prubic...

Cg rbflilr gc prubic, y cntbs kb b`pbzcr c rbsdgvbrgc, bsfrlic su ndìrb, ný`brd kb fcrnì, ný`brd kb fbntrd y obfec, bn gc pcrtb supbrldr. Gbc ctbntc`bntb gcs lnstruffldnbs cntbs fdntbstcr. Vl tlbnb kukc, fdnsugtb c su `cbstrc d `cbstrd drlbntckdr.

Nd sb —ctcsqub‐ bn nlnjýn bmbrflfld. B`plbfb pdr gds bmbrflflds qub sbpc fdn sbjurlkck y gb qubkcrã `ãs tlb`pd pcrc pbnscr bn gds qub tbnjc kukc. Cg olncglzcr su bxc`bn, rbgbc tdkcs sus rbspubstcs y vbc sl cgjd sb gb pcsö pdr cgtd. Xrbsbntb su prubic gl`plc y drkbnckc.

959

LJBY ∙ [cfcnã

Fgcvbs

Suà`lfc LL ∙ Fgcvbs

956

Vb`cnc 35

Vb`cnc 3<

¡Xcrc fd`bnzcr!

¡Xcrc fd`bnzcr!

8) Nd fu`pgb gc rbjgc kbg dftbtd pdrqub tlbnb sdgd un bgbftrön bn su ýgtl`d nlvbg kb bnbrjàc. 3) Nd fu`pgb gc rbjgc kbg dftbtd pdrqub tlbnb sdgd fuctrd bgbftrdnbs bn su ýgtl`d nlvbg kb bnbrjàc. 9) Và fu`pgb gc rbjgc kbg dftbtd pdrqub tlbnb dfed bgbftrdnbs bn su ýgtl`d nlvbg kb bnbrjàc. 6) bgbftrdnbs Và fu`pgb bn gc su rbjgc kbg nlvbg dftbtd ýgtl`d kb pdrqub bnbrjàc.tlbnb dfed

Bmbrflfld 3

c. i. f. k. b.

3< Ė <Ė gb sdircn 3Ė +3

Bmbrflfld 3 6 8) Bg NE fd`pubstd bstã odr`ckd pdr= 3 ãtd`d kb nltröjbnd 6 ãtd`ds kb elkröjbnd

Gc rbkcfflön vcrlcrã pbrd kbib `cntbnbr gc lkbc fbntrcg. 3) D6 Gb prbsbntc`ds un bmb`pgd. Bg fd`pubstd bstã odr`ckd pdr= Bg bngcfb quà`lfd bs gc oubrzc qub unb c gds ãtd`ds 6 ãtd`ds kb dxàjbnd y gbs pbr`ltb cjrupcrsb pcrc odr`cr fd`pubstds d `dgìfugcs. 9) Cj9D6 Bg fd`pubstd bstã odr`ckd pdr= Bmbrflfld 9 9 ãtd`ds kb pgctc 6 ãtd`ds kb dxàjbnd C. 8) `btãglfd 6) FD9 3) fdvcgbntb Bg fd`pubstd bstã odr`ckd pdr= 9) lönlfd 3 ãtd`d kb fcridnd 6) fdvcgbntb 9 ãtd`ds kb dxàjbnd I. 9 8) bngcfb `btãglfd ;) Bg FuIr fd`pubstd bstã odr`ckd pdr= 3) bngcfb fdvcgbntb 3 ãtd`d kb fdirb 9) bngcfb lönlfd 9 ãtd`ds kb ird`d


Bmbrflfld 9

Xcsd 3 Bg odfd nd bnflbnkb fdn gc scg bn bstckd söglkd pdrqub C. gds fd`pubstds lönlfds sdgd fdnkufbn gc bgbftrlflkck 3) 2 ãtd`ds pdr j kb F ;8 ãtd`ds pdr j kb E klsubgtds bn cjuc.

9) 2 ãtd`ds kb F ú 2 0 2 Xcsd 9 ;8 ãtd`ds kb E ú 2 0 5 Bg odfd sà bnflbnkb pdrqub gc scg bs un fd`pubstd lönlfd qub fdnkufb gc bgbftrlflkck cg klsdgvbrsb bn cjuc. Gc oörùgc b`pàrlfc kbg fd`pubstd bs= F 2E5 I. 3) 3.; ãtd`ds pdr j kb Nc 8.: ãtd`ds pdr j kb V

9.5 ãtd`ds pdr j kb D 9) 3.; ãtd`ds ú 8.: 0 9 8.: ãtd`ds ú 8.: 0 3 9.5 ãtd`ds ú 8.: 0 ; Gc oörùgc b`pàrlfc kbg fd`pubstd bs Nc 9VD;

95;

LJBY ∙ [cfcnã

Vb`cnc 98 Bmbrflfld 6

¡Xcrc fd`bnzcr!

3) c. F; E: 0 ;(39 j) + :(3 j) 0 ;5 j + : j 0 22 j i. 338 j ú 22 j 0 9 f. F; x 9 E: x 9 0 F5E3; Gc oörùgc `dgbfugcr bs= F 5 E3; 9) c. F6E;D6 0 6(39 j) + ;(3 j) + 6(3? j) 0 6? j + 5 j + ;5 j 0 <9 j i. 3:? j ú <9 j 0 3.< 0 9 f. F6 x 9 E; x 9 D6 x 9 0 F?E5 D?

8) fd`pubstd ilncrld 3) fd`pubstd tbrncrld 9) fd`pubstd tbrncrld 6) fd`pubstd fuctbrncrld ;) fd`pubstd ilncrld 2) fd`pubstd tbrncrld

¡C gc flbnflc pdr gc bxpbrlbnflc! _csbglnc= F6E2(DE)6 Ilfcridnctd kb sdkld= NcEFD6 [cgfd= @j6Vl;D38(DE)9

Bmbrflfld 3 8) öxlkd iãslfd 3) 9) 6)

∙9 öxlkd ãflkd elkröxlkds

Bmbrflfld 9 fd`pubstd

ounflön quà`lfc

GlDE

icsb

@jD

öxlkd

EIr

ãflkd

NcO

scg

FrD

öxlkd

EL

ãflkd

AFg Cu9D

scg öxlkd

Fc(DE)9

icsb

¡C gc flbnflc pdr gc bxpbrlbnflc! ´Suì sufbklö4 Bg mujd kb gl`ön y bg vlncjrb fdntlbnbn ãflkd, y bg ãflkd kbilgltc bg pcpbg. Bg ãflkd sb qubkc bn bg pcpbg cunqub bg mujd sb sbqub. Fucnkd sb sdstlbnb bg pcpbg fbrfc kbg fcgdr d gc guz, gcs pcrtbs kbg pcpbg qub tlbnbn ãflkd sb qub`cn `ãs rãplkd y ckqulbrbn un fdgdr fcoì.


952

Vb`cnc 93 Bmbrflfld 3

;) Öxlkd kb tltcnld (L_) ([lD9) Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= tltcnld Ný`brd kb dxlkcflön kbg bgb`bntd= ;

Gc nd`bnfgcturc quà`lfc

bs

Bg fdnmuntd kb rbjgcs qub sb ecn bstcigbflkd pcrc ndìrcr c gds fd`pubstds quà`lfds. Ecy trbs slstb`cs=

bstbquld`ìtrlfd

Vtdfa

Bmbrflfld 9 8) [rlirdùrd kb frd`d FrIr6 Xrbolmd (3)= trl Ndìrb jbnìrlfd= irdùrd Xrbolmd (9)= nd tlbnb Ndìrb bspbfàolfd= frd`d 3) Ebptcöxlkd kb klfgdrd Fg9D: Xrbolmd (3)= ebptc Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= kl Ndìrb bspbfàolfd= fgdrd 9) @dnöxlkd kb klpdtcsld A9D Xrbolmd (3)= `dnd Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= kl Ndìrb bspbfàolfd= pdtcsld

Bmbrflfld 6 3) Irdùrd kb frd`d (LLL) FrIr6 Ndìrb jbnìrlfd= irdùrd Ndìrb kbg bgb`bntd= frd`d Ný`brd kb dxlkcflön kbg bgb`bntd= 6 9) Öxlkd kb fgdrd (_LL) Fg9D: Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= fgdrd Ný`brd kb dxlkcflön kbg bgb`bntd= : 6) Ndìrb Öxlkd kbjbnìrlfd= pdtcsld (L) A9D öxlkd Ndìrb kbg bgb`bntd= pdtcsld Ný`brd kb dxlkcflön kbg bgb`bntd= 3

95?

LJBY ∙ [cfcnã

trcklfldncg

2) Elkröxlkd kb frd`d (LLL) Fr(DE)6 Ndìrb jbnìrlfd= elkröxlkd Ndìrb kbg bgb`bntd= frd`d Ný`brd kb dxlkcflön kbg bgb`bntd= 6 ?) Öxlkd kb fdirb (LL) (FuD) Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= fdirb Ný`brd kb dxlkcflön kbg bgb`bntd= 9

Vb`cnc 99 ¡Xcrc fd`bnzcr!

Bmbrflfld 6

3) Dxàjbnd `dgbfugcr 9) Bn gc gltdsobrc odr`c slglfctds y bn gc elkrdsobrc, cjuc 6) Xubkb sbr= • dxàjbnd `dgbfugcr (D9) • dzdnd (D 6) • klöxlkd kb slglfld (VlD 9) • klöxlkd kb fcridnd (FD 9) • `dnöxlkd kb fcridnd (FD) • klöxlkd kb nltröjbnd (ND 9) • `dnöxlkd kb nltröjbnd (ND) • klöxlkd kb czuorb (VD 9)

3) ]nD Xrbolmd (3)= `dnd Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= nd tlbnb Ndìrb bspbfàolfd= zlnf Ndìrb kbg fd`pubstd= `dnöxlkd kb zlnf 9) A9D

Bmbrflfld 3 8)

Fu9D

fdirb (`btcg)

vcgbnflc ∙9

kbg dxàjbnd 3)

`cnjcnbsd (`btcg)

@n9D6

dxàjbnd vcgbnflc +3 kbg fdirb dxàjbnd

vcgbnflc ∙9 vcgbnflc +6 kbg kbg dxàjbnd

Bmbrflfld 9 C. 8)

czuorb (nd `btcg)

VD9

vcgbnflc ∙9

kbg dxàjbnd 3)

sbgbnld

Vb9D6


Xrbolmd (3)= `dnd Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= kl Ndìrb bspbfàolfd= pdtcsld Ndìrb kbg fd`pubstd= `dnöxlkd kb klpdtcsld 6) FD9 Xrbolmd (3)= kl Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= nd tlbnb Ndìrb bspbfàolfd= fcridnd Ndìrb kbg fd`pubstd= klöxlkd kb fcridnd ;) N9D6 Xrbolmd (3)= trl Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= kl Ndìrb bspbfàolfd= nltröjbnd Ndìrb kbg fd`pubstd= trlöxlkd kb klnltröjbnd

`cnjcnbsd

Bmbrflfld ;

dxàjbnd

3) Ej9D Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= `brfurld Ný`brd kb vcgbnflc kbg bgb`bntd= 3 Ndìrb kbg fd`pubstd= öxlkd kb `brfurld (L)

vcgbnflc +; kbg czuorb dxàjbnd vcgbnflc +6 kbg sbgbnld

9) Fg9D: Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= fgdrd Ný`brd kb vcgbnflc kbg bgb`bntd= : Ndìrb kbg fd`pubstd= öxlkd kb fgdrd (_LL)

I. 8) Vl= nd `btcg öxlkd ãflkd

6) Cs9D6 Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= crsìnlfd Ný`brd kb vcgbnflc kbg bgb`bntd= 6 Ndìrb kbg fd`pubstd= öxlkd kb crsìnlfd (LLL)

3) Fd= `btcg öxlkd iãslfd 9) Fg= nd `btcg öxlkd ãflkd 6) Ob= `btcg öxlkd iãslfd

;) N9D; Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= nltröjbnd Ný`brd kb vcgbnflc kbg bgb`bntd= ; Ndìrb kbg fd`pubstd= öxlkd kb nltröjbnd (L_) Suà`lfc LL ∙ Fgcvbs

95:

Vb`cnc 96 Bg ùnkd kb gc quà`lfc

;) EjDE 3 ãtd`d kb `brfurld Bmbrflfld 3 3 ãtd`d kb dxàjbnd Gc rbkcfflön pubkb vcrlcr, pbrd kbib `cntbnbr gc lkbc 3 ãtd`d kb elkröjbnd fbntrcg. Xdr bmb`pgd= 3) Gds ãtd`ds fd`pcrtbn gds bgbftrdnbs, pbrd ìstds sb 2) CjFg 3 ãtd`d kb pgctc ùbvbn pdr tdkc gc cgbcflön odr`cnkd unc nuib kb 3 ãtd`d kb fgdrd bgbftrdnbs. 9) Gds bgbftrdnbs sb trcnsolbrbn kb un ãtd`d c dtrd. Bmbrflfld ? 9 2 6) bngcfbs. Gds bgbftrdnbs sb fd`pcrtbn bn pcrbs odr`cnkd 3) c. E j0 ú9 9< (39jj)0 +9.88? 2 (3 cprdxl`ckc`bntb j) 0 9< j i. F 25.9 9 f. F9 x 9E2 x 9 Bmbrflfld 9 Gc oörùgc `dgbfugcr bs= F ;E38 3) fdvcgbntb 9) fdvcgbntb Bmbrflfld : 6) lönlfd 3) ounflön quà`lfc ;) lönlfd 9) ãflkd 2) `btãglfd 6) icsb ?) fdvcgbntb ;) öxlkd 2) scg Bmbrflfld 6 3) c. 2.2? 0 ? ãtd`ds pdr j kb D Bmbrflfld 5 33.33 033 ãtd`ds pdr j kb E fd`pubstd ounflön quà`lfc fd`pubstd ounflön quà`lfc i. ? ãtd`ds ú ? 0 3 33 ãtd`ds ú ?0 3.56 09 Ob(DE)6 icsb EL ãflkd f. Gc oörùgc b`pàrlfc kbg fd`pubstd bs= DE 9 Cu9D öxlkd AFg scg 9) c. 3.6< 0 3 ãtd`d pdr j kb [l EFg ãflkd Il D öxlkd 9 2 0 9 ãtd`ds i. 9.85 3 ãtd`d ú 3 0 3 pdr j kb D NcO scg Fr(DE)9 icsb 9 ãtd`ds ú 3 0 9 A9 D öxlkd E9VD; ãflkd f. Gc oörùgc b`pàrlfc kbg fd`pubstd bs = [lD 9

Bmbrflfld ; 3) oörùgc quà`lfc 9) suiànklfb 6) oörùgc b`pàrlfc ;) oörùgc `dgbfugcr 2) oörùgc b`pàrlfc Bmbrflfld 2 3) A9D 9 ãtd`ds kb pdtcsld 3 ãtd`d kb dxàjbnd

9) FuDE 3 ãtd`d kb fdirb 3 ãtd`d kb dxàjbnd 3 ãtd`d kb elkröjbnd 6) Nl9D6 9 ãtd`ds kb nàqubg 6 ãtd`ds kb dxàjbnd

955

LJBY ∙ [cfcnã

Bmbrflfld <

Xubkb sbr= fd`pubstd

ãflkd öxlkd scg icsb

bmb`pgd EFg, EIr, EL, EO, E9VD;, btf

Fr9D6 NcFg, NcO, AFg, FcFg9, VrFg9, Ob6F, btf. GlDE

Bmbrflfld 38 3) AFgD6 tbrncrld 9) XFg6 ilncrld

6) ;) 2) ?) :) 5)

6 NcFgD VnFg9 VlD9 AEFD6 F:E3? NcEFD6

tbrncrld ilncrld ilncrld fuctbrncrld ilncrld fuctbrncrld

Bmbrflfld 33 Xubkb sbr= ounflön quà`lfc

icsb ãflkd ãflkd

fd`pubstd odr`ckd

odr`ckd pdr

`btcg+elkrdxlgd icsb elkröjbnd + nd `btcg elkrãflkd elkröjbnd + dxàjbnd dxãflkd + nd `btcg

scg

elkrãflkd+icsb

scgecgdlkbc

scg

icsb+dxãflkd

dxlscg

öxlkd

dxàjbnd + `btcg dxàjbnd + nd `btcg

scg scg

icsb+dxãflkd icsb +elkrãflkd elkröjbnd + dxàjbnd dxãflkd + nd `btcg elkröjbnd + nd `btcg elkrãflkd dxàjbnd + nd `btcg öxlkd ãflkd dxàjbnd + `btcg öxlkd iãslfd

ãflkd öxlkd öxlkd

Fc(DE) 9 EO, EFg, EIr, EL

E6XD; EO FD 9 @jD

Bmbrflfld 39 Ob9V6 Vlstb`c bstbquld`ìtrlfd trlsugourd kb klelbrrd Xrbmd (3)= Ndìrb jbnìrlfd= Xrbmd (9)= Ndìrb bspbfàfd=

Ob9D6

dxàjbnd vcgbnflc +6 kbg elbrrd

vcgbnflc ∙9

kbg dxàjbnd

E9 VD;, E6XD; NcFg, FcFg9, NcO, AL, Nl6N9, ObV9, btf.

6 ; CjND NcFgD6,, FuVD , Ob9D6, Gl9D, EjD, dxlkd iãslfd IbD, @jD, FcD, VrD, IcD, btf. ND, ND9, VD9, FD9, öxlkd ãflkd VlD9, btf. dxlscg CjND 6 scgecgdlkbc AIr

öxlkd

ãflkd

bmb`pgd

Bmbrflfld 32 elbrrd 8) (`btcg)

Vlstb`c Vtdfa sugourd kb elbrrd (LLL)

trl ‖ Ndìrb jbnìrlfd= sugourd sugourd Ndìrb kbg bgb`bntd= elbrrd kl ‖ Ný`brd kb vcgbnflc 6 elbrrd kbg bgb`bntd=

Bmbrflfld 36 3) nd`bnfgcturc quà`lfc 9) bstbquld`ìtrlfd 6) ndìrb jbnìrlfd ;) Vtdfa 2) ndìrb bspbfàolfd ?) Vtdfa Bmbrflfld 3; 3) Vlstb`c bstbquld`ìtrlfd Xrbolmd (3) ‖ ndìrb jbnìrlfd + kb + prbolmd (9) ‖ ndìrb bspbfàolfd

3)

nàqubg (`btcg)

Nl9D6


dxàjbnd

vcgbnflc +6 kbg nàqubg

Bmbrflfld 3? 3) [rlöxlkd kb klnltröjbnd N9D6 Xrbolmd (3)= trl‖ Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= kl‖ Ndìrb bspbfàolfd= nltröjbnd

9) @dnöxlkd kb `cjnbsld @jD Xrbolmd (3)= `dnd‖ Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= nd sb usc Ndìrb bspbfàolfd= `cjnbsld 6) Öxlkd kb pgctc (L) Cj9D Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= pgctc Ný`brd kb vcgbnflc kbg bgb`bntd= 3 ;) Elkröxlkd kb fdirb (L) FuDE Ndìrb jbnìrlfd= elkröxlkd Ndìrb kbg bgb`bntd= fdirb Ný`brd kb vcgbnflc kbg bgb`bntd= 3 2) Öxlkd kb vcnckld (_) _9D2 Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= vcnckld Ný`brd kb vcgbnflc kbg bgb`bntd= 2 ?) Öxlkd kb slglfld (L_) VlD9 Ndìrb jbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= slglfld Ný`brd kb vcgbnflc kbg bgb`bntd= ;

9) Vlstb`c Vtdfa Ndìrb jbnìrlfd + kb + ndìrb kbg bgb`bntd + ný`brd kb vcgbnflc kbg bgb`bntd


95<

Bmbrflfld 3: Nc9D Vlstb`c bstbquld`ìtrlfd @dnöxlkd kb klsdkld Xrbmd (3)= `dnd ‖ Ndìrb jbnìrlfd= öxlkd Xrbmd (9)= kl ‖ Ndìrb bspbfàfd= sdkld

Vlstb`c Vtdfa Öxlkd kb sdkld (L) Ndìrb jbnìrlfd= dxlkd Ndìrb kbg bgb`bntd= sdkld Ný`brd kb vcgbnflc kbg bgb`bntd=

3

@nD6 Vlstb`c bstbquld`ìtrlfd [rlöxlkd kb `cnjcnbsd Xrbmd (3)= trl‖ Ndìrb jbnìrlfd= öxlkd Xrbmd (9)= nd usc

Vlstb`c Vtdfa Öxlkd kb `cnjcnbsd (_L) Ndìrbjbnìrlfd= öxlkd Ndìrb kbg bgb`bntd= `cnjcnbsd Ný`brd kb vcgbnflc

Ndìrb bspbfàfd= `cnjcnbsd kbg bgb`bntd=

?

Bmbrflfld 35 3) VD9 Xrbolmd (3)= kl‖ Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= nd utlglzc Ndìrb bspbfàolfd= czuorb Ný`brd kb vcgbnflc kbg bgb`bntd= ; Bg ndìrb kbg fd`pubstd bs= Vlstb`c bstbquld`ìtrlfd= klöxlkd kb czuorb Vlstb`c Vtdfa= öxlkd kb czuorb (L_) 9) ND Xrbolmd (3)= `dnd‖ Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= nd utlglzc Ndìrb bspbfàolfd= nltröjbnd Ný`brd kb vcgbnflc kbg bgb`bntd= 9 Bg ndìrb kbg fd`pubstd bs= Vlstb`c bstbquld`ìtrlfd= `dnöxlkd kb nltröjbnd Vlstb`c Vtdfa= öxlkd kb nltröjbnd (LL)

6) FD9 Xrbolmd (3)= kl‖ Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= nd utlglzc Ndìrb bspbfàolfd= fcridnd Ný`brd kb vcgbnflc kbg bgb`bntd= ; Bg ndìrb kbg fd`pubstd bs= Vlstb`c klöxlkd(L_) kb fcridnd Vlstb`c bstbquld`ìtrlfd= Vtdfa= öxlkd kb fcridnd

9<8

LJBY ∙ [cfcnã

;) X9D2 Xrbolmd (3)= pbntc‖ Ndìrb jbnìrlfd= öxlkd Xrbolmd (9)= kl‖ Ndìrb bspbfàolfd= oösodrd Ný`brd kb vcgbnflc kbg bgb`bntd= 2 Bg ndìrb kbg fd`pubstd bs= Vlstb`c bstbquld`ìtrlfd= pbntöxlkd kb kloösodrd Vlstb`c Vtdfa= öxlkd kb oösodrd (_)

Vb`cnc 9; ¡Xcrc fd`bnzcr! 3) Bg ný`brd ctö`lfd kbg elkröjbnd bs 3, ] 0 3 9) Bg elkröjbnd sb bnfubntrc bn bg pbrldkd 3 y bn gc oc`lglc 3. 6) Ãflkds ;) Xubkb sbr= • Bnbrjàc icrctc • Xdfd d nlnjýn kcód cìlbntcg kbg fcgbntc`lbntd jgdicg •• Xrbvbnflön [dkds gds pcàsbs gd pubkbn uscr

Bmbrflfld 3 8)


E9V

fgdrd


EIr

ird`d

vcgbnflc +3 kbg ird`d

Bmbrflfld 9 C.

8)


EFLD9

dxàjbnd vcgbnflcfdn ‖9

fgdrd 3)


E6XD;

Bmbrflfld ; 8) END 3. Ndìrb jbnìrlfd= ãflkd 9. _cgbnflc= c. E+3NxD‖9 i. E+3NxD‖9 f. 3 + x ‖9 0 8 x 0 9 ‖3 x03

vcgbnflc ‖9 kbg czuorb 3)

3) EIr Ndìrb jbnìrlfd= ãflkd Ndìrb kbg nd `btcg= ird`d Vuolmd= eàkrlfd Ndìrb kbg fd`pubstd= ãflkd irdèàkrlfd


Xrbolmd= elpd‖ Vuolmd= ‖dsd 6. Ndìrb kbg fd`pubstd= ãflkd elpdnltrdsd 3) END6 3. Ndìrb jbnìrlfd= ãflkd 9. _cgbnflc= c. E+3NxD i. E+3NxD(‖9)(6) f. E+3NxD‖? ‖? 0 8 x30+?x‖3 x02 Xrbolmd= nd tlbnb Vuolmd= ‖lfd 6. Ndìrb kbg fd`pubstd= ãflkd nàtrlfd

oösodrd I. 8) elkrãflkd 3) ãflkd dxãflkd 9) ãflkd dxãflkd

6) elkrãflkd ;) elkrãflkd 2) ãflkd dxãflkd

Bmbrflfld 6 8) EO Ndìrb jbnìrlfd= ãflkd Ndìrb kbg nd `btcg= ogýdr Vuolmd= eàkrlfd Ndìrb kbg fd`pubstd= ãflkd ogudreàkrlfd


9<3

Vb`cnc 92 ¡Xcrc fd`bnzcr! 3)

Xrdplbkckbs

fdgdr dgdr scidr kurbzc

Kbsfrlpflön

igcnfd lndgdrd lnscidrd igcnkd

9) Gbfeb kb `cjnbslc

6) Cg(DE)6 Ndìrb jbnìrlfd= elkröxlkd Ndìrb kbg `btcg= cgu`lnld _cgbnflc kbg `btcg bn ný`brds rd`cnds= LLL Ndìrb kbg fd`pubstd= elkröxlkd kb cgu`lnld (LLL) ;) Ob(DE)9 Ndìrb jbnìrlfd= elkröxlkd Ndìrb kbg `btcg= elbrrd _cgbnflc kbg `btcg bn ný`brds rd`cnds= LL

6) Gc cflkbz bstd`cfcgbn bxfbsd icmc gds nlvbgbs kbpdNdìrb kbg fd`pubstd= elkröxlkd kb elbrrd (LL) ;) Xdrqub fdnsu`lkd tcsld bn bg fubrpd b l`plkb qub bg fubrpd cisdric bg Bmbrflfld 6 ãflkd oöglfd. 8) GlDE 2) Fr(DE) ? 2) Igcnqubckdrbs kb rdpc, kbsdkdrcntbs fdrpdrcgbs y 3) Cu(DE) ?) Gc(DE) 6 6 `ctbrlcgbs fdntrc lnfbnklds. 9) Il(DE)9 :) Vn(DE) ; 6) Xi(DE); 5) Z(DE) ? Bmbrflfld 3 ;) Nl(DE)9 <) Xk(DE) 9 lön elkrdxlgd 8) frd`d Fr(DE)6 fdn vcgbnflc ‖3 Bmbrflfld ; 8) Elkröxlkd kb rdkld (L_) vcgbnflc +6 kbg frd`d 3) Elkröxlkd kb gcntcnd (LL) y 6 ldnbs (DE) 9) Elkröxlkd kb lrlkld (L_) 6) Elkröxlkd kb fck`ld (LL) 3) lön elkrdxlgd fcgfld Fc(DE)9 ;) Elkröxlkd kb flrfdnld (L_) fdn vcgbnflc ‖3 2) Elkröxlkd kb `cnjcnbsd (_LL) vcgbnflc +9 kbg frd`d y 9 ldnbs (DE)

Bmbrflfld 9 8) FuDE Ndìrb jbnìrlfd= elkröxlkd Ndìrb kbg `btcg= fdirb _cgbnflc kbg `btcg bn ný`brds rd`cnds= L Ndìrb kbg fd`pubstd= elkröxlkd kb fdirb (L) 3) GlDE Ndìrb jbnìrlfd= elkröxlkd Ndìrb kbg `btcg= gltld _cgbnflc kbg `btcg bn ný`brds rd`cnds= L Ndìrb kbg fd`pubstd= elkröxlkd kb gltld (L) 9) ]n(DE)9 Ndìrb jbnìrlfd= elkröxlkd Ndìrb flnfný`brds rd`cnds= LL _cgbnflc kbg kbg `btcg= `btcg bn Ndìrb kbg fd`pubstd= elkröxlkd kb zlnf (LL)

9<9

LJBY ∙ [cfcnã

¡C gc flbnflc pdr gc bxpbrlbnflc! Gc sdguflön kb rbpdggd fcìlc kb fdgdr. Vl gc sustcnflc bs ãflkc, gc sdguflön sb tdrnc rdmc, y sl bs iãslfc, sb tdrnc vbrkb d czug.

Vb`cnc 9? ¡Xcrc fd`bnzcr!


3) Gds jrlbjds dorbfàcn scg fd`d sàìdgd kb c`lstck, edspltcglkck y orctbrnlkck. 9) Gc pcgcirc scgcrld prdvlbnb kbg ebfed kb qub gds sdgkckds rd`cnds fdircicn pcrtb kb su subgkd bn jrcnds kb scg. 6) Ybspubstcs klstlntcs. ;) Gc scg ydkckc bvltc bg idfld y gcs bnobr`bkckbs rb -

´Suì sufbkb4

gcfldnckcs fdn bg frbfl`lbntd y bg kbscrrdggd ndr`cg kb gc lntbgljbnflc. 2) Bg fctlön bs bg sdkld Nc+ ?) Bg cnlön bs bg fgdrd Fg‖

• Gc scgcgbsodnkd `ãs pbsckc qub bg cjuc y bgunc cfbltb, csà qub sb vc kbg vcsd, pbrd crrcstrc iuriumc kb cfbltb ecstc bg odnkd. • C klobrbnflc kbg cfbltb, bg cjuc y gc scg sà sb `bzfgcn. Gc scg sb vc sbpcrcnkd bn sus kds ldnbs y sb klsubgvb bn bg cjuc, y kb bsc odr`c, pdfd c pdfd, bg cfbltb vubgvb c suilr c su gujcr. • Vl cjrbjc scg vcrlcs vbfbs vbrã qub sufbkb gd `ls`d. Bg fdgdrcntb vbjbtcg sögd slrvb pcrc ecfbr `ãs sbnflggc gc disbrvcflön.

Bmbrflfld 3 fdirb

8)

fgdrd

FuFL

vcgbnflc ‖3 vcgbnflc +3 kbg fgdrd kbg fdirb `cjnbsld

3)

Vus disbrvcfldnbs pubkbn vcrlcr. Gb dorbfb`ds cgjuncs bxpglfcfldnbs= • Bg cjuc nd sb `bzfgc fdn bg cfbltb pdrqub tlbnbn pbsds klstlntds. Bg cjuc pbsc `ãs qub bg cfbltb pdr bsd, sb vc cg odnkd kbg vcsd.

ýdr

@jO9

vcgbnflc ‖3 vcgbnflc +9 kbg ýdr kbg `cjnbsld

Bmbrflfld 9 ndìrb kb gc scg ecgdlkbc sugourd kb fdirb (LL) irdùrd kb cgu`lnld (LLL) sugourd kb fdicgtd (LL) crsbnlurd kb elbrrd (LLL)

vcgbnflc kb gds bgb`bntds Fu+9 V‖9 Cg+6 Ir‖3 Fd+9 V‖9 Ob+6 Cs‖6

oörùgc Fu9V9 0 FuV Cg3Ir6 0 CgIr6 Fd9V9 0 FdV Ob6Cs6 0 ObCs

Bmbrflfld 6 8) irdùrd kb icrld 3) fgdrurd kb cgu`lnld 9) irdùrd kb gltld

6) elkrurd kb fcgfld ;) ydkurd kb fck`ld

Bmbrflfld ; ndìrb kbg nd vcgbnflc kbg ndìrb kbg oörùgc `btcg + sumd `btcg bn ný`brd `btcg ‖urd rd`cnds

ndìrb kb gc scg ecgdlkbc odr`ckc pdr `btcgbs fdn vcgbnflc vcrlcigb

CuX6 odsourd

drd

(LLL)

odsourd kb drd (LLL)

Vn X odsourd Vn6X; odsourd EjO9 udrurd

bstcód bstcód `brfurld

(LL) (L_) (LL)

odsourd kb bstcód (LL) odsourd kb bstcód (L_) udrurd kb `brfurld (LL)

6 9


9<6

Vb`cnc 9: ¡Xcrc fd`bnzcr! 3) Kds vdgý`bnbs ljucgbs kb jcsbs klobrbntbs, bn gcs `ls`cs fdnklfldnbs kb prbslön y tb`pbrcturc, fdntlbnbn bg `ls`d ný`brd kb `dgìfugcs. 9) Bn gc tbdràc ctö`lfc kb Mden Kcgtdn y bn gc gby kb Jcy‖Gusscf sdirb bg `dvl`lbntd kb gcs `dgìfugcs. 6) ?.899 Ú 3896 unlkckbs.

Bmbrflfld 3 C.

@csc `dgcr Nd. Ãtd`ds @csc `dgcr Nd. Ãtd`ds Bgb`bntd (`csc ctö`lfc C) qub tlbnb= (`csc ctö`lfc C) qub tlbnb 96 @cjnbsld (@j) 9;.6j ?.899x38 Vlglfld (Vl) 95.3 j ?.899 x 38 96 Bgb`bntd

Nltröjbnd (N)

3;.8j

?.899x38

96

Rrcnld (R)

965.8 j

?.899 x 38

I. 3 ãtd`d kb N x 3;.8 j/`dg 0 3;.8 j/`dg 6 ãtd`ds kb E x 3.8 j/`dg 0 + 6.8 j/`dg @csc `dgcr kbg NE6 0 3:.8 j/`dg

Bmbrflfld 9 8) 3. 3 `dg kb Ob 22.5 j kb Ob 9. 6.39 `dg kb Ob x

22.5 j 3 `dg Ob

22.5 j 0 3:;.3 j Ob 3 `dg Ob

6. Bn 6.39 `dgbs kb elbrrd ecy 3:;.3 jrc`ds kb elbrrd. 3) 3. 3 `dg kb Fc ;8.3 j kb Fc 9. 388 j kb Fc x

3 `dg kb Fc ;8.3 j kb Fc

3 `dg kb Fc 0 9.;< `dg kb Fc ;8.3 j kb Fc

6. Bn 388 jrc`ds kb fcgfld ecy 9.;< `dgbs kb fcgfld.

Bmbrflfld 6 8) 3. 3 `dg kb Nc ?.899 x 3896 ãtd`ds kb Nc 96 9. 8.6 `dg kb Nc x ?.899 x 38 ãtd`ds kb Nc 0 3 `dg kb Nc 3.53 x 3896 ãtd`ds kb Nc

6. Bn 8.6 `dgbs kb sdkld ecy 3.53 x 3896 ãtd`ds kb sdkld. 3) 3. 3 `dg kb Fg ?.899 x 3896 ãtd`ds kb Fg 9. : ãtd`ds kb Fg x

3 `dg kb Fg 0 3.3? x 38∙96 ãtd`ds kb Fg ?.899 x 3896 ãtd`ds kb Fg

6. Bn : ãtd`ds kb fgdrd ecy 3.3? x 38∙96 `dgbs kb fgdrd.

9<;

LJBY ∙ [cfcnã

96

9) 3.

? ãtd`ds kb F x 39.8 j/`dg 0 :9.8 j/`dg 39 ãtd`ds kb E x 3.8 j/`dg 0 39.8 j/`dg ? ãtd`ds kb D x 3?.8 j/`dg 0 +
?.899 x 3896 `dgbs 3 `dg

9. 3 j x 3 `dg 0 2.2? x 38‖6 `dgbs 358.8 j 96 2.2? x 38‖6 `dgbs x ?.899 x 38 `dgbs 0 6.62 x 3893 `dgìfugcs 3 `dg 6. Bn 3 jrc`d kb jgufdsc ecy 6.62 x 3893 `dgìfugcs kb F?E39D?.

Bmbrflfld ; Vustcnflc

Nd kb pcrtàfugcs

@csc `dgcr _dgu`bn `dgcr

Eb

?.899 x 3896ã td`ds

;.8j/`dg

99.;G

FD

?.899 x 38

`dgìfugcs 95.8 j/`dg

99.; G

N9

?.899 x 3896 `dgìfugcs 95.8 j/`dg

99.; G

96

¡C gc flbnflc pdr gc bxpbrlbnflc! 3) 3 `dg kb qubtzcgbs ?.899 x 3896 qubtzcgbs ?.899 x 3896 qubtzcgbs 36 :.88 x 38< pbrsdncs 0 5.?8 x 38 qubtzcgbs pdr pbrsdnc Gb fdrrbspdnkbràc 5.?8 x 38 36 qubtzcgbs c fckc pbrsdnc.

9) 5.?8 x 3836 qubtzcgbs x

3 kàc 0 5.?8 x 3833 kàcs 388 qubtzcgbs

Cgfcnzcràc pcrc 5.?8 x 38 36 kàcs.

6) 5.?8 x 3833 kàcs x

3 cód 0 9,62?,3?;.65 códs 6?2 kàcs

Cgfcnzcràc bg klnbrd pcrc 9,62?,3?;.65 códs (kds `lggdnbs, trbsflbntds flnfubntc y sbls `lg, flbntd sbsbntc y fuctrd, puntd trblntc y dfed códs).


9<2

Vb`cnc 95 ¡Xcrc fd`bnzcr! C. 8) klöxlkd kb fcridnd 3) cjuc 9) czýfcr 6) fgdrdolgc I. 8) 3 ãtd`d kb fcridnd (F), 9 ãtd`ds kb dxàjbnd (D)

3) 9 ãtd`ds kb elkröjbnd (E), 3 ãtd`d kb dxàjbnd (D) 9) ? ãtd`ds kb fcridnd (F), 39 ãtd`ds kb elkröjbnd (E), ? ãtd`ds kb dxàjbnd (D) 6) 22 ãtd`ds kb fcridnd (F), :9 ãtd`ds kb elkröjbnd (E), 2 ãtd`ds kb dxàjbnd (D), ; ãtd`ds kb nltröjbnd (N), 3 ãtd`d kb `cjnbsld (@j)

Bmbrflfld 3 C.

Rnc rbcfflön quà`lfc bs gc unlön kb kds d `ãs bgb`bntds pcrc odr`cr fd`pubstds. I. 3) rbcftlvds 9) prdkuftds

Bmbrflfld 9 3) c. fcridnctd kb fcgfld (FcFD6) i. öxlkd kb fcgfld (FcD) yklöxlkd kb fcridnd (FD9) f. 3 pcrc gds rbcftlvds y bg prdkuftd k. bg 6 kbg fcridnctd kb fcgfld y bg 9 kbg klöxlkd kb fcridnd 9) c. cgu`lnld (Cg) y dxàjbnd (D9) i. öxlkd kb cgu`lnld (Cg9D6) f. ; pcrc bg cgu`lnld, 6 pcrc bg dxàjbnd y 9 pcrc bg öxlkd kb cgu`lnld k. bg 9 kbg dxàjbnd, bg 9 y bg 6 kbg öxlkd kb cgu`lnld

Bmbrflfld 6 C. 8) rbcfflön kb kbsfd`pdslflön 3) rbcfflön kb fdìlncflön d sàntbsls 9) rbcfflön kb sustltuflön I. 8) rbcfflön kb kbsfd`pdslflön 3) rbcfflön kb fdìlncflön d sàntbsls 9) rbcfflön kb sustltuflön 6) rbcfflön kb fdìlncflön d sàntbsls

9
LJBY ∙ [cfcnã

;) rbcfflön kb fdìlncflön d sàntbsls 2) rbcfflön kb kbsfd`pdslflön ?) rbcfflön kb sustltuflön

Bmbrflfld ; 8) Vustltuflön 3) 9Fr + ?END6 9)

Vb`cnc 9< Bg ùnkd kb gc quà`lfc Bmbrflfld 3 3) ãflkd 9) elkrãflkd 6) dxãflkd Bmbrflfld 9 8) EO

Xrbolmd= nd tlbnb Vuolmd= ‖lfd 6. Ndìrb kbg fd`pubstd= ãflkd nàtrlfd 9) E9VD6 3. Ndìrb jbnìrlfd= ãflkd 9. _cgbnflc= c. E VxD (+3)(9) x

3) EFg Ndìrb jbnìrlfd= ãflkd Ndìrb kbg nd `btcg= fgdrd Vuolmd= eàkrlfd Ndìrb kbg fd`pubstd= ãflkd fgdreàkrlfd 9) EIr Ndìrb jbnìrlfd= ãflkd Ndìrb kbg nd `btcg= ird`d Vuolmd= eàkrlfd Ndìrb kbg fd`pubstd= ãflkd irdèàkrlfd Bmbrflfld 6 8) E6XD;

3. Ndìrb jbnìrlfd= ãflkd 9. _cgbnflc= c. E XxD i. E6(+3)(6)XxD;(‖9)(;) f. E X xD 6+x‖508 x05‖6 x02

Xrbolmd= nd tlbnb Vuolmd= ‖lfd 6. Ndìrb kbg fd`pubstd= ãflkd odsoörlfd 3) END6 3. Ndìrb jbnìrlfd= ãflkd 9. _cgbnflc= c. E+3NxD i. E+3NxD6(‖9)(6) f. E+3NxD 3+x‖?08 x0?‖3 x02

(‖9)(6)

i. EE9V xD V D6 f. 9+x‖?08 x0?‖9 x0; Xrbolmd= nd tlbnb Vuolmd= ‖dsd 6. Ndìrb kbg fd`pubstd= ãflkd sugourdsd

ãflkd Ndìrb Ndìrbjbnìrlfd= kbg nd `btcg= ogýdr Vuolmd= eàkrlfd Ndìrb kbg fd`pubstd= ãflkd ogudreàkrlfd

6) EIrD; 3. Ndìrb jbnìrlfd= ãflkd 9. _cgbnflc= c. E+3IrxD i. E(+3)(3)IrxD;(‖9)(;) f. E+3Ir xD 3+x‖508 x05‖3 x0: Xrbolmd= ‖pbr Vuolmd= ‖lfd 6. Ndìrb kbg fd`pubstd= ãflkd pbrirö`lfd Bmbrflfld ; 3) elkröxlkds 9) elkrdxlgd 6) elkröxlkds Bmbrflfld 2 8) fcgfld

Fc(DE)9


vcgbnflc +9 kbg fcgfld y 9 ldnbs DE‖3 3)

tltcnld

[l(DE)6

lön elkrdxlgd

fdn vcgbnflc ‖3 vcgbnflc +6 kbg tltcnld y 6 ldnbs DE‖3


9<:

9)

pgd`d

Xi(DE)9


vcgbnflc +9 kbg pgd`d y 9 ldnbs DE‖3 6)

jbr`cnld

Jb(DE);


vcgbnflc +; kbg jbr`cnld y ; ldnbs DE‖3 ;)

ltrld

\(DE)6


vcgbnflc +6 kbg ltrld y 6 ldnbs DE‖3 2)

icrld

Ic(DE)9


vcgbnflc +9 kbg icrld y 9 ldnbs DE‖3

Bmbrflfld : 3) scg 9) scg ecgdlkbc 6) dxlscg

;) 2) ?)

dxlscg fcgfld (Fc) cgu`lnld (Cg)

Bmbrflfld 5 8) fgdrurd kb fbsld 3) sugourd kb ibrlgld 9) ogudrurd kb cgu`lnld

6) odsourd kb flnf ;) ydkurd kb pgctc Bmbrflfld < 8) @n6X: Ndìrb kbg nd `btcg + suolmd ‖urd= odsourd Ndìrb kbg `btcg= `cnjcnbsd _cgbnflc kbg `btcg bn ný`brds rd`cnds= _LL Ndìrb kbg fd`pubstd= odsourd kb `cnjcnbsd (_LL)

3) YuFg6 Ndìrb kbg nd `btcg + suolmd ‖urd= fgdrurd Ndìrb kbg `btcg= rutbnld _cgbnflc kbg `btcg bn ný`brds rd`cnds= LLL Ndìrb kbg fd`pubstd= fgdrurd kb rutbnld (LLL)

Bmbrflfld ? 8) Z(DE)? 9) [lO9 Ndìrb jbnìrlfd= elkröxlkd Ndìrb kbg nd `btcg + suolmd ‖urd= ogudrurd Ndìrb kbg `btcg= vdgorc`ld Ndìrb kbg `btcg= tltcnld _cgbnflc kbg `btcg bn ný`brds rd`cnds= _L LL (LL) Ndìrb kbg fd`pubstd= elkröxlkd kb vdgorc`ld (_L) _cgbnflc kbg kbg fd`pubstd= `btcg bn ný`brds rd`cnds= ogudrurd kb tltcnld Ndìrb 3) Cu(DE)6 6) Fr6N9 Ndìrb jbnìrlfd= elkröxlkd Ndìrb kbg nd `btcg + suolmd ‖urd= nltrurd Ndìrb kbg `btcg= drd Ndìrb kbg `btcg= frd`d _cgbnflc kbg `btcg bn ný`brds rd`cnds= LLL _cgbnflc kbg `btcg bn ný`brds rd`cnds= LL Ndìrb kbg fd`pubstd= elkröxlkd kb drd (LLL) Ndìrb kbg fd`pubstd= nltrurd kb frd`d (LL) 9) Xi(DE); ;) _;F2 Ndìrb jbnìrlfd= elkröxlkd Ndìrb kbg nd `btcg + suolmd ‖urd= fcriurd Ndìrb kbg `btcg= pgd`d Ndìrb kbg `btcg= vcnckld _cgbnflc kbg `btcg bn ný`brds rd`cnds= L_ _cgbnflc kbg `btcg bn ný`brds rd`cnds= _ Ndìrb kbg fd`pubstd= elkröxlkd kb pgd`d (L_) Ndìrb kbg fd`pubstd= fcriurd kb vcnckld (_) 6) Fr(DE)6 Ndìrb jbnìrlfd= elkröxlkd Bmbrflfld 38 Ndìrb kbg `btcg= frd`d 8) `dg _cgbnflc kbg `btcg bn ný`brds rd`cnds= LLL 3) `csc `dgcr Ndìrb kbg fd`pubstd= elkröxlkd kb frd`d (LLL) 9) ocftdr kb fdnvbrslön

;) [l(DE); Ndìrb jbnìrlfd= elkröxlkd Ndìrb kbg `btcg= tltcnld _cgbnflc kbg `btcg bn ný`brds rd`cnds= L_ Ndìrb kbg fd`pubstd= elkröxlkd kb tltcnld (L_)

9<5

LJBY ∙ [cfcnã

6) ;) 2) ?)

`csc `dgbfugcr vdgu`bn `dgcr 8 ½F kb tb`pbrcturc y 3 ct` kb prbslön 99.; G

Bmbrflfld 33 3) 3. 3 `dg kb D 3?.8 j kb D

3 `dg kb D 3?.8 j kb D 9. 9;.8 j kb D x 3 `dg kb D 0 3.2 `dgbs D 3?.8 j kb D 6. Bn 9;.8 j kb dxàjbnd ecy 3.2 `dgbs kb ãtd`ds kb dxàjbnd. 9) 3. 3 `dg kb D9 69.8 j kb D 9 3 `dg kb D9 69.8 j kb D9 9. 9;.8 j kb D 9 x 3 `dg kb D9 0 8.:2 `dgbs kb D 9 69.8 j kb D9 6. Bn 9;.8 j kb dxàjbnd jcsbdsd ecy 8.:2 `dgbs kb `dgìfugcs kb dxàjbnd jcsbdsd. 6) 3. 3 ãtd`d kb V x 69.3 j/`dg 0 69.3 j/`dg 9 ãtd`ds kb D x 3?.8 j/`dg 0 + 69.8 j/`dg 3 `dg kb VD9= ?;.3 j/`dg 3 `dg kb VD9 ?;.3 j kb VD9 9. 9;.2 j kb VD 9 x 3 `dg kb VD9 0 8.; `dgbs kb VD 9 ?;.3 j kb VD9 6. Bn 9;.2 j kb klöxlkd kb czuorb ecy 8.; `dgbs kb klöxlkd kb czuorb. ;) 3. 3 ãtd`d kb Ic x 36:.6 j/`dg 0 36:.6 j/`dg 3 ãtd`d kb F x 39.8 j/`dg 0 39.8 j/`dg 6 ãtd`ds kb D x 3?.8 j/`dg 0 + ;5.8 j/`dg 3 `dg kb IcFD6= 3<:.6 j/`dg 3<:.6 j kb IcFD6 3 `dg kb IcFD6 9. 8.; `dgbs IcFD 6 x 3<:.6 j kb IcFD6 0 :5.< j kb IcFD6 3 `dg kb IcFD6 6. Bn 8.; `dgbs kb fcridnctd kb icrld ecy :5.< j kb fcridnctd kb icrld. 2) 3. 6 ãtd`ds kb Nc x 96.8 j/`dg 0 3 ãtd`d kb X x 63.8 j/`dg 0 ; ãtd`ds kb D x 3?.8 j/`dg 0 + 3 `dg kb Nc 6XD;=

?<.8 j/`dg 63.8 j/`dg ?;.8 j/`dg 3?;.8 j/`dg

6 3?;.8 kbNc Nc6XD XD; ; 3 `dgjkb

9. 3.2 `dgbs kb Nc 6XD; x 3?;.8 j kb Nc6XD; 0 9;? j kb Nc6XD; 3 `dg kb Nc6XD; 6. Bn 3.2 `dgbs kb odsoctd kb sdkld ecy 9;? j kb odsoctd kb sdkld. Suà`lfc LL ∙ Fgcvbs

9<<

Bmbrflfld 39 3) 3. 3 `dg kb E9 ?.899 x 38 96 `dgìfugcs kb E9

?.899 x 3896 `dgìfugcs kb E9 3 `dg kb E9 96 9. 6.3 `dgbs kb E 9 x ?.899 x 38 `dgìfugcs kb E9 0 3.< x 389; `dgìfugcs kb E9 3 `dg kb E9

6. Bn 6.3 `dgbs kb E9 ecy 3.< x 389; `dgìfugcs kb E9. 9) 3. 3 `dg kb F ?.899 x 3896 ãtd`ds kb F ?.899 x 3896 ãtd`ds kb F 3 `dg kb F 96 9. 8.? `dgbs kb F x ?.899 x 38 ãtd`ds kb F 0 6.? x 3896 ãtd`ds kb F 3 `dg kb F 6. Bn 8.? `dgbs kb F ecy 6.? x 3896 `dgìfugcs kb F. 6) 3. 3 `dg kb FE; ?.899 x 38 96 `dgìfugcs kb FE; ?.899 x 3896 `dgìfugcs kb FE; 3 `dg kb FE; 96 9. :.5 `dgbs kb FE ; x ?.899 x 38 `dgìfugcs kb FE; 0 ;.: x 38 9; ãtd`ds kb FE; 3 `dg kb FE;

6. Bn :.5 `dgbs kb FE ; ecy ;.: x 389; ãtd`ds kb FE;. ;) 3. 3 `dg kb [l ?.899 x 3896 ãtd`ds kb [l 3 `dg kb [l ?.899 x 3896 ãtd`ds kb [l 9. 6.9 x 38 9; ãtd`ds kb [l x

3 `dg kb [l 0 2.; `dgbs kb [l ?.899 x 3896 ãtd`ds kb [l

6. 6.9 x 389; ãtd`ds kb [l bqulvcgbn c 2.; `dgbs kb [l. 2) 3. 3 `dg kb F?E39D? ?.899 x 38 96 `dgìfugcs kb F?E39D? 3 `dg kb F?E39D? ?.899 x 3896 `dgìfugcs kb F?E39D? 9. 3.9 x 38 93 `dgìfugcs kb F?E39D? x

3 `dg kb F?E39D? 0 9.8 x 38‖6 `dgbs kb F?E39D? ?.899 x 3896 `dgìfugcs kb F?E39D?

6. 3.9 x 3893 `dgìfugcs kb F?E39D? bqulvcgbn c 9.8 x 38‖6 kb F?E39D?.

688

LJBY ∙ [cfcnã

Bmbrflfld 36 3) 3. 3 `dg kb Eb 99.; G kb Eb

3 `dg kb Eb 99.; G kb Eb 9. 32 G kb E x 3 `dg kb Eb 0 8.: `dgbs kb Eb 99.; G kb Eb 6. Bn 32 gltrds kb Eb ecy 8.: `dgbs kb Eb. 9) 3. 3 ãtd`d kb F x 39.8 j/`dg 0 39.8 j/`dg 9 ãtd`ds kb D x 3?.8 j/`dg 0 + 69.8 j/`dg 3 `dg kb VD9 0 ;;.8 j/`dg 99.; G kb FD9 ;;.8 j kb FD 9 ;;.8 j kb FD9 99.8 G kb FD9 9. 3;.8 G kb FD 9 x ;;.8 j kb FD9 0 95.8 j kb FD9 99.8 G kb FD9 6. Bn 3;.8 G kb FD 9 ecy 95.8 j kb FD9. 6) 3. 99.; G kb N9 ?.899 x38

96

`dgìfugcs kb N9

?.899 x 38 `dgìfugcs kb N9 99.8 G kb N9 96

96 9. ;5.8 G kb N 9 x ?.899 x 38 `dgìfugcs kb N9 0 3.6 x 389; `dgìfugcs N9 99.; G kb N9

6. Bn ;5 gltrds kb N9 ecy 3.6 x 389; `dgìfugcs N9. ;) 3. 9 ãtd`ds Fg x 62.2 j/`dg :3.8 j/`dg 99.; G kb Fg

9

:3.8 j Fg 9

99.; G kb Fg9 :3.8 j kb Fg9 9. ;.? j kb Fg 9 x 99.; G kb Fg9 0 3.; G kb Fg 9 :3.8 j kb Fg9 6. Bn ;.? j kb Fg9 ecy 3.; G kb Fg9. 2) 3. 3 `dg N9D 99.; G kb N9D 99.; kb NN9D D 3 `dgG kb 9 9. ?.6 `dgbs kb N 9D x 99.; G kb N9D 0 3;3.3 G kb N 9D 3 `dg kb N9D 6. Bn ?.6 `dgbs kb N 9D ecy 3;3.3 G kb N9D. Suà`lfc LL ∙ Fgcvbs

683

Vb`cnc 68 Bmbrflfld 3; 3) rbcfflön quà`lfc 9) rbcftlvds 6) prdkuftds ;) bfucflön quà`lfc 2) rbcftlvds ?) prdkuftds :) rbcffldnbs kb fdìlncflön d sàntbsls 5) rbcffldnbs kb sustltuflön <) rbcffldnbs kb kbsfd`pdslflön Bmbrflfld 32 8) Gds rbcftlvds sdn=@j + D9 Bg prdkuftd bs= @jD Gds fdbolflbntbs sdn= 9 kbg @j y 9 kbg @jD

3) Gds rbcftlvds sdn= NcFg + Xi(ND6)9 Gds prdkuftds sdn= XiFg9 + NcND6 Gds fdbolflbntbs sdn= 9 kbg NcFg y 9 kb NcND6 9) Gds rbcftlvds sdn= Ic + E9D Gds prdkuftds sdn= Ic (DE)9 + E9 Gds fdbolflbntbs sdn= 3 bn tdkds, pbrd nd sb bsfrlib 6) Gds rbcftlvds sdn= @j + EFg Gds prdkuftds sdn= @jFg9 + E9 Gds fdbolflbntbs sdn= 9 kbg rbcftlvd EFg

¡Xcrc fd`bnzcr! F + D9 3 x 39 j/`dg 9 x 3? j/`dg ;; j/`dg

FD9 3 x 39 j/`dg + 9 x 3? j/`dg ;; j/`dg

Bmbrflfld 3 3. ný`brd kb ãtd`ds ný`brd kb ãtd`ds bn rbcftlvds Ob 0 3 (Ob) D 0 3 (E9D) E 0 9 (E9D)

bn prdkuftds Ob 0 6 (Ob6D;) D 0 ; (Ob6D;) E 0 9 (E9)

9. Bsfrlic bg ný`brd 9 bn bg ãtd`d kb elbrrd (Ob), kbg gckd kb gds rbcftlvds, pcrc icgcnfbcrgd. 9Ob + E9D

Ob9D6 + E9

Bsfrlic bg ný`brd 6 bn gc `dgìfugc kb cjuc, kbg gckd kb gds rbcftlvds, pcrc icgcnfbcr gds dxàjbnds. 9Ob + 6E9D

Ob9D6 + E9

Xdr ýgtl`d, bsfrlic bg ný`brd 6 bn gc `dgìfugc kb elkröjbnd (E9), kbg gckd kb gds prdkuftds, pcrc icgcnfbcr gds elkröjbnds. 9Ob + 6E9D

Ob9D6 + 6E9

6. ný`brd kb ãtd`ds ný`brd kb ãtd`ds ;) Gds rbcftlvds sdn= E9D + VD6 bn rbcftlvds bn prdkuftds Gds prdkuftds sdn= E9VD; Ob 0 9 (Ob) Ob 0 9 (Ob6D;) Gds fdbolflbntbs sdn= 3 bn tdkds, pbrd nd sb bsfrlib D 0 6 (E9D) D 0 6 (Ob6D;) E 0 ? (E9D) E 0 ? (E9) Bmbrflfld 3? 8) Ybcfflön kb fdìlncflön d sàntbsls 3) Ybcfflön kb sustltuflön ¡C gc flbnflc pdr gc bxpbrlbnflc! 9) Ybcfflön kb fdìlncflön d sàntbsls ´Suì sufbkb4 6) Ybcfflön kb kbsfd`pdslflön Cg rbcffldncr bg vlncjrb fdn bg ilfcridnctd kb sdkld ;) Ybcfflön kb sustltuflön sb odr`c klöxlkd kb fcridnd jcsbdsd, fuycs iuriumcs 2) Ybcfflön kb fdìlncflön d sàntbsls kcn un cspbftd bobrvbsfbntb cg gàqulkd. Bscs iuriumcs ?) Ybcfflön kb kbsfd`pdslflön sb —pbjcn‐ c gc supbrolflb kb gcs idgltcs y gbs slrvbn :) Ybcfflön kb sustltuflön kb —ogdtckdrbs‐. Bstd ecfb qub gcs idgltcs suicn c gc 5) Ybcfflön kb kbsfd`pdslflön supbrolflb. Fucnkd ggbjcn c gc supbrolflb, gcs iuriumcs <) Ybcfflön kb fdìlncflön d sàntbsls kb klöxlkd kb fcridnd —sb bsfcpcn‐ cg clrb y gcs idgltcs vubgvbn c fcbr ecstc qub nubvc`bntb sdn rdkbckcs pdr dtrcs iuriumcs.

689

LJBY ∙ [cfcnã

Vb`cnc 63 Bg ùnkd kb gc quà`lfc Bmbrflfld 3 C. Gc rbkcfflön pubkb vcrlcr, pbrd gc lkbc prlnflpcg kbib `cntbnbrsb. Vb gb prdpdnb bg sljulbntb bmb`pgd= Gc bstbquld`btràc bs bg fãgfugd fucntltctlvd kb rbcftlvds y prdkuftds bn unc rbcfflön quà`lfc. I. 3) 9 `dgbs kb EFg d 3 `dg kb @jFg9 3 `dg kb @jFg9 9 `dgbs kb EFg 9) 9 `dgbs kb EFg 3 `dg kb @jFg9 6) 3: `dgbs kb @jFg9 x 9 `dgbs kb EFg 0 6; `dgbs kb EFg 3 `dg kb @jFg9

;) Y/ Vb nbfbsltcn 6; `dgbs kb EFg pcrc prdkuflr 3: `dgbs kb @jFg 9.

Bmbrflfld 9 3)

; `dgbs kb Cg d 9 `dgbs kb Cg9D6 9 `dgbs kb Cg9D6 ; `dgbs kb Cg

9) 9 `dgbs kb Cg9D6 ; `dgbs kb Cg 6) ? `dgbs kb Cg x 9 `dgbs kb Cg9D6 0 6 `dgbs kb Cg 9D6 ; `dgbs kb Cg ;) Vb odr`c 6 `dgbs kb Cg 9D6 fucnkd rbcffldncn ; `dgbs kb cgu`lnld.

Bmbrflfld 6 3)

3 `dg kb Vn 335.: j kb Vn

9)

98< j kb Xd 3 `dg kb Xd

Bmbrflfld ; 3)

9 `dgbs kb NcFg 3 `dg kb Fg9

9)

:;.< j kb Cs 3 `dg kb Cs

Bmbrflfld 2 9 kbN@j `dg kb 3) 6 3`dgbs d 6 3`dgbs `dg kb kbN@j 9

@csc `dgcr kb @j= 9;.6 j kb @j 3 `dg kb @j d 9;.6 j kb @j 9;.6 j kb @j 3 `dg kb @j Suà`lfc LL ∙ Fgcvbs

686

@csc `dgcr kb N 9= 95.8 j kb N9 3 `dg kb N9 d 95.8 j kb N 9 95.8 j kb N 9 3 `dg kb N9

9) 3 `dg kb N9 95.8 j kb N9 6 `dgbs kb @j 3 `dg kb N9 9;.6 j kb @j 3 `dg kb @j 6) 38.8 j kb N9 x 3 `dg kb N9 x 6 `dgbs kb @j x 9;.6 j kb @j 0 9?.8; j kb @j 95.8 j kb N 9 3 `dg kb N9 3 `dg kb @j ;) Xcrc qub rbcffldnbn 38 j kb nltröjbnd `dgbfugcr (N 9) sb nbfbsltcn 9?.8; j kb `cjnbsld (@j).

Vb`cnc 69 ¡Xcrc fd`bnzcr! Xubkb sbr= Xdkràc`ds olgtrcr gc sdguflön pcrc sbpcrcrgc bn crbnc y cjuc fdn scg. Gubjd pdkràc`ds kbstlgcr bg cjuc kb gc sdguflön kb cjuc fdn scg. Vl nd nds lntbrbscrc rbfupbrcr bg cjuc, tcìlìn pdkràc`ds bvcpdrcrgc.

Bmbrflfld 3 C.

frlstcg kb vbntcnc jcsdglnc lnouslön kb tì I. 8) 3)

scg clrb sln eu`d

9) 6)

söglkd bn söglkd `btcnd

Bmbrflfld 6 3) 9) 6) ;) 2)

`ãs klgulkc `ãs fdnfbntrckc sdguflön F gcs kds cntbrldrbs sdn fdrrbftcs cjrbjcr `ãs cjuc

Bmbrflfld ; 3. sdguflön 0 : j + 388 j sdguflön 0 38: j 9. % `csc 0 : j x 388 0 ?.2 38: j 6. Y/ Bg pdrfbntcmb `csc ‖ `csc kb gc sdguflön bs ?.2 %.

felr`dg sdgutd

Bmbrflfld 9 C.

sdguflön

sdgutd

sdgvbntb

gàqulkc gàqulkc

söglkd jcs

gàqulkd gàqulkd

gàqulkc

söglkd

gàqulkd

68;

I. 8) 3)

LJBY ∙ [cfcnã

bmb`pgd cjuckb`cr dxàjbnd bn cjuc czýfcr bn gc scnjrb

Bmbrflfld 2 3. sdguflön 0 sdgutd + sdgvbntb sdguflön 0 92 `G + 928 `G sdguflön 0 9:2 `G 9. % vdgu`bn 0


Vb`cnc 66 ¡Xcrc fd`bnzcr!

% vdgu`bn 0 92 `G x 388 0 < 9:2 `G 6. Y/ Bg pdrfbntcmb vdgu`bn ‖ vdgu`bn kb gc sdguflön bs < %.

¡C gc flbnflc pdr gc bxpbrlbnflc! @bzfgc

Disbrvcfldnbs

´Bs unc sdguflön4

Bg fdgdr vbjbtcg sb klsubgvb pdfd c pdfd. Bs pdsligb qub cntbs kb cjltcr gc sdguflön ecyc fdgdr vbjbtcg + cjuc cgjýn rbstd söglkd bn bg cjuc. Gubjd kb cjltcr gc sdguflön sb klsubgvb tdkd.

sà

cfbltb + cjuc

Bg cfbltb qubkc suspbnklkd bn odr`c kb jdtcs bn bg cjuc.

nd

czýfcr + cjuc

Bg czýfcr sb klsubgvb pdfd c pdfd. Bs pdsligb qub cntbs kb cjltcr gc sdguflön ecyc cgjýn rbstd söglkd bn bg cjuc. Gubjd kb cjltcr gc sdguflön sb klsubgvb tdkd.

sà

Bg ecrlnc nd sb klsubgvb bn bg cjuc, cg `bnds nd tdkc. Gubjd kb cjltcrgd sb klsubgvb un pdfd `ãs, pbrd nd tdtcg`bntb.

nd

Bg cgfdedg sb klsubgvb ln`bklctc`bntb bn bg cjuc sln nbfbslkck kb cjltcrgd.

sà

ecrlnc + cjuc

cgfdedg + cjuc

Gc rbkcfflön vcrlcrã kbpbnklbnkd kbg klffldncrld fdnsugtckd. Gb prbsbntc`ds cgjunds bmb`pgds= Klffldncrld kb gc Ybcg Cfckb`lc Bspcódgc= • Fdgdlkb= klspbrslön kb pcrtàfugcs d `cfrd`dgìfugcs bn un `bkld fdntlnud. Klffldncrld CNC\C= • Fdgdlkb= kàfbsb kbg fubrpd qub, cg klspbrscrsb bn un `bkld ed`djìnbd (jcsbdsd, gàqulkd d söglkd) pcrbfb klsubgtd, cg sbr gcs pcrtàfugcs klspbrscs kb un tc`cód fd`prbnklkd bntrb unc kìfl`c y unc `lgìsl`c kb `lfrc. Klffldncrld BVXCVC sbfunkcrlc= • Fdgdlkb= rbobrlkd c flbrtds fubrpds kb `dgìfugc ùy jrcnkb, fd`d gc cgiý`lnc kbg eubvd, qub, pdr bsc flrfunstcnflc, cg klsdgvbrgds bn un gàqulkd y vbrtbr bstb nd ctrcvlbscn unc `bìrcnc pdrdsc, fd`d, pdr bmb`pgd, unc tbgc.

Bmbrflfld 3 8) 3) 9) 6)

`lfbgcs vlsfdsc cfbltb `lfrdsfdpld

Bmbrflfld 9 8) `cntbqulggc 3) bspu`c 9) mcgbc ¡C gc flbnflc pdr gc bxpbrlbnflc! Bg fdgdlkb bs gc jbgctlnc pdrqub sb pubkbn vbr fd`d gcs pbqubócs `lfbgcs ‗irlggcn‐ fucnkd bg ecz kb guz kb gc glntbrnc gcs ctrcvlbsc. Bstd nd sufbkb fdn gc `bzfgc kb cjuc fdn scg pdrqub bs unc sdguflön.


682

Vb`cnc 6; Bg ùnkd kb gc quà`lfc Bmbrflfld 3 8) 9 3) 9 9) 9 6) 6 ;) ? 2) 2

?) Gc bfucflön bstã icgcnfbckc. Bmbrflfld 9 3) 3. ný`brd kb ãtd`ds ný`brd kb ãtd`ds bn rbcftlvds

N 0 3 (END6) D 0 6 (END6) E 0 3 (END6)

bn prdkuftds

N 0 9 (N9D2) D 0 ? (N9D2 + E9D) E 0 9 (E9D)

Bmbrflfld 6 ?.899 x 3896 ãtd`ds kb Nb 8) 3.8 `dg kb Nb

3)

3 `dg kb Xi 98:.9 j kb Xi

9)

36:.6 j kb Ic 3 `dg kb Ic

6)

99.; G kb Fg9 3 `dg kb Fg9

;)

9 `dgbs kb NcFg 3 `dg kb Nc9Fr9D:

2)

3 `dg kb F?8 ?.899 x 3896 `dgìfugcs kb F?8

Bmbrflfld ;

9. Bsfrlic bg ný`brd 9 bn gc `dgìfugc kb END6, pcrc 3) Gc bfucflön icgcnfbckc bs=F9E2DE + 6D9 9FD9+ 6E9D icgcnfbcr bg nltröjbnd, elkröjbnd y dxàjbnd. 3. 3 `dg kb F9E2DE d 9 `dgbs kb FD9 9END6 N9D2 + E9D 9 `dgbs kb FD9 3 `dg kb F9E2DE 6. ný`brd kb ãtd`ds ný`brd kb ãtd`ds 9 `dgbs kb FD 9 9. bn rbcftlvds bn prdkuftds 3 `dg kb F9E2DE ND N D6)) D0 0 9? ((99E EN 6 E 0 9 (9END6)

9) 3. ný`brd kb ãtd`ds bn rbcftlvds

@j 0 3 (@j) Fg 0 3 (EFg) E 0 3 (EFg)

N0 0 ?9 (N (N9D D2) D 9 2 + E9D) E 0 9 (E9D)


@j 0 3 (@jFg9) Fg 0 9 (@jFg9) E 0 9 (E9)

9. Bsfrlic bg ný`brd 9 bn gc `dgìfugc kb EFg, pcrc icgcnfbcr bg fgdrd y bg elkröjbnd. @j + 9EFg 6.

@jFg9 + E9

9 6. 6 `dgbskb F9E2DE x 9 `dgbs kb FD 0 ? `dgbs FD 9 3 `dg kb F9E2DE

;. Y/ Cg qub`cr 6 `dgbs kb F 9E2DE sb ditlbnbn ? `dgbs kb FD9. 9) Gc bfucflön icgcnfbckc bs= 9F5E35 + 92D9 3?FD9 + 35E9D 3. @csc `dgcr kbg F5E35= 33;.8 j/`dg •

3 `dg kb F5E35 d 33;.8 j kb F5E35 33;.8 j kb F5E35 3 `dg kb F5E35

• 9 `dgbs kb F5E35 d 3? `dgbs kb FD9 3? `dgbs kb FD9 9 `dgbs kb F5E35

ný`brd kb ãtd`ds

ný`brd kb ãtd`ds

• @csc `dgcr kbg FD 9= ;;.8 j/`dg

@jbn0rbcftlvds 3 (@j) Fg 0 9 (9EFg) E 0 9 (9EFg)

@jbn0 prdkuftds 3 (@jFg9) Fg 0 9 (@jFg9) E 0 9 (E9)

• 3 `dg kb FD9 d ;;.8 j kb FD9 ;;.8 j kb FD9 3 `dg kb FD9

68?

LJBY ∙ [cfcnã

3 `dg kb F5E35 33;.8 j kb F5E35 • 3? `dgbs kb FD9 9 `dgbs kb F5E35 • ;;.8 j kb FD9 3 `dg kb FD9 6. 2.8 j kb F5E35 x 3 `dg kb F5E35 x 3? `dgbs kb FD9 x ;;.8 j kb FD9 0 32.; j kb FD9 33;.8 j kb F5E35 9 `dgbs kb F5E35 3 `dg kb FD9 9. •

;. Y/ Vb prdkufbn 32.; j kb FD 9 fucnkd sb qub`cn 2.8 j kb F5E35. 6) Gc bfucflön icgcnfbckc bs= 6@j+ N9

@j6N9

3. @csc `dgcr kbg N9= 95.8 j/`dg • 3 `dg kb N9 d 95.8 j kb N9 95.8 j kb N9 3 `dg kb N9 3 `dg kb N 9 • d 6 `dgbs kb @j 6 `dgbs kb @j 3 `dg kb N9 @csc `dgcr kbg @j= 9;.6 j/`dg • 3 `dg kb @j d 9;.6 j kb @j 9;.6 j kb @j 3 `dg kb @j 3 `dg kb N 9 9. • 95.8 j kb N9 6 `dgbs kb @j • 3 `dg kb N9 • 9;.6 j kb @j 3 `dg kb @j 6. <.6 j kb N9 x 3 `dg kb N9 x 6 `dgbs kb @j x 9;.6 j kb @j 0 9;.9 j kb @j 95.8 j kb N9 3 `dg kb N9 3 `dg kb @j ;. Y/ Vb nbfbsltcn 9;.9 j kb @j pcrc qub rbcffldnb fdn <.6 j kb N9. ;) Gc bfucflön icgcnfbckc bs= 9VD9 + D9 3. 3 `dg kb D9 d 9 `dgbs kb VD9 9 `dgbs kb VD9 3 `dg kb D9

9VD6

@csc `dgcr kbg D 9= 69.8 j/`dg 3 `dg kb D9 d 69.8 j kb D9 69.8 j kb D9 3 `dg kb D9 3 `dg kb D 9 9. • 9 `dgbs kb VD9 69.8 j kb D9 • 3 `dg kb D9 6. 6.8 `dgbs kb VD9 x 3 `dg kb D9 x 69.8 j kb D9 0 ;5.8 j kb D 9 9 `dgbs kb VD9 3 `dg kb D9 ;. Y/ Vb nbfbsltcn ;5.8 j kb D9. Suà`lfc LL ∙ Fgcvbs

68:

2) Gc bfucflön icgcnfbckc bs= ;Ob +6D9

9Ob9D6

3. @csc `dgcr kbg D9= 69.8 j/`dg • 3 `dg kb D9 d 69.8 j kb D9 69.8 j kb D9 3 `dg kb D9 6 `dgbs kb D 9 • d 9 `dgbs kb Ob9D6 9 `dgbs kb Ob9D6 6 `dgbs kb D9 @csc `dgcr kbg Ob 9D6= 32<.? j/`dg • 3 `dg kb Ob9D6 d 32<.? j kb Ob9D6 32<.? j kb Ob9D6 3 `dg kb Ob9D6 3 `dg kb D 9 9. • 69.8 j kb D9 • 9 `dgbs kb Ob9D6 6 `dgbs kb D9 32<.? j kb Ob9D6 • 3 `dg kb Ob9D6 6. 9.2 j kb D9 x 3 `dg kb D9 x 9 `dgbs kb Ob9D6 x 32<.? j kb Ob9D6 0 5.6 j kb Ob 9D6 69.8 j kb D9 6 `dgbs kb D9 3 `dg kb Ob 9D6 ;. Y/ Vb prdkufbn 5.6 j kb Ob 9D6. ?) Gc bfucflön icgcnfbckc bs=9E9 + D9

9E9D4

3. @csc `dgcr kbg D9= 69.8 j/`dg • 3 `dg kb D9 d 69.8 j kb D9 69.8 j kb D9 3 `dg kb D9 3 `dg kb D 9 • d 9 `dgbs kb E9D 9 `dgbs kb E9D 3 `dg kb D9 @csc `dgcr kbg E 9D= 35.8 j/`dg • 3 `dg kb E 9D d 35.8 j kb E9D 35.8 j kb E9D 3 `dg kb E9D 3 `dg kb D 9 9. • 69.8 j kb D9 • 9 `dgbs kb E9D 3 `dg kb D9 35.8 j kb E9D • 3 `dg kb E9D 3 `dg kb D9 9 `dgbs kb E9D 35.8 j kb E9D 6. 69.8 j kb D9 x 69.8 j kb D9 x 3 `dg kb D9 x 3 `dg kb E9D 0 6?.8 j kb E9D ;. Y/ Vb odr`cn 6?.8 j kb E9D c pcrtlr kb gc fdnvbrslön kb 69.8 j kb D9.

685

LJBY ∙ [cfcnã

:) Gc bfucflön icgcnfbckcbs= F?E39D?

9F9E2DE + 9FD9

3. @csc `dgcr kbg F?E39D?= 358.8 j/`dg •

3 `dg kb F?E39D? d 358.8 j kb F?E39D? 358.8 j kb F?E39D? 3 `dg kb F?E39D?

•

3 `dg kb F?E39D? d 9 `dgbs kb F9E2DE 9 `dgbs kb F9E2DE 3 `dg kb F?E39D?

@csc `dgcr kbg F 9E2DE= ;?.8 j/`dg • 3 `dg kb F9E2DE d ;?.8 j kb F9E2DE ;?.8 j kb F9E2DE 3 `dg kb F9E2DE 9. •

3 `dg kb F?E39D? 358.8 j kb F?E39D?

• 9 `dgbs kb F9E2DE 3 `dg kb F?E39D? • ;?.8 j kb F9E2DE 3 `dg kb F9E2DE 6. 38.8 j kb F?E39D? x 3 `dg kb F?E39D? x 9 `dgbs kb F9E2DE x ;?.8 j kb F9E2DE 0 2.3 j kb F 9E2DE 358.8 j kb F?E39D? 3 `dg kb F?E39D? 3 `dg kb F9E2DE ;. Y/ Vb prdkufbn 2.3 j kb F9E2DE c pcrtlr kb gc fdnvbrslön kb 38.8 j kb F?E39D?. Bmbrflfld 2 C. 8) sdgvbntb 3) czýfcr 9) dxàjbnd bn cjuc 6) scturckc I. sdguflön

cjuc dxljbnckc `bklflncg

bstckd kb gc sdguflön

sdgutd

pbröxlkd kb elkröjbnd gàqulkd (E9D9 ) scg fd`ýn (NcFg) y subrd drcg gàqulkd czýfcr (F39E99D33) dxàjbnd `bklflncg jcsbdsd dxàjbnd (D9) cgfdedg kb ocr`cflc gàqulkd cgfdedg (FE6FE9DE) cjuc kb `cr gàqulkd scg fd`ýn (NcFg) dxàjbnd (D9) y klöxlkd ct`ösobrc jcsbdsd kb fcridnd (FD9) cjuc jcsbdsc d klöxlkd kb fcridnd gàqulkd (FD9) fcridnctckc c`cgjc`c kbntcg söglkd `brfurld `btãglfd (Ej) nlfrd`d söglkd nàqubg (Nl)

bstckd kbg sdgutd

sdgvbntb

bstckd kbg sdgvbntb

gàqulkd

cjuc

gàqulkd

söglkd

cjuc

gàqulkd

jcsbdsd nltröjbnd (N9) jcsbdsd gàqulkd cjuc gàqulkd söglkd cjuc gàqulkd jcsbdsd nltröjbnd (N9) jcsbdsd jcsbdsd cjuc

gàqulkd

gàqulkd söglkd

söglkd söglkd

pgctc (Cj) frd`d (Fr)


68<

Bmbrflfld ?

3) % `/` 0 % `/` 0

`csc kb sdgutd x 388 `csc kb sdguflön 38 j x 388 0 98 % 28 j

Y/ Bg pdrfbntcmb ` ‖ ` kb gc sdguflön bs 98 %. `csc kb sdgutd 9) % `/` 0 `csc kb sdguflön x 388 `csc kb sdgutd 2%0 x 388 928 2 x 928 j 0 `csc kb sdgutd 388 `csc kb sdgutd 0 39.2 j Y/ Vb kbibn klsdgvbr 39.2 j kb scg bn cjuc. 6) c. Bg sdgvbntb bs bg cjuc y bg sdgutd, gc jgufdsc. `csc kb sdgutd i. % `/` 0 x 388 `csc kb sdguflön `csc kb sdgutd 22 % 0 x 388 28 j 22 x 28 j `csc kb sdgutd 0 0 9:.2 j kb sdgutd 388 Y/ Bn bg pgctd qubkcràcn 9:.2 j kb jgufdsc. ;) `csc kb sdguflön 0 `csc kb sdgutd + `csc kb sdgvbntb `csc kb sdguflön 0 39 j + <5 j 0 338 j `csc kb sdgutd % `/` 0 x 388 `csc kb sdguflön % `/` 0

39 j x 388 0 38.< % 338 j kb sdguflön

Y/ Bg pdrfbntcmb ` ‖ ` kb gc sdguflön bs 38.< %. 2) vdgu`bn kb sdguflön 0 vdgu`bn kb sdgutd + vdgu`bn kb sdgvbntb vdgu`bn kb sdguflön 0 28 `G + 3;8 `G 0 3<8 `G vdgu`bn kb sdgutd % v/v 0 vdgu`bn kb sdguflön x 388 28 `G % v/v 0 x 388 0 9?.6 % 3<8 `G Y/ Bg pdrfbntcmb v ‖ v kb gc sdguflön bs kb 9?.6 %.

638

LJBY ∙ [cfcnã

?) % v/v 0

vdgu`bn kb sdgutd x 388 vdgu`bn kb sdguflön

vdgu`bn kb sdgutd x 388 92 `G 6 x 92 `G vdgu`bn kb sdgutd 0 0 8.:2 `G kb sdgutd 388

6%0

Y/ 92 `G kb cjuc dxljbnckc cg 6 % v/v fdntlbnbn 8.:2 `G kb pbröxlkd kb elkröjbnd. :) Gds fãgfugds tcìlìn pubkbn rbcglzcrsb bn gltrds sln qub vcràb gc rbspubstc. vdgu`bn kb sdguflön 0 9888 `G + 98888 `G 0 99888 `G % v/v 0

vdgu`bn kb sdgutd x 388 vdgu`bn kb sdguflön

% v/v 0

9888 `G x 388 0 <.3 % 99888 `G

Y/ Bg pdrfbntcmb v ‖ v kb gc klsdguflön bs kb <.3 %. 5) c. % `/` 0 % `/` 0

`csc kb sdgutd x 388 `csc kb sdguflön 3 x 388 0 ;.3: % 9;

Y/ Bg pdrfbntcmb ` ‖ ` kb gc cgbcflön kb 3 qulgctb bs kb ;.3: %. i. % `/` 0 % `/` 0

`csc kb sdgutd x 388 `csc kb sdguflön 35 x 388 0 :2 % 9;

Y/ Bg pdrfbntcmb ` ‖ ` kb gc cgbcflön kb 35 qulgctbs bs kb :2 %. f. Bg pdrfbntcmb ` ‖ ` kb gc cgbcflön kb 35 qulgctbs bs kb :2 %, sl bn tdtcg ecy ; aj, bs kbflr ;888 j. `csc kb sdgutd x 388 `csc kb sdguflön % `/` x `csc kb sdguflön 0 `csc kb sdgutd 388 :2 x ;888 j `csc kb sdgutd 0 0 6888 j kb sdgutd 388

% `/` 0

Y/ Bn 3 glnjdtb kb drd kb 35 qulgctbs fdn unc `csc kb ; aj ecy 6 aj kb drd purd.


633

Bmbrflfld : ocsb klspbrsc

mciön cjuc plj`bntd vbnbnd


söglkd gàqulkd söglkd gàqulkd

gàqulkd cjuc jcs clrb pdgvd kb fcridnd söglkd



ndìrb kbg fdgdlkb

sustcnflc rbsugtcntb

cjucfdnmciön nlbigc plnturc kb cfbltb lnsbftlflkc

cjuc clrb sdgvbntb `lnbrcg jcs c prbslön

gàqulkd jcs gàqulkd jcs

sdg cbrdsdg gàqulkd sd g cbrdsdg gàqulkd

cfbltb vbjbtcg pgãstlfd clrb

söglkd söglkd jcs

bùgslön söglkc `crjcrlnc bspu`c söglkc bspdnmc cbrdsdg gàqulkd eu`d

Bmbrflfld 5 3) Bs unc `bzfgc bn gc qub unc sustcnflc fd`pubstc pdr pcrtàfugcs sb klspbrsc kb `cnbrc unlodr`b bn un sdgvbntb. 9) Obnö`bnd qub sb prdkufb fucnkd gds fdgdlkbs sdn ctrcvbsckds pdr un rcyd kb guz y bstb sb klspbrsc. 6) @dvl`lbntd rãplkd, lrrbjugcr y vljdrdsd kb gcs pcrtàfugcs qub odr`cn un fdgdlkb. ;) Vdn gcs pcrtàfugcs qub sb bnfubntrcn suspbnklkcs odr`cnkd un fdgdlkb y sb ggc`cn `lfbgcs.

639

LJBY ∙ [cfcnã

Iligldjrcoàc CNC\C. Klffldncrld

Cncyc kb gc Gbnjuc. Cncyc, Bspcóc, 3<<3.

FECNJ, Y. Suà`lfc. @fJrcw-Elgg, @ìxlfd, 3<<2. KCRI, J. y. VBBVB, Z.Suà`lfc. Xrbntlfb Ecgg, @ìxlfd, 3<
Xãjlncs wbi fdnsugtckcs= ettp=//bnflnc.pntlf.`bf.bs/~msco8889/p;6.et`#Bfucfldnbs%98qu%F6%CK`lfcs1%98sljnlolfckd. ettp=//www.jdilbrndkbfcncrlcs.drj/bkufcfldn/6/Rsrn/gbntlsfcg/3-FKSul`lfc-[LF/F[VC/FD@BN[CYLD%98 KB%98[BU[DYbkdxI.pko ettp=//fdnfursd.fnlfb.`bf.bs/fnlfb9882/62TgcsTrbcffldnbsTqul`lfcs/fursd/rbT8;.et`g ettp=//fdnfursd.fnlfb.`bf.bs/fnlfb9882/62TgcsTrbcffldnbsTqul`lfcs/fursd/lnkbx.et`g ettp=//www.bls.uvc.bs/~qjlntrd/bstbq/tutdrlcg-86.et`g ettp=//www.fbsprd.fd`/@ctbrlcs/@ctFdntbnlkds/Fdntqul`lfc/SRL@LFCTLNDYJCNLFC/bstbquld`btrlc.et` ettp=//www.fuckbrndlntbrfugturcg.fd`/`ctbrlcgbs/r-dnglnb/trcnsvbrscgbs9/ ettp=//pgctbc.pntlf.`bf.bs/p`crtl3/bkufcfldn/6TbsdT`ctbrlcgbs/iTll/6bsdTigdqubTll.et`#cpcrtckdT; ettp=//www.`dndjrcolcs.fd`/trcicmds33/`dklsdg/`dklsdg.set`g ettp=//www.rbnc.bku.vb/[brfbrcBtcpc/Sul`lfc/[email protected]`g ettp=//bnkrlnd.pntlf.`bf.bs/edtp88?
636

Bstuklcr

gb fcìlcrã gc

vlkc

Vl jc gd s p cs ds .. . Gbc bg fdntbnlkd kb gc sb`cnc Bsfufeb gc fgcsb rcklcg fdn gds flnfd sbntlkds Kbspuìs kb gc fgcsb rcklcg… bstukld y cutdfdntrdg Fdnsugtb sus kukcs Cslstc cg fbntrd kb drlbntcflön

Lnstltutd Juctb`cgtbfd kb Bkufcflön Yckldoönlfc y Jrupd Ycklcg ¡uy, uy, uy!

[bg= 9;39 ???? www.ljbr.bku.jt ljbrHljbr.bku.jt

Libro Tacaná Química II 2º. Semestre 10

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