^EHSN\PHMBM KBXA\ MN PBE BEM\NP CB@^I]BM CB@^I]B M MN HEONEHN\HB @^\PA LBPH@A RK@ - 2:=
Z\B@]H@B E´ ?
Nstumhbetn4 ]h`ae ]h`aeb b Ruhspn Nihzblntf Ma`netn4
Heo. K. P`. \alnrta Zbrrb Tnlbiias
Cn`fb mn rnbihzb`hðe4 2: mn kbya mn <:23 Cn`fb mn netrnob4
2? mn kbya mn <:23
<:23
Z\NZB\B@HÐE MNI BI^KL\N MN BI^KHEHA 2. ALDN]HSAP 2.2. ALDN]HSA ONEN\BI
Altnenr biuklrn mn bkaeha, mn patbsha y euknra mn kains mn fhmrbtb`hðe
2.<. ALDN]HSAP NPZN@HCH@AP
Altnenr biuklrn mn bkaeha
Altnenr ni biuklrn mn patbsha.
Nxpih`br ibs `aemh`haens ne ib qun sn carkb ueb sbi malin.
Mns`rhlhr ibs `brb`tnrësth`bs kâs hkpartbetns mni biuklrn
@bi`uibr ni rnemhkhneta mni biuklrn mn bkaeha.
<. C^EMBKNE]A ]NA\H@A Ni biuklrn ns ue khenrbi qun sn prnsnetb ne ib ebturbinzb ne carkb mn `rhstbi. Pn althnen mn ueb ra`b kbokâth`b, mn arhone vai`âeh`a, mneakhebmb trbquhtb biueëcnrb, qun ueb vnz pra`nsbmb sn `aevhnrtn ne biuklrn patâsh`a. Ias mnpðshtas khenrbins mn biuklrn sn arhohebe ne mhsthetbs cbsns mni ibroa pra`nsa onaiðoh`a qun sucrne ibs ra`bs vai`âeh`bs, pra`nmnetns mn ib kbsb ne cushðe nxhstnetn ne ni hetnrhar mn ib thnrrb. Ias `rhstbins mn biuklrn punmbe tnenr vbrhb`haens ne bpbrhne`hb, `aiar a tnxturb, buequn tamas kbethnene sus praphnmbmns. Pn `aea`n `aka biuklrn b ue thpa mn suicbta malin `akpunsta par ni suicbta mn ue kntbi trhvbinetn, `aka ni biukheha, y atra mn ue kntbi kaeavbinetn. ]bklhèe sn punmne `rnbr mas saiu`haens4 ueb saiu`hðe sbturbmb ne `bihnetn y ueb saiu`hðe
sbturbmb ne crëa. Onenrbiknetn sn rnchnrn bi biuklrn patâsh`a GBiPA =)<¿2
<.2. ^PAP Ias usas mni biuklrn sae heeuknrblins4
Ns uea mn ias prhe`hpbins heornmhnetns mn qun sn shrvne ias thetarnras pbrb mbr b ias `aiarns kâs lrhiia y kâs vhvb`hmbm, `aesaihmâemaias salrn ib nstacb a pramu`hnema ni khska ncn`ta qun ni boub mn oakb7 ns ueb nspn`hn mn karmhnetn qun chdb ias `aiarns y ias uen, hkphmhnema b ibs pbrtë`uibs kâs chebs nvbparbrsn7 ias thetarnras biuklrbe tambs ibs nstacbs qun quhnrne tnòhr, salrn tama ne `brknsë, she ia qun ea rn`hlne lhne nstn `aiar7
Ne ku`fas `bsas, ueb `artb `bethmbm mn fhnrra, qun nesu`hb shnkprn kâs a kneas bue ias kndarns biuklrns, ea punmn pnrdumh`br ias luneas rnsuitbmas ne su bpih`b`hðe `aka karmhnetn pnra `ae crn`une`hb tbklhèe nstn suicbta mn fhnrra ns kuy mn tnknr, y betns mn fb`nr usa mni biuklrn ns prn`hsa purhch`bria par mhsaiu`haens y `rhstbihzb`haens rnpnihmbs4 uea mn nstas `bsas ns ni mn ias fnrkasas thetns mn bioamðe ne rada mn Bemrheapaih y ne atras `aiarns vhvas7 parqun `aevhnen sblnr qun ni bioamðe ns, mn tamas ias tndhmas aroâeh`as, ni kâs sneshlin b ib prnsne`hb mni fhnrra7
B ib en`nshmbm mn ueb orbe purnzb mni biuklrn pbrb `hnrtas thetns, pbrb ib `aiarb`hðe mn ias kbrraquëns, nt`., sn mnln ne orbe pbrtn b ia kneas ib prnnkhene`hb `ae`nmhmb par tbe ibroa thnkpa bi biuklrn mn \akb, y `ubiquhnr biuklrn lhne purhch`bma punmn mbr ias khskas rnsuitbmas7
Ni biuklrn hkpura, kuy `brobma mn suicbta mn fhnrra, nrb tbklhèe kuy lus`bma, prhe`hpbiknetn par ias `urthmarns mn vbquntbs mn Kas`avhb, quhnens prntnemëbe qun nstb vbrhnmbm mblb pnsa b sus `unras libe`as7
Phrvn tbklhèe pbrb altnenr `bsh tambs ibs ib`bs7
Zbrb prnsnrvbr ibs phnins y ias carras mn snr btb`bmas par ias hesn`tas7
Zbrb biuklrbr ni pbpni mn ns`rhlhr7
Zbrb nemurn`nr ni snla ne ib cblrh`b`hðe mn vnibs7
Zbrb rntbrmbr ib putrncb``hðe mn ias `bmâvnrns7
@ibrhch`b tamas ias iëquhmas bsë `aka tamas ias ih`arns, pnra ins `akueh`b `hnrta ousta qun beue`hb su prnsne`hb7 sn fb`n ku`fa usa mn èi pbrb `ibrhch`br ni bzô`br mn rnkaib`fbs ne ibs câlrh`bs mn nstn pramu`ta.
N e ib s bium Bethoubknetn, ni biuklrn sn bmkhehstrblb mn euknrasbs kbenrbs, `aka bstrheonetn
pamnrasa
prn`aehzbma
ne
ue
sheeôknra
mn
necnrknmbmns.
Nxtnrebknetn, sn usblb `aetrb ibs nx`rn`ne`hbs cueoasbs, ibs ôi`nrbs, ias maiarns mn ibs ne`ëbs, ias sblbòaens, nt`.2 Nstas usas sn fbe blbemaebma, buequn sn shoun uthihzbema `aka bmyuvbetn ne vb`uebs y `aka `abouibetn ne sbeorbma mn ðrobeas hetnreas.
N e quëkh`b Pn usbe bkpihbknetn ne quëkh`b ne ib pbrtn fôknmb mni pra`nsa mn cblrh`b`hðe mni pbpni, par su shoehch`bthva ncn`ta cia`uibetn7 ne ni ne`aibma ne kbsb mni pbpni, pbrb prn`hphtbr ib `aiacaehb salrn ibs chlrbs `niuiðsh`bs. Ne ib Nmbm Knmhb, bmquhrhnrae ue orbe vbiar mnlhma b su uthihzb`hðe pbrb ib chdb`hðe mn thetns ne ib rapb, netrn atras usas.
^s a `as kèth`a ^ea mn ias usas kâs ne laob mni biuklrn mn patbsha (y ea mn atras thpas mn biuklrn) ns su usa `askèth`a `aka mnsamarbetn y bethtrbesphrbetn ebturbi. Bi fuknmn`nrsn y bpih`brsn salrn ib phni, mndb ueb `bpb mn khenrbins `ae ncn`ta lb`tnrh`hmb, par ia qun nihkheb ni aiar mn ibs bxhibs, `aka ni nx`nsa mn sumarb`hðe. ]bklhèe punmn bpih`brsn ne ias phns `aka mnsamarbetn y mnspuès mni bcnhtbma y mn ib mnphib`hðe par rbsurb`hðe. Zbrb nstas usas, sn sunin prnsnetbr nstn khenrbi ne ue carkbta raii-ae, qun cb`hihtb su bpih`b`hðe.
<.<. NI BI^KL\N MN BKAEHA (Bkkaehuk biuk), par su pbrtn, sn cblrh`b b lbsn mn sbins mn bkaeha, rnshmuas mn ib hemustrhb quëkh`b pnsbmb bshâth`b ( ue sulpramu`ta mni `bpraib`tbka qun pra`nmn mn ibs hemustrhbs mn cblrh`b`hðe mni eyiae prhe`hpbiknetn), qun sae rnboiaknrbmbs betns mn vnemnrsn lbda nstb mneakheb`hðe. Pn trbtb puns, mn ueb phnmrb netnrbknetn shetèth`b y ni biukheha qun ia `akpaen ea sn fhmrbtb y punmn chdbrsn ne ib phni. Ni pbsa b ib sbeorn mni biukheha ns pralinkâth`a (he`iusa par knmha mn ibs vb`uebs a ib bihknetb`hðe) yb qun nstb pralbma qun nstbs kaiè`uibs sn b`ukuibe ne ni `nrnlra y nstn cneðknea snrëb, netrn atrbs, ueb mn ibs `busbs mn ib necnrknmbm mn Bizfnhknr. B`tubiknetn, fby qun snòbibr qun saibknetn ni `iarfhmrbta mn biukheha sn paen ne netrnmh`fa par ia qun sn rnchnrn b ue pashlin pbsa trbes`utâena". Ib phnmrb mn biuklrn ns, prhe`hpbiknetn, ueb orbe bethsèpth`b y bstrheonetn. Mn fn`fa, sn ib nkpinb `aka uea mn ias mnsamarbetns ebturbins kâs ncn`thvas qun nxhstne. ]hnen ib `bpb`hmbm mn `nrrbr paras y rnouibr ib sumarb`hðe, nihkhebema, b su vnz, b ibs lb`tnrhbs qun pamrëbe iinobr b prava`br aiar.
<.0. NI BI^KL\N MN ZA]BPHA (Zatbsshuk biuk) ns ueb ph nmrb netnrbknetn ebturbi. Pn in iibkb tbklhèe ’suicbta mn biukheha y patbsha‛ a ’suicbta malin mn patbsha y mn biukheha fhmrbtbma‛. Ni
biukheha fhmrbtbma ns ueb carkb nstblin mn biukheha qun ea sn chdb ne ib phni. Pn nihkheb shkpinknetn b trbvès mni cneðknea mn ib trbesphrb`hðe a ne ni kakneta mn ib mu`fb. Ne ncn`ta, ns quëkh`bknetn henrtn (ne nstn nstbma ea rnb``haeb quëkh`bknetn). Zar ia tbeta, ea sn `arrn ni rhnsoa mn qun sn ihlnrn ni biukheha (bi `aetrbrha qun ias fhmrbtas mn `iarura mn biukheha `aetnehma ne bioueas mnsamarbetns `iâsh`as). Zar atra ibma, ni biukheha lbda carkb mn fhmrðxhma u ðxhma (biôkheb) ns ni `akpaenetn nsne`hbi mn br`hiibs mn tama thpa y ea ns ne blsaiuta ea`hva pbrb ni arobehska. Ne rnsukne, ib b``hðe mni biuklrn mn patbsha ns `utâena nx`iushvbknetn, ea pbsb ebmb b ib sbeorn.
<.=. SNE]BDBP MNI BI^KL\N
Snetbdbs mni biuklrn
Ns ue lune mnsamarbetn, `h`btrhzbetn, rnbchrkbetn y bethsèpth`a.
]hnen ue ncn`ta lb`tnrh`hmb ebturbi, she bethtrbesphrbetns, par `aeshouhnetn, nvhtb ib bpbrh`hðe mni aiar `arparbi.
Ea alstruyn ias paras mn ib phni. Pðia pnrkben`n ne ib phni she pnrdumh`br ib rnsphrb`hðe ebturbi mn eunstra `unrpa.
Zasnn praphnmbmns bstrheonetns, bethhecibkbtarhbs y bethfnkarrâoh`bs par ia qun sn punmn bpih`br mnspuès mn ib mnphib`hðe y bcnhtbma.
Ea `aethnen bi`afai eh pnrcukn.
Ea `aethnen `iarfhmrbta mn biukheha eh `hr`aeha mn biukheha.
Ea `aethnen mnrhvbmas mni pntrðina, mhsaivnetns eh quëkh`as pnihorasas.
Hemh`bma pbrb phnins sneshlins a `ae binrohbs.
Ncn`thva b ia ibroa mni mëb.
Ns mn ibrob murb`hðe. \nsuitb n`aeðkh`a.
Ea mndb kbe`fbs eh ne ib phni eh ne ib rapb.
Ns hevhshlin ne ib phni.
Ea ns pnobdasa.
Ea `aetbkheb.
0. Z\A@NMHKHNE]A NVZN\HKNE]BI 0.2. Z\NZB\NB@HAE MNI BI^KL\N, EF=BI(PA=) F
HEH@HA @aia`br 2 o mn vhrutbs mn Bi ne ue vbsa mn <>: ki
Bòbmhr <> ki mn EbAF bi 2:%
Bi `nsbr ib ncnrvns`neth`b, fnrvhr mn 2> b <: khe, `akpintbema ib mhsaiu`hðe mni biukheha
Mhiuhr `ae boub fbstb ni malin mn su vaiukne heh`hbi
PH ±Fby prn`hphtbmas1
EA Mhiuhr fbstb <:: ki y enutrbihzbr `ae â`hma suicôrh`a =E, kbetnehnema ib mhsaiu`hðe `bihnetn y ne bohtb`hðe.
Ni ðxhma mn biukheha mn b iukheha fhmrbtbma sn prn`hphtb sbi
Chitrbr she su``hðe
Chitrbr ni rnshmua
Ibvbr ni prn`hphtbma `ae boub `bihnetn.
\nthrbr ni chitrbma
Bebmhr =:ki mn b`. Puicôrh`a =E, rnkavnr `ae vbrhiib, pnrcarbema ni
Mndbr qun ib mhsaiu`hðe y ne saihma `bhobe ne ni vbsa.
Brrbstrbr ni prn`hphtbma bmfnrhma, `ae ib khskb mhsaiu`hðe `bihnetn, fbstb qun ea qunmn sðihma biouea ne ni chitra
Mhsaivnr ni ðxhma mn Bi par `binetbkhneta
Bebmhr <:ki mn EF =AF
\n mhsaivnr `ubiquhnr pnqunòb `bethmbm mn axhma mn biukheha, `ae â`hma suicôrh`a =E.
@ae`netrbr par nvbparb`hðe, bpraxhkbmbknetn b ib khtbm.
Mndbr ne necrhbr fbstb ni mëb shouhnetn, ias `rhstbins sn sn`be y sn pnsbe
0.<. PHE]NPHP MNI BI^KL\N, Bi G(PA=)< F
HEH@HA Iinvbr b nluiih`hðe >: ki mn boub mnsthibmb ne ue vbsa mn prn`hphtbmas m 2:: ki
2.606o mn G
Mhsaivnr `ae 2>ki mn boub qun fb `binetbma, `ae ueb pralntb.
?.:<6o mn Bi < (PA=)0 ne ue kbtrbz Nrineknynr sn`a y ihkpha
Mhsaivnr `ae 2: ki mn boub `bihnetn.
Bòbmhr ibs betnrharns mhsaiu`haens ne ue vbsa mn prn`hphtbmas mn 2:: ki ne qun sn rnbihzbrb ib sëetnshs
Necrhbr ib mhsaiu`hðe hetramu`hnema ni vbsa mn prn`hphtbma ne ue vbsa `ae fhnia
Nspnrn ib prn`hphtb`hðe mni biuklrn, sae such`hnetns 0: khe.
Chitrbr bi vb`ëa.
\nthrbr `ae ku`fa `uhmbma n b iuklrn shetnthzbma, mnpasëtnia ne ue vhmrha mn rniad ihkpha sn`a y prnvhbknetn pnsbma
Hetramuz`b ni vhmrha ne ib nstucb maemn mnlnrâ º
^eb vnz sn`a ni biuklrn sn fb altnehma.
0.0. MN]N\KHEB@HAE MN IBP KAIÈ@^IBP MN FM\B]B@HAE MNI BI^KL\N
HEH@HA @binetbr `ae sapintn ueb `bpsuib mn par`nibeb
Pn trblbdbrb `ae Bi < (PA=)0*26F
@binetbr ib kunstrb ne ib pib`b fbstb qun sn alsnrvn mnsprnemhkhneta mn boub
Beatbr ias cneðkneas alsnrvbmas murbetn ni `binetbkhneta.
Mndbr necrhbrn ib `bpsuib y pnsbr.
=. @ÂI@^IAP X \NP^I]BMAP =.2. Z\NZB\NB@HAE MNI BI^KL\N, EF=BI(PA=) F ki mn EbAF4 <> ∟
2:
; <>
2::
=: ki mn F
= 2:::
∟
86 <
∟
2 2.6=
; =.<3
\nb``haens quëkh`bs a`urrhmbs ne ni pra`nsa
+ 0 ↜ ( ) + 0 \nb``hðe mn malin susthtu`hðe qun sn pramu`n mn kbenrb nspaetâenb.
< + ↜ ( ) + < \nb``hðe mn malin susthtu`hðe qun sn pramu`n mn kbenrb nspaetâenb.
( ) + ( ) + 2< ↜ ( ) ∟
\nb``hðe mn sëetnshs, qun sn pramu`n mn carkb nspaetbenb Alsnrvb`haens4
Ib saiu`hðe mn â`hma suicôrh`a y axhma mn biukheha ns ncnrvns`netn y mnsprnemn ue mnsborbmblin aiar.
Pn pra`nmhð `ae tama ni trbtbkhneta y sn mndð pbrb qun `rhstbihzbrb, y bi mëb shouhnetn sn pumhnrae alsnrvbr ias `rhstbins ne carkb mn phnmrhtbs he`aiarbs.
Pn chitrbrae y sn pnsbrae pumhnema eatbr ue pnsa mn 2.86o mn `rhstbins mn biuklrn mn bkaeha.
=.<. PHE]NPHP MNI BI^KL\N, Bi G(PA=)< F
@bi`uia mni rnemhkhneta4
↜
8=6 o
Kbsb tnðrh`b4 <.:32 ∟
8=6 ()∟ 2?=
Kbsb altnehmb nxpnrhknetbiknetn4 % ;
; . ( ) ∟
; ?.0?6
∟ 2::%
% ;
?.0?6 22.<0
∟ 2::%
% ; . % Alsnrvb`haens4
Ias `rhstbins sn altuvhnrae b pbrthr mn ueb rnb``hðe mhrn`tb b mhcnrne`hb mni betnrhar biuklrn, ib mhcnrne`hb cun qun ni pra`nsa cun ku`fa kâs râphma pumhnema eatbr ue biuklrn mn `aiar libe`a, `ae ueb tnxturb shkhibr bi bzô`br.
=.0. MN]N\KHEB@HAE MN IBP KAIÈ@^IBP MN FM\B]B@HAE MNI BI^KL\N Pn trblbdð `ae Bi < (PA=)0*26F= ; <.820 ∜ 2.<>= ; 2.3>8
]nðrh`a4 <.820Bi (P)∟F ∟
0<=F 0=<Bi (P)
∟
2 A 26F
; .
N xpnrhknetbi4 2.3>8F ∟
2 A 26F
; .
>. HE]N\Z\N]B@HAE MN \NP^]BMAP Ias rnsuitbmas sn altuvhnrae ib kbyarëb nspnrbmas par tnarëb, yb qun pumhkas altnenr prn`hphtbmas a ncnrvns`ne`hbs `aka sn hemh`blb ne ib ouëb. Pn pumhnrae alsnrvbr ias mas biuklrns y pamnr mhcnrne`hbrias yb qun uea nrb shkhibr bi atra pnra ea `akpintbknetn houbins, sn altuva ue rnemhkhneta mni biuklrn mn patbsha mn ue 3>% qun ia pamnkas hetnrprntbr `aka lunea. Buequn ne ib prâ`th`b sn alsnrvð qun sn altuva kâs nch`bzknetn ni biuklrn mn patbsha, yb qun ni biuklrn mn bkaeha eas `asta altnenria.
3. @AE@I^PHAENP Pn
altuvhnrae ias biuklrns mn bkaeha y mn patbsha knmhbetn mhcnrnetns rnb``haens
quëkh`bs y trbtbkhnetas.
Pn pibetnbrae ibs mhcnrnetns rnb``haens quëkh`bs qun sn nxpnrhknetbrae ne iblarbtarha, houbiâemaibs par shkpin tbetna.
Pn
rnbihzð ni pra`nmhkhneta y sn alsnrvbrae ibs rnb``haens pbrb ib carkb`hðe mn ias
biuklrn mn patb`hðe y mn bkaeha. Pn
puma eatbr qun ibs rnb``haens sn pramu`ne ne `bihnetn.
^eb
vnz kâs sn pumhnrae eatbr ibs praphnmbmns cësh`bs y quëkh`bs mn ias mhvnrsas
ninknetas mn ib tblib pnrhðmh`b, yb nstumhbmas ne prâ`th`bs betnrharns. Pn
fhsa ni `âi`uia mni rnemhkhneta pbrb ni biuklrn mn patbsha.
Pn
mnsfhmrbta ueb sbi, par `binetbkhneta mn ib khskb `ae ue sapintn pbrb bi`bezbr
ib tnkpnrbturb bmn`ubmb.
?. @^NP]HAEB\HA 2) ±Ruè ns ue biuklrn y qun nstru`turb prnsnetbe mh`fbs sustbe`hbs1 Ns ue thpa mn suicbta malin `akpunsta par ni suicbta mn ue kntbi trhvbinetn, `aka ni biukheha, y atra mn ue kntbi kaeavbinetn.
<) Ns`rhlb tambs ibs rnb``haens qun `aemu`ne b ib carkb`hðe mni biuklrn.
Biuklrn mn bkaeha4 + 0 ↜ ( ) + 0 < + ↜ ( ) + < ( ) + ( ) + 2< ↜ ( ) ∟
Biuklrn mn patbsha4 ( ) + + <= ↜ () ∟ 0) Dusthchqun tnðrh`bknetn ias pbsas nxpnrhknetbins Ibs rnb``haens a`urrne mn carkb nspaetâenb ne ue knmha `bihnetn, yb qun nstb ns ib `aemh`hðe pbrb qun sn carkn ueb sbi malin `aka i ns ue biuklrn, ns par nsa qun ibs rnb``haens sn fh`hnrae `ae knmhas `bihnetns. =) Znsa mn ias `rhstbins altnehmas y `âi`uia mni rnemhkhneta. Biuklrn mn patbsha4
Kbsb tnðrh`b4 <.:32 ∟
8=6 ()∟ 2?=
Kbsb altnehmb nxpnrhknetbiknetn4 % ;
; . ( ) ∟
; ?.0?6
% ;
?.0?6 22.<0
∟ 2::%
∟ 2::%
% ; . %
>) @akntn y ns`rhlb ibs rnb``haens `arrnspaemhnetns b ibs prunlbs bebiëth`bs.
Biuklrn mn bkaeha4 ( ) + ( ) + 2< ↜ ( ) ∟ Pn altuva par rnb``hðe ne prhe`hpha mn ias rnb`thvas mn nstb rnb``hðe.
Biuklrn mn Zatbsha4 () + + <= ↜ () ∟ Pn altuva par rnb``hðe mhrn`tb mn ( ) y ne ue knmha b`uasa `bihnetn.
6. LHLIHAO\BCHB
Ouëbs nxpnrhknetbins mn Ruëkh`b Hearoâeh`b ‐ \alnrta Zbrrb Tnlbiias
R^HKH@B ‐ \bykaem @fbeo
fttp4//www.tnxtas`hentach`as.`ak
fttp4//ns.k.whghpmhb.aro
fttp7//www.n`urnm.`u
BENVAP4 Biuklrn mn bkaeha4
Biuklrn mn Zatbsha4
Mnsfhmrbtb`hðe mni biuklrn4