XJOTHQUOMIM WÜA@OEI MH H@ I@]F ÉQHI< OJKHJOHQÎI EIQQHQI< OJKHJOHQÎI H@HE]QOEI
@IAFQI]FQOF J·5 H@ HU]IMF KIUHFUF
I@XNJF<
QFAHQ NIQEOI@ IWI\I EIXJI KQXWF< F
MFEHJ]H< OJK. CXIJEI ECFYXH HM[OJ QXAHJ
@i Wiz ― Af`ovoi 1719
9. FALH]OTFU 9.9. FALH]OTF KHJHQI@ Hstumoir h` efnpfrtinohjtf mh `fs kishs omhi`hs cieohjmf usf mh nithroi`hs y rhietovfs mh `iafritfrof. 9.1. FALH]OTFU HUWHEODOEFU • Qhi`ozir nhmoeofjhs nhmoeofjhs mh i`turis nijfnïtroeis • Mhthrnojir `i hquovi`hjeoi mh prhsofjhs nijfnïtroeis • Xto`ozir ojstrunhjtfs piri rhi`ozir nhmoeofjhs mh prhsoõj, vf`unhj y thnphrituri. • Efnprfair `is `hyhs hnpîroeis • Fathjhr uj kis cünhmf
1.- DXJMINHJ]F ]HÕQOEF @fs trhs hstimfs hstimfs mh `i nithroi, tohj tohjhj hj `i prfpoh prfpohmim mim mh quh puhmhj feupir tfmf tfmfss `fs hspieofs mfjmh hstuvohri efjdojimf i uji mhthrnojimi prhsoõj y thnphrituri. Hstis trhs viroia`hs phrnothj hstumoir i hsth hstimf lujtf efj `i nithroi kishfsi. ]fmis `is `hyhs hnpîroeis rhsu`tirfj mh uj hstumof hxphronhjti` nijthjohjmf uji viroi vir oia` a`h h ef efjst jstij ijth th y ci cieo eohj hjmf mf vir viroi oirr ftri ftri vi viro roia ia`h `h.. I` I`ku kuji ji hs hsti hstiss `h `hyh yhss hnphroeis sfj `is sokuohjths<
1.9 @H_ MH AF_@H @hy mh Afy`h ojmoei quh i jünhrf mh nf`hs efjstijth y thnphrituri efjstijth ‐`i prhs prhsoõ oõj j ia iasf sf`u `uti ti mh uj kis kis virî virîi i ojvh ojvhrs rsin inhj hjth th pr prfp fpfr freo eofj fji` i` i` vf`u vf`unh nhj j „.Nithnétoeinhjth pumh hxprhsirnh nhmoijth `i sokuohjth heuieoõj< W ι 9/T
Wiri mfs efjmoeofjhs modhrhjths sh puhmh idornir quh< W 7T 7 > W 9T 9
1.1 @H_ MH ECIQ@HU @hy mh Ecir`hs ojmoei quh i jünhrf mh nf`hs efjstijth y prhsoõj efjstijth, ‐h` vf`unhj mh uj kis virîi hj dfrni morhetinhjth prfpfreofji` i `i thnphriturh iasf`uti„. Nithnétoeinhjth sh puhmh hxprhsir nhmoijth `i sokuohjth heuieoõj< T ι ]
Wiri mfs efjmoeofjhs modhrhjths sh puhmh idornir quh< 9/] 9 T 7 /] 7 > T 9/
1.5 @H_ MH KI_-@XUUIE
@hy mh Kiy-@ussie ojmoei quh i jünhrf mh nf`hs efjstijth y vf`unhj efjstijth, ‐`i prhsoõj mh uj kis virîi hj dfrni morhetinhjth prfpfreofji` i `i thnphrituri iasf`uti„. Nithnétoeinhjth sh puhmh hxprhsir nhmoijth `i sokuohjth heuieoõj< W ι ]
Wiri mfs efjmoeofjhs modhrhjths sh puhmh idornir quh< W 7 /] 7 > W 9/ 9/] 9
Efnf sh vhré hs jhehsirof rhi`oz rhi`ozir ir nhmoeofjhs mh T,W,] y mh `is `heturis quh sh fathjkij mhahj rhi`ozirsh uj ijé`osos mh` efnpfrtinohjtf mh moecis viroia`hs.
1.= @H_ EFNAOJIMI MH @FU KIUHU @i `hy khjhri`ozimi f `hy efnaojimi mh `fs kishs sh ``ini isî pfrquh efnaoji `is `hyhs mh Afy`h, Ecir`hs y Kiy-@ussie hj uji üjoei heuieoõj. Hsti `hy hstia`heh `i rh`ieoõj hjtrh thnphrituri, prhsoõj y vf`unhj mh uj kis. W 9∛T 9 W 1∛T 1 1 > ] 9 ] 1 1
1.8. HYXOTI@HJEOI MH WQHUOFJHU NIJFNÏ]QOEIU Wiri eimi nhmomi mhthrnojir `i prhsoõj nijfnïtroei mh ikui y mh iehoth hj ujomimhs mh` Uosthni Ojthrjieofji` y mh ieuhrmf i `i sokuohjth heuieoõj. W > C k ω 1.4. WQHUOÕJ NIJFNÏ]QOEI Uh ``ini prhsoõj nijfnïtroei f prhsoõj rh`itovi i `i modhrhjeoi hjtrh `i prhsoõj iasf`uti f rhi` y `i prhsoõj itnfsdïroei. Uh ip`oei tij sf`f hj iquh``fs eisfs hj `fs quh `i prhsoõj hs suphrofr i `i prhsoõj itnfsdïroei2 euijmf hsti eijtomim hs jhkitovi sh ``ini prhsoõj mh vieîf.
5. MHUIQQF@@F _ IJÉ@OUOU 5.9. HYXOTI@HJEOI MH WQHUOFJHU NIJFNÏ]QOEIU
Xjor mfs (f trhs) nijõnhtrfs mh modhrhjth `îquomf nijfnïtroef nhmoijth uji ujoõj ‐]„ efnf sh nuhstri hj `i Dokuri - 9<
Hj h` hxtr hxtrhn hnf f iaoh iaohrt rtf f i `i itnf itnfsd sdhr hri i mh `i uj ujoõ oõj j ‐] ‐]„„ ef`f ef`fei eirr uj uji i lhro lhrojk jki, i, ishkurirsh quh mhspuïs mh ef`feir `i lhrojki hxosti uj hquo`oarof mh prhsofjhs hj `fs arizfs mh eimi nijõnhtrf. Hlhrehr uji phquhùi prhsoõj hj h` ïnaf`f mh `i lhrojki mh nijhri hxosti uji modhrhjeoi modhrh jeoi mh i`turi nijfnïtroei mh ikui mh y fashrvir `i i`turi nijfn nijfnïtroei ïtroei hj h` arizf mh` ftrf nijõnhtrf (iehoth), rhkostrir `is i`turis nijfnïtroeis hj `i ]ia`i9 y rhphtor h` nosnf prfehmonohjtf piri 97 mitfs.
Jª I`turi ikuiRn n^ I`turi iehothR nn^
9 9ee 55nn
1 1ee 47n n 1ee 41n n
5 = 8 4 ; 3 5ee =ee 8ee 8,8ee 4ee 4,8ee ;8nn 978nn 9=1n 947n 9;8n 938nn n n n 9ee 5ee =ee 8ee 8,8ee 4ee 4,8ee 1;nn ?7nn 991nn 987n 947n 9;8n 933nn n n n ]ia`i 9 Efj `fs mitfs mh `i tia`i 9, efnpirir inafs vi`frhs y piri eimi nhmomi< Wiri h` ikui< ck*Cck>x*Cx
Cck>x*Cx/ ck Cck>9*958,;nnC1F/ 95,4 >?,?;3 nnCk
W> kc> 95,4*?,;;8* ?,?;3 nnCk >9514.=; nnCk
? ;ee 178n n ;ee 171n n
9977 ;,8ee 19;n ;,8ee 19;n
Wiri h` iehoth<
ck*Cck>x*Cx
Cck>x*Cx/ ck Cck>7,?*953,5nnC1F/ 95,4 >?,981 nnCk
W> kc> 95,4*?,;;8* ?,981 nnCk >9194.44 nnCk
5.1. @H_ MH AF_@H Wronhrinhjth, irnir h` hquopf ti` efnf nuhstri `i Dok ― 1, ujohjmf `i lhrojki i uj arizf mh` nijõnhtrf (h` nijõnhtrf puhmh shr efj mh ikui f mh iehoth). @fkrir quh jf hxosti modhrhjeoi mh i`turi hjtrh `fs arizfs mh` nijõnhtrf (vhrodoeir quh jf hxostij dukis mh iorh hjtrh h` tuaf hj ‐X„ y `i lhrojki). Hlhrehr uji phquhùi prhsoõj hj h` hnaf`f mh `i lhrojki piri `fkrir uji modhrhjeoi mh i`turi nijfnïtroei (Dok ― 1), sh sukohrh quh `i i`turi C7 shi mh 97 nn i 17 nn. - Qhphto Qhphtorr h` ijthro ijthrofr fr prfehmo prfehmonohjt nohjtf f (iprfxonimin (iprfxoniminhjth hjth piri 3 mitfs), iunhjt iunhjtijmf ijmf uji prhsoõj i` ïnaf`f mh `i lhrojki y rhkostrir `i thnphrituri inaohjth, `i i`turi C7, C9, h` moénhtrf ojthrjf mh` tuaf hj ‐X„ y h` vf`unhj mh iorh hj `i lhrojki. (]ia`i 1)
Dokuri 1 Wiri eimi mitf, mhthrnojir `i Eth mh Afy`h nhmoijth BA > WoTo Ci``ir h` vi`fr prfnhmof mh BA
@fs eé`eu`fs sh `f rhi`ozirfj hj Hxeh`
]ia`i 1
Kridoei mh W vs 9/T <
5.5. @H_ EFNAOJIMI Irnir h` hquopf ti` efnf nuhstri `i Dok ― 5, ujohjmf `i lhrojki i uj arizf mh` nijõnhtrf (h` nijõnhtrf puhmh shr efj mh ikui f mh iehoth) y hjehjmhr `i cfrjo cf rjo````i i h` h`ïe ïetr troe oei i so soj j ei eina naoi oirr h` vf vf`u `unh nhj j mh mhjt jtrf rf mh `i lh lhro rojk jki i y rhk rhkos ostr trir ir `i thnphrituri. C7, C9, ] eimi vhz quh hxosti iunhjtf mh thnphrituri mhaomf i` ei`hjtinohjtf mh` ikui mhjtrf mh` visf mh prheopotimfs y ``hjir `i ]ia`i 5 efj hsfs mitfs fathjomfs.
Dokuri 5 Wiri eimi nhmomi< Ei`eu`ir h` vf`unhj mh` kis efjdojimf tijtf hj h` tuaf eo`îjmroef y hj `i lhrojki Efj `fs mitfs sieimfs mh` `iafritfrof ei`eu`infs `i efjstijth B piri eimi nhmomi
Jrf
9
1
5
=
8
4
;
3
CfRn nC1F ^ CfRn nCk^ C9Rn n^C1 F C9Rn n^Ck
3
17
1=
54
81
4=
;3 ;3
?4
7.833
9.=;
9.;4
1.4=;
5.31
=.;
8.;5
;,783
83=
8?7
8?1
8?3
474
491 49=
=1,?= 99;4 8
=5,5315 =5,81?= =5,?;78 ==,8833 =8 158 331 993 81?
87 515
88 513
47 555
48 553
=?4,=;
=?4,;4
=?;,4=; =?3,31
]R·E^ ]R·B^
WkisR =?8,8 nnCk 33 ^
;7 5=5
]ia`i 5 Tkis1> 17nn C1F M>?nn Wiri eimi mitf mh W,T,] ei`eu`ir `i rh`ieoõj mh< B> Wo]∛oTo
Wrfnhm of
413
=8,9=;7 =4,9;4= ;74 833
;8 37 5=3 585
38 583
=?? 877,;5 ,;
871,783 =?3,=;9
5=7,8
Ei`eu`ir `i prhsoõj mh` kis WKIU > Witn+ Wnij (hj nnCk ) Witn> =?8nnCk
Wiri eimi nhmomi< Ei`eu`ir h` vf`unhj mh` kis efjdojimf tijtf hj h` tuaf eo`îjmroef y hj `i lhrojki TKIU >Teo`ojmrf +Tf`unhj mh` kis hj `i lhrojki Tkis> χ r 1* C 9 + Tkis1
Ei`eu`f mh` vf`unhj mh` kis hj n` y prfnhmof mh Tf`unhj > 99,=9 n`
Wfr `f tijtf tijtf h` vi`fr mh B > (5=7,8)*(=?3,=;)/(99,=9)> 97?,;4
=. EXHU]OFJIQOF i) Hjujeoir h` Wrojeopof mh Wisei` @i prhsoõj hlhreomi hj eui`quohr `ukir mh uj d`uomf hjehrrimf hs ojefnprhsoa`h ojefnprhsoa`h sh trijsnoth pfr okui` hj tfmis `is morheeofjhs hj tfmf h` d`uomf, `i prhsoõj hj tfmf h` d`uomf hs efjstijth.
a) Ojvhstokir `i i`turi mh Eoumim Uitï`oth y su prhsoõj itnfsdïroei Witn Eoumim Uitï`oth> =?8nnCk.
e) Mh quï mhphjmh `i prhsoõj mh vipfr mh uji sustijeoi @i prhsoõj mh vipfr mh uji sustijeoi mhphjmh mh `i thnphrituri.
m) Uo ]fr ]frroeh roeh``o ``o cua cuaohr ohri i rhi rhi`oz `ozimf imf su hxphron hxphronhjt hjtf f pir piri i mht mhthrno hrnojir jir `i prh prhsoõ soõj j itnfsdïroei ¶Eué` shrîi su vi`fr hj pohs mh uj iehoth euyi mhjsomim rh`itovi hs 7,336 C ck∛¶c ck> C iehoth* c iehoth C iehoth> 9]frr*95.4Rk/n`^ / 7.33Rk/n`^ >98.=8 ]frr mh iehroth
h) Ojvhstokir Yuï hs Airõnhtrf ijhrfomh y eué` hs su uto`omim
H` airõnhtrf ijhrfomh hs uj airõnhtrf prheosf y préetoef mfjmh `i prhsoõj itnfsdïroei mhdfrni `i pirhm h`éstoei mh uj eo`ojmrf hj h` quh sh ci checf uj vieîf pireoi`, `f quh i su vhz nuhvh uji ikuli.
d) Xj kis pfshh uji prhsoõj mh 91 itnõsdhris, `uhkf mh uj prfehsf osftïrnoef sh efnpronh cisti uj nhmof mh su vf`unhj ojoeoi`. Uiaohjmf quh `i modhrhjeoi mh prhsofjhs hjtrh h` vi`fr doji` y h` ojoeoi` hs 91 itn. Mhthrnojir `i prhsoõj ojoeoi` mh` kis. Wf*T f > Wd *T d (9) Efjmoeoõj T d > T 7/1 y
Wd - W7>91itn (1)
(1) hj (9) 1 W7> Wd >: 1 W7- W7>91itn >: W7>91itn y Wd >1=itn
c) Euirtf `otrf mh uj kis mhsefjfeomf hs rhefkomf sfarh iehtfji i mohz krimfs Eh`sous ailf ehrf y ;;7 nn Ck mh prhsoõj. H` kis tohjh uji nisi mh 9,5= k y `i prhs prhsoõ oõj j mh vipf vipfrr mh `i ieht iehtfj fji i i `i thnp thnphr hrit itur uri i ojmo ojmoei eimi mi hs 5? nn Ck. Ck. Mhthrnojir h` phsf nf`heu`ir mh` kis mhsefjfeomf. Q]n 41,=∛135∛9,5= > 59,7? Rk/nf`^ > ( ;77∑5? )∛9 WT
N>
efnpfsoeoõj vf`unïtr vf`unïtroei oei mh` iorh hs 19% mh fxîkhjf2 ;3 % mh jotrõkhj jotrõkhjf fy 9 o) @i efnpfsoeoõj % mh irkõj. Mhthrnojir `i prhsoõj mh eimi kis hj Eoumim Uitï`oth (Érhi mh Ojkhjohrîi ― XWHI) Wit> =?8nnck Wiorh> nnck Wiorh> 7.19*=?8nnck 7.;3*=?8nnck > > 975.?8 534.9 nnck Wiorh> 7.79*=?8nnck > =.?8 nnck nnck
l) Xji visoli iaohrti hj Eoumim Uitï`oth mfjmh `i thnphrituri hs mh 3 ¼E, sh ei`ohjti i prhsoõj efjstijth cisti 517 ¼E. Mhthrnojir `i drieeoõj mh nisi mh iorh ojoeoi`nhjth efjthjomf hj `i visoli quh hs hxpu`simf. ]d> 8?5ªB T>eth y W >eth W 9∛T 9∛ N Wd ∛Td ∛ N > hjtfjehs ] 9 n 9 ]dnd
Q>
n1*]1>n9*]9 >: n1*8?5>139*n9 >: n9> 1,99n1
%n9>
1,99 n 1 n9 > *977%> 4;,3=% n 9 + n 1 1,99 n 1 + n 1
8. EFJE@XUOFJHU _ QHEFNHJMIEOFJHU Uh rhefnohjmi `hhr `i kuîi mh `iafritfrof ijths mh hnphzir i rhi`ozir`f piri jf thjhr ojefjvhjohjths. Hj eimi mitf tfnimf piri eimi nhmomi phmomi sh mhah mh ciehr `i niyfr eijtomim mh nhmomis isî sieir uj prfnhmof mh tfmis `is nhmomis piri thjhr uj mitf eiso hxietf mh` auseimf. Uh rhefnohjmi jftir euomimfsinhjth `fs einaofs mh nhmomis mh` `iafritfrof quh sh prfmuehj mh nijhri nuy répomi piri jf thjhr prfa`hnis hj `fs eé`eu`fs phmomfs. Uh ei`eu`f `i krédoei phmomi hj `i `hy mh Afy`h y jftinfs `i rheti quh sh dfrnõ hj `i krédoei W vs 9/T.
4.- AOA@OFKQIDÎI -Efnf rhsf`vhr prfa`hnis hj quînoei ― Ojk. @hfjirmf K. Efrfjh` Qfmrîkuhz -Dujminhjtf mh quînoei (Qiynfjm Ecijk 1799). - ECIJK, Q. Wrojeopofs Hshjeoi`hs mh Yuînoei Khjhri`, Euirti hmoeoõj, NeKriwCo``. -Wr -Wrojeo ojeop pofs ofs mh Yu Yuîîno noei ei (@ (@fs fs eino einojf jfss mh` mhseu hseuar aron onoh ohjt jtf) f),, Hm Hm.. Nï Nïmo moei ei Wijinhroeiji, Auhjfs Iorhs, 1774. - NIU]HQ]FJ, [
[email protected] CXQ@H_, E.J. Yuînoei -Yuînoei Khjhri` (Lfj N. Ah``ini 9??5) -I`virhz I`drhmf ht i` Wrietoeis mh quînoei khjhri` 177=
