OH_CMCFÓ@ XÆC@FCM F@H_SX\FMJ EM]_F@MS BO\\MEFO@XMS FF
M^_@XOS HO CJMSO XOEM;
CMLO[MJ
HFQ FQFS FSI\ HO JM A\OSMHI\M
?.„ HFQFSFI@ CF\C_JM\ HO JM A\OSMHI\M
?.=.- Hfvfsfi` cfrcujmr.
Sf silro jm arosmhirm so hosom grmhumr u` hfsci, tmjjmr u`m arosm, tmjmhrmr mgukoris oqufhfstm`tos silro u`m suporafcfo có`fcm, i romjfzmr trmlmkis sfefjmros, bm ho utfjfzmrso jm hfvfsfó` cfrcujmr.
^mrm romjfzmr osto tfpi ho trmlmki, jm pfozm bm ho ostmr sieotfhm m u` eivfefo`ti ho gfri pir cmhm hfvfsfó` quo so okocuto. ?.<.- Ostuhfi ho jis hfaoro`tos tfpis ho hfvfsiros cfrcujmros y eihi ho ipormr ci` jis efseis.
Oj mpmrmti i cmlozmj hfvfsir, os u`i ho jis mccosirfis eís fepirtm`tos ho jm arosmhirm, eohfm`to oj cumj so puoho cijicmr jm borrmefo`tm silro jms hfaoro`tos pmrtos ho u`m pfozm, provfmeo`to ojogfhms y hotoref`mhms pir u`m hfeo`sfó` m`gujmr. Ci` arocuo`cfm ostms pmrtos suojo` sor oqufhfstm`tos y silro suporafcfos cfjå`hrfcms i có`fcms (ruohms ho`tmhms, arosms, okos ostrfmhis, otc.). Jis mpmrmtis hfvfsiros utfjfzmhis puoho` o` oso`cfm, rosuefrso o`; m) Mpmrmtis hfvfsiros sfepjos; Ho pjmti ho mgukoris • Ho hfsci rm`urmhi. • l) Mpmrmtis hfvfsiros ho tir`fjji sf`aå` y ciri`m bojfcifhmj; Ho pjmti ho mgukoris (Hfvfsir u`fvorsmj) • Ho o`grm`mkos • Eosm gfrmtirfm i pjmti cfrcujmr hfvfsir. • Xmelfæ` pihråm o`cumhrmrso ho`tri ho osto grupi oj hfvfsir óptfci, pori pir trmtmrso ho u` mpmrmti ho usi pici arocuo`to silro jm arosmhirm, os pir ji quo `i so oxpi`o o` osto toxti.
?.<.=. Mpmrmti hfvfsir sfepjo ho pjmti ho mgukoris. Ci`stm ho u` cuorpi ho au`hfcfó` (?) y ho u` oko prf`cfpmj (7) quo so bmco gfrmr eohfm`to oj lrmzi em`fvojm (=). Silro oj cuorpi vm ei`tmhi afki u` pjmti (8) privfsti ho mgukoris, jis cumjos bm` sfhi eocm`fzmhis oqufhfstm`tos o`tro så y silro cfrcu`aoro`cfms ci`cæ`trfcms. Oj lrmzi (=), eohfm`to u`m rm`urm y jm tuorcm (<), riscmhm silro oj oko prf`cfpmj, puoho sftumr oj postfjji (3) silro cumjqufor cfrcu`aoro`cfm ho mgukoris ho quo ostí privfsti oj pjmti.
Oj oko prf`cfpmj jjovm u` ci`i f`torfir pmrm mjikmr mj pu`ti (=>) y oxtorfireo`to vm oqufpmhi ci` u`m riscm pmrm ei`tmr f`hfstf`tmeo`to oj pjmti ho gmrrms (2) i oj lrmzi ho mrrmstro (6). Eohfm`to oj em`hi W so ljiquom ci` eís sogurfhmh oj oko prf`cfpmj (7) efo`trms so eocm`fzm jm pfozm. Oj cuorpi (?) vm privfsti o` su cmrm ho mpiyi, ho u`m rm`urm ji`gftuhf`mj, hi`ho puoho` mjikmrso jms cbmvotms (==) quo mkustm` o` jm rm`urm co`trmj ho jm eosm, quohm`hi mså mjf`omhi oj mpmrmti cum`hi so hosoo tmj pisfcfó`. Jm pfozm m eocm`fzmr puoho fr ei`tmhm silro pu`tis, silro pjmti-pu`ti i sijmeo`to silro pjmti, o` oj prfeor cmsi oj oko prf`cfpmj hoj mpmrmti y pfozm so u`o` rågfhmeo`to eohfm`to oj lrmzi (6) y oj porri ho mrrmstro (=<). Oj ci`trmpu`ti (=8) os oj mccosirfi hoj mpmrmti hfvfsir hostf`mhi m sorvfr ho mpiyi m jms pfozms cum`hi æstms ji roquform`, su oko O-O puoho sor rogjmhi o` jm citm B puos oj cuorpi co`trmj (=3) so hosjfzm vortfcmjeo`to pir jms rm`urms (=?). Mj fgumj quo oj oko prf`cfpmj hoj cmlozmj hfvfsir, oj oko hoj ci`trmpu`ti puoho tmelfæ` ljiquomrso. Jm emyiråm ho jis hotmjjos trmtmhis o` osto hfvfsir, si` mpjfcmljos m jis rostm`tos mpmrmtis hfvfsiros quo so oxpi`o` o` ostm soccfó`. Jm airem ho ipormr ci` osto mpmrmti os ciei sfguo; So ojfgo u`m cfrcu`aoro`cfm cuyis mgukoris si` eûjtfpjis ho jms hfvfsfi`os m romjfzmr y so hfvfho pir oj `ûeori ho ostms hfvfsfi`os, oj cicfo`to si` jis f`torvmjis o`tro mgukoris, quo
so bm` ho pmsmr silro jm cfrcu`aoro`cfm ojogfhm, pmrm cmhm hfvfsfó` quo so romjfco silro jm pfozm. Sf (D) os oj `ûeori ho mgukoris ho jm cfrcu`aoro`cfm ojogfhm y (@) oj `ûeori ho hfvfsfi`os m romjfzmr, jis f`torvmjis (R) o`tro mgukoris quo so bm` ho pmsmr silro jm cfrcu`aoro`cfm ojogfhm sorí`; R 5
D @
Okoepji; \omjfzmr sofs hfvfsfi`os silro u`m pfozm ei`tmhm o` u` mpmrmti hfvfsir sfepjo, privfsti hoj sfgufo`to pjmti ho mgukoris =? - =1 - =7 - =2 - =6 - <>. So ojfgo jm cfrcu`aoro`cfm ho =2; R 5
D @
5
=2 1
5
3
So pmsmrm` ci` oj å`hfco tros f`torvmjis o` jm cfrcu`aoro`cfm =2. ?.<.<. Mpmrmti hfvfsir sfepjo ho pjmti rm`urmhi. Osto hfvfsir os u`m vmrfm`to hoj m`torfir, silro su oko prf`cfpmj (=) vm ei`tmhi afki u` hfsci (<) privfsti ho o`tmjjms oqufhfstm`tos, silro jms cumjos so mjikm oj postfjji (3) afki mj cuorpi hoj mpmrmti.
Su eihi ho ipormr os fgumj mj f`hfcmhi pmrm oj mpmrmti m`torfir, pori o` voz ho ipormr silro cfrcu`aoro`cfms ho mgukoris, os silro hfscis ci` o`tmjjms, ho jis quo oj mpmrmti pisoo u` kuogi. ?.<.3. Hfvfsir u`fvorsmj ho pjmti ho mgukoris. Su cmrmctoråstfcm oso`cfmj os quo oj oko prf`cfpmj (=), rocflo oj eivfefo`ti m trmvæs ho u` tir`fjji sf`aå` (<) y ho u`m ruohm có`cmvm bojfcifhmj (3) (ciri`m).
Osto mpmrmti ostí airemhi pir his eocm`fseis, u`i mjikmhi o` oj f`torfir ho jm cmrcmsm (8) y ci`stftufhi pir oj o`grm`o sf`aå` ciri`m. Ciei oj oko hoj sf`aå` (<) vm mpiymhi silro cikf`otos oxcæ`trfcis (?), puoho hosci`octmrso ho jm ciri`m (cum`hi so hosoo), sf so gfrm ci`vo`fo`toeo`to jm pmjm`cm (1) quo so afkm eohfm`to oj prfsfi`ori (7) mj sipirto (2). Oj itri eocm`fsei4 ostí f`togrmhi ciei so puoho ilsorvmr, pir jms ruohms cfjå`hrfcms g-b y jms có`fcms e-` (go`ormjeo`to tihms ojjms ci` rojmcfó` ho trm`sefsfó` =;=)4 vm` mjikmhms o` jm cmrcmsm (6) afkm mj sipirto (2) hoj mpmrmti. Oj pjmti ho mgukoris vm ei`tmhi sijfhmrfi silro oj culi hoj pfýó` có`fci (`).
\ocflo oj `ielro ho ci`stm`to hoj hfvfsir jm rojmcfó` ho trm`sefsfó` o`tro oj oko ho jm em`fvojm y oj oko prf`cfpmj hoj mpmrmti, os hocfr, oj `ûeori ho vuojtms quo bmy quo hmr m jm em`fvojm pmrm quo oj oko prf`cfpmj hoj hfvfsir hæ u`m vuojtm ciepjotm. Jm cmrcmsm (8) eohfm`to jis mpiyis (=>) vm ei`tmhm o` oj sipirto (2) silro jis cikf`otoscu`m (==). Jm afgurm, euostrm oj mpmrmti mremhi y o` pisfcfó` f`cjf`mhm puos jm cmrcmsm so puoho gfrmr silro oj oko OO bmstm pi`or mj oko prf`cfpmj (=) o` pisfcfó` vortfcmj.
Ostis mpmrmtis hfvfsiros vm` privfstis ho hfspisftfvis pmrm cirroccfó` ho bijgurms prihucfhms pir hosgmsto, msfefsei vm` oqufpmhis ho cbmvotms o` su lmso y ho aro`i o` oj oko prf`cfpmj. Su ei`tmko silro jm eosm y oj memrro ho pfozms silro oj mpmrmti so romjfzm hoj efsei eihi quo o` oj hfvfsir sfepjo. Jm afgurm euostrm osquoeítfcmeo`to u` hfvfsir o` quo jm cmrcmsm (8), gfrm eohfm`to cijms ho efjm`i silro oj sipirto (2).
?.<.3.=.- Eætihis ho hfvfsfó`. Eætihi sfepjo.- Jms vuojtms y ospmcfis o`tro mgukoris mgukoris (f`torvmjis) quo so bm` ho pmsmr ci` jm em`fvojm silro jm mhocumhm cfrcu`aoro`cfm si`; R 5
D @
Sfo`hi D jm ci`stm`to hoj hfvfsir y @ oj `ûeori ho hfvfsfi`os oqufhfstm`tos m romjfzmr. Bm ho bmcorso `itmr quo oj mpmrmti hfvfsir u`fvorsmj puoho ci`vortfrso o` u` hfvfsir sfepjo ho pjmti rm`urmhi4 pmrm tmj af`, bm ho hosci`octmrso oj sf`aå` ho jm ciri`m bojfcifhmj y ipormr ci` oj postfjji (C) silro oj pjmti rm`urmhi (^) afki mj oko prf`cfpmj hoj mpmrmti, hfcbi pjmti go`ormjeo`to ostí privfsti ho <8 rm`urms. ^jmtis ho mgukoris f`torcmelfmljos eís arocuo`toeo`to usmhis; ^jmti `»=; ^jmti `»<; ^jmti `»3;
=?- =1 - =7 - =2 - =6 - <> <= - <3 - <7 - <6 - 3= - 33 37 - 36 - 8= - 83 - 87 - 86
mgukoris. mgukoris. mgukoris.
M vocos os ci`vo`fo`to romjfzmr romjfzmr jm hfvfsfó` smjtomhm, os hocfr, `i okocutmr jm próxfem rm`urm m ci`tf`umcfó` ho jm quo so mcmlm ho eocm`fzmr, ci` ilkoti ho ovftmr orriros o` jm pfozm eocm`fzmhm pir hfjmtmcfó` ho jm zi`m.
Hfvfsfó` smjtomhm.-
Jm airem ho pricohor os jm sfgufo`to; So oaoctûm oj cíjcuji pricohfo`hi sogû` jm aóreujm f`hfcmhm m`torfireo`to y oj rosujtmhi so eujtfpjfcm pir u` `ûeori o`tori (hfvfsfi`os m smjtmr) quo `i som hfvfsfljo ho jms hfvfsfi`os m romjfzmr.
Okoepji; Ci`stm`to hoj mpmrmti 8>, pjmti hfspi`fljo oj `ûeori =, hfvfsfi`os m romjfzmr <8. \osijucfó`; R 5
D @
5
8> =2
5
= 5=+
=1 <8
So ojfgo oj `ûeori ? quo `i os hfvfsfljo pir jms <8 hfvfsfi`os m romjfzmr. ? ⋏ (= +
=1 2> ) 5?+ <8 8>
5
2+
2 <8
5
2+
= ? 52+ 3 =?
So hmrí` m jm em`fvojm icbi vuojtms o`torms y cf`ci f`torvmjis o` jm cfrcu`aoro`cfm ho =? mgukoris. So rocuorhm quo pmrm soýmjmr jm armccfó` ho vuojtm m hmr m jm em`fvojm, oxfsto u` ciepís ho mjfhmhm (C) ei`tmhi m rizmefo`ti silro jm efsem pfozm quo oj pjmti (^). Jms ruohms có`fcms e y ` si` jms soýmjmhms ci` jms efsems jotrms o` jm aågurm.
Jm pfozm (A) tfo`o pir efsfó` msogurmr oj pjmti ci`trm u` pisfljo hosjfzmefo`ti gfrmtirfi. O` jm afgurm, so ilsorvm oj ciepís ci` jm mhocumhm mlorturm pmrm romjfzmr jm hfvfsfó` hoj m`torfir okoepji. Jms pmtms hoj ciepís puoho` rogujmrso ci`vo`fo`toeo`to, ljiquoí`hiso u`m ci` itrm eohfm`to oj tir`fjji (X).
Eætihi hfaoro`cfmj.-Sf utfjfzm`hi jis pjmtis f`hfcmhis so hosom` romjfzmr 23 hfvfsfi`os, oj
priljoem `i tfo`o sijucfó` pir oj eætihi ho hfvfsfó` sfepjo quo so bm oxpuosti.
Oxfsto` itris pricohfefo`tis ho hfvfsfó` quo mepjåm` jm pisflfjfhmh hoj mpmrmti, u`i ho
ojjis os oj eætihi hfaoro`cfmj. Ci`sfsto osto eætihi o` romjfzmr oj ei`tmko ho jm afgurm.
Sf so sfguo oj so`tfhi ho gfri ho su cmho`m cf`oeítfcm, so ilsorvm quo oj pjmti gfrm sfeujtí`omeo`to ci` oj lrmzi, pmrm ji cumj bm ho rotfrmrso jm pfozm (A) quo so f`hfcó o` jm afgurm. Oj tro` ho o`grm`mkos m l c h, vm ei`tmhi silro u`m jfrm mhocumhm. ^mrm airemr osto tro`, jms ruohms ho quo go`ormjeo`to so hfspi`o si` ho <8, <2, 3<, 8>, 88, 82, ?<, ?1, 18, 7<, 21, 61 y =>> hfo`tos. Sf (@), os oj `ûeori ho hfvfsfi`os m romjfzmr (D) jm ci`stm`to hoj hfvfsir, y ym so pmrto ho quo jm hfvfsfó` os frromjfzmljo pir oj eætihi sfepjo, so ciefo`zm ojfgfo`hi u` `ûeori ho hfvfsfi`os (@') ho airem quo so puohm oepjomr oj roaorfhi eætihi sfepjo4 osto `ûeori puoho sor emyir i eo`ir quo (@). (O` osto cmsi so supi`o @' : @). = , jm em`fvojm tfo`o quo @ D D gfrmr R 5 , pori sf m jm efsem so jo hm u` gfri ho R ¸5 , so bmlrí cieotfhi oj @ @ ¸
^mrm quo oj oko prf`cfpmj oaoctûo oj gfri hosomhi, os hocfr,
sfgufo`to orrir o` oj pripfi gfri ho jm em`fvojm; o5
D @ ¸
∜
D @
Sf cum`hi so euovo jm em`fvojm ci` oj pripósfti ho bmcorjm gfrmr
D @ ¸
pmrm fr m luscmr oj
mgukori (M), so ci`sfguo quo oj pjmti romjfco sfeujtí`omeo`to u` gfri (o) (o` osto cmsi o` so`tfhi ci`trmrfi m jm em`fvojm), oj postfjji i pu`zó` (^), bmlrí o`ci`trmhi oj mgukori M, procfsmeo`to cum`hi jm em`fvojm sóji bmym gfrmhi
D @
, quo os ji quo o` romjfhmh so
hosom4 puos o` tmj cmsi oj oko prf`cfpmj hoj mpmrmti y, pir tm`ti, jm pfozm bmlrí` gfrmhi = . @
Sóji lmstm cmjcujmr oj tro` m, l, c, h, quo trm`sefto oj eivfefo`ti hoj oko prf`cfpmj (=) mj oko (<), quo os procfsmeo`to oj culi hoj pfýó` có`fci ` silro oj cumj vm ei`tmhi sijfhmrfmeo`to oj pjmti, romjfzm`hi æsto oj gfri (o). Jm rojmcfó` ho trm`sefsfó` o`tro ostis his okos os; vuojtms Y ho(=) vuojtms Y ho( <)
= 5
@
o
5
^r ihucti Y hfo`tos Y ci`hucfhms ^r ihucti Y hfo`tos Y ci`huctirms
= @ D D ∜ @ ¸ @
5
@ ¸
5
D ⋏ ( @ ∜ @ ¸)
D ⋏ ( @ ∜ @ ¸) @ ¸
5
m⋏c l ⋏ h
5
l ⋏ h m⋏c
l ⋏ h m⋏c
(F)
@mturmjeo`to, ostm aóreujm sorí mpjfcmljo cum`hi @' : @ quo os oj cmsi supuosti4 mhoeís oj so`tfhi ho ritmcfó` hoj pjmti holoråm sor ci`trmrfi m jm em`fvojm. Sf mj ojogfr oj `ûeori ho hfvfsfi`os, bulfoso icurrfhi quo @' 0 @, sfgufo`hi jis efseis rmzi`mefo`tis so jjogmrjm m jm aóreujm; D ⋏ ( @ ¸∜ @ ) @
5
m⋏c l ⋏ h
(FF)
o` tmj cmsi oj pjmti y lrmzi holo` gfrmr o` oj efsei so`tfhi. Sf mj ei`tmr oj tro` cmjcujmhi rosujtm quo oj gfri hoj pjmti `i tfo`o oj so`tfhi quo so hosom, bmlrí quo f`torcmjmr u`m ruohm f`toreohfm. Oj ciepís ho mjfhmhm (J) quo mlmrcm
D @ ¸
gfrmrí ci` oj pjmti.
O` jms aóreujms m`torfiros so bm ci`sfhormhi quo tm`ti jis o`grm`mkos cfjå`hrfcis g-b ciei jis có`fcis e-`, tfo`o` u`m rojmcfó` ho trm`sefsfó` ho = ; =, ym quo mså os ciei `iremjeo`to so ci`struyo` jis mpmrmtis. Bm ho bmcorso `itmr quo cum`hi so oepjom oj eætihi hfaoro`cfmj `i os pisfljo f`cjf`mr oj
oko hoj hfvfsir. Okoepji =;
O` u` mpmrmti hfvfsir u`fvorsmj cuym ci`stm`to os 8>, so hosom romjfzmr 23 hfvfsfi`os. Cmjcujmr; m) Oj gfri ho em`fvojm pmrm bmcor jm hfvfsf1` (siji so hfspi`o hoj pjmti `ûeori =). l) Oj tro` ho ruohms m cijicmr o` oj hfvfsir. c) Oj so`tfhi ho gfri hoj pjmti.
\osijucfó`; m) So ojfgo @' 5 2>, juogi; R ¸5
D @ ¸
5
8> 2>
5
6 =2
Jm em`fvojm bmlrí quo hfspi`orjm pmrm gfrmr `uovo f`torvmjis o` jm cfrcu`aoro`cfm ho =2. l) Ciei @ 5 23 y @' 5 2>, so tfo`o quo @' : @, juogi bmlrí quo mhiptmr jm aóreujm (F). D ⋏ ( @ ∜ @ ¸) @ ¸
5
m⋏c l ⋏ h
4
8> ⋏ (23 ∜ 2>) 2>
5
7< 82
5
m l
Jm ruohm ho 7< hfo`tos sorí jm ci`huctirm ei`tmhm silro oj oko prf`cfpmj hoj mpmrmti y jm ho 82 hfo`tos sorí jm ci`hucfhm. c) Oj gfri hoj pjmti bm ho sor ci`trmrfi m jm em`fvojm, pir ji quo bm ho f`torcmjmrso u` `ûeori fepmr ho okos f`toreohfis.
Okoepji <.; m) R ¸5
8> 6>
Sijucfi`mr oj okorcfcfi m`torfir cum`hi so ojfgo @'5 6>. 5
2 =2
l)
D ⋏ ( @ ¸∜ @ ) @
5
m⋏c l ⋏ h
4
8> ⋏ (6> ∜ 23) 6>
5
<2> 6>
5
?1 × 3< <8 × <8
5
m ⋏c l ⋏ h
c) Oj gfri hoj pjmti bm ho to`or oj efsei so`tfhi quo jm em`fvojm, sfo`hi `ocosmrfi f`torcmjmr u` `ûeori pmr ho okos f`toreohfis. O` jm afgurm so bm roproso`tmhi oj osquoem hoj tro` y jm vfstm pir jm pmrto pistorfir hoj mpmrmti. Xmelfæ` os mpjfcmljo o` osto eætihi jm hfvfsfó` smjtomhm pori to`fo`hi sfoepro o` cuo`tm ho gufmrso pir oj ciepís ho mjfhmhm. Sf o` oj okoepji m`torfir so hosom romjfzmr jm hfvfsfó`, smjtm`hi sfoto ospmcfis, oj gfri m hmr m jm em`fvojm sorí; 7×
2 =2
5
?1 =2
5
3+
< =2
So ci`tmrí` tros vuojtms tiem`hi sfoepro ciei roaoro`cfm jm prfeor pmtm hoj ciepís, mu`quo æsto so euovm hurm`to oj gfri ho jm em`fvojm4 juogi so pmsmrí` his f`torvmjis o` jm cfrcu`aoro`cfm ho =2, jis cumjos ostmrí` ciepro`hfhis o`tro jms his pmtms hoj ciepís.
o`cuo`trm su kustfafcmcfó` cum`hi `i so Eætihi ciepuosti.- Mj fgumj quo oj hfaoro`cfmj o`cuo`trm
puoho oepjomr oj eætihi sfepjo. ^mrm pihor oepjomr oj eætihi ciepuosti, os `ocosmrfi quo oj hfvfsir hfspi`gm ho u` sogu`hi postfjji afki mj cuorpi hoj mpmrmti y ei`tmhi pir jm itrm cmrm hoj pjmti. Ho ostm airem oj gfri m romjfzmr ci` jm em`fvojm so puoho hosciepi`or o` his gfris, u`i pir cmhm cmrm hoj pjmti. Aícfjeo`to so hohuco quo eohfm`to osto eætihi `i os pisfljo romjfzmr jm hfvfsfó` ho `ûeoris prfeis.
?.<.8. Mpmrmti hfvfsir ho o`grm`mkos. O` jm afgurm, so roproso`tm osquoeítfcmeo`to jm cmho`m cf`oeítfcm ho u`i ho ostis hfvfsiros. Jms hfvfsfi`os so romjfzm` m vuojtm ciepjotm hoj em`ulrfi i lrmzi (8) quo eohfm`to oj tro` ho ruohms m l c h, oj sf`aå` (=) y jm ciri`m (<), cieu`fcm` oj eivfefo`ti mj mj oko prf`cfpmj (FFF). Silro oj cmsqufjji (F) quo os procfsmeo`to oj oko ci`huctir, vm` ei`tmhis oj em`ulrfi (8) y jm ruohm (m). Oj oko (FF) gfrm silro cmsqufjjis afkis mj sipirto (3).
Jjmem`hi (@) oj `ûeori ho hfvfsfi`os m romjfzmr, (B) mj `ûeori ho hfo`tos ho jm ciri`m y (S) mj `ûeori ho o`trmhms hoj sf`aå`, jm rojmcfó` ho trm`sefsfó` hosho oj oko ci`huctir (F) mj ci`hucfhi (FFF) sorí; vuojtms Y ho( F ) vuojtms Y ho( FFF )
5
^r ihucti Y hfo`tos Y ruohms Y ci`hucfhms ^r ihucti Y hfo`tos Y ruohms Y ci`huctirms
Sustftuyo`hi vmjiros; B D m ⋏ c = l ⋏ h ⋏ B pori ciei 5 D (ci`stm`to hoj mpmrmti) so tfo`o quo 5 5 = S @ l ⋏ h m ⋏ c ⋏ S @
Osto mpmrmti hfspi`o ho u`m jfrm jfr m mhocumhm pmrm ei`tmr oj tro` ho o`grm`mkos. Okoepji; Cmjcujmr oj tro` m ei`tmr o` u` hfvfsir ho o`grm`mkos pmrm pmrm romjfzmr 13 hfvfsfi`os, sfo`hi jm ci`stm`to hoj mpmrmti 8>. So hfspi`o ho jms ruohms hmhms pmrm oj sfstoem hfaoro`cfmj. D @
5
m⋏c l ⋏ h
4
8> 13
5
8> × 3< <2 × 7<
?.<.? Eosm gfrmtirfm i pjmti cfrcujmr hfvfsir. So trmtm, o` oso`cfm, ho u` mpmrmti hfvfsir ho tir`fjji sf` af` y ciri`m bojfcifhmj, pori æstm tfo`o su oko o` pisfcfó` vortfcmj. Silro hfcbi oko vm ei`tmhm u`m eosm rm`urmhm (<) hi`ho so afkm jm eirhmzm i hfroctmeo`to jms pfozms m eocm`fzmr, pir osto eitfvi jm eosm gfrmtirfm so utfjfzm pmrm ipormcfi`os ho ci`tir`omhi y ipormcfi`os ho hfvfsfó` o` pfozms quo pir su airem y tmemýi `i puoho` sor ei`tmhms silro jis hfvfsiros oxpjfcmhis. O` su pmrto co`trmj jjovm u` mjikmefo`ti cfrcujmr (3) ci` oj af` ho sorvfr ho roaoro`cfm m jms pfozms quo so bm` ho ei`tmr silro jm efsem.
\oaoro`to m jm airem ho ipormr, so sogufrí` jms efsems `irems hmhms pmrm jis hfvfsiros u`fvorsmjos, puosti quo su ci`stftucfó` au`hmeo`tmj os fgumj4 tmelfæ` jjovm o` oj oko hoj em`ulrfi oj pjmti ho mgukoris (8), pmrm romjfzmr jms armccfi`os ho vuojtm (mjgu`is eihojis jjovm` tmelir grmhumhi privfsti ho `i`fus) y u` em`hi (?) pmrm ljiquomr jm eosm hospuæs ho cmhm gfri. Jm ci`stm`to ho ostis pjmtis hfvfsiros suojo` sor 1>, 6> y =<>. @i os mpjfcmljo o` ostms eosms jm hfvfsfó` hfaoro`cfmj. M vocos oj gfri quo so hosom ilto`or o` jm pfozm ei`tmhm silro u` hfvfsir u`fvorsmj i eosm cfrcujmr, ostí oxprosmhi o` u`fhmhos m`gujmros, o` tmj cmsi hfcbm oxprosfó` bmy quo trm`sairemrjm o` armccfó` ho vuojtm. Okoepji j; Silro u`m eosm eosm cfrcujmr so hosom hosom eocm`fzmr o` jm pfozm ho jm afgurm, afgurm, jm cmrm M M quo bm ho airemr ci` oj oko ho jm pfozm u` í`guji ν 5 =?¾ =<'. ¹Cóei so bm ho pricohor smlfo`hi quo jm ci`stm`to ho jm eosm os 6>9 \osijucfó`; Oj í`guji quo so bm ho bmcor gfrmr oj pjmti os procfsmeo`to ν. Sf oj trmlmki `i auoso ho eucbm procfsfó`, so puoho romjfzmr hfcbi gfri, muxfjfí`hiso ho jm grmhumcfó` (=). ^mrm romjfzmr eís oxmctmeo`to oj gfri so pricohorí hoj sfgufo`to eihi.
@ûeori ho vocos quo oj í`guji ν ostí ci`to`fhi o` u` gfri ciepjoti ho jm eosm, os hocfr, `ûeori ho hfvfsfi`os m romjfzmr. @ 5
31> × 1> <=.1>> 5 =? × 1> + =<= 6=<
Gfri m hmr m jm em`fvojm; R 5
D @
5
6> <=.1>> 6=<
5
6> × <=< <=.1>>
5
6=< <8>
5
?7 =?
5
3+
=< =?
So hmrí mj em`ulrfi 3 vuojtms ciepjotms y juogi =< f`torvmjis o` jm cfrcu`aoro`cfm ho F? mgukoris cirrospi`hfo`tos mj pjmti `ûeori =. @i sfoepro oj priljoem tfo`o sijucf1` oxmctm, m ci`tf`ucf1` so proso`tm u` okoepji o` oj cumj so bm cmjcujmhi oj orrir ho ostm f`oxmctftuh. Okoepji <; So hosom romjfzmr o` u` oko his rm`urms ji`gftuhf`mjos quo aireo` o`tro sf u` í`guji ho <1¾ ==' ½ 7'. Hfcbi oko oko ostí ei`tmhi silro u` hfvfsir u`fvorsmj ho D 5 8>, hfspi`fo`hi sijmeo`to hoj pjmti `ûeori =. Jm airem ho pricohor os jm sfgufo`to; <1¾ ==' 5 =?7j' R 5
D @
5
8> <=.1>> =?7=
5
=?7= ?8>
Ciei ostm armccfó` `i os sfepjfafcmljo y ciei tmepici oxfsto jm cfrcu`aoro`cfm ho ?8> mgukoris, so cmjcujm` jms rohucfhms hfroctms ho hfcbm armccfó`.
Ilto`cfó` ho jms rohucfhms ho u`m armccfó`.- Oj eætihi príctfci pmrm ilto`or jms rohucfhms ho u`m armccfó` (so tiem ciei okoepji oj cmsi m`torfir
=?7= ) os oj sfgufo`to; ?8>
So hotoref`m` jis cicfo`tos pir oj eætihi ho jms hfvfsfi`os sucosfvms (cóei pmrm bmjjmr oj e.c.h.). < ?8> >86
=.?7= 86=
= 86= >>=
=> 86 >>
86 =
Jm prfeorm rohucfhm so iltfo`o hfvfhfo`hi oj prfeor cicfo`to pir jm u`fhmh; \=
5
< =
Jm sogu`hm rohucfhm so iltfo`o mýmhfo`hi mj prfeor cicfo`to u`m armccfó` quo tfo`o pir `ueormhir jm u`fhmh y pir ho`ief`mhir oj sogu`hi cicfo`to. \<
5
<+
= 3 5 = =
Jms sfgufo`tos rohucfhms so iltfo`o` eujtfpjfcm`hi oj cicfo`to cirrospi`hfo`to, pir cmhm u`i ho jis tæref`is ho jm armccfó` m`torfir y suem`hi tæref`i m tæref`i jm armccfó` m`toprocoho`to. \3
5
=> × 3 + < => × = + =
\8
5
86 × 3< + 3 =?7= 5 86 × == + = ?8>
5
3< ==
Jm ûjtfem armccfó` ilto`fhm bm ho sor fgumj m jm armccfó` irfgf`mj rohucfhm m su eís sfepjo oxprosfó`, ji quo sfrvo ho cieprilmcfó`. Irho`m`hi jms m`torfiros armccfi`os; < =
3 =
3< ==
=.?7= ?8>
so ilsorvm quo jm armccfó` ho irho` fepmr tfo`o u` vmjir eo`ir quo jm oxmctm, efo`trms quo jm ho irho` pmr tfo`o u` vmjir emyir, ci` jm pmrtfcujmrfhmh ho quo oj orrir os tm`ti eo`ir cum`hi eís corcm so ojfkm jm rohucfhm ho jm armccfó` irfgf`mj, os hocfr4 ho jm ûjtfem rohucfhm; Mj f`to`tmr ojogfr u`m rohucfhm rohucf hm pmrm ci` jm efsem pihor romjfzmr oj gfri gf ri o` oj pjmti `» = y quo, msfefsei, ostæ ji eís corcm pisfljo m jm armccfó` irfgf`mj, rosujtm sor jm sogu`hm
rohucfhm; \<
5
3 53 =
os hocfr, quo bmlrí quo hmr tros vuojtms ciepjotms m jm em`fvojm hoj hfvfsir. Oj orrir cieotfhi sogû` so bm pricohfhi sorí; R ¸5
D @ ¸
5
8> <=.1>> E ¸
3 =
5
E¸5 =.1<>¸
orrir 5 =.1<> - =.?7= 5 86 ' (pir oxcosi) @i os pisfljo ojogfr ostm rohucfhm (\ < pir cum`ti quo oj orrir os emyir quo oj mheftfhi. ^mrm smjvmr osto f`ci`vo`fo`to, so rocurro m jms rohucfhms f`torcmjmros. \ohucfhms f`torcmjmros.- Sf jms rohucfhms hfroctms `i smtfsamco` oj priljoem, so puoho` cmjcujmr u`ms armccfi`os quo so ho`ief`m` f`torcmjmros, cielf`m`hi jms hfroctms o`tro sf. Si` vmrfis jis pricohfefo`tis quo so puoho` oepjomr pmrm jm ilto`cfó` ho jms roaorfhms f`torcmjmros. _`i euy príctfci os oj sfgufo`to; Sf so hosom f`torcmjmr o`tro jms rohucfhms \ = y \ <, so eujtfpjfcm` jis his tæref`is ho jm rohucfhm \ <, pir u` efsei `ûeori (so puoho sogufr jm sorfo `mturmj ho jis `ûeoris) y so jo suem tæref`i m tæref`i jm rohucfhm m`torfir \ =. Ciei ym so bm hfcbi, o` jms rohucfhms hoj okoepji m`torfir, so vo quo rospocti m jm armccfó` irfgf`mj ho jm sogu`hm
=.?7= < , oj orrir ho jm prfeorm (fepmr) os pir hoaocti, efo`trms quo oj ?8> =
3 (pmr) os pir oxcosi4 o`tro æstms so puoho` f`torcmjmr f`af`ftms armccfi`os =
y, `mturmjeo`to, jms bmlrí ho vmjir euy mprixfemhi m jm irfgf`mj. Cíjcuji ho mjgu`ms rohucfhms f`torcmjmros o`tro jm sogu`hm
< 3 y , eujtfpjfcm`hi jis his tæref`is ho = =
3 pir jm sorfo `mturmj ho jis `ûeoris y sueí`hijo tæref`i m tæref`i jm =
< ; = 2 == 3 8
prfeorm ? <
=8 ?
=7 1
<> 7
<3 2
<1 6
<6 ……… =>
Ho ostms armccfi`os f`torcmjmros cmjcujmhms, si` vmrfms jms quo hm` sijucfó` mj priljoem, pori so ojfgo jm
<6 =>
pir sor ci` jm quo eo`is orrir so cieoto;
<6 =>
5
?2 <>
5
<+
=2 <>
So hmrí` his vuojtms ciepjotms y =2 f`torvmjis o` jm cfrcu`aoro`cfm ho <>. Oj orrir sorí; R ¸5
D @ ¸
5
8> <=.1>> E ¸
5
<6 =>
E¸ 5 =.?11¸
Orrir5 =.?7= – =.?11 5 ?¸ Ostí ho`tri ho jm tijorm`cfm mheftfhm. Mjgu`ms vocos, cum`hi o` u` hfvfsir so bm ho romjfzmr u` gfri o` oj cumj so hotoref`o jm tijorm`cfm hoj efsei, suojo sfepjfafcmrso oj cíjcuji sf so sustftuyo ho m`toem`i oj vmjir `ief`mj pir itri vmjir ojogfhi ci`vo`fo`toeo`to y quo ostæ ho`tri ho jm tijorm`cfm mheftfhm. Bm ho bmcorso `itmr quo ostis eætihis mprixfemhis `i si` mpjfcmljos, pir okoepji, o` jm hfvfsfó` ho jis hfo`tos ho u` o`grm`mko, pir cum`ti quo oj orrir so mcueujmrjm o` jm ûjtfem hfvfsfó` quohm`hi hoaoctuisi oj ûjtfei hfo`to. ?. <.1. ^jmti cfrcujmr hfvfsir oqufpmhi ci` tmelir grmhumhi y `i`fus. Ciei ym so f`hfcó, mjgu`is pjmtis hfvfsiros ostí` oqufpmhis ci` tmelir grmhumhi, o` voz ho ci` pjmti ho mgukoris, eohfm`to u` okoepji so oxpi`o oj eætihi go`ormj ho ipormr o` tmj cmsi. @mturmjeo`to, osto eætihi os mpjfcmljo m tihi eocm`fsei quo ostæ fgumjeo`to ci`stftufhi, ciei icurro o` jm irfo`tmcfó` hoj oko prf`cfpmj, o` jm emyiråm ho jms arosmhirms vortfcmjos. Bm ho bmcorso `itmr quo oj oepjoi hoj tmelir grmhumhi o` jis hfvfsiros sóji os mpripfmhi pmrm romjfzmr u` hotoref`mhi gfri oxprosmhi o` u`fhmhos m`gujmros, puos rosujtm o`girrisi y ho procfsfó` rojmtfvm pmrm gfris quo oxfkm` grm` rogujmrfhmh, os hocfr, quo bmym` ho sor ji eís pisfljoeo`to fgumjos o`tro sf, ciei icurro o` oj tmjjmhi ho u`m ruohm ho`tmhm4 mhoeís `i sfoepro so ci`sfguo` sijucfi`os oxmctms. Okoepji.-_` pjmti cfrcujmr hfvfsir tfo`o u`m ci`stm`to ho 6>, su tmelir ostí grmhumhi o` 82 hfvfsfi`os y oj `i`fus tfo`o cf`ci hfvfsfi`os (e' 5 ?) quo cif`cfho` ci` cumtri hoj tmelir (e'-=58). Cmjcujmr; m) Oj gfri (B) hoj pjmti pir cmhm vuojtm ciepjotm hoj tmelir4
l) Oj gfri (G) hoj pjmti pir cmhm hfvfsfó` hoj tmelir4 c) Oj grmhi ho mprixfemcfó` (g) muxfjfí`hiso hoj `i`fus4 h) Oj `ûeori ho vuojtms o`torms y hfvfsfi`os quo so bm ho gfrmr oj tmelir grmhumhi, mså ciei oj `ûeori ho hfvfsfó` o` oj `i`fus, quo so bm ho bmcor cif`cfhfr pmrm romjfzmr u` gfri ho =8¾ =7'. \osijucfó`; m) Ciei so smlo, jm rojmcfó` ho trm`sefsfó` o`tro oj vijm`to i em`fvojm hoj tmelir grmhumhi y oj oko ho jm ciri`m bojfcifhmj os f 5
D
=
.
Sf mj vijm`to so jo bmco gfrmr u`m
vuojtm, oj gfri hoj pjmti oxprosmhi o` armccfó` ho vuojtm. sorí; D
=
5
= B
B 5
= D
y oxprosmhi o` u`fhmhos m`gujmros (grmhis); B 5
= 31> × 31> 5 D D
l) 8¾ 5 <8>'
Sustftuyo`hi B 5
G
5
31> 6>
5
8»
<8>¸ 5 ?¸ 82
c) Sf oj `i`fus ostí privfsti ho e' hfvfsfi`os quo cif`cfho` ci` e' - = hfvfsfi`os hoj tmelir grmhumhi, oj grmhi ho mprixfemcfó` os; g
5
G
g
e¸
5
?¸ 5 =¸ ?
h) Cíjcuji ho jms vuojtms hoj tmelir. =8»=7¸ =8»=7¸ 5 5 3 vuojtms y u` rosti ho <¾ =7' 8» B
Cíjcuji ho jms hfvfsfi`os hoj tmelir <»=7¸5=37¸ 4
=37 G
5
=37¸ 5 <7 hfvfsfi`os y u` rosti ho <' ?
Cíjcuji ho jms hfvfsfi`os hoj `i`fus, <¸ < 5 g =
5
< hfvfsfi`os
