Curso de Pedreiro - Aula 03

Sudèrej CQPSJ MA RAMPAEPJ HQLH 3 LJCHÏÃJ MH J@PH A IQGMHÏÑAS

Egtrjmuïãj Iugmhïãj mh J`rh Aschvhïãj mh J`rh Iugmhïñas Hlecarcas Shphth Cjrremh @hlmrhda Phmear Cegths ma Hdhrrhïãj Hlecarcas ad ]arragjs Egcleghmjs Egcleghmjs Egsthlhïñas Su`tarràgahs Edpardahèlezhïãj Yanh sa Hpragmau Paspjsths mj Yanh sa Hpragmau – Hulh 0

Egstetutj Qgevarshl @rhselaerj Hmdegestrhïãj Luez Iarghgmj Megez Ghsj Njså Chrljs Megez Ghsj Egîs Megez Ghsj Oaragta Oarhl Djmastj Rhgthlåh

Meratjrh Oarhl Eraga Pjmreouas ma Jlevaerh ]aexaerh Peàerj Cjjrmaghïãj Memètech _hlmjderj Paccfe Ijtjorhh

Meraïãj ma Hrta Chrljs Amuhrmj R. Ghsj

Pjàrtj Chrljs Hlvas

Hssestagta Nurämech Phihalh Ghsj

Hutjr _hlmjderj Paccfe

Rrjmuïãj Dhrcjs Rrhmj ma Chrvhlfj

Ametjrhïãj Egstetutj Qgevarshl @rhselaerj

Edhoags Hlaxhgmra Djrsellh

Edprassãj EQ@PH - Egmþstreh Orèch a Ametjrh Ltmh. Pjmjveh Asthmuhl @jetuvh - Eparó, kd 8,8 Chdpjs ma @jetuvh - @jetuvh - SR CAR 86112-222

Pavesãj Pjsale Hghstècej Selvh Dhrceh Djraerh ma Chrvhlfj

]jmjs js meraetjs sãj rasarvhmjs. Gãj å pardetemh h raprjmuïãj tjthl ju phrcehl masta cursj.

HQLH 3 LJCHÏÃJ MH J@PH A IQGMHÏÑAS

H ljchïãj mava sar iaeth palj cagtrj (aexj) mjs aladagtjs qua sarãj trhgspjrthmjs phrh j tarragj a, pjstarejrdagta pjstarejrdagta,, palhs legfhs mhs ihcas mhs phramas a mj hlegfhdagtj phrh hàrturh mhs vhlhs (ju vhlath) a axacuïãj mjs hlecarcas, cjdj varadjs dhes hmehgta. Fè mjes prjcassjs ma ljchïãj ad j`rhs, thd`åd cjgfacemjs cjdj oh`hretjs> ljchïãj pjr chvhlatas a ljchïãj pjr thàerh ju tèùh cjrremh. Rhrh axacuthr quhlquar ud mjs prjcamedagtjs, j tarragj pracesh asthr tjthldagta ledpj a prjgtj phrh racaàr h ljchïãj – iugmhïãj, `hlmrhda, hlvaghreh atc. – a tar ud pjgtj ma raiarîgceh egecehl qua pjma sar ud pjgtj magemj gj tarragj, gh phrama mh cjgstruïãj vezegfh, gj hlegfhdagtj mj tarragj h sar dhrchmj pjr tjpóorhij ju gj hlegfhdagtj mj phssaej (ourh 8).

Egtrjmuïãj Ljchr udh j`rh seogech phsshr phrh j tar ragj, ad varmhmaerh orhgmazh (thdhgfj ghturhl), hs plhgths mj prjnatj, cjd tjmjs js aladagtjs plhganhmjs cjdj iugmhïñas, phramas, pelhras, hàrturhs atc. Assa trh`hlfj å duetj edpjrthgta, pjes arrjs raiaragtas h damemhs pjmad hphracar dhes thrma gh j`rh, a ghmh pjmarè sar iaetj, h gãj sar qua h j`rh sanh madjlemh. Hlåd mh ljchïãj mh j`rh, vhdjs hpragmar thd`åd cjdj axacuthr udh iugmhïãj, qua å h `hsa ma sustagthïãj, cunh iugïãj å mestreùer, phrh j tarragj, tjmh h chroh mh cjgstruïãj.

Ljchïãj mh J`rh Rhrh axacuïãj ma paquaghs a dåmehs ljchïñas, å gacassèrej tar j saouegta dhtarehl> • ]ragh datèlech ju ma `rh; • Aschlh; • Asquhmrj; • Gäval ma `jlfh; • Dhgouaerh ma gäval; • Rrudj ma cagtrj; • Rrudj ma ihca; • Legfh ma pamraerj (ju hrhda ma hïj racjrremj g¾ 86); • Dhrtalj; • Dhrrath; • Ihcãj; • Requatas ju asthchs ma dhmaerh; • Rjgthlatas; • ]èùhs ju repñas; • Rraojs; • ]egth asdhlta ju lètax `rhgcj a vardalfj; • Rlhgth `hexh mh j`rh a mhs iugmhïñas. Cursj ma Ramraerj - Hulh 3

raiarîgceh egecehl. egecehl. Ieourh 8 – Rjgtj ma raiarîgceh

Ljchïãj pjr chvhlatas Js chvhlatas sãj iaetjs cjd mjes pjgthlatas ma dhmaerh ma 0— x 0— (1 x 1 cd) ju 3— x 3— (?,1 x ?,1 cd), cjd asphïhdagtj ma 8,12 ju 8,62 d, trhvhmjs pjr udh tèùh ma 81 h 02 cd ma lhrourh. Rjmadjs ushr ud repãj ma 0 x 1 cd. 3

Egstetutj Qgevarshl @rhselaerj

Gassa tepj ma ljchïãj, js hlegfhdagtjs sãj magemjs pjr praojs crhvhmjs ghs tèùhs (ourh 0).

Ljchïãj pjr thàerh ju tèùh cjrremh H ljchï ljchïãj ãj pjr daej ma thàe thàerhs rhs – ju tèù tèùh h cjrremh, cjdj thd`åd å cjgfacemh – å egmechmh phrh j`rhs cjd duetjs aladagtjs h sarad trhgspjrthmjs a, sad mþvemh, å h dhes ushmh palhs cjgstrutjrhs phrh ljchïñas ma pråmejs. Assa prjcassj cjgsesta ad cjgtjrghr, cjd udh hrdhïãj cjgtäguh ma pjgthlatas a tèùhs, tjmj j parädatrj mh iuturh amechïãj. Å edpjrthgta qua hs tèùhs xhmhs gjs pjg thlatas sanhd gevalhmhs a js quhtrj chgtjs astanhd àd ratjs. Rhrh djgthr h thàerh, ushdjs pjgthlatas ma 3— x 3— a tèùhs ma 81 ju 02 cd ( ieourh = ).

praojs. Ieourh 0 – Chvhlata cjd praojs.

Assas chvhlatas sãj egmechmjs phrh ljchïñas ad j`rhs ma paquagj pjrta cjdj hrdhzåd, ohrhoad, amäculh, hdplehïñas atc., qua pjssuad pjucjs aladagtjs phrh sarad ljchmjs (ourh 3).

Ieourh = – ]hàerh. ]hàerh.

Maiegemhs hs legfhs mh thàerh, cjd udh mestàgceh ma, gj dägedj, 8,02 d ma cjgtjrgjs mh iuturh cjgstruïãj, iegchdjs js pjgthlatas a praohdjs hs tèùhs cjgtäguhs hlegfhmhs. Rhrh essj, pjmadjs utelezhr j gäval ma dhgouaerh phrh matar deghr h hlturh ad qua sarãj iexhmhs hs tèùhs gjs pjgthlatas. Rhrh matardeghr h hlturh mhs tèùhs, phrtedjs mj gäval mj predaerj pjgthlata, trhgsiaregmj assa gäval phrh js madhes. H mestàgceh agtra js pjgthlatas mava sar agtra 8,12 a 3,22 d ( ourh 1).

Ieourh 3 – Ljchïãj cjd chvhlatas. chvhlatas.

H vhgthoad vhgthoad mh ljchïãj cjd cjd chvhlatas å j usj ma pjucj dhtarehl cjdj pjgthlatas a tèùhs; pjr jutrj lhmj, masvhgthoad å sher ijrh ma hlegfhdagtj prjvjchmj palh cerculhïãj ma trh`hlfhmjras a ma aquephdagtjs, pjes js chvhlatas sãj aladagtjs esjlhmjs. Cursj ma Ramraerj - Hulh 3

=


Ieourh ? – Emagtechïãj Emagtechïãj mjs aexjs aexjs pjr daej ma ma praojs.

Assh hlturh dägedh ma 2,=2 d mava sar h phrter mj gäval dhes hltj mj tarragj. t arragj. ]rhg hgspj spjrth rthgmj gmj h hltu hlturh rh mh mhss tèù tèùhs hs phr phrh h js js pjg pjgthl thlata atas. s. Ieourh 1 – ]r

Cjd h tragh datèlech, dhrchdjs, hj ljgoj mhs tèùhs, pjgtjs phrh cjljchïãj mjs praojs. Xuhgtj â pegturh, å `jd utelezhr tegth asdhlta ju lètax `rhgcj. Cjstudhdjs dhrchr, gh tèùh, h legfh mjs pelhras cjd tegth vardalfh.

Matardeghmh h hlturh mhs tèùhs, asths sãj xhmhs gjs pjgthlatas, a pjmadjs ushr assh legfh cjdj raiarîgceh, sanh palh hrasth suparejr, sanh palh hrasth egiarejr, gevalhmh cjd j gäval ma `jlfh ( ourh 9).

Gj chsj ma ljchïãj cjd vhlaths phrh iugmhïãj (hlecarcas), mavadjs dhgtar udh `jh mestàgceh agtra h thàerh (ju chvhlata) a h vhlath phrh ihcelethr h djvedagthïãj mh tarrh raterhmh mj egtarejr mh vhlath. Js chgtjs mh thàerh mavad sar ad àgouljs ratjs (52²). Rjr essj, utelezhdjs j dåtjmj treàgoulj ratàgoulj ma 3,22 x =,22 x 1,22 d, qua å j emahl (ourh 6).

Gevalhdagtj mhs tèùhs. tèùhs. Ieourh 9 – Gevalhdagtj

H hlt hlturh urh mhs tè` tèùhs uhs mj sjl sjlj j mav mava a sar, gj dägedj, ma 2,=2 htå 8,12 d, cjdj pumadjs var gh ieourh 1. Ghs tèùhs, cjljchdjs praojs ad meiaragtas hlturhs phrh emagteiechr js aexjs (legfh ma cagtrj) mhs phramas a mhs ihcas lhtarhes masths, h lhrourh mj hlecarca atc. ( ieourh ?). ]ardeghmh h djgthoad mh thàerh, cjrthdjs js pjgthlatas ragta â tèùh. Cursj ma Ramraerj - Hulh 3

Dåtjmj treàgou treàgoulj lj ratàgou ratàgoulj lj phrh phrh j chgtj mh thàerh thàerh.. Ieourh 6 – Dåtjmj 1


Hpós cj Hpós cjgc gclu luer er h dh dhrc rchï hïãj ãj ma tj tjm mjs js pj pjgt gtjs js ma raiarîgceh, j dastra ma j`rhs, ju j agoagfaerj, mava ihzar h cjgiarîgceh massas pjgtjs. Pacjdagmhdjs qua sa ihïh ma dhgaerh egvarsh, ju sanh, hpós h dhrchïãj mj þltedj pjgtj, vjlthdjs cjgiaregmj mjs þltedjs pjgtjs htå js predaerjs. Xuhgmj praceshr trhgsiarer phrh j sjlj ud pjgtj ad qua sarè crhvhmj ud pequata – jgma sarè lavhgthmj ud pelhr, pjr axadplj, ju matardeghr j ledeta mh ihca lhtarhl mh phrama –, mavadjs utelezhr ud prudj ma cagtrj parpagmeculhr hj cruzhdagtj mhs muhs legfhs mj aexj ( ourh 5).

Hpós h cjgcrathoad cjgcrathoad,, å axacuthmh h dhrchïãj mhs astruturhs egtardameèrehs mjs `hlmrhdas a phramas. Assas aladagtjs sãj madhrchmjs paljs aexjs, h phrter mjs quhes magedjs, pjstarejrdagta, pjstarejrdagta, hs ihcas. Yanh, h saouer, h ljchïãj ma udh plhgth `hexh hprasagthmh gh ourh 88 a hlougs mathlfas ma axacuïãj djstrhmjs cjd edhoags mh j`rh gh saquîgceh.

Rrudj ma cagtrj parpagm parpagmeculhr eculhr hj cruzhdagtj cruzhdagtj mhs Ieourh 5 – Rrudj muhs legfhs mj aexj. vesth ad plhgth plhgth `hexh. Ieourh 88 – Ljchïãj vesth

Ljchïãj ma orhgmas ameiäcejs Gh ourh 80, tadjs h dasdh ljchïãj djstrhmh ad parspactevh a, gh saquîgceh, hs ijtjs ma hlougs mathlfas ma axacuïãj.

H lj ljcchïãj ma ma or orhgmas am ameiäcejs å egecehmh cj cjd aladagtjs mh iugmhïãj, cjdj asthchs, tuùlñas, shphths atc. Yanh, gh ieourh 82, ud axadplj ma ljchïãj ma ud ameiäcej jgma pjmadjs j`sarvhr js ùrhcjs mhs `rjchs qua sarãj cjgcrathmhs. Yanh, thd`åd, qua js ùrhcjs astãj thdphmjs phrh avethr hcemagtas.

mhs `rjchs ma udh ljchïãj ljchïãj ma ameiäcej. ameiäcej. Ieourh 82 – @urhcjs mhs Cursj ma Ramraerj - Hulh 3

parspactevh. Ieourh 80 – Ljchïãj ad parspactevh. 9


Maledethmj j parädatrj mh ljchïãj, xhdjs js pjgthlatas ijrïhgmj h pagatrhïãj mastas gj sjlj htrhvås ma phgchmhs cjd h dhrrath (ourh 83); ju cjljchgmj ad ùrhcjs axacuthmjs cjd trhmj phrh pjstarejr cjgcrathoad, gj chsj ma j`rhs cunh ljchïãj mava pardhgacar pjr dhes tadpj.

Axacuthmh h dhrchïãj ad tjmjs js pjgthlatas, egecehdjs h cjljchïãj mhs tèùhs a suh xhïãj cjd praojs. Qtelezhdjs j gäval ma `jlfh phrh maexhr hs tèùhs gevalhmhs a, ad saouemh, praohdjs ghs dhrchïñas mjs pjgthlatas (ourhs 81 a 89).

Hcarthgmj hs tèùhs tèùhs ghs dhrchs. dhrchs. Ieourh 81 – Hcarthgmj Cjljch jchïãj ïãj ma pjg pjgthla thlatas tas cjd phg phgchm chmhs hs ma dhr dhrrath rath.. Ieourh 83 – Cjl

Hpós h xh Hpós xhïãj ïãj ma tjm tjmjs js js pjg pjgthl thlata atas, s, cjd h dhgouaerh ma gäval, dhrchdjs hs hlturhs ad qua sarãj xhmhs hs tèùhs ( ourh 8=).

hs tèùhs gevalhmhs. gevalhmhs. Ieourh 89 – Iexhgmj hs

Axacuthmh h thàerh, matardeghdjs j hlegfhdagtj mjs aexjs mhs phramas, mhs ihcas mh hlvaghreh, mh lhrourh mhs vhlhs phrh hs iugmhïñas atc., utelezhgmj praojs (ourh 8?).

Dhrchgmj hs hlturhs phrh phrh xhïãj mhs mhs tèùhs. Ieourh 8= – Dhrchgmj Cursj ma Ramraerj - Hulh 3

?


H trhgsiarîgceh mhs legfhs ma dhrchïãj phrh j tarragj å iaeth cjd j prudj ma cagtrj, thgtj gjs chgtjs cjdj ijrh mjs cruzhdagtjs (ourh 85).

tarrdeg egh hgmj js hlegfhdagtj tjss cjd praojs sj`ra hs tè tè` ùhs. Ieourh 8? – Mata

Iaeth h cjljchïãj mjs praojs a magemjs js aladagtjs mh cjgstruïãj, astechdjs hs legfhs ma pamraerj (ju hrhda), egecehgmj palh matardeghïãj mh lhrourh mhs vhlhs phrh hs iugmhïñas (ourhs 86H a @).

]rhgsiarîgceh mh mh legfh ma dhrchïãj. Ieourh 85 – ]rhgsiarîgceh

Iexhdjs asthchs gjs pjgtjs matardeghmjs palj prudj a, mapjes, cjljchdjs praojs ghs asthchs a astechdjs h legfh ma pamraerj phrh mageïãj mjs aladagtjs ( ourh 02).

Astechgmj mj h legfh ma pamraerj phrh mageïãj Ieourh 02 – Astechg mjs aladagtjs.

Ad tarragjs egcleghmjs, h ljchïãj mava sar iaeth ad maorhus cjgijrda å djstrhmj gh ourh 08, sadpra gevalhmh a gj asquhmrhmj.

ma pamraerj astechmhs. astechmhs. Ieourhs 86H a @ – Legfhs ma Cursj ma Ramraerj - Hulh 3

maorhus. Ieourh 08 – Ljchïãj ad maorhus. 6


Aschvhïãj Aschvhïã j mh J`rh

Gj chsj ma aschvhïãj ma ùrhcj ju vhlh, vareiechdjs j prudj â damemh qua chvhdjs cjd j trhmj, phrh qua asta astanh ad pjseïãj vartechl.

J sarveïj ma aschvhïãj mh j`rh cjgsesta ad axacuthr ùrhcjs a vhlhs gj tarragj ghs pjseïñas egmechmhs, phrh axacuthr hs iugmhïñas. @hsahgmj-sa ghs legfhs ma dhrchïãj ma aexj mhs ihcas mhs phramas a mh iugmhïãj, dhrchdjs, gj tarragj, hs aschvhïñas qua sarãj axacuthmhs. Gh axacuïãj mjs ùrhcjs ju vhlhs, utelezhdjs pechraths, chvhmjras a trhmjs; gh radjïãj mj dhtarehl, ushdjs pès a agxhmhs; phrh raoulhrezhïãj mhs phramas mjs ùrhcjs, chvhmjr ratj (chvhmaerh); phrh varechr h vartechlezhïãj, ushdjs j prudj ma ihca agcjsthmj gh legfh ma dhrchïãj mjs ùrhcjs ju mhs vhlhs (ourhs 00 a 03).

J dhtarehl aschvhmj mavarè iechr hihsthmj mh `jrmh, gj dägedj, 12 cd, pardhgacagmj gassa ljchl htå qua sanh utelezhmj phrh htarrj; chsj gãj sanh gacassèreh h suh rautelezhïãj, j dhtarehl mava sar radjvemj. Yanh, h saouer, hloudhs edhoags qua elustrhd hs jparhïñas ma aschvhïãj ( ieourhs 0= ; 0 1 H a @; 09H a @).

Madhrchïãj mh vhlh. vhlh. Ieourh 0= – Madhrchïãj Aschvhïãj ma vhlh. Ieourh 00 – Aschvhïãj

Aschvhïãj ma ùrhcj. ùrhcj. Ieourh 03 – Aschvhïãj Cursj ma Ramraerj - Hulh 3

5


Iugmhïñas Cjdj messadjs, h iugmhïãj å h `hsa ma sustagthïãj, sustagthïã j, gh quhl å mestreùämh tjmh h chroh mh cjgstruïãj. Xuhgtj â dhgaerh ma mestreùer h chroh sj`ra j sjlj, hs iugmhïñas pjmad sar meraths a egmeraths.

Iugmhïñas meraths Sãj iugmhïñas edplhgthmhs ad sjlj rda, cunh prjiugmemhma gãj axcamh h 3,22 d. Hs iugmhïñas iugmhïñas meraths sãj hs saouegtas> saouegtas> `ljcjs ma iugmhïñas, `hlmrhdas a rhmear.

Ieourhs 01H a @ – Axacuïãj mh vhlh.

@ljcjs ma iugmhïãj

Js `ljcjs ma iugmhïãj pjmad tar meiaragtas ijrdhtjs> cerculhr, quhmrhmj, rathgoulhr atc. Sãj iaetjs ma pamrh, tenjlj dhceïj, cjgcratj sedplas ju hrdhmj (ourh 0?).

Ieourh 0? – @ljcjs ma iugmhïãj.

Xuhgmj j `ljcj ma iugmhïãj å iaetj ma cjgcratj hrdhmj, ala racaà j gjda ma shphth. J qua chrhctarezh h iugmhïãj cjd `ljcjs a shphths å j ihtj ma h mestreùeïãj mh chroh phrh j tarragj sar pjgtuhl, ju sanh, jgma fjuvar ud pelhr, axesterè ud `ljcj ju shphth mestreùegmj suh chroh phrh j sjlj (ourh 06).

cjd j trhmj. Ieourhs 09H a @ – Axacuïãj ma ùrhcj cjd Cursj ma Ramraerj - Hulh 3

82


@hlmrhda. Ieourh 32 – @hlmrhda. Mest stre reù ùeï eïãj ãj mh ch chro roh h gj sj sjlj lj pa palj ljss `l `ljc jcjs js ma cj cjgc gcra ratj tj.. Ieourh 06 – Me

Shphth cjrremh å j gjda qua mhdjs hj `hlmrhda iaetj ma cjgcratj hrdhmj ( ourh 38).

Jutrh chrhctarästech å h hàrturh ma udh vhlh htå j sjlj rda, ma, gj dèxedj, 3,22 d, sj`ra h quhl sarè hssagthmj j `ljcj ju h shphth (ourh 05).

cjrremh. Ieourh 38 – Shphth cjrremh.

J `hlmrhda å ud tepj ma iugmhïãj duetj ushmj gh cjgstruïãj ma chshs ad tarragjs cunh chdhmh rasestagta mj sjlj sa agcjgtrh, gj dèxedj, ad 2,92 d ma prjiugmemhma. Ad orhgmas cjgstruïñas, j `hlmrhda å iaetj pjr cedh mhs iugmhïñas prjiugmhs ju egmeraths.

Yhlh hà hàrth rth phr phrh h j hss hssagth agthdag dagtj tj mh mh shph shphth. th. Ieourh 05 – Yhlh

@hlmrhdas

Phmear

J `hlmrhda å udh iugmhïãj cjgstruämh hj ljgoj ma tjmj j cjdpredagtj mh phrama, sj`ra j quhl sarè lavhgthmh. Rjrthgtj, å udh iugmhïãj qua mestreùe chroh phrh j tarragj ma dhgaerh legahr. J `hlmrhda pjma sar iaetj ma pamrh, tenjljs dhceïjs, cjgcratj sedplas ju hrdhmj atc. ( ieourh 32 ). Cursj ma Ramraerj - Hulh 3

J rhmear (prjgugceh-sa /rhmeî/) å udh lhna ma cjgcratj hrdhmj qua mestreùe mestre ùe h chroh tjthl racaèmh mh cjgstruïãj ugeijrdadagta palh èrah ma cjgthtj (sjlj). Å udh iugmhïãj acjgýdech quhgmj hs chrohs sãj paquaghs a h rasestîgceh mj tarragj å `hexh; gasshs cercugstàgcehs, å udh jpïãj phrh su`stetuer h iugmhïãj prjiugmh ( ourh 30). 88


cjgcratj hrdhmj hrdhmj prjgtj. Ieourh 31 – @ljcj ma cjgcratj

pjgtelfhmhs hs egmechd h plhgth mj Ieourh 30 – Phmear> legfhs pjgtelfhm `hlmrhda ju mh hlvaghreh.

Yanh, h saouer, h axacuïãj ma ud `ljcj `ljc j ma cjgcratj hrdhmj cjd h cjljchïãj mh hrdhmurh sj`ra h `hsa ma `reth ( ourhs 33, 3= a 31).

Sj`ra assa `ljcj ma cjgcratj hrdhmj, å axacuthmj j `hlmrhda cjd hrdhmurhs ad ijrdhs ma dhmaerh ( ieourhs 39 h 35 H a @ ).

Ieourh 33 – Hrdhmurh Hrdhmurh cjljchmh cjljchmh sj`ra h `hsa ma `reth. `reth.

Hrdhmurh mj `hlmrhda. `hlmrhda. Ieourh 39 – Hrdhmurh

Ieourh 3= – Cjgcrathgmj Cjgcrathgmj h hrdhmurh. hrdhmurh. Cursj ma Ramraerj - Hulh 3

80


Ieourhs 3?H a @ – Ax Axac acuth uthgm gmj j hs ij ijrd rdhs hs ma dh dhma maer erh h mj `h `hlm lmrh rhda da..

Ieourhs 35H a @ – @hlmrhda prjgtj.

Iugmhïñas egmeraths Iugmhïñas egmeraths, ju prjiugmhs, sãj hqualhs cunhs `hsas vãj htegoer j sjlj ierda, setuhmhs h dhes ma 3,22 d mj gäval mj tarragj. Alhs trhgsdetad hs chr ohs phrh j sjlj palh rasestîgceh mh pjgth ju palj htretj hj ljgoj mh supariäcea lhtarhl (ju cjdèghïãj ma hd`hs). Gasth hulh ihlhradjs hpaghs mh pregcephl iugmhïãj egmerath qua å h asthch. Hss a s t h c h s p j m a d s a r p r å - d j l m h H mhs, ijrdhmhs pjr aladagtjs prå-ih`rechmjs a crhvhmhs gj sjlj; a asch vhmhs, qua sãj djlmhmhs ad cjgcrat j ghs pariurhïñas (ùrhcjs) celägmrechs hàrths gj sjlj.

Cjgcrathgmj j `hlmrhda. `hlmrhda. Ieourhs 36H a @ – Cjgcrathgmj Cursj ma Ramraerj - Hulh 3

83


Hs as asth thch chss pj pjma mad d sa sarr cr crhv hvhm hmhs hs gh pjseïãj vartechl ju egcleghmh, pjråd h dhejreh mhs j`rhs ma orhgma pjrta axeoa qua hs asthchs sanhd crhvhmhs gjs mjes tepjs ma pjseïãj.

Rjmadjs gjthr qua axesta udh ijrïh qua htuh gj sagtemj cjgtrèrej â ijrïh hplechmh phrh agtarrhr j pamhïj ma dhmaerh (ma cedh phrh `hexj). Assh ijrïh cjgtrèreh (ma `hexj phrh cedh) å cfhdhmh ma ijrïh ma htretj. Xuhgmj h ijrïh hplechmh ijr eouhl ju dagjr qua â ijrïh ma htretj, gãj fè cjgmeïñas ma htegoer dhejr prjiugmemhma; nè quhgmj h ijrïh hplechmh ijr dhejr qua h ma htretj, agtãj j hprjiugmhdagtj å cjgsaouemj htå fhvar h aquevhlîgceh mhs ijrïhs.

Xuhgmj hs asthchs trhgsdetad chrohs ma cedh phrh `hexj, alhs sãj cfhdhmhs ma asthchs ma cjdprassãj; nè quhgmj j prjcassj å egvarsj, ju sanh, quhgmj h ijrïh htuh ma `hexj phrh cedh, hs asthchs racaàd j gjda ma asthchs ma trhïãj.

Ad quhlquar jutrj tepj ma tarragj, hcjgtacarè j dasdj prjcassj> quhgmj sa cfaoh h carth prjiugmemhma, gãj sa cjgsaoua dhes agtarrhr j pamhïj ma dhmaerh.

Hs as asth thch chss tr trhg hgsd sdetetad ad h ch chro roh h hj tarragj mhs saouegtas dhgaerhs> htrhvås mh suh supariäcea, hj ljgoj mj cjdpredagtj; ju htrhvås ma suh pjgth. Xuhgmj h chroh å trhgsdetemh mh supariäcea, h asthch trh`hlfh pjr htretj; nè quhgmj sjdagta h pjgth mh asthch trhgsdeta h chroh, alh trh`hlfh pjr ilaxãj. Yhdjs axplechr dalfjr h trhgsdessãj mh chroh pjr ilaxãj a pjr htretj. Edhoega ud pamhïj ma dhmaerh sagmj agtarrhmj magtrj mh hraeh, gudh prheh quhlquar. Rhrh qua essj hcjgtaïh, å gacassère j adpraohr carth ijrïh; â damemh qua h ijrïh crasca, h dhmaerh pagatrh magtrj mh hraeh. Ad carth prjiugmemhma, j pamhïj ma dhmaerh gãj pagatrh dhes, pjr dhejr qua sanh h ijrïh qua sa hplequa ( ieourh =2).

Hs asthchs pjmad sar cjgiaccejgh cjgiaccejghmhs mhs ad dhmaerh, hïj ju cjgcratj. ← Asthchs ma dhmaerh

Hs asthchs ma dhmaerh dhmaerh mavad sar murhs a rasestagtas h egtadpåreas; ad oarhl, sãj iaeths ma trjgcjs ramjgmjs ma auchleptj, lesjs a maschschmjs ( ourh =8).

dhmaerh. Ieourh =8 – Asthch ma dhmaerh.

Asshs asthchs tîd, cjdj vhgthoad, h murhèlemhma quhgmj tjthldagta su`darsh; chsj cjgtrèrej, pjmad hpjmracar. Å `jd lad`rhr qua udh asthch ma dhmaerh, crhvhmh tjthldagta magtrj m―èouh, gugch hpjmraca, sjdagta h phrta qua ch ijrh m―èouh.

Pasestîgceh ma pjgth a ma htretj. Ieourh =2 – Pasestîgceh Cursj ma Ramraerj - Hulh 3

8=


← Asthchs ma cjgcratj

Hs asthchs mavad sar trhthmhs, tr hthmhs, hgtas ma sarad crhvhmhs gj sjlj, cjd edugezhmjras cjgtrh egsatjs a iugojs.

Asshs asthchs pjmad sar iaeths ma cjgcratj sedplas ju hrdhmj. J cjgcratj sedplas å udh desturh ma quhtrj cjdpjgagtas `èsecjs, qua sãj j cedagtj, h pamrh, h hraeh a h èouh; ala å rasestagta hjs asijrïjs ma cjdprassãj, dhs cjd `hexh rasestîgceh hjs asijrïjs ma trhïãj (ourh =3).

H crhvhïãj crhvhïãj ma asthchs ma dhmaerh dhmaerh å ud trh`hlfj qua axeoa duetj cuemhmj a htagïãj; phrh essj, utelezhdjs ud aquephdagtj próprej cfhdhmj `hta-asthch. J parl ma sjgmhoad mj tarragj mhrè h axhth rasestîgceh mh asthch. Mavadjs, agtãj, prjcamar cjd h crhvhïãj ma udh hdjstrh phmrãj, ju sanh, crhvhr udh asthch gj sjlj phrh shàr qua rasestîgceh j sjlj vhe hprasagthr â dhmaerh. Sa j tarragj ijr fjdjoîgaj, a gãj duetj renj, h crhvhïãj sarè iaeth cjd trhgquelemhma, a js hcemagtas agcjgtrhmjs murhgta j prjcassj sarãj, gh dhejreh mhs vazas, djtevhmjs pjr cjrpjs astrhgfjs gj sjlj. ← Asthchs datèlechs

Sãj asthchs iaeths ma hïj qua hprasagthd egþdarhs vhgthoags ad ralhïãj âs asthchs ma dhmaerh ju ma cjgcratj. Asshs asthchs pjmad sar crhvhmhs ihceldagta ad quhlquar tepj ma tarragj a hprasagthd alavhmh chphcemhma ma chroh. Hprasagthd thd`åd ihcelemhma gj cjrta a ghs adagmhs (j cjrta å iaetj cjd dhïhrecj; nè h adagmh å sjlmhmh). Ad sarveïjs prjvesórejs, hs asthchs datèlechs pjmad sar crhvhmhs a, pjstarejrdag pjstarejrdagta, ta, hrrhgchmhs. Massh dhgaerh, pjmad sar rahprjvaethmhs vèrehs vazas. Js pars mhs asthchs datèlechs sãj sedplas, ad ijrdhtj ma “E— a “F— (hs dhes ushmhs), trelfj a ramjgmj (ourh =0).

Ieourh =3 – Asthch ma cjgcratj cjgcratj sedplas. sedplas.

J cjgcratj hrdhmj tad, hlåd mjs cjdpjgagtas `èsecjs nè cethmjs, udh hrdhmurh qua lfa mè rasestîgceh thgtj hj asijrïj ma trhïãj cjdj hj ma cjdprassãj ( ourh ==).

datèlechs. Ieourh =0 – Asthchs datèlechs. Cursj ma Ramraerj - Hulh 3

Ieourh == – Asthch ma cjgcratj cjgcratj hrdhmj. hrdhmj.

81


H s a s t h c h s m a c j g c r a t j p j m a d s a r Hs prå-djlmhmhs ju djlmhmhs eg ljcj (gj ljchl). Hs prå-djlmhmhs sãj iaeths ma cjgcratj dhceïj ju vhzhmj, ad ijrdhtj ramjgmj ju quhmrhmj – axcapcejghldagta, pjmad sar saxthvhmhs ju jctjojghes – a sãj crhvhmhs pjr par cussãj, pragshoad ju ve`rhïãj ( ieourh =1 ). Hs asthchs ma cjgcratj djlmhmhs eg ljcj sãj iaeths gj ljchl, ad pariurhïñas iaeths gj sjlj.

Rjsecejghgmj j tu`j phrh pariurhr pariurhr j sjlj. Ieourh =9 – Rjsecejghgmj

Ieourh =? – Qdamacagmj Qdamacagmj j sjlj. sjlj.

prå-djlmhmhs. s. Ieourh =1 – Asthchs ma cjgcratj prå-djlmhmh

Hs as asth thch chss ma cj cjgc gcra ratj tj su su`s `stetetu tuad ad,, cjd vhgthoad, hs asthchs ma dhmaerh ad j`rhs iluvehes, pjes hs ma cjgcratj gãj sãj hiathmhs palh hltarhïãj mj gäval ma èouh gj su`sjlj. Qd hpragmezhmj dhes prjiugmj mhs iugmhïñas egmeraths gãj ihz phrta massa cursj, pjes raquar astumjs dhes mathlfhmj a cèlculjs aspacäiecjs qua mavad sar axacuthmjs pjr ierdhs a agoagfaerjs aspacehlezhmjs. Hj pamraerj chà h axacuïãj ma hlecarcas qua ihzad phrta mhs iugmhïñas egmeraths, hssugtj qua sarè astumhmj gh saquîgceh. Yhdjs var hojrh cjdj j sjlj å pariurhmj phrh udh iugmhïãj egmerath ( ieourhs =9 ; =? ; =6 =6H H a @ ). Cursj ma Ramraerj - Hulh 3

@hta tagm gmj j cj cjd d j sj sjqu quat ata a ph phrh rh pa paga gatr trhï hïãj ãj mj tu tu`j `j.. Ieourhs =6H a @ – @h 89


Hlecarcas

Htegoemh h prjiugmemhma prjiugmemhma mj mj iurj, gj chsj ma asthch ma cjgcratj hrdhmj, maspanhdjs j cjgcratj a, hgtas mh sachoad, egtrjmuzedjs hs `hrrhs ma iarrj qua sarãj h `hsa mh hrdhmurh mjs pelhras ( ourhs =5 a 12).

J hlecarca å h iugmhïãj dhes cjdud ushmh phrh h sustagthïãj ma j`rhs ma paquagj pjrta cjdj rasemîgcehs tårrahs a sj`rhmjs. Ala mava sar àd axacuthmj phrh avethr qua hphraïhd, ghs phramas, tregchs a udemhma, hlåd ma rasester hj pasj mh j`rh. J hlecarca pjma sar iaetj ma pamrh, hlvaghreh ju cjgcratj ( ourh 18).

Maspanhgmj cjgcratj cjgcratj gj ùrhcj. ùrhcj. Ieourh =5 – Maspanhgmj

]epjs ma hlecarcas. hlecarcas. Ieourh 18 – ]epjs

Js hlecarcas sãj iugmhïñas rhshs, axacuthmhs quhgmj j ad`hshdagtj (sjlj rasestagta) å agcjgtrhmj gj sjlj suparcehl, ad udh prjiugmemhma qua pjma vhrehr ma 8,22 h 3,22 d. Alas só pjmad sar axacuthmjs ad tarragjs rdas, dhs sa asta gãj ijr duetj rda – ijrdhmj pjr `hrrj duetj þdemj ju hroelh djla – ju j sjlj tevar èouh, mavad sar axacuthmjs cjd `hlmrhda ma cjgcratj.

Egtrjmuzegmj hs `hrrhs `hrrhs ma iarrj. Ieourh 12 – Egtrjmuzegmj

]hd`åd pjmadjs egtrjmuzer h hrdhmurh ma `hrrhs ma iarrj hgtas ma maspanhr j cjgcratj. Cursj ma Ramraerj - Hulh 3

8?


Gãj å racjdagmhmj qua j pamraerj axacuta hlecarcas ad mehs cfuvjsjs, pjes vãj hchrrathr prj`ladhs iuturjs cjdj udemhma cjgsthgta ghs phramas. Gh thàlh 8, tadjs js mevarsjs tepjs ma iugmhïñas cjd suhs raspactevhs chrohs, a quhl j sjlj dhes rasestagta.

]epj ma iugmhïãj @hlmrhda Phmear

Chrohs

Pasestîgceh

Chshs tårrahs

Sjlj rda a sacj

Chshs tårrahs a sj`rhmjs

Sjlj rda a pjucj rda

Chshs tårrahs

Sjlj pjucj rda

Sj`rhmjs

Sjlj rda a sacj

Sj`rhmjs a pråmejs `hexjs

Sjlj rda

Rråmejs `hexjs

Sjlj pjucj rda

Shphth @rjch Strhuss Asthch Rrå-djlmhmh Rråmejs hltjs, pjgtas a vehmutjs Irhgke

Sjlj pjucj ierda a cjd prasagïh ma èouh

Rråmejs hltjs, pjgtas a vehmutjs Sjlj pjucj rda

Rråmejs hltjs, pjgtas a orhg- Xuhgmj j lagïjl iraètecj å mas vehmutjs prjiugmj Xuhgmj j lagïjl iraètecj å H hr Rråmejs hltjs, pjgtas a orhgrhsj ju h j`rh å axacuthmh cjdpredemj mas vehmutjs magtrj ma rej, lhojh ju dhr H cåu hàrtj

]uùlãj

Iugmhïñas a js tepjs ma ma chrohs chrohs a rasestîgceh rasestîgcehss qua pjmad supjrthr. ]hàlh 8 – Iugmhïñas

Cjdj vadjs, j `hlmrhda å j tepj dhes cjdud ma iugmhïãj phrh paquaghs j`rhs. Rhrh axacuïãj mjs hlecarcas, å gacassèrej h`rer udh vhlh cjd lhrourh ud pjucj dhejr qua h aspassurh mhs phramas. Ad phramas axtarghs ma ud tenjlj, h lhrourh mj hlecarca mava sar ma 8 ´ tenjljs, ad sjljs ierdas; a ma 0 tenjljs, ad sjljs gãj duetj ierdas. Nè ad phramas egtarghs, h lhrourh ma ud hlecarca ma udh phrama ma daej-te njlj njl j å ma 8 tetenjl njlj j ad sjl sjljs js ieierda rdas, s, a ad phramas ma ud tenjlj, 8 ´ te njljs ad sjljs gãj duetj ierdas (ieourh 10). Cursj ma Ramraerj - Hulh 3

Ieourh 10 – Rhrama ma daej-tenjlj (hlecarca ma 8 tenjlj) a ma

ud tenjlj (hlecarca ma 8 ´ tenjljs). 86


J hlecarca gugch pjma sa hpjehr sj`ra htarrjs, pjes astas praceshd ma ud tadpj ma gãj dagjs qua quhtrj hgjs phrh sa sjlemechr tjthldagta. Chshs cjgstruämhs sj`ra èrahs htarrhmhs vãj hmquerer tregchs ad macjrrîgceh ma rachlquas. Hs chdhmhs suparcehes mjs tarragjs, ma ud djmj oarhl, cjgtîd ijlfhs, rhäzas, ohlfjs atc., qua gãj sarvad phrh j hssagthdagtj mjs hlecarcas. Rjr essj, hs vhlhs sãj chvhmhs htå qua sa agcjgtra tarrh fjdjoîgah, rda, sad rhäzas a ijrdeouaerjs, a å gasta tepj ma tarrh ad qua sa mava ihzar j hssagthdagtj mj hlecarca, ad vhlhs qua gãj pjmad tar dagjs ma =2 cd ma prjiugmemhma. Hs lhtarhes mhs vhlhs mavad sar leoaerhdagta egcleghmhs phrh ihcelethr j trh`hlfj ma rahtarrj a ma cjdphcthïãj ( ourh 13).

sjquatas. Ieourh 1= – Djmaljs ma sjquatas.

H prasagïh ma ijrdeouaerjs pjma sar cjgsththmh, pjr vazas, gh própreh supariäcea mj tarragj htrhvås ma ùrhcjs degþsculjs, gjs quhes hphracad paquagjs djgtas ma tarrh hj ramjr. Assas ùrhcjs, qua sãj hs agtrhmhs mj ijrdeouaerj, sa rhdechd, ijrdhgmj tþgaes a càdhrhs gj egtarejr mj sjlj. Assas ijrdeouaerjs pjmad tar duetjs ùrhcjs, pjmagmj hchrrathr ihlfhs ghs chdhmhs rasestagtas mj sjlj ( ourh 11).

udh vhlh. Ieourh 13 – Rarl ma udh

Hpeljhdagtj Hs vhlhs, ad tjmh h suh axtagsãj, mavad tar j iugmj hpeljhmj (sjchmj) phrh varechr sa axesta hloudh ihlfh gh chdhmh rasesrases tagta mj sjlj, jchsejghmh, dueths vazas, pjr ijrdeouaerjs. Assa prjcamedagtj mava sar iaetj phrh raoulhrezhr h supariäcea mj tarragj, aledeghgmj, pjr cjdprassãj, paquagjs djgtegfjs ma tarrh. Rhrh essj, utelezhdjs ud sjquata, qua pjma sar iaetj gh própreh j`rh cjd udh lhth (ohlãj), ud ch`j ma dhmaerh cjd praojs gh pjgth – ju ud chgj ohlvhgezhmj cjrthmj a mj`rhmj ghs pjgths – a cjgcratj ( ourh 1=). Cursj ma Ramraerj - Hulh 3

Ieourh 11 – Hpeljhgmj tjmh h axtagsãj mh vhlh (j`sarva j

luohr mj ijrdeouaerj).

Sa gãj ijr tjdhmj j mavemj cuemhmj, pjmadjs cjgstruer j hlecarca sj`ra ud ijrdeouaerj. Gassa chsj, quhgmj j pasj tjthl mh cjgstruïãj cfaohr hj sjlj, fhvarè ud rachlqua edamehtj gh raoeãj, a cjdaïhreh h hphracar tregchs ghs phramas. 85


Rhrh avethr qua essj hcjgtaïh, j iugmj mh vhlh mava sar sadpra (hpeljhmj) sjchmj, pjes, sa fjuvar hloud ijrdeouaerj gj ljchl, pjmadjs rasjlvar j prj`ladh h tadpj, htarrhgmj assa ijrdeouaerj ju cjgstruegmj udh veoh ma cjgcratj phrh raijrïhr assa tracfj mh iugmhïãj.

cjgcratj), j quhl pjma sar ma hlvaghreh sad cegth ma hdhrrhïãj ma cjgcratj; asta å j hlehle carca dhes sedplas phrh phramas ma daej-tenjlj a ma ud tenjlj (ourhs 1? a 16).

Axacuïãj mj hlecarca Hpeljhmj tjmj j iugmj mhs vhlhs, pjmadjs egecehr h axacuïãj mj hlecarca, j quhl gãj pjma chr ad cjgthtj meratj cjd j sjlj. Rjr essj, mavadjs ihzar ud lhstrj (`hsa) ma cjgcratj dhorj ma 1 cd ma hlturh phrh raoulhrezhïãj mj iugmj mh vhlh, qua sarè h `hsa mj hlecarca (ourh 19).

Hlecarca sad cegth cegth ma hdhrrhïãj hdhrrhïãj phrh phrh phrama ma ma Ieourh 1? – Hlecarca daej-tenjlj.

cjgcratj dhorj. dhorj. Ieourh 19 – Lhstrj ma cjgcratj

J cjgcratj dhorj å h chdhmh ma cjgcratj irhch, ma `hexh rasestîgceh, praphrhmj cjd pjucj cedagtj, duetj horaohmj a pjuch èouh, cjd udh cjgsestîgceh “ihrjihmh—, cjdj å metj gh cjgstruïãj cevel. J cjgcratj dhorj mava sar praphrhmj cjd js saouegtas cjdpjgagtas>

Ieourh 16 – Hlecarca sad cegth ma hdhrrhïãj phrh phrama

ma ud tenjlj.

H hlvag hlvaghreh hreh cjd cegt cegth h ma hdhrr hdhrrhïãj, hïãj, cjd iarrhoad gh hlturh mj rasphlmj mh iugmhïãj, tad h ghlemhma ma mestreùer, ma dhgaerh ugeijrda, tjmh h chroh a, hssed, h`sjrvar js paquagjs rachlquas phrh avethr tregchs ghs phramas. Assh cegth pjma tar meiaragtas damemhs ad iugïãj mh dhgaerh cjdj sa hssagthd hs hmhs ma tenjljs phrh h ijrdhïãj mh chghlath.

• 8 shcj ma 12 ko ma cedagtj; • 6´ lhths (86 letrjs chmh) ma hraeh dåmeh; • 88´ lhths ma `reth g¾ 0; • 0 lhths ma èouh. Sj`ra assh `hsa ma cjgcratj qua hssagthdjs j hlecarca (tenjljs dhceïjs ju `ljcjs ma Cursj ma Ramraerj - Hulh 3

02


Gassh chghlath, h iarrhoad å cjljchmh gh phrta egiarejr hihsthmh mj iugmj htrhvås ma paquagjs chlïjs. Assa hihsthdagtj å edpjrthgta phrh qua j cjgcratj agtra pjr `hexj, agvjlvagmj tjthldagta assh iarrhoad. Ad saouemh, maspanhdjs j cjgcratj cjd mjshoad ma 8>0´>= (8 lhth ma cedagtj; 0´ lhths ma hraeh orjssh; = lhths ma pamrh g¾ 0) a, mapjes, hmecejghdjs h èouh. Hgtas ma cjgcluer h cjgcrathoad a ma praagcfardjs tjmh h chghlath, cjljchdjs js iarrjs gh phrta suparejr, quhgmj ijr j chsj. Å hcjgsalfèval qua j hssagthdagtj mjs tenjljs phrh h ijrdhïãj mh chghlath sanh iaetj cjd cedagtj a hraeh gh mjshoad ma 3 lhths ma hraeh phrh chmh lhth ma cedagtj. Rjmadjs var, gh ieourh 15 , ud hlecarca phrh phramas ma ud te njlj, ad qua hs lhtarhes qua ijrdhd h chghlath sãj ma ´ tenjlj, a js mjes iarrjs mh cegth ma hdhrrhïãj hprasagthd meàdatrj ma 82 dd (3/6—).

Hlecarca cjd cegth cegth ma hdhrrhïãj hdhrrhïãj ma trîs iarrjs. iarrjs. Ieourh 92 – Hlecarca

Rjmadjs j`sarvhr, gh ieourh 98 , ud hlecarca cjd hs lhtarhe s mh chghlath iaeths cjd quhtrj tenjljs hssagthmjs ad aspalfj. Gh cegth ma hdhrrhïãj, ijrhd cjljchmjs quhtrj iarrjs> mjes egiarejras ma 82 dd ma meàdatrj a mje s suparejras ma 9,3 dd.

Hlecarca cjd cegth cegth ma hdhrrhïãj hdhrrhïãj ma mjes mjes iarrjs. Ieourh 15 – Hlecarca

Gh ieourh 92 , pjmadjs var ud hlecarca cjd hs lhtarhes mh chghlath axacuthmhs cjd mjes tenjljs hssagthmjs ad aspalfj. Gh cegth ma hdhrrhïãj, ijrhd cjljchmjs trîs iarrjs> mjes e giarejras cjd meàdatrj ma 82 dd a ud suparejr cjd meàdatrj ma 9,3 dd (8/=—). Cursj ma Ramraerj - Hulh 3

Ieourh 98 – Hlecarca cjd cegth ma hdhrrhïãj ma quhtrj iarrjs.

J`sarva, ghs ieourhs 90H a @ , js hlecarcas phrh phramas ma daej-tenjlj, cjd cegths ma hdhrrhïãj ma mjes a trîs iarrjs. 08


hdhrrhïãj cjd cjd mjes iarrjs iarrjs ma 6 dd. Ieourh 93 – Cegth ma hdhrrhïãj

Rhrh dhgtar h pjseïãj mjs iarrjs cjljchmjs gh cegth, pjmadjs ushr astre`js cjd asphïhdagtj ma, dhes ju dagjs, 8,22 d ( ieourh 9= ).

Ieourhs 90H a @ – Hlecarcas Hlecarcas phrh phrh phramas phramas ma daej-tenjlj daej-tenjlj cjd cjd

cegth ma hdhrrhïãj ma mjes a trîs iarrjs.

Jutrh dhgaerh ushmh phrh ihzar ud hlecarca ad phramas ma daej-tenjlj å h cegth iaeth cjd mjes iarrjs ma 6 dd (1/89—), cjljchmjs gh hrohdhssh ma hssagthdagtj mh þltedh iehmh ma tenjljs ( ieourh 93 ) . Cursj ma Ramraerj - Hulh 3

Hrdhïãj ma quhtrj quhtrj a trîs iarrjs iarrjs cjd astre`js. astre`js. Ieourh 9= – Hrdhïãj 00


Shphth Cjrremh

Jutrj tepj ma hlecarca, cjd hs dasdhs chrhctarästechs mj hgtarejr, å iaetj cjd `ljcjs chghlaths a muhs cegths ma hdhrrhïãj, sagmj udh ljoj hcedh mh shphth a jutrh gj rasphlmj mj hlecarca ( ieourh 99 ).

H shphth cjrremh å ud tepj ma iugmhïãj i ugmhïãj ma cjgcratj hrdhmj, cjd `hrrhs ma iarrj (varohlfñas) qua pjmad ju gãj sarad djgthmjs cjd astre`js. Alh å egmechmh phrh tarragjs rdas ad vhlhs ma htå 2,92 d ma prjiugmemhma, cjgstruämh sj`ra udh chdhmh ma cjgcratj dhorj lhgïhmj gj iugmj massh vhlh; å sj`ra assh chdhmh qua sãj cjljchmhs hs `hrrhs ma hïj cjd asphïhmjras (chlïjs) phrh qua asths quad suspagshs, a, hssed, aveth-sa j cjgthtj meratj cjd h `hsa ma cjgcratj dhorj. J cjgcratj mava tar trhïj 8>3,1>= (cedagtj>hraeh>`reth), qua mava sar lhgïhmj gh vhlh sj`ra h iarrhoad. Iaetj j lhgïhdagtj, j cjgcratj mava sar asphlfhmj ma dhgaerh ugeijrda a ve`rhmj phrh suh pariaeth hcjdjmhïãj. Axestad aquephdagtjs próprejs phrh j trh`hlfj ma ve`rhïãj mj cjgcratj; chsj h j`rh gãj mespjgfh massas aquephdagtjs, pjmadjs utelezhr h própreh cjlfar ma pamraerj ju sjchr j cjgcratj cjd udh `hrrh ma iarrj.

Hl ecarca cjd `ljcjs chghlath chghlathss a muhs cegths Ieourh 99 – Hlecarca ma hdhrrhïãj.

@hlmrhda Qd axadplj ma axacuïãj ma shphth cjrremh å cjd hlecarca ma tenjljs dhceïjs sj`ra h iugmhïãj, cjd trîs `hrrhs ma iarrj a cjgcratj cjd trhïj 8>3,1>=. Gj rasphlmj mj hlecarca, å cjljchmh udh cegth ma hdhrrhïãj cjd quhtrj `hrrhs cjrremhs, sad astre`js, cjd cjgcratj gj trhïj 8>0,1>=. Gãj mavadjs gjs asquacar ma edpardahèlezhr assa hlecarca ( ourh 91).

J `hlmrhda pjma sar iaetj tjmj ma cjgcratj hrdhmj ju cjd `ljcjs chghlaths htå 2,92 d ma prjiugmemhma, quhgmj j tarragj ijr rda (ourhs 9? a 96).

Hlecarc carca a cjd cjd tenjl tenjljs js cjdu cjdugs gs sj`r sj`ra a h shp shphth hth cjrr cjrremh emh.. Ieourh 91 – Hle Cursj ma Ramraerj - Hulh 3

Ieourh 9? – @hlmrhda ma cjgcratj hrdhmj.

03


Gj chsj mj `hlmrhda sar axacuthmj hj gäval mj sjlj, å pracesj axacu thr ijrdhs phrh cjljchïãj ma hrdhmurhs a, mapjes, axacuthr h cjgcr athoad ( ieourh ?2 ) .

`ljcjs chghlaths. Ieourh 96 – @hlmrhda cjd `ljcjs

Gj chsj ma sjljs ierdas h dhes ma 2,92 d ma prjiugmemhma, j `hlmrhda å iaetj sj`ra `rjchs. Gassa chsj, h iarrhoad mhs `rjchs mava sa agohsthr (adùter) gh iarrhoad mj `hlmrhda ( ieourh 95). hrdhmurh phrh phrh `hlmrhda. `hlmrhda. Ieourh ?2 – Ijrdh a hrdhmurh

Phmear J rhmear, cjdj ije metj hgtas , å udh lhna sj`ra h quhl sa hpjehd hs iugmhïñas, j quhl iugcejgh thd`åd cjdj cjgtrhpesj a chlïhmh. Ala só mava sar axacuthmj sa tjmj j tarragj ijr sjlj ierda; tarragjs cjd phrtas ierdas a irhchs gãj pjmad sar utelezhmj s phrh axacuïãj ma rhmear. Assa tepj ma iugmhïãj mava jcuphr tjmh h medagsãj mh j`rh, dhes j axcamagta phrh chlïhmhs ad suh vjlth. Madhrchmj assa asphïj, ra`hexhdjs j sjlj ad 82 cd a cjgstruädjs, ad tjmh suh vjlth, udh ijrdh ma dhmaerh. Gj iugmj, njohdjs udh chdhmh ma `reth a, sj`ra alh, udh chdhmh `hsa ma cjgcratj dhorj. Sj`ra assh chdhmh, cjljchdjs hs `hrrhs ma iarrj gjs mjes sagtemjs a maspanhdjs j cjgcratj ijrta cjd trhïj 8>1>9´ (cedagtj>hraeh>`reth), cjd aspassurh ma 80 cd ( ieourh ?8 ) .

`rjchs. Ieourh 95 – @hlmrhda sj`ra `rjchs. Cursj ma Ramraerj - Hulh 3

0=


Gjs `hlmrhdas, hs cegths ma hdhrrhïãj gãj sãj gacassèrehs pjrqua asta mestreùe h chroh a supjrth pjssävaes hssagthdagtjs (“hcjdjmhïñas—) qua jcjrrad gh cjgstruïãj. Assas hssagthdagtjs hcjgtacad ghs phramas a iugmhïñas quhsa sadpra ad macjrrîgceh ma prj`ladhs gh rasestîgceh mj sjlj. Egialezdagta, å `hsthgta cjdud vareiechrdjs, ad cjgstruïñas gjvhs, paquaghs tregchs palhs phramas. Cjgtumj, å pjssäval cjgsarthr assas maiaetjs phrh gãj tjrghrad h hcjgtacar. Hs rhcfhmurhs hcjgtacad mavemj â hcjdjmhïãj mj cjrpj mh chsh. Hssed, Hss ed, pjma p jmadjs djs var va r h edpjrt edpj rtàgce àgceh h mhs cegths ma hdhrrhïãj iaeths ma cjgcratj hrdhmj gj rasphlmj mhs iugmhïñas. Essj ihz cjd qua h chroh trhgsdetemh palhs phramas sanh àd mestreùämh, h`sjrvagmj, pjr cjgsaquîgceh, hs pjssävaes maieceîgcehs ma rasestîgceh mj sjlj, hlåd ma avethr j hphracedagtj ma tregchs. Hs ceg cegths ths ma hdhr hdhrrhï rhïãj ãj cjgs cjgstru truämh ämhss hj ljgoj ma tjmj j rasphlmj, pjtagcehldagta hdhrrhrãj tjmhs hs phramas agtra se, prjpjrcejghgmj cjgsemarèval reoemaz, supjrthgmj, pariaethdagta, paquagjs rachlquas sad h`hlhr hs iugmhïñas.

Phmear. Ieourh ?8 – Phmear.

J rhmear mava sar àd gevalhmj a edpardahèlezhmj cjd udh chdhmh ma hrohdhssh ma gevalhdagtj cjd edpardahèlezhgta. Ala å axacuthmj ad j`rhs sedplas sad pelhras a lhna suparejr; gj agthgtj, hlougs cjgstrutjras cjstudhd lavhgthr asparhs gh iarrhoad `hsa mhs phramas phrh axacuthr js pelhras a, avagtuhldagta, hs lhnas. Gh axacuïãj mj rhmear, hgtas mh cjgcrathoad, å edpjrthgta maexhr prjgtjs h tuùlhïãj ma èouh a ma asojtj, js rhljs atc.

Hlecarcas ad ]arragjs Egcleghmjs

Cegths ma Hdhrrhïãj

Ad tarragjs egcleghmjs, j hlecarca gãj pjma hcjdphgfhr suh egcleghïãj, pjes pjma jcjrrar ascjrraohdagtj ju maslezhdagtj mh hlvaghreh hssagthmh sj`ra j hlecarca ( ieourh ?0 ) .

Rhrh j`rhs ma paquagj pjrta cjdj chshs tårrahs a sj`rhmjs, hs cegths ma hdhrrhïãj sãj edpjrthgtas phrh js rasphlmjs mh iugmhïãj. H axacuïãj masshs cegths å gacassèreh pregcephldagta ghs cjgstruïñas ad qua hs hlvaghrehs sarãj iaeths cjd tenjljs dhceïjs ju caràdecjs, `ljcjs ma cjgcratj gãj astruturhes a jutrjs dhtarehes ma pjuch rasestîgceh; essj pjrqua, gasshs cjgstruïñas, js dhtarehes sãj suceagtas hpaghs âs paquaghs chrohs ushmhs gj macjrrar mj sarveïj, gãj rasestegmj h paquagjs rachlquas qua pjmad jchsejghr tregchs ghs phramas. Cursj ma Ramraerj - Hulh 3

Hlecarca eghmaquhmj eghmaquhmj phrh phrh tarragj egcleghmj. egcleghmj. Ieourh ?0 – Hlecarca 01


Egsthlhïñas Su`tarràgahs

Rhrh assas chsjs, j hlecarca mava sar axacuthmj ad vhlhs aschljghmhs (maorhus) – ourh ?3.

Rhrh egsthlhïñas su`tarràgahs cjdj asojtj, egsthlhïñas alåtrechs, ma oès a ma talaijga, mavadjs ihzar ghs iugmhïñas, ma ud djmj oarhl, udh phsshoad phrh asshs egsthlhïñas cjd egmapagmîgceh, estj å, sad cjgthtj räoemj agtra j hlecarca a j tu`j ma phsshoad masshs leohïñas. Rjr axadplj, ud tu`j ma asojtj gãj pjma pardhgacar iexj gj hlecarca, pjes quhlquar djvedagtj massa hlecarca, pjr dagjr qua sanh, pjmarè jchsejghr tregchs gassa tu`j, prjvjchgmj vhzhdagtjs. Gassa chsj, ushdjs ud tu`j ma dhejr meàdatrj cfhdhmj chdesh iexhmj gj hlecarca, magtrj mj quhl vhe cjrrar j tu`j ma asojtj (ieourh ?9). Ad egsthlhïñas cjd iejs cjgmutjras, uteleza tu`js ilaxävaes.

Ieourh ?3 – Hlecarca Hlecarca aschljghmj. aschljghmj.

H hltltu urh mjs maorh rhu us gãj mava ultltrrhphss ssh hr 12 cd ma hlturh; chsj cjgtrèrej, fhvarè duetj asijrïj lhlhtarhl gj tarragj jchsejghmj palj pasj mh phrama qua sa hpjeh gj maorhu ma cedh. Xuhgmj essj hcjgtaca, j pareoj ma ascjrraohdagtj å edegagta (ourh ?=).

Ieourh ?= – Asijrïj lhtarhl lhtarhl qua jcjrra jcjrra ad maorhus maorhus hltjs.

Gj chsj ma h egcleghïãj mj tarragj sar suparejr h 82%, hs iugmhïñas mavad sar axacuthmhs sj`ra asthchs cjgijrda pjmadjs var gh ourh ?1. ]u`j ma asojtj magtrj ma udh udh chdesh. Ieourh ?9 – ]u`j

Edpardahèlezhïãj Edpardahèlezhr seogeiech hplechr prjmutjs aspacäiecjs qua ijrdhd udh chdh mh ma prjtaïãj, gãj pardetegmj h phsshoad ma èouh ju udemhma mhs iugmhïñas phrh h hlvaghreh. Js tenjljs dhceïjs ju caràdecjs sãj pjrjsjs, ju sanh, hprasagthd jreiäcejs ad suh cjgstetueïãj. Massa djmj, ad cjgthtj cjd h èouh, alas iechd agcfhrchmjs, pjes h udemhma jcuph tjmjs js jreiäcejs agcjgtrhmjs galas.

Iugmhïñas sj`ra asthchs. asthchs. Ieourh ?1 – Iugmhïñas Cursj ma Ramraerj - Hulh 3

09


H dasd dasdh h cje cjesh sh hcjg hcjgtac taca a cjd h hlv hlvaaghreh ma iugmhïãj, qua iech ad cjgthtj cjd h tarrh. Gassa chsj, h hlvaghreh iech agcfhrchmh pjrqua j tarragj qua sa agcjgtrh h`hexj mh supariäcea å sadpra þdemj, a assh udemhma å h`sjrvemh rhpemhdagta palh pjrjsemhma mh própreh hlvaghreh, sad asquacar ma qua h èouh mh cfuvh thd`åd pjma cjgtreùer phrh agcfhrchr h astruturh, pagatrhgmj gj sjlj a udamacagmj hegmh dhes j tarragj. H astrut ast ruturh urh mh iug iugmhï mhïãj, ãj, san sanh h ma m a hlva h lva-ghreh ju ma cjgcratj, sa tevar pjrjsemhma, vhe h`sjrvar tjmh h èouh a udemhma mj sjl j a, ihthldagta, fhvarè egieltrhïãj gh shphth, gh hlvaghreh, gh cegth ma hdhrrhïãj, gj `hlmrhda a gh hlvaghreh ma alavhïãj. Rhrh avethr j prj`ladh ma udemhma hscagmagta, gh quhl å h èouh qua pagatrh gjs pjrjs mjs cjdpjgagtas mhs iugmhïñas ju hlecarcas a vhe suègmj palh hlvaghreh ma vamhïãj htå prjvjchr udemhma gasshs iugmhïñas h udh hlturh ma 8,12 d, å pracesj edpardahèlezhr hs iugmhïñas.

H cjgsestî cjgse stîgce gceh h massh mas sh hrohd hr ohdhss hssh h edpardahèlezhgta mava sar rhzjèval; pjrthgtj, å gacassèrej tar cuemhmj cjd h quhgtemhma ma èouh utelezhmh. Gh hplechïãj mh hrohdhssh, cjljchdjs thleschs (pamhïjs ma dhmaerh ju ma caràdech) gh aspassurh qua sa masanh phrh h chdhmh ma hrohdhssh edpardahèlezhmjrh; h aspassurh dèxedh racjdagmhmh å ma 0 cd – ieourh ??.

H edpardahèlezh edpardahèlezhïãj ïãj mava mava sar iaeth iaeth hgtas ma axacuthr h hlvaghreh ma alavhïãj. Rraphrhdjs udh hrohdhssh ma cedagtj cjd hraeh lhvhmh gh mjshoad 8>3 cjd 8 ko ma edpardahèlezhgta. Ma pregcäpej, desturhdjs h sacj h hraeh cjd j cedagtj a, gh èouh mj praphrj mh hrohdhssh, hmecejghdjs j edpardahèlezhgta. Rjmadjs ushr, cjdj edpardahèlezhgta, j Yamhcet ®, qua å udh phsth `rhgch hplechmh gh desturh mj cedagtj a hraeh, ju cedagtj a chl, sadpra meluämj gh èouh phrh sar ushmj. Hplechmj gh desturh, creh-sa udh hrohdhssh qua edpama h hïãj mh èouh. J Yamhcet®, hssed cjdj quhlquar jutrj edpardahèlezhgta, å agcjgtrhmj ad mapósetjs ma dhtarehes ma cjgstruïãj. Js hmetevjs edpardahèlezhgtas ijrgacemjs pjr mevarsjs ih`rechgtas pjssuad htreùtjs próprejs. Rjr essj, suoaredjs qua j pamraerj seoh reojrjshdagta h racjdagmhïãj quhgtj â mjshoad a hplechïãj, egmechmh ghs ad`hlhoags mjs prjmutjs. Cursj ma Ramraerj - Hulh 3

Ieourh ?? – Hp Hplele ch ïã j ma hr oh ohdh dh ss h cj cjd d ed pa pard rd ah èlezhgta.

Cjdj messadjs, h aspassurh dèxedh mh hrohdhssh mava sar ma 0 cd. Sa ultrhphsshr assh damemh, j ravastedagtj pjma tregchr cjd dhes ihcelemhma, pjes ala cjgtåd duetj cedagtj. Hssed fhvarè h phsshoad mh udemhma palhs tregchs; massh dhgaerh, racjdagmhdjs udh aspassurh ma 8,1 cd. Assh hrohdhssh mava sar prjljgohmh, ravastegmj hs lhtarhes mj hlecarca gudh ihexh ma 82 h 81 cd ma lhrourh, cjd cuemhmj phrh hrramjgmhr js chgtjs cjgijrda pjmadjs var gh ieourh ?6 . 0?


Chdh dhmh mh ma ed edpa pard rdah ahè èlelezh zhgt gta a gj ra rasp sphl hlmj mj mj hl hlec ecar arca ca.. Ieourh ?6 – Ch

Edpardah dahèl èlezh ezhïãj ïãj ad tjm tjmh h h axta axtagsã gsãj j mj mj hleca hlecarca rca.. Ieourh 62 – Edpar

Rhrh hplechr h hrohdhssh ghs lhtarhes, racjdagmhdjs h cjljchïãj ma udh råouh (pjma sar udh tèùh) hpjehmh gh supariäcea. H aspassurh mh hrohdhssh mava hvhgïhr phrh hs lhtarhes, h quhl mava tar, gj dèxedj, 0 cd (ourh ?5).

Gj chsj mh veoh `hlmrhda hssagthmh sj`ra `rjchs ju asthchs, h hplechïãj mj edpardahèlezhgta å iaeth ad tjmh h veoh mh dasdh dhgaerh, dhs, ad oarhl, utelezhdjs h dhgth edpardahèlezhgta läquemh, hplechmh cjd pegcal. Cjdj messadjs, h chdhmh iegh ma hrohdhssh tad dhes cfhgca ma gãj tregchr, dasdj sagmj hplechmh ad mehs quagtas. Dhs, sa jcjrrarad tregchs, pjmadjs hplechr trîs madãjs ma tegth hsièltech sj`ra tjmhs hs ihlfhs prjvjchmhs palhs tregchs, utelezhgmj udh `rjxh. Rhrh dhejr ohrhgteh ma qua h cjgstruïãj iequa àd prjtaoemh cjgtrh udemhma, racjdagmhdjs qua, palj dagjs, hs muhs ju trîs predaerhs iehmhs mh hlvaghreh ma alavhïãj sanh cjd hrohdhssh ma cedagtj a hraeh cjd edpardahèlezhgta. Iaeth h edpardahèlezhïãj, axacuthdjs j htarrj, thdphgmj hs vhlhs mhs iugmhïñas. Mavadjs aiatuhr j htarrhdagtj ad chdhmhs a sjchr àd h tarrh qua mava sar ma `jh quhlemhma, sad rhäzas, ijlfhs ju rasämujs cjdj lhths, plèstecjs atc. ( ieourh 68 ) .

Hrohdhssh ghs ghs lhtarhes. Ieourh ?5 – Hrohdhssh

Assh edpardahèlezhïãj mava sar iaeth ad tjmj j hlecarca (ourh 62). Cursj ma Ramraerj - Hulh 3

06


Htarrj. Ieourh 68 – Htarrj.

Edpardahèlezhïãj cjgcluämh. cjgcluämh. Ieourhs 63H a @ – Edpardahèlezhïãj

J`sarvhïñas • H edpardah edpardahèlez èlezhïãj hïãj å udh athph edpjrthgta gh j`rh. Rjr essj, mava sar àd iaeth a raspaethr hs racjdagmhïñas mh ad`hlhoad mjs prjmutjs. • Gãj å `jd qua sa ihïh h edpardahèlezhïãj ad tadpj cfuvjsj. Mavadjs houhrmhr h dalfjrh mj tadpj.

H sa saou ouer er,, van vanh h ed edho hoag agss qua qua elelus ustr trhd hd h edp edpar ar-dahèlezhïãj mj `hlmrhda a j egäcej mj hssagthdagtj mh hlvaghreh sj`ra asta (ourhs 60 h 61).

Hssagthdagtj mh mh hlvaghreh. hlvaghreh. Ieourhs 6=H a @ – Hssagthdagtj Edpardahèlezhgmj cjd h tregcfh. tregcfh. Ieourh 60 – Edpardahèlezhgmj

Ljchlezhïãj mjs pelhras. pelhras. Ieourh 61 – Ljchlezhïãj Cursj ma Ramraerj - Hulh 3

05


Yanh sa Hpragmau 8. Ljchr udh j`rh seogech phsshr phrh j tarragj>

h) ( `) ( c) ( m) (

) sjdagta sjdagta j parädatrj mh j`rh. ) j thdhgfj ghturhl mhs mhs plhgths plhgths mj prjnatj ) só h plhgth plhgth mhs mhs mevesñas mevesñas egtarghs. ) dathma mhs plhgths mj prjnatj.

0. Hsseghla (Y) phrh varmhmaerj a (I) phrh ihl sj; ad saouemh, dhrqua h hltarghtevh

cjrrath. E - ( ) H ljchïãj pjr chvhlatas å egmechmh ad j`rhs ma paquagj pjrta cjdj hrdhzåd, ohrhoad, amäculh atc. EE - ( ) Qdh mhs masvhgthoags mh ljchïãj pjr chvhlatas å j usj ma duetj dhtarehl. EEE - ( ) H ljchïãj pjr thàerhs å egmechmh ad j`rhs dhejras cjdj pråmejs. EY - ( ) H thàerh thd`åd å cjgfacemh cjdj tèùh cjrremh. h) ( `) ( c) ( m) (

) I– Y–Y –I ) Y–Y –I–I ) Y– I–Y –Y ) I– I–Y –I

3. Qdh mhs iarrhdagths qua pjmadjs utelezhr phrh axacuthr vhlhs å h>

h) ( `) ( c) ( m) (

) pè. ) dhrrath. ) agxhmh. ) chvhmjrh.

=. Qdh mhs iugmhïñas meraths å>

h) ( `) ( c) ( m) (

) h asthch ma dhmaerh. ) j `hlmrhda. ) j tuùlãj. ) h asthch ma cjgcratj.

1. H shphth cjrremh å ud tepj ma iugmhïãj ma cjgcratj hrdhmj cjd>

h) ( `) ( c) ( m) (

) `hrrhs ma iarrj. ) `reth. ) asthch ma dhmaerh. ) pamraoulfj pamraoulfj..

Cursj ma Ramraerj - Hulh 3

32


9. J qua mavadjs ihzar ghs iugmhïñas phrh prjtaoar h hlvaghreh cjgtrh h phsshoad ma

èouh ju ma udemhma: h) ( `) ( c) ( m) (

) Cjgcrathr. ) Hplechr hzulanjs. ) Edpardahèl Edpardahèlezhr. ezhr. ) Pa`jchr.

Paspjsths mj Yanh sa Hpragmau – Hulh 0 8. h;

0. `;

3. m;

=. `;

1. `;

9. c.

?.

80,12 d

d 2 2 , 0 8

d 2 2 , 0 8

d 2 2 , 9

?,12 d H 4 80 + 9 x ?,1 0

H 4 80,1 80,1 x 80

?,12 d d 2 2 , 0 8

H 4 80 80 + ?,1 0

H 4 812,22 d°

H 4 5 x ?,1

H 4 52 52 0

H 4 9?,12 d° H 4 =1,22 d°

]jthl> 9?,1 + 812 + =1 4 090,12 d°

Cursj ma Ramraerj - Hulh 3

38


Curso de Pedreiro - Aula 03

Recommend Documents