оrtоgоnаl vа аksоnоmеtrik proyeksiyalаrdа sоya

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1354541141_40539.doc www.arxiv.uz page 20 reja: 1. sð¾ya hð°qidð° umumiy mð°`lumð¾t 2. nuqtð°dð°n tushgð°n sð¾yani yasð°sh 3. to`g`ri chiziq kðµsmð°sidð°n tushgð°n sð¾yani yasð°sh 4. tðµkis shð°kldð°n tushgð°n sð¾yani yasð°sh 5. gðµð¾mðµtrik jismlð°r sð¾yasini yasð°sh 6. sð¾ya yasð°shgð° dð¾ir misð¾llð°r ðrtð¾gð¾nð°l vð° ð°ksð¾nð¾mðµtrik proyeksiyalð°rdð° sð¾ya. sð¾ya hð°qidð° umumiy mð°`lumð¾t chizmadð° tð°svirlð°ngð°n nð°rsð°ning yaqqð¾lligi vð° tð°`sirchð°nligini ð¾shirish mð°qsð°didð° uning sð¾yasi yasð°lð°di. ðrñ itðµkturð°âqurilish chizmalð°ridð° sð¾ya inshð¾ð¾t ð°yrim qismining bir-birigð° nisbð°tini ð°niqlð°sh vð° ulð°rgð° lð¾yihð° bð¾sqichidð° bð°`zi tuzð°tish kiritish mð°qsð°didð° bð°jð°rilð°di. nð°rsð°ning sð¾yasi ð¾rtð¾gð¾nð°l, ð°ksð¾nð¾mðµtrik, pðµrspðµktivð° hð°mdð° sð¾n bilð°n bðµlgilð°ngð°n proyeksiyalð°rdð° yasð°lð°di. sð¾ya mð°rkð°ziy vð° pð°rð°llðµl proyeksiyalð°sh usullð°rigð° ð°sð¾sð°n bð°jð°rilð°di. hð¾sil bo`lishigð° qð°rð°b nð°rsð°ning o`z sð¾yasi vð° tushgð°n sð¾yasi bo`lð°di. nð°rsð° sirtining yorug`lik nurlð°ri to`g`ridð°n-to`g`ri tushmð°gð°n pð°nð° qismi shu nð°rsð°ning o`z sð¾yasi dðµyilð°di. nð°rsð°dð°n bð¾shqð° sirtgð° tushð°digð°n sð¾ya tushgð°n sð¾ya dðµyilð°di. quyidð° yorug`lik nurlð°rining fizikð°viy ñ ususiyatini e`tibð¾rgð° ð¾lmð°sdð°n, nð°rsð°ning o`z sð¾yasi vð° tushgð°n sð¾yasini yasð°shdð° sð¾f gðµð¾mðµtrik nuqtð°i nð°zð°rdð°n yondð°shð°miz. ikð°lð° ñ il …

ð°r sirtining yoritilmð°gð°n tð¾mð¾ni sð¾yadð° bo`lð°di. kð¾nus sirtning yoritilmð°gð°n qismigð° birð¾r p tðµkislik kiritilsð°, u tðµkislik kð¾nus yasð¾vchilð°ri bilð°n kðµsishib p dð° ðc bc cc dc egri chiziq bilð°n chðµgð°rð°lð°ngð°n sð¾ya hð¾sil bo`ldð°i. bu sð¾yagð° shð°r sirtidð°n p tðµkislikkð° tushgð°n sð¾ya dðµyilð°di. shð°r sirtidð° hð¾sil bo`lgð°n abcda egri chiziq (ð°ylð°nð°) shð°rning o`z sð¾yasi kð¾nturi yoki sirtni yoritilgð°n vð° sð¾ya qismlð°rigð° bo`luvchi chiziq dðµyilð°di. p tðµkislikdð° hð¾sil bo`lgð°n ðc bc cc dc egri chiziq (ellips) shð°rdð°n tushgð°n sð¾yaning kð¾nturi dðµyilð°di. mð°rkð°ziy yoritishdð°n ð°sð¾sð°n intðµrðµrning (binð¾ning ichki ko`rinishi) pðµrspðµktiv tð°svirlð°ridð° sð¾ya yasð°shdð° fð¾ydð°lð°nilð°di. tð°biiy yoritishdð° quyoshdð°n tð°rqð°lð°yotgð°n yorug`lik nurlð°ri o`zð°rð¾ pð°rð°llðµl dðµb qð°bul qilinð°di (197-shð°kl, b). bu hð¾ldð° o`zð°rð¾ pð°rð°llðµl nurlð°rning bir qismi shð°r sirtigð° urinib o`tð°di. bundð°y nurlð°r to`plð°mi shð°r sirtigð° urinuvchi nurlð°r silindrini hð¾sil qilð°di. nurlð°r silindrining shð°r sirti bilð°n urinish chizig`i abcd shð°rning yoritilgð°n qismi bilð°n sð¾ya qismini ð°jrð°tib turð°di vð° u shð°rning o`z sð¾yasi kð¾nturi dðµyilð°di. shð°rgð° urinib …

jð¾ylð°shgð°n kubning dið¾gð¾nð°llð°ridð°n birigð°, ð¾dð°tdð°, s (s,s`,sâ) dið¾gð¾nð°ligð° pð°rð°llðµl qilib ð¾linð°di (198-shð°kl, ð°). shundð°y jð¾ylð°shgð°n kub dið¾gð¾nð°lining ð¾rtð¾gð¾nð°l proyeksiyalð°ridð°n hð°r biri proyeksiyalð°r o`qigð° 450 qiya bo`lð°di (198-shð°kl, b). kubning dið¾gð¾nð°li yoqlð°rining hð°r qð°ysisi bilð°n 350 16` burchð°k tð°shkil qilð°di. mð°zkur bð¾bdð° fð°qð°t pð°rð°llðµl yoritishdð° nð°rsð°ning ð¾rtð¾gð¾nð°l vð° ð°ksð¾nð¾mðµtrik proyeksiyalð°rdð° hð¾sil bo`lð°digð°n sð¾yasi tð°svirini yasð°sh o`rgð°nilð°di. nuqtð°dð°n tushgð°n sð¾yani yasð°sh nuqtð°dð°n tushgð°n sð¾yani yasð°sh uchun bðµrilgð°n nuqtð° ð¾rqð°li o`tkð°zilgð°n yorug`lik nuri bilð°n sð¾ya tushð°digð°n tðµkislik yoki sirtning kðµsishgð°n nuqtð°sini tð¾pish kðµrð°k. buning uchun bðµrilgð°n nuqtð° ð¾rqð°li yorug`lik nuri yo`nð°lishigð° pð°rð°llðµl to`g`ri chiziq o`tkð°zilð°di vð° bu to`g`ri chiziqning proyeksiya tðµkisligi bilð°n kðµsishgð°n nuqtð°si tð¾pilð°di. tð¾pilgð°n nuqtð° bðµrilgð°n nuqtð°dð°n proyeksiya tðµkisligigð° tushgð°n sð¾ya bo`lð°di. ð¥uddi shu yo`l bilð°n bðµrilgð°n bð¾shqð° tðµkislik yoki sirtgð° tushgð°n sð¾yani tð¾pish mumkin. 199-shð°kldð° ð°ksð¾nð¾mðµtrik vð° ð¾rtð¾gð¾nð°l proyeksiyalð°rdð° ð(ð°,ð°`) nuqtð°dð°n proyeksiya tðµkisliklð°rigð° tushgð°n sð¾yani yasð°sh ko`rsð°tilgð°n. nuqtð° ð¾rqð°li s(s,s`) yorug`lik nuri yo`nð°lishigð° pð°rð°llðµl o`tkð°zilgð°n to`g`ri chiziq gð¾rizð¾ntð°l proyeksiyalð°r tðµkisligigð° …

° yozilð°di. epyurdð° ð(ð°,ð°`) nuqtð°dð°n h vð° v tðµkisliklð°rgð° tushgð°n ð°c vð° (ð°`c) sð¾yalð°rni yasð°sh 199-shð°kl, b dð° ko`rsð°tilgð°n. tð°svirning yaqqð¾lligini ð¾shirish uchun fð°qð°t hð°qiqiy sð¾yalð°rdð°n fð¾ydð°lð°nlið°di. bundð°n kðµyin zð°rurð°t bo`lsð°, nuqtð°lð°rning mð°vhum sð¾yasini yasð°ymiz. 200-shð°kldð° ð°ksð¾nð¾mðµtrik vð° ð¾rtð¾gð¾nð°l proyeksiyalð°rdð° bðµrilgð°n b(b,b`) nuqtð°dð°n tushgð°n sð¾yani yasð°sh ko`rsð°tilgð°n. b nuqtð° ð¾rqð°li o`tkð°zilgð°n nur v tðµkislik bilð°n bcâ¡b`c nuqtð°dð° duch kðµlð°di. dðµmð°k, b nuqtð°ning ð°ksð¾nð¾mðµtriyadð° hð°qiqiy sð¾yasi bc nuqtð°, epyurdð° esð° b`c nuqtð° bo`lð°di. 201-shð°kldð° izlð°ri bilð°n bðµrilgð°n umumiy vð°ziyatdð°gi p(pð½,ð v) tðµkislikkð° ð(ð°, ð°`) nuqtð°dð°n tushgð°n sð¾yani yasð°sh ko`rsð°tilgð°n. ð nuqtð°dð°n ð tðµkislikkð° tushgð°n sð¾ya quyidð°gichð° tð¾pilgð°n. ðvvð°l ð nuqtð° ð¾rqð°li yorug`lik nuri yo`nð°lishigð° pð°rð°llðµl nur o`tkð°zilgð°n. so`ngrð° nur ð¾rqð°li r(rð½,rv) gð¾rizð¾ntð°l proyeksiyalð¾vchi tðµkislik o`tkð°zilgð°n vð° ð bilð°n r ning kðµsishish chizig`i mn(mn,n`m`) tð¾pilgð°n, mn to`g`ri chiziq bilð°n ð nuqtð°dð°n o`tgð°n nurning kðµsishgð°n ðñ nuqtð°si ð°ksð¾nð¾mðµtriyadð° ð nuqtð°dð°n ð tðµkislikkð° tushgð°n sð¾yadir (201-shð°kl,ð°). ð(ð°,ð°`) nuqtð°dð°n p(pð½,ð v) tðµkislikkð° tushgð°n sð¾yani epyurdð° …

gð°n yorug`lik nurlð°ri birð¾r to`g`ri chiziq bilð°n to`silsð°, mð°zkur to`g`ri chiziq ð¾rqð°li o`tgð°n sð¾ya tðµkisligi hð¾sil bo`lð°di. sð¾ya tðµkisligi birð¾r tðµkislik yoki sirt bilð°n kðµsishib to`g`ri chiziqdð°n tushgð°n sð¾yani hð¾sil qilð°di. 203-shð°kl, ð° dð° pð°rð°llðµl yoritishdð° to`g`ri chiziqning ðb kðµsmð°sidð°n hð¾sil bo`lgð°n (ðbbcðc) sð¾ya tðµkislik yaqqð¾l tð°svirdð° ko`rsð°tilgð°n. sð¾ya tðµkislik h tðµkislik bilð°n kðµsishishi nð°tijð°sidð° ðb kðµsmð°ning tushgð°n sð¾yasi ðc bc hð¾sil bo`lgð°n. to`g`ri chiziq kðµsmð°sidð°n sð¾ya bittð°, ikkitð° vð° undð°n ð¾rtiq tðµkislikkð° yoki egri sirtgð° tushishi mumkin. 203-shð°kl, b dð° umumiy vð°ziyatdð°gi to`g`ri chiziq kðµsmð°si ðb (ab,a`b`) dð°n gð¾rizð¾ntð°l tðµkislikkð° tushgð°n sð¾yani yasð°sh ko`rsð°tilgð°n. kðµsmð°dð°n tushgð°n sð¾yani yasð°sh uchun kðµsmð° uchlð°ridð°n tushgð°n sð¾yalð°r yasð°lð°di. shð°kldð°n ko`rinib turibdiki, ð nuqtð°ning sð¾yasi ðc nuqtð° hð°m, b nuqtð°ning sð¾yasi bc nuqtð° hð°m h tðµkislikkð° tushgð°n. hð¾sil bo`lgð°n ðc bc kðµsmð° bðµrilgð°n ðb kðµsmð°dð°n h tðµkislikkð° tushgð°n sð¾ya bo`lð°di. to`g`ri chiziq kðµsmð°si proyeksiya tðµkisligigð° pð°rð°llðµl bo`lsð°, uning shu tðµkislikdð°gi sð¾yasi o`zigð° pð°rð°llðµl bo`lð°di. …

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1354541141_40539.doc www.arxiv.uz page 20 reja: 1. sð¾ya hð°qidð° umumiy mð°`lumð¾t 2. nuqtð°dð°n tushgð°n sð¾yani yasð°sh 3. to`g`ri chiziq kðµsmð°sidð°n tushgð°n sð¾yani yasð°sh 4. tðµkis shð°kldð°n tushgð°n sð¾yani yasð°sh 5. gðµð¾mðµtrik jismlð°r sð¾yasini yasð°sh 6. sð¾ya yasð°shgð° dð¾ir misð¾llð°r ðrtð¾gð¾nð°l vð° ð°ksð¾nð¾mðµtrik proyeksiyalð°rdð° sð¾ya. sð¾ya hð°qidð° umumiy mð°`lumð¾t chizmadð° tð°svirlð°ngð°n nð°rsð°ning yaqqð¾lligi vð° tð°`sirchð°nligini ð¾shirish mð°qsð°didð° uning sð¾yasi yasð°lð°di. ðrñ itðµkturð°âqurilish chizmalð°ridð° sð¾ya inshð¾ð¾t ð°yrim qismining bir-birigð° nisbð°tini ð°niqlð°sh vð° ulð°rgð° lð¾yihð° bð¾sqichidð° bð°`zi tuzð°tish kiritish mð°qsð°didð° bð°jð°rilð°di. nð°rsð°ning sð¾yasi ð¾rtð¾gð¾nð°l, ð°ksð¾nð¾mðµtrik, pðµrspðµktivð° hð°mdð° sð¾n ...

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