manal kanakkukoottal

bii. sii. moonnaam noottaandile purathana greak ganithashaasthranjanaaya archemidies rachicha oru kruthiyaanu sand reconnor (πσαντες πσανπιτες, πσανπιτες πσανπιτες), athil prapanchavumaayi poruthappedunna manal kanangalude ennathinu oru uyarnna paridhi nirnnayikkaan addeham purappettu. ithu cheiyunnathinu, samakaalika maathruka anusarichu prapanchatthinte valippam kanakkaakkukayum valare valia samkhyakalekkurichu samsaarikkanulla oru maargam kandupidikkukayum cheyyendathundu. 
laattin bhashayil "aranarius" ennum ariyappedunna eee kruthi ekadesham ettu pejukal dairkhyamulla vivarthanamaan, ithu sirakusan rajaavaaya gelo randaamane (hairo randaamante makan) abhisambodhana cheiyunnu. aarkkimideesinte ettavum axus cheyyaavunna srishtiyaayi ithu kanakkaakkappedunnu.
valia samkhyakalkku peru nalkuka.
aadyam, valia samkhyakalkku peridunnathinulla oru samvidaanam archemediesinu kandupidikkendivannu. akkaalat upayogichirunna samkhyaasampradaayam ennamatta samkhyakal (ruyers-10,000) vare prakadippikkaan kazhiyumaayirunnu, koodaathe "ennamatta" enna vaakk upayogikkunnathiloode, ellah samkhyakalkkum ennamatta ennangal (108) vare peridunnathilekku ithu udan vyaapippikkaan kazhiyum. archemidies 108 vareyulla samkhyakale "phastt oordar" ennu vilikkukayum 108 neey "second oordarinte yoonit" ennu vilikkukayum cheythu. eee yoonittinte gunithangal pinneedu randaam kramamaayi maari, eee yoonit vare ennamatta thavana, 108·108 = 1016 eduthu. ithu "moonnaam kramatthinte yoonit" aayi maari, athinte gunithangal moonnaam kramamaayirunnu, angane. 108-aamm kramatthinte yoonittinte ennamatta madangu vare archemidies eee reethiyil samkhyakalkku peridunnathu thudarnnu.iii., (108) ^ (108)
ithu cheythathinushesham, archemidies thaan nirvachicha utharavukale "aadya kaalaghattatthile kramangal" ennu vilikkukayum avasaanatheth "formula _ 1", "randaam kaalaghattatthinte yoonit" ennu vilikkukayum cheythu. thudarnnu aadyakaalakhattathile kramangal nirmmicha reethikk samanamaaya reethiyil eee yoonittinte gunithangal eduthu addeham randaam kaalaghattatthile kramangal nirmmichu. eee reethiyil thudarnnukondu addeham oduvil ennamatta-misttar kaalaghattatthile utharavukalil ethi. archemidies namakaranam cheytha ettavum valia samkhya eee kaalaghattatthile avasana samkhyayaayirunnu, athaayath
eee samkhyaye vivarikkunnathinulla mattoru maarggam (hraswa skeyil) enpathu kwaadrilyan (80·1015) poojyangal pinthudarunna onnaanu.
aarkkimideesinte samvidaanam adisthaana 108 ulla oru sthaana samkhyaa samvidaanathe anusmarippikkunnu, kaaranam purathana greekkukaar samkhyakal ezhuthaan valare lalithamaaya oru samvidaanam upayogichirunnu, ithu 1 muthal 9 vareyulla unitukalkku aksharamalayile 27 vyathyastha aksharangal upayogikkunnu, 10 muthal 90 vareyulla unitukal, noorukanakkinu 100 muthal 900 vareyulla unitukal.
10-nte sakthikal kaikaaryam cheiyunnathinu aavashyamaaya formula _ 3 enna ghaathaamkangalude niyamavum archemidies kandethukayum theliyikkukayum cheythu.
prapanchatthinte valippathinte kanakk.
prapanchatthe niraykkaan aavashyamaaya manal kanangalude ennathinu oru uyarnna paridhi archemidies kanakkakki. ithu cheiyunnathinu addeham saamosile aristaarkkasinte suryakendra maathruka upayogichu. aristaarkkasinte yadhaartha kruthi nashtappettu. ennirunnaalum, bhoomi sooryane parikramanam cheyyumbol suuryan anangathe thudarunna addehathinte sidhaanthathekkurichulla avasheshikkunna churukkam chila paraamarsangalil onnaanu aarkkimideesinte eee kruthi. aarkkimideesinte swantham vaakkukalil
eee maathrkayude valuppathinte kaaranam, labhyamaya saankethikavidyakal upayogichu greekkukalkku nakshatra paralax nireekshikkaan kazhiyaathathaan, ithu soochippikkunnathu eathu paralax valare cheruthaanennum athinaal nakshathrangal bhoomiyil ninnu valare akale sthaapikkanam (suryakendram sariyaanennu karuthuka).
aarkkimideesinte abhipraayathil, nakshathrangal bhoomiyil ninnu ethra akaleyaanennu aristaarkkas paranjittilla. athinaal archemediesinu inipparayunna anumanangal nadathendivannu
bhoomiyude bhramanapathathinu chuttumulla chalanam moolamundaakunna nakshatra paralax bhoomiye chuttipattiyulla chalanam moolamundaakunna soura paralaxinu thulyamaanennu paranjukondu eee anumaanam prakadippikkaanum kazhiyum. oru anupatham iduka
formula _ 4
oru upper boundu nedunnathinaayi, aarkkimidikal avayude alavukalekkurichu inipparayunna anumanangal nadatthi
prapanchatthinte vyaasam 1014 stadiyangalil kaviyillennum (aadhunika yoonittukalil, ekadesham 2 prakashavarsham) athil niraykkaan 1063 daanyangalil kooduthal manal aavasyamillennum archemidies pinneedu nigamanam cheythu. eee alavukal upayogichu, aarkkimideesinte chinta-pareekshanatthile oro manal dhaanyathinum ekadesham 19 micrometer (<aii. dii. 1> emm. emm) vyaasamundaakumaayirunnu.
aristaarshyan prapanchatthile manal daanyangalude ennam kanakkaakkuka.
arikil idunna naalpat poppi vithukal ekadesham 19 millimeter (naalil moonnu inch) neelamulla oru greak dactylene (viral veethiyulla) thulyamaakumennu archemidies avakaashappedunnu. vooliyam oru rekheeya alavile cubai munnott pookunnathinaal ("golangalkku avayude vyaasathinte paraspara triguna anupaathamundennu theliyikkappettittund") appol oru golatthil oru daaktail vyaasathil 403, allengil 64,000 poppi vithukal adangiyirikkum (nammude nilavile nambar sisttam upayogichu).
oro poppi vithilum ennamatta (10,000) manal daanyangal adangiyirikkaamennu addeham (thelivukalillaathe) avakashappettu. rund akkangaleyum orumichu gunichu addeham oru golatthile saangalppika manal kanangalude ennamaayi oru daaktail vyaasamulla manal kanangalude ennamaayi 640,000,000 nirddeshichu.
kooduthal kanakkukoottalukal eluppamaakkunnathinu, aadya samkhya randaamathethinekkaal cheruthaanennum athinaal pinneedu kanakkakkiya manal daanyangalude ennam yadhaartha daanyangalude ennathe kaviyumennum maathram soochippichukondu addeham 640 dasalaksham muthal oru bilyan vare samaaharichu. prapanchatthile manal kanangalude ennam krithyamaayi kanakkakkaan mathramalla, munbu asaadhyamaayi kanakkaakkappettirunna valia samkhyakal upayogichu engane kanakkaakkaamenn kaanikkuka ennathaayirunnu eee lekhanathodoppam aarkkimideesinte mettaa goal ennu oorkkuka.
oru greak stadiyathinu 600 greak adii neelavum oro adikkum 16 dactile neelavumundaayirunnathil oru stadiyathil 9,600 dactile undaayirunnu. kanakkukoottalukal eluppamaakkunnathinu archemidies eee samkhya 10,000 (ennamattathu) vare raundu cheythu, thathfalamaayundaakunna ennam yadhaartha manal daanyangalude ennathe kaviyumennu veendum shradhichu.
10, 000 cube oru trilyan (1012) aanu; oru bilyan (oru daaktail-golatthile manal daanyangalude ennam) oru trilyan (oru stediya-golatthile daaktail-golangalude ennam) kondu gunichaal 1021 labikkum, oru stadium-golatthile manal daanyangalude ennam.
aristaarkkiyan prapanchatthinu 1014 stediya vyaasamundennu archemidies kanakkaakkiyirunnu, athinaal athinanusarichu prapanchatthil (1014) 3 stediya golangal undaakum, allengil 1042.1021 neey 1042 kondu gunichaal 1063 labikkum, ithu aristaarshyan prapanchatthile manal daanyangalude ennamaanu.
oru poppi vithile ennamatta (10,000) manalkkashanangalekkurichu aarkkimideesinte kanakkukoottalinethudarnna; oru daaktail-golatthil 64,000 poppi vithukal; oru stadiyathinte neelam 10,000 daaktailukal; oru daakttailinte veethiyaayi 19 millimeter sweekarikkuka, aarkkimideesinte saadhaarana manal dhaanyathinte vyaasam 18.3 micrometer aayirikkum, athine innu nammal cheli daanyam ennu vilikkum. nilavil, ettavum cheria manal dhaanyathe 50 micrometer vyasamullathaayi nirvachikkum.
adhika kanakkukoottalukal.
archemidies rasakaramaaya chila pareekshanangalum kanakkukoottalukalum nadatthi. bhoomiyil ninnu kaanunnathupole sooryante koneeya valuppam kanakkaakkuka ennathaayirunnu oru pareekshanam. kanninte pupilinte parimithamaaya valippam kanakkiledukkunnathinal aarkkimideesinte reethi prathyekichum rasakaramaan, athinaal manushyante daaranayude mechanicsumaayi bandhapetta manashaasthratthinte shaakhayaaya psychophysicsile pareekshanatthinte aadyathe ariyappedunna udaaharanamaayirikkaam ithu, athinte vikasanam saadhaaranayaayi herman voonn helmholts aanu. mattoru rasakaramaaya kanakkukoottal solar paralax bhoomiyude kendratthil ninno sooryodayasamayathu bhoomiyude uparithalathil ninno kaanunna kazhchakkaaranum suryan thammilulla vyathyastha doorangalum soochippikkunnu. solar paralax kaikaaryam cheiyunna aadyathe ariyappedunna kanakkukoottalaayirikkam ithu.

