aarkimideej

seraakyoos ka aarkimideej (yoonaani: Άaaρaaχaaιaaμaaήaaδaaηaaς)
Domenico-Fetti Archimedes 1620.jpg
janm 287 E.poo.
seraakyoos, sisili
maigna graasiya
nidhan 212 E.poo.
seraakyoos
yug puraatan darshanashaastr
kshetr shaastreeya yoonaani darshanashaastr
School alekjeindriya ka yooklid
praakrutik darshanashaastr
abhiruchi ganit, bhautiki, abhiyaantriki, khagol vigyaan, avishkaar
ullekhaneeya vichaar jal sthaitiki, uttolak,
aparimit

seraakyoos ke aarkimideej (yoonaani:Ἀaρaχaιaμaήaδaηaς; 287 E.poo. - 212 E.poo.), ek yoonaani ganitjnya, bhautik vigyaani, abhiyanta, aavishkaarak aur khagol vigyaani the. haalaanki unke jeevan ke kuchh hi vivran gyaat hain, unhein shaastreeya puraatanata ka ek agrani vaigyaanik maana jaata hai. bhautik vigyaan mein unhonein jalasthaitiki, saankhyiki aur uttolak ke siddhaant ki vyaakhya ki neev rakhi thi. unhein naveeneekrut masheenon ko design karne ka shreya diya jaata hai, inmein seej engine aur skroo pamp shaamil hain. aadhunik prayogon se aarkimideej ke in daavon ka pareekshan kiya gaya hai ki darpanon ki ek pankti ka upayog karte hue bade aakramanakaari jahaajon ko aag lagaai ja sakti hain.[1]

aamtaur par aarkimideej ko praacheen kaal ka sabse mahaan ganitjnya maana jaata hai aur sab samay ke mahaanatam logon mein se ek kaha jaata hai.[2][3] unhonne ek paravalaya ke chaap ke neeche ke kshetrafal ki ganana karne ke liye poornata ki vidhi ka upayog kiya, iske liye unhonne aparimit shrrunkhala ke sameshan ka upayog kiya aur pai ka ullekhaneeya sateek sannikt maan diya.[4] unhonne ek aarkimideej sarpil ko bhi paribhaashit kiya, jo unke naam par aadhaarit hai, ghoornan ki satah ke aayatan ke liye sootr diye aur bahut badi sankhyaaon ko vyakt karne ke liye ek saral pranaali bhi di.

aarkimideej seraakyoos ki gheraabandi ke dauraan maare gaye jab ek roman sainik ne unki hatya kar di, haalaanki yeh aadesh diya gaya tha ki unhein koi nuksaan naheen pahunchana chaahiye. sisro aarkimidij ka makabara, jo ek belan ke andar andar sthit gunbad ki tarah hai, par jaane ka varnan karte hain ki, aarkimideej ne saabit kiya tha ki gole ka aayatan aur iski satah ka kshetrafal belan ka do tihaai hota hai (belan ke aadhaar sahit) aur ise unki ek mahaanatam ganiteeya upalabdhi maana jaata hai.

unke aavishkaaron ke vipreet, aarkimideej ke ganiteeya lekhan ko praacheen kaal mein bahut kam jaana jaata tha. elegajenadariya se ganitjnyaon ne unhein padha aur uddhrut kiya, lekin pehla vyaakhyaatmak sankalan si. tak naheen kiya gaya tha. yeh 530 E. mein miletas ke isidor ne kiya, jab chhathi shataabdi E. mein yutokiyaas ne aarkimideej ke kaaryon par tippaniyaan likheen aur pehli baar inhein vyaapak roop se padhane ke liye upalabdh karaaya gaya. aarkimideej ke likhit kaarya ki kuchh pratilipiyaan jo madhya yug tak bani raheen, ve punarjaagaran ke dauraan vaigyaaniko ke liye vichaaron ka pramukh srot theen,[5] haalaanki aarkimideej paalimpset mein aarkimideej ke dvaara pehle se kiye gaye agyaat kaarya ki khoj 1906 mein ki gayi thi, jisse is vishay ko ek nayi antardrushti pradaan ki ki unhonne ganiteeya parinaamon ko kaise praapt kiya.[6]


anukram

jeevani

aarkimideej ki yeh kaansya pratima barlin mein archenhold vedhashaala mein hai. is moorti ko gerhaard theem ne banaaya aur iska anaavaran 1972 mein kiya gaya

aarkimideej ka janm 287 E.poo. seraakyoos, sisili ke bandargaah shahar mein maigna graasiya ki ek basti mein hua tha. unke janm ki taareekh, beejaantin yoonaani itihaasakaar John jetajes ke kathan par aadhaarit hai, iske anusaar aarkimideej 75 varsh tak jeevit rahe.[7] the seind rekonar mein, aarkimideej apne pita ka naam fidiaas bataate hain, unke anusaar ve ek khagol vigyaani the, jiske baare mein kuchh bhi gyaat naheen hai. plootaark ne apni perelal laaivj mein likha ki aarkimideej seraakyoos ke shaasak, raaja hero se sambandhit the.[8] aarkimideej ki ek jeevani unke mitr heeraaklids ke dvaara likhi gayi, lekin unka kaarya kho gaya hai, jisse unke jeevan ke vivran aspasht hi rah gaye hain.[9] udaaharan ke liye, yeh agyaat hai ki vah shaadi shuda the ya naheen ya unke bachche the ya naheen. sambhavat: apni javaani mein aarkimideej ne alekjeindriya, misr mein adhyayan kiya, jahaan ve saamos ke konan aur saayareen ke iretosthenej samakaaleen the. unhein unke mitr ki tarah saamos ke konan se sandarbhit kiya jaata tha, jabki unke do kaaryo (yaantrik prameya ki vidhi aur ketal samasya (the Cattle Problem)) ka parichay iretosthenej ke sambodhan se diya jaata tha.[20]


aarkimideej ki mrutyu c 212 E.poo. doosare punik yuddh ke dauraan hui jab roman senaaon ne general maarkas klaaudiys maarselas ke netrutv mein do saal ki gheraabandi ke baad seraakyoos shahar par kabja kar liya. plootaark ke dvaara diye gaye lokapriya vivran ke anusaar, aarkimideej ek ganiteeya chitr par vichaar kar rahe the, jab shahar par kabja kiya gaya.

ek roman sainik ne unhein aakar general maarselas se milne ka aadesh diya, lekin unhonne yeh kehkar inkaar kar diya ki unhein apni samasya par kaam poora karna hai. isse sainik naaraaj ho gaya aur usane apni talavaar se aarkimideej ko maar daala. plootaark aarkimideej ki mrutyu ka bhi ek vivran dete hain lesser-known jismein yeh kaha gaya hai ki sanbhavataya unhein tab maar diya gaya jab ve ek roman sainik ko samarpan karne ka prayaas kar rahe the. is kahaani ke anusaar, aarkimideej ganiteeya upakaran le ja rahe the aur unhein isliye maar diya gaya kyonki sainik ne socha ki ye keemati saamaan hai. kaha jaata hai ki aarkimideej ki mrutyu se general maarselas bahut krodhit hue, kyonki ve unhein ek amoolya vaigyaanik sampati maanate the aur unhonne aadesh diye the ki aarkimideej ko kisi bhi prakaar ka nuksaan naheen pahunchaaya jaana chaahiye.[10]

ek gole ka aayatan aur iski satah ka kshetrafal isko gherane vaale belan ka do tihaai hota hai. aarkimideej ke anurodh par ek gole aur ek belan ko unke makabare par rakha gaya tha.

maana jaata hai ki aarkimideej ke antim shabd the, "mere vruton ko pareshaan mat karo (Do not disturb my circles)" (yoonaani : μaή μaaοaaυ τaοaύaς κaaύaaκaaλaaοaaυaaς τaaάaaρaaαaaτaaτaaε), yahaan vruton ka sandarbh us ganiteeya chitr ke vruton se hai jise aarkimideej us samay adhyayan kar rahe the jab roman sainik ne unhein pareshaan kiya. in shabdon ko aksar laitin mein "Noli turbare circulos meos" ke roop mein varnit kiya jaata hai, lekin is baat ke koi bharosemand pramaan naheen hain ki aarkimidij ne ye shabd kahe the aur ye plootaark ke dvaara diye gaye vivran mein naheen milte hain.[10]


aarkimideej ke makabare par unka pasandeeda ganiteeya pramaan chitrit kiya hua hai, jismein samaan unchaai aur vyaas ka ek gola aur ek belan hai. aarkimideej ne pramaanit ki gole ka aayatan aur satah ka kshetrafal belan (aadhaar sahit) ka do tihaai hota hai. 75 E.poo. mein, unki mrutyu ke 137 saal baad, roman vakta sisro sisili mein koshaadhyaksh ke roop mein sevaarat the. unhonne aarkimideej ke makabare ke baare mein kahaaniyaan suni theen, lekin sthaaneeya logon mein se koi bhi iski sthiti bataane mein saksham naheen tha. antat: unhonne is makabare ko seraakyoos mein egreejeintaain gate ke paas khoj liya, yeh bahut hi upekshit haalat mein tha aur is par bahut adhik jhaadiyaan ugeen huin theen. sisro ne makabare ko saaf kiya aur iske oopar hui nakkaashi ko dekh paae aur us par shilaalekh ke roop mein upasthit kuchh chhandon ko padha.[11]

aarkimideej ke jeevan ke maanak sanskaranon ko unki mrutyu ke lambe samay baad praacheen rom ke itihaasakaaron ke dvaara likha gaya. polibiys ke dvaara diya gaya seraakyoos ki gheraabandi ka vivran unki yoonivrsal history (Universal History) mein aarkimideej ki mrutyu ke lagbhag 70 varsh ke baad likha gaya aur ise baad mein plootaark aur livi ke dvaara ek srot ke roop mein prayukt kiya gaya. yeh ek vyakti ke roop mein aarkimideej par thoda prakaash daalata hai aur un yuddh masheenon par dhyaan keindrit karta hai, jinhein maana jaata hai ki unhonne shahar ki raksha karne ke liye banaaya tha.

khojein aur aavishkaar (Discoveries and inventions)

sone ka mukut (The Golden Crown)

aarkimideej ne sambhavat: apne utplaavakata ke siddhaant ka upayog karke yeh nirdhaarit kiya ki sone ka mukut thos sone se kam ghana hai ya naheen

aarkimideej ke baare mein sabse vyaapak roop se gyaat tathya (anecdote) yeh bataata hai ki kis prakaar se unhonne ek aniyamit aakruti ke ek vastu ke aayatan ko nirdhaarit karne ke liye vidhi ki khoj ki. vitrooviys ke anusaar, raaja hero II ke liye ek laurel vreth ke aakaar ka ek naya mukut banaaya gaya tha aur aarkimideej se yeh pata lagaane ke liye kaha gaya ki yeh mukut shuddh sone se bana hai ya beimaan sunaar ne ismein chaandi milaayi hai.[12] aarkimideej ko mukut ko nuksaan pahunchaae bina is samasya ka samaadhaan karna tha, isliye vah iske ghanatv ki ganana karne ke liye ise pighla kar ek niyamit aakaar ki vastu mein naheen badal sakta tha.

nahaate samay, unhonne dekha ki jab ve tab ke andar gaye, tab mein paani ka star oopar uth gaya aur unhonne mahasoos kiya ki is prabhaav ka upayog mukut ke aayatan ko nirdhaarit karne ke liye kiya ja sakta hai. vyavahaarik prayojanon ke liye paani ko sanpeedit naheen kiya ja sakta hai,[13] isliye dooba hua mukut apne aayatan ki baraabar maatra ke paani ko pratisthaapit karega. mukut ke bhaar ko pratisthaapit paani ke aayatan se vibhaajit karke, mukut ka ghanatv praapt kiya ja sakta hai. yadi ismein saste aur kam ghanatv vaale dhaatu milaaye gaye hain to iska ghanatv sone se kam hoga. fir kya tha, aarkimideej apni is khoj se itne jyaada uttejit ho gaye ki ve kapade pahanana hi bhool gaye aur nagn avastha mein galiyon mein bhaagte hue chillaane lage "yooreka (Eureka)!" (yoonaani: "εaaὕaaρaaηaaκaaα!," arth "mainne ise pa liya!")[14][15]

sone ke mukut ki kahaani aarkimideej ke gyaat kaaryon mein prakat naheen hoti hai. iske alaava, paani ke visthaapan ke maapan mein aavashyak sateekata ki atyadhik maatra ke kaaran, iske dvaara varnit vidhi ki vyavahaarikta par savaal uthaaye gaye hain.[16] sambhavat: aarkimideej ne ek aisa hal diya jo jalasthaitiki mein aarkimideej ke siddhaant naamak siddhaant par laagoo hota hai, jise ve apne ek granth on floting bodeej (on Floating Bodies) mein varnit karte hain.

is siddhaant ke anusaar ek taral mein doobi hui vastu par ek utplaavan bal (buoyant force) lagta hai jo iske dvaara hataaye gaye taral ke bhaar ke baraabar hota hai.[17] is siddhaant ka prayog karte hue, sone ke mukut ke ghanatv ki tulana thos sone se karna sambhav ho gaya hoga, iske liye pehle mukut ko sone ke ek namoone ke saath ek paimaane par santulit kiya gaya hoga, fir tantr ko paani mein dubaaya gaya hoga. yadi mukut sone se kam ghana tha, isne apne adhik aayatan ke kaaran adhik paani ko pratisthaapit kiya hoga aur is prakaar is par lagne vaale utplaavan bal ki maatra namoone se adhik rahi hogi. utplaavakata mein yeh antar paimaane par dikhaayi diya hoga. gaileeliyo ne maana ki "sanbhavataya aarkimideej ne isi vidhi ka upayog kiya hoga, choonki, bahut sateek hone ke saath, yeh khud aarkimideej ke dvaara diye gaye pradarshan par aadhaarit hai."[18]


aarkimidij

aarkimideej skroo paani ko kushalata se utha sakta hai.

engineering ke kshetr mein aarkimideej ke dvaara kiye gaye kaarya ka ek bada hissa, uske apne shahar seraakyuj ki jarooraton ko poora karne se hi hua. yoonaani lekhak naukraatis ke ethenyoos ne varnit kiya ki kaise raaja heeron II ne aarkimideej ko ek vishaal jahaaj, siraakusiya (Syracusia) design karne ke liye kaha, jise vilaasitaapoorn yaatra karne ke liye, saamaan ki saplaai karne ke liye aur nausena ke yuddhapot ke roop mein prayukt kiya ja sake. maana jaata hai ki siraakusiya praacheen kaal ka sabse bada jahaaj tha.[19] ethenyoos ke anusaar, yeh 600 logon ko le jaane mein saksham tha, saath hi iski suvidhaaon mein ek bageeche ki sajaavat, ek vyaayaamashaala aur devi efordaait ko samarpit ek mandir bhi tha. choonki is aakaar ka ek jahaaj patavaar ke maadhyam se paani ki ek badi maatra ka risaav karega, is paani ko hataane ke liye aarkimideej ka skroo banaaya gaya.

aarkimiddij ki machine ek ek upakaran thi, jismein ek belan ke bheetar ghoornan karte hue skroo ke aakaar ke blade the. ise haath se ghumaaya jaata tha aur isak prayog paani ke ek low-lying nikaaya se paani ko sinchaai ki nahar mein sthaanaantarit karne ke liye bhi kiya ja sakta tha. aarkimideej ke skroo ka upayog aaj bhi drav aur kaneeya thos jaise koyala aur anaaj ko pamp karne ke liye kiya jaata hai. roman kaal mein vitrooviys ke dvaara varnit aarkimideej ka skroo sanbhavataya skroo pamp par ek sudhaar tha jiska upayog bebeelon ke latakate hue bageechon (Hanging Gardens of Babylon) ki sinchaai karne ke liye kiya jaata tha.[20][21][22]

aarkimideej ka panja (The Claw of Archimedes)

aarkimideej ka panja (The Claw of Archimedes) ek hathiyaar hai, maana jaata hai ki unhonne seraakyoos shahar ki raksha ke liye ise design kiya tha. ise "the ship shekar (the ship shaker)" ke naam se bhi jaana jaata hai, is panje mein ek kren ke jaisi bhuja thi, jisse ek bada dhaatu ka huk lataka hua tha. jab is panje ko ek aakraman karte hue jahaaj par daala jaata tha, bhuja oopar ki or uthati thi aur jahaaj ko ko uthaakar paani se baahar nikaalati thi aur sanbhavat: ise dooba deti thi. is panje ki vyavahaaryata ki jaanch ke liye aadhunik parikshan kiye gaye hain aur 2005 mein super vepans of the enashiyeint world (Superweapons of the Ancient World) naamak ek television vrutachitr ne is panje ke ek sanskaran ko banaaya aur nishkarsh nikaala ki yeh ek kaaryasheel upakaran tha.[23][24]

aarkimideej ki ooshma kiran (The Archimedes Heat Ray)- mithk ya vaastavikta?

sanbhavataya aarkimideej seraakyoos par aakraman karne vaale jahaajon ko jalaane ke liye ek saath sangrahit kiye gaye darpanon ko ek paravalaya paraavartak ke roop mein prayog karte the

2 shataabdi E. ke lekhak lusiyn ne likha ki seraakyoos ki gheraabandi ke dauraan (c. 214-212 E.poo.), aarkimideej ne aag se shatru ke jahaajon ko nasht kar diya. sadiyon baad traalej ke enthemiyaas ne jalate hue kaanch ka ullekh aarkimideej ke hathiyaar ke roop mein kiya.[25] yeh upakaran, kabhi kabhi "aarkimideej ki ushma kiran" kahalaata hai, iska upayog lakshya jahaaj par soorya ke prakaash ko focus karne ke liye kiya jaata tha, jisse ve aag lakad lete the.


yeh kathit hathiyaar punarjaagaran ke baad se hi bahas ka vishay raha hai. rene desakaartes ne ise galat kah kar khaarij kar diya, jabki aadhunik vaigyaaniko ne keval unheen saadhanon ka upayog karte hue us prabhaav ko pun: utpann karne ki koshish ki hai, jo aarkimideej ko upalabdh the.[26] yeh sujhaav diya gaya hai ki bahut adhik paulish ki gayi kaanse ya taambe ki paraton ka ek bada samooh darpan ke roop mein kaarya karta hai, sanbhavataya isi ka upayog jahaaj par soorya ke prakaash ko focus karne ke liye kiya jaata tha. ismein paravalaya paraavarti ke siddhaant ka upayog kiya jaata tha, jaise saur bhatti mein kiya jaata hai.


aarkimideej ushma kiran ka ek pareekshan 1973 mein yoonaani vaigyaanik lonnis sakkaas ke dvaara kiya gaya.

yeh prayog Athens ke baahar skaaraamajes nausena base par kiya gaya. is samay 70 darpanon ka upayog kiya gaya, pratyek par ek taambe ki paulish ki gayi thi aur isak aakaar lagbhag 5x3 feet tha (1.5 x 1 meter). darpan, lagbhag 160 feet (50 meter) ki doori par ek roman yuddhapot ke ek plaaivud mock-up ki disha mein rakhe gaye the. jab darpanon ko theek prakaar se focus kiya gaya, jahaaj kuchh hi kshanon mein aag ki lapaton mein jalne laga. plaaivud jahaaj par taar ke peint ki paulish thi, jisne dahan mein aur adhik yogadaan diya.[27]

October 2005 mein mesaachusets prodyogiki sansthaan ke vidyaarthiyon ke samooh ne 127 ek foot (30 seinteemeetar) ki vargaakaar darpan taailon ke saath ek prayog kiya, inhein lagbhag 100 feet (30 meter) ki doori par sthit lakdi ke ek mock-up jahaaj par focus kiya. jahaaj ke ek sthaan par lapatein foot padeen, lekin keval tab jab aakaash mein baadal naheen the aur jahaaj lagbhag das minute ke liye isi sthiti mein bana raha. yeh nishkarsh nikla gaya ki yeh upakaran in paristhitiyon mein ek vyavahaarya hathiyaar tha. MIT samooh ne television sho mithbastars (MythBusters), ke liye is prayog ko doharaaya, jismein lakshya ke roop mein sen Francisco mein ek lakdi ki machhali pakadne waali naav ka upayog kiya gaya. ek baar fir se aisa hi hua, kam maatra mein aag lag gayi.

aag pakadne ke liye, lakdi ko apne jvalan bindu (flash point) tak pahunchana hota hai, jo lagbhag 300 degree celcius (570 degree faarenhaait) hota hai.[28]

jab mithbastars ne January 2006 mein sen Francisco ke parinaam ka prasaaran kiya, is daave ko "asafal" ki shreni mein rakha gaya, kyonki is dahan hone ke liye samay ki upayukt lambaai aur mausam ki aadarsh paristhitiyaan anivaarya hain. is baat par bhi ishaara kiya gaya ki kyonki seraakyoos poorv ki or soorya ke saamane hai, isliye roman bede ko darpanon se anukool prakaash ekatrit karne ke liye subah ke samay aakraman karna padta hoga. mithbastars ne yeh bhi kaha ki paaramparik hathiyaar, jaise jvalant teer ya ek gulel se bheje gaye teer, kam doori se jahaaj ko jalne ka adhik aasaan tareeka hai.[1]

anya khojein ya aavishkaar (Other discoveries and inventions)

jabki aarkimideej ne leevar ki khoj naheen ki, unhonne ismein shaamil siddhaant ka kathor vivran sabse pehle diya. elegajenadriya ke peppas ke anusaar, leevars par unke kaarya se unhonne tippani di: "mujhe khade hone ki jagah do aur main pruthvi ko gati de doonga." (yoonaani : δaaῶaaς μaaοaaι πaaᾶ σaaτaaῶ κaαaὶ τaaὰaaν γaaᾶaaν κaaιaaνaaάaaσaaω)[29] plootaark ne is baat ka varnan kiya ki kaise aarkimideej ne block-aur-taikal (block-and-tackle) ghirni pranaali ko design kiya, jisse aisi vastuon ko uthaane mein naavikon ne leevarej ka siddaant istemaal kiya, jo itni bhaari theen ki unhein anyatha hilaana bhi bahut mushkil hota tha.[30] aarkimideej ko gulel ki kshamata aur sateekata ke sudhaar ka shreya bhi diya gaya hai aur pehle punik yuddh ke dauraan unhonne odomeetar ka aavishkaar kiya. odomeetar ko ek giyr se yukt ek gaadi ki pranaali ke roop mein varnit kiya gaya hai, jo har ek meal chalne ke baad ek geind ko ek paatr mein daalati hai.[31]


sisro (106-43 E.poo.) apne samvaad de re pablika (De re publica) mein sankshep mein aarkimideej ka ullekh karte hain, jismein seraakyoos ki gheraabandi ke baad 129 E.poo. mein hui ek kaalpanik baatcheet ka chitran kiya gaya hai, c .kaha jaata hai ki 212 E.poo., general maarkas klaaoodiys maarselas (Marcus Claudius Marcellus) rom mein do pranaaliyaan vaapas laaye, jinhein khagol vigyaan mein sahaayataarth prayukt kiya jaata tha, jo soorya, chandrama aur paanch grahon ki gati ko darshaata hai. sisro usi tarah ki pranaali ka ullekh karte hain jaisi pranaali miletas ke thels aur needas ke yudoksas ke dvaara design ki gayi. is samvaad ke anusaar maarselas ne ek upakaran ko seraakyoos se ki gayi apni niji loot ke roop mein rakha aur anya sabhi ko rom mein tempal of varchyoo ko daan kar diya. sisro ke anusaar maarselas ki pranaali ko geiyaas salpikaas gelas ke dvaara lyukiyaas fyuriyaas fils ko darshaaya gaya, jisne ise is prakaar se varnit kiya:


Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. — When Gallus moved the globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth, when the Sun was in line.[32][33]

yeh ek taaraamandal (planetarium) ya oreri (orrery)) ka varnan hai.elegajenadriya ke peppas ne kaha ki aarkimideej ne in nirdisht pranaaliyon ke nirmaan par ek paandulipi likhi hai (jo ab kho chuki hai) On Sphere-Making.

is kshetr mein aadhunik adhyayan enteekaaithera pranaali par dhyaan kendrit karta hai, yeh praacheen kaal ka ek anya upakaran tha jise sanbhavataya samaan uddeshya ke liye design kiya gaya tha. is prakaar ki nirmaanaatmak pranaali ke liye avakal giyring ke parishkrut gyaan ki aavashyakta rahi hogi. ise ek baar praacheen kaal mein upalabdh takaneek ke rejan ke baahar maana jaata tha, lekin 1902 mein enteekaaithera pranaali ki khoj ne sunishchit kar diya ki is prakaar ke upakaran praacheen yoonaaniyon ko gyaat the.[34][35]

ganit (Mathematics)

haalaanki aarkimideej ko aksar yaantrik upakaranon ka designer kaha jaata hai, unhonne ganit ke kshetr mein bhi yogadaan diya. plootaark ne likha tha: "unhonne un shuddh vivranon mein apna poora sneh aur mahatvaakaanksha daal di, jahaan jeevan ki asabhya jarooraton ke liye koi sandarbh naheen ho sakta."[36]

aarkimideej ne n ke sannikt maan ka pata lagaane ke liye poornata ki vidhi ka upayog kiya.

aarkimideej aparimit shrrunkhalaaon (infinitesimals) ka upayog usi tareeke se kar sakte the jaise ki aadhunik samaakal kalan (integral calculus) mein kiya jaata hai.

virodhaabhaas ke dvaara pramaan ke maadhyam se (reductio ad absurdum), ve un seemaaon ko nirdisht karte hue, sateekata ke ek yaadruchhik ansh tak kisi samasya ka hal de sakte the, jinmein uttar hota tha. yeh takaneek poornata ki vidhi (method of exhaustion) kahalaati hai aur unhonne iska prayog pai (π (pi)) ke sannikt maan ka pata lagaane mein kiya.

unhonne iske liye ek vrat ke baahar ek bada bahubhuj chitrit kiya aur vrat ke bheetar ek chhota bahubhuj chitrit kiya.

jaise jaise bahubhuj ki bhujaaon ki sankhya badhti hai, vrat ka sanniktan adhik sateek ho jaata hai. jab pratyek bahubhuj mein 96 bhujaaen theen, unhonne unki bhujaaon ki lambaai ki ganana ki aur darshaaya ki π ka maan 317 (lagbhag 3.1429) aur 31071 (lagbhag 3.1408) ke beech tha, yeh iske vaastavik maan lagbhag 3.1416 ke anuroop tha. unhonne yeh bhi pramaanit kiya ki vraton ka kshetrafal π aur vrat ki trijya ke varg ke gunanafal ke baraabar tha.

ek vrat ke maapan mein, aarkimideej 3 ke varg mool ke maan ko 265153 (lagbhag 1.7320261) se adhik aur 1351780 (lagbhag 1.7320512) se kam bataate hain. vaastavik maan lagbhag 1.7320508 hai jo bahut hi sateek anumaan hai. unhonne is parinaam ko dene ke saath, ise praapt karne mein prayukt vidhi ka koi spashteekaran naheen diya. aarkimideej ke kaarya ke is pahaloo ke kaaran John vaalis ne tippani di ki ve :"jaanaboojh kar apni jaanch ko chhupaana chaahate the jaise ki ve apni jaanch ki vidhi ko rahasya bana kar rakhana chaahate the, jabki iske parinaamon ko sabse saamane laana chaahate the. "[37]

jaisa ki aarkimideej ne saabit kiya, upari aakruti mein paravalaya khand ka kshetrafal neechali aakruti mein antar vrat ke 4/3 ke baraabar hai

paravalaya ke varg ki ganana mein, aarkimideej ne saabit kiya ki ek paravalaya aur ek seedhi rekha se ghira hua kshetrafal iske bheetar upasthit tribhuj ke kshetrafal ka 43 guna hota hai, jaisa ki daayeen aur diye gaye chitr mein darshaaya gaya hai. unhonne is samasya ke hal ko saamaanya anupaat se yukt ek aparimit jyaamiteeya shrrunkhala ke roop mein vyakt kiya14:

yadi is shrrunkhala mein pehla pad tribhuj ka kshetrafal hai, to doosra do tribhujon ke kshetrafal ka yog hai, jinke aadhaar do chhoti chhedika rekhaaen hain aur isi prakaar. yeh pramaan shrrunkhala 1/4 + 1/16 + 1/64 + 1/256 + · · · ki bhinnata ka upayog karta hai, jiska yog 13 hai.

the seind rikonar mein, aarkimideej ne is brahmaand mein upasthit mitti ke kanon ki sankhya ki ganana karne ke liye ek samuchchaya diya. aisa karne mein, unhonne is dhaarana ko chunauti di ki mitti ke kanon ki sankhya itni badi hai ki iski ganana naheen ki ja sakti hai. unhonne likha: "kuchh log, raaja gelo (gelo II, hero II ka putr) sochate hain ki mitti ki sankhya anant mein aparimit hai; aur mera maanana hai ki mitti na keval seraakyoos aur shesh sisili mein hai balki har us kshetr mein hai jahaan aavaas hai ya aavaas naheen hai. is samasya ka hal karne ke liye, aarkimideej ne asankhya (myriad) ke aadhaar par ganana ki ek pranaali di.

yeh shabd greek μaaυaaρaaιaaάaaς murias se bana hai; yeh 10,000 ki sankhya ke liye hai. unhonne asankhya ki ek asankhya ghaat (100 million) ki ek ank pranaali ki prastaavana di aur nishkarsh nikaala ki mitti ke kanon ki sankhya jo ek brahmaand ko bharne ke liye aavashyak hai vah 8 vijintileeyan, ya 8 ×a1063 hai.[38]

lekhan (Writings)

aarkimideej ke kaarya ko dorik yoonaani mein likha gaya, jo praacheen seraakyoos ki boli hai.[39] yukleed ki tarah aarkimideej ka likhit kaarya bhi maujood naheen hai aur unke saat granthon ki upasthiti ko jaana jaata hai, jiska sandarbh anya lekhakon ke dvaara diya gaya hai. elegajenadriya ke peppas on sfeeyar meking (On Sphere-Making) ka aur bahukoneeya aakruti par kiye gaye anya kaarya ka ullekh karte hain, jabki elegajenadriya ke thiyon now-lostketopatrik se apavartan ke baare mein ek tippani ka uddharan dete hain. [b] uske jeevanakaal ke dauraan, aarkimideej ne elegajenadriya mein ganitjnyaon ke saath patraachaar ke maadhyam se apne kaarya ko prasiddh banaaya. aarkimideej ke lekhan ko miletas ke beejaantin vaastukaar isidor ke dvaara sangrahit kiya gaya. (c .530 E.), jabki aarkimideej ke kaaryon par tippaniyon ko chhathi shataabdi E. mein yutokiyaas ke dvaara likha gaya, unhonne unke kaarya ke liye vyaapak darshak ekatrit kiye. aarkimideej ke kaarya ko thaabit ibn kyurra (Thāabit ibn Qurra) ke dvaara arabi mein anuvaadit kiya gaya (836-901 E.) aur seraamona ke jeraard ke dvaara laitin mein anuvaadit kiya gaya (c. 1114-1187 E.). punarjaagaran ke dauraan, greek aur laitin mein aarkimideej ke kaarya ke saath, editiyo prinseps (Editio Princeps) ko 1544 mein johaan harvegan ke dvaara Bessel (Basel) mein prakaashit kiya gaya.[40] aisa prateet hota hai ki varsh 1586 ke aas paas gaileeliyo gaileeli ne aarkimideej ke kaarya se prerit hokar vaayu aur jal mein dhaatuon ka bhaar gyaat karne ke liye jalasthaitik tula ka aavishkaar kiya.[41]

upasthit kaarya

kaha jaata hai ki aarkimideej ne uttolak par tippani di: mujhe khade hone ki jagah do aur main pruthvi ko hila doonga.
  • talon ki saamyaavstha (do khand)
pehli pustak pandrah prastaavon mein aur saat avadhaaranaaon se yukt hai, jabki doosari pustak das prastaavon mein hai.

is kaarya mein aarkimideej uttolak ke niyam ko spasht karte hain, kehte hain, "unke bhaar ki vyutkramaanupaati dooriyon mein aayaam saamyaavastha mein hain.".

aarkimideej jyaamiteeya aakrutiyon jaise tribhuj, samaanaantar chaturbhuj aur paravalaya ke kshetrafal aur gurutv kendra ki ganana karne ke liye vyutpann siddhaanton ka upayog karte hain.[42]
  • ek vrat ka maapan
yeh ek chhota kaarya hai jo teen prastaavon se yukt hai. ise pelusiym ke doseethiyaas ke saath patraachaar ke roop mein likha gaya hai, jo saamos ke konon ke vidyaarthi the.

prastaav II mein, aarkimideej darshaate hain ki π (pi (pai)) ka maan 22371 se adhik aur 227se kam hota hai. baad vaale aankade (aankik maan) ko madhya yug mein π (pi) ke sannikt maan ke roop mein prayukt kiya gaya. aur aaj bhi iska upayog kiya jaata hai jab ek rough maan ki aavashyakta hoti hai.

  • on spaairals (On Spirals)
28 prastaav ka yeh kaarya bhi doseethiyaas ko sambodhit hai. yeh granth vartamaan ke aarkimideej sarpil ko paribhaashit karta hai.

yeh un binduon ka bindupath hai jo ek aise bindu ki sthiti se sambandhit hai jo samay ke saath ek sthir gati se ek aisi rekha par chalte hue ek sthir bindu se door ja raha hai jo sthir koneeya veg ke saath ghoornan kar rahi hai.

iske tulya, dhruveeya nirdeshaankon (r, θ) mein ise is sameekaran ke dvaara varnit kiya ja sakta hai.


jahaan a aur b vaastavik sankhyaayein hain. yeh ek yoonaani ganitjnya ke dvaara vichaar kiya gaya ek yaantrik vakr (ek gatisheel bindu ke dvaara banaaya gaya vakr) ka praarambhik udaaharan hai.
  • gola aur belan (do khand)
doseethiyaas ko sambodhit is granth mein, aarkimideej ne vah parinaam praapt kiya jiske liye unhein sabse jyaada garv tha, yeh tha ek samaan unchaai aur vyaas ke belan aur iske bheetar upasthit gole ke beech sambandh.

gole ka aayatan 43πr 3 aur belan ka aayatan ka 2πr 3 tha.

gole ki satah ka kshetrafal 4πr 2, aur belan ki satah ka kshetrafal 6πr 2 (do aadhaar sahit), jahaan r gole aur belan ki trijya hai. gole ka aayatan aur satah ka kshetrafal belan ka two-thirds hai. aarkimideej ke anurodh par unke makabare par ek gola aur belan banaaya gaya hai.


  • shankubh aur golaabh
yeh doseethiyaas ko sambodhit kaarya hai jo 32 prastaavon mein hai.

is granth mein aarkimideej shanku, gole aur paravalaya ke bhaagon ke kshetrafal aur aayatan ki ganana karte hain.


  • plavit pind (do khand)
is granth ke pehle bhaag mein, aarkimideej taral ke saamyaavastha ke niyam ko bataate hain aur saabit karte hain ki ek gurutv kendra ke chaaron aur paani ek gole ka roop le leta hai.

yeh samakaaleen greek khagolavidon iretosthenej ke is siddhaant ko spasht karne ka prayaas ho sakta hai ki pruthvi gol hai. aarkimideej dvaara varnit taral padaarth self-gravitating naheen hain, choonki ve ek aise bindu ke astitv ko maanate hain jiski or sabhi cheejein golaakaar aakruti utpann karne ke liye girti hain.


chitr:Archimedes greece 1983.png
aarkimideej ke yaad mein unhein 1983 ke ek greek daak ticket par dikhaaya gaya.
doosare bhaag mein, ve paravalaya ke bhaag ki santulan (ekvalibriym) ki sthiti ki ganana karte hain.

yeh shaayad jahaaj ke hul ki aakruti ke liye banaaya gaya aadarsh tha. inmein se kuchh sekshan paani ke neeche aadhaar ke saath tairate hain aur paani ke oopar sheersh par rahate hain, theek vaise hi jaise ek aaisabarg tairata hai.

aarkimideej ka utplaavakata ka siddhaant is kaarya mein diya gaya hai, jise is prakaar se bataaya gaya hai:

Any body wholly or partially immersed in a fluid experiences an upthrust equal to, but opposite in sense to, the weight of the fluid displaced.
  • the kvaadarachar of the peraabola (The Quadrature of the Parabola)
24 prastaavon ka yeh kaarya doseethiyaas ko samabodhit hai, aarkimideej do vidhiyon se yeh siddh karte hain ki ek paravalaya aur ek seedhi rekha se ghira hua kshetrafal, samaan aadhaar aur unchaai ke tribhuj ke kshetrafal ka 4/3 guna hota hai.

vah ise ek jyaamiteeya shrrunkhala ke maan ki ganana ke dvara praapt karte hain, jiska yog anupaat ke saath 14 hai.

  • stomachion
yeh tenagraam ke samaan ek vichhedan paheli hai aur ise varnit karne wala granth aarkimideej palimpsest mein adhik poorn roop mein paaya gaya hai. aarkimideej 14 khandon ke kshetrafal ki ganana karte hain, jinhein mila kar ek varg banaaya ja sakta hai.

2003 mein stainaford university ke dau॰ reeveel netj ke dvaara prakaashit shodh mein tark diya gaya ki aarkimideej yeh pata lagaane ka prayaas kar rahe the ki kitne tareekon se tukadon ko mila kar ek varg ka gola banaaya ja sakta hai. dau॰ netj ne ganana ki ki tukadon se 17,152 tareekon se varg banaaya ja sakta hai.[43] vyavasthaaon ki sankhya 536 hai jabki ghoornan aur pratibiban ke tulya parinaamon ko shaamil naheen kiya gaya hai.[44] paheli sanyojan vigyaan mein praarambhik samasya ke ek udaaharan ko ka pratinidhitv karti hai.

paheli ke naam ki utpati spasht naheen hai aur yeh sujhaav diya gaya hai ki ise praacheen greek se ghaale, ya gulet ya aamaashaya ke liye liya gaya hai. (σaaτaaόaaμaaαaaχaaοaaς).[45]

osoniyaas ne is paheli ko ostomekiyn kaha hai, yeh greek sanyukt shabd hai jo ὀaaσaaτaaέaaοaaν (ostiyn, asthi) aur μaaάaaχaaη (maache-ladaai) se bana hai. is paheli ko lokulas of aarkimideej ya aarkimideej ke box ke roop mein bhi jaana jaata hai.[46]

  • aarkimideej' ketal probalam (Archimedes' cattle problem)
ise greek paandulipi mein gothold efrem lesing ke dvaara khoja gaya, yeh 44 laainon ki kavita se bani hai, jise volfaanabuttel, Germany mein harjog August pustakaalaya mein paaya gaya.

yeh eretosthenej aur elegajenadriya ke ganitjnyaon ko sambodhit hai. aarkimideej unhein chunauti dete hain ki ve soorya ke jhund mein maveshiyon ki sankhya ki ganana karein, iske liye svat: daayofentaain sameekaran ki ek sankhya ke hal ka upayog kiya jaaye. is samasya ka ek aur adhik mushkil sanskaran hai, jismein kuchh uttar varg sankhyaaen honi chaahiyein. samasya ke is sanskaran ka hal pehle ai emthar[47] ke dvaara 1880 mein kiya gaya aur ek badi sankhya mein uttar diya gaya jo lagbhag 7.760271×a10206544 tha.[48]

  • the seind rekonar (The Sand Reckoner)
is granth mein, aarkimideej is poore brahmaand mein upasthit ret ke kanon ki sankhya ki ganana karte hain. is pustak mein saamos ke eristaakaas ke dvaara prastaavit saur tantr ke soorya keindri siddhaant ka ullekh kiya gaya hai, saath hi dharati ke aakaar aur bhinn aakaasheeya pindon ke beech ki doori ke baare mein samakaaleen vichaar bhi diye gaye hain.

asankhya (myriad) ki ghaat par aadhaarit sankhya pranaali ka upayog karte hue, aarkimideej ne nishkarsh nikaala ki brahmaand ko bharne ke liye aavashyak mitti ke kanon ke kanon ki sankhya aadhunik sanketan mein 8×a1063 hai. parichay patra kehte hain ki aarkimideej ke pita ek khagolavijnyaaani the jinka naam fidiaas tha. the seind rekonar (The Sand Reckoner) ya samites (Psammites) ekamaatr upasthit kaarya hai jismein aarkimideej khagolavijnyaaan ke baare mein apne vichaaron ki charcha karte hain.[49]

  • the methad of mekenikl thyorams (The Method of Mechanical Theorems)
maana jaata hai ki yeh granth 1906 mein aarkimideej ke palimpsest ki khoj tak kho chuka tha.

is kaarya mein aarkimideej aparimit shrrunkhalaaon ka upayog karte hain aur darshaate hain ki ek number ko asankhya sankhyaaon mein ya asankhya chhote chhote bhaagon mein tod kar kaise aayatan ya kshetrafal ka pata lagaaya ja sakta hai. aarkimideej ne maana ki is tareeke mein aupachaarik kathorata ki kami hai, isliye unhonne parinaam paane ke liye poornata ki vidhi (method of exhaustion) ka bhi prayog kiya. ketal samasya ki tarah, the methad of mekenikl thyoram ko elegajenadriya mein iretosthenej ko likhe gaye ke patra ke roop mein likha gaya.

managadhnt kaarya (Apocryphal works)

aarkimideej ki book of Lemmas or Liber Assumptorum ek granth hai jismein vruton ki prakruti par pandrah prastaav diye gaye hain. is paathya ki praacheenatam gyaat pratilipi arabi mein hai. vidvaanon ti L heeth aur maarshal klaagett ne tark diya ki yeh apne vartamaan roop mein aarkimideej ke dvaara naheen likha ja sakta, sanbhavataya anya lekhakon ne ismein sanshodhan ke prastaav diye hain. lemmaas aarkimideej ke praarambhik kaarya par aadhaarit ho sakta hai, jo ab kho chuka hai.[50]

yeh daava bhi kiya gaya hai ki ek tribhuj ke bhujaaon ki lambaai se kshetrafal ki ganana karne ke liye heeron ka sootr aarkimideej ke dvaara hi diya gaya.[c] haalaanki, is sootr ke liye pehle bharosemand sandarbh pehli shataabdi E. mein elegajenadriya ke heeron ke dvaara diye gaye.[51]

aarkimideej palimpsest

stomekiyn aarkimideej ke palimpsest mein ek vichhedan paheli hai.

sabse praacheen dastaavej jismein aarkimideej ka kaarya hai, vah hai aarkimidij palimpsest. 1906 mein, Denmark ke profesar, John ludavig heebarg ne kaansteintinopal ka daura kiya aur 13 veen sadi E. mein likhit praarthana ki gotskin charmapatr ki jaanch ki. unhonne paaya ki yeh ek palimpsest tha, ek paathya se yukt ek dastaavej jise mitaae gaye puraane kaarya ke oopar likha gaya tha. palimpsest ko banaane ke liye us par upasthit syaahi ko khurach kar nikaal diya gaya aur usaka pun: upayog kiya gaya, yeh madhya yug mein is aam pratha thi, kyonki charmapatr mahanga hota tha. palimpsest mein upasthit puraane kaarya ko vidvaanon ne10 veen sadi E mein aarkimideej ke pehle se agyaat granth ke roop mein pahachaana.[52] charmapatr sainkadon varshon tak kaansteintinopal mein ek math ke pustakaalaya mein pada raha, 1920 mein ise ek niji collector ko bech diya gaya.

29 October 1998 ko ise nyuyork mein kristi mein neelaami ke dvaara ek agyaat khareedadaar ko 2 million dollar mein bech diya gaya.[53] palimpsest mein saat granth hain, jismein mool greek mein on floting bodeej (On Floating Bodies) ki ekamaatr maujooda pratilipi bhi shaamil hai. yeh the methad of mekenikl thyorams (The Method of Mechanical Theorems), ka ekamaatr gyaat srot hai, ise suidaas se sandarbhit kiya jaata hai aur man jaata hai ki hamesha ke liye kho gaya hai. stomekeeyan ko bhi palimpsest mein khoja gaya, jismein pichhle paathyon ki tulana mein paheli ka adhik poorn vishleshan diya gaya hai.

palimpsest ko ab vaaltars kala sangrahaalaya, baalteemor, mereelaind mein rakha gaya hai, jahaan is par kai parikshan kiye gaye hain, jinmein ovararaait kiye gaye paathya ko padhne ke liye paraabaingani aur x-ray prakaash ka upayog shaamil hai.[54]


aarkimideej palimpsest mein granth hain: on the ikvalibriym of plens (On the Equilibrium of Planes), on spaairals (On Spirals), mejarameint of a circle (Measurement of a Circle), on the sfeeyar end the silindar (On the Sphere and the Cylinder), on floting bodeej (On Floating Bodies), the methad of mekenikl thyorams (The Method of Mechanical Theorems) aur stomekeeyan (Stomachion) .

viraasat

Fields medal par aarkimideej ka chitr

chaand ki satah par ek gaddha hai jise aarkimideej ke sammaan mein aarkimideej gart (29.7° N, 4.0° W) naam diya gaya hai, saath hi chaaaind ki ek parvat shrrunkhala ko bhi aarkimideej parvatamaala (25.3° N, 4.6° W) naam diya gaya hai.[55] esteroid 3600 aarkimideej ka naam bhi unke naam par diya gaya hai.[56]

ganit mein utkrusht upalabdhi ke liye field medal mein aarkimideej ka chitr hai, saath hi unka ek pramaan bhi ek gole aur belan ke roop mein diya gaya hai. aarkimideej ke sar ke chaaron or laitin mein likha gaya hai: "Transire suum pectus mundoque potiri" (apne oopar uthaana aur duniya ko pakadna).[57]

aarkimideej poorvi Germany (1973), yoonaan (1983), Italy (1983), nikaaraaguaa (1971), sain mairino (1982) aur Spain (1963) ke dvaara jaari ki gayi daak tikton par bhi dikhaayi diye.[58]

yooreka! ke vismayaadibodhak ko aarkimideej ke sammaan mein California ka ek aadarsh vaakya banaaya gaya hai. is udaaharan mein yeh shabd 1848 mein sutar ki mil ke paas sone ki khoj se sandarbh rakhata hai jo keliforniya gold rash mein saapane aaya.[59]

naagrikon se yukt ek aisa aandolan jo sanyukt raajya ke oregon raajya mein svaasthya raksha ke liye saarvabhaumik pahunch ko lakshya banta hai, ise "aarkimideej aandolan" naam diya gaya hai, iske adhyaksh poorv oregon Governor John kitsaabar hain.[60]

yeh bhi dekhein.

  • aarkimideej ka swayam siddh kathan
  • aarkimideej ki sankhya
  • aarkimideej ka virodhaabhaas
  • aarkimideej ki sampatti
  • aarkimideej ka skroo
  • aarkimideej ka thos
  • aarkimideej ke dohare vrat
  • aarkimideej ka aparimit shrrunkhalaaon ka upayog
  • daayokals
  • jalasthaitiki
  • computer varg moolon ki vidhiyaan
  • chhadm aarkimideej
  • selinon
  • steem kenan
  • vitrooviys
  • jheing heing

nots aur sandarbh

nots

a. ^ on spaairals (On Spirals) ki prastaavana mein pelusiym ke doseethiys ko sambodhit kiya gaya, aarkimideej kehte hain ki "kenan ki mrutyu ke baad kai saal gujar gaye hain". samos ka konon rahate the c. 280–220 BC sujhaav hai ki aarkimideej ek puraane jab apne kaam se kuchh likhne aadmi ho sakta hai.

b. ^ aarkimideej ke granthon ki upasthiti keval anya lekhakon ke kaaryon ke maadhyam se hi gyaat hoti hai: on sfeeyar meking aur elegajenadriya ke peppas ke dvaara ullekhit bahukoneeya aakruti par kaarya; ketaupatrika, elegajenadriya ke thiyon ke ke dvaara ullekhit prakaashiki par kaarya; prinsipls, jeyuksippas ko sambodhan aur the seind rikonar, on beleinses end leevars, on seintars of greviti, on the keleindar .

aarkimideej ke upasthit kaarya mein se, ti. L. heth nimn sujhaav dete hain, jinhein is kram mein likha gaya hai: on the ekvlibriym of plens I, the kvadraachar of the peraabola, on the ekvlibriym of plens II, on the sfeeyar end silindar I, on spaairals, on konoids end sfeeroid, on floting bodeej I, II, on the mejarameint of a circle, the seind rikonar .


s. ^ boyar, kaarl beinjaamin, a history of methemetiks (1991) ISBN 0-471-54397-7 "arabi vidvaan hamein jaankaari dete hain ki teenon bhujaaon ke padon mein ek tribhuj ke kshatrafal ke liye parichit sootr, heeron ka sootr kahalaata hai- k = √(s (sa)(sb)(sc)), jahaan s arddhaparidhi hai-yeh heeron se sadiyon pehle aarkimideej ko gyaat tha. arabi vaigyaanik "thyoram of the brokan kord ka shreya bhi aarkimideej ko hi dete hain"- arabi logon ke anusaar aarkimideej ne kai pramaan aur prameya Dean.

sandarbh

Wikisource-logo.svg
vikisors mein is lekh se sambandhit, mool paathya upalabdh hai:
  1. a aa "Archimedes Death Ray: Testing with MythBusters". MIT. http://web.mit.edu/2.009/www//experiments/deathray/10_Mythbusters.html. abhigman tithi: 2007-07-23.
  2. Calinger, Ronald (1999). A Contextual History of Mathematics. Prentice-Hall. pp. 150. aai॰aऍsa॰abee॰aऍna॰ 0-02-318285-7. "Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse (ca. 287 212 BC), the most original and profound mathematician of antiquity."
  3. "Archimedes of Syracuse". The MacTutor History of Mathematics archive. January 1999. http://www-history.mcs.st-and.ac.uk/Biographies/Archimedes.html. abhigman tithi: 2008-06-09.
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  29. sinaagoge mein elegajenadriya ke peppas ke dvaara uddharit
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agrim pathan

  • Boyer, Carl Benjamin (1991). A History of Mathematics. New York: Wiley. aai॰aऍsa॰abee॰aऍna॰ 0-471-54397-7.
  • Dijksterhuis, E.J. (1987). Archimedes. Princeton University Press, Princeton. aai॰aऍsa॰abee॰aऍna॰ 0-691-08421-1. aarkimideej ke 1938 ke adhyayan aur un ke kaarya ke anuvaad ka ek vaigyaanik itihaasakaar ke dvaara pun: prakaashan.


aarkimideej ke kaarya online

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