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Eratosthenes: Ek saaye se naapi gayi zameen

Atemad E-Magazine 20 October 2026 · 6 minute ka mutalia

Aaj hum khala mein ghoomte satellites se zameen ko naapte hain. Magar sawa do hazar saal pehle Misr ke shehar Iskandariya mein ek kutub khane ke nigran ne yehi kaam ek seedhi chhari, uske saaye aur thodi si geometry se kar dikhaya tha. Un ka naam Eratosthenes (Eratosthenes) tha, aur un ka hasil kiya hua jawab hairat angez hadd tak durust nikla.

Iskandariya ka librarian

St Andrews University ke MacTutor archive ke mutabiq Eratosthenes aaj ke Libya ke shehar Cyrene (Cyrene) mein paida hue aur kuch baras Athens mein Taleem hasil ki. Misr ke badshah Ptolemy III ne unhein apne bete ka ataleeq bana kar Iskandariya bulaya. Taqriban 240 qabl masih mein apne ustad Callimachus ki wafat ke baad woh Iskandariya ke mashhoor kutub khane ke teesre nigran bane, jis ke bare mein kaha jata hai ke is mein lakhon tomar the.

Woh kai uloom ke mahir the: riyazi, falakiyat, jughrafiya aur tareekh. MacTutor ke mutabiq un ke hum asar unhein "Beta" kehte the, yaani har maidan mein doosre number par, agarche un ke kai kaam aaj bhi science ke tareeqon ki bunyad hain. Aadad ke nazariye mein mufrad aadad chhantne ka "Eratosthenes ki chhalni" naami tareeqa aaj bhi parhaya jata hai. World History Encyclopedia ke mutabiq unhon ne "Jughrafiya" ke naam se teen jildon ki ek kitab bhi likhi.

Saaye ka hisab

Zameen ki paimaish par Eratosthenes ki apni kitab gum ho chuki hai. Is ki tafseel hum tak baad ke musannifeen, khusoosan Cleomedes (Cleomedes), ke zariye pahunchi hai. British muarrikh-e-riyazi T. L. Heath ne 1913 ki apni kitab mein yeh tareeqa yun bayan kiya hai.

Mausam-e-garma ke sab se lambe din, yaani taqriban 21 June, ko dopahar ke waqt janubi Misr ke shehar Syene (Syene), jo aaj ka Aswan hai, mein sooraj bilkul sar ke upar hota tha aur koi saaya nahin banta tha. Usi waqt shimal mein Iskandariya mein ek pyala numa dhoop ghari ki sui saaya dalti thi. Eratosthenes ne naapa ke yeh saaya poore daire ka pachaswan hissa banata hai, yaani taqriban sawa saat darje.

Ab unhon ne do mafroze qayam kiye. Ek, sooraj itna door hai ke us ki kirnein zameen par har jagah mutawazi parti hain. Do, Iskandariya aur Syene ek hi shimal janub lakeer par hain. Agar yeh durust ho to saaye ka zawiya wohi hai jo zameen ke markaz par in donon shehron ke darmiyan banta hai. Yaani donon shehron ka fasla zameen ke poore muheet ka pachaswan hissa hai.

Donon shehron ka fasla paanch hazar stadia mana jata tha. Heath ke mutabiq yeh ghaliban ek gol adad tha. Pachas zarb paanch hazar: zameen ka muheet dhai lakh stadia.

Jawab kitna durust tha

Yahan ek uljhan hai. Heath likhte hain ke Cleomedes dhai lakh ka adad deta hai, magar Yunani jughrafiya dan Strabo ke mutabiq Eratosthenes ka adad do lakh bawan hazar stadia tha, aur qadeem zamane mein yehi zyada naqal hua. Heath ke khayal mein mumkin hai Eratosthenes ne khud baad mein ise badla ho taake ek darje ke liye saat sau stadia ka gol adad ban jaye.

Asal sawal yeh hai ke ek stadia kitna lamba tha, kyunke Yunani duniya mein yeh paimana jagah jagah mukhtalif tha. MacTutor ke mutabiq agar Roomi musannif Pliny ki bunyad par ise taqriban 157 meter mana jaye to Eratosthenes ka jawab hairat angez hadd tak durust hai, aur agar taqriban 167 meter mana jaye to kam durust. NASA ke mutabiq aaj zameen ka ausat nisf qutar 6,371 kilometer hai, jis se muheet taqriban chalis hazar kilometer banta hai. Chhota stadia lein to Eratosthenes ka adad isi ke qareeb aata hai.

MacTutor ek aur raye bhi bayan karta hai: muhaqqiq Rawlins ke mutabiq Eratosthenes ne ghaliban khud sirf Iskandariya ka zawiya naapa, aur baqi maloomat doosre zaraye se lien. Tafseelat par bahas apni jagah, magar tareeqa bilkul durust tha, aur asal karnama yehi hai.

Biruni aur Nandana ka qila

Eratosthenes ke barah sau saal se zyada arse baad zameen naapne ka ek aur mashhoor tajurba aaj ke Pakistan mein hua. Paris Observatory ki falakiyati lughat ke mutabiq Abu Rehan al-Biruni (973 ta 1048) ne yeh paimaish zila Jhelum ke namak ke pahari silsile mein Nandana ke qile par ki. Eratosthenes ke tareeqe mein do door daraz shehron ki zaroorat thi, magar Biruni ne ek hi jagah se kaam chalaya.

Pehle unhon ne astrolabe se do jagahon se zawiye le kar ek pahari ki unchai maloom ki. Phir choti par chadh kar dekha ke ufaq aankh ki seedh se kitna neeche nazar aata hai. In donon se musallasaat ke zariye zameen ka nisf qutar nikala. MacTutor ke mutabiq un ka jawab 6,339.6 kilometer tha. Paris Observatory ki lughat yeh bhi kehti hai ke itni durusti juzvi tor par ittefaq thi, kyunke maidan bilkul hamwar nahin tha.

Aaj ka sabaq

Eratosthenes ka tajurba aaj duniya bhar ke schools mein dohraya jata hai. Is ke liye sirf ek seedhi chhari, ek feeta aur kisi doosre shehar ke dost ki zaroorat hai jo usi din, usi waqt, apni chhari ka saaya naape. Quetta aur Karachi ke do schools mil kar yeh tajurba kar sakte hain. Sabaq wohi hai jo Iskandariya ke librarian ne diya tha: bare sawal ka jawab kabhi kabhi ek saaye mein chhupa hota hai, bas ise soch samajh kar naapna aana chahiye.

Makhaz

J. J. O'Connor and E. F. Robertson, "Eratosthenes of Cyrene", MacTutor History of Mathematics Archive, University of St Andrews. https://mathshistory.st-andrews.ac.uk/Biographies/Eratosthenes/ — born in Cyrene, studied in Athens; called to Alexandria by Ptolemy III as tutor; third librarian after Callimachus' death about 240 BC; nickname "Beta"; sieve of primes; Syene–Alexandria noon shadows at midsummer, parallel rays, 250,000 stadia; stade of 157.2 m (Pliny) or 166.7 m (Gulbekian); Rawlins on the Alexandria zenith distance.
T. L. Heath, Aristarchus of Samos, the Ancient Copernicus, Oxford: Clarendon Press, 1913, pp. 339–340, archive.org scan. https://archive.org/details/aristarchusofsam00heatuoft — no shadow at Syene at the summer solstice; gnomon in a scaphe at Alexandria showing one-fiftieth of the circle; 5,000 stades probably a round figure; 250,000 (Cleomedes) versus 252,000 (Strabo); possible correction to 700 stades per degree; stade of 157.5 m from Pliny.
Joshua J. Mark, "Eratosthenes", World History Encyclopedia. https://www.worldhistory.org/Eratosthenes/ — head librarian at Alexandria; Syene (Aswan) well lit at the solstice; measurement c. 240 BCE; three-volume Geography.
NASA Goddard Space Flight Center, NSSDCA, "Earth Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html — volumetric mean radius 6,371 km (equatorial 6,378.137 km, polar 6,356.752 km).
"Biruni's method", An Etymological Dictionary of Astronomy and Astrophysics, Observatoire de Paris. https://dictionary.obspm.fr/terms/birunis-method/ — Biruni (973–1048) measured the Earth's radius on-site at Nandana Fort in the Salt Range; hill height by two sightings with an astrolabe, then the dip of the horizon; precision partly fortuitous.
J. J. O'Connor and E. F. Robertson, "Abu Arrayhan Muhammad ibn Ahmad al-Biruni", MacTutor. https://mathshistory.st-andrews.ac.uk/Biographies/Al-Biruni/ — radius of the Earth found to be 6,339.6 km.
Iftikhar Ahmad, "Al-Bairuni's Lab: Heritage goldmine Nandna fort undergoing conservation work", Associated Press of Pakistan. https://www.app.com.pk/features/al-bairunis-lab-heritage-goldmine-nandna-fort-undergoing-conservation-work — Nandna fort in Pind Dadan Khan, District Jhelum, Salt Range, where al-Biruni calculated the Earth's radius.

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