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Al-Biruni ki paimaishein: Nandana ki pahari se sone ke wazan tak

Is silsile ke pachisweein mazmoon mein hum ne dekha tha ke Abu Rehan al-Biruni (al-Biruni) ne zila Jhelum ke Nandana qile par zameen ka nisf qutar naapa. Is baar hum isi paimaish ko qareeb se dekhenge: unhon ne theek theek kya kya, hisab kaise lagaya, aur kahan ghalti ka imkan tha. Phir hum…

Atemad E-Magazine 20 October 2026 · 7 minute ka mutalia

Al-Biruni ki paimaishein: Nandana ki pahari se sone ke wazan tak — Alamati tasveer

Ek bemisal muhaqqiq

St Andrews University ke MacTutor Archive ke mutabiq al-Biruni 15 September 973 ko Khwarizm ke shehar Kath ke qareeb (aaj ka Uzbekistan) paida hue aur 13 December 1048 ko Ghazni (aaj ka Afghanistan) mein faut hue. MacTutor, muarrikh Kennedy ke hawale se, batata hai ke unhon ne taqriban 146 kitabein likhin jin ke kul safhat taqriban terah hazar bante hain, magar in mein se panchwan hissa bhi aaj baqi nahin.

Al-Biruni ki pehchan un ki bareek beeni hai. MacTutor ke mutabiq unhon ne 990 mein sooraj ki sab se zyada bulandi naap kar Kath ka arz-e-balad nikala, 1018 se 1020 ke douran Ghazni ka, aur Punjab aur Kashmir ke gyarah shehron ka arz-e-balad maloom kiya. Un ki kitab "Qanun-e-Masudi" mein taqriban 600 muqamat ke mahal-e-woqoo ki fehrist hai.

Nandana: pehla qadam, pahari ki oonchai

Paris Observatory ki falakiyati lughat ke mutabiq al-Biruni ka tareeqa do qadmon par mushtamil tha. Pehle unhein ek pahari ki theek oonchai chahiye thi. Is ke liye woh maidan mein do aisi jagahon par khade hue jo pahari ki chotti ke sath ek hi seedh mein theen, aur donon jagahon ka darmiyani fasla naapa. Phir astrolabe se donon jagahon se chotti ka zawiya-e-bulandi liya.

In do zawiyon aur darmiyani fasle se, musallas ke tangent ke qaide ke zariye, pahari ki oonchai nikal aati hai. Lughat ke mutabiq qaida yeh hai: oonchai barabar hai fasla zarb pehle zawiye ka tangent zarb doosre zawiye ka tangent, taqseem donon tangent ke farq par. Is hisab se pahari ki oonchai taqriban 321.5 meter nikli.

Doosra qadam: ufuq kitna jhuka hua hai

Ab al-Biruni chotti par chadhe aur door hamwar maidan ke ufuq ki taraf dekha. Agar zameen chapti hoti to ufuq bilkul aankh ki seedh mein hota. Magar zameen gol hai, is liye oonchai se ufuq thora sa neeche nazar aata hai. Isi jhukao ke zawiye ko "ufuq ka jhukao" kehte hain, aur al-Biruni ne ise naapa.

Ab zara tasawwur kijiye. Chotti se ufuq tak jane wali nazar ki lakeer zameen ko sirf ek nuqte par chhooti hai. Is nuqte se zameen ke markaz tak ki lakeer, yaani nisf qutar, is nazar ki lakeer par amood hoti hai. Yoon ek qaima zawiya musallas banti hai: ek zila nisf qutar, aur witr nisf qutar jama pahari ki oonchai. Markaz par banne wala zawiya wohi hota hai jo ufuq ka jhukao hai. Lughat ke mutabiq is se yeh qaida nikalta hai: nisf qutar barabar hai oonchai zarb is zawiye ka cosine, taqseem ek minus cosine par.

Jawab aur is ki hadein

Paris Observatory ki lughat ke mutabiq al-Biruni ka jawab 12,851,369.845 haath (cubit) tha, jo mowafiq paimana lene par taqriban 6,335.725 kilometer banta hai. MacTutor yehi nateeja 6,339.6 kilometer likhta hai. NASA ke mutabiq zameen ka ausat nisf qutar 6,371 kilometer hai, yaani farq bohat kam hai.

Muhaqqiqa Amelia Sparavigna (Amelia Sparavigna) ke 2013 ke ek tehqeeqi maqale ke mutabiq al-Biruni ka apna aala taqriban das minute qaus tak ka zawiya naap sakta tha, is liye paimaish ki durustgi ka bara raaz zawiyon ke sine ki durust qadron mein tha, jo unhon ne ghaliban Hindustani riyazi ke makhazon se li theen. Paris Observatory ki lughat yeh bhi kehti hai ke itni durustgi juzwi taur par ittifaq thi, kyunke maidan samundar ki tarah bilkul hamwar nahin tha, aala itna bareek nahin tha, aur hawa mein roshni ka mudna bhi nateeje par asar dalta hai. Tareeqa magar bilkul durust tha.

Sona, para aur jawahirat

Al-Biruni ne sirf zameen nahin, cheezon ka "wazan fi hajm" yaani kasafat bhi naapi. MacTutor ke mutabiq unhon ne sona, para, seesa, chandi, kansa, tamba, pital, loha aur qalai ki kasafat ka ek doosre se muwazna kiya.

Sparavigna ke mutabiq is kaam ke liye unhon ne ek makhrooti bartan istemal kiya jis ki gardan ke paas ek nalki lagi thi. Bartan ko pani se itna bhara jata ke pani nalki se behne lage. Phir toli hui cheez andar dali jati, aur jitna pani bahar nikalta use tarazu ke palle mein jama kar ke tola jata. Cheez ka wazan aur hatae gaye pani ka wazan, donon ki nisbat se kasafat mil jati. Yeh bartan baad mein barhwin sadi ke alim al-Khazini ne apni "Kitab Mizan al-Hikma" mein bayan kiya. Al-Biruni ka mashwara tha ke namoona jitna bara ho, nateeja utna durust hoga.

Jawahirat ki kitab "Kitab al-Jamahir" se Sindhi Adabi Board ki shaya karda ek jadwal ke mutabiq al-Biruni ne pani ke muqable mein sone ki kasafat 19.05, pare ki 13.58 aur lohe ki 7.74 nikali. Isi jadwal mein 1876 ki jadeed paimaishein bil-tarteeb 19.30, 13.568 aur 7.79 darj hain. Sparavigna ke mutabiq al-Biruni ne jawahirat ko sirf rang se pehchanne par aitraz kiya aur kaha ke kasafat, chamak aur sakhti asal khususiyat hain.

Kitab al-Hind: ek science mushahida

Barre-saghir mein qiyam ke douran al-Biruni ne Sanskrit seekhi. MacTutor ke mutabiq un ki kitab "Kitab al-Hind" mein yahan ke likhne ke tareeqon, adad ke nizam, jughrafiye, falakiyat aur taqweem ka tafseeli bayan hai, aur unhon ne kai Sanskrit kitabon ka Arabi mein tarjuma kiya. Nandana ka qila aaj bhi Punjab ke namak ke pahari silsile mein mojood hai. Is ki chotti se nazar aane wala ufuq yaad dilata hai ke ek hazar saal pehle isi manzar se poori zameen naapi gayi thi.

Makhaz

"Biruni's method", An Etymological Dictionary of Astronomy and Astrophysics, Observatoire de Paris. https://dictionary.obspm.fr/terms/birunis-method/ — on-site at Nandana Fort; hill height from two sightings with an astrolabe, h = d tanθ1 tanθ2 / (tanθ2 − tanθ1), 321.5 m; dip of the horizon, R = h cosθ / (1 − cosθ); 12,851,369.845 cubits, about 6,335.725 km with favourable units; precision partly by chance (uneven plain, instrument, refraction).
J. J. O'Connor and E. F. Robertson, "Abu Arrayhan Muhammad ibn Ahmad al-Biruni", MacTutor History of Mathematics Archive, University of St Andrews. https://mathshistory.st-andrews.ac.uk/Biographies/Al-Biruni/ — born 15 Sep 973 near Kath, died 13 Dec 1048 Ghazna; about 146 works, under one fifth surviving; latitudes of Kath (990), Ghazna (1018–1020), eleven towns in Punjab and Kashmir; 24 May 997 eclipse with Abu'l-Wafa; about 600 places in the Mas'udic Canon; recorded discarded observations; Earth radius 6,339.6 km; specific weights of nine metals; Kitab al-Hind contents and Sanskrit translations.
Amelia Carolina Sparavigna, "The Science of al-Biruni", arXiv:1312.7288 (2013). https://arxiv.org/abs/1312.7288 — instrument reading to about 10 arc minutes, sine values from Indian sources; overflow cone-shaped vessel described by al-Khazini (fl. 1115–1130); weighing displaced water; large samples for accuracy; gems judged by specific gravity, brilliance and hardness rather than colour (after Razaullah Ansari).
Sindhi Adabi Board, table of al-Biruni's specific gravities from Kitab al-Jamahir, with Clement-Mullet (1858) and Bolton (1876) values. https://sindhiadabiboard.org/Catalogue/Personalties/Book47/Book_page25.html — gold 19.05 (Bolton 19.30), mercury 13.58 (13.568), iron 7.74 (7.79).
NASA Goddard Space Flight Center, NSSDCA, "Earth Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html — volumetric mean radius 6,371 km.

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