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Euclid ki ‘Usool’: do hazar saal ki nisabi kitab

Pakistan ke kisi bhi school ki geometry ki copy kholein to ek jumla zaroor milega: "Saabit kijiye ke...". Phir ek shakl, kuch mufrooze, aur qadam ba qadam daleel. Yeh tareeqa taqriban teis sau saal pehle Misr ke shehar Iskandariya…

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

Euclid ki ‘Usool’: do hazar saal ki nisabi kitab — Alamati tasveer

Pakistan ke kisi bhi school ki geometry ki copy kholein to ek jumla zaroor milega: "Saabit kijiye ke…". Phir ek shakl, kuch mufrooze, aur qadam ba qadam daleel. Yeh tareeqa taqriban teis sau saal pehle Misr ke shehar Iskandariya mein ek Yunani ustad ne munazzam kiya tha. Us ka naam Euclid tha aur us ki kitab "Usool" (Elements) duniya ki kamyab tareen nisabi kitabon mein shumar hoti hai.

Euclid kaun tha

Hairat ki baat yeh hai ke itni mashhoor kitab ke musannif ke baare mein hum taqriban kuch nahin jaante. America ki Clark University ke riyazi-daan David Joyce ke mutabiq Euclid taqriban 300 qabl masih mein Iskandariya mein rehta tha, aur yeh andaza bhi panchvin sadi eesvi ke falsafi Proclus ki ek tehreer par mabni hai, jo Euclid se taqriban aath sau saal baad hua.

Proclus ke mutabiq Euclid Aflatoon ke shagirdon ke baad aur Archimedes se pehle ke zamane ka tha, aur Misr ke badshah Ptolemy awwal ke daur mein raha. Usi ne yeh qissa bhi naqal kiya ke badshah ne geometry seekhne ka koi aasan raasta poochha to Euclid ne jawab diya ke geometry ka koi shahi raasta nahin.

St Andrews University ke MacTutor archive ke mutabiq baaz mu-arrikhin ne yeh sawal bhi uthaya ke kya "Usool" ek hi shakhs ki tasneef hai ya Iskandariya ke riyazi-daanon ki ek jamaat ka kaam. Taham do hazar saal tak aam taur par ise ek hi musannif ki kitab maana gaya hai.

Kitab mein kya hai

"Usool" terah hisson par mushtamil hai. MacTutor ke mutabiq pehle chhe hisse sathi geometry yaani musallas, mutawazi khutoot, murabba aur daire ke baare mein hain. Satvein se nauvein hisse mein adaad ka nazariya hai, jis mein do adaad ka aad-e-azam maloom karne ka woh tareeqa bhi shamil hai jise aaj Euclidean algorithm kehte hain. Daswan hissa ghair natiq miqdaron par hai, aur aakhri teen hisse thos ashkal par hain. Kitab is saboot par khatam hoti hai ke baqaida thos ashkal sirf paanch ho sakti hain.

Kitab ki asal taqat us ki tarteeb hai. Euclid pehle tareefein deta hai, phir paanch bunyadi mufrooze, aur kuch "aam tasawwurat", masalan yeh ke jo cheezein ek hi cheez ke barabar hon woh aapas mein bhi barabar hoti hain. Us ke baad har nateeja pichhle nataij se daleel ke zariye nikala jata hai. Pehla mufroza yeh hai ke kisi bhi do nuqton ke darmiyan seedhi lakeer kheenchi ja sakti hai. Panchwan, mashhoor "mutawazi khutoot ka mufroza", sadiyon tak bahas ka mauzu raha.

MacTutor ke mutabiq kitab ke zyada tar nataij shayad Euclid ne khud daryaft nahin kiye the. Eudoxus aur Theaetetus jaise pehle ke riyazi-daanon ka kaam is mein shamil hai. Magar mawad ki tarteeb aur peshkash yaqinan Euclid ki hai, aur yahi us ka asal karnama hai.

Sab se purane nuskhe

Euclid ke haath ka likha kuch baqi nahin. MacTutor, mu-arrikh David Fowler ke hawale se, batata hai ke is mawad ki sab se purani jhalak mitti ke chhe thikron par milti hai jo 1906 se 1908 ke douran darya-e-Nile ke jazire Elephantine se mile. Un ki tareekh teesri sadi qabl masih ki teesri chauthai batai jati hai. Un par terahwein hisse ke mazameen hain, magar alfaz kitab ke matan se mukhtalif hain, jaise koi talib-e-ilm mushkil mawad samajhne ki koshish kar raha ho.

Misr ke qadeem shehar Oxyrhynchus se mila papyrus ka ek tukra, jo ab America ke Penn Museum mein hai, dusre hisse ke panchwein masle ka matan aur shakl dikhata hai. Us ki tareekh par hawale mukhtalif hain: baaz ise pehli ya dusri sadi eesvi ka batate hain aur baaz teesri ya chauthi sadi ka.

Arabi se Latini tak

Yunan ke baad is kitab ko zinda rakhne mein Arabi mutarjimeen ka bara hissa hai. MacTutor ke mutabiq Al-Hajjaj bin Yusuf ne "Usool" ka Yunani se Arabi mein tarjuma kiya, aur baad mein riyazi-daan Al-Nayrizi (wafat taqriban 922) ne Al-Hajjaj ke dusre tarjume par nazar-e-sani ki aur us par sharh likhi, jo aaj bhi maujood hai. Terahwin sadi mein Nasir al-Din Tusi (1201 ta 1274) ne bhi Euclid ke kaam ka nazar-e-sani shuda Arabi matan tayyar kiya.

England ke Adelard of Bath, jo 1075 mein paida hua aur 1160 mein faut hua, ne Arabi makhaz se "Usool" ka Latini tarjuma kiya. MacTutor ke mutabiq us ne apne pehle, mukammal tarjume mein ghaliban Al-Hajjaj ke Arabi tarjume ko bunyad banaya, aur us ke tarjume sadiyon tak Europe mein geometry ki bunyadi kitab rahe. 1482 mein yeh kitab pehli baar chhapi, aur tab se us ke ek hazar se zyada edition shaya ho chuke hain.

Aaj ki zindagi mein Euclid

MacTutor ke mutabiq unneesvin sadi tak "Usool" geometry ki daleel ka bunyadi makhaz rahi. Usi sadi mein riyazi-daanon ne panchwan mufroza chhor kar nayi, ghair Euclidean geometriyan baniyan, jo baad mein jadeed tabiyat ke kaam aayin.

Magar rozmarra zindagi mein Euclid har jagah hai. Mistri jab deewar ka kona seedha karne ke liye dhaage aur paimaish se zaviya-e-qaima banata hai, engineer jab sadak aur pul ka naqsha kheenchta hai, ya computer jab do adaad ka aad-e-azam nikalta hai, to woh isi kitab ki mantiq istemal kar raha hota hai. Sab se barh kar Euclid ne yeh sikhaya ke kisi baat ko maan lena kafi nahin, ise saabit karna hota hai. School ki copy mein likha "Saabit kijiye" isi purani riwayat ki goonj hai.

Makhaz

J. J. O'Connor and E. F. Robertson, "Euclid of Alexandria", MacTutor History of Mathematics Archive, University of St Andrews (1999). https://mathshistory.st-andrews.ac.uk/Biographies/Euclid/ — Proclus' account and the "no royal road" story; the three hypotheses about authorship; contents of the 13 books, postulates and common notions; results mostly due to predecessors, organisation due to Euclid; Elephantine ostraca (1906–08, third quarter of the 3rd century BC) after Fowler; fragment of AD 75–125; more than 1,000 editions since first printing in 1482; main source of geometric reasoning until the 19th century.
David E. Joyce, "Euclid", Euclid's Elements (online edition), Clark University. https://mathcs.clarku.edu/~djoyce/java/elements/Euclid.html — lived in Alexandria about 300 BCE; dating rests on Proclus, writing about 800 years later; full Proclus passage.
J. J. O'Connor and E. F. Robertson, "Adelard of Bath", MacTutor. https://mathshistory.st-andrews.ac.uk/Biographies/Adelard/ — born 1075, died 1160; Latin translations of the Elements from Arabic, chief geometry textbooks in the West for centuries; first version probably based on al-Hajjaj's Arabic translation.
J. J. O'Connor and E. F. Robertson, "Al-Nayrizi", MacTutor. https://mathshistory.st-andrews.ac.uk/Biographies/Al-Nayrizi/ — born c. 865, died c. 922; surviving commentary on the Elements; revision of al-Hajjaj's second Arabic translation, which has not survived.
J. J. O'Connor and E. F. Robertson, "Nasir al-Din al-Tusi", MacTutor. https://mathshistory.st-andrews.ac.uk/Biographies/Al-Tusi_Nasir/ — 1201–1274; revised Arabic versions of works by Euclid and other Greek authors.
Wikimedia Commons, "P.Penn. Museum inv. E02748 Euclid's Elements 2.5.jpg" (P.Oxy. 29). https://commons.wikimedia.org/wiki/File:P.Penn._Museum_inv._E02748_Euclid%27s_Elements_2.5.jpg — originally P.Oxy. 29, now Penn Museum inv. E02748; fragment of Book II, Proposition 5, dated there to the 3rd–4th century CE; CC BY-SA 4.0.
"Euclid's Elements", Wikipedia (pointer only). https://en.wikipedia.org/wiki/Euclid%27s_Elements — P.Oxy. 29 dated c. AD 75–125 in the body text; cross-check for and the Elephantine ostraca.

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