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Archimedes: Lever ka usool aur pani ka uchhaal

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

Gaari ka pahiya badalte waqt jack ka lamba dasta, kunwen ka dhenkli, ya Karachi ki bandargah par langar andaz hazaron ton wazni jahaz. In sab ke peechhe do saada usool hain jo taqriban sawa do hazaar saal pehle Sicily ke shehar Syracuse (Syracuse) ke ek riyazi daan ne saabit kiye. Un ka naam Archimedes (Archimedes) tha. Ek usool batata hai ke chhoti taqat bada bojh kaise utha sakti hai, doosra yeh ke pani har doobi hui cheez ko upar ki taraf kyun dhakelta hai.

Syracuse ka aalim

St Andrews University ke MacTutor archive ke mutabiq Archimedes 287 qabl masih mein Syracuse mein paida hua aur 212 qabl masih mein wahin faut hua. Us ka baap Phidias maahir-e-falakiyat tha, aur yeh baat hamein khud Archimedes ki ek kitab se maloom hoti hai. Ghalib imkan hai ke jawani mein us ne Iskandariya mein Euclid ke jaanasheenon se taleem pai, kyunke woh wahan ke riyazi daanon ko apne nataij bhejta raha.

Qadeem muarrikh Plutarch ke mutabiq woh Syracuse ke badshah Hieron doam ka dost aur rishtedar tha. Us ki shohrat apne zamane mein bhi bahut thi, magar zyada tar us ki banai hui machinon ki wajah se, jo 212 qabl masih mein Roomi muhasre ke dauran shehar ke difa mein istemal hui.

Lever ka usool

Lever yaani ek seedhi salakh jo kisi tek ya mehwar par rakhi ho, Archimedes se pehle bhi istemal hoti thi. New York University ke riyazi daan Chris Rorres ke mutabiq Aristotle ke pairokaaron se mansoob ek kitab mein bhi bataya gaya tha ke mehwar se jitna door zor lagaya jaye, bojh uthana utna aasaan hota hai.

Archimedes ka karnama yeh tha ke us ne ise geometry ki zubaan mein ek qanoon ki shakl di. Apni kitab "Sathon ka tawazun" (On the Equilibrium of Planes) ke pehle hisse mein us ne likha ke do wazan us waqt tawazun mein hote hain jab mehwar se un ke faasle un ke wazan ke ulte tanasub mein hon. Aasaan lafzon mein: agar ek wazan doosre se das guna bhaari hai to halke wazan ko mehwar se das guna door rakh kar dono ko barabar kiya ja sakta hai. Isi kitab mein us ne musallas aur mutawazi-ul-azla jaisi ashkal ka markaz-e-saql bhi maloom kiya.

Rorres yeh bhi batate hain ke maahireen mein is par bahas rahi hai ke Archimedes ne darasal kya saabit kiya aur us ke saboot mein kaun se mafroze chhupe hue the.

Isi usool se Archimedes ka mashhoor jumla juda hai, jo taqriban paanch sadi baad Iskandariya ke Pappus (Pappus) ne naqal kiya: "Mujhe khade hone ki jagah do, main zameen ko hila doon ga." Plutarch ek qissa bhi bayan karta hai ke Archimedes ne gharniyon ke nizam se, akele, saman aur musafiron se lada ek jahaz khushki par kheench kar dikhaya.

Pani ka uchhaal

Doosri badi daryaft Archimedes ki kitab "Tairte ajsam" (On Floating Bodies) mein hai. MacTutor ke mutabiq is kitab ne mayeaat ke sukoon yaani hydrostatics ki bunyad rakhi. Bartanvi muarrikh-e-riyazi T L Heath ke angrezi tarjume ke mutabiq is mein saabit kiya gaya hai ke jo thos cheez maye se halki ho aur use zabardasti dubaya jaye, maye use ek quwwat se upar dhakelta hai; aur jo cheez maye se bhaari ho woh tah mein baith jati hai magar maye mein us ka wazan itna kam ho jata hai jitna us ke hataye hue maye ka wazan hai.

Yehi "usool-e-Archimedes" hai. Isi se samajh aata hai ke lohe ka jahaz kyun tairta hai: us ki shakl itna pani hatati hai jis ka wazan jahaz ke wazan ke barabar ho jaye. Archimedes ne mukhtalif shaklon ke tairte ajsam ke tawazun par bhi kaam kiya.

Sone ka taaj aur "Eureka"

Is daryaft se juda qissa duniya bhar mein mashhoor hai, magar yeh Archimedes ki apni tehreer mein nahin balke taqriban do sadi baad Roomi maahir-e-tameeraat Vitruvius (Vitruvius) ki kitab mein milta hai. Is ke mutabiq badshah Hieron ko shak tha ke sunar ne taaj ke sone mein chandi mila di hai. Archimedes ghusl ke liye tub mein utra to dekha ke jitna jism doobta hai utna pani bahar nikalta hai. Woh khushi se "Eureka, Eureka" yaani "main ne pa liya" pukarta hua ghar ki taraf dauda. Phir us ne taaj ke barabar wazan ke sone aur chandi ke tukdon se nikalne wala pani naap kar milawat saabit kar di.

Rorres ke mutabiq qisse mein bayan kiya gaya tareeqa us daur ke aalaat ke lihaz se bahut bareek farq naapne ka taqaza karta, is liye bahut se maahireen ka khayal hai ke Archimedes ne tarazu aur uchhaal ka usool istemal kiya hoga. Heath ki raye mein "Tairte ajsam" ka satvan masla hi is sawal ka asal hal batata hai.

Miti hui tehreer se nayi daryaft

Archimedes ki kai kitaben sadiyon tak gum rahin. Archimedes Palimpsest project ke mutabiq terahvin sadi ki ek duaiya kitab ke safhat ke neeche, kai sadi purani mitai hui tehreeren maujood hain, jin mein Archimedes ki do aisi kitaben bhi hain jo kahin aur nahin milti: "Tareeqa" (The Method) aur "Stomachion". Yeh nuskha 29 October 1998 ko neelami mein farokht hua aur phir America ke Walters Art Museum mein rakha gaya, jahan jadeed aksbandi se us ka matan padha gaya.

Aaj ki zindagi mein

Lever ka usool har qainchi, hathore ke panje, cycle ke pedal aur hand pump ke daste mein kaam kar raha hai. Uchhaal ka usool jahaz, kashti aur aabdoz ke design ki bunyad hai, aur Gwadar se Karachi tak hamari sahili zindagi ki har kashti isi par tairti hai. Archimedes ne dikhaya ke rozmarra ki machinon ke peechhe aise qanoon hain jinhen riyazi se saabit kiya ja sakta hai. Yehi soch baad ki saari tabiyaat ki bunyad bani.

Makhaz

J. J. O'Connor and E. F. Robertson, "Archimedes of Syracuse", MacTutor History of Mathematics Archive, University of St Andrews (1999). https://mathshistory.st-andrews.ac.uk/Biographies/Archimedes/ — born 287 BC, died 212 BC, Syracuse; father Phidias the astronomer; probable study in Alexandria; relation of Hieron II (Plutarch); war machines in the siege of 212 BC; Plutarch's ship story; On plane equilibriums (centres of gravity) and On floating bodies (foundations of hydrostatics, Archimedes' principle); The Method found by Heiberg in 1906.
Chris Rorres, "Archimedes' Lever: Introduction" and "Law of the Lever", Archimedes Home Page, New York University. https://math.nyu.edu/~crorres/Archimedes/Lever/LeverIntro.html and https://math.nyu.edu/~crorres/Archimedes/Lever/LeverLaw.html — Pappus' quotation (Collection VIII, c. AD 340); the law as stated in On the Equilibrium of Planes I, Props. 6–7; debate over the proof; earlier Peripatetic Mechanica.
Chris Rorres, "The Golden Crown: Introduction", Archimedes Home Page, NYU. https://math.nyu.edu/~crorres/Archimedes/Crown/CrownIntro.html — Vitruvius' story and why the overflow method would have been too imprecise.
Vitruvius, The Ten Books on Architecture, Book IX, Introduction §9–12, tr. Morris Hicky Morgan (1914), Project Gutenberg eBook #20239. https://www.gutenberg.org/cache/epub/20239/pg20239.txt — the crown of Hiero, the bath, "Eureka", and the overflow test.
T. L. Heath (ed. and tr.), The Works of Archimedes, Cambridge University Press, 1897, "On Floating Bodies" I, Props. 6–7 and note, archive.org scan. https://archive.org/details/worksofarchimede029517mbp — upward force on an immersed body lighter than the fluid; a heavier body lighter in the fluid by the weight of fluid displaced; Heath's note linking Prop. 7 to the crown.
The Archimedes Palimpsest Project (Walters Art Museum). https://www.archimedespalimpsest.org/ — 13th-century prayer book over erased texts including The Method and Stomachion, found nowhere else; sold at auction 29 October 1998; deposited at the Walters Art Museum.

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