Safha-e-Awwal› E-Magazine ›100 Bari Daryaftein aur Ijadat

Logarithm: Zarb ko jama mein badalne ka gur

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

Aaj koi badi zarb karni ho to hum jeb se mobile nikal lete hain. Magar chaar sau saal pehle mahireen-e-falakiyat, jahaz ranon aur zameen ki pemaish karne walon ko saat saat hindson ki zarbein aur taqseemein haath se karni padti thin. Ek hisab mein kai ghantay lag jate aur zara si ghalti sara kaam bigaad deti. 1614 mein Scotland ke ek zamindar riyazi dan ne ek aisi tarkeeb pesh ki jis ne yeh mushaqqat aadhi kar di. Un ka naam John Napier tha aur un ki tarkeeb ko logarithm kaha jata hai.

Merchiston ka riyazi dan

St Andrews University ke MacTutor Archive ke mutabiq Napier 1550 mein Edinburgh ke Merchiston Castle mein paida hue aur 4 April 1617 ko Edinburgh hi mein faut hue. Woh pesha war ustad nahin the balke apni jagir sambhalte the, aur riyazi un ka shauq tha. MacTutor likhta hai ke logarithm par un ka zyada tar kaam us zamane mein hua jab woh 1574 ke baad Gartness mein rehte the.

1614 mein unhon ne latini zaban mein ek kitab shaya ki jis ka naam tha “Mirifici logarithmorum canonis descriptio”, yani “logarithm ke hairat angez jadwal ki tafseel”. 1616 mein Edward Wright ne us ka angrezi tarjuma kiya.

Tarkeeb kya hai?

Logarithm ka bunyadi khayal sada hai. 10 ko 10 se zarb dein to 100 banta hai, yani 10 do baar. 1,000 mein 10 teen baar zarb hota hai. Ab agar hamein 100 aur 1,000 ko zarb dena ho to sirf “do” aur “teen” ko jama kar lein: paanch. Yani jawab mein 10 paanch baar zarb hoga, aur woh hai ek lakh. Yeh “do” aur “teen” hi in aadad ke logarithm hain.

Yehi usool har adad par laagu hota hai, chahe woh 10 ki seedhi taqat na ho. Agar kisi ke paas ek jadwal ho jis mein har adad ke samne us ka logarithm likha ho, to woh do aadad ke logarithm jadwal se dekhega, unhein jama karega aur hasil ko dobara jadwal mein dhoond kar jawab parh lega. Zarb, jama ban jati hai aur taqseem, tafreeq. Jazr nikalna ho to logarithm ko aadha kar diya jaye.

MacTutor ke mutabiq Napier ne yeh khayal algebra se nahin balke harkat ki ek misal se nikala tha: do nuqte do lakiron par alag alag andaz se chalte hain aur un ke faslon ka talluq logarithm deta hai. Unhon ne bunyadi lakir ki lambai ek karor (10 ki saat taqat) rakhi, kyunke us zamane ke behtareen musallasati jadwal saat ashariya maqam tak durust the. Un ke nizam mein 1 ka logarithm sifar nahin tha, aur aaj ki tarah koi “bunyad” bhi tay nahin thi.

Henry Briggs aur das ki bunyad

Napier ki kitab London pahunchi to Gresham College ke geometry ke professor Henry Briggs us par fareefta ho gaye. MacTutor un ka yeh jumla naql karta hai ke unhon ne kabhi koi aisi kitab nahin dekhi jis ne unhein is se zyada khush aur hairan kiya ho. Woh 1615 ki garmiyon mein London se Edinburgh gaye aur taqriban ek mahina Napier ke sath rahe, phir 1616 mein dobara gaye.

In mulaqaton mein donon ne tay kiya ke naye jadwal das ki bunyad par hon aur 1 ka logarithm sifar ho. Unhein aaj “aam logarithm” kaha jata hai. Napier 1617 mein faut ho gaye, is liye yeh kaam Briggs ne aage barhaya. Unhon ne usi saal ek hazar aadad ka pehla mukhtasar jadwal shaya kiya, aur 1624 mein “Arithmetica logarithmica” mein 1 se 20,000 aur 90,000 se ek lakh tak ke aadad ke logarithm chaudah ashariya maqam tak diye. MacTutor ke mutabiq darmiyan ka khala Holland ke Adriaan Vlacq ne 1628 mein pur kiya.

Ek aur mojid

Switzerland ke ghari saaz aur mahir-e-aalat Jost Burgi ne bhi logarithm jaisa nizam alag se banaya. MacTutor ke mutabiq un ka tareeqa Napier se mukhtalif tha, zyada tar muarrikhin ke khayal mein unhon ne yeh taqriban 1588 mein ijad kiya, magar un ka kaam 1620 mein chhapa, yani Napier ki kitab ke chhe saal baad.

Falakiyat se slide rule tak

Logarithm ka sab se bada faida falakiyat ko pahuncha. MacTutor ke mutabiq German mahir-e-falakiyat Johannes Kepler logarithm hi ki madad se apne mushahidat ka hisab kar sake, aur yehi kaam aage chal kar Newton ke kashish-e-saqal ke nazariye ki bunyad bana. French riyazi dan Laplace ka qaul mashhoor hai ke logarithm ne mehnat ghata kar mahir-e-falakiyat ki umr dugni kar di.

Logarithm se ek aala bhi nikla. MacTutor ke mutabiq angrez riyazi dan Edmund Gunter ne 1620 mein ek patti par logarithmi paimana banaya. William Oughtred ne do aisi pattiyan sath sath rakh kar unhein ek doosre par sarkane ka tareeqa nikala, aur 1630 mein gol slide rule banaya. Zarb ka nishan “×” bhi Oughtred hi ne raij kiya. Slide rule par do paimane sarkane se logarithm jama hote hain aur zarb ka jawab samne aa jata hai. London ke Victoria and Albert Museum ke mutabiq slide rule 1970 ki dahai tak aam istemal mein rahe, jab un ki jagah barqi calculatoron ne le li.

Aaj ka logarithm

Aaj logarithm ke chhape hue jadwal aur slide rule ajaib ghar mein rakhe jate hain, magar khud logarithm riyazi aur science ki kitabon mein mojood hai, aur calculator par “log” ka button aaj bhi usi ki yaad dilata hai. Napier ka khayal sada tha: badi mushaqqat ko chhote qadmon mein badal do. Chaar sadiyan guzarne ke baad bhi science usi khayal se faida utha rahi hai.

Maakhaz

J. J. O'Connor and E. F. Robertson, "John Napier", MacTutor History of Mathematics Archive, University of St Andrews. https://mathshistory.st-andrews.ac.uk/Biographies/Napier/ — born 1550 at Merchiston Castle, died 4 April 1617 in Edinburgh; work done largely at Gartness (from 1574); Mirifici logarithmorum canonis descriptio 1614, English translation by Edward Wright 1616; dynamical basis, line of 10^7 because sine tables were to seven places, log 1 not zero, no base; Briggs's visits 1615 and 1616; Kepler reduced his observations with logarithms; Laplace's remark.
J. J. O'Connor and E. F. Robertson, "Henry Briggs", MacTutor. https://mathshistory.st-andrews.ac.uk/Biographies/Briggs/ — Gresham professor of geometry from 1596; base 10 with log 1 = 0 agreed with Napier; Logarithmorum chilias prima 1617; Arithmetica logarithmica 1624 (1 to 20,000 and 90,000 to 100,000, 14 places); Vlacq filled 20,000 to 90,000 in 1628.
J. J. O'Connor and E. F. Robertson, "Jost Burgi", MacTutor. https://mathshistory.st-andrews.ac.uk/Biographies/Burgi/ — logarithms discovered independently by a different method; most historians date the invention c. 1588; printed 1620.
J. J. O'Connor and E. F. Robertson, "William Oughtred", MacTutor. https://mathshistory.st-andrews.ac.uk/Biographies/Oughtred/ — Gunter's logarithmic scale 1620; Oughtred's use of two rulers; circular slide rule 1630; Circles of Proportion 1632; the × sign for multiplication.
Victoria and Albert Museum, "Slide rule", object record. https://collections.vam.ac.uk/item/O1129969 — slide rules first developed in the 1600s, based on logarithms; in use until the 1970s, when they were generally replaced by electronic calculators.

100 Bari Daryaftein aur Ijadat: tamam tehreerein →