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The Development of Arabic Mathematics pdf

Roshdi Rashed (auth.)-The Development of Arabic Mathematics_ Between Arithmetic and Algebra-Springer Netherlands (1994).pdf
book-icon-openmaktabaBook Title: The Development of Arabic Mathematics
author-icon-openmaktabaBook Author: Roshdi Rashed
number-of-pages-icon-openmaktabaTotal Pages: 392
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  Roshdi Rashed (auth.)-The Development of Arabic Mathematics_ Between Arithmetic and Algebra-Springer Netherlands (1994).pdf

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THE BEGINNINGS OF ALGEBRA11found In al-Hajlأ¤l’s tr sln i-Hallأ¤l we contemEuclld’s Elements. B أ¼ Mأ¼sأ¤ dd, sospeak, e colleagu ofal-Kh –rlzmi,at e “House Wsdom”. The extenslone notialgebralc wers effected, furthermo , aft a slngle readlngal-Khwأ¤rizmi’s b k byleast two maa em n ICls Ind endentlyd Slnأ¤n Ibn -Fn h.8 The In tof each o’ er, Abأ¼ Kأ¤mll Shujأ¤Cexplicltly f mur ed e gena -shive integer -wer. t seems, t On,If -Kh—-rizmi Ilmlted e usagealgebralc t mss not er ulta mlsund -standlnge hlgh -w stwo, itof e unknown, but – flec a whole c c -talgebdomaln,d I scope. It Is e -ally necessary returnec stltuentc calgebralc• e y In dund –st d -Kh—-rlzmi’s IntentldIs deliber e Ilm-at e same tlme g sp e sense and e Imp -tltn ion prlmitlve t ms. he princlp0 c cused by al-Kh rl zmi are flrst d sec d-deg e equ n IIn ed binom10s dtrlnom10 s, en m 0 f m,e alg -lthmlc soluti , and e dem st billtye solutlf cep are real’ zedHowev if e wis As und -st d howdc -rdinated In t orlglnal geb -ic eory, e best me’ od isa -pldHavlng Introduced e termsperusa of -Kh –rlzmi’s explhis eory, awrlt : “Of’ – ee types, some c be equ 0 to os,as w an you say: s –ar *r -ts, s – -a sa eaa number.” (Mushar fa d Ahmad, eds.,number, ra equal1939, p. 17) He contlnues:”I have founde three typal-durأ¼b, modus — which a tcombine,de foremuqtarina, genera composita — whlcha squanumb ; squar plus a numb – equa rs –ar ” (Mushar -fa and Ahmad, eds., 1939, p., Libri, 1967, p. 255). It cen be seenthree binomial ei- s d three trlnomial equ n 1 sax2 = bx, ax = c, bx = c;ax2 + bx = c, ax2 + c = bx, ax2 = bx + c. e dlstinctEven at thls stage, -Khwأ¤rizmi’s text c be seenso from Dioph tus’ly from t Babyltablets, butnot* square: mأ¤l (the square of the unknown).es – -a s d • e numberse com -slte kinds — ajnأ¤ss, plus reaplus a numb e18 d Ln In tr sla–Kh –rlzmi retains

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