Toscead betweox fadungum "Rīmagiefung"

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Líne 7:
[[biliþ:Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala.jpg|thumb|Trament fram [[:en:Muhammad ibn Musa al-Khwarizmi|Al-Khwārizmī]]'s ''[[Sēo Sceortlice Bōc be Rīmweorcinge þurh Fulfillinge and Efensettunge|al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala]]'']]
 
Þā þā [[Plato]] cōm, [[Crēcisc rīmlārrīmcræft]] hæfde gefēred micele andwendunge. Þā [[Gamol Crēcland|Crēcas]] sciepedon [[eorþmetlic stæfrīmtācning|eorþmetlice stæfrīmtācninge]] on þǣm þe besetednessa wǣron tācnod fram sīdum eorþmetlicra þinga, oftost līna, þā hæfdon stafan gesibb him.<ref>Fram "Europe in the Middle Ages" on þǣm 258 tramente: "On þǣm rīmcræftlicum foresetednessum in Euclides ''Hēafodsceaft'' fram VII oþ IX, rīm hæfdon gebēon tācnod fram līndǣlum on þǣm þe stafan hæfdon gebēon geseted, and þā eorþmetlican bēhþa in al-Khwarizmis bēc ''Stæfrīmtācning'' notoded stæfbǣra gefēgednessa; ac ealle fæstmanigfealdendas in þǣm efenweorþfindungum gebrocen in þǣre bēc ''Algebra'' sind amearcode agyldan; ǣghwæðer þe hīe sīen tācnod fram rīmum oþþe gewriten on wordum. Sēo oncnāwness brādnesse is abēacnod in al-Khwarizmis amearcunge, ac hē næfde nāne wīsan tō ēowienne stæfrīmtācniende þā gewunelican forþsetednessa þe sind swā gearu in eorþmete."</ref> [[Diophantus]] (þe lifode on þǣm 3 hundgēare AD), hwīlum gehāten "se fæder stæfrīmtācninge", wæs [[Alexandria]]nisc [[Crēcisc rīmlār|rīmlārmann]] and se wrītere endebyrdnesse bōca gehāten ''[[Arithmetica]]''. Þās gewritu standaþ be þǣre arāflinge [[stæfrīmtācningisc efenweorþfindung|stæfrīmtācningiscra efenweorþfindunga]].
 
Stæfrīmtācninge staðol biþ gefunden on gamolregamolum [[Indisc rīmlārrīmcræft|Indiscre rīmlārerīmcræft]]e, þe [[Muhammad ibn Mūsā al-Khwārizmī]] (lifode of þǣm 780 gēare oþ þæt 850 gēar) hefige onfēng on mōde. Hē leornode Indisce rīmlāre and inlēd hīe in þā Alladōmiscan dǣl þǣre worulde þurh his wīdcūðe rīmlārisce gewrit, ''Bōc be Ēacnunge and Animunge æfter þǣre Wīsan þāra Indisceba''.<ref>http://www.brusselsjournal.com/node/4107/print</ref><ref>''A History of Mathematics: An Introduction (on ōðerre ūtsendnesse) (cartbæced) fram Victor J katz Addison Wesley; on ōðerre ūtsendnesse (on þǣm 6 dæge Hrēðmōnaðes þæs 1998 gēares)</ref> Hē lator awrāt ''[[Sēo Sceortlice Bōc be Rīmweorcinge þurh Fulfillinge and Efensettung]]'', þe gesette stæfrīmtācninge tō rīmlāriscum cræfe se is ānstandende fram [[eorþmet]]e and [[grundrīmlārgrundrīmcræft]]e.<ref>{{citation|title=Al Khwarizmi: The Beginnings of Algebra|author=Roshdi Rashed|publisher=[[Saqi Books]]|date=November 2009|isbn=0863564305}}</ref>
 
Þā staðolas stæfrīmtācninge cunnon wesan gefunden on þǣm gamolum [[Babylonisc rīmlār|Babyloniscum]] ,<ref>Struik, Dirk J. (1987). ''A Concise History of Mathematics''. New York: Dover Publications.</ref> þā forðodon forðode rīmmetende endebyrdnesse þurh þā þe hīe cūðdon dōn rīmweorcunga in rīmendebyrdnessiscre wīsan. Þā Babyloniscan forðodon endebyrdnessa tō weorcienne arāflunga cnottena þe sindgewunelīce arāfled tōdæg be þǣre nytte [[līnlicra efenweorþfindunga]], [[fēowerscētra efenweorþfindunga]], and [[unrīm efenweorþfindung|unrīmra līnlicra efenweorþfindunga]]. Tō ungelīcnesse, þæt mǣste dǣl [[Egyptisc rīmlār|Egyptiscena]] þisre tīde, and [[Crēcisc rīmlār|Crēciscena]] and [[Cīnisc rīmlār|Cīniscena]] rīmlārmanna in þǣm [[1 þūsendgēare fōre Crīste]], gewunelīce arāflede swelca efenweorþfindunga þurh eorþmetlica endebyrdnesse, swelce þās amearcod in þǣm ''[[Rhind Rīmlāriscan Papyrus]]'', [[Euclides Gesceaft|Euclides ''Gesceaft'']], and ''[[Þā Nigone Hēafodwearda on þǣre Rīmlāriscanþǣm LīsteRīmcræfte]]''. Þæt eorþmetlice weorc þāra Crēciscena, ēowod in þǣre bēc ''Gesceaft'', macode þæt grundweorc for þǣre gewuneliclǣcunge endebyrdnessa begeondan þā arāflunge sumra cnottena on maniga gewunelica endebyrdnessa secgunge and arāflunge efenweorþfindunga, þēah þe þis ne scolde wesan gecūþ oþ þā [[rīmlārrīmcræft in midealdum Alladōme|midealdan Alladōmiscan rīmlārmennrīmcræftmenn]].
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The [[Hellenistic civilization|Hellenistic]] mathematicians [[Hero of Alexandria]] and [[Diophantus]] <ref>[http://library.thinkquest.org/25672/diiophan.htm Diophantus, Father of Algebra]</ref> as well as [[Indian mathematics|Indian mathematicians]] such as [[Brahmagupta]] continued the traditions of Egypt and Babylon, though Diophantus' ''[[Arithmetica]]'' and Brahmagupta's ''[[Brahmasphutasiddhanta]]'' are on a higher level.<ref>[http://www.algebra.com/algebra/about/history/ History of Algebra]</ref> For example, the first complete arithmetic solution (including zero and negative solutions) to [[quadratic equation]]s was described by Brahmagupta in his book ''Brahmasphutasiddhanta''. Later, Arabic and Muslim mathematicians developed algebraic methods to a much higher degree of sophistication. Although Diophantus and the Babylonians used mostly special ad hoc methods to solve equations, Al-Khwarizmi was the first to solve equations using general methods. He solved the linear indeterminate equations, quadratic equations, second order indeterminate equations and equations with multiple variable.
Líne 208:
The rational numbers, the real numbers and the complex numbers are all examples of fields.
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