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Toscead betweox fadungum "Rīmagiefung"

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'''Stæfrīmtācning''' (on [[Nīwum Englisce]] hāteþ ''algebra'') is dǣl [[rīmcræft]]es be þǣre cnēorlǣcinge þāra laga of [[weorcing (on rīmcræfte)|woercinge]] and [[gesibbness (on rīmcræfte)|gesibbnessum]], and þǣm timbrum and oncnāwnessum þe arīsaþ from heom, begānde [[besetednessa (on rīmcræfte)|besetednessa]], [[manigsetednessa]], [[efenweorðfindung]]a and [[stæfrīmtācningisc timber|stæfrīmtācningisce timbras]]. Andefen [[eorþmet]]es, [[rīmcræftlic arāflung|arāflung]]e, [[stōwlār]]e, [[tellingalār]]a, and [[rīma flītcræft]]es is stæfrīmtācning ān þāra hēafodlicena dǣla [[smǣte rīmlār|smǣtre rīmlāre]].
 
Þæt dǣl stæfrīmtācninge gehāten [[grundstaðoliende stæfrīmtācning]] is oft dǣl þǣre lāre in [[ōðerlic lǣrung|ōðerlicre lǣrunge]] and inlǣdeþ þā oncnāwnesse [[missenrīm (on rīmcræfte)|missenrīma]] þe tācniaþ [[rīm]]. Cwidas gestaðolode on þissum missenrīmum sind gestēorede notiende þā laga weorcinga þā mann mæg wyrcan mid rīmum, swelce [[ēacnung (on rīmcræfte)]]. Þis mæg wesan gedōn for missenlicum intingum, befōnde [[efenweorþfindung]]. Stæfrīmtācning is swīðe brādre þonne grundstaðoliende stæfrīmtācning; hēo is sēo cnēorlǣcing þæs gelimpeþ þǣr missenlica laga weorcinge sind gebrocen and þǣr weorcinga sind worht tō ōðrum þingum ōðer rīm. <!--Ēacnung and [[manigfealding]] cunnon wesan brǣded and heora forrihtan tōmearcunga inlǣdaþ [[stæfrīmtācningisc timbtimber|stæfrīmtācningisce timbras]] swelce [[groupþrēat (mathematicson rīmlāre)|groupsþrēatas]], [[ringhring (mathematicson rīmlāre)|ringshringas]] and [[fieldfeld (mathematicson rīmlāre)|fieldsfelda]], studiedþe sind cnēorlǣht inon theþǣm areadǣle ofrīmlāre mathematicsþe calledhāteþ [[abstractbrād algebrastæfrīmtācing]].
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== HistoryStǣr ==▼
 
[[Filebiliþ:Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala.jpg|thumb|ATrament page fromfram [[:en:Muhammad ibn Musa al-Khwarizmi|Al-Khwārizmī]]'s ''[[The Compendious Book on Calculation by Completion and Balancing|al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala]]'']]▼
▲== History ==
{{Main|History of algebra}}
{{See also|Timeline of algebra}}
 
ByÞā the time ofþā [[Plato]] cōm, [[GreekCrēcisc mathematicsrīmlār]] had undergone a drastic change. The [[Ancient Greece|Greeks]] created a [[geometric algebra]] where terms were represented by sides of geometric objects, usually lines, that had letters associated with them.<ref>{{Harv|Boyer|1991|loc="Europe in the Middle Ages" p. 258}} "In the arithmetical theorems in Euclid's ''Elements'' VII-IX, numbers had been represented by line segments to which letters had been had been attached, and the geometric proofs in al-Khwarizmi's ''Algebra'' made use of lettered diagrams; but all coefficients in the equations used in the ''Algebra'' are specific numbers, whether represented by numerals or written out in words. The idea of generality is implied in al-Khwarizmi's exposition, but he had no scheme for expressing algebraically the general propositions that are so readily available in geometry."</ref> [[Diophantus]] (3rd century AD), sometimes called "the father of algebra", was an [[Alexandria]]n [[Greek mathematics|Greek mathematician]] and the author of a series of books called ''[[Arithmetica]]''. These texts deal with solving [[algebraic equation]]s. ▼
▲[[File:Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala.jpg|thumb|A page from [[:en:Muhammad ibn Musa al-Khwarizmi|Al-Khwārizmī]]'s ''[[The Compendious Book on Calculation by Completion and Balancing|al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala]]'']]
 
▲By the time of [[Plato]], [[Greek mathematics]] had undergone a drastic change. The [[Ancient Greece|Greeks]] created a [[geometric algebra]] where terms were represented by sides of geometric objects, usually lines, that had letters associated with them.<ref>{{Harv|Boyer|1991|loc="Europe in the Middle Ages" p. 258}} "In the arithmetical theorems in Euclid's ''Elements'' VII-IX, numbers had been represented by line segments to which letters had been had been attached, and the geometric proofs in al-Khwarizmi's ''Algebra'' made use of lettered diagrams; but all coefficients in the equations used in the ''Algebra'' are specific numbers, whether represented by numerals or written out in words. The idea of generality is implied in al-Khwarizmi's exposition, but he had no scheme for expressing algebraically the general propositions that are so readily available in geometry."</ref> [[Diophantus]] (3rd century AD), sometimes called "the father of algebra", was an [[Alexandria]]n [[Greek mathematics|Greek mathematician]] and the author of a series of books called ''[[Arithmetica]]''. These texts deal with solving [[algebraic equation]]s.
 
While the word ''algebra'' comes from the [[Arabic language]] (''al-jabr'', [[wikt:الجبر|الجبر]] literally, ''restoration'') and much of its methods from [[Islamic mathematics|Arabic/Islamic mathematics]], its roots can be traced to earlier traditions, most notably ancient [[Indian mathematics]], which had a direct influence on [[Muhammad ibn Mūsā al-Khwārizmī]] (c. 780-850). He learned Indian mathematics and introduced it to the Muslim world through his famous arithmetic text, ''Book on Addition and Subtraction after the Method of the Indians''.<ref>http://www.brusselsjournal.com/node/4107/print</ref><ref>''A History of Mathematics: An Introduction (2nd Edition) (Paperback) Victor J katz Addison Wesley; 2 edition (March 6, 1998)</ref> He later wrote ''[[The Compendious Book on Calculation by Completion and Balancing]]'', which established algebra as a mathematical discipline that is independent of [[geometry]] and [[arithmetic]].<ref>{{citation|title=Al Khwarizmi: The Beginnings of Algebra|author=Roshdi Rashed|publisher=[[Saqi Books]]|date=November 2009|isbn=0863564305}}</ref>
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