Toscead betweox fadungum "Rīmagiefung"

'''StæfrīmtācningRīmaȝiefunȝ''' (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 [[stæfrīmtācningiscrīmaȝiefunȝisc timber|stæfrīmtācningiscerīmaȝiefunȝisce timbras]]. Andefen [[eorþmet]]es, [[rīmcræftlic arāflung|arāflunge]], [[stōwlār]]e, [[tellingalār]]a, and [[rīma flītcræft]]es is stæfrīmtācningrīmaȝiefunȝ ān þāra hēafodlicena dǣla [[smǣte rīmlār|smǣtre rīmlāre]].

Þæt dǣl stæfrīmtācningerīmaȝiefunȝe gehāten [[grundstaðoliende stæfrīmtācningrīmaȝiefunȝ]] 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]]. StæfrīmtācningRīmaȝiefunȝ is swīðe brādre þonne grundstaðoliende stæfrīmtācningrīmaȝiefunȝ; 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 [[stæfrīmtācningiscrīmaȝiefunȝisc timber|stæfrīmtācningiscerīmaȝiefunȝisce timbras]] swelce [[þrēat (on rīmlāre)|þrēatas]], [[hring (on rīmlāre)|hringas]] and [[feld (on rīmlāre)|felda]], þe sind cnēorlǣht on þǣm dǣle rīmlāre þe hāteþ [[brād stæfrīmtācing]].

Þā þā [[Plato]] cōm, [[Crēcisc rīmcræft]] hæfde gefēred micele andwendunge. Þā [[Gamol Crēcland|Crēcas]] sciepedon [[eorþmetlic stæfrīmtācningrīmaȝiefunȝ|eorþmetlice stæfrīmtācningerīmaȝiefunȝe]] 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 ''StæfrīmtācningRīmaȝiefunȝ'' 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 stæfrīmtācningerīmaȝiefunȝe", wæs [[Alexandria]]nisc [[Crēcisc rīmlār|rīmlārmann]] and se wrītere endebyrdnesse bōca gehāten ''[[Arithmetica]]''. Þās gewritu standaþ be þǣre arāflinge [[stæfrīmtācningiscrīmaȝiefunȝisc efenweorþfindung|stæfrīmtācningiscrarīmaȝiefunȝiscra efenweorþfindunga]].

StæfrīmtācningeRīmaȝiefunȝe staðol biþ gefunden on gamolum [[Indisc rīmcræft|Indiscre rīmcræfte]], 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 stæfrīmtācningerīmaȝiefunȝe tō rīmlāriscum cræfe se is ānstandende fram [[eorþmet]]e and [[grundrīmcræft]]e.<ref>{{citation|title=Al Khwarizmi: The Beginnings of Algebra|author=Roshdi Rashed|publisher=[[Saqi Books]]|date=November 2009|isbn=0863564305}}</ref>

Þā staðolas stæfrīmtācningerīmaȝiefunȝe 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 þǣm Rīmcræfte]]''. 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 [[rīmcræft in midealdum Alladōme|midealdan Alladōmiscan rīmcræftmenn]].

[[Flocc:StæfrīmtācningRīmaȝiefunȝ]]