Toscead betweox fadungum "Rīmagiefung"

'''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|arāflunge]], [[stōwlār]]e, [[tellingalār]]a, and [[rīma flītcræft]]es is stæfrīmtācning ān þāra hēafodlicena dǣla [[smǣte rīmlār|smǣtre rīmlāre]].

 

 

== Stǣr ==

 

 

Þā þā [[Plato]] cōm, [[Crēcisc rīmcræft]] 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]].

 

 

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 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]].

* I.N. Herstein: ''Topics in Algebra''. ISBN 0-471-02371-X

* R.B.J.T. Allenby: ''Rings, Fields and Groups''. ISBN 0-340-54440-6

* Isaac Asimov ''Realm of Algebra'' (Houghton Mifflin), 1961

 

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