Toscead betweox fadungum "Rīmagiefung"

'''RīmaȝiefunȝRīmagiefung''' (on NīƿumNīwum EnȝlisceEnglisce hāteþ ''algebra'') is dǣl [[rīmcræft]]es be þǣre cnēorlǣcinȝecneordlǣcinge þāra laȝalaga of ƿeorcunȝeweorcunge and gesibbnessum, and þǣm timbrum and oncnāƿnessumoncnāwnessum þe arīsaþ from heom, ēac besetednessum, maniȝsetednessummanigsetednessum, efenƿeorðfindunȝumefenweorðfindungum, and rīmaȝiefunȝlicumrīmagiefunglicum endebyrdnessum. Andefen eorþmetes, arāflunȝearāflunge, stōƿlārestōwlāre, tellinȝalāretellingalāre, and rīma flītcræftes is rīmaȝiefunȝrīmagiefung ān þāra hēafodlicena dǣla smǣtes rīmcræftes.

Se dǣl rīmaȝiefunȝerīmagiefunge ȝehātengehāten ȝrundstaðoliendegrundstaðoliende rīmaȝiefunȝrīmagiefung is oft dǣl þǣre lāre in æfterran lǣrunȝelǣrunge and inlǣdeþ þā oncnāƿnesseoncnāwnesse missenrīma þe tācniaþ rīm. Cwidas þā sind ȝestaðolodegestaðolode on þissum missenrīmum sind gestēorede notiende þā laȝalaga ƿeorcunȝaweorcunga þā sind ȝehapagehapa rīmum, sƿilceswilce ēacnunȝēacnung. Mann mæȝmæg dōn þis for missenlicum intinȝumintingum, ēac efenƿeorþfindunȝeefenweorþfindunge. RīmaȝiefunȝRīmagiefung is swīðe brādre þonne ȝrundstaðoliendegrundstaðoliende rīmaȝiefunȝrīmagiefung and is sēo cnēorlǣcinȝcnēorlǣcing þǣre ȝelimpeþgelimpeþ sēo nytt missenlica laȝalaga weorcinge and sēo ȝesettunȝgesettung weorcinȝaweorcinga tō ōðrum þinȝumþingum būtan rīmum. ĒacnunȝĒacnung and manigfealdinȝmanigfealding cann mann settan on ȝemǣnregemǣnre endebyrdnesse laȝalaga and heora fullan, rihtan tōmearcunȝatōmearcunga inlǣdaþ rīmaȝiefunȝlicerīmagiefunglice endebyrdnessa sƿilceswilce þrēatas, hrinȝashringas and līchāmaslīchamas, þe sind cnēorlǣhte on þǣm dǣle rīmcræftes þe hāteþ brād rīmaȝiefunȝrīmagiefung.

[[Biliþ:Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala.jpg|thumb|Tramet fram [[:en:Muhammad ibn Musa al-Khwarizmi|Al-Khwārizmī]]'s ''Sēo Sceortlice Bōc be RīmƿeorcinȝeRīmweorcinge þurh FulfillinȝeFulfillinge and EfensettunȝeEfensettunge''

Þā þā [[Plato]] cōm, [[Crēcisc rīmcræft]] hæfde ȝefēredgefēred micele andƿendunȝeandwendunge. Þā Crēcas sciepedon eorþmetlice rīmaȝiefunȝerīmagiefunge on þǣre þe besetednessa ƿǣronwǣron tācnod fram sīdum eorþmetlicra þinȝaþinga, oftost līna, þā hæfdon stafan ȝeþēotegeþēote ƿiþwiþ hīe.<ref>Fram "Europe in the Middle Ages" on þǣm 258 tramente: "On þǣm rīmcræftlicum sōþfōresetednessum in Euclides ''HēafodȝesceaftHēafodgesceaft'' fram VII oþ IX, rīm sind tācnod fram līndǣlum on þǣm þe stafan sind gesette, and þā eorþmetlican bēhþa in al-Khwarizmies bēc ''RīmaȝiefunȝRīmagiefung'' notode stæfbǣra ȝefēȝednessagefēgednessa; ac ealle efenƿyrcendasefenwyrcendas in þǣm efenƿeorþfindunȝumefenweorþfindungum þā sind gebrocena in þǣre bēc ''RīmaȝiefunȝRīmagiefung'' sind amearcod rīm, ǣghwæðer þe hīe sīen tācnode fram rīmstafum oþþe sīen ȝeƿritenegewritene on ƿordumwordum. Sēo oncnāƿnessoncnāwness brādnesse is abēacnod in al-Khwarizmies amearcunȝeamearcunge, ac hē næfde nāne ƿīsanwīsan tō tācnienne rīmaȝiefunȝlīcerīmagiefunglīce þā ȝeƿunelicangewunelican fōresetednessa þe sind sƿāswā ȝearƿagearwa in eorþmete."</ref> Diophantus (þe lifode on þǣm 3. hundȝēarehundgēare æfter Crīste), þe hƿīlumhwīlum is ȝehātengehāten "se fæder rīmaȝiefunȝerīmagiefunge", ƿæswæs Alexandrianisc rīmcræftmann and se ƿrīterewrītere endebyrdnesse bōca þā hātaþ ''Rīmcræft''. Þās ȝeƿritugewritu standaþ be þǣre arāflinȝearāflinge rīmaȝiefunȝlicrarīmagiefunglicra efenƿeorþfindunȝaefenweorþfindunga.

RīmaȝiefunȝeRīmagiefunge staðol biþ ȝefundengefunden on ȝamolumgamolum Indiscum rīmcræfte, þe [[Muhammad ibn Mūsā al-Khwārizmī]] (lifode fram þǣm 780. ȝēaregēare oþ þæt 850. ȝēargēar) hefiȝehefige onfēnȝonfēng on mōde. Hē leornode Indiscne rīmcræft and inlēd hīe in þā Allahdōmiscan dǣlas þǣre ƿoruldeworulde þurh his ƿīdcūðwīdcūð rīmcræftlic ȝeƿritgewrit, ''Bōc be ĒacnunȝeĒacnunge and AnimunȝeAnimunge æfter þǣre ǷīsanWīsan þāra Indiscena''.<ref>http://www.brusselsjournal.com/node/4107/print</ref><ref>''A History of Mathematics: An Introduction (on ōðerre ūtsendnesse) (sōftbōc) 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 rīmaȝiefunȝerīmagiefunge 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 rīmaȝiefunȝerīmagiefunge 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]].

Þā Crēciscan rīmcræftmenn [[Hero Alexandrie]] and [[Diophantus]] <ref>[http://library.thinkquest.org/25672/diiophan.htm Diophantus, Father of Algebra]</ref> and Indisce rīmcræftmenn, swelce [[Brahmagupta]], hēoldon þā þēawas [[Ægypte]]s and [[Babylōn]]ie, þēah þe Diophantus ''[[Arithmetica]]'' and Brahmaguptan ''[[Brahmasphutasiddhanta]]'' standaþ on hīeran efenette.<ref>[http://www.algebra.com/algebra/about/history/ History of Algebra]</ref> Tō bȳsne, sēo forme fulle rīmcræftisce arāfling (befōne nāwihtrīm and underran arāflunga) [[fēowerscētra efenweorþfindunga]] wæs amearcod fram Brahmaguptan in his bēc ''Brahmasphutasiddhanta''. Þǣræfter, Arabisce and Muslime rīmcræftmenn forðodon rīmaȝiefunȝiscarīmagiefungisca endebyrdnessa on swīðe hīeran strengðe manigfealdnesse. Þēah Diophantus and þā Babylōniscan brucon oftost ānlica endebyrdnessa tō arāflenne efenweorþlǣcinga, Al-Khwarizmi wæs se forma þe arāflede efenweorþlǣcinga þā hwīle þe hē brēac brāda endebyrdnessa. Hē arāflede þā līnlican unfæstlican efenweorþlǣcinga, fēowerscēta efenweorþlǣcinga, unfæstlica efenweorþlǣcinga þǣre ōðerre endebyrdnesse and efenweorþlǣcinga mid manigfealdum unfæstrīmum.

[[Flocc:RīmaȝiefunȝRīmagiefung]]