Rīmagiefung

**Rīmagiefung** (on Nīƿenglisce hātte *algebra*) is dǣl rīmcræftes be þǣre cneordlǣcinge þāra laga of ƿeorcunge and gesibbnessum, and þǣm timbrum and oncnāƿnessum þe arīsaþ from heom, ēac besetednessum, manigsetednessum, efenƿeorðfindungum, and rīmagiefunglicum endebyrdnessum. Andefen eorþmetes, arāflunge, stōƿlāre, tellingalāre, and rīma flītcræftes is rīmagiefung ān þāra hēafodlicena dǣla smǣtes rīmcræftes. 

Se dǣl rīmagiefunge gehāten grundstaðoliende rīmagiefung is oft dǣl þǣre lāre in æfterran lǣrunge and inlǣdeþ þā oncnāƿnesse missenrīma þe tācniaþ rīm. Cƿidas þā sind gestaðolode on þissum missenrīmum sind gestēorede notiende þā laga ƿeorcunga þā sind gehapa rīmum, sƿilce ēacnung. Mann mæg dōn þis for missenlicum intingum, ēac efenƿeorþfindunge. Rīmagiefung is sƿīðe brādre þonne grundstaðoliende rīmagiefung and is sēo cnēorlǣcing þǣre gelimpeþ sēo nytt missenlica laga ƿeorcinge and sēo gesettung ƿeorcinga tō ōðrum þingum būtan rīmum. Ēacnung and manigfealding cann mann settan on gemǣnre endebyrdnesse laga and heora fullan, rihtan tōmearcunga inlǣdaþ rīmagiefunglice endebyrdnessa sƿilce þrēatas, hringas and līchamas, þe sind cnēorlǣhte on þǣm dǣle rīmcræftes þe hātte brād rīmagiefung.

## Stǣr
[thumb|Tramet fram [:en:Muḥammad ibn Mūsā al-Khwārizmī|Al-Khƿārizmī's *Sēo Sceortlice Bōc be Rīmƿeorcinge þurh Fulfillinge and Efensettunge*]]

Þā þā Plato cōm, Crēcisc rīmcræft hæfde gefēred micele andƿendunge. Þā Crēcas sciepedon eorþmetlice rīmagiefunge on þǣre þe besetednessa ƿǣron tācnod fram sīdum eorþmetlicra þinga, oftost līna, þā hæfdon stafan geþēote ƿiþ hīe. Diophantus (þe lifode on þǣm 3. hundgēare æfter Crīste), þe hƿīlum is gehāten "se fæder rīmagiefunge", ƿæs Alexandrianisc rīmcræftmann and se ƿrītere endebyrdnesse bōca þā hātaþ *Rīmcræft*. Þās geƿritu standaþ be þǣre arāflinge rīmagiefunglicra efenƿeorþfindunga. 

Rīmagiefunge staðol biþ gefunden on gamolum Indiscum rīmcræfte, þe Muhammad ibn Mūsā al-Khƿārizmī (lifode fram þǣm 780. gēare oþ þæt 850. gēar) hefige onfēng on mōde. Hē leornode Indiscne rīmcræft and inlēd hīe in þā Allahdōmiscan dǣlas þǣre ƿorulde þurh his ƿīdcūð rīmcræftlic geƿrit, *Bōc be Ēacnunge and Animunge æfter þǣre Ƿīsan þāra Indiscena*. Hē lator aƿrāt *[[Sēo Sceortlice Bōc be Rīmweorcinge þurh Fulfillinge and Efensettung|Sēo Sceortlice Bōc be Rīmƿeorcinge þurh Fulfillinge and Efensettung]]*, þe gesette rīmagiefunge tō rīmlāriscum cræfe se is ānstandende fram eorþmete and grundrīmcræfte.

Þā staðolas rīmagiefunge cunnon ƿesan gefunden on þǣm gamolum Babyloniscum , þā forðodon forðode rīmmetende endebyrdnesse þurh þā þe hīe cūðdon dōn rīmƿeorcunga in rīmendebyrdnessiscre ƿīsan. Þā Babyloniscan forðodon endebyrdnessa tō ƿeorcienne arāflunga cnottena þe sindgeƿunelīce arāfled tōdæg be þǣre nytte līnlicra efenƿeorþfindunga, fēoƿerscētra efenƿeorþfindunga, and unrīmra līnlicra efenƿeorþfindunga. Tō ungelīcnesse, þæt mǣste dǣl Egyptiscena þisre tīde, and Crēciscena and Cīniscena rīmlārmanna in þǣm 1 þūsendgēare fōre Crīste, geƿunelīce arāflede sƿelca efenƿeorþfindunga þurh eorþmetlica endebyrdnesse, sƿelce þās amearcod in þǣm *[[Rhind Rīmlāriscan Papyrus]]*, Euclides ''Gesceaft'', and *[[Þā Nigone Hēafodwearda on þǣm Rīmcræfte|Þā Nigone Hēafodƿearda on þǣm Rīmcræfte]]*.  Þæt eorþmetlice ƿeorc þāra Crēciscena, ēoƿod in þǣre bēc  *Gesceaft*, macode þæt grundƿeorc for þǣre geƿuneliclǣcunge endebyrdnessa begeondan þā arāflunge sumra cnottena on maniga geƿunelica endebyrdnessa secgunge and arāflunge efenƿeorþfindunga, þēah þe þis ne scolde ƿesan gecūþ oþ þā midealdan Alladōmiscan rīmcræftmenn.

Þā Crēciscan rīmcræftmenn Hero Alexandrie and Diophantus and Indisce rīmcræftmenn, sƿelce Brahmagupta, hēoldon þā þēaƿas Ægyptes and Babilōnie, þēah þe Diophantus *[[Arithmetica]]* and Brahmaguptan *[[Brahmasphutasiddhanta]]* standaþ on hīeran efenette. Tō bȳsne, sēo forme fulle rīmcræftisce arāfling (befōne nāƿihtrīm and underran arāflunga) fēoƿerscētra efenƿeorþfindunga ƿæs amearcod fram Brahmaguptan in his bēc *Brahmasphutasiddhanta*.  Þǣræfter, Arabisce and Muslime rīmcræftmenn forðodon rīmagiefungisca endebyrdnessa on sƿīðe hīeran strengðe manigfealdnesse. Þēah Diophantus and þā Babylōniscan brucon oftost ānlica endebyrdnessa tō arāflenne efenƿeorþlǣcinga, Al-Khƿarizmi ƿæs se forma þe arāflede efenƿeorþlǣcinga þā hƿīle þe hē brēac brāda endebyrdnessa. Hē arāflede þā līnlican unfæstlican efenƿeorþlǣcinga, fēoƿerscēta efenƿeorþlǣcinga, unfæstlica efenƿeorþlǣcinga þǣre ōðerre endebyrdnesse and efenƿeorþlǣcinga mid manigfealdum unfæstrīmum.  

## Ǣrendgeƿritunclu

## Fruman
* Donald R. Hill, *Islamic Science and Engineering* (Edinburgh University Press, 1994).
* Ziauddin Sardar, Jerry Ravetz, and Borin Van Loon, *Introducing Mathematics* (Totem Books, 1999).
* George Gheverghese Joseph, *The Crest of the Peacock: Non-European Roots of Mathematics* (Penguin Books, 2000).
* John J O'Connor and Edmund F Robertson, *[[MacTutor History of Mathematics archive]]* (University of St Andrews, 2005).
* 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
* L. Euler: *[http://web.mat.bham.ac.uk/C.J.Sangwin/euler/ Elements of Algebra] *, ISBN 978-1-899618-73-6
* Isaac Asimov *Realm of Algebra* (Houghton Mifflin), 1961

## Ūƿearde hlencan

* 4000 Years of Algebra , tǣcing fram Robin Ƿilson, æt Gresham College on þǣm 17 dæge Ƿinterfylleðes þæs 2007 gēares (gēare for MP3 and MP4 onbehlæsting, and geƿrit).