Toscead betweox fadungum "Rīmagiefung"

Content deleted Content added
Gottistgut (motung | forðunga)
No edit summary
Gottistgut (motung | forðunga)
No edit summary
Líne 8:
 
Þā þā [[Plato]] cōm, [[Crēcisc rīmlār]] 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]].
<!--
Stæfrīmtācninge staðol biþ gefunden on gamolre [[Indisc rīmlār|Indiscre rīmlāre]], 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 ''[[Th 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>
 
Stæfrīmtācninge staðol biþ gefunden on gamolre [[Indisc rīmlār|Indiscre rīmlāre]], 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 ''[[ThSēo CompendiousSceortlice BookBōc onbe CalculationRīmweorcinge byþurh CompletionFulfillinge and BalancingEfensettung]]'', whichþe establishedgesette algebrastæfrīmtācninge as arīmlāriscum mathematicalcræfe discipline thatse is independentānstandende offram [[geometryeorþmet]]e and [[arithmeticgrundrīmlār]]e.<ref>{{citation|title=Al Khwarizmi: The Beginnings of Algebra|author=Roshdi Rashed|publisher=[[Saqi Books]]|date=November 2009|isbn=0863564305}}</ref>
The roots of algebra can be traced to the ancient [[Babylonian mathematics|Babylonians]],<ref>Struik, Dirk J. (1987). ''A Concise History of Mathematics''. New York: Dover Publications.</ref> who developed an advanced arithmetical system with which they were able to do calculations in an algorithmic fashion. The Babylonians developed formulas to calculate solutions for problems typically solved today by using [[linear equation]]s, [[quadratic equation]]s, and [[indeterminate equation|indeterminate linear equations]]. By contrast, most [[Egyptian mathematics|Egyptians]] of this era, as well as [[Greek mathematics|Greek]] and [[Chinese mathematics|Chinese]] mathematicians in the [[1st millennium BC]], usually solved such equations by geometric methods, such as those described in the ''[[Rhind Mathematical Papyrus]]'', [[Euclid's Elements|Euclid's ''Elements'']], and ''[[The Nine Chapters on the Mathematical Art]]''. The geometric work of the Greeks, typified in the ''Elements'', provided the framework for generalizing formulae beyond the solution of particular problems into more general systems of stating and solving equations, though this would not be realized until the [[Mathematics in medieval Islam|medieval Muslim mathematicians]].
 
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 þǣre Rīmlāriscan Līste]]''. 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 [[rīmlār in midealdum Alladōme|midealdan Alladōmiscan rīmlārmenn]].
<!--
The [[Hellenistic civilization|Hellenistic]] mathematicians [[Hero of Alexandria]] and [[Diophantus]] <ref>[http://library.thinkquest.org/25672/diiophan.htm Diophantus, Father of Algebra]</ref> as well as [[Indian mathematics|Indian mathematicians]] such as [[Brahmagupta]] continued the traditions of Egypt and Babylon, though Diophantus' ''[[Arithmetica]]'' and Brahmagupta's ''[[Brahmasphutasiddhanta]]'' are on a higher level.<ref>[http://www.algebra.com/algebra/about/history/ History of Algebra]</ref> For example, the first complete arithmetic solution (including zero and negative solutions) to [[quadratic equation]]s was described by Brahmagupta in his book ''Brahmasphutasiddhanta''. Later, Arabic and Muslim mathematicians developed algebraic methods to a much higher degree of sophistication. Although Diophantus and the Babylonians used mostly special ad hoc methods to solve equations, Al-Khwarizmi was the first to solve equations using general methods. He solved the linear indeterminate equations, quadratic equations, second order indeterminate equations and equations with multiple variable.
[[File:Gerolamo Cardano.jpg|thumb|200px|In 1545, the Italian mathematician [[Girolamo Cardano]] published ''[[Ars Magna (Gerolamo Cardano)|Ars magna]]'' -''The great art'', a 40-chapter masterpiece in which he gave for the first time a method for solving the general [[quartic equation]].]]