Polynomials and equations in arabic algebra

Abstract It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Oaks, Jeffrey A. [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	2008

Schlagwörter:	Unknown Quantity Algebraic Solution Arabic Text Arabic Word Algebraic Notation

Systematik:	TA 1000

Anmerkung:	© Springer-Verlag 2008

Übergeordnetes Werk:	Enthalten in: Archive for history of exact sciences - Springer-Verlag, 1960, 63(2008), 2 vom: 14. Nov., Seite 169-203
Übergeordnetes Werk:	volume:63 ; year:2008 ; number:2 ; day:14 ; month:11 ; pages:169-203

Links:	Volltext

DOI / URN:	10.1007/s00407-008-0037-7

Katalog-ID:	OLC2030925551

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allfields	10.1007/s00407-008-0037-7 doi (DE-627)OLC2030925551 (DE-He213)s00407-008-0037-7-p DE-627 ger DE-627 rakwb eng 900 500 VZ HIST DE-210 fid TA 1000 TA 1000 VZ rvk (DE-625)rvk/143701: 30.00 bkl Oaks, Jeffrey A. verfasserin aut Polynomials and equations in arabic algebra 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. Unknown Quantity Algebraic Solution Arabic Text Arabic Word Algebraic Notation Enthalten in Archive for history of exact sciences Springer-Verlag, 1960 63(2008), 2 vom: 14. Nov., Seite 169-203 (DE-627)129061948 (DE-600)521-6 (DE-576)014392720 0003-9519 nnns volume:63 year:2008 number:2 day:14 month:11 pages:169-203 https://doi.org/10.1007/s00407-008-0037-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-HIST SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OPC-ANG GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_130 GBV_ILN_171 GBV_ILN_2003 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4251 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4325 GBV_ILN_4700 TA 1000 Referateblätter und Zeitschriften Allgemeine Naturwissenschaft Allgemeine Naturwissenschaft Referateblätter und Zeitschriften (DE-625)rvk/143701: (DE-576)329105892 30.00 VZ AR 63 2008 2 14 11 169-203
spelling	10.1007/s00407-008-0037-7 doi (DE-627)OLC2030925551 (DE-He213)s00407-008-0037-7-p DE-627 ger DE-627 rakwb eng 900 500 VZ HIST DE-210 fid TA 1000 TA 1000 VZ rvk (DE-625)rvk/143701: 30.00 bkl Oaks, Jeffrey A. verfasserin aut Polynomials and equations in arabic algebra 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. Unknown Quantity Algebraic Solution Arabic Text Arabic Word Algebraic Notation Enthalten in Archive for history of exact sciences Springer-Verlag, 1960 63(2008), 2 vom: 14. Nov., Seite 169-203 (DE-627)129061948 (DE-600)521-6 (DE-576)014392720 0003-9519 nnns volume:63 year:2008 number:2 day:14 month:11 pages:169-203 https://doi.org/10.1007/s00407-008-0037-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-HIST SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OPC-ANG GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_130 GBV_ILN_171 GBV_ILN_2003 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4251 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4325 GBV_ILN_4700 TA 1000 Referateblätter und Zeitschriften Allgemeine Naturwissenschaft Allgemeine Naturwissenschaft Referateblätter und Zeitschriften (DE-625)rvk/143701: (DE-576)329105892 30.00 VZ AR 63 2008 2 14 11 169-203
allfields_unstemmed	10.1007/s00407-008-0037-7 doi (DE-627)OLC2030925551 (DE-He213)s00407-008-0037-7-p DE-627 ger DE-627 rakwb eng 900 500 VZ HIST DE-210 fid TA 1000 TA 1000 VZ rvk (DE-625)rvk/143701: 30.00 bkl Oaks, Jeffrey A. verfasserin aut Polynomials and equations in arabic algebra 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. Unknown Quantity Algebraic Solution Arabic Text Arabic Word Algebraic Notation Enthalten in Archive for history of exact sciences Springer-Verlag, 1960 63(2008), 2 vom: 14. Nov., Seite 169-203 (DE-627)129061948 (DE-600)521-6 (DE-576)014392720 0003-9519 nnns volume:63 year:2008 number:2 day:14 month:11 pages:169-203 https://doi.org/10.1007/s00407-008-0037-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-HIST SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OPC-ANG GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_130 GBV_ILN_171 GBV_ILN_2003 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4251 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4325 GBV_ILN_4700 TA 1000 Referateblätter und Zeitschriften Allgemeine Naturwissenschaft Allgemeine Naturwissenschaft Referateblätter und Zeitschriften (DE-625)rvk/143701: (DE-576)329105892 30.00 VZ AR 63 2008 2 14 11 169-203
allfieldsGer	10.1007/s00407-008-0037-7 doi (DE-627)OLC2030925551 (DE-He213)s00407-008-0037-7-p DE-627 ger DE-627 rakwb eng 900 500 VZ HIST DE-210 fid TA 1000 TA 1000 VZ rvk (DE-625)rvk/143701: 30.00 bkl Oaks, Jeffrey A. verfasserin aut Polynomials and equations in arabic algebra 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. Unknown Quantity Algebraic Solution Arabic Text Arabic Word Algebraic Notation Enthalten in Archive for history of exact sciences Springer-Verlag, 1960 63(2008), 2 vom: 14. Nov., Seite 169-203 (DE-627)129061948 (DE-600)521-6 (DE-576)014392720 0003-9519 nnns volume:63 year:2008 number:2 day:14 month:11 pages:169-203 https://doi.org/10.1007/s00407-008-0037-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-HIST SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OPC-ANG GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_130 GBV_ILN_171 GBV_ILN_2003 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4251 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4325 GBV_ILN_4700 TA 1000 Referateblätter und Zeitschriften Allgemeine Naturwissenschaft Allgemeine Naturwissenschaft Referateblätter und Zeitschriften (DE-625)rvk/143701: (DE-576)329105892 30.00 VZ AR 63 2008 2 14 11 169-203
allfieldsSound	10.1007/s00407-008-0037-7 doi (DE-627)OLC2030925551 (DE-He213)s00407-008-0037-7-p DE-627 ger DE-627 rakwb eng 900 500 VZ HIST DE-210 fid TA 1000 TA 1000 VZ rvk (DE-625)rvk/143701: 30.00 bkl Oaks, Jeffrey A. verfasserin aut Polynomials and equations in arabic algebra 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. Unknown Quantity Algebraic Solution Arabic Text Arabic Word Algebraic Notation Enthalten in Archive for history of exact sciences Springer-Verlag, 1960 63(2008), 2 vom: 14. Nov., Seite 169-203 (DE-627)129061948 (DE-600)521-6 (DE-576)014392720 0003-9519 nnns volume:63 year:2008 number:2 day:14 month:11 pages:169-203 https://doi.org/10.1007/s00407-008-0037-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-HIST SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-PHA SSG-OPC-ANG GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_130 GBV_ILN_171 GBV_ILN_2003 GBV_ILN_2010 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4251 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4325 GBV_ILN_4700 TA 1000 Referateblätter und Zeitschriften Allgemeine Naturwissenschaft Allgemeine Naturwissenschaft Referateblätter und Zeitschriften (DE-625)rvk/143701: (DE-576)329105892 30.00 VZ AR 63 2008 2 14 11 169-203
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source	Enthalten in Archive for history of exact sciences 63(2008), 2 vom: 14. Nov., Seite 169-203 volume:63 year:2008 number:2 day:14 month:11 pages:169-203
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author	Oaks, Jeffrey A.
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title	Polynomials and equations in arabic algebra
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title_sort	polynomials and equations in arabic algebra
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abstract	Abstract It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. © Springer-Verlag 2008
abstractGer	Abstract It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. © Springer-Verlag 2008
abstract_unstemmed	Abstract It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. © Springer-Verlag 2008
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title_short	Polynomials and equations in arabic algebra
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