Algebra - Revision history

Admin at 04:05, 26 December 2022

2022-12-26T04:05:40Z

← Older revision		Revision as of 09:35, 26 December 2022
Line 258:		Line 258:
	== References ==		== References ==
	<references />		<references />

			[[Category:Articles using infobox templates with no data rows]]
			[[Category:Articles with hCards]]
	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Organic Articles English]]		[[Category:Organic Articles English]]
	[[Category:~~Vigyan Ready~~]]		[[Category:Pages using duplicate arguments in template calls]]

Indicwiki: 30 revisions imported from :alpha:Algebra

2022-12-24T05:13:27Z

30 revisions imported from alpha:Algebra

← Older revision	Revision as of 10:43, 24 December 2022
(No difference)

alpha>Ramamurthy S: Category added

2022-11-15T07:31:00Z

Category added

← Older revision		Revision as of 13:01, 15 November 2022
Line 259:		Line 259:
	<references />		<references />
	[[Category:Mathematics]]		[[Category:Mathematics]]
			[[Category:Organic Articles English]]
			[[Category:Vigyan Ready]]

alpha>Ramamurthy S: /* References */

2022-09-29T09:08:11Z

References

← Older revision		Revision as of 14:38, 29 September 2022
Line 192:		Line 192:
	All these concepts are summarized by Kṛṣṇa Daivajña in his commentary as follows:		All these concepts are summarized by Kṛṣṇa Daivajña in his commentary as follows:

	ऋणत्वमिह त्रिधा तावदस्ति देशतः कालतः वस्तुतश्चेति ... तच्च वैपरीत्यमेव। ... तत्रैकरेखा स्थिता द्वितीया दिक विपरीता दिगित्युच्यते । यथा पूर्वविपरीता पश्चिमा दिक् । यथा उत्तरदिग्विपरीता दक्षिणा दिगित्यादि । तथा च पूर्वापरदेशयोर्मध्ये एकतरस्य धनत्वे कल्पितं तं प्रति तदितरस्य ऋणत्वम्।<ref>~~Bijapallava~~ on Bījagaṇita p.13</ref>		ऋणत्वमिह त्रिधा तावदस्ति देशतः कालतः वस्तुतश्चेति ... तच्च वैपरीत्यमेव। ... तत्रैकरेखा स्थिता द्वितीया दिक विपरीता दिगित्युच्यते । यथा पूर्वविपरीता पश्चिमा दिक् । यथा उत्तरदिग्विपरीता दक्षिणा दिगित्यादि । तथा च पूर्वापरदेशयोर्मध्ये एकतरस्य धनत्वे कल्पितं तं प्रति तदितरस्य ऋणत्वम्।<ref>Bījapallava on Bījagaṇita p.13</ref>

	“Negativity is of three kinds - according to place, time and things. It is in short the contrary. Just as west is the contrary direction to east and south to north. Thus between two places situated in the east and west, If one is taken to be positive the other is relatively negative."		“Negativity is of three kinds - according to place, time and things. It is in short the contrary. Just as west is the contrary direction to east and south to north. Thus between two places situated in the east and west, If one is taken to be positive the other is relatively negative."

alpha>Ramamurthy S: Citation updated

2022-09-29T09:06:29Z

Citation updated

← Older revision		Revision as of 14:36, 29 September 2022
Line 192:		Line 192:
	All these concepts are summarized by Kṛṣṇa Daivajña in his commentary as follows:		All these concepts are summarized by Kṛṣṇa Daivajña in his commentary as follows:

	ऋणत्वमिह त्रिधा तावदस्ति देशतः कालतः वस्तुतश्चेति ... तच्च वैपरीत्यमेव। ... तत्रैकरेखा स्थिता द्वितीया दिक विपरीता दिगित्युच्यते । यथा पूर्वविपरीता पश्चिमा दिक् । यथा उत्तरदिग्विपरीता दक्षिणा दिगित्यादि । तथा च पूर्वापरदेशयोर्मध्ये एकतरस्य धनत्वे कल्पितं तं प्रति तदितरस्य ऋणत्वम्।<ref>Bijapallava on ~~Bijagaṇita~~ p.13</ref>		ऋणत्वमिह त्रिधा तावदस्ति देशतः कालतः वस्तुतश्चेति ... तच्च वैपरीत्यमेव। ... तत्रैकरेखा स्थिता द्वितीया दिक विपरीता दिगित्युच्यते । यथा पूर्वविपरीता पश्चिमा दिक् । यथा उत्तरदिग्विपरीता दक्षिणा दिगित्यादि । तथा च पूर्वापरदेशयोर्मध्ये एकतरस्य धनत्वे कल्पितं तं प्रति तदितरस्य ऋणत्वम्।<ref>Bijapallava on Bījagaṇita p.13</ref>

	“Negativity is of three kinds - according to place, time and things. It is in short the contrary. Just as west is the contrary direction to east and south to north. Thus between two places situated in the east and west, If one is taken to be positive the other is relatively negative."		“Negativity is of three kinds - according to place, time and things. It is in short the contrary. Just as west is the contrary direction to east and south to north. Thus between two places situated in the east and west, If one is taken to be positive the other is relatively negative."

alpha>Ramamurthy S: Citation updated

2022-09-29T09:03:22Z

Citation updated

← Older revision		Revision as of 14:33, 29 September 2022
Line 192:		Line 192:
	All these concepts are summarized by Kṛṣṇa Daivajña in his commentary as follows:		All these concepts are summarized by Kṛṣṇa Daivajña in his commentary as follows:

	ऋणत्वमिह त्रिधा तावदस्ति देशतः कालतः वस्तुतश्चेति ... तच्च वैपरीत्यमेव। ... तत्रैकरेखा स्थिता द्वितीया दिक विपरीता दिगित्युच्यते । यथा पूर्वविपरीता पश्चिमा दिक् । यथा उत्तरदिग्विपरीता दक्षिणा दिगित्यादि । तथा च पूर्वापरदेशयोर्मध्ये एकतरस्य धनत्वे कल्पितं तं प्रति तदितरस्य ऋणत्वम्।<ref>Bijapallava~~, com.~~ on ~~Bijagaạita~~ p.13</ref>		ऋणत्वमिह त्रिधा तावदस्ति देशतः कालतः वस्तुतश्चेति ... तच्च वैपरीत्यमेव। ... तत्रैकरेखा स्थिता द्वितीया दिक विपरीता दिगित्युच्यते । यथा पूर्वविपरीता पश्चिमा दिक् । यथा उत्तरदिग्विपरीता दक्षिणा दिगित्यादि । तथा च पूर्वापरदेशयोर्मध्ये एकतरस्य धनत्वे कल्पितं तं प्रति तदितरस्य ऋणत्वम्।<ref>Bijapallava on Bijagaṇita p.13</ref>

	“Negativity is of three kinds - according to place, time and things. It is in short the contrary. Just as west is the contrary direction to east and south to north. Thus between two places situated in the east and west, If one is taken to be positive the other is relatively negative."		“Negativity is of three kinds - according to place, time and things. It is in short the contrary. Just as west is the contrary direction to east and south to north. Thus between two places situated in the east and west, If one is taken to be positive the other is relatively negative."

alpha>Ramamurthy S: Internal link added

2022-05-10T13:08:55Z

Internal link added

← Older revision		Revision as of 18:38, 10 May 2022
Line 32:		Line 32:
	"The Hindus were the first to make systematic use of the letters of the alphabet to denote unknowns. They were also the first to classify and make a detailed study of equations. Thus they may be said to have given birth to the modern science of algebra." <ref>Datta, 1938, Vol.2, Preface</ref>		"The Hindus were the first to make systematic use of the letters of the alphabet to denote unknowns. They were also the first to classify and make a detailed study of equations. Thus they may be said to have given birth to the modern science of algebra." <ref>Datta, 1938, Vol.2, Preface</ref>

	''<big>ś</big>ulbasūtrās'' mentions variable quantity. ''āryabhaṭīya'' of [[Aryabhata\|''āryabhaṭa'']] mentions solution to linear and quadratic equations. Brahmagupta in his ''Brāhma- sphuṭa - siddhānta'' mentions the operations performed on unknowns using symbols. ''kuṭṭakādhyāya'' (chapter 18) explains the ''parikarma'' (calculations) with avyakta (or algebraic symbols). Hence Brahmagupta is treated as the father of algebra. The other texts on algebra includes Mahāsiddhānta of ''āryabhaṭa II ,siddhāntaśekhara ''of ''śripati, Bījagaṇita'' of ''Bhāskara II, bījagaṇitāvataṃsa'' of ''nārāyaṇa paṇḍita.''		''<big>ś</big>ulbasūtrās'' mentions variable quantity. ''āryabhaṭīya'' of [[Aryabhata\|''āryabhaṭa'']] mentions solution to linear and quadratic equations. Brahmagupta in his ''Brāhma- sphuṭa - siddhānta'' mentions the operations performed on unknowns using symbols. ''kuṭṭakādhyāya'' (chapter 18) explains the ''parikarma'' (calculations) with avyakta (or algebraic symbols). Hence Brahmagupta is treated as the father of algebra. The other texts on algebra includes Mahāsiddhānta of ''āryabhaṭa II ,siddhāntaśekhara ''of ''śripati, Bījagaṇita'' of ''Bhāskara II, bījagaṇitāvataṃsa'' of ''[[Development of Mathematics\|nārāyaṇa paṇḍita.]]''

	''Brahmagupta'' has given the rules for arithmetic operations with positive numbers, negative numbers and zero in ''kuṭṭakādhyāya'' of ''Brāhma- sphuṭa - siddhānta. Also equations with one unknown, equations with many unknowns, equations with products of unknowns and indeterminate equations of first and second order (kuṭṭaka and varga-prakṛti) are dealt by Brahmagupta.''		''Brahmagupta'' has given the rules for arithmetic operations with positive numbers, negative numbers and zero in ''kuṭṭakādhyāya'' of ''Brāhma- sphuṭa - siddhānta. Also equations with one unknown, equations with many unknowns, equations with products of unknowns and indeterminate equations of first and second order (kuṭṭaka and varga-prakṛti) are dealt by Brahmagupta.''

alpha>Ramamurthy S: Infobox added

2022-05-10T12:49:06Z

Infobox added

← Older revision		Revision as of 18:19, 10 May 2022
Line 1:		Line 1:
	'''Algebra''' is one of the broad areas of Mathematics. The Hindu name for the science of algebra is bījagaṇita. Bīja means "element" or "analysis" and gaṇita means " the science of calculation". Bījagaṇita literally means "science of calculation with elements or the science of analytical calculation.		'''Algebra''' is one of the broad areas of Mathematics. The Hindu name for the science of algebra is bījagaṇita. Bīja means "element" or

			{{Infobox person
			\| name = Algebra
			\| image = Quadratic root.svg
			\| alt = Algebra
			}}

			"analysis" and gaṇita means " the science of calculation". Bījagaṇita literally means "science of calculation with elements or the science of analytical calculation.

	[[Brahmagupta\|Brahmagupta (628)]] calls algebra as ''kuṭṭaka - gaṇita'' or ''kuṭṭaka''. ''Kuṭṭaka'' means pulveriser. Algebra is also called as ''avyakta - gaṇita'' or the science of calculation with unknowns (''avyakta'' means unknown) in contrast to the name ''vyakta - gaṇita'' the science of calculation with knowns (''vyakta'' means known'')'' for arithmetic including geometry and mensuration.		[[Brahmagupta\|Brahmagupta (628)]] calls algebra as ''kuṭṭaka - gaṇita'' or ''kuṭṭaka''. ''Kuṭṭaka'' means pulveriser. Algebra is also called as ''avyakta - gaṇita'' or the science of calculation with unknowns (''avyakta'' means unknown) in contrast to the name ''vyakta - gaṇita'' the science of calculation with knowns (''vyakta'' means known'')'' for arithmetic including geometry and mensuration.

alpha>Ramamurthy S at 12:21, 10 May 2022

2022-05-10T12:21:56Z

← Older revision		Revision as of 17:51, 10 May 2022
Line 233:		Line 233:

	be known terms, proceed with the remainder in the same way after taking the square-root of the knowns."		be known terms, proceed with the remainder in the same way after taking the square-root of the knowns."

			== See Also ==

			* [[बीजगणित]]

	== External Links ==		== External Links ==

alpha>Ramamurthy S: External Links updated

2022-04-20T10:49:22Z

External Links updated

← Older revision		Revision as of 16:19, 20 April 2022
Line 235:		Line 235:

	== External Links ==		== External Links ==
	[http://www.ms.uky.edu/~sohum/ma330/files/brahmagupta_algebra.pdf Brahmagupta's Algebra - Mathematics]
			* [http://www.ms.uky.edu/~sohum/ma330/files/brahmagupta_algebra.pdf Brahmagupta's Algebra - Mathematics]
			* [https://rarebooksocietyofindia.org/book_archive/196174216674_10152963932466675.pdf Bija Ganita or The algebra of the Hindus]
			* [https://rarebooksocietyofindia.org/book_archive/196174216674_10152963932466675.pdf Algebra]

	== Further Reading ==		== Further Reading ==
Line 242:		Line 245:

	== References ==		== References ==

	~~=== Citations ===~~
	<references />		<references />
	[[Category:Mathematics]]		[[Category:Mathematics]]