Trairāśika (Rule of Three) - Revision history

Ramamurthy S: Internal links updated

2022-11-30T08:43:58Z

Internal links updated

← Older revision		Revision as of 14:13, 30 November 2022
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	==Trairāśika (Rule of Three)==		==Trairāśika (Rule of Three)==
	[[File:Rule-of-3.png\|alt=Rule of Three\|thumb\|Rule of Three]]		[[File:Rule-of-3.png\|alt=Rule of Three\|thumb\|Rule of Three]]
	The Hindu name for the Rule of Three is called "''trairāśika''" (three terms, hence the rule of three)<ref>{{Cite book\|last=Datta\|first=Bibhutibhusan\|title=History of Hindu Mathematics\|last2=Narayan Singh\|first2=Avadhesh\|publisher=Asia Publishing House\|year=1962\|location=Mumbai}}</ref>. The term ''trairāśika'' occurs in [[~~Bakhshali~~ Manuscript\|Bakshālī]] manuscript, Āryabhaṭīya. [[~~Bhaskara I\|~~Bhāskara I]] (c. 525) remarked on the origin of this name as "Here three quantities are needed (in the statement and calculation) so the method is called ''trairāśika (''the rule of three terms)". A problem on the rule of three has this form : if ''p'' yields ''f'' , what will ''i'' yield ?. The three terms used are ''p,'' ''f'' , ''i'' . Hindus called the term p (''pramāṇa'' - argument), f(''phala'' - fruit) and i (''icchā -'' requisition'').'' Sometimes they are referred to simply as the first ,second and third respectively.		The Hindu name for the Rule of Three is called "''trairāśika''" (three terms, hence the rule of three)<ref>{{Cite book\|last=Datta\|first=Bibhutibhusan\|title=History of Hindu Mathematics\|last2=Narayan Singh\|first2=Avadhesh\|publisher=Asia Publishing House\|year=1962\|location=Mumbai}}</ref>. The term ''trairāśika'' occurs in [[Bakhshālī Manuscript\|Bakshālī]] manuscript, Āryabhaṭīya. [[Bhāskara I]] (c. 525) remarked on the origin of this name as "Here three quantities are needed (in the statement and calculation) so the method is called ''trairāśika (''the rule of three terms)". A problem on the rule of three has this form : if ''p'' yields ''f'' , what will ''i'' yield ?. The three terms used are ''p,'' ''f'' , ''i'' . Hindus called the term p (''pramāṇa'' - argument), f(''phala'' - fruit) and i (''icchā -'' requisition'').'' Sometimes they are referred to simply as the first ,second and third respectively.

	[[Aryabhata\|Āryabhaṭa II]] gave different names as ''māna, vinimaya'' and ''icchā'' respectively to the three terms''.''		[[Aryabhata\|Āryabhaṭa II]] gave different names as ''māna, vinimaya'' and ''icchā'' respectively to the three terms''.''

Admin at 09:19, 29 November 2022

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	== References ==		== References ==
	<references />		<references />

			[[Category:Arithmetic]]
	[[Category:Mathematics]]		[[Category:Mathematics]]
	~~[[Category:Arithmetic]]~~
	[[Category:Organic Articles English]]		[[Category:Organic Articles English]]
	[[Category:~~Vigyan Ready~~]]		[[Category:Pages with broken file links]]

Indicwiki: 24 revisions imported from :alpha:Trairāśika_(Rule_of_Three)

2022-11-28T10:08:55Z

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alpha>Abhishek: Abhishek moved page Trairasika (Rule of Three) to Trairāśika (Rule of Three) without leaving a redirect

2022-11-28T09:44:32Z

Abhishek moved page Trairasika (Rule of Three) to Trairāśika (Rule of Three) without leaving a redirect

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	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Arithmetic]]		[[Category:Arithmetic]]
			[[Category:Organic Articles English]]
			[[Category:Vigyan Ready]]

alpha>Ramamurthy S: Internal link added

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	====== Amount becoming 'n' times the principal : ======		====== Amount becoming 'n' times the principal : ======
	Śrīdhara has stated the formula to find when the principal will double or triple or quadruple after 'N' months at R% per month.		[[Sridhara\|Śrīdhara]] has stated the formula to find when the principal will double or triple or quadruple after 'N' months at R% per month.

	कालप्रमाणघातः फलभक्तो व्येकगुणहतः कालः ।<ref>{{Cite book\|last=Shukla\|first=Kripa Shankar\|title=The Patiganita Of Sridharacharya\|publisher=Lucknow University\|year=1959\|location=Lucknow\|pages=60}}</ref> <small>(Pāṭīgaṇita III R.52, p.60)</small>		कालप्रमाणघातः फलभक्तो व्येकगुणहतः कालः ।<ref>{{Cite book\|last=Shukla\|first=Kripa Shankar\|title=The Patiganita Of Sridharacharya\|publisher=Lucknow University\|year=1959\|location=Lucknow\|pages=60}}</ref> <small>(Pāṭīgaṇita III R.52, p.60)</small>

alpha>Ramamurthy S: internal link added

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	[[Aryabhata\|Āryabhaṭa II]] gave different names as ''māna, vinimaya'' and ''icchā'' respectively to the three terms''.''		[[Aryabhata\|Āryabhaṭa II]] gave different names as ''māna, vinimaya'' and ''icchā'' respectively to the three terms''.''

	Brahmagupta gives the rule as "In the rule of three ''pramāṇa (''argument''),'' ''phala(''fruit'')'' and ''icchā(''requisition'')'' are the (given) terms; the first and the last terms must be similar. The ''icchā'' multiplied by the ''phala'' and divided by the ''pramāṇa'' gives the fruit (of the demand) ".		[[Brahmagupta]] gives the rule as "In the rule of three ''pramāṇa (''argument''),'' ''phala(''fruit'')'' and ''icchā(''requisition'')'' are the (given) terms; the first and the last terms must be similar. The ''icchā'' multiplied by the ''phala'' and divided by the ''pramāṇa'' gives the fruit (of the demand) ".

	Bhāskara I in his Āryabhaṭīya-bhaṣya talks about the Trairāśika		Bhāskara I in his Āryabhaṭīya-bhaṣya talks about the Trairāśika

alpha>Ramamurthy S: Internal link added

2022-08-17T09:03:43Z

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	==Trairāśika (Rule of Three)==		==Trairāśika (Rule of Three)==
	[[File:Rule-of-3.png\|alt=Rule of Three\|thumb\|Rule of Three]]		[[File:Rule-of-3.png\|alt=Rule of Three\|thumb\|Rule of Three]]
	The Hindu name for the Rule of Three is called "''trairāśika''" (three terms, hence the rule of three)<ref>{{Cite book\|last=Datta\|first=Bibhutibhusan\|title=History of Hindu Mathematics\|last2=Narayan Singh\|first2=Avadhesh\|publisher=Asia Publishing House\|year=1962\|location=Mumbai}}</ref>. The term ''trairāśika'' occurs in ~~Bakshālī~~ manuscript, Āryabhaṭīya. [[Bhaskara I\|Bhāskara I]] (c. 525) remarked on the origin of this name as "Here three quantities are needed (in the statement and calculation) so the method is called ''trairāśika (''the rule of three terms)". A problem on the rule of three has this form : if ''p'' yields ''f'' , what will ''i'' yield ?. The three terms used are ''p,'' ''f'' , ''i'' . Hindus called the term p (''pramāṇa'' - argument), f(''phala'' - fruit) and i (''icchā -'' requisition'').'' Sometimes they are referred to simply as the first ,second and third respectively.		The Hindu name for the Rule of Three is called "''trairāśika''" (three terms, hence the rule of three)<ref>{{Cite book\|last=Datta\|first=Bibhutibhusan\|title=History of Hindu Mathematics\|last2=Narayan Singh\|first2=Avadhesh\|publisher=Asia Publishing House\|year=1962\|location=Mumbai}}</ref>. The term ''trairāśika'' occurs in [[Bakhshali Manuscript\|Bakshālī]] manuscript, Āryabhaṭīya. [[Bhaskara I\|Bhāskara I]] (c. 525) remarked on the origin of this name as "Here three quantities are needed (in the statement and calculation) so the method is called ''trairāśika (''the rule of three terms)". A problem on the rule of three has this form : if ''p'' yields ''f'' , what will ''i'' yield ?. The three terms used are ''p,'' ''f'' , ''i'' . Hindus called the term p (''pramāṇa'' - argument), f(''phala'' - fruit) and i (''icchā -'' requisition'').'' Sometimes they are referred to simply as the first ,second and third respectively.

	[[Aryabhata\|Āryabhaṭa II]] gave different names as ''māna, vinimaya'' and ''icchā'' respectively to the three terms''.''		[[Aryabhata\|Āryabhaṭa II]] gave different names as ''māna, vinimaya'' and ''icchā'' respectively to the three terms''.''

alpha>Ramamurthy S: Image added

2022-08-12T06:43:45Z

Image added

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	==Trairāśika (Rule of Three)==		==Trairāśika (Rule of Three)==
			[[File:Rule-of-3.png\|alt=Rule of Three\|thumb\|Rule of Three]]
	The Hindu name for the Rule of Three is called "''trairāśika''" (three terms, hence the rule of three)<ref>{{Cite book\|last=Datta\|first=Bibhutibhusan\|title=History of Hindu Mathematics\|last2=Narayan Singh\|first2=Avadhesh\|publisher=Asia Publishing House\|year=1962\|location=Mumbai}}</ref>. The term ''trairāśika'' occurs in Bakshālī manuscript, Āryabhaṭīya. [[Bhaskara I\|Bhāskara I]] (c. 525) remarked on the origin of this name as "Here three quantities are needed (in the statement and calculation) so the method is called ''trairāśika (''the rule of three terms)". A problem on the rule of three has this form : if ''p'' yields ''f'' , what will ''i'' yield ?. The three terms used are ''p,'' ''f'' , ''i'' . Hindus called the term p (''pramāṇa'' - argument), f(''phala'' - fruit) and i (''icchā -'' requisition'').'' Sometimes they are referred to simply as the first ,second and third respectively.		The Hindu name for the Rule of Three is called "''trairāśika''" (three terms, hence the rule of three)<ref>{{Cite book\|last=Datta\|first=Bibhutibhusan\|title=History of Hindu Mathematics\|last2=Narayan Singh\|first2=Avadhesh\|publisher=Asia Publishing House\|year=1962\|location=Mumbai}}</ref>. The term ''trairāśika'' occurs in Bakshālī manuscript, Āryabhaṭīya. [[Bhaskara I\|Bhāskara I]] (c. 525) remarked on the origin of this name as "Here three quantities are needed (in the statement and calculation) so the method is called ''trairāśika (''the rule of three terms)". A problem on the rule of three has this form : if ''p'' yields ''f'' , what will ''i'' yield ?. The three terms used are ''p,'' ''f'' , ''i'' . Hindus called the term p (''pramāṇa'' - argument), f(''phala'' - fruit) and i (''icchā -'' requisition'').'' Sometimes they are referred to simply as the first ,second and third respectively.

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	== Inverse Rule of Three ==		== Inverse Rule of Three ==
			[[File:Rule-of-3-3.png\|alt=Inverse Rule of Three\|thumb\|Inverse Rule of Three]]
	The Hindu name for the Inverse Rule of Three is ''Vyasta''-''trairāśika'' ("inverse rule of three terms").		The Hindu name for the Inverse Rule of Three is ''Vyasta''-''trairāśika'' ("inverse rule of three terms").

alpha>Ramamurthy S: Citation added

2022-08-12T06:32:35Z

Citation added

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	Śrīdhara has stated the formula to find when the principal will double or triple or quadruple after 'N' months at R% per month.		Śrīdhara has stated the formula to find when the principal will double or triple or quadruple after 'N' months at R% per month.

	कालप्रमाणघातः फलभक्तो व्येकगुणहतः कालः । <small>(Pāṭīgaṇita III R.52, p.60)</small>		कालप्रमाणघातः फलभक्तो व्येकगुणहतः कालः ।<ref>{{Cite book\|last=Shukla\|first=Kripa Shankar\|title=The Patiganita Of Sridharacharya\|publisher=Lucknow University\|year=1959\|location=Lucknow\|pages=60}}</ref> <small>(Pāṭīgaṇita III R.52, p.60)</small>

	"The product of the time and the argument divided by the fruit and (then) multiplied by the multiple minus one, gives the required time."		"The product of the time and the argument divided by the fruit and (then) multiplied by the multiple minus one, gives the required time."