The Rule of Three in Līlāvatī - Revision history

Ramamurthy: Headings modified

2023-08-30T15:41:35Z

Headings modified

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	~~==Introduction==~~
	The rule of three is a form that allows the resolution of problems of proportionality between three known values and an unknown, in other words, the rule of three is an operation that allows us to find a fourth term with respect to a given proportion.		The rule of three is a form that allows the resolution of problems of proportionality between three known values and an unknown, in other words, the rule of three is an operation that allows us to find a fourth term with respect to a given proportion.

	==Verse 79==		==Verse 79==
	प्रमाणमिच्छा च समानजातिः		प्रमाणमिच्छा च समानजातिः

Ramamurthy: Category updated

2023-08-16T12:55:42Z

Category updated

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	<references />		<references />
	[[Category:Mathematics in Līlāvatī]]		[[Category:Mathematics in Līlāvatī]]
			[[Category:General]]

Ramamurthy: /* Example 1 */

2023-06-26T05:54:07Z

Example 1

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	प्राप्यते सपदि मे वणिग्वर ब्रूहि निष्कनवकेन तत्कियत् ॥८१॥		प्राप्यते सपदि मे वणिग्वर ब्रूहि निष्कनवकेन तत्कियत् ॥८१॥

	If <math>2\frac{1}{2}</math> [~~https://vidyalyawiki.~~in~~/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB~~#~~Translation_4~~ pala] of saffron costs <math>\frac{3}{7}</math>[~~https://vidyalayawiki.~~in~~/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB~~#~~Translation_2~~ niṣkas] O you expert businessman tell me quickly what quantity of saffron can be bought for 9 niṣkas .		If <math>2\frac{1}{2}</math> [[Weights & Measures in Līlāvatī#Translation 4\|pala]] of saffron costs <math>\frac{3}{7}</math>[[Weights & Measures in Līlāvatī#Translation 2\|niṣkas]] O you expert businessman tell me quickly what quantity of saffron can be bought for 9 niṣkas .

	'''Comment''':		'''Comment''':

Ramamurthy: /* Example 1 */

2023-06-26T05:52:13Z

Example 1

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	कुंकुमस्य सदलं पलद्वयं निष्कसप्तमलवेत्रिभिर्यदि ।		कुंकुमस्य सदलं पलद्वयं निष्कसप्तमलवेत्रिभिर्यदि ।

	प्राप्यते सपदि मे वणिग्वर ब्रूहि निष्कनवकेन तत्कियत् ॥८१॥		प्राप्यते सपदि मे वणिग्वर ब्रूहि निष्कनवकेन तत्कियत् ॥८१॥

	If <math>2\frac{1}{2}</math> [https://vidyalyawiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_4 pala] of saffron costs <math>\frac{3}{7}</math>[https://vidyalayawiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 niṣkas] O you expert businessman tell me quickly what quantity of saffron can be bought for 9 niṣkas .		If <math>2\frac{1}{2}</math> [https://vidyalyawiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_4 pala] of saffron costs <math>\frac{3}{7}</math>[https://vidyalayawiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 niṣkas] O you expert businessman tell me quickly what quantity of saffron can be bought for 9 niṣkas .

Ramamurthy: /* Example 2 */

2023-06-26T05:50:42Z

Example 2

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	'''Comment''': This is also an example of direct proportion.		'''Comment''': This is also an example of direct proportion.

	16 [~~https://vidyalayawiki.~~in~~/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB~~#~~Translation_2~~ paṇas] = 1 [~~https://vidyalayawiki.~~in~~/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB~~#~~Translation_2~~ dramma]		16 [[Weights & Measures in Līlāvatī#Translation 2\|paṇas]] = 1 [[Weights & Measures in Līlāvatī#Translation 2\|dramma]]

	Hence 2 drammas = 32 paṇas		Hence 2 drammas = 32 paṇas

Ramamurthy: Internal link updated.

2023-06-26T05:47:57Z

Internal link updated.

← Older revision		Revision as of 11:17, 26 June 2023
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	प्राप्यते सपदि मे वणिग्वर ब्रूहि निष्कनवकेन तत्कियत् ॥८१॥		प्राप्यते सपदि मे वणिग्वर ब्रूहि निष्कनवकेन तत्कियत् ॥८१॥

	If <math>2\frac{1}{2}</math> [https://~~alpha.indicwiki~~.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_4 pala] of saffron costs <math>\frac{3}{7}</math>[https://~~alpha.indicwiki~~.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 niṣkas] O you expert businessman tell me quickly what quantity of saffron can be bought for 9 niṣkas .		If <math>2\frac{1}{2}</math> [https://vidyalyawiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_4 pala] of saffron costs <math>\frac{3}{7}</math>[https://vidyalayawiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 niṣkas] O you expert businessman tell me quickly what quantity of saffron can be bought for 9 niṣkas .

	'''Comment''':		'''Comment''':
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	'''Comment''': This is also an example of direct proportion.		'''Comment''': This is also an example of direct proportion.

	16 [https://~~alpha.indicwiki~~.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 paṇas] = 1 [https://~~alpha.indicwiki~~.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 dramma]		16 [https://vidyalayawiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 paṇas] = 1 [https://vidyalayawiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 dramma]

	Hence 2 drammas = 32 paṇas		Hence 2 drammas = 32 paṇas

Ramamurthy: Category updated

2023-06-22T10:43:35Z

Category updated

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	==References==		==References==
	<references />		<references />
	[[Category:Mathematics]]		[[Category:Mathematics in Līlāvatī]]
	~~[[Category:~~Līlāvatī]]

Ramamurthy: See Also link updated

2023-05-22T15:59:59Z

Ramamurthy: New Page created

2023-05-18T21:05:08Z

New Page created

New page

==Introduction==
The rule of three is a form that allows the resolution of problems of proportionality between three known values and an unknown, in other words, the rule of three is an operation that allows us to find a fourth term with respect to a given proportion.
==Verse 79==
प्रमाणमिच्छा च समानजातिः

आद्यन्तयोस्तत्फलमन्यजातिः ।

मध्ये तदिच्छाहतमाद्यहृत्स्यात्

इच्छाफलं व्यस्तविधिर्विलोमे ।। LXXIX ।।
==Translation==
There are three quantities involved herein.<ref>{{Cite book|title=Līlāvatī Of Bhāskarācārya - A Treatise of Mathematics of Vedic Tradition|publisher=Motilal Banarsidass Publishers|year=2001|isbn=81-208-1420-7|location=New Delhi|pages=77-79}}</ref> The first one on the left (a) is called pramāṇa (scale), the second (b) phala (result or fruit) and third (c) icchā (desire or requisition). The answer to be found (d) is called icchā-phala (desired result). Here a and c must be of the same kind and b should be different from a and c. The formula is <math>d = \frac {b \ X \ c}{a}

</math> . d is of the same kind as b.
==Example 1==
कुंकुमस्य सदलं पलद्वयं निष्कसप्तमलवेत्रिभिर्यदि ।

प्राप्यते सपदि मे वणिग्वर ब्रूहि निष्कनवकेन तत्कियत् ॥८१॥

If <math>2\frac{1}{2}</math> [https://alpha.indicwiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_4 pala] of saffron costs <math>\frac{3}{7}</math>[https://alpha.indicwiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 niṣkas] O you expert businessman tell me quickly what quantity of saffron can be bought for 9 niṣkas .

'''Comment''':

This is direct proportion, since more money buys more saffron.

As per rule of three.

Cost in niṣkas ⇒ Qty of Saffron

<math>\frac{3}{7}</math>⇒ <math>\frac{5}{2}</math>

9 ⇒ d

Hence <math>d = \frac{ 9\ X \frac{5}{2}}{\frac{3}{7}}

</math> =<math>\frac{105}{2}</math>palas.
==Example 2==
द्रम्मद्वयेन साष्टांशा शालितण्डुलखारिका ।

लभ्या चेत् पणसप्तत्या तत्किं सपदि कथ्यताम् ॥८३॥

<math>1\frac{1}{8}</math> khārikās of rice can be bought for 2 drammas, then how much rice can be bought for 70 paṇas ?

'''Comment''': This is also an example of direct proportion.

16 [https://alpha.indicwiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 paṇas] = 1 [https://alpha.indicwiki.in/index.php?title=Weights_&_Measures_in_L%C4%ABl%C4%81vat%C4%AB#Translation_2 dramma]

Hence 2 drammas = 32 paṇas

Cost in paṇas ⇒ Qty of rice

32 ⇒ <math>1\frac{1}{8}</math>

70 ⇒ d

<math>d = \frac{ 70\ X \frac{9}{8}}{32}

</math> = <math>\frac{630}{256}</math>=<math>\frac{315}{128}</math>=<math>2\frac{59}{128}</math>khārikās
==See Also==
[https://alpha.indicwiki.in/index.php?title=%E0%A4%B2%E0%A5%80%E0%A4%B2%E0%A4%BE%E0%A4%B5%E0%A4%A4%E0%A5%80_%E0%A4%AE%E0%A5%87%E0%A4%82_%27%E0%A4%A4%E0%A5%80%E0%A4%A8_%E0%A4%95%E0%A4%BE_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE%27 लीलावती में 'तीन का नियम']
==References==
<references />
[[Category:Mathematics]]
[[Category:Līlāvatī]]

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	</math> = <math>\frac{630}{256}</math>=<math>\frac{315}{128}</math>=<math>2\frac{59}{128}</math>khārikās		</math> = <math>\frac{630}{256}</math>=<math>\frac{315}{128}</math>=<math>2\frac{59}{128}</math>khārikās
	==See Also==		==See Also==
	[https://alpha.indicwiki.in/index.php?title=%E0%A4%B2%E0%A5%80%E0%A4%B2%E0%A4%BE%E0%A4%B5%E0%A4%A4%E0%A5%80_%E0%A4%AE%E0%A5%87%E0%A4%82_%27%E0%A4%A4%E0%A5%80%E0%A4%A8_%E0%A4%95%E0%A4%BE_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%AE%27 लीलावती में 'तीन का नियम']		[[लीलावती में 'तीन का नियम']]
	==References==		==References==
	<references />		<references />
	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Līlāvatī]]		[[Category:Līlāvatī]]