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	<math>=\frac{\frac{21}{2} \times \frac{37}{4}}{\frac{5}{4}}</math><math>=\frac{21 \times 37 \times 4}{2 \times 4 \times 5}</math><math>=\frac{21 \times 37}{2 \times 5}</math><math>=\frac{777}{10}</math>''paṇas''		<math>=\frac{\frac{21}{2} \times \frac{37}{4}}{\frac{5}{4}}</math><math>=\frac{21 \times 37 \times 4}{2 \times 4 \times 5}</math><math>=\frac{21 \times 37}{2 \times 5}</math><math>=\frac{777}{10}</math>''paṇas''
	==See Also==		==See Also==
	[https://alpha.indicwiki.in/index.php?title=%E0%A4%AA%E0%A4%BE%E0%A4%9F%E0%A5%80%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A4%AE%E0%A5%8D_%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 पाटीगणितम् में 'तीन का नियम']		[[पाटीगणितम् में 'तीन का नियम']]
	==References==		==References==
	<references />		<references />
	[[Category:Mathematics in Pāṭīgaṇitam]]		[[Category:Mathematics in Pāṭīgaṇitam]]
	[[Category:General]]		[[Category:General]]

Ramamurthy: New Page created

2023-09-19T17:56:47Z

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The Rule of Three is a Mathematical Rule that allows us to solve problems based on proportions. Rule of Three is known as '''''Trairāśika''''' in Samskrita.

==Verse==
आद्यन्तयोस्त्रिराशावभिन्नजाती प्रमाणमिच्छा च ।

फलमन्यजातिमध्ये तदन्त्यगुणमादिना विभजेत् ॥४३॥
==Translation==
In (solving problems on) the rule of three, the argument (pramāṇa) and the requisition (icchā), which are of the same denomination, should be set down in the first and last places; the fruit (phala), which is of a different denomination, should be set down in the middle<ref>{{Cite book|last=Shukla|first=Kripa Shankar|title=The Pāṭīgaṇita of Śrīdharācārya.|publisher=Lucknow University|year=1959|location=Lucknow|pages=22-23}}</ref>. (This having been done) that (middle quantity) multiplied by the last quantity should be divided by the first quantity.

<math>required \ fruit= \frac{fruit \ X \ requisition}{argument}
</math>
===Example===
If 1 ''pala'' and 1 ''karṣa'' of sandal wood are obtained for ten and a half ''paṇas'', then for how much will 9 ''palas'' and 1 ''karṣa'' (of sandal wood of the same quality) be obtained?

Here

argument - 1 ''pala'' and 1 ''karṣa ='' <math>1\frac{1}{4}</math> or <math>\frac{5}{4}</math>''palas''

we know ''4 karṣas = 1 pala.''

fruit = <math>10\frac{1}{2}</math> or <math>\frac{21}{2}</math>''paṇas''

requisition = 9 ''palas'' and 1 ''karṣa ='' <math>9\frac{1}{4}</math> or <math>\frac{37}{4}</math>''palas''

Writing these quantities as directed in the rule, we have
{| class="wikitable"
|+
|'''argument (pramāṇa)'''
|'''fruit (phala)'''
|'''requisition (icchā)'''
|-
|5
4
|21
2
|37
4
|}Then applying the rule, the required result

<math>required \ fruit= \frac{fruit \times requisition}{argument}
</math>

<math>=\frac{\frac{21}{2} \times \frac{37}{4}}{\frac{5}{4}}</math><math>=\frac{21 \times 37 \times 4}{2 \times 4 \times 5}</math><math>=\frac{21 \times 37}{2 \times 5}</math><math>=\frac{777}{10}</math>''paṇas''
==See Also==
[https://alpha.indicwiki.in/index.php?title=%E0%A4%AA%E0%A4%BE%E0%A4%9F%E0%A5%80%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A4%AE%E0%A5%8D_%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 पाटीगणितम् में 'तीन का नियम']
==References==
<references />
[[Category:Mathematics in Pāṭīgaṇitam]]
[[Category:General]]

Rule of Three in Pāṭīgaṇitam - Revision history

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