Difference between revisions of "Rule of Three in Pāṭīgaṇitam"
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<math>=\frac{\frac{21}{2} \times \frac{37}{4}}{\frac{5}{4}}</math><math>=\frac{21 \times 37}{2 \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 == |
Latest revision as of 13:40, 19 September 2023
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[1]. (This having been done) that (middle quantity) multiplied by the last quantity should be divided by the first quantity.
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 = or palas
we know 4 karṣas = 1 pala.
fruit = or paṇas
requisition = 9 palas and 1 karṣa = or palas
Writing these quantities as directed in the rule, we have
argument (pramāṇa) | fruit (phala) | requisition (icchā) |
5
4 |
21
2 |
37
4 |
Then applying the rule, the required result
paṇas
See Also
References
- ↑ Shukla, Kripa Shankar (1959). The Pāṭīgaṇita of Śrīdharācārya. Lucknow: Lucknow University. pp. 22–23.