Lilavati 52

Lilavati

...infinity is demonstrated through the rules of arithmetic original: "paṭīsūtra". These are the foundational rules or "strings" of mathematical procedures.. In the context of algebra original: "bīja". Literally "seed," referring to seed-mathematics or algebra., it appears in many ways; there is no fixed rule for those who do not understand the underlying meaning.

Rule for Adding or Subtracting a Multiple of the Square Root

Now, the calculation rule original: "karaṇa sūtra" for the variety of problems where a multiple of the square root is added to or subtracted from a quantity:

Verse 56: To find the desired quantity when a multiple of its square root is known: Add the square of half the coefficient The "coefficient" is the number multiplying the square root. to the given visible quantity. Take the square root of this sum, then add or subtract half the original coefficient and square the entire result. This will be the desired quantity.

Verse 57: If the quantity was originally increased by a fraction, first divide the visible quantity and the coefficient of the root by that fraction plus one. Then, proceed with the calculation as previously described to find the quantity.

Explanation: In a case where a quantity is seen to be diminished by its own square root multiplied by some coefficient: the square root of the sum of the visible quantity and the square of half the coefficient should be increased by half the coefficient. If the quantity was seen to be increased by the square root multiple, then it should be diminished by half the coefficient. The square of that result is the quantity.

Example: The Flock of Swans

Verse 58: O young girl, a flock of swans was seen on the bank of the Kalindatapini A poetic name for the Yamuna River.. Moving slowly due to the burden of their own playfulness, they were seen engaging in love-quarrels. Two original: "yugmam". A pair. were seen on the bank, while the rest were seven times the square root of half the total flock The OCR reads "mūlaguṇaḥ 7", indicating the coefficient is 7. remaining in the water. Tell me the total number in the flock of swans.

Statement of the problem:
Coefficient of the root: 7
Visible quantity: 2

Bhaskaracharya Lilavati 105 Astronomy/Mathematics Other/Additional