Shri Raghunath Sanskrit Research Institute Library,

Jammu

No. 860 — Gha original: ८६० — घ

Title Lilavati A 12th-century masterpiece of Indian mathematics and algebra written by Bhaskara II, named after his daughter.

Author Bhaskaracharya Also known as Bhaskara the Teacher, one of the most celebrated astronomers and mathematicians of medieval India.

Extent 10 [folios] Age [Not stated]

Subject Astronomy/Mathematics original: Jyotisham Incomplete original: Apurnam

20

Circle 1 first term original: ādi 1 common difference original: caya 5 number of terms original: gaccha 8 total sum original: sarvadhana 148 last term original: antyadhana 36.

In this case, when the number of terms original: gaccha is an even number, there is no single middle day. Therefore, one must understand that the "middle value" is derived from the average of the two middle terms. To find the first term original: ādi, the following rule original: sūtra is given:

Rule for Finding the First Term

The total sum divided by the number of terms, and then decreased by half the product of the common difference and the number of terms minus one, results in the first term.

Example:
The total sum result of the progression original: śreḍhīphala is one hundred and five (105). There are seven terms original: sapta-pada, and the common difference original: caya is three. Tell me, what is the first term starting value original: vadana; literally "the face"?

Numerical Setup:
First term: 0 This indicates the value to be found
Common difference: 3
Number of terms: 7
Total sum: 105
Result: The first term is 6.

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Rule for Finding the Common Difference

The total sum divided by the number of terms, minus the first term, and then divided by half the number of terms minus one, shall be the common difference original: caya.

Example:
A wise traveler first traveled eight yojanas A traditional Indian measure of distance, roughly 8-13 kilometers on the first day. Over the course of seven days, he covered a total distance of one hundred and five. Tell me, O learned one, what was the daily increase original: caya; common difference in his speed?

Numerical Setup:
First term: 8
Number of terms: 7
Total sum: 105
Common difference: 0 The value to be calculated
Result: The common difference is 2 and 1/3 Calculation: [(105 / 7) - 8] / [(7 - 1) / 2] = [15 - 8] / 3 = 7 / 3.