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The following are some texts of pati-ganita:
Vakshali Manuscript (c. 300 A.D.) Slate mathematics of Shri Dhar and Trisatika (c. 750 A.D.) Ganita Sar-Sangraha (c. 850 A.D.) Ganita Tilaka (1039 A.D.)
Lilavati (1150 A.D.) • Ganita Kaumudi (1356 A.D.) and • Pati-sar written by Munisvara (c. 1658 A.D.)
Besides, Bhaskara-II had mentioned that Lalla had authored a separate text on pati-ganita.
These treatises comprise twenty operators and eight forms of calculations. Examples have also been given along with the aphorism for explaining the application thereof.
Example of Arithmetic Progression An example of treatment of series is presented here. It is like a ladder hence, it is called 'progression' in mathematics. A person gives four rupees to another person. Every next day he adds five rupees to the previous day's amount, continuing up to fifteen days, then what is the total amount so given?
Whatever he gives on the first day is called the 'initial-amount'; incremental amount is called the common difference'. The number of days for which the amount is given is called the 'period'. The total sum is called the 'samvardhana'. Whatever is given on the last day is called the 'last-amount'. Whatever is given in the middle of the period is called the 'middle-amount'.
Method
The period is 15.
Subtracting 1, we get 15-1 = 14.
Multiplying it with common difference, gives 14x5 = 70.
Adding the initial term, it gives 70 + 4 = 74.
This is the 'last-amount'.
Then half of 74 + 4 is half of 78 is 39 which is the middle term.
The sum total is 39 x 15 (number of terms) = 585.
Similarly, the sum of the natural number from one to nine, or sum of more numbers, sum of the sums, sum of the square and cube are the topics of this mathematics.
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