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JAIN MATHEMATICS AND KARMAVAD/141
eight forms of calculations. Examples have also been given along with the aphorism for explaining the application thereof. 4. Example -
An example of treatment of series is presented here. It is like a ladder hence, it is called 'progression' in mathematics. Say a person gives four rupees to another. 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 'lastamount'. Whatever is given in the middle of the period is called the 'middleamount'.
4.1. 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.
5. Other Operators -
5.1. Rajju: This is called mensuration. Through this, the depth of a
lake (tank), height of a tree, etc. are measured. Its geometrical organs are the side, height, hypotenuse, diameter, circular area and circumference etc. This basically involves measurements using rope.
5.2. Rashi (Volume): This is called treatment of volume using heaps
of grains.
5.3. Kala-Savarna (Fraction): The number which is not an integer,
and is in part, is called Kala-Savarna, when it is made similar. This is called operation of making denominators equal, or the
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