Book Title: Jainism
Author(s): M R Gelra
Publisher: Createspace

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Page 120
________________ 2. Units of Calculations 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. Rashi (Volume) : This is called treatment of volume using heaps of grains. 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 process of making denominators similar. (History of Hindu Mathematics. p. 179). The upper part is called 'numerator' and the lower part is called 'denominator'. For example: 1/2 and 1/3. Its meaning as Kala Savarna will be 3/6; 2/6 respectively. Yavat-tavat: As the name suggests, it means the multiplication series can be extended up to as far as possible. It is also used in summation of series. Varga (Square): The word varga means 'pankti' or row, or assembly (Samudaya). But in mathematics, its meaning is 'vargaghat' and 'vargakshetra' or its area. The predecessor preceptors have given its general definition as a square region (Samacaturastra). The product of two numbers is also square. The word Kriti is also used for varga implication, but rarely. This is also called 'Samadurasighata' various scholars have described its various processes. Ghana (Cube): This has been used to indicate solid cube and product of three equal numbers in geometrical and mathematical implications. The opinion of Aryabhatta is the product of three equal numbers and a solid with twelve equal angles (as well as sides) is also a cube. The word Vrnda has also been used at some places with the meaning as ghana (cube). This is also called 'Samatrirasaghata'. There is also difference in the processes of calculating the cube. According to statement of Sridhara, Mahavira and Bhaskara, the cube is the product of three equal numbers. Varga-varga (Square-Square): Multiplication of square by square. This is also called 'samacaturghata' (raised to power four). First the original number is multiplied by the same number. Then the product is multiplied by the same product. Whatever number results, is called varga-varga phala (square of square). For example 4x4=16, 16 x16=256. Krakach: In Kala mathematics, it is called 'treatment of Saw Mathematics (krakacavyavahara)'. This is a kind of patiganita. This gives the knowledge of sawing of wood and toiling of stones. For example, a wood piece is 20 fingers thick as the base and 16 fingers thick at the top. It is 100 fingers in length. If it is sawed at four places, what will be its sawed up measure 120

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