Jinamanjari 1996 09 No 14

Author(s): Jinamanjari
Publisher: Canada Bramhi Jain Society Publication

Page 60

Geometric Formulas in the Dhavalā of Virasena (780 C.E.)
Dr. Takao Hayashi
Introduction
The Dhavalā, Vīrasena's commentary on the Chakkhandāgama (Canon in Six Books', abbr. CK) of Puspadanta and Bhūtabali, was completed on November 3, 781 C.E. (See CESS 5, 714a for the date). In it, he uses many geometric formulas in relation to the computation of the fields (khettas) which the jīvas ('souls' or 'spirits') occupy or live in at various stages of their evolution. Some of those formulas bear special importance in the history of Indian mathematics. So far as is known, Vīrasena is the first in India to calculate the value, 355/113 (= 3.14159292 ...), for "r." He also used, for the first time in India, a formula for the sum of an infinite geometric progression. The geometric formulas used by him in Chapters 3 (khetta-uņugama) and 4 (phosaņa-aņuguma) of Book I (jīvathāņu) are examined in the following. (For Vīrasena and his mathematics, see also J.P. Jain 1948, L.C. Jain & A. Jain 1985, L.C. Jain 1982 and 1992, and Singh 1984.)
Rate of Increase
The rate of increase is used for calculating the length of a horizontal section of a trapezoid, which occurs in the Jaina cosmography as a vertical section of the Lower and the Upper Worlds.
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