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takes the volume of the 'world space' to be equal to one cubic loga or the cube of one jaga-sedhi ('world line') of seven rajjus. Hence the volume of the 'world space' is 73 = 343) cubic rajjus. This mathematical requirement perhaps caused the Digambara Jainas to invent the rectilinear figure of the Three Worlds. See, $3 above.
According to the Svetāmbara tradition, on the other hand, the Three Worlds consist of three truncated cones piled one above another (Fig. 5), whose total volume is less than half of 73 cubic rajjus. Vīrasena actually carries out the computation of the volume of each truncated cone in order to prove it (Dhavalā on CK 1.3.2; vol.4, pp. 12 18). Characteristic features of his computation here are the use of the sum of an infinite geometric progression and the transformation of geometric figures without changing their volumes.
Formulas Used
Vīrasena employs the following formulas and properties in his computation of the volume of a truncated cone (see Singh 1949/50 for the actual process of Vīrasena's computation)
1. Formula for the circumference of a circle:
C = 3d +
160 + 16
45 113
160 and C= 3d + 10
113
2. Formula for the area of a circle:
A-Cd
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