Nandanvana

Author(s): N L Jain
Publisher: Parshwanath Vidyapith

Page 228

(208) : Nandanavana
where h is the height and 'b' is the depth. As per Jaina and Hayashi? calculation of this volume could have been done by some easier process instead of applying infinite cutting procedure. He could have used the formula for the value of cone, V= Ah/3. The process has been called innumerated by Vīrasena where the sum of an infinite series has been practically applied.
Virasena has also calculated the volume of concentric rings surrounding the circular universe system. TP gives better description about them. For geometrical progression,
Sum = (first term / 1 - common ratio) when the common ration is less than unity. (c) Volumes of Irregular Solids.o2
A bee has been assumed to be a semi-cylinder. If a(1) is the length, (b), h is the height (1/2) and c/2 = yojana is circumference, the volume of bec will be
V= c/2 12 h.a = 3/8 Utsedha Yojana (Vol. 4, page 34) The centipede (gomhi) has been taken as semi-rectangular solid. Using the same symbols (a= length 3/4 y, b= width 1/8 ya and h = thickness = 1/2 b), the volume of the centipede,
V= a b h = 3/4 .3/32.3164 = 27/8192 uy3 A conch is an irregular cone whose volume is
A = [d2 - m/2 + m2/2] X/2 + 4 and hence V = A. (d-m+h/4) x a uy3 (Vol. 4 p. 35) where a= length = 12y, m = mouth = 4y, the height is not given.
A fish is taken as an elliptic cylinder or a rectangular solid. Vīrasena has given the formula for the volume of a big fish assuming values for a, b and h like the centipede. Modal Measures (Bhava-pramāna)
Vīrasena has mentioned eight additional methods, besides the eight fundamental operations, for calculating the number of different kinds of Jīvas. They are normally, analytical methods named as (1) Pramāņa (measure) (2) Káraņa (reason) (3) Nirukti (etymology) (4) Vikalpa (abstraction or permutation and combination) (5) Khandita (cut) (6) Bhājita (divided) (7) Viralana (spreading) and (8) Apahta (removal, substraction). Out of them, the last five have been used,