________________
That means when a trapezoid cut in half the base 'a' and the middle line 'm', both increased by the top 'b', multiplied the result by the square of seven and made them into one, there will be the volume of the world in cubic rajjus.
Volume of Cylindrical Spaces
Let 'V' and 'h' are respectively the volume and height of a cylinder and 'd', 'c' and 'A' are respectively the diameter, the circumference and the area of its base. Then the formula for the volume which taken for granted by Virasena is
Also
The first formula for area is cited in a different wording as a formula of 'practical' nature as against 'exact'.
31
The Jaina mathematician Mahavira also prescribes it in a section for geometrical formulas of 'practical' nature of his Ganitasarasamgraha.
and
The second formula and its variation, A.(c/2). (d/2) has been used in India since at least the times of Umāsvāti.
32
Circumference of a circle
There are two formulas for the circumference of a circle given by Virasena,
C = ✓10d2
86
V = Ah where A = 3 d A = c.
4
16d + 16 C = 3d + 113
355 d + 16 113
33
The second formula will be more accurate than the first one." Virasena also uses the formula (in addition to above) -
Jain Education International
d, 2
C = 3d +
C =
355
113
16d
113
d
Thus, Virasena uses the three approximations for л which is 3, ✓10
355
113
The first value is for the area and the rest values for the circumference.
Arhat Vacana, 14(2-3), 2002
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