________________
ARHAT VACANA Kundakunda Jñanapiha, Indore
Vol. 12, No. 4, October 2000, 61-66
ON THE QUADRATURE OF A CIRCULAR ANNULUS Dipak Jadhav
1 In his cosmographical treatise, Trilokasara1 (abbreviated as TLS, 'An essence of three regions of the universe). Nemicandra2 (c. 981 A.D.) produces, in Prakrit, the following rule (gatha) of great geometrical interest.
लवणंबुहिहुमफले चउरस्से एक जोयणस्सेव । सुहुमफलेणवहरिदे वट्टं मूलं सह स्सवेहगुणं ॥
The above rule rendered into Sanskrit runs:
लवणाम्बुधिसूक्ष्मफले चतुरखे एकयोजनस्यैव । सूक्ष्मफलेनापहृते वृत्तं मूलं सहस्रवेघगुणम् ॥
(TLS, v.103, p. 95)
(TLS, v.103, p. 96)
Translation Quadrilating (caturastre) the subtle area (sukṣmaphala) of the Lavana sea (Lavanambudhi): divide (the square of the area) by (the square of) the subtle area of the circle of diameter one yojana. Take the square-root (of the quotient) and then multiply (the result) by the effective height (vedha) of (measure) 1000 (yojanas) (to calculate the numbers of the kundas [cylinders] of diameter one yojana and depth one yojana).
In this paper, we will concentrate upon the following statement only.
लवणाम्बुधिसूक्ष्मफले चतुरसे
Translation Quadrilate the subtle area (sukṣmaphal) of the Lavana sea (Lavanambudhi).
In Jaina cosmography, it is supposed that the Jambudvipa (Jambu-Island) and Lavana sea are of diameters one lac (abbreviated as 'T) yojanas and 51 yojanas respectively (cf. Figure 1 - Next page).
Thus the Lavanambudhi (salt sea) is circular annulus in shape and is of inner diameter 11 yojanas, outer diameter 51 yojanas and breadth 21 yojanas.
It can be inferred from the above statement that Nemicandra knew how to quadrilate a circular annulus but did not set down its process.
Research Scholar-Kundakunda Jñanapitha, Indore, Lecturer in Mathematics, J.N. Govt. Model H.S. (Residential) School, Barwani-451 551 India
