Jain Journal 2001 10

Author(s): Jain Bhawan Publication
Publisher: Jain Bhawan Publication

Page 25

JADHAV : THE VOLUME OF A RIGHT CIRCULAR CYLINDER
77 As the TLS is based on the TP, Nemicandra might have got the idea of the formula (3] from the same source, although his another famous treatise named Gommatasāra is based on the Dhavalā. The essence of the following two rules of the TP is rather identical with the present rule (v. 17) of the TLS.
sama-vatta-vāsa-vagge, dahaguride karaņi-parihio hodi/ vitthāra-turiya-bhāge, parihi hade tassa khetta-phalam// 117// unavisa-joyanesum caüvisehim tahāyaharidesum/ tiviha-viyappe palle, ghana-khetta-phalam hu patteyam // 118//
Translation : When the square of the diameter vyāsa) of a uniformcircle (samavrtta) (that is to say, a righr circular cylinder) is multiplied by ten and the square root of the product is found, it becomes the circumference (paridhi). When a quarter of the diameter is multiplied by the circumference, it gives the area (ksetraphala). When 19 yojanas is divided by 24, it gives the volume (ghanakşetraphala) of each of the three palyas (pits).
B.B. Datta 10 followed by H.L. Kapadiall, M.B.L. Agrawal12 and others inferred the formula (5) from the present rule (v. 17) of the TLS for a prism.
It is obvious that his inference is incorrect. After all, every cylinder is prism, but every prism is not cylinder. Nemicandra has set forth the rule (v. 17) only for finding the capacity (khātaphala) of a circular pit of uniform depth.
9.
TP, w. 117-118, p. 26. Here is the illustrative explanation for v. 118.
d=1 yojana, C= v1.1.10 = V10 = -2
1
19
=
and therefore
V = - =- cubic yojanus.
24 24 10. B.B. Datta, (1935), Mathematics of Nemicandra, The Jaina Antiquary,
1(2), 25-44, Arrah, p. 37. 11. H.R. Kapadia, (1937), Introduction to the Ganita-tilaka, Gaikwad Oriental
Series No. 78, Baroda, p. 43. 12. M.B.L. Agrawal, (1972), Contributions of Jainācāryās in the Development
of Mathematics and Astronomy, Doctoral Thesis in Hindi, Agra University, Agra, p. 92.