Jain Journal 2001 10

SR No.: 520144
Original Sutra Author: N/A
Author: Jain Bhawan Publication
Publisher: Jain Bhawan Publication
Publication Year: 2001
Total Pages: 49
Language: English
Classification: Magazine, India_Jain Journal, & India
File Size: 3 MB

Page 24

76
JAIN JOURNAL: Vol-XXXVI, No. 2 October, 2001 In fact, the Sulba-sūtrās do not speak of the volume of a right circular cylinder directly. But their authors must have been familiar with the concept of a right circular cylinder, since they used to fix the height as well as the number of layers and total number of bricks in the fire altars of circular shape.
Till we reach the Tiloyapannatti? (abbreviated as TP) where Yativrsabha (sometime between 473 A.D. and 609 A.D.) uses the formula (4] with = V10 for finding the capacity (ghanakşetraphala) of the imaginary palya (circular pit of uniform depth), we do not come across any authentic mention of the volume of a cylinder in India. It may be, here, noted that the TP is a representative of a much more ancient tradition.
Without mentioning the name of the solid, the formula [5] for finding volume (samakhātaphala) occurs in the Brāhma-sphuţa-siddhānta* of Brāhmagupta (c. 628 A.D.), Trisatikās of Sridhara (c. 799 A.D.) and Ganita-sāra-samgraho of Mahāvīra (c. 850 A.D.).
Takao Hayashi? has found that Virasena (c. 816 A.D.) employed the formula (3) in the Dhavalā commentary on the Satkhandāgama of Puşpadanta and Bhutabali (1-2nd century A.D.).
Tiloyapannatti, ed. with Āryika Visuddhamati's Hindi commentary by C.P. Patni, Sri 1008 Candraprabha Digambara Jaina Atisayaksetra, DehraTijārā (Raj.), Part-1, Third Edition, 1997, p. 26. See also L.C. Jain, (1958), The Mathematics of the TP (in Hindi), published with the Jambūddvipa-pannatti-samgho, Jaina Samskrti Samraksaka Samgha (JSSS), 1108, Sholapur, pp. 20-21 and Sarsvathiamma, T.A. (1961-62), The Mathematics in the First Four Mahādhikāras of the Triloka-prajñāpti, Journal of Ganganath Research Institute, 18, 27-51, p. 29. Brāhma-sphuta-siddhānta, ed. with his own commentary by Sudhakara Dvivedin, Benaras, 1902, Originally published in the Pandita, 23-24, 1901-1902, v. 12.44, ksetra-phalam vedhagunam samakhāta-phalam. Trisatikā, ed. by Sudhakara Dvivedin, Benaras, 1899, v. 53, p. 38. sama-vistara-hata-dairdhye vedhena samāhate phalam bhavati. Gaạita-sāra-Samgraha, ed. by and translated into Hindi by L.C. Jain, JSSS, Sholapur, 1963, v. 8.4, p. 252. kşetraphalam vedhaguņam samakhāte. Hayashi, Takao (1996), Geometric Formulas in the Dhavalā of Virasena (780 C.E.), Jina-manjari, 14(2), 53-76, Ontario, pp. 57, 61 and 71. Dhavalā, ed. with a Hindi Translation by H.L. Jain et.al. vol. 4, Book 4, Amaraoti, 1940-58, Reprinted, JSSS, Sholapur, 1984, v. 1. 3.2, p. 34.
6.
8.