Arhat Vachan 2002 01

SR No.: 526553
Original Sutra Author: N/A
Author: Anupam Jain
Publisher: Kundkund Gyanpith Indore
Publication Year: 2002
Total Pages: 108
Language: Hindi
Classification: Magazine, India_Arhat Vachan, & India
File Size: 7 MB

Page 13

a modified form of (13) in his Trisatikā, (sutra 47) as follows5
जीवाशरैक्यदलहतशरस्य वर्ग दशाहतं नाभिः।
विभजेदवाप्तमूलं प्रजायते कार्मुकस्य फलम्।। 47 ॥ 'Take ten times the square of the product of the arrow and half the sum of the chord and arrow, and divide by nine. The square - root of the quotient (so obtained) gives the area of the bow - figure.' That is, A= [h.(c+h)/2].(10/9)
........... (15) Clearly this is a modification of (13) based on an adjustment of a from the rough value st = 3 to the better (Jaina) value r = 10. The rule (15) is also found in the Prakrit work Ganitasāra (III, 46) of the Jaina author Thakkura Pherū (14th century). Although it is possible that (13) was known to ancient Jainas and (15) was its natural modification for t = 10, for accurate calculations they invented a simpler rule which will be discussed in the next section. Another practical rule will also be dealt therein. 3. SPECIAL JAINA RULE FOR AREA OF BOW - FIGURE
The Tiloyapannatti, IV, 2401, of Yativrasabha contains the following verbal statement of a sūksma ('accurate') rule.
SV - 9 - forg-utan, ufdical G1-4 i qui
C atar, iaita - n11 2401 || 'The square of the product of a quarter isu (=h) and the chord (=c) is multiplied by ten. The square - root of the result is the accurate (suhuma) area of the bow - figure.' That is, A = 10(c.h/4)
........... (16) The same rule is said to be found in the Brhatksetra - samāsa (1, 122) of Jinabhadra Gani (H.A.D. 609). The first half of a gātha quoted by Bhaskara I in his commentary (A.D. 629) on the Aryabhatiya (under II, 10) reads
इसुपायगुणा जीवा दसिकरणि भवेद विगणिय पदम। The product of the chord and a quarter of the arrow when further multiplied by the sqaure - root of ten becomes the area of the bow - figure.' That is, A = 10 c.h/4
............. (17) which is just a simplified form of (16) and which is also found in the GSS, VII, 70 (p. 198) of Mahavira. Nemicandra follows Mahavira in this respect. 9
For a semi circle, the rule (16) or (17) gives the area
Arhat Vacana, 14(1), 2002