Ganittilakam Savrtuttikam

SR No.: 003174
Original Sutra Author: N/A
Author: Hiralal R Kapadia
Publisher: Oriental Research Institute Vadodra
Publication Year: 1937
Total Pages: 214
Language: Hindi
Classification: Book_Devnagari
File Size: 11 MB

Page 43

XLII
INTRODUCTION
(3) c = Van (d-) (4) = (d-Vdc )
(5) = V6hi+c21 (6) d = ( +2)/h Here C stands for the circumference of a circle of diameter d and A for its area. The arc of a segment of a circle less than a semicircle, its chord and its height or arrow are denoted as a, c and h respectively.
Over and above these 6 formulæ mentioned above, the Bhasya (p. 258) gives us a rule as below:
The portion of the circumference of a circle between (bounded by) two parallel chords is equal to half the difference between the corresponding arcs.
In Ksetrasamāsa of which the authorship is attributed to Umāsvāti, only the fourth formula is not to be found. Further. more, the rule pertaining to finding out the arrow mentioned there can be expressed as a = V(a-c4)/6 ।
This topic is dealt with by Ratnas'ekhara Sūri in his Laghuksetrasamāsa in the following hemistiches of the gāthās 188-190:
"विक्खंभवग्गदहगुणमूलं वस्स परिरओ होइ" "विउसुपिहुत्ते चउगुणउसुगुणिए मूलमिह जीवा"4
"उसुवग्गि छगुणि जीवावग्गजुए मूलं होइ धणुपिटुं" Trilokasāra, too, furnishes us with the formulæ here given and some more. All of them can be mentioned as under:
"परिही ति लक्ख सोलस सहस्स दो य सय सत्तवीसऽहिया ।
कोसतिय अट्ठवीसं धणुसय तेरंगुलऽद्धहियं ।” [ परिधिस्त्रयो लक्षाः षोडश सहस्रा द्वे च शते सप्तविंशत्यधिके ।
क्रोशत्रिकमष्टाविंशं धनुःशतं त्रयोदशाङ्गुलानि अर्धाधिकानि ॥] 1 Compare Gañitasārasangraha VII 43, 734, and Mahāsiddhānta (Benares odn. XV, 90, 94, 95, of Aryabhatta.
According to the Grook Heron of Alexandria (c. 200) a = V4h+ca+ or V4h+c + (V40+c-c).
The Chinese Hue who died in 1075 A. D. gives the formula asaecx
2 In K setrasamösa (v.7) as well as in the cūrni on Jambūdväpaprajñapti, instead of मूलं there is करणी. 3-5 Sanskrit rendering: -
विष्कम्भवर्गदशगुणमूलं वृत्तस्य परिधिर्भवति । वी(विगते) पृथुत्वे चतुर्गुणेषुगुणिते मूलमिह जीवा। इषुवर्गे षड्गुणे जीवावर्गयुते मूलं भवति धनुःपृष्ठम् ।