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JANUARY, 1979
91
This approximate formula is found in the Ganita-sära-sangraha (=GSS), VII, 43 of the Jaina author Mahaviracarya (c. 850 A.D.) in the following words
saravargāt-pancagunāj-jyāvargayutātpadam kāştham 1/43//
“The square-root of the sum of five times the square of the fara (height of the segment) and the square of the chord is the arc.'
However, the commonly used value of 1 by the Jainas was vio which will yield k equal to 6 by (8) and (7) will become s =(c2+6 ha)
... (10)
This formula is found almost in all Jaina works on mathematics and cosmography (in Prakrit and Sanskrit). For example, the Bhāșya on the Tattvārthādhigama-sūtra (=TDS), III, 11, says
işuvargasya şadguṇasya jyāvargayutasya kytasya mūlam dhanuhkästham
'Take the sum of the six times the square of the işu (height of the segment) and the square of the chord ; its square-root is the arc. *
Some other references to (10) are :
(i) Kșetrasamāsa whose authorship is attributed to Umasvatis.
(ii) GSS, VII, 731 (p. 198) as an accurate rule.
: The GSS edited with Hindi translation by L. C. Jain, p. 190, Sholapur, 1963
(Jain Samskriti Samrakshaka Sangha). * The present author proposes to prepare a separate paper on this Jaina value of
h. Also see his article on 'Some Ancient Values of Pi and Their Use in India' (Glimpses of Ancient Indian Mathematics or G.A.I.M. No. 13), The Mathematics Education, Vol. IX, No. 1 (March, 1975), Sec. B, pp. 2-3. See the Sabhasya- TDS edited with Hindi translation of Khuba Chandra, p. 170, Bombay, 1932 (Paramasruta Prabhavaka Mandala). The date of Umasvati (the author of TDS) is about 40-90 A.D, according to J. P. Jain, Jaina Sources of the History of Ancient India, p. 267, Delhi 1964 (Munshi Ram Manohar Lal); and about 4th or 5th century A.D. according to Nathu Ram Premi, Jaina Literature and History (in Hindi), p. 547, Bombay, 1956 (Hindi Grantha Ratnakara). Premi maintains that the author of the TDS is also the author of the TDS-Bhasya which we have quoted. But there is a
disagreement on this point also among the scholars. * See H. R. Kapadia (editor), Ganita Tilaka, Introduction, p. XL II, Baroda, 1937
(Oriental Institute).
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