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 17

PEFQ whose area is (c + c/2).h/2 which gives the formula (19). Finally by adjusting (19) to the better value a = 10, we get the Jaina rule (16) or (17).
References and Notes - 1. R.C. Gupta, Jaina Formulas for the Arc of a Circular Segment, Jain Journal,
13(3), (1979), 89-94. 2. GSS, edited by L.C. Jain, with Hindi translation, Sholapur, 1963. The chord is called
guna ('cord' or 'string') here. 3. See the Trilokasāra with commentary of Madhavacandra and Hindi translation of | Argika Visuddhamati, Mahāviraji, 1975, p. 597. 4. The details are given by the present author in a paper submitted for a felicitation
volume. 5. Sudhakara Dvivedi (editor), Trisatikā of Sridhara, Benares, 1899, p. 35. 6. A.Nahata and B. Nahata (editors), Ratnapariksādi Saptagrantha sangraha (including
Ganita sāra), Jodhpur, 1961, p. 56 in Part II. 7. See the Tiloyapannatti, edited with Hindi translation of Aryikā Visuddhamali, Vol.
II, 1986, p. 636. Yafiursabha is placed between A.D. 473 and 609. 8. See the Aryabhatiya with the Commentary of Bhāskara I etc., ed. by K.S.
Shukla, New Delhi, 1976, p. 73. 9. Trilokasāra (see ref. 3 above) gathā 762, p. 597. Visuddhamati's translation is
slightly wrong. Dasakarani means 10 which she missed. 10. R.C. Gupta, 'On Some Rules from Jaina Mathematics', Ganita Bhārati, 11 (1989),
18-26. 11. Gupta, "Mahāviracārya on the Perimeter and Area of an Ellipse', The Mathematics
Education, 8(1), 1974, Sec. B, 17-19; and T. Hayashi, Narayana's Rule for
a Segment of a Circle'. Ganita Bhārati, 12(1990), 5-7. 12. See the Apastamba Sulbasūtra, ed. by D. Srinivasachar and N. Narasimhachar,
Mysore, 1931, p. 124. 13. R.C. Gupta, Mensuration of a Circular segment in Babylonian Mathematics.
Ganita Bhārati, Vol. 23 (2001). It also contains a rationale of the rule (24). 14. Hayashi, op.cit. (see ref. 10 above), pp. 2-3. 15. The rule (25) for the triangle comes from the famous and universal 'surveyor's
rule' for the area of a quadrilateral (of sides a, b, c, d) namely
area = (a+c)
(+)
12 when the (top) fourth side d = 0 (for triangle). For details see R.C. Gupta's, 'Primitive
Area of a Quadrilateral and Averaging', Ganita Bhārati, 19 (1997), 52-59. 16. See original text etc. in the Ganita Kaumudi, ed. by Padmakara Dvivedi, Part
II, Benares, 1942, p. 11 and some modern exposition in Ganita Bhārati, Vol. 21
(1999), p. 15. 17. See R.C. Gupta, The Process of Averaging in Ancient and Medieval Math.',
Ganita Bhārati, 3 (1981), 32-42.
Received - 3.7.2001
Arhat Vacana, 14(1), 2002
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