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But some basic mathematical rules (of the GSS) are found in his translation of the PG. We give two cases:
1. To find the area in kuntas of a quadrangular field, take half the amount of the bamboos of the north and south sides, multiply it by half the amount of the east and west sides. The product will be the number required. (Cf. GSS, VII.7)
2. To find area of a Sarkha Figure, deduct half the amount of the short diameter from the long diameter, square the remainder, do the same with half of the short diameter and add the two products together. Multiply the amount by three. Divide this product by four. The quotient is the area. that is,
Area = [(D-d/2)2 + (d/2)2). (3/4)
which may be compared with the GSS (VII. 23) from.
1 Area = (p/2) + (3/4).(d/2)2
where p = 3(D-d/2)2.
Thus we see that PG from is just a simplification of the GSS form. A figure is also drawn.
Heyne could not procure the Sanskrit original of the Telugu PG which, he was told, is a translation of the former whose name and details were also not, apparantly, told to him. Heyne also complained of some imperfections in the copy of PG he consulted. Of course, the presentation of the English version of the PG by Heyne is also poor. Any way, he studied indirectly (i.e. via PG) and even unknowingly the selected portion of GSS in its Teugu version by Mallana and this happened more than 190 years ago. A study of PG is automatically a study of GSS and may throw some new light in the field. Publication of some ancient commetary (whether in Sanskrit, Telugu or Kanada) of GSS is also highly desirable.
References
1. R.C. Gupta, Mallana, The First Telugu Writer of Mathematics, Ganita Chandrika, 2(2), 2001, 5-8 and 293), 9.
2. R.C. Gupta, World's Longest Lists of Decuple Terms, Ganita Bharati, 23, 2001, 83-90.
3. B. Heyne, Tracts, Historical and Statistical on India, London, 1814, PG's portion appears on pp. 172-180
4. L.C. Jain (ed.), GSS with Hindi translation, Sholapur, 1963
5. S.R. Sharma, The Pavuluriganitamu, Studien zue Indologie and Iranistik, Hefft, 13/14 (1987), 163-176.
6. V.P. Sastri (ed.) Sarasamgraha-ganitamu, (of Mallana), Part-1, Tirupati, 1952 (s.V.O.R.S. No. 38) (metioned by S.R. Sharma).
Received: 10.06.02
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