Ganittilakam Savrtuttikam

Author(s): Hiralal R Kapadia
Publisher: Oriental Research Institute Vadodra

Page 60

LIX
INTRODUCTION Over and above these four jātis', some enumerate two more. They are:
(1) Bhāga-bhāga i. e. the form (a:) or (a).
(2) Bhāga-māt? i. e. combinations of two or more of the five jātis mentioned above.3
VALLĪSAVARŅANA As the next topic S'rīpati introduces on p. 39, vallisavarnana, and on the same page gives us a rule whereby we can reduce a chain of measures into a proper fraction. MISCELLANEOUS PROBLEMS INVOLVING THE USE OF FRACTIONS
Just as Mahāvīrācārya has given ten varieties of the mis. cellaneous problems involving fractions viz., (1) bhāga, (2) s'eșa, (3) mūla, (4) s'eşamūla, (5) dviragras'esamüla, (6) añs'amūla, (7) bhāgābhyāsa, (8) ańs'avarga,(9) mūlamis'ra and (10) bhinnadrs'ya, so has S'rīpati given 9 varieties as under:
(1) Drs'ya, (2) s'esa, (3) vis'lesa, (4) s'esamüla, (5) mūlā. grabhāga, (6) ubhayāgradrs'ya, (7) bhinnabhāgadrs'ya, (8) bhāga. müla and (9) hūnavarga.
At a cursory glance one can see that the 2nd and the 4th varieties are completely identical. Furthermore, on comparison, it will be found that (i) the first variety in each case is the same, though differently styled', (ii) same is the case with
1 Cf. Datta and Singh, l. c., p. 190ff. 2 Since there seems to be no special symbol to indicate division, this is
written as 16, and it is honce likely that this may be confounded with a +
also written in the same way.
3 Mahävīräcārya has noted that there can be 26 (=5C24.5C3 +504 +505) combinations.
4 All these ton varieties are explained by M. Rangācārya in his translation (pp. 70-71) of Ganitasārasangraha.
5 In order that this remark may be realized, I may reproduce the pertinent portion from the English translation (p. 70) of Ganitasärasargraha, It runs as under :
"The Bhäga variety consists of problems wherein is given tho numerical value of the portion remaining after removing certain specified fractional parts of the total quantity to be found out. The fractional parts removed are each of them called a bhäga, and the numerical value of the known remainder is tormed drs'ya."
From this it follows that Mahāvīrācārya while naming the first variety considers bhāga as an important factor, whereas S'rīpati, drs'ya.