Ganittilakam Savrtuttikam

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

Page 13

XII
INTRODUCTION
Abhayadeva Sūri, the navārgāvrttikāra explains this verse while commenting upon this anga. According to his interpretation these ten Mathematical topics respectively represent calculations pertaining to (1) summation etc., well-known to a Mathematician, (2) Srenivyavahāra etc., treated in Pātīganita or arithmetic, (3) plane geometry so far as its calculations are carried on by means of a rope, (4) a heap of corn etc., usually called rāșīvyavahāra, (5) fractions, (6) multiplication or summation of natural numbers, (7) square, (8) cube, (9) fourth power, and (10) splitting wood by means of a saw styled as krākacavyavahāra.
There is a very wide gulf between this interpretation and that of Dr. B. Datta, since the latter has translated these ten topics as (1) fundamental operations, (2) subjects of treatment, (3) geometry (4) mensuration of solid bodies, (5) fractions, (6) simple equations, (7) quadratic equations; (8) cubic equations, (9) biquadratic equations, and (10) permutations and combinations.*
(1) pudgala, ( 2 ) yāvat-tāvat, (3) ghiana ( 4 ) ghanamüla (cube root), (5) varga and ( 6 ) vargamūla ( square root ). Thus the number of types will be eleven and not ten, a fact hardly admissible, when it contradicts a canonical statement. Moreover it is not clear as to what is actually meant here by pudgala.
1. If this implies summation of series, a meaning assigned to it in Ganitasārasangraha, the 6th type must mean multiplication; and thus there is no chance left for the alternative suggested by the commentator on p. 7.
2. The third type viz. Rajjusankhyāna can be equated to sulba sūtra; for, in Katyayana sūtra, paris'ista (1, 1) we note the like " HTY 28TH:” Further. more that Ksetraganita signifies geometry is corroborated by Ganitasärasani. graha (ch. VI). Geometry is spoken of in Sūtrakrta (II, 1, 154 ) as the lotus in Mathematics, the rest being considered as inferior to it.
It may be mentioned in this connection that over the entrance to the academy of Plato, one of the great philosophers of ancient Ionina, there was the following inscription:
"Let no one unacquainted with geometry enter here."
3. In this connetion the Bulletin of Calcutta Mathematical Society (Vol XXI, No. 2, pp. 121-124 ) deserves to be carefully read.
4. See 716th sätra which runs as under:"दस सुहुमा पण्णत्ता, तं जहा-पाणसुहुमे पणगसुहुमे जाव सिणेहसुहुमे गणियसुहुमे भंगसुहुमे।"
The commentator while explaining ganiyasuhuma makes the following noteworthy observation :
"गणितसूक्ष्म-गणितं सङ्कलनादि तदेव सूक्ष्मं सूक्ष्मबुद्धिगम्यत्वात्, श्रूयते च वज्रान्तं गणितमिति।"