पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

xvi INTRODUCTION
cause it found very few applications in everyday life. The
mathematics of zero which Śrīdharācārya listed as the ninth
determination, is Śrīdharācārya’s own contribution. Unfortu-
nately this topic is missing from our manuscript.
In mixtures of things (miśraka), Śrīdharācārya deals with
(i) simple interest, (ii) alligation of gold, (iii) partnership, (iv)
purchase and sale, (v) meeting of two travellers, (vi) wages
and payments, (vii) the well-known cistern problem, (viii)
wages paid out of the commodity, (ix) combination of savours,
and (x) certain special problems reducing to the solution of
simple and quadratic equations. In series (śreḍhī) he deals
with arithmetic and geometric series as well as with series of
squares, cubes, and successive sums of series in arithmetic
progression. In the surviving part of the section dealing with
plane figures, he gives rules for finding the areas of triangles
and quadrilaterals.
The following are the special features of the Pāṭīgaṇita :
(1) Rule for reducing a chain of measures. (Rule 42)
This rule is not found to occur in the Āryabhaṭīya
Brāhma-sphuṭa-siddhānta, Gaṇita-sāra-saṅgraha, or in any
other work written before the tenth century A.D., and
seems to have been first introduced by Śrīdharācārya.
Udayadivākara (1073 A.D.) ascribes it to Śrīdharācārya.
Its occurrence in the Mahā-siddhānta of Āryabhaṭa II
. (c. 950 A.D.) and the Gaṇita-tilaka of Śrīpati (1039 A.D.)
is evidently due to Śrīdharācārya’s influence.
(2) A special rule for finding the time in which a sum lent
out on simple interest will be paid back by equal monthly
instalments. (Rule 49-50). Also the example set on this
rule. (Ex. 55-56).
This rule and example, too, do not occur in any
work written before the tenth century A.D. and seem to
be due to Śrīdharācārya. The occurrence of this rule and