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

xl INTRODUCTION
In fact, the modern formula reduces to Śrîdharâ-
cârya's formula, if we take π = 3⅙.
(ii) Śrîdharâcârya's formula for the area of a segment
of a circle, viz.
(√10 / 3) × ((chord + arrow) / 2) × arrow,
is also superior to that given by Mahâvîra, viz.
(√10 × chord × arrow) / 4
The above-mentioned formulæ of Śrîdharâcârya were
subsequently adopted by Âryabhaṭa II and Śrîpati (1039 A.D.).
Had Śrîdharâcârya been anterior to Mahâvîra, as supposed
by Dîkṣita, Mahâvîra must also have adopted them in his
Gaṇita-sâra-saṅgraha. Śrîdharâcârya had earned a great name
in his lifetime and his works were quite well-known, and there
is little possibility of his rules having remained unknown to
scholars coming after him. It is noteworthy that Mahâvîra
has regarded his own formulae, given above, as accurate.
This is another proof to show that Mahâvîra lived in an age
when Śrîdharâcârya was yet to be born to discover more accu-
rate formulae.
(iii) Absence of the following important rules of Śrî-
dharâcârya from the Gaṇita-sâra-saṅgraha :
(a) Rule for reducing a chain of measures. PG, Rule 41)
(b) A special rule for finding the time in which a sum
lent out on simple interest will be paid back by
equal monthly instalments. (PG, Rule 49-50) Also the
example on this rule. (PG, Ex. 55-56)
(c) Rule telling us how two travellers starting with differ-
speeds and accelerations would meet each other two
two times on the way. (PG, Rule 97-98)
Absence of these interesting rules from an exhaustive
work like the Gaṇita-sâra-saṅgraha cannot be explained unles we
assume its priority over the works of Śrîdharâcârya. The first
Indological Truths