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

INTRODUCTION xxxix
are in the âryâ metre, and there are reasons to believe
that the rules in Śrîdharâcârya's Bîjagaṇita were also
in the same metre. We may mention here that the
verse quoted by Bhâskara II from Śrîdharâcârya's
Bîjagaṇita is in the âryâ metre.
(iii) No rule occurring in the miśraka-vyavahâra of the
Pâṭîgaṇita or Triśatikâ is common to Raṅgâcârya's
edition of the Gaṇita-sâra-saṅgraha.
Therefore, the conclusion drawn by Dîkṣita on the basis of
his argument cannot be regarded as satisfactory and reliable.
There are other reasons also to reject his view, which shall be
set forth below.
(3) A better estimate of Śrîdharâcârya's time.
A comparative study of the works of Śrîdharâcârya
with those of Mahâvîra and other Hindu mathematicians has
led us to the conclusion that Śrîdharâcârya was posterior to
Mahâvîra (850 A.D.) but anterior to Âryabhaṭa II (c. 950
A.D.).
The following facts revealed by the above study show
that Śrîdharâcârya was posterior to Mahâvîra :
(i) Śrîdharâcârya's formula for the volume of a sphere,
viz.
((diameter)³ / 2) ( 1 + 1/18 ) = (4·22....)r³,
is much better than that given by Mahâvirâ, viz.,
(9 / 2) · (9 / 10) r³ = 4·05r³.
We have shown above that Śrîdharâcârya's formula
closely approximates to the modern formula
4/3 πr³ = (4·188....)r³.