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

xlii INTRODUCTION
is as follows : Mahâvîra states that the formula
√(s−a) (s−b) (s−c) (s−d)
gives the accurate (sûkṣma) area of a quadrilateral.¹ Ârya-
bhaṭa II, on the other hand, criticises those wish to find out
the area of a quadrilateral with the help of its sides only.
Says he : “The mathematician who wishes to tell the altitude
or the area of a quadrilateral without knowing a diagonal,
must be a fool or a blunderer.”² Śrîdharâcârya seems to be
in a fix regarding the above formula. For he seems to be
doubtful about is accuracy, but at the same time he is unable
to replace it by a better one. So he lays down two rules for
finding the area of a quadrilateral, one for quadrilaterals with
equal altitudes and the other for quadrilaterals with unequal
altitudes. For the former he gives the formula :³
½ (base + face) × altitude,
and for the latter he prescribes the faulty formula⁴
√(s−a) (s−b) (s−c) (s−d) •
This clearly shows that Śrîdharâcârya lived in an age when
the accuracy of the above formula as giving the area of any
quadrilateral had begun to be questioned, but this formula
had not yet been abandoned.
From the arguments adduced above it is proved without
any shadow of doubt that Śrîdharâcârya lived sometime
between Mahâvîra (850 A.D.) and Âryabhaṭa II (c. 950 A.D.).
5·3. His place. At present there is hardly any
evidence to enable us to throw light on the place where
Śrîdharâcârya lived and performed his literary activities.
Some writers, however, have ventured to make certain con-
jectures in this direction also. Thus N. C. Jaina associates
him with South Karnataka on the presumption that he was a
¹ GSS, vii. 50(i).
² कर्णज्ञानेन विना चतुरस्रे लम्बकं फलं यद्वा ।
वक्तुं वाञ्छति गणको योऽसौ मूर्खः पिशाचो वा ॥ (MSi, xv. 70).
³ PG, Rule 115.
⁴ PG, Rule 117.