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

INTRODUCTION xix
The abovementioned formulæ of Śrîdharâcârya re-ap-
pear in the Mahâ-Siddhânta of Âryabhaṭa II (c. 950 A.D.),
evidently under the influence of Śrîdharâcârya.
3·3. Criticism of Brahmagupta. In none of the
above two works does Śrîdharâcârya refer to any ancient
writer or work by name. At one place in the Pâṭîgaṇita,¹
however, he refers to an ancient rule and finds fault with it.
He writes :
स्थूलफलं त्रिचतुर्भुजबाहुप्रतिबाहुयोगदलघातः ।
अवलम्बपार्श्वभुजयोर्यस्यान्तरमल्पकं तस्य ॥
अन्येषां क्षेत्राणां दूरभ्रष्टं यथा त्रयोदशके ।
त्र्यश्रस्य भुजद्वितये त्रिगुणाष्टभुवः फलं स्थूलम् ॥
षड्युतमध्यर्धशतं सूक्ष्मं षष्टिः प्रजायते यस्मात् ।
सूक्ष्मफलस्यैवाहं साधनकरणानि वक्ष्यामि ॥
i.e., "(It is said that) the product of half the sums of the
sides and counter sides (i.e., the product of half the sum
of the base and face and half the sum of the flank sides)
of a triangle or a quadrilateral, gives the gross value of
the area. But this result is true only for those figures in
which the difference between the altitude and the flank
sides is small. In the case of other figures the above
result is far removed from the truth ; as for example, in
the case of the triangle having 13 for the two (flank) sides
and 24 for the base, the gross value of the area is 156,
whereas the accurate value of the area is 60. I shall,
therefore, state the methods for obtaining the accurate
results only."
The rule which has been so mildly criticised in the
beginning of the above passage is due to Brahmagupta. The
author has very carefully tried to make his remark against
that great writer (Brahmagupta) look like an argument for his
proposal to deal with accurate methods only. But his inten-
tion is clearly understood when we see that the first line of
the passage giving the rule criticised by him is a literal quota-
¹ Rule 112-114.