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

INTRODUCTION vii
Professors Maskarî Pûraṇa, Mudgala, and others. How can
that be stated by the Âcârya (Âryabhaṭa) in a small work (like
the Âryabhaṭîya)? So we have rightly said ‘a bit of mathema-
tics.’”¹ The works of Maskarî Pûraṇa and Mudgala referred
to above have not survived the ravages of time, but from what
Bhâskara I says about them they must have been exclusively
devoted to pâṭīgaṇita and algebra. Some of them might have
existed before the time of Âryabhaṭa I. Bhâskara I has
quoted a numbers of arithmetical rules from those works,
which tend to show that early works on arithmetic, though
generally of the same nature as later works, now available to
us, had the special peculiarity of including rules for verifying
the results of calculation. Those who have had the opportu-
nity of going through the Bakhshâlî Manuscript must have
noted that varification forms an intrinsic part of solutions given
in that manuscript. In the Âryabhaṭîya, too, we find a rule
meant for the verification of areas of plane figures. (See
Â, ii. 9(i)). Bhâskara I has also sometimes verified his solutions.
In later works we seldom come across any rules dealing with
the verification of answers.
There is another important Hindu mathematician,
Skandasena by name, who lived prior to the ninth century
A.D. Pṛthûdakasvâmî (860 A.D.) has referred to this
mathematician three times in his commentary on Chapter XII
of the Brâhma-sphuṭa-siddhânta of Brahmagupta. He has made
the following remarks in connection with that mathematician :
(1) “The sum (of the series) which Âcârya Skandasena
has interpreted with the help of a series-figure (śreḍhî) is meant
to illustrate the figure (of the series).”²
(2) “The Âcârya (Brahmagupta) has stated here only
five varieties (of fractions). The sixth variety has been omitted,
as it consists of the rest and is therefore virtually taught. It

¹ Bhâskara I’s comm. on Â, i. 1.
² यच्च स्कन्दसेनाचार्येण श्रेढीन्यायेन सङ्कलितं प्रदर्शितं तत् सङ्कलनं क्षेत्रप्रदर्शनाय ।
See Pṛthûdakasvâmî’s comm. on BrSpSi, xii. 2.