ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

156 BRAHMAGUPTA AND ARITHMETIC
hence it means the science of calculation which requires the uses
of writing material (the board). The word pāṭī is not Sanskrit
(it originated in the non-Sanskrit literature in India); the oldest
term in Sanskrit for the board is Phalaka or paṭṭa. However this
term got currency in the Sanskrit literature also about the
beginning of the seventh century. Brahmagupta does not use
the term pāṭīgaṇita: he favours the use of the term dhūlikarma or
writing figures on dust spread on a board or on the ground. The
word pāṭīgaṇita was translated into Arabic as ilm-hisab-al-takht
(calculation on board) and the word dhūlikarma as hisab-al-ghobār
(calculation on dust).
Brahmagupta, in the very first verse in the Chapter XII
(Gaṇitādhyāya) refers to twenty operations (parikarma) and
eight determinations :
He who distinctly and severally knows the twenty logistics,
addition etc.. and the eight determinations (vyavahāra)
inculding (measurement by) shadow is a gaṇaka (mathe-
matician).¹
The commentators have given the list of these logistics
(parikarma) and determinations (vyavahāra) as follows;
(A) Parikarma or logistics

1. Saṁkalitam (addition)
2. Vyavakalitam (subtraction)
3. Gaṇanam (multiplication)
4. Bhāgahāraḥ (division)
5. Vargaḥ (square)
6. Vargamūlam (square-root)
7. Ghanaḥ (cube)
8. Ghanamūlam (cube root)
9. 13. Five standard forms of fractions (Pañca-jāti)
10. Trairāśikam (the rule of three)
11. Vysta-trairāśikam (the inverse rule of three)
12. Pañca-rāśikam (the rule of five)
13. Sapta-rāśikam (the rule of seven)
14. Nava-rāśikam (the rule of n ine)

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1. परिकर्म विंशतिं यः संकलिताद्यं पृथक् विजानाति ।
   अष्टौ च व्यवहारान् छायान्तान् भवति गणकः सः ॥ —BrSpSi. XII. 1