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

166 BRAHMAGUPTA AND ARITHMETIC number (this accounts for keeping the results of each of the four operations at the next place). Square-Root Indian synonyms for square-root are vargamūla or pada of a kṛti. The word mūla means the "root" of a tree, which may also mean the "foot" or the lowest part or bottom of a thing and hence "pada" or foot also became a synonym of root. Brahma- Gupta defines square-root as follows : The pada (root) of a kṛti (square) is that of which it is the square.¹ While the word mūla for root is the oldest in Indian litera- ture (it occurs in Anuyogadvāra-sūtra, c. 100 B.C.), the word pada for root probably for the first time occurs in the writings of Brahmagupta. The term mūla was borrowed by the Arabs who translated it by jadhr, meaning "basis of square". The Latin term radix also is a translation of the term mūla. In the Śulba litera- ture and in the Prākṛta texts, we find a term karaṇī for square- root. In geometry, this term karaṇī means a "side", In later days, the term karaṇī was reserved for surds, i.e. a square-root which cannot be exactly evaluated, but which may be represented by a line. We would like to quote here a rule for determining square- root of numbers from the Āryabhaṭīya : Always divide the even place by twice the square-root (upon the preceding odd place); after having subtracted from the odd place the square (of the quotient), the quotient put down at the next place (in the line of the root) gives the root². As an illustration, we shall proceed to find the square-root of 18225. The odd and even places are marked out by vertical (I) and horizontal (—) lines : The other steps are as follows :

1. पदं कृतिय॑त् तत् BrSpSi. XVIII. 35
2. भागं हरेदवर्गान्नित्यं द्विगुणेन वर्गमूलेन । वर्गाद्वर्गे शुद्धे लब्धं स्थानान्तरे मूलम् ॥ — Ārya, II. 4.