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

SQUARE 161 bhājaka, bhāgahāra or simply hara; quotient is known as labdhi or labdha (or "what is obtained"). India never regarded this operation as a difficult one; in Europe, this operation was regarded as a tedious one till the 15th century or so. Division was such a common operation that Āryabhaṭa did not regard it as worth being included in his treatise. But since he has given the methods of extracting square-roots and cube-roots, which obviously depend on division, we conclude that the method of division was known to him. Most Siddhānta writers have followed Āryabhaṭa I in omitting this operation from their texts, this being regarded too elementary to be included. Brahmagupta does not give details of this operation. The later treatises on Arithmetic as Śrīdhara's Triśatikā and the Pāṭīgaṇita (I.20) and Āryabhaṭa II (c.950 A.D.) have given the details of this operation. Square The Sanakrit term for square is varga or kṛti (varga lite- rally means "rows" or "troops" of similar things). In mathema- tics, it usually means the square power and also the square figure or its area. Thus we find in the Āryabhaṭīya : A square figure of four equal sides (and the number representing its area) are called varga. The product of the two equal quantities is also varga¹. The term kṛti means "doing", "making" or "action". It carries with it the idea of specific performance probably the gra- phical representation. For the first time we have a definite rule for squaring in the writings of Brahmagupta. But it does not mean that prior to him it was not known. It must have been known to Āryabhaṭa I since he has given the square-root method. Brahmagupta gives his method of squaring briefly as follows : Combining the product, twice the digit in the less (lowest) place into the several others (digits) with its (i.e. of the digit in the lowest place) square (repeatedly) gives the square.²

1. वर्गस्समचतुरश्रः फलञ्च सदृशद्वयस्य संवर्गः। —Ārya. II. 3.
2. राशेरूनं द्विगुणं बहुतरगुणमूनकृतियुतं वर्गः। —BrSpSi. XII. 63.