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

PLAN FOR WRITING EQUATIONS 205 yā 197 kā 1644̇ nī 1̇ rū 0 yā 0 kā 0 nī 0 rū 6302 Here the first unknown x is represented by yā(vat), the second unknown y by kā(laka) and the third unknown z by nī- (laka) and the term without unknown, a mere number is written by rū(paka). The two sides, one written below the other if written in the present form, would appear as : 197x—1644y—z+0=0x+0y+0z+6302. The Bījagaṇita of Bhāskara II also follows the same proce- dure. One instance from it would be quoted here to illustrate the method of expressing equations. 8x³+4x²+10y²x=4x³+12y²x or 8x³+4x²+10y²x=4x³+0x²+12y²x is written as follows on Bhāskara's or Brahmagupta's plan : x³ is ghana of yāvat (abbreviated as yā gha) x² is varga of yāvat (abbreviated as yā va) y² is varga of kālaka (abbreviated as kā va) the coefficients 10 and 12 are bhāvita (abbreviated as bhā). The equation is : yā gha 8 yā va 4 kā va yā. bhā 10 yā gha 4 yā va 0 kā va yā. bhā 12 Datta and Singh state that the use of the old plan of writ- ing equations is sometimes met with in later works also. For instance, in the MS. of Pṛthūdaka Svāmī's commentary¹ on the Brāhmasphuṭasiddhānta, an incomplete copy of which is preserv- ed in the library of the Asiatic Society of Bengal (No. I B6), we find a statement of equations thus : “first side yāvargaḥ 1 yāvakaḥ 200 rū 0; second side yāvargaḥ 0 yāvakaḥ 0 rū 1500. Śodhana or Clearance of an Equation After nyāsa or statement of an equation, the operation to be performed is known as śodhana (clearance) or saṁśodhana (equi-clearance or complete clearance). The nature of this clearance varies according to the kind of equation In the case of an equation in one unknown only, whether linear,

1. BrSpSi. XII. 15 (com.)