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.)