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

206 BRAHMAGUPTA AS AN ALGEBRAIST
quadratic or of higher powers, one side of it is cleared of the
unknowns of all denominations and the other side of it of the
absolute terms, so that the equation is ultimately reduced to one
of the form
ax² + bx = c,
where a, b, c may be positive or negative; some of them may
even be zero. Thus Brahmagupta observes :
From which the square of the unknown and the un-
known are cleared, the known quantities (rūpāṇi) are
cleared (from the side) below that.¹
On this Pṛthūdaka Svāmī comments as follows :
This rule has been introduced for that case in which
the two sides of the equation having been formed in
accordance with the statement of the problem, there are
present the square and other powers of the unknown
together with the (simple) unknown. The absolute
terms should be cleared off from the side opposite to
that from which are cleared the square (and other
powers) of the unknown and the (simple) unknown.
When perfect clearance (saṁśodhana) has been thus
made...²
Śrīdhara and Bhāskara II have also given the rules of
clearance almost on the same lines. Thus the equation
yā va 0 yā 10 rū 8̇
yā va 1 yā 0 rū 1
after perfect clearance having been made will be (according to
Pṛthūdaka Svāmī)
yā va 1 yā 10 rū 9̇
i.e. the equation 10x - 8 = x² + 1
after clearance would become
x² - 10x = -9.
Classification of Equations
Usually equations are classified as :
simple equation : yāvat-tāvat
quadratic : varga

1. वर्गाव्यक्ताः शोध्या यस्माद् रूपाणि तदधस्तात् ॥ — BrSpSi. XVIII. 43.
2. BrSpSi. XVIII. 43 (com.)