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

238- BRAHMAGUPTA AS AN ALGEBRAIST
cular case only of the more general latter equation. Of course, there
is a little justification also for treating it separately, since both
the types of equations represent two different physical conditions
of the astronomical problems. In the case of by=ax±c, the
conditions are such that the value of either y or x, more particu-
larly of the latter, has to be found and the rules for solution
formulated with that objective. But in the case of the equation
by=ax±1, the physical conditions require the values of both
y and x.
The equation by=ax±1 is usually known by the name
sthira-kuṭṭaka, literally meaning the 'constant pulveriser' Pṛthū-
daka Svāmī also names it as dṛḍha-kuṭṭaka meaning firm-pulveri-
ser. Later on this term dṛḍha-was confined to another sense,
equivlent to nicched (having no divisor) or nirapavarta (irreduci-
ble). The origin of the name sthira-kuṭṭaka or constant pulveriser
has been explained by Pṛthūdaka Svāmī as being due to the fact
that the interpolator (±1) is here invariable.
For the solution of this equation, we shall quote Bhāskara
I's rule and the rule by Brahmagupta. Bhāskara I writes in this
connection as follows :
The method of the pulveriser is applied also after
subtracting unity. The multiplier and quotient are
respectively the numbers above and underneath. Multi-
plying those quantities by the desired number divide
by the reduced divisor and dividend; the residues are
in this case known to be the (elapsed) days and (resid-
ues of) revolutions respectively¹.
The pulveriser
ax - c
-------- = y ... (1)
b
may be written as
aX - 1
-------- = Y ... (2)
b
where x=cX and y=cY. If X=α, Y=β is a solution of (2), then
x=cα, y=cβ will be a solution of (1). Hence the above rule.

1. रूपमेकमपास्यापि कुट्टाकारः प्रसाध्यते ।
   गुणकारोऽथ लब्धं च राशी स्यातामुपर्यधः ॥
   —MBh. I. 45