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

ALGEBRAIC OPERATIONS 203
This means that the numerical coefficients of x cannot be
added to or subtracted from the numerical coefficients of y
or x² or x³ or xy and so on because these terms belong to different
jāti or they do not belong to the category of the "like".
Again, regarding multiplication, Brahmagupta says :
The product of the two like unknowns is a square; the
product of three or more like unknowns is a power of
that designation. The multiplication of unknowns of
unlike species is the same as the mutual product of
symbols; it is called bhāvita (product or factum).¹
Having given the rules of the operations for addition, sub-
traction and multiplication, Brahmagupta does not think
it necessary to deal with other operations. His section on the
calculations with zero, negative and positive quantities ends here.
How is an Equation Formed?
Pṛthūdaka Svāmī while commenting on a verse in Brāhma-
sphuṭasiddhānta speaks as follows :
In this case, in the problem proposed by the questioner,
yāvat-tāvat is put for the value of the unknown quantity.
Then performing multiplication, division etc. as required
in the problem the two sides shall be carefully made
equal. The equation being formed in this way, then
the rule (for its solution) follows.²
Plan for Writing Equations
When in regards to a given problem, an equation has been
formed, it has to be written down for further operations.
This writing down of an equation is technically known
as nyāsa Perhaps the oldest record of nyāsa is to be found in the
Bakhshālī Manuscript. According to the procedure prescribed in
this work, the two sides of an equation are put down one after the
other in the same line without any sign of equality being inter-
posed. Thus the equations :
√(x+5)=s, √(x-7)=t
appear as

1. सदृशद्विवधो वर्गस्त्र्यादिवधस्तद् गतोऽन्यजातिवधः ।
   अन्योन्यवर्णघातो भावितकः पूर्ववच्छेदम् ॥ —BrSpSi.XVIII. 42.
2. BrSpSi. XVIII. 43 (com)