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

CLASSIFICATION OF EQUATIONS 207
cubic : ghana
biquadratic : varga-varga
Brahmagupta classified them as
(i) equations in one unknown quantity : eka-varṇa
samīkaraṇa.
(ii) equations in several unknowns : aneka-varṇa samī-
karaṇa.
(iii) equations involving products of unknowns :
bhāvita.
Eka-varṇa samīkaraṇas (equations with one unknown) are
further divided into (i) linear equations, and (ii) quadratic equa-
tions (avyakta-varga samīkaraṇa).
Pṛthūdaka Svāmī has classified equations in a different
manner as follows :
(i) linear equations with one unknown : eka-varṇa
samīkaraṇa.
(ii) linear equations with more unknowns : aneka-
varṇa samīkaraṇa.
(iii) equations with one, two or more unknowns in their
second or higher powers : madhyamāharaṇa.
(iv) equations involving products of unknowns : bhā-
vita.
As the method of solution of an equation of the third class
(i.e. equations with one or several unknowns in their second or
higher powers) is based upon the principle of the elimination
of the middle term, that class is called by the term madhyama
(middle) āharaṇa (elimination). The classification of Brahma-
gupta and Pṛthūdaka Svāmī more or less received recognition by
later writers on algebra as Bhāskara II and others.
Linear Equations with
One Unknown and Their Solutions
The first solution of a linear equation with one unknown is
obtainable in the Śulba Sūtras but not through an algebraic
process,—the Śulba process is geometrical. It is said that there
is a reference in the Sthānāṅga Sūtra (c. 300 B.C.) to a linear
equation by its name yāvat-tāvat. There has been a good deal of