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