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 jati 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 bhavita (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? Prthūdaka Svāmī while commenting on a verse in Brahma- sphutasiddhanta speaks as follows: In this case, in the problem proposed by the questioner, yavat-tavat 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. 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 nyasa Perhaps the oldest record of nyasa is to be found in the Bakhasalı 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. सहशद्विवधो वर्गस्त्र्या दिवधस्तद् गतोऽन्यजातिवधः । अन्योऽन्यवघातो भाक्तिकः पूर्ववच्छ्रेषम् ॥ 2. BrSpSi. XVIII. 43 (com) -BrSpSi.XVIII. 42.
