Equations
Forming Equations
Before proceeding to the actual solution of an equation of any type, certain preliminary operations have necessarily to be carried out in order to prepare it for solution.
Still more preliminary work is that of forming the equation (sami-karana, sami-kara or sami-kriya; from sama, equal and kṛ , to do; hence literally , making equal) from the conditions of the proposed problem. Such preliminary work may require the application of one or more fundamental operations of algebra or arithmetic.
Bhaskara II says: "Let yavat-tavat be assumed as the value of the unknown quantity. Then doing precisely as has been specifically told-by subtracting, adding, multiplying or dividing the two equal sides of an equation should be very carefully built.
Algebraic Notations
- The symbols used for unknown numbers are the initial syllables yа̄ of yа̄vat-tа̄vat (as much as), kа̄ of kа̄laka (black), nī of nīlaka (blue), pī of pīta (yellow) etc.
- The product of two unknowns is denoted by the initial syllable bhā of bhāvita (product) placed after them. The powers are denoted by the initial letters va of varga (square), gha of ghana (cube); vava stands for vargavarga, the fourth power. Sometimes the initial syllable ghā of ghāta (product) stands for the sum of powers.
- A coefficient is placed next to the symbol. The constant term is denoted by the initial symbol rū of rūpa (form).
- A dot is placed above the negative integer
- The two sides of an equation are placed one below the other. Thus the equation X4 - 2X2 - 400x = 9999; is written as
यावव १ याव २● या ४००● रू ०
यावव १ याव ० या ० रू ९९९९