Bhaskara II Bijaganita (“Algebra”) was a work in twelve chapters. It was the first text to recognize that a positive number has two square roots (a positive and negative square root). His work Bijaganita is effectively a treatise on algebra and contains the following topics:
- Positive and negative numbers.
- The ‘unknown’ (includes determining unknown quantities).
- Determining unknown quantities.
- Surds (includes evaluating surds).
- Kuttaka (for solving indeterminate equations and Diophantine equations).
- Simple equations (indeterminate of second, third and fourth degree).
- Simple equations with more than one unknown.
- Indeterminate quadratic equation (of the type ax2 + b = y2).
- Solutions of indeterminate equations of the second, third and fourth degree.
- Quadratic equations.
- Quadratic equations with more than one unknown.
- Operations with products of several unknowns.
Bhaskara derived a cyclic, chakravala method for solving indeterminate quadratic equations of the form ax2 + bx + c = y. Bhaskara’s method for finding the solutions of the problem Nx2 + 1 = y2 (the so-called “Pell’s equation”) is of considerable importance.
to be continue………….