Bhaskara II Bijaganita (“Algebra”)

Bhaskaracharya Karmaveera Special 11 May 2014 E

Algebra

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.
  • Zero
  • 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………….

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