History of Hindu Mathematics: A Source Book v2.c17.s9.1

v2.c17.s9.1

**Cubic and Biquadratic.** The Hindus did not achieve much in the solution of the cubic and biquadratic equations. Bhâskara II (1150) attempted the application of the method of the *madhyamâharaṇa* (elimination of the middle) to those equations also so as to reduce them by means of advantageous transformations and introduction of auxiliary quantities to simple and quadratic equations respectively. He thus anticipated one of the modern methods of solving the biquadratic. "If, however," observes Bhâskara II, "due to the presence of the cube, biquadrate, etc., the work (of reduction) cannot proceed any further, after the performance of such operations, for want of a root of the unknown side (of an equation), then multiplied by 200 and added to the square of the number, and then multiplied by 2 and subtracted from the fourth power of the number will become one myriad less unity? Tell that number if thou be conversant with the operations of analysis.