History of Hindu Mathematics: A Source Book v2.c17.s8.1

v2.c17.s8.1

**Early Treatment.** It has been shown before that the altar-construction of the Vedic Hindus involved the solution of the complete quadratic equation $ax² + bx = c,$ (1) as well as of the pure quadratic ax² = c. The equation that had to be solved was $7x² + ½x = 7½ + m,$ which gives $x = 1/28(√(841 + 112m) - 1),$ or $x² = 1/784 842 + 112m - 2√(841 + 112m).$ Simplifying and neglecting higher powers of m, we get $x² = 1 + 4m/29, approximately.$ Kâtyâyana gives the value² $x² = 1 + m/7.$