History of Hindu Mathematics: A Source Book v2.c17.s1.48

v2.c17.s1.48

**Origin of Hindu Algebra.** The origin of Hindu algebra can be definitely traced back to the period of the *Sulba* (800-500 B.C.) and the *Brâhmaṇa* (*c.* 2000 B.C.). But it was then mostly geometrical.² The geometrical method of the transformation of a square into a rectangle having a given side, which is described in the important *Sulba* is obviously equivalent to the solution of a linear equation in one unknown, *viz.*, $ax = c².$ The quadratic equation has its counterpart in the construction of a figure (an altar) similar to a given one but differing in area from it by a specified amount. The usual method of solving that problem was to increase the unit of measure of the linear dimensions of the figure. One of the most important altars of the obligatory Vedic sacrifices was called the *Mahâvedi* (the Great Altar). It has been described to be of the form of an isosceles trapezium whose face is 24 units long, base 30 and altitude 36. If x be the enlarged unit of measure taken in increasing the size of the altar by m units of area, we must have $36x × ((24x + 30x))/2 = 36 × ((24 + 30))/2 + m,$ or 972x² = 972 + m.