A Concise History of Science in India c7.s2.t3.2

c7.s2.t3.2

We have already stated that the various *śulba-sūtras* that have come down to us as parts of the *Śrauta-sūtras* are Brāhmaṇic geometrical manuals for the construction of sacrificial altars. In the various rules given, certain assumptions resembling Euclidean postulates are taken for granted. Thus a straight line is capable of division into an infinite number of equal parts; a circle can be divided into any number of parts by drawing diameters; each diagonal bisects a rectangle and both diagonals bisect each other, dividing the rectangle into four parts with the vertically opposite ones equal in all respects; a straight line joining the vertex with the middle point of the opposite side divides an isosceles triangle into two equal halves; parallelograms drawn on the same base and between the same parallels are equal to one another; a square inscribed within a circle and touching the circumference is the maximum, and so on. The texts give several rules as to how to construct a straight line perpendicular to another straight line, a square with a given side, a rectangle with given sides, an isosceles trapezium of a