The Science of the Shulba: A Study in Early Hindu Geometry c9.4

c9.4

In the geometry of the *Sulba*, it is oftentimes required to divide a given finite straight line into a specified number of equal parts. For example in one instance, the diameter of a given circle is divided into 8 equal parts, each of these again into 29 parts and so on into other number of divisions.¹ There are indeed numerous such instances.² Now it will be naturally asked how it was used to be done. Certainly not arithmetically. At least it is not always possible to do so. For we find instances of division of straight lines which cannot be expressed in terms of commensurate numbers. In circling a square, such a straight line has to be divided into three parts¹ and in another case into twelve parts.² Sometimes the given straight line is such that the parts when expressed arithmetically will contain big fractions. Thus the side of a square of 96 *aṅgulis* has to be divided into 7 equal parts.³