Mathematics in Ancient and Medieval India c6.s2.27

c6.s2.27

1) *Ekarajjuvidhi* was given by Āpastamba¹ as such. Having joined a cord of 18 *prakramas* (= BC) to another of 36 *prakramas*, (= AB), marks are to be given at 12 and 15 *prakramas* (CD=12, CG=15) from the free end of the smaller cord (Fig. 1). The two free ends of the combined cord are then fixed on a *prācī* line (= EF), the distance between which is that of the longer cord i.e. 36 *prakramas*, the free end of the longer cord being tied to the peg at the eastern end (E) and that of the shorter cord to the peg at the western end (F). Holding the combined cord at its mark (G) at 15, pull towards south as far as it goes and fix it there (G') by means of a pole. The part of the cord of length 15 *prakramas* now becomes the line of *tiryaṅmānī* (FG'). Such marks (G', Q', Q' and G″) on the ground, which fall on the *tiryaṅmānī* when the cord is fully stretched, called *nirañchana* marks. The same operation is repeated in the north. Obviously it gives the same result. Identical results are obtained if the free ends of the combined cord are interchanged. When the four points on the *tiryaṅmānī* thus obtained and joined, it gives the figure of an isosceles trapezium ( D″G″G′D′ ). This is the method of construction of an altar of definite shape with lengths of two sides of its face being 24 and 30 *prakramas* and the perpendicular distance between them being 36 *prakramas*.