The Science of the Shulba: A Study in Early Hindu Geometry c17.31

c17.31

The geometrical operations to be followed in this method of construction are shortly these:² At first is drawn a square of an area equal to m square puruṣas. It is then divided into 15 equal parts. This may be done either by dividing one side of the square into 15 equal parts and then drawing lines parallel to the perpendicular sides, *or* by dividing one side into 3 parts and a perpendicular side into 5 parts and then drawing parallels. Two of the rectangular portions are then combined into a square and to that is again added a unit square puruṣa so as to form a third square. A side of this resulting square will be easily found to be √(1+2m/15) puruṣas long. With this length as the unit, construct an altar in the same way as the original falcon-shaped altar. This will be the required figure. For its area will be $7½×(1+(2 m)/15) or (7½+ m)$ square puruṣas and its shape will be clearly similar to that of the given figure.