The Science of the Shulba: A Study in Early Hindu Geometry c11.31

c11.31

The commentators disagree about the method actually implied in the above rules. According to some,⁴ it is this: Find a square equivalent to three times the given square. Then divide a side of this square into three equal parts. A square drawn on any of these parts will be equivalent to one-third of the given square. For, on drawing parallel lines through the points of division, the second square will be divided into nine (square) parts. Hence each part (square) is equal to one-ninth of it and so to one-third of the given square. According to others,¹ the method is this: Divide the given square into nine equal squares. Combine three of these squares into one. And it will be equivalent to the third part of the given area. Some² are of opinion that both the methods are implied by the text.