The Science of the Shulba: A Study in Early Hindu Geometry c20.s2.7

c20.s2.7

"Suppose they drew a square the side of which was 17 padas long, and divided it into 17 × 17 = 289 small squares. If the side of the square could now be shortened by so much, that its area would contain not 289 but only 288 such small squares, then the measure of the side would be exact measure of the diagonal of the square, the side of which is equal to 12 (12² + 12² = 288). When the side of the square is shortened a little, the consequence is that two sides of the square a stripe is cut off; therefore a piece of that length had to be cut off from the side that the area of the two stripes would be equal to one of the 289 small squares. Now, as square is composed of 17 × 17 squares, one of the two stripes cuts off a part of 17 small squares and the other likewise of 17, both together of 34 and since these 34 cut off pieces are to be equal to one of the squares, the length of the piece to be cut off the side is fixed thereby; it must be the thirty-fourth part of the side of one of the 289 small squares.