The Science of the Shulba: A Study in Early Hindu Geometry c11.20

c11.20

That is, if *n* be the number of equal squares to be combined together into one, form the triangle *ABC* whose base *BC* is of length (*n*—1) times a side of a square and twice the sides *AB* and *AC* of which are severally equal to (*n*+1) times a side of a square. The method of drawing the triangle, which will be consistent with the geometrical methods of the *Śulba* is this: Draw the line *BC* of length (*n*—1) times a side of a square. Fix two poles at *B* and *C*. Take a cord of length (*n*+1) times a side of a square. Fasten its two ends at the two poles and stretch the cord sidewise having taken it by the middle point. Let *A* be the point reached. Bisect *BC* at *D* and join *AD*. Then the square on *AD* will be equivalent to the sum of n given squares. For $AD² = AC² - DC²,$ $= ((n+1)/2)² a² - ((n-1)/2)² a²,$ $= na².$