The Science of the Shulba: A Study in Early Hindu Geometry c14.70

c14.70

It is thus learnt that the figure² *EFGH* obtained by joining the middle points of the sides of a square *ABCD* was known to be square in shape and half the original square in area. Now the original square *ABCD* was naturally recognised as equivalent to the square on *EG* which is the east-west line. For as has been described before the usual practice of the Hindus for the construction of a square (or indeed any other regular figure) of given sides was to construct it in such a way as to make it lie symmetrically on the east-west line. This *EG* is again the diagonal of the newly formed square *EFGH*. So this figure leads in a very simple and vivid way to the discovery and proof of the theorem of the square of the diagonal of a square. If we join *HF*, we at once obtain the construction forming the basis of Bürk's hypothesis.