The Science of the Shulba: A Study in Early Hindu Geometry c16.21

c16.21

Thibaut accepts as correct the reading of the text as given by Karavindasvāmī but has discarded his further explanation of the matter. So he renders the passage as: “this line gives a circle exactly as large as the square; for as much as there is cut off from the square (*viz*., the corners of the square), quite as much is added to it (*viz*., the segments of the circle, lying outside the square).”¹ Bürk has closely followed Thibaut in this respect. The interpretation of Kapardisvāmī has been criticised by Thibaut thus: “But I am afraid we should not be justified in giving to Āpastamba the benefit of this explanation. The words ‘yāvaddhīyate, etc.’ seem to indicate that he was perfectly satisfied with the accuracy of his method and not superior, in this point, to so many circle-squarers of later times. The commentator who, with the mathematical knowledge of his time, knew that the rule was an imperfect one, preferred very naturally the interpretation which was more creditable to his author.''¹ Kapardisvāmī explains that the remark *yāvaddhīyate*, etc., implies only a nearer approximation but not exact equality.