Page:Indian mathematics, Kaye (1915).djvu/14

 authors. gave the period as lying between 500 and 200 B.C.; gave 800 B.C.;  places the origin of the ApastambaĀpastamba [sic] school as probably somewhere within the last four centuries before the Christian era, and Baudhāyana somewhat earlier;  gives the limits as 500 B.C. and A.D. 200, and so on. As a matter of fact the dates are not known and those suggested by different authorities must be used with the greatest circumspection. It must also be borne in mind that the contents of the S'ulvasūtras, as known to us, are taken from quite modern manuscripts; and that in matters of detail they have probably been extensively edited. The editions of Āpastamba, Baudhāyana and Kātyāyana which have been used for the following notes, indeed, differ from each other to a very considerable extent. The S'ulvasūtras are not primarily mathematical but are rules ancillary to religious ritual—they have not a mathematical but a religious aim. No proofs or demonstrations are given and indeed in the presentation there is nothing mathematical beyond the bare facts. Those of the rules that contain mathematical notions relate to (1) the construction of squares and rectangles, (2) the relation of the diagonal to the sides, (3) equivalent rectangles and squares, (4) equivalent circles and squares. 5. In connection with (1) and (2) the theorem is stated quite generally. It is illustrated by a number of examples which may be summarised thus: