The Science of the Shulba: A Study in Early Hindu Geometry c18.41

c18.41

It is not at all easy to determine the rationale of Kātyāyana's formulæ (3) and (5), whether they were obtained in the way indicated above by the method of the solution of a complete quadratic equation, or in any other way. It is found that there are discrepancies between the results calculated by the former method and those found in the extant copies of the manuscripts of his works. How to explain them? Whether by the crudeness of his method of solving the quadratic equation or of the calculations attendent on it,¹ if he had at all followed that method, or in any other way? Now the discrepancy need not be considered very serious in the general case, especially if we remember the degree of accuracy that can be naturally expected in those early times, or that is ordinarily found to have been followed then. Even in modern times 7 will be considered to be a very fair approximation to 7¼. What will appear to be serious is in the other case which requires an emendation of the existing text in order to explain away the discrepancy with the result calculated as above. But, we would remark, that by itself should not be considered a very formidable objection against our hypothesis as regards the method of Kātyāyana. For those who have dealt with ancient manuscripts are quite aware that they doubtless require emendations here and there. That discrepancy can be explained away much more easily and reasonably by supposing that the result (5) was derived from the modified result (3) by substituting the value, m = 94. but was not calculated directly from the equation (1) as we have done above.