The Science of the Shulba: A Study in Early Hindu Geometry c20.s3.37

c20.s3.37

Let us therefore test as far as possible how far the commentators can be relied upon in the matter of that interpretation. For it might be argued by modern critics that being acquainted with the real state of things from the mathematical knowledge of their time, the commentators naturally gave an interpretation to the texts which was more creditable to their authors.¹ Looking into the ancient literatures of India, we find in the early canonical works of the Jainas copious instances of the employment of the term *viśeṣa* in the same connection as we find it in the *Sulba*. Thus in the *Sūryaprajñapti* (c. 500 B. C.)¹ the circumference of a circle whose diameter is 99640 yojanas is stated as 315089 yojanas and a little over (*kiñcidviśeṣādhika*); that of a circle of diameter 100660 yojanas is stated to be 318315 and a little less (*kiñcidviśeṣoṇa*). In the *Jambudvīpaprajñapti* (c. 300 B.C.),² the circumference of the Jambudvīpa which is of the shape of a circle of 100000 yojanas in diameter, is mentioned as 316227 yojanas 3 gavyutis 128 dhanus 13½ aṅgulis and a little over (*kiñcid-viśeṣādhika*). In all these cases,³ it will be seen that the value actually recorded is only an approximate one and the *viśeṣa* refers to a small quantity which has not been recorded—in fact it cannot be accurately determined—but which we shall have to add to or subtract from the recorded value in order to get the accurate value of the quantity sought. Those who are acquainted with the technique of Sanskrit and Sanskritic languages will at once recognise that the expression *kiñcid-viśeṣādhika* has the identical significance as the term *saviśeṣa*. Indeed we really find the use of the word *saviśeṣa* in exactly the same sense in a Jaina work of later times. Nemicandra (c. 975 A. D.) writes: *tattiūṇaṁ parirayeṇa saviseṣaṁ* or "thrice that with a little over (*saviśeṣa*) is the circumference."⁴ Now the early canonical works of the Jainas belong to a period not much separated from that of the *Śulba*. Some works of either classes probably belong to the same age. So we can accept without any hesitation that the term *saviśeṣa* was employed originally in the *Śulba* with the same significance as that with which it is found to have been employed in the early canonical works of the Jainas. Thus it is found conclusively that Kapardisvāmī and Karavindasvāmī are thoroughly reliable as regards their interpretation of the original significance of the term *saviśeṣa*. So it is proved that the irrationality of √2 was known to the ancient Hindus.