The Science of the Shulba: A Study in Early Hindu Geometry c20.s3.30

c20.s3.30

"*Saviśeṣa* is its technical name. The measure of the side (of a square) after having been operated upon by the rule 'increase the measure by its one-third, etc.' is called the *saviśeṣa*. For instance, increase a measure of twelve aṅgulis by four aṅgulis; increase that four aṅgulis by one aṅguli minus one tila. The experts (in measure) say that thirty-four tilas placed breadthways make one aṅguli. It will be stated (later on in the text) 'add to half (the length of the east-west line) its *viśeṣa*,'¹ 'enclose with two half-bricks having their *viśeṣa* outwards,'² etc. What (are the correct meanings) of 'fasten *saviśeṣa* to the middle (pole),'³ 'with one-fourth puruṣa and with the *saviśeṣa* of one-fourth puruṣa,'⁴ etc. There it should be understood that 'being with the *viśeṣa*,' that is 'the measure with the *viśeṣa*' is the *saviśeṣa*. What is the need of this big term? So that its true significance may be intelligible by itself. What is that? The root *śiṣ* when prefixed by *vi* denotes in all cases 'a correction in excess.' As the rule mentions of an excess qualified by the prefix *vi* (it should be understood that the accurate value of) the diagonal differs by something from, exceeds over the exceeding part of the above value of the *dvi-karaṇī* over the measure of the side: and that is the *viśeṣa*. Or else the *viśeṣa* is that little area by which (the square of the diagonal as calculated by the rule) differs from or exceeds over (twice the area of the given square) at the time of measurement. For instance, since it has been stated that thirty-four tilas make one aṅguli, the square of the number of tilas in twelve aṅgulis is 166464 square areas of tilas; the square of the tilas in seventeen aṅgulis minus one tila is 332929 square areas of tilas. In the latter a square of one tila is present in excess over twice the area of the (given)