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hodi |
The square rooi of ten times the square of the diameter (d) is the circumference (C) of a circle. (Stanza Sab cited in the Dhavalā on CK 1.4.28; vol. 4, p. 209)
C= V10
vyāsaṁ șodaśagunitaṁ sodaśasahitam triūparūpahrtam
vyāsatriguņitasahitam sūkṣmād api tad bhavet sūkşmam
The diameter (d) is multiplied by sixteen, increased by sixteen, divided by one-one-three (113), and increased by three times the diameter. It will be (a value for the circumference (C)) more accurate than the accurate one. (Stanza 9 cited in the Dhavalā on CK 1.4.38; vol. 4, pp. 221 - 222)
C = 3d + 160 + 16 C= 30 + 113
( = 355d + 16
113 )
113
113
In the acutal use of the first formula, the approximation, 19/6, is employed instead of V10. The verse for the second formula is repeated with a minor variant (trirūparūpair bhaktam for trirūparūpahạtam) as Stanza 14 on CK 1.3.3 (vol.4, pp.42 43). The same formula is silently employed also on CK 1.3.2 (vol.4, p. 12) and on CK 1.3.4 (vol.4, p.48 and p.49). On CK 1.3.2 (vol.4, p. 13, lines 6 7), V'rasena uses, in addition to the above,
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