________________
[1b]
P= 3 (-1) A = (E) (E)
[2b]
For subtle results :
वदना?नो व्यासो दशपदगुणितो भवेत्परिक्षेपः । मुखदलरहितव्यासार्धवर्ग मुखचरणकृतियोगः॥ दशपदगुणित: क्षेत्रे कम्बुनिभे सूक्ष्मफलमेतत्॥
(GSSw. 7.65-65.5, p. 463)
The diameter (vyasa) diminished by half the face (vadana) 'm' and (then) multiplied by the square - root of 10, becomes the perimeter (pariksepa) 'P'. The square of half the diameter d' as diminished by half the face (mukha) 'm' and the square of quarter (carana) of the face 'm' are added (together). The (resulting) sum is multiplied by the square - root of 10. This (result) gives rise to the subtle (sūksma) (measure) of the area in the case of the conchiform (plane) figure (kambunibhaksetra).
[10]
P = /10 (d ) A = 410 [((0 - 1)) • ()]
[20] It is, according to Hayashis, unlikely that the formula [2a] was obtained first, and then transformed into the ones [2b] and [2c] although he has shown that the formulae [1b] and [2b] with 3 for m. and ones [1c] and [2c] with
/10 for r are modifications of the one [1a] and [2a] respectively.10 3. NARAYANA
In his text, Ganita - kaumudi, Nārāyana gives the following formulae for a conch-like plane figure.
मुखदलरहितो व्यासस् त्रिघन: शंखे प्रजायते परिधिः। व्यासदलकृति वृत्यांशहतास्योनिता फलम् त्रिघना॥
वदनदलोनो व्यासो वदनदलं यत तदर्धवर्गक्यम्। त्रिगुणितम् अथ वा गणितम् स्थूलं शंखाकृती भवति॥
(GK, ksetra, w. 10-1, pp. 6-7) Tho diamer (vyāsa) 'd' diminished by half the face (mukha) 'm' and (then) multiplied three, becomes the perimeter (paridhi) 'P' of a conch (-like plane figur (samkha). The square of half the diameter 'd' diminished
Arhat Vacana, 14(1), 2002
33
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