Jinamanjari 1996 09 No 14

Author(s): Jinamanjari
Publisher: Canada Bramhi Jain Society Publication

Page 65

Three times the square of half the diameter (d) is the entire fruit (area, A) (of a circle). (Dhavalā on CK 1.4.8; vol. 4, p. 168)
A= 3)
A=31
vikkhambhacaūbbhūgo pariravagunido have guņidam ||
A fourth of the diameter (d), multiplied by the circumference (C), will be the value calculated (i.e., the area, A). (Stanza Scd cited in the Dhavalā on CK1.4.28; vol. 4, p. 209)
A=C.
The first formula is cited in a different wording as a formula of 'practical' (vyāvahārika) nature as against 'exact' (sükşma) one by Bhāskara I in his commentary (AD 629) on Āryabhuťīya 2.7ab (p. 60). The Jaina mathematician Mahāvīra also prescribes it in a section for geometrical formulas of 'practical' nature of his Ganitasarasamgruha (7.19; ca. AD 850).
The second formula and its variation, A (C/2).(d/2), has been used in India since at least the times of Umāsvāti (Tattvārthadhigumasūtrabhāsva 3.11, the 5th (1st? or 6th?) century AD) and of Aryabhața (Āryabhaļīya 2.7, AD 499 or a little later).
Circumference of a circle:
vikkhumbhuvagyudasagunakuruņi vatļussa puriruo
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