________________
to find the area of various regions of Jambūdvīpa (Jambu Island). These regions are of the circular segment form.
The formula (3.21) in its general form may be considered as
(3.22) A = tlh/4 = tr?sin) (1 - COSÕV2. However, the true area of Ao is given by the following:
A0= Area of the sector OAMB - Area of the triangle OAB. That is (3.23) Ap=12 (Ó - sinò coső). The percentage of error Ee will furnish the degree of accuracy of the area given by (3.22) (see Table 3.2A):
5 - CÃ - 1] x 100 = [e in
11 x 100 =
asino(1 – cos) 2e - sin cos
mo
- 1] x 100
- 1 x 100
Table 3.2A
Eo = 0 E15 = 17.80 E30 = 16.11 E45 = 13.98 E60 = 10.74 E75 = 6.19 E90 = 0
E105 = -8.29 E120 = - 19.26 E135 = - 13.61 E150 = -51.96 E165 = -80.53 E180 =. 100.00
Notice that he following formula for the area of a circular segment
(3.24)
A = a (1 + h)h/6
appears in various texts, viz., the Ganitapañcavissī, the Trisstikā of Śrīdhara (ca. 8th century C.E.), the GSS, the Mahāsiddhānta of Āryabhața II (ca. 950 C.E.), the Ganitasāra of Thakkura Pherū (ca. 1315 C.E.) and the Pañcaviñsatikā (ca. 1428 C.E.) (see [13]). In polar form, the formula (3.24) may be written as
(3.35) A = 1 r2 (2sino + 1 - COSÕ) (1 - COSÕ}/6,
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