________________
and that the corresponding percentage error is given by the following formula (see Table 3.2B)
r
(2 sino + 1- cos )(1-сoso) - 11 x 100
• 600-sin cose)
Table 3.2B
Eo = 0 E15 = - 16.60 E30 = - 12.18 E45 = -8.27 E60 = -4.86 E75 = - 2.04 E90 = 0
E 105 = 0.98 E120 = 0.44 E135 = - 2.32 E150 = -8.22 E165 = - 18.32 E180 = - 33.33
It may be conclusion that the formulae (3.22) and (3.24) furnish the true area only when = 90°. The formula (3.22) is practically applicable when ő is near approximately 0° and 90° whereas (3.24) is technically suitable in and near about 0° <Ó < 120°.
3.3 The Bșhatkşetrasamāsa (cf.[7]) of Jinabhadra Gani (6th century C.E.) uses the following formulae to find the area of the zone of the circle (see Figure 4 also).
Figure 4: Zone of the Circle
DID
(3.31) A1 = Y; (c1 +c2)b.
Clearly it represents the area of the inscribed isosceles trapezium ABCD and is less than the true area and so it can be treated as a rough approximation.
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