________________
Greek Heron of Alexendria (c. +200) finds107 s= 4 h2+c2 + 1 h or s = v 4 h2+c2 + {v 4 h2+c2-c} } The Chinese Ch'en Huo (1075) gives108 s =c+2 had
The formula (4) requires the solution of a quadratic equation. The Hindu values are older and neater, for Aryabhata II (c. +950) gives
1288 s (neat) = / 49 h2+c2 . Similar formulas occur in Kşetra samāsa and Laghukşetrasamāsa.
Except the formula for the volume of frustum of a cone in the Dhavalā text discussed earlier, the following formulae are available in the Tiloyapaņņatti :
1. Volume of a right circular cylinder (v.1.116) =
10
h
2. Volume of the wedge shaped universe in the form of a frustum
of a right prism (v. 1.165)=Area of the Base x height of prism where Area of the Base='
mukha (mouth)+bhūmi (ground) | perpendicular distance
between sides 3. p=w d2 x 10
(v.4.6) 4. (Chord of a quadrant arc)2 = 2:2 (v.4.70)
5. c= / 4 [)-( * - )] [v.1.180]]
[v.2.23; 6.9)
J. P. gives the rule
c=N 4.h (d – h) 6. S=> 2 [(d+h)2 – (d)2]
J. P. gives the rule s=N 6 (h)2+(c)2
[v.4.181]
[v.2.24,29,6.10]
107. Cf. Health, op. cit. Vol. 2, p. 331. 108. Y. Mikami, The Development of Mathematics in China and Japan,
Leipzig, 1913, p. 62.
46
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