196 Problems by Bipu Deva Shastri. © 
+. @de 149 | 
Then the sagitta of A= AV Gn (j —30"-a2400”" t+ 448000” 5-+&&c. 
- =3V 6(.24014) 
. =3 x2-44949 x 24014 
3 
=1:76466=1 ri nearly. 
Prosiem [I.* 
| _ Given an arc and its chord to find the sagitta. 
a ~Rule.—Multiply the given are by 100,000 and divide the pro- 
t by the given chord. Diminish the quotient by the nearest 
tabular quotient in col. 4 and set down the difference. (a) 
Take the said tabular quotient from the one immediately 
Rfeuins it, and similarly find the difference of the corresponding 
‘tabular chords and sagitta, 
3. Multiply the difference (a) by the 2nd and 3d of the three 
last ~ differences respectively, and divide the products 
aa? 
—A . these quotients respectively, by the tabular chords 
hdd. sagitta which have been made subtrahends (¢ 2.) Multiply 
- the 2d sum by the given chord and divide the product by the Ist, 
and the result is the value of the sagitta required. 
Similarly the chord may be determined when the arc and the 
sagitta are given. But in making the calculation the chord is to 
be considered as the sagitta and vice versa. 
Also when the tabular difference ($ 2.) is not less than the one 
immediately following it, it must be subtracted from that imme- 
diately preceding it. ” And i in ($ 4.) the quotients are to be sub-. 
tracted from the minuends. 
Dem.—The ratios of similar arcs and their chords being equal, 
100,000 timest+ the ratios of arcs and their chords are easily 
found and set down in tables. Opposite to these the chords 
of similar arcs and their sagittas are also given. Hence the value 
rd sagitta may be easily determined by simple proportion. 
JA similar demonstration will apply to the rule for determining 
> chord, when the arc and its sagitta are given. 
SPaSUNNGR ESE ORAM SMR ON TT 
This Bo is printed in the Benares Recorder 
1€ ratios have been multiplied by 100,000 in order to avoid fractions. 
