सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

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the result being subtracted from or added to as the case
may be (added in the case of Hversines) the arithmetic
mean of the preceding and succeeding H sine-differences
gives the rectified H sine-difference while finding the arc
for a given H sine.
Comm. Let the given H sine be that of 24° found
before i.e. 48·72. We could subtract 21 and 20 from this
and the remainder is 7·72; half of this is 3·86 which
multiplied by (20-19) is 3·86. This divided by the succeed-
ing difference namely 19 is ·2 approximately. The arith-
metic mean of the preceding and succeeding si (20 + 19) / 2
= 19·5. If the above result is subtracted from this, we
have 19·5 − ·2 = 19·3. If for 19·3 we have 10° increment
what shall we have for 7·72. The answer is (10 × 7·72) / 19·3
= 10 × ·4 = 4°. Hence the required arc is 20° + 4° = 24°.
The proof is analogous to the previous proof. Having
subtracted 21 and 20, the remainder is 7·72, (Ref. fig. 8)
Fig. 8
so that BX = 7·72. Now during the course of the succeed-
ing interval of 19, there has been a decrease of 19·5 −
19 = ·5 or to put it in general terms, during the course of
y the succeeding interval BC there has been a decrease