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

119 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