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

114 Suppose the H sine of θ° could be subtracted. Let the remainder be r. Then (r × 225) / D where D is the difference between the previous and next H sines, added to θ gives the angle corresponding to x'. Comm. Evidently this is the converse of the previous process and this also is based on Rule of three.' Verses 12—15. The H sine of the obliquity of the ecliptic taken to be 24° is 1397. Now, the successive diffe- rences of the H sines will be given (on the basis of taking R = 120) which are known as Laghu-Jyās intended for ease in Computations, namely 21, 20, 19, 17, 15, 12, 9, 5, 2. These are given for intervals of 10°, so that if it be required to find the H sine of x°, let q be the quotient and r the remainder when x is divided by 10. q gvies the number of the previous H sine. Then (r × D) / 10 where D is the next difference or jyākhanda as it is called, added to the previous H sine gives the required H sine. In this table the H sine of 24° is 48' — 45". Also the H versines in this table are got by the reverse differences. To get the angle θ° for a given H sine say x' subtract the sum of as many differences (Jyā—Khandas) as could be from x. Let the remainder be r. Then (r × 10) / D where D is the next jyā—Khanda added to the previous angle upto which the jyākhandas have been subtracted, gives the required angle. The H sine will be more accurate if the Bhōgya-Khanda or the next H sine—difference is rectified (as per the rule of interpola- tion next given). Comm. H vers θ = R—H Cos θ = R—H sin (90—θ) so that H verse 3¾° = 3438—H sin (86¼°) = 3438—3431=7 as given in the previons table. Similarly in the above table of Laghu-Jyās, H vers 10° = R — H cos 10° = 120 — H sin 80° = 120 — (21 + 20 + 19 + ... + 5) = 2 so that the