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