ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

ŚRĪPATI'S SECOND INEQUALITY OF THE MOON 121 the total equation = ∓301′. This does not agree with Bhās- kara's statement that the total equation = ∓(301′ ± 78′). Case V. nt—a=0, nt—θ=±45°, θ—a=±45°, the total equation =0′—76′+40′=—36′ or 0′+76′—40′=+36′. This fairly agrees with Bhāskara's observation. Case VI. nt—a=180°, nt—θ=±45°, θ—a=180°∓45° the total equation =0′+76′+40′=0′+116′, or 0—76+40′=0′—36′. This does not agree with Bhāskara's statement. Bhāskara then states his first system of 24 equations corres- ponding to 24 sines in a quadrant to be 6′, 13′, 21′, 27′, 33′, 39′, 45′, 51′, 56′, 61′, 65′, 68′, 70′, 72′, 74′, 75′, 75′, 76′, 76′ 77′, 77′, 78′, 78′, 78′.¹ These equations, he says—"are negatively added to the equation of apsis when that is negative and positively added to the same when that is positive"². In other words his new equa- tions are complements of the equation of apsis, the two together being represented by —301′ 46″. 8 sin (nt—a)—78′ sin (nt—a) i.e., by—379′ 46″. 8 sin (nt—a). Hence next states his second set of equations depending on θ—D, to be 6′, 9′, 13′, 17′, 22′, 24′, 27′, 30′, 32′, 33′, 34′, 34′, 34′, 33′, 31′, 29′, 26′, 24′, 20′, 16′, 11′, 8′, 3′, 0′³ and says : "These minutes are negative in the odd quadrants of the argument and are positive in other quadrants.⁴" When the value of the argument is 15°, the equation is 17′, ,, ,, " 45° " 34′, ,, ,, " 90° " 0′,

1. Bījopanaya, 26-28.
2. ˙˙˙फलं ऋणे ऋणं । धने धनं मन्दफलेन संयुतम् ॥ 28 ॥
3. Bījopanaya, 29-32.
4. एताः कला ओजपदे ऋणं स्युर्धनं तदन्यत्र भवन्ति भूयः ।