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

MAÑJULA'S MOON'S EQUATION 115
original not only from this but also from other considerations.
It sought to correct the constants as were obtained from the
Babylonian and the Greek systems as has in some cases been
shown already.
Mañjula's Second Equation of the Moon (932 A.D.)
We now take up in detail Mañjula's second equation of
Moon. It is, however, necessary to say something about his first
inequality.
This is given in the form
—488 sin (nt—a')
————————————————————— degrees,
96+ (488/120) cos (nt—a')
where nt stands for the Moon's mean longitude, a'—that of the
apogee.
488°
Hence when nt—a'=90°, the equation = ———— =5°4'=304'
96
showing an excess of 4' over the modern value.
It is further necessary to modify the expression for
the Moon's modern form of the equation by chang-
ing a to 180°+a, as in ancient Indian astronomy anomaly
is measured not from the perigee but from the apogee.
The modified form is
=—301' sin (nt—a)+13 sin 2(nt—a)......
—152' sin (nt—θ) cos (θ—a)+40' sin 2(nt—θ)+...
Mañjula's lines giving the second equation are—
The (mean) daily motion of the Moon diminished by
11° and multiplied by the "cosine" of the longitude of
the Sun diminished by that of the Moon's apogee is the
multiplier of the "sine" and the "cosine" of the longi-
tude of the Moon diminished by that of the Sun,
divided severally by 1 and 5. The results taken as
minutes are to be applied negatively and positively to
the Moon and to her daily motion if the quantities
multiplied together are of opposite signs and in the
reverse order if they are of the same sign.¹

1. इन्दूच्चोनार्ककोटिघ्ना गत्यंशा विभवा विधोः ।
   गुणो व्यर्केन्दुदोः कोट्यो रूप पंचाप्तयोः क्रमात् ॥
   फले शशाङ्क--तद्गत्योर्लिप्तास्ते स्वर्णयोर्वधे ।
   ऋणं चन्द्रे धनं भुक्तौ स्वर्णं साम्य वधेऽन्यथा ॥ —11, 12