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

MEAN LONGITUDE OF PLANET 299
revolution number of planet × ahargaṇa
Mean longitude = ——————————————————————————————————————
civil days in a yuga
Similar expression is given by more recent Indian astro-
nomers also.
(ii) Mean longitude of desired planets in minutes
(mean longitude of the known planet in revolu-
tions etc. reduced to minutes) × (revolution number
of the desired planet)
= ————————————————————————————————————————————————
revolution number of the known planet.
This rule is common to Brahmagupta¹ and Bhāskara I².
(iii) An alternative rule for deriving the mean longitude of
the Moon from that of the Sun and vice versa has been given
by Bhāsakara I and Brahmagupta both.
Multiply the ahargaṇa by the number of intercalary
months in a yuga and divide (the product) by the
number of civil days (in a yuga) : the result is in the
terms of revolutions etc. Add that to thirteen times
the mean longitude of the Sun. (This is the process)
to obtain the mean longitude of the Moon³.
Mean longitude of the Moon
(intercalary months in a yuga) × ahargaṇa
= ————————————————————————————————————————— revolutions
civil days in a yuga

1. ज्ञातभगणादिभुक्तं सविकलमिष्टयुग भगणसंगुणितम् ।
   ज्ञात युगभगणभक्तं मध्यो भगणादि फलमिष्टः ॥ — BrSpSi. XIII. 27
2. निशाकरं वाग्रहमुच्चमेव वा कलीकृतं तत्सहयातमण्डलैः ।
   यथेष्ट नक्षत्रगणैर्हतं हरेत् तदीयनक्षत्र गणैस्ततः कला ॥ MBh. I. 10
   The (mean) longitude of the Moon, the planet, or the Ucca
   (whichever is known) together with the revolutions performed
   should be reduced to minutes. The resulting minutes should
   then be multiplied by the revolution-number of the desired
   planet and (the product obtained should be) divided by the
   revolution-number of that (known) planet. The result is
   (the mean longitude of the desired planet) in minutes.
3. द्युगणं युगाधिमासैर्गुणितं युग भूदिनैर्हृतेऽलब्धम् ।
   भगणादि मध्यमार्के त्रयोदश गुणार्धिकं चन्द्रः ॥ —BrSpSi. XIII. 33
   युगाधिमासैर्धुगणं हतं हरेत् क्ष्मादिनैर्वां भगणादि लभ्यते ।
   त्रयोदशघ्ने सवितर्यथा क्षिपेन्निशीथिनीनां पतिचारसिद्धये ॥ —MBh. I. 11