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

104 BRAHMASPHUṬASIDDHĀNTA'S KHAṆḌAKHĀDYAKA
Brahmagupta corrects
Dimensions of the Epicycle of Apsis
Brahmagupta corrects the dimensions of the epicycles of
apsis of the Sun and Moon by—1/42 nd part and 1/48th parts
respectively. The reference may be made to the following verse
in the Uttara Khaṇḍakhādyaka :
The Sun's equations are to be made less by dvikṛtāṁ-
śonam (1/42nd) and the Moon's equations, increased by
vasuvedabhāgayutam (1/48th). Multiply the Sun's equa-
tion a planet's daily motion in minutes and divide by
the number of minutes of a whole circle and this is
called Bhujāntara correction and applied in the same
way to the planet as the equation is applied to the Sun.¹
The Sun's epicycle of apsis has the dimension 14° in the
Khaṇḍakhādyaka proper. With the correction introduced here,
the value becomes 14° {1 - 1/42} = 13° 40'.
The correction to the Moon's equations would make the
epicycle's dimension changed from 31° to 31° {1 + 1/48} = 31°38'45''.
Pṛthūdaka's commentary further corrects it to 31°(1 + 1/52) = 31°35'
Brahmagupta 's correction to Saturn's epicycle of apsis
is—1/5th part and that to the Śīghra epicycle of Mercury 1/16th
part as seen in the verse :
Of Mars the apogee (the aphelion point) is to be
increased by 17°, that of Jupiter by 10°; from the
Śīghra of Venus 74' are to be subtracted ; Saturn's
equation of apsis should be decreased by its one-fifth
and the Śīghra equation of Mercury should be
increased by one-sixteenth.²
In the Khaṇḍakhādyaka proper (II.6), we have been given
the longitudes of the apogee of planets : Mars 11°, Mercury 22°,
Jupiter 160°, Venus 80° and Saturn 240°. Now with these correc-
tions introduced in the Uttara Khaṇḍakhādyaka in the above

1. द्विकृतांशोनं रविफलमिन्दोर्वसुवेदभागयुतम् ।
   अर्कफलभुक्तिघाताद् भगणकलाप्तं भुजान्तरं रविवत् ॥ UKK. IX. 9
2. सप्तदशांशैरधिकं भौमस्योच्चं गुरोर्दशभिरंशैः ।
   सितशीघ्रात् कृतमुनयो लिप्ताः शोध्याः शनेः फलं मान्द्यम् ।
   पञ्चांशोनं शैघ्यं षोडशभागाधिकं बुधस्य फलम् ॥ UKK.IX.11