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

ARYABHAṬA & BRAHMAGUPTA CONTROVERSY 81
The minor work of Brahmagupta known as Khaṇḍakhādyaka
has two distinct parts : Khaṇḍakhādyaka proper and the Uttara
Khaṇḍakhādyaka. In the first part the astronomical constants
are the same as those of Āryabhaṭa's ardharātrika system, but
the methods of spherical astronomy, calculation of eclipses and
other topics are almost the same as in the Brāhmasphuṭasidd-
hānta. The corrections for parallax in calculating a solar eclipse
is here an important illustration.¹
In the Uttarakhaṇḍakhādyaka, Brahmagupta gives correc-
tions to the Khaṇḍakhādyaka proper. In it are to be found the
neat and original methods of interpolation and correction to the
longitudes of the aphelia, as also to the dimensions to the
epicycles of apsis of the Sun and the Moon.² while a few addi-
tional chapters supply what else is necessary to the first seven
chapters of the first part, to make the whole a complete treatise
on Indian scientific astronomy. It was perhaps through the in-
fluence of this supplementary part of the Khaṇḍakhādyaka that
Brahmagupta's great work, the Brāhmasphuṭasiddhānta came to
be valued among a distinct school of Indian astronomers. For
long in this country India, this Siddhānta of Brahmagupta has
been forming the basis for the calculation of almanacs by astro-
nomers of the orthodox school of Rājasthān, Bombay and others.
We might at this stage take up the question : Was
Āryabhaṭa the author of two distinct systems of astronomy ?
Undoubtedly he was. Several authors have written on this
subject. I may specially mention the name of Prabodha
Chandra Sengupta (Journal of the Department of Letters,
Calcutta University, vol. XVIII; Bulletin, Calcutta Mathemati-
cal Society, vol. XXII. Nos. 2 and 3). The reasons advanced by
him may be restated in slight details thus. In his Brāhma-

1. व्यासार्धेन विभक्ता दृग्गतिजीवा चतुर्गुणा लब्धम् ।
   लम्बननाड्यः पञ्चदश गुणिताया त्रिज्यया भक्ता ॥
   दृक्क्षेपज्या मुहुत्यन्तरा हता लब्धमवनतिर्भवति ।
   स्फुटयोजनकर्णाभ्यां भू-यासेन च विना स्फ०टे ॥
   आर्यभटेनास्मिन् सति लघुनि किमर्थं महत् कृतं कर्म ।
   गणिताज्ञानाज् जाड्यं विजानता यदि ततः सुतराम् ॥
   —BrSpSi. XI. 23-25, also KK. V.
2. See UKK. 9.