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

DIMENSIONS OF THE EPICYCLE OF APSIS 105
verse, the aphelion point of Mars in 499 A.D. had a longitude
of 110 plus 17=127°; of Jupiter 160 plus 10=170°.
According to Newcomb's rule, the longitude of the aphelion
point of Mars in 499 A.D. works out to have been 128°28'12''.
The same according to Conn. des Temps rule would be 128°27'51''.
Hence Brahmgupta's determination of Mars's aphelion is correct
within 1°30', and may be, therefore, regarded as very satisfactory.
According to the Khaṇḍakhādyaka proper this value was, as
already said, 110°, while according to the Āryabhaṭīya, it was
118°.
The same may be said regarding Jupiter's aphelion. Accord-
ing to the Khaṇḍakhādyaka proper the value of its longitude is
160°, according to the Āryabhaṭīya it was 180°; according to
Conn. des. Temps' rule, it would be in 499A. D. 170°25', and the
value given by Brahmagupta in the Uttara Khaṇḍakhādyaka, it
is 170°.
We have thus shown by many illustrations the important
corrections introduced by Brahmagupta in his Khaṇḍakhādyaka
specially the Uttara part. Brahmagupta was highly original in his
methods of calculations, accuracies and interpolations. He intro-
duced new ideas in mathematics. He went much ahead Āryabhaṭa
in many details. He so many times did not follow Āryabhaṭa
in calculations. In the Khaṇḍakhādyaka proper, his treatment
of parallax in the calculation of solar eclipses is different from
that of Āryabhaṭa. The methods followed here are the same as
propounded by him in the Brāhmasphuṭasiddhānta.¹
Senagupta is right when he says : As has already been
remarked, these corrections and innovations in the Uttara
Khaṇḍakhādyaka paved the way for the acceptance of his great
work the Brāhmasphuṭasiddhānta as a standard work on astrono-
my by the western Indian school of astronomers. The directness
of the treatment of topics, and the simplicity of calculations
taught in the Khaṇḍakhādyaka made it very neat handbook
for the beginner. These two works of Brahmagupta were
perhaps the only astronomical works in circulations in western
India when the Arabs conquered Sind early in the eighth century

1. On Parallax—
   नाडी चतुष्कविधिना सर्वत्र समो यतस्ततः स्थूलः ।
   मानार्थं कर्म महत् कृतमार्यभटेन लघुनि सति ॥ BrSpSi. XI. 33