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