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

66 BRAHMASPHUṬASIDDHĀNTA & KHAṆḌAKHĀDYAKA of celestial mathematics (18—21) like dṛṣṭi-sthāna (intersection of horizontal and vertical axis—pūrvāparadiggatā rekhā and adha- ūrdhva-diggatā rekhā). Dṛṅ-maṇḍala, dṛgkṣepamaṇḍala (dṛgkṣepa is the zenith distance of that point of a planet's orbit which is at the shortest distance from the zenith). Then the Bhūbhagola instrument is described (22, 23). Then follow the formulæ for calculating lagna (the horizon ecliptic point in the East), kāla etc. comprising the Tripraśnādhikāra (24—33). In the next verses, we have lambaka or Rsine of colatitude (34); dṛk-karma (35) and ayana-dṛk-karma (36). Then follow the calculations of lunar and solar eclipses (37--47). Verse 48 describes the coordi- nates of the Sun which are determined by the conjunction of hori- zon with the Sun, of the Moon by the conjunction of the Sun and the Moon, of planets by the conjunction of the Moon and planets or stars. Verse 49 describes how this jewel treatise has been pro- cured out of an ocean of true and untrue knowledge with the help of a boat of intellect. This means that the author has taken special pains in discriminating true knowledge from falsehood with respect to the prevalent notions of astronomy. In the last verse he says that he has not given anything new; he has given that very knowledge which was imparted by the Svayambhu in the earliest times (50). The Pañchāṅgas prepared according to the rules and for- mulæ of the Āryabhaṭīyam are still regarded with reverence by the Vaiṣṇavas in the South. Brahmagupta was a great critic of Āryabhaṭa, but finally he wrote his treatise, the Khaṇḍakhād- yaka, on the basis of this very Āryabhaṭīya (this treatise is a kara- ṇagrantha i.e. one containing a principal element of the Indian Calendar). The four commentaries of the Āryabhaṭīya available in Sanskrit are of Bhāskara I, Sūryadeva Yajvā, Parameśvara and Nīlakaṇṭha. Two English translations by P.C. Senagupta (1927) and W.E. Clark (1930) are also available. Major Landmarks Indian astronomy which reached its zenith in the times of Āryabhaṭa and Brahmagupta shows its evolution in the following stages :

1. Rudiments of astronomy in the Vedas and Brāhmaṇa Books like the Taittirīya Saṁhitā and the Śatapatha Brāhmaṇa. This period is associated with the dis-