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-