Pre-Ptolemaic system What is to be stressed here is that the Greek astronomy
transmitted to India was not the system of Ptolemy who was active in the middle
of the second century in Alexandria, but that of certain schools belonging to the
earlier period. This can be shown from several technical aspects: for example, the
effect of the evection (second anomaly) in lunar motion, the equant point in
the planetary model, and the spherical trigonometry, which were first used by
Ptolemy, are all absent in Indian astronomy.
It is interesting that Indian astronomy preserved some older elements of
Greek astronomy which disappeared in their homeland. One of the good exam-
ples in this respect is trigonometry. It was by tracking backward along this line
of transmission that the first chord table ascribed to Hipparchus (fl. 150 bc) was
recovered by G. J. Toomer (Toomer 1973: 6–28) from an Indian sine table.
Toomer showed that some numerical values ascribed to Hipparchus in Ptolemy’s
Almagest could be explained by hypothesizing the use of this reconstructed table.
It does not follow, however, that the Indian astronomers were only uncritical
receivers of Greek astronomy. Rather, they introduced the foreign elements in a
very limited time through a very small number of texts, and after this initial
stage of introduction all the developments were made by themselves without
foreign influence.
With the introduction of Greek astronomy, Indian astronomical constants
were greatly improved. After A ̄ryabhat.a the constants were given as the rota-
tions in a maha ̄yuga(4,320,000 years) or in a kalpa(4,320,000,000 years).
The number of civil days (D) in a maha ̄yugais the difference between the
number of the rotations of fixed stars (Rs) and those of the Sun (Y). Similarly,
the number of lunar months (M) is the difference between the Moon’s rotations
(Rm) and those of the Sun. As we have seen in the jyotis.aveda ̄n.ga, the difference
between the number of lunar months and that of solar months (12Y) is the
number of intercalary months (A). In the same way the difference between the
number oftithis(T) and that of civil days is the number of omitted days (K).
Let us give a set of these numbers according to the later Su ̄ ryasiddha ̄nta,
belonging to about the eighth or ninth century. From table 18.3 we can get the
length of a solar (i.e. sidereal) year and that of a synodic month:
calendar, astrology, and astronomy 389Table 18.3
Fixed stars Rs 1,582,237,828
Solar years Y 4,320,000
Civil days D=Rs-Y 1,577,917,828
Sidereal months Rm 57,753,336
Synodic months M=Rm-Y 53,433,336
Intercalary months A=M- 12 Y 1,593,336
Tithis T= 30 ¥M 1,603,000,080
Omitted days K=T-D 25,082,580