VEDAS AS SOURCE
The four Vedas comprise the
Samhitas - texts of prayers and hymns, charms,
invocations and sacrificial formulae. The Rig
Veda is the Book of Devotional Verse, the Yajur
Veda is the Book of Sacrificial Formulae, the
Sama Veda is the Book of Chants, and the Atharva
Veda is the book of Mysticotherapeutic Priestcraft.
Their composition precedes their arrangement
into the four Samhitas by a long period of oral
Rig Veda and Atharva Veda hymns
point to the observance of a lunar year. The
Moon itself was regarded as the 'maker of months'
- masakrt. Many indications are present as to
the awareness of the autumn equinox - references
to Aditi (this corresponds to Pollux, longitude
113°). Daksha (Vega longitude 284°),
Rudra (Betelgeuse, longitude 88°) and Rohini
(Aedebaran, longitude 69°). The changing
longitudes mentioned are a consequence of the
precession of the equinoxes. These details are
useful for another reason: they reveal the date
of composition. Thus, allowing for 72 years
per degree (plus, allowance for error) the years
should be 6200 BC, 5400 BC, 4350 BC and 3070
BC respectively. Hymn 1.164 of the Rig Veda
composed by the sage Dirghatamas refers to a
wheel of time with a year 0f 360 lunar days
and twelve lunar months. The year mentioned
in the hymn begins with the Autumn star Agni
(Alcyon, longitude 59°5), corresponding
to the year circa 2350 BC. (The numbering of
the hymns demonstrates use of the decimal system).
Yajur Veda and Atharva Veda
reveal a definite calendrical awareness - many
sacrifices, including the Gavam Ayana, are of
different lengths of time based on the daily
cycle of the Sun. For reasons of ritual, the
day was divided into 3,4,5 or 15 equal divisions,
each with a different name. Apart from naming
twenty seven stars beginning with Krttika, these
Vedas mention five planets and name two of them
- Juipter (Brihaspati) and Venus (Vena).
The Taittriya Brahmana speaks
highly of nakshatravidya (nakshatra= stars,
vidya= knowledge) and states clearly the existence
of scholars of this science.
JAIN LITERATURE AS SOURCE
The Ardha-Magadhi Prakrit texts
are composed of the fragments and oral traditions
of the original Jain texts known as Punva. This
recasting was the effort of the Svetambara sect,
and this body of work consists of forty five
or fifty books. The basic texts are:
a) Angas: these concern rituals, legends, and
doctrines. Of the twelve Angas, two - Sthananga
and Bhagavatisutra - relate to astronomy and
mathematics. The others are - Acaranga, Sutrakrtanga,
Samavayanga, Jnatrdharmakatha, Upasakadasa,
Antakrtadasa, Anuttera-aupapa-tikadasa, Prasna-Vyakarana,
Vipakasutra and Drstivada.
b) Upangas - these too are
twelve in number, of which Suryaprajnapati,
Candraprajnapati and the Seventh Section of
Jamudvipaprajnapati concern themselves with
astronomy. The second section of Jambudvipaprajnapati
discusses Time, the concept ranging from asankhyata
('inscrutable infinitesimal Time') to sirsaprahelika
i.e. millions of years.
c) Prakirnakas - these are
miscellaneous texts, ten in number.
d) Chedasutras - these nine
books state the rules that govern monastic life,
e) Mulasutras - of the four
Mulasutras - Uttaradhyayana, Avasyaka, Dasavaikalika
and Pinda-inryukti - the first contains some
facts on astronomy and mathematics.
The Culikasutra of two parts
- Nandisutra and Anuyogadvarasutra- is a treatise
on astronomy and mathematics.
Jain post-canonical literature
is represented by work such as Tattvarthadhigama
Sutra by Umasvati (AD 185-219) on astronomy
and cosmology; the 7000-verse Trilokaprajnapati
by Yati Vrsabha (AD 473-609) of which chapter
27 is on astronomy; Jyotisakarandaka by Padaliptacharya
(based on the Suryaprajnapati) that contains
the total of Jain views and observations on
astronomy; Karananuyoga or Ganitanuyoga of the
Digambara sect, a comprehensive text on Jain
The Centre of the Universe
Mount Meru was regarded as
the central axis of the Earth, the latter seen
as a motionless planet. These two, along with
the constellations, planets, continents, rivers,
seas and mountains constitute Jambudvipa (literally,
'rose-apple land'). Certainly, this had a metaphysical
aspect as well- Mount Meru is the subtle inner
essence that generates everything (or Reality).
Awareness of the subjective reality of all creation
(that everything is connected) is sometimes
expressed through the diagram of the Jambuvriksha,
i.e. the world tree. The cosmic diagrams of
Jain literature depict Mount Meru at the centre,
and the outermost limit illustrates the twelve
months, the planetary cycles and the movements
of the Sun the Moon. The Polar Star is depicted
as being directly above Mount Meru.
In addition to these works,
there were the books on astronomical yantras
(devices). Mahendra Suri's (AD 1348) Yantraraja
was followed by the Ustaralayayantra by Meghalaya
(circa AD 1500) which discusses the use and
construction of the astrolabe (an instrument
to determine the altitude of planets and stars).
These two are the major works in this field.
THE SIDDHANTAS AS SOURCE
Of the eighteen early siddhantas written by
Pitamaha, Surya, Vyasa, Atri, Vasistha, Kasyapa,
Parasara, Narada, Garga, Manu, Marici, Lomasa
(Romaka), Angiras, Bhrgu, Paulisa, Cyavana,
Yavana, Saunaka, only five survive as extracts.
Panchasiddhanta by Varahamihira (composed in
AD 578) includes the siddhantas of Surya, Vasistha,
Pitamaha, Paulisa and Romaka.
The later siddhantas represent
a considerable advance in astronomy- they were
far more precise and calculations were accurate
and easier than in the past.
The Aryabhatiya (AD 499) of
Aryabhata the First discussed spherical astronomy
in addition to calculations for planetary positions
and their mean. Solar and lunar eclipses were
elaborated upon, as also the fact that the Earth's
shadow was responsible for the phases of the
Moon, that the Earth rotated on its axis, and
the Moon revolved round the Earth.
Bhaskara the First's works-
Mahabhaskariya and Laghubhaskariya- were commentaries
on the Aryabhatiya. He calculated complete revolutions
performed by a planet using Aryabhata's rule.
Bhaskara's equation y=ax-C/b is a variation
of Aryabhata's x=by+c/a. In Bhaskara's equation,
a=bhajya (revolution number of planets), b=hara
(divisor or civil days in a yuga), c=agra (residue
of the revolution of the planets), x=gunkara
(complete revolutions of a planet, i.e. ahargana)
and y=phala (complete revolutions performed
by a planet).
ASTRONOMY IN KERALA
Aryabhata the First's system
was followed by astronomers in Kerala (a state
of southern India) who in AD 683 met in Tirunavay
to launch the Parahita system of computation.
This new method was an amendment of the former.
The major texts were Grahacaranibandhana and
Mahamarganibandhana by Haridatta. However, over
the centuries it was found that observations
did not correlate to the results as calculated
by the Parihata system. Thus, in 1431, Parmesvara's
(1360-1455) Drk system gained ascendance.
During this period, a host
of other literary works on astronomy were written
based on the Parihita and Drk systems. Known
as Karana literature, this included:
a) Karanaratna by Devacarya. The eight chapters
deal with calculations for the longitudes of
the Sun, Moon, and the planets, eclipses, gnomon
shadow (the shadow on a sundial cast by a stationary
arm), helical visibility, planetary conjunctions
and the rising of the Moon.
b) Vakyakarana (AD 1300) and
Drkharana by Jyesthadeva
(AD 1500- 1610).
c) Karanasara by Sankara Variyar
d) Karanamrta by Citrabhanu
e) Sadratnamala by Sankara
Vakyas are the mnemonics used
by both systems to generate different astronomical
tables. For instance, the work Candravakyas
of Vararuci yields the two hundred and forty
eight daily longitudes of the Moon for nine
anomalistic months. Other vakyas provide, for
instance, the 3031 daily lunar longitudes for
110 anomalistic months.
The Aganita-grahacara by Madhava
is replete with information on the Moon, the
longitudes of planets stretching over many years,
and planetary motions. All of it is neatly organized
Computing the shadow of the
Moon aided the calculation of time and planetary
positions. Many works were composed on this
topic, the major ones being: Candracchyaganita
I by Paramesvara, followed by Candracchayaganita
II by Nilakantha, and Candracchayaganita III
and IV that remain anonymous. Other works include
Chayaslaka by Acyuta Pisarati, and three anonymous
texts Candracchayanayanopavah, Chayaganita (four
different volumes), and Suryacchayadiganita
(two different works).
There were eight important
texts on astronomical rationale:
a) Lagnaprokarana by Madhava
(1360 - 1440) discussing the computation of
b) Grahanayayadipaka by
Paramesvara that dealt with the computation
c) Yuktibhasa by Jyesthadeva
on astronomy and mathematics.
d) Rasigolasphutaniti by
Acyuta Pisarati that provided calculations for
measuring planetary longitudes on the ecliptic.
e) Nyayaratna by Putumana
f) Ganitayuktayah on astronomical
g) Jyotirmimamsa by Nilakantha,
composed in 1504. This work focussed on the
vital role of observation in astronomy, as well
as the need to correct parameters regularly
on the basis of the eclipses, Sun, Moon and
h) Grahapariksakarana, also
by Nilakantha, that provided details of methods
of practical astronomy.
1.History of science
and technology in India.
2.The Art of Tantra : Philip Rawson.
3.Reader's Digest :Did you know.