Subject: Re: [HM] Indian astronomy and mathematics
From: K. Subramaniam (subra@hbcse.tifr.res.in)
Date: Fri Feb 04 2000 - 01:01:45 EST
I am seeking a clarification on Kim Plofker's post.
I too looked up Shukla and Sarma's critical edition of Aryabhatiya mentioned
by K.P.
The discussion of the lost work Aryabhata-siddhanta appears on pgs.lxiii-
lxviii.
Shukla and Sarma say that Brahmagupta's Khanda-khadyaka was planned in two
parts. (p.lxvii) The first part summarized the teachings of Aryabhata-
siddhanta without making any alteration, modification or addition (except
one or two rules). Part II set forth Brahmagupta's corrections and
modifications.
The opening stanzas of Part I and part II are quoted in English translation.
It seems to me then that the best place to look for Aryabhata-siddhanta's
cosmology is part I of Brahmagupta's Khandakhadyaka.
But the comments by Shukla and Sarma are not clear about whether BOTH parts
of the Khandakhadyaka have survived or only Part II has survived.
If part I has survived what does it reveal about the claims made regarding
Aryabhata-siddhanta by Dinesh?
Subramaniam
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K.Subramaniam,
Homi Bhabha Centre for Science Education,
Tata Institute of Fundamental Research,
V.N. Purav marg, Mankhurd, Mumbai - 400 088,
INDIA
e-mail: subra@hbcse.tifr.res.in
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On Thu, 3 Feb 2000, Kim Plofker wrote:
>
> > "As a side note, I wonder if Aryabhata's [476-550AD] astronomy
> > text Siddhanta (not Aryabhatitya) which deals with a heliocentric
> > model of the solar system, the notion of earth rotation, the
> > causes of solar/lunar eclipses and the notion of elliptical
> > planetary orbits were ever translated to Arabic/Persian."
>
> The _Aryabhata-siddhanta_ (also generally known as his Ardharatrika
> or midnight system, owing to its using a midnight epoch as opposed
> to the sunrise epoch of the _Aryabhatiya_) is discussed in K. S. Shukla's
> and K. V. Sarma's edition of the _Aryabhatiya_ (New Delhi 1976). This
> work is lost in Sanskrit, although a condensed version in the form of
> an astronomical handbook, the _Khandakhadyaka_ composed by Brahmagupta
> in the seventh century, survives in Sanskrit and was also translated
> into Arabic (as was the _Aryabhatiya_ itself). I know of no Islamic
> version of the _Aryabhata-siddhanta_, although there is an Arabic
> translation of a Sanskrit work called _Mahasiddhanta_ which I believe is
> known to be the work of the *second* Aryabhata, who lived in the tenth
> century (this can get confusing!).
>
> As for the content of Aryabhata (I)'s lost work, we know from the
> seventh-century _Mahabhaskariya_ of Bhaskara (I), as Shukla and
> Sarma point out, that it used somewhat different parameters from the
> _Aryabhatiya's_ for the distances and mean motions of the planets.
> Neither Shukla and Sarma nor Bhaskara (nor any other author that I
> know of) claims that the basic cosmology of the _Ardharatrika_ =
> _Aryabhatasiddhanta_ was different from that of the _Aryabhatiya_,
> and I'd be interested in seeing specific citations that support that
> assertion. The concept of a rotating earth is quite clearly put
> forward in verse 1, 6 of the _Aryabhatiya_ (although the statement was
> "corrected" by more conservative later authors), but there is no mention
> of a heliocentric system: the sun is given an orbital circumference
> and a mean orbital motion, just like the rest of the planets (and
> unlike the Earth). The "causes of solar and lunar eclipses", namely,
> the fact that they were caused by the interposition of the lunar disk
> and the earth's shadow respectively, were perfectly well understood by
> Aryabhata's time. The "notion of elliptical planetary orbits" is no
> more evident in the _Aryabhatiya_ than is the notion of a heliocentric
> system: the planets' orbits are treated in longitude computations as
> circles, and so are the epicycles and eccentrics used to account for
> their longitudinal anomalies. (The use of iterative techniques to
> modify the orbital radius in these calculations *does* generate a
> non-circular orbital path, and these techniques should be investigated
> further; but there is no explicit mention of elliptical orbits.)
>
> I am finding it difficult to keep up with the self-imposed task of sifting
> out fact from fancy in these posts on various aspects of Indian astronomy,
> especially when their assertions are unsupported by verifiable references
> to specific Sanskrit (or other Indic) texts. I'm therefore going to
> drop out of these threads altogether, but I'd like to urge the list to
> keep in mind a few basic historiographical precepts: i) While there is
> indeed a great deal that remains unknown or unverified about all aspects
> of Indian astronomy---and while the "standard view" of them will certainly
> be changed in many ways by future discoveries---much is known, and much
> has been published. ii) Much of the material disseminated in such an open
> forum as the WWWeb, in any field, is notoriously untrustworthy.
> iii) Earth-shattering and truly revolutionary discoveries in any field
> are rare: the truth of such claims often works out to be about inversely
> proportional to their impressiveness and their frequency.
>
> With best wishes,
>
> Kim Plofker
> Department of History of Mathematics
> Brown University
>
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