Subject: Re: [HM] Indian astronomy and mathematics
From: Kim Plofker (Kim_Plofker@Brown.edu)
Date: Sun Feb 06 2000 - 01:07:12 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
>
> ---------------------------------------------------------------------
> 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
Well, I swore I'd give up this thread, but this is such a thoughtful and
reasonable question I can't resist it. ("For my _next_ final
appearance..." :-) Both parts of the _Khandakhadyaka_ do survive, and
have been edited with an English translation by Bina Chatterjee (2 vols:
New Delhi, 1970). The eight chapters of the Purva-khandakhadyaka deal
in the usual fashion with the main questions of classical Indian astronomy:
mean motions of the planets (including the sun), corrections for true
motions of the planets, Three Questions (on direction, place, and time),
lunar eclipse, solar eclipse, planetary risings and settings, size and
orientation of the lunar crescent, planetary conjunctions, and locations
of fixed stars. Nothing is said about rotation or revolution of the earth
or about elliptical orbits. (To be fair, it must be pointed out that since
the _Khandakhadyaka_ is a typical karana or astronomical handbook rather than
a siddhanta or treatise, it contains only the briefest possible formulation
of the necessary rules for computations of time and position, rather than
discussions of geometrical models or cosmology; we would hardly expect to
see the cosmology of the _Aryabhatasiddhanta_ explicitly discussed in a karana
text, no matter how unusual it might be. But the rules themselves employ the
standard terminology of geocentric mean orbital motions, apogees of circular
epicycles for correcting anomaly, diurnal rotation of the celestial sphere
rather than the earth, etc. I repeat that I know of no reason for
concluding that the lost _Aryabhatasiddhanta_'s cosmology was in any
important way different from that of other siddhantas, much less that it
might have been "proto-Keplerian" in its outlook.)
With best wishes,
Kim Plofker
Department of History of Mathematics
Brown University
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