The History of Mathematical Proof in Ancient Traditions

(Elle) #1

Contextualizing Playfair and Colebrooke 239


Th e article draws extensively, need I say almost exclusively, upon the
Mémoirs of Le Gentil published by the Académie des Sciences, Paris and
Bailly’s Astronomie Indienne.^55 Th is article of Playfair’s was of prime impor-
tance for Indologists working on the history of Indian astronomy for the
next four decades.
Playfair’s central contribution resided in re-appropriating Bailly’s Traité
in the light of the contributions of Davis and Burrow and proposing a
set of tasks that could well be considered a research programme for the
Asiatic Society. Th ese included: (a) to search for and publish works on
Hindu geometry, (b) to procure any books on arithmetic and to ascertain
those arithmetical concerns whose trace is not to be found among the
Greeks, (c) to complete the translation of the Surya Siddhanta as initi-
ated by Samuel Davis, (d) to compile a catalogue raisonné , with a scholarly
account of books on Indian astronomy, (e) to examine the heavens with
a Hindu astronomer in order to determine their stars and constellations,
(f ) to obtain descriptions and drawings of astronomical buildings and
instruments found in India. 56
If Bailly had stirred a hornet’s nest in his time by suggesting that the
origins of astronomy were in India, albeit that this astronomy was inher-
ited by the Indians from an even more ancient people, Burrow’s paper did
the same with the origins of algebra. It is at this time diffi cult to separate
the discussion on the history of astronomy from the history of algebra;
for both the Académiciens and the Indologists oft en turn to the history of
astronomy to evoke computational procedures that were analysed math-
ematically. Th is programme of the recovery of the mathematical literature
from the astronomical literature was taken up by Colebrooke, who may be
seen as providing translations from the Sanskrit into English of the fi rst
texts supposedly dedicated solely to algebra and arithmetic. I say suppos-
edly because portions of some of the texts Colebrooke discovered for the
English-speaking world were essentially the mathematical sections of larger
astronomical canons of the Indian tradition.
We come now to Colebrooke’s translation practices. In order to describe
them we need to understand how Colebrooke identifi ed an authenticated
version of the texts that he set out to translate. It needs to be pointed out
that at the very outset no fi nal version of the three texts, from which only
portions were translated, was readily available to him. Consequently,
he worked with his Brahmin interlocutors and collected and collated


55 Le Gentil 1789; Bailly 1787.
56 Playfair 1792 : 152–5.

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