Contextualizing Playfair and Colebrooke 235
It is also generally reported that the Brahmins calculate their eclipses, not by astro-
nomical tables as we do, but by rules... If they (the rules) be as exact as ours,... it
is a proof that they must have carried algebraic computation to a very extraordinary
pitch, and have well understood the doctrine of ‘continued fractions’, in order to
have found those periodical approximations... 31
Th e rules for computing eclipses employed by the Brahmins were not only
diff erent, but their complexity varied with the requisite degree of exactness:
... which entirely agrees with the approximation deduced from algebraic formulae
and implies an intimate acquaintance with the Newtonian doctrine of series... and
therefore it is not impossible for the Brahmins to have understood Algebra better
than we do. 32
Th is was to become the central point from which in subsequent papers
Burrow would build his argument for the existence of an advanced algebra
among the Indians. Th e problem was taken up again by Colebrooke dis-
cussed below, and in a paper published slightly later by Edward Strachey,
‘On the early history of algebra’. 33 Th e paper emphasized the originality
and importance of algebra among the Hindus and contained extracts that
were translated from the Bija-Ganita and Lilavati.^34 Th ese extracts were
translations into English from Persian translations of the original Sanskrit
texts.^35 But Burrow admits that these extracts were translated in 1784, but
he deferred publishing them till a full text was obtained. 36 But he prizes
the moment: ‘when no European but myself... even suspected that the
Hindoos had any algebra’. 37 Th e rationale provided for the existence of
treatises on algebra in India in Burrow’s 1790 paper on the knowledge of
the binomial theorem among the Indians is the same as that suggested in
the earlier one ( 1783 ). Many of the approximations used in astronomy were
‘deduced from infi nite series; or at least have the appearance of it’. 38 Th ese
included fi nding the sine from the arc and determining the angles of a
31 Burrow 1783 (1971): 101.
32 Burrow 1783 (1971): 101.
33 Strachey 1818.
34 Th ese works were authored by the twelft h-century mathematician Bhaskara II, and while the
fi rst of these deals with problems in algebra and the solution of equations, the latter focuses
more on arithmetic.
35 Strachey’s paper will not be discussed here, since the focus will be on the translation of versions
of Sanskrit texts into English and not the manner in which these Sanskrit texts were reported
in translations of Persian and Arab mathematical works.
36 Burrow 1790.
37 Burrow 1790: 115.
38 Ibid.