242 dhruv raina
Th e point needs some reaffi rmation since both Colebrooke and Davis,
who worked with commentaries of canonized astronomical and math-
ematical texts respectively, do mention the existence of demonstrations,
and rules in the texts they discuss. In Colebrooke’s introduction to his
Algebra with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta
and Bhascara , there are four terms of concern to us here, namely demon-
stration, rule, proof and analysis, that come up oft en, but it is only the last
of these that Colebrooke clarifi es. Further, as will be noticed in the next
section the terms demonstration and proof are used interchangeably by
Colebrooke. Noted by its absence in the title is the term ‘geometry’, as a
systematized science; on the contrary, the translation does allude to men-
suration as discussed in the books he translates. Th e crucial problematic for
Colebrooke was, as with Burrow before him, to determine the origins of
Indian algebra. Inspired, as it were, by the textual exemplars of Davis and
Burrow, and guided by the research programme John Playfair had drawn
up for the researchers of the Asiatic Society, Colebrooke highlighted the
pathway to his own work:
In the history of mathematical science, it has long been a question to whom the
invention of algebraic analysis is due, among what people, in what region was
it devised, by whom was it cultivated and promoted, or by whose labours was it
reduced to form and system. 61
Th e subsequent narrative focuses upon establishing that ‘the imperfect
algebra of the Greeks’, that had through the eff orts of Diophantus advanced
no further than solving equations with one unknown, was transmitted
to India. Th e Indian algebraists, through their ingenuity, advanced this
‘slender idea’ to the state of a ‘well arranged science’. 62 In his reading,
Colebrooke shares a fundamental historiographic principle, disputed by
current scholarship, with Burrow, one that enjoyed currency among his-
torians of mathematics into the twentieth century. In this historiographic
frame: ‘... the Arabs themselves scarcely pretend to the discovery of
Algebra. Th ey were not in general inventors but scholars , during the short
period of their successful culture of the sciences.’ 63
Th e science of ‘algebraic analysis’, a term Colebrooke would later
expand upon, existed in India before the Arabs transmitted it to modern
Europe. 64 Th e evidence for these claims resided in the translations of61 C1817: ii (emphasis added).
62 C1817: xxiv.
63 C1817: ii (emphasis added).
64 Ibid.