Contextualizing Playfair and Colebrooke 245
analysis is then for Colebrooke: ‘ calculation attended with the manifestation
of its principles ’. Th is is manifest in the Indian mathematical texts being
discussed since they intimate to the reader a ‘ method aided by devices ,
among which symbols and literal signs are conspicuous’. 72 I n t h i s s e n s e
Indian algebra bears an affi nity with D’Alembert’s conception of analysis
as the ‘method of resolving mathematical problems by reducing them to
equations’.^73 Delambre and Biot would subject these views of Colebrooke
to trenchant criticism, but that is another subject. 74 Th e issue at stake here
is that Colebrooke had insinuated the idea that Indian mathematics was
not lacking in methodological refl ection or generality, a feature that had
hitherto been denied.
Did Colebrooke’s view of algebraic analysis provide for demonstra-
tions or proofs of its rules or procedures? Citing specifi c sutras from the
Brahmasphutasiddhanta , the Bija-Ganita and the Lilavati , Colebrooke
moves to a characterization of Indian algebra, just as Diophantus is evoked
to characterize early Greek algebra. Th us, we are informed that these Indian
algebraists applied algebraic methods both in astronomy and geometry, and
in turn, geometric methods were applied to ‘ the demonstration of algebraic
rules ’. Obviously, Colebrooke was construing the visual demonstrative
procedures employed by Bhaskara to which we come as exemplifying geo-
metrical demonstration. Further, he goes on to state that:
In short, they cultivated Algebra much more, and with greater success than geom-
etry; as is evident in the comparatively low state of their knowledge in the one, and
the high pitch of their attainments in the other. 75
Th is passage came to be quoted ever so oft en in subsequent histories of
science, and in the writings of mathematicians as evidence of the algebraic
nature of Indian mathematics. 76 Th e power of its imagery resides in its
ability to draw the boundary between diff erent civilizational styles of math-
ematics. In this contrast between Western and Indian mathematics it could
be suggested that Colebrooke’s qualifi cation concerning the ‘comparatively
72 C1817: xix–xx.
73 Ibid.
74 Raina 1999.
75 C1817: xv.
76 Th e nineteenth-century British mathematician Augustus De Morgan, a self-proclaimed
afi cionado of Indian mathematics, wrote a preface to the book of an Indian mathematician
punctuated with aperçus from Colebrooke’s introduction. Th e introduction in fact provides
him the ground to legitimate the work of the Indian mathematician for a British readership
(Raina and Habib 1990 ).