246 dhruv raina
low’ state of one and ‘high pitch’ of the other was lost sight of and the con-
trast between the two traditions came to be subsequently accentuated.
Th is leads me to conjecture that Colebrooke’s translation is a watershed
in the occidental understanding of the history of Indian mathematics on a
second count as well, this being that it inadvertently certifi ed the bound-
ary line drawn between Indian algebra and Greek geometry. Th is was not
Colebrooke’s intention at all, but a consequence of the comparative method
he had adopted. Colebrooke’s particular comparative method consisted in
displaying where India’s specifi c contributions to mathematics resided, and
he always contrasted these contributions with the Greek and Arab tradi-
tions of mathematics. 77 Th is attempt to accentuate the contrast certainly
revealed the diff erences, but with the loss of the context of the contrast, it
was fi rst transformed into a caricature and then stabilized as a characteriza-
tion. Th e boundary lines had however been marked out before Colebrooke’s
time. Th is passage is crucial because it is followed by a discussion of some
procedures of demonstration in Indian algebra that I shall briefl y lay out.
Th us the specifi c areas in which ‘Hindu Algebra appears particularly
distinguished from the Greek’ are four. 78 Some of these have been men-
tioned above. Th e additional one that has not been mentioned concerns
the application of algebra to ‘astronomical investigation and geometrical
demonstration’, in other words algebra is applied to the resolution of geo-
metrical questions. In the process the Indian algebraists, Colebrooke sug-
gests, developed portions of mathematics that were reinvented recently.
Th is last statement of his prompted a very severe reaction. He then takes up
three instances, which he considers ‘anticipations of modern discoveries’
from the texts he discusses and lays out their procedures of demonstration.
Th ere is nothing in the subsequent portion of the introduction to suggest
that he did not consider these as demonstrations.Proofs and demonstrations in Colebrooke’s translations
of Indian algebraic work
Colebrooke’s Algebra with Arithmetic and Mensuration was completed
shortly aft er his departure from India for England in 1814. Th e volume
comprises the translation of four Sanskrit mathematical texts, namely
the Bija-Ganita and Lilavati of Bhaskara, and the Ganitadhyaya and
Kuttakadhyaya of Brahmagupta. Th ese translations were undertaken during
77 Going by his text alone, he appears to have been totally oblivious of Chinese mathematics.
78 C1817: xvi.