248 dhruv raina
Th e really interesting feature is the convergence in the reading of
Colebrooke the son and Banerji concerning the mathematical style of
Bhaskara. In the introduction to this translation Banerji was to write about
Bhaskara: ‘Th e author does not state the reasons for the various rules given
by him. I have tried to supply the reasons as simply and shortly as they
occurred to me; but still some cases... and shorter demonstrations may
possibly be given.’ 83 Banerji proceeded to edit Colebrooke’s translation of
these mathematical works by keeping those demonstrations given chiefl y
by Ganesa and Suryadasa ‘which are satisfactory and instructive’ and omit-
ting those which ‘are obscure and unsatisfactory’. 84 In other words Banerji
exercises his editorial prerogative and omits some proofs or demonstra-
tions, insisting that the omitted geometrical proofs for these formulas were
given in Euclid ii .5 and 9. Th e reason he off ers for omitting the ‘proofs’ of
Ganesa is because Banerji clarifi ed that he had introduced these proofs to
facilitate calculations required in §134 of the Lilavati.^85 Whatever may be
the reason, it is obvious that Banerji’s reading of these texts is located within
the ‘historiography of the absence of proof ’. 86
Colebrooke’s magnum opus was published in 1817 and the introduc-
tion to the work is hereaft er referred to as the ‘dissertation’, which is what
it is titled in any case. Very briefl y, I shall just mention the chapterization
of this work. Th e fi rst chapter consists of the defi nitions of technical terms.
Drawing upon these defi nitions the second chapter deals with numeration
and the eight operations of arithmetic, which included rules of addition and
subtraction, multiplication, division, obtaining the square of a quantity and
its square root, the cube and the cube root. Th e discussion up to Chapter 6
comprises the statement and exemplifi cation of arithmetical rules for
manipulating integers, and fractions. Th e examples provided illustrate
the diff erent operations. It is in Chapter 6 that we come to the plane
fi gures and it is here that §134 states the equivalent of the Pythagorean
Th eorem. 87
Th e discussion below will centre around rule §135 of the Lilavati in
Colebrooke’s translation, where Colebrooke suggests that Ganesa had83 Banerji 1927 : vi.
84 Banerji 1927 : xv.
85 Banerji 1927 : xvi.
86 An equally insightful exercise would be to see how and where Banerji’s text diff ers from
that of Colebrooke; on which portions of the text does Banerji fi nd it necessary to comment
upon Colebrooke’s translation and interpretation; and at what points does he insert his own
commentary and replace that of Colebrooke. Th is would be a separate project, suffi cient
though it be to point out that Banerji is more of a practising mathematician than Colebrooke.
87 C1817: 59.