The History of Mathematical Proof in Ancient Traditions

(Elle) #1

240 dhruv raina


fragments of the works of Bhaskara and Brahmagupta before proceeding to
fi nalize versions of the three texts translated. But the enormous task was to
fi nalize and authenticate a version as the version of these texts. Th e central
question then was: how were the fragments of the texts to be ordered into
a sequence or other fragments spliced into appropriate sections of the
sequence of fragments in order to complete the collation of the text. His
native interlocutors were thus assigned the task of providing him with an
exhaustive commentary(ies) on these texts and most certainly worked with
him through the process of translation. Th e larger the set of commentaries
available on a given text, say the Lilavati , the greater the importance of the
text within the canon. Th e commentaries themselves served two exceed-
ingly important functions. In the fi rst instance the commentaries were
employed to identify the missing portions of the fragments available, and
to fi x the sequence of chapters. In other words it is through the commen-
taries that the text was fi nalized. Second, the commentaries were employed
to illustrate and explain semantically and technically obscure portions and
procedures expounded in the main text.
A typical page of Colebrooke’s translation thus comprises an upper half
or two-thirds that are translations from the Sanskrit of fi nalized versions
of the texts of Bhaskara and Brahmagupta, while the lower half or third
comprises: (1) Colebrooke’s explication of the text when need be, with ref-
erences to other texts, which is done with footnotes, (2) translations from
one or several commentaries that clarify the meaning of a term or terms
or procedures mentioned in the portion of the text on the upper portion
of the page, but at no point in Colebrooke’s text is the entire commentary
translated. In fact the text comprises translations from portions of several
commentaries, and it is Colebrooke who decided which part of one of
several commentaries or portions of several commentaries best elaborates
or clarifi es a portion of the master text being translated. But the com-
mentaries are internally paired off against each other in order to arrange
chronologically the commentaries and thus provide a diachronic relation
between them.
Colebrooke drew upon a rich commentarial tradition while working
on his translation of the Lilavati. Th e fi rst of these was a commentary by
Gangādhara dated ad 1420. Th e commentary was limited to the Lilavati ,
but as Colebrooke informs us, it authenticated an important chapter from
the Bija-Ganita. 57 Further, Suryadasa’s Ganitámrita dated ad 1538 was
a commentary on the Lilavati and the Surya-pracāsa was a commentary

57 C1817: xxv.
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