Th e Sanskrit tradition: the case of G. F. W. Th ibaut 267
Th is geometrical basis distinguished the śulbasūtra s from medieval or
classical Indian mathematical treatises. Once again, Th ibaut took this occa-
sion to show his preference for geometry over arithmetic:
Clumsy and ungainly as these old sūtra -s undoubtedly are, they have at least the
advantage of dealing with geometrical operations in really geometrical terms, and
are in this point superior to the treatment of geometrical questions which we fi nd
in the Līlāvatī and similar works. 32
As is made clear from the above quotation, Th ibaut was a presentist his-
torian of science who possessed a set of criteria which enabled him to judge
the contents and the form of ancient texts. In another striking instance,
Th ibaut gives us a clue that Euclid is one of his references. Commenting on
rules to make a new square of which the area is the sum or the difference of
two known squares, Th ibaut states in the middle of his own translation of
Baudhāyana’s śulbasūtra s:
Concerning the methods, which the Śulvasūtras teach for caturasrasamāsa (sum of
squares) and caturasranirhāra (subtraction of squares), I will only remark that they
are perfectly legitimate; they are at the bottom the same which Euclid employs. 33
Contemptuous as he may be of the state of Indian mathematics, Th ibaut did
not believe that the śulbasūtra s were infl uenced by Greek geometry. 34
For Th ibaut, history of mathematics ought to reconstruct the entire
deductive process from the origin of an idea to the way it was justifi ed.
Although later commentaries may include some useful information, they
do not give us the key to understanding how these ideas were developed
at the time when the treatises were composed. Th is lack of information
provoked Th ibaut to complain about Indian astronomical and mathe-
matical texts.
Th ibaut clearly considered the texts to have been arranged haphazardly
because the order of the rules do not obey generative logic. He thus defi ned
his task: ‘I shall extract and fully explain the most important sūtra -s (.. .)
and so try to exhibit in some systematic order the knowledge embodied in
these ancient sacrifi cial tracts.’ 35 H e r e , Th ibaut assumed that these works –
not treatises but ‘tracts’ (presumably with derogatory connotations) – are
not clear and systematic. Further, Th ibaut felt the need to disentangle
(‘extract’) the knowledge they contain.
32 Th ibaut 1875 : 60.
33 Th ibaut 1877: 76. Translations within brackets are mine.
34 Th ibaut 1875 : 4. Th is however was still being discussed as late as Staal 1999.
35 Th ibaut 1875 : 5.