Th e Sanskrit tradition: the case of G. F. W. Th ibaut 271
For instance, Th ibaut examined the many various caturaśrakaran. a –
methods to construct a square – given by diff erent authors. 43 Ā p a s t a m b a ,
Baudhāyana and Kātyāyana each gave two methods to accomplish this
task. I will not expound these methods here; they have been explained
amply and clearly elsewhere. 44 Th ibaut also remarked that in some cases,
Baudhāyana gives a rule and its reverse, although the reverse cannot be
grounded in geometry. Such is the case with the procedure to turn a circle
into a square:
Considering this rule closer, we fi nd that it is nothing but the reverse of the rule
for turning a square into a circle. It is clear, however, that the steps taken according
to this latter rule could not be traced back by means of a geometrical construction,
for if we have a circle given to us, nothing indicates what part of the diameter is to
be taken as the atiśayat. r. tīya (i.e. the segment of the diameter which is outside of
the square). 45
I am no specialist in śulba geometry and do not know if we should see the
doubling of procedures and inverting of procedures as some sort of ‘proofs’,
but at the very least they can be considered ef forts to convince the reader
that the procedures were correct. Th e necessity within the śulbasūtra s to
convince and to verify has oft en been noted in the secondary literature, but
has never fully or precisely studied. 46 Th ibaut, although puzzled by the fact,
never addressed this topic. Similarly, later historians of mathematics have
noted that commentators on the śulbasūtra s sought to verify the procedures
while setting aside the idea of a regular demonstration in these texts. Th us
Delire notes that Dvārakānātha used arithmetical computations as an easy
method of verifi cation (in this case of the Pythagorean Th eorem). 47 Th e use
of two separate procedures to arrive at the same result, as argued in another
chapter in this volume, 48 could have been a way of mathematically verifying
the correctness of an algorithm – an interpretation that did not occur to
Th ibaut.
43 Th ibaut 1875 : 28–30.
44 Th ibaut 1875 : 28–30; Bag and Sen 1983 in CESS , vol. 1; Datta 1993 : 55–62; and fi nally Delire
2002 : 75–7.
45 Th ibaut 1875 : 35.
46 See for instance Datta 1993 : 50–1.
47 Delire 2002 : 129.
48 See Keller, Chapter 14 , this volume.