244 dhruv raina
Colebrooke begins by pointing out that Aryabhata was the fi rst of the
Indian authors known to have treated of algebra. As he was possibly a con-
temporary of Diophantus, the issue was important for drawing an arrow of
transmission from Alexandria to India or vice versa. Colebrooke leaves the
issue of the invention of algebra open by suggesting that it was Aryabhata
who developed it to the high level that it attained in India; 67 this science he
called an ‘analysis’. 68 It is here for the fi rst time that a portion of the Indian
mathematical tradition is referred to as analysis, and it is important to get
to the sense in which he employs the term.
It is noticed that the use of a notation and algorithms is crucial to this
algebraic practice; which Colebrooke then proceeds to elaborate upon, sub-
sequently stating the procedures not merely for denoting positive or negative
quantities, or the unknowns but of manipulating the symbols employed. 69
An important feature of this algebra is that all the terms of an equation do
not have to be set up as positive quantities, there being no rule requiring that
all the negative quantities be restored to the positive state. Th e procedure
is to operate an equal subtraction ( samasodhana ) ‘for the diff erence of like
terms’. Th is operation is compared with the muqabalah employed by the
Arab algebraists. 70 Th e presence of this ‘analytic art’ among the Indians was
apparent from the mathematical procedures evident in the variety of math-
ematical texts that were becoming available to the Indologists.
Th e analytic art comprised procedures that included, according to
Colebrooke, the arithmetic of surd roots, the cognizance that when a fi nite
quantity was divided by zero the quotient was infi nite, an acquaintance
with the procedure for solving second degree equations and ‘touching
upon’ higher orders, solving some of these equations by reducing them
to the quadratic form, of possessing a general solution of indetermi-
nate equations in the fi rst degree. And fi nally, Colebrooke fi nds in the
Brahmasphutasiddhanta (§18:29–49) and Bija-Ganita (§75–99) a method
for obtaining a ‘multitude’ of integral solutions to indeterminate second-
degree equations starting from a single solution that is plugged in. It was
left to Lagrange to show that problems of this class would have solutions
that are whole numbers. 71 Th e analytic art of the Indians or algebraic67 Th e high level of attainment was ascribed to the ability of the Indian algebraists to solve
equations involving several unknowns; and of possessing a general method of solving
indeterminate equations of the fi rst degree (C1817: x).
68 C1817: ix.
69 C1817: x–xi.
70 C1817: xiv.
71 C1817: xiv–xv.