Page 297 of: Glories of India (Culture and Civilization)

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INDIAN CULTURE AND CIVILIZATION
equations of the first degree (ax + by = c). It
defines that 'the product of three equal numbers is a
cube and it also has twelve edges. His notation is
expressed in consonants, viz. K and M for 1 to 25, Y to
H for 30 to 100, vowels denoting multiplication by powers
of 100, A being 100 and B 1000.
Brahmagupta's work covers 'the ordinary arith-
metical operations, square and cube rules, rule of three,
interest, progressions, geometry, including treatment
of the rational right-angled triangle, and the elements
of the circle, elementary mensuration of solids, shadow,
problems, negative and positive quantities, cipher,
surds, simple algebraic identities, indeterminate equa-
tions of the first and second degrees (in considerable
detail), and simple equations of the first and second
degrees, and cyclic quadrilaterals being specially
treated.'
The Ganita-sara-sangraha (9th century) of Mahavirä-
charya gives many examples of solutions of indeter-
minates but not the cyclic method of Brahmagupta ;
introduces geometrical progressions, and alone deals
with ellipses, but has no formal algebra. The Trisati
of Sudhana (born 991) deals, in addition, with quadratic
equations. The Bija-ganita of Bhaskaracharya, which
agrees with Brahmagupta, contains the fullest and
most systematic account of algebra, and his Lilavati
includes combinations. The Bakhshali Ms. of the 3rd
or 4th century also refers to Hindu mathematics.
Professor Keith does not believe in the Greek
influence on Indian Mathematics. "The facts are that,
as regards indeterminates equations, the Greeks
by the 4th century had achieved rational solutions,
not necessarily integral, of the
the
equations of the
first and second degree and of some cases of the third
degree. The Indian records go distinctly beyond this.
Brahmagupta shows a complete grasp of the integral
solution ax byc, and indicates the method of
composition of the solution of on "
= q. Bhaskarā-
charya adds the cyclic method. The combination of
these two methods gives integral solutions, the finest
thing achieved in the theory of these numbers. "To find an
ultimate Greek origine for these discoveriese," concludes
Professor Keith, “seems due rather to a parti pris
than to justice."
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