|Born: about 830 in India
Died: about 890 in India
Prthudakasvami is best
known for his work on solving equations.
solution of a first-degree indeterminate equation by a method called
kuttaka (or "pulveriser") was given by Aryabhata I. This method of
finding integer solutions resembles the continued fraction process
and can also be seen as a use of the Euclidean algorithm.
Brahmagupta seems to have used a method involving continued fractions
to find integer solutions of an indeterminate equation of the type ax
+ c = by. Prthudakasvami's commentary on Brahmagupta's work is
helpful in showing how "algebra", that is the method of calculating
with the unknown, was developing in India. Prthudakasvami discussed
the kuttaka method which he renamed as "bijagnita" which means the
method of calculating with unknown elements.
see just how this new idea of algebra was developing in India, we
look at the notation which was being used by Prthudakasvami in his
commentary on Brahmagupta's Brahma Sputa Siddhanta. In this
commentary Prthudakasvami writes the equation 10x + 8 = x2 + 1 as:
yava 0 ya 10 ru 8
yava 1 ya 0 ru 1
Here yava is an abbreviation for yavat avad varga which means the
"square of the unknown quantity", ya is an abbreviation for yavat
havat which means the "unknown quantity", and ru is an abbreviation
for rupa which means "constant term". Hence the top row reads
0x2 + 10x + 8
while the second row reads
x2 + 0x + 1
The whole equation is
0x2 + 10x + 8 = x2 + 0x + 1
10x + 8 = x2 + 1.
by: J J O'Connor and E F Robertson