Brahmagupta is one ofthe most
distinguished Mathematician and
Astronomer in the 7th century. He was the
son of Vishnu Gupta and was born in
Punjab. He lived in Ujain and worked in
great astrological laboratory
at
Ujain.
He
wrote his first book Brahm-sp-hutasidhanta' or 'Brahmasidhanta' at this
place at the age of 30. It consists of 21
knowledge
arithmetic, geometry, algebra and
astronomy.
chapter
and contains great
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on
He gave 22/7 as value of t and suggested 3
as a practical value. In chapter an arithmetic,
he has given a detailed account of progression,
areas of triangles and quadrilaterals, volumes
of trenches and slopes and amount of grains, in
heaps etc. He also invented four different
methods of
multiplication, namely
Gan Mutrika
Khanda
Bheda
Ista
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inversion
He explained the method
the first time in the following way:
of
for
"Beginning from the end, make the
multiplier divisor, the divisor multiplier,
make addition subtraction and subtraction
addition, make square, square-root and
square-root. This gives the required
quantity."
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He gave the method of
cubing
extracting square root as well as cube
squaring,
root. Also he gave the exact concept of
zero. He defined it as a-a=0. He gave
the following rules to deal with negative
numbers,
Negative multiplied or divided by
2.
negative becomes positive.
Negative subtracted from zero is
also positive.
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He solved the equation x-10x=-9 by a
rule which is equivalent to the quadratic
formula. He multiplied the constant
term by the coefficient of x, added
the square of half the coefficient of
X and found the square root of this
sum. He then subtracted half the
coefficient of x and divided it by the
coefficient of x, The quotient gave
the solution of the eguation.
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His works on arithmetic includes
integer, fractions, progressions, barter,
simple interest, the mensuration of plane
figures and problems on volumes.
He found the formula for addition of
geometrical progression,
a+ar+ar+..n terms
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=
a(r")/r-1
I n the field
upon the
of geometry, he elaborated
properties of right angled
triangles and for the first time gave the
solution of a right angled triangle by giving
the following value of its sides;
a=2mn; b=m2-n; c=m+n? and
a=m;
h=(m/n-n)/2; c=(m/n+n)/2 where
m and n are two in equal integers.
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He also gave, for the first
time, suggestions for the
construction of a cyclic quadrilateral having its sides as
rational numbers. Two of the following formulae given by
him
1
are
in use
even
at
present,
cyclic quadrilateral havinga, b, c and d
of
a
sides is equal to N(s-a)(s-b)(s-c)(s-d) where
Area
as
ts
a+b+c+d=2s, s is perimeter of the quadrilateral.
Length of one of the diagonals of the cyclic
quadrilateral is equal to (bc+ad/ab+cd) (ac+bd)
Length of the other diagonal is equal to
(ab+cd/bC+ad)(ac+bd)
Brahmagupta
was
the first Indian writer, who
applied algebra to astronomy. He was a great
mathematician, an astronomer and a poet
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