The mathematician of Brahmagupta.

The indian mathematician Brahmagupta Born on  598 AD, died 665 AD. Brahmagupta s father's name was Jisnu Gupta.  Grandfather's name is Bishnugupta.  It is speculated that Brahmagupta was born in a place called Bhinmal, the real name being Bhinmala.

 Contributions of Brahmagupta: 628 AD He wrote Brahmasputa Siddhanta.  (Majumdar, 1995).  Divided into 25 chapters. 

 • 655 AD: Khandakhadyaaka wrote a tragedy (Majumdar, 1995) The 12th chapter of the Brahmaputra decision is the mathematics chapter.

*He defined 0 (2010) in the Bratmafoot decision.  The result obtained by subtracting the number from the corner is zero (0).  That is, if a is a number in a corner, then a - a = 0.

*  He mentions some religions of zero.
 * If a zero angle is added or subtracted with a number, the number remains unchanged;  And if the number in the corner is multiplied by zero.  Then the product is zero.  That is, if a is a number.
 (i) a + 0
 (ii) a - 0 = a
 (iii) a x 0 = 0
* The result of dividing zero by zero is called zero.  But if you divide the number in the corner by zero.  Is a fraction whose denominator is zero.
  That is 0/ 0 = 0 (this definition is not acceptable) = a  /0 = a/0

 Chapter 18 of the Brassfoot Decision he mentions some mathematical rules (did not use terminology).  He used the language of the city.  Used Fortunes for the positive and Debts for the negative.


1. Debt separation zero = debt
 2. Wealth - zero = wealth
3. Zero - zero = zero
 4. ‘Dividing a debtor from zero is‘ fortune ’.
 5. Dividing ‘wealth’ from zero is ‘Debt’.
  6. Multiplying ‘wealth’ or ‘debt’ with zero, the product will be zero. 
7. Multiplying zero by zero will be zero. 
8. The product or quotient of two ‘wealths’ will be ‘wealth’ i.e. the product of two positive numbers will be positive.
  9, The product or quotient of two ‘debts’ will be a ‘wealth’ i.e. the product or quotient of two negative sums will be a positive sum. 
10. The product or quotient of a ‘loan’ and a wealth will be a ‘loan’ i.e. a negative amount and the product or quotient of a positive amount will be a negative amount.
 11. The product or quotient of a ‘wealth’ and a ‘debt’ will be a ‘debt’ i.e. a positive amount and the product or quotient of a negative amount will be a positive amount.
 • Brasnagupta mentions 4 methods of multiplication.  These are:
(i) Gasutrik
 (ii) Bang
 (iii) Veda
(iv) Isht 
Some of the equations solved by  Brahmagupta are presented
(i) Equation in one unknown quan tity
(in) ax +  c = bx + d
(ii) He presented the method of solving indefinite equations.  by ax+c=by
(iii) He made some algebraic symbols and discussed the method of solving quadratic equations. 
(iv) He solved the unexpressed quadratic equation whose size is (Stillwell, 2004):

ax² + c=y^2

 ax² - c=y^2    Nx² + 1=y^2  (pell -equation)

example : 8x²+1=y^2
solved  : (x,y)= (1,3),(6,17),(35,99),(204,577)
(v)11x²+1=y^2,  its quadratic equation  he provied.