The main work of Brahmagupta, Brahmasphuta-siddhanta (The Opening of the Universe), written in the year c.628, contains some remarkably advanced ideas, including a good understanding of the mathematical role of zero, rules for manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and some quadratic equations, and rules for summing series, Brahmagupta's identity, and the Brahmagupta’s theorem. The book was written completely in verse.

Brahmasphuta-siddhantas rules for numbers

Brhmasphuta-siddhanta is one of the first mathematical books to provide concrete ideas on positive numbers, negative numbers, and zero. He wrote the following rules:[1]

• The sum of two positive quantities is positive
• The sum of two negative quantities is negative
• The sum of zero and a negative number is negative
• The sum of zero and a positive number is positive
• The sum of zero and zero is zero.
• The sum of a positive and a negative is their difference; or, if they are equal, zero
• In subtraction, the less is to be taken from the greater, positive from positive
• In subtraction, the less is to be taken from the greater, negative from negative
• When the greater however, is subtracted from the less, the difference is reversed
• When positive is to be subtracted from negative, and negative from positive, they must be added together
• The product of a negative quantity and a positive quantity is negative
• The product of a negative quantity and a negative quantity is positive
• The product of two positive, is positive.
• Positive divided by positive or negative by negative is positive
• Positive divided by negative is negative. Negative divided by positive is negative
• A positive or negative number when divided by zero is a fraction with the zero as denominator
• Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator
• Zero divided by zero is zero

The last of these is incorrect; however it is notable that it was the earliest attempt to define division by 0.[2]

References

1. ^ Henry Thomas Colebrooke. Algebra with Arithmetic of Brahmagupta and Bhaskara. London 1817.
2. ^ Kaplan, Robert (1999). The nothing that is: A natural history of zero. New York: Oxford University Press. pp. 68–75. ISBN 0195142373. 

External links

• Text of some chapters of Brahma Sphuta Siddhanta in Devanagari
• Text of some chapters of Brahma Sphuta Siddhanta in Unicode Roman
• http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Brahmagupta.html