The main work of Brahmagupta
, Brahmasphuta-siddhanta (The Opening of the Universe)
, written in the year 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:
- 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.