Brahmasphutasiddhanta

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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.

[edit] 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.