Brahmasphutasiddhanta

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:[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.

References

1. ^ Henry Thomas Colebrooke. Algebra with Arithmetic of Brahmagupta and Bhaskara. London 1817.

External links

Brahmagupta (ब्रह्मगुप्त) ( ) (598–668) was an Indian mathematician and astronomer.
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7th century · 8th century
590s 600s 610s 620s 630s 640s 650s
625 626 627 628 629 630 631
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Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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0 (zero) is both a number and a numerical digit used to represent that number in numerals. It plays a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures.
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A negative number is a number that is less than zero, such as −3. A positive number is a number that is greater than zero, such as 3. Zero itself is neither positive nor negative.
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In mathematics, a square root of a number x is a number r such that , or in words, a number r whose square (the result of multiplying the number by itself) is x.
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A linear equation is an equation in which each term is either a constant or the product of a constant times the first power of a variable. Such an equation is equivalent to equating a first-degree polynomial to zero.
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In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is



where a ≠ 0. (For a = 0, the equation becomes a linear equation.
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In mathematics, a series is often represented as the sum of a sequence of terms. That is, a series is represented as a list of numbers with addition operations between them, for example this arithmetic sequence:

1 + 2 + 3 + 4 + 5 + ... + 99 + 100.

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In algebra, Brahmagupta's identity, also sometimes called Fibonacci's identity, implies that the product of two sums of two squares is itself a sum of two squares. In other words, the set of all sums of two squares is closed under multiplication.
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