The main work of Brahmagupta

Brahmagupta

Brahmagupta was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta , written in 628 in Bhinmal...

, Brāhmasphuṭasiddhānta ("Correctly Established Doctrine of Brahma"), written c.628

628

Year 628 was a leap year starting on Friday of the Julian calendar. The denomination 628 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.- Asia :* January – Third Perso-Turkic War: Emperor...

, contains ideas including a good understanding of the mathematical

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 role of zero

0 (number)

0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...

, rules for manipulating both negative and positive numbers, a method for computing square root

Square root

In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...

s, methods of solving linear

Linear equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable....

 and some quadratic equation

Quadratic equation

In mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...

s, and rules for summing series

Series (mathematics)

A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely....

, 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
  Division by zero
  In mathematics, division by zero is division where the divisor is zero. Such a division can be formally expressed as a / 0 where a is the dividend . Whether this expression can be assigned a well-defined value depends upon the mathematical setting...
  
   is zero

The last of these rules is not correct as division by zero is undefined for a Field

Field (mathematics)

In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms...

; however it is notable that it was the earliest attempt to define division by 0.

External links

• http://wikisource.org/wiki/ब्रह्मस्फुटसिद्धान्त Text of some chapters of Brahma Sphuta Siddhanta in Devanagari
  Devanagari
  Devanagari |deva]]" and "nāgarī" ), also called Nagari , is an abugida alphabet of India and Nepal...
  
   ]
• Text of some chapters of Brahma Sphuta Siddhanta in Unicode Roman at GRETIL
  GRETIL
  The Göttingen Register of Electronic Texts in Indian Languages is a comprehensive repository of e-texts in Sanskrit and other Indian languages.It contains several texts related to Indology, such as philosophical texts...