The ''Brāhmasphuṭasiddhānta'' ("Correctly Established

Doctrine Doctrine (from la, doctrina, meaning "teaching, instruction") is a codification of beliefs or a body of teachings or instructions, taught principles or positions, as the essence of teachings in a given branch of knowledge or in a belief system ...

Brahma Brahma ( sa, ब्रह्मा, Brahmā) is a Hindu god, referred to as "the Creator" within the Trimurti, the trinity of supreme divinity that includes Vishnu, and Shiva.Jan Gonda (1969)The Hindu Trinity Anthropos, Bd 63/64, H 1/2, pp. 21 ...

", abbreviated BSS) is the main work of Brahmagupta, written c. 628. This text of mathematical astronomy contains significant mathematical content, including a good understanding of the role of

zero 0 (zero) is a number representing an empty quantity. In place-value notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or ...

, rules for manipulating both

negative and positive numbers In mathematics, the sign of a real number is its property of being either positive, negative, or zero. Depending on local conventions, zero may be considered as being neither positive nor negative (having no sign or a unique third sign), or it ...

, a method for computing

square root In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or  ⋅ ) is . For example, 4 and −4 are square roots of 16, because . E ...

s, methods of solving

linear Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...

and

quadratic equation In algebra, a quadratic equation () is any equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where represents an unknown (mathematics), unknown value, and , , and represent known numbers, where . (If and then the equati ...

s, and rules for summing

series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used in ...

Brahmagupta's identity In algebra, Brahmagupta's identity says that, for given n, the product of two numbers of the form a^2+nb^2 is itself a number of that form. In other words, the set of such numbers is closed under multiplication. Specifically: :\begin \left(a^2 + n ...

, and Brahmagupta theorem. The book was written completely in verse and does not contain any kind of mathematical notation. Nevertheless, it contained the first clear description of the

quadratic formula In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, g ...

(the solution of the quadratic equation).Bradley, Michael. ''The Birth of Mathematics: Ancient Times to 1300'', p. 86 (Infobase Publishing 2006).

Positive and negative numbers

''Brāhmasphuṭasiddhānta'' is one of the first books to provide concrete ideas on

positive number In mathematics, the sign of a real number is its property of being either positive, negative, or zero. Depending on local conventions, zero may be considered as being neither positive nor negative (having no sign or a unique third sign), or it ...

negative number In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed m ...

s, and zero. Henry Thomas Colebrooke. ''Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara'', London 1817, p. 339
online
For example, it notes that the sum of a positive number and a negative number is their difference or, if they are equal, zero; that subtracting a negative number is equivalent to adding a positive number; that the product of two negative numbers is positive. Some of the notions of fractions differ from the modern

rational number In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ration ...

system. For example, Brahmagupta allows

division by zero In mathematics, division by zero is division (mathematics), division where the divisor (denominator) is 0, zero. Such a division can be formally expression (mathematics), expressed as \tfrac, where is the dividend (numerator). In ordinary ari ...

resulting in a fraction with a in the denominator, and defines . In modern mathematics, division by zero is undefined for any

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

References

External links

''Brahmasphutasiddhanta''
at

GRETIL The Göttingen Register of Electronic Texts in Indian Languages (GRETIL) is a comprehensive repository of e-texts in Sanskrit and other Indian languages. It contains several texts related to Indology Indology, also known as South Asian studies, is ...

(mathematical chapters: 12, 18-20, 21.17-23) * {{DEFAULTSORT:Brahmasphutasiddhanta Indian mathematics Mathematics manuscripts Sanskrit texts 7th-century manuscripts History of algebra Treatises Indian astronomy texts Brahmagupta