When was the  Brāhmasphuṭasiddhānta written?
1884234#0
The Brāhmasphuṭasiddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS)
is the main work of Brahmagupta, written c. 628. Τhis text of mathematical astronomy contains significant mathematical content, including a good understanding of the role of zero, rules for manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and quadratic equations, and rules for summing series, Brahmagupta's identity, and Brahmagupta’s theorem.
Brāhmasphuṭasiddhānta
59217#68
The Indian mathematician Brahmagupta (597–668 AD) explicitly described the quadratic formula in his treatise "Brāhmasphuṭasiddhānta" published in 628 AD, but written in words instead of symbols. His solution of the quadratic equation was as follows: "To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value."
This is equivalent to:
Quadratic formula
251478#9
In 628, the Indian mathematician Brahmagupta wrote "Brāhmasphuṭasiddhānta" which includes, among many other things, a study of equations of the form . In particular he considered what is now called Pell's equation, , and found a method for its solution. In Europe this problem was studied by Brouncker, Euler and Lagrange.
Quadratic form
297206#0
Brahmagupta () (born , died ) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the "Brāhmasphuṭasiddhānta" (BSS, "correctly established doctrine of Brahma", dated 628), a theoretical treatise, and the "Khaṇḍakhādyaka" ("edible bite", dated 665), a more practical text.
Brahmagupta
297206#4
In the year 628, at an age of 30, he composed the "Brāhmasphuṭasiddhānta" (the improved treatise of Brahma) which is believed to be a revised version of the received "siddhanta" of the Brahmapaksha school. Scholars state that he incorporated a great deal of originality to his revision, adding a considerable amount of new material. The book consists of 24 chapters with 1008 verses in the ārya metre. A good deal of it is astronomy, but it also contains key chapters on mathematics, including algebra, geometry, trigonometry and algorithmics, which are believed to contain new insights due to Brahmagupta himself.
Brahmagupta
1884234#1
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 (the solution of the quadratic equation).
Brāhmasphuṭasiddhānta
1741183#2
The "Zīj", written around 770, was based on a Sanskrit work, thought to be similar to the "Brāhmasphuṭasiddhānta". This work was brought to the court of al-Mansūr from Sindh, reportedly by a Sindhi astronomer named Kankah.
Yaʿqūb ibn Ṭāriq
185663#8
The "Brāhmasphuṭasiddhānta" of Brahmagupta (598–668) is the earliest known text to treat zero as a number in its own right and to define operations involving zero. The author could not explain division by zero in his texts: his definition can be easily proven to lead to algebraic absurdities. According to Brahmagupta,
Division by zero
1741105#3
Along with Yaʿqūb ibn Ṭāriq and his father he helped translate the Indian astronomical text by Brahmagupta (fl. 7th century), the "Brāhmasphuṭasiddhānta", into Arabic as "Az-Zīj ‛alā Sinī al-‛Arab"., or the "Sindhind". This translation was possibly the vehicle by means of which the Hindu numerals were transmitted from India to Islam.
Muḥammad ibn Ibrāhīm al-Fazārī
708399#27
Brahmagupta's Brāhmasphuṭasiddhānta is the first book that mentions zero as a number, hence Brahmagupta is considered the first to formulate the concept of zero. The current system of the four fundamental operations (addition, subtraction, multiplication and division) based on the Hindu-Arabic number system also first appeared in Brahmasphutasiddhanta. It was also one of the first texts to provide concrete ideas on positive and negative numbers.
List of important publications in mathematics