↑ Bhattacharyya 2011: "Brahmagupta, one of the most celebrated mathematicians of the East, indeed of the world, was born in the year 598 c.e., in the town of Bhillamala during the reign of King Vyaghramukh of the Chapa Dynasty."
1 2 Boyer (1991, "China and India" p. 221) "he was the first one to give a general solution of the linear Diophantine equation ax + by = c, where a, b, and c are integers. [...] It is greatly to the credit of Brahmagupta that he gave all integral solutions of the linear Diophantine equation, whereas Diophantus himself had been satisfied to give one particular solution of an indeterminate equation. Inasmuch as Brahmagupta used some of the same examples as Diophantus, we see again the likelihood of Greek influence in India – or the possibility that they both made use of a common source, possibly from Babylonia. It is interesting to note also that the algebra of Brahmagupta, like that of Diophantus, was syncopated. Addition was indicated by juxtaposition, subtraction by placing a dot over the subtrahend, and division by placing the divisor below the dividend, as in our fractional notation but without the bar. The operations of multiplication and evolution (the taking of roots), as well as unknown quantities, were represented by abbreviations of appropriate words."
↑ Brahmasputha Siddhanta, Translated to English by H.T Colebrook, 1817 AD
↑ Plofker (2007, tr. 422) The reader is apparently expected to be familiar with basic arithmetic operations as far as the square-root; Brahmagupta merely notes some points about applying them to fractions. The procedures for finding the cube and cube-root of an integer, however, are described (compared the latter to Aryabhata's very similar formulation). They are followed by rules for five types of combinations: [...]
↑ Plofker (2007, tr. 423) Here the sums of the squares and cubes of the first n integers are defined in terms of the sum of the n integers itself;
↑ Kaplan, Robert (1999). The Nothing That Is: A Natural History of Zero. London: Allen Lane/The Penguin Press. tr. 68–75. Bibcode:2000tnti.book.....K.
↑ Boyer (1991, tr. 220): However, here again Brahmagupta spoiled matters somewhat by asserting that 0 ÷ 0 = 0, and on the touchy matter of a ÷ 0, he did not commit himself.
↑ Stillwell (2004, tr. 44–46): In the seventh century CE the Indian mathematician Brahmagupta gave a recurrence relation for generating solutions of x2 − Dy2 = 1, as we shall see in Chapter 5. The Indians called the Euclidean algorithm the "pulverizer" because it breaks numbers down to smaller and smaller pieces. To obtain a recurrence one has to know that a rectangle proportional to the original eventually recurs, a fact that was rigorously proved only in 1768 by Lagrange.
↑ Plofker (2007, tr. 424) Brahmagupta does not explicitly state that he is discussing only figures inscribed in circles, but it is implied by these rules for computing their circumradius.
