《婆罗摩历算书》中有四章半讲的是纯数学，第12章讲的是演算系列和少许几何学。第18章是关于代数，婆羅摩笈多在这里引入了一个解二次丟番圖方程如nx² + 1 = y²的方法。
當中方程 的解是 ，而色是指常數項c和e。他然後進一步給了二次方程兩個解：
這裏婆羅摩笈多所給的頭 個自然數的平方和立方的算法，分別為 和
婆羅摩笈多的定義不實用，比如他認為 。而他並沒有保證 且 的說法是對的。
設一個圓內接四邊形的四條邊為p﹑q﹑r﹑s，大約面積為 ，設 ，準確面積則為 。
- 英文原文是：“18.44. Diminish by the middle [number] the square-root of the rupas multiplied by four times the square and increased by the square of the middle [number]; divide the remainder by twice the square. [The result is] the middle [number].”
- 英文原文是：“18.45. Whatever is the square-root of the rupas multiplied by the square [and] increased by the square of half the unknown, diminish that by half the unknown [and] divide [the remainder] by its square. [The result is] the unknown.”
- 英文原文是：“12.20. The sum of the squares is that [sum] multiplied by twice the [number of] step[s] increased by one [and] divided by three. The sum of the cubes is the square of that [sum] Piles of these with identical balls [can also be computed]”
- 英文原文是：“18.30. [The sum] of two positives is positives, of two negatives negative; of a positive and a negative [the sum] is their difference; if they are equal it is zero. The sum of a negative and zero is negative, [that] of a positive and zero positive, [and that] of two zeros zero. [...]”
- 英文原文是：“18.32. A negative minus zero is negative, a positive [minus zero] positive; zero [minus zero] is zero. When a positive is to be subtracted from a negative or a negative from a positive, then it is to be added [...]”
- 英文原文是：“18.33. The product of a negative and a positive is negative, of two negatives positive, and of positives positive; the product of zero and a negative, of zero and a positive, or of two zeros is zero.”
- 英文原文是：“18.34. A positive divided by a positive or a negative divided by a negative is positive; a zero divided by a zero is zero; a positive divided by a negative is negative; a negative divided by a positive is [also] negative.”
- 英文原文是：“18.35. A negative or a positive divided by zero has that [zero] as its divisor, or zero divided by a negative or a positive [has that negative or positive as its divisor]. The square of a negative or of a positive is positive; [the square] of zero is zero. That of which [the square] is the square is [its] square-root.”
- 英文原文是：“12.21. The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral. The accurate [area] is the square root from the product of the halves of the sums of the sides diminished by [each] side of the quadrilateral.”
- 英文原文是：“12.40. The diameter and the square of the radius [each] multiplied by 3 are [respectively] the practical circumference and the area [of a circle]. The accurate [values] are the square-roots from the squares of those two multiplied by ten.”
- Seturo Ikeyama. Brāhmasphuṭasiddhānta (CH. 21) of Brahmagupta with Commentary of Pṛthūdhaka, critically edited with English translation and notes. INSA. 2003.
- Brahmagupta biography. School of Mathematics and Statistics University of St Andrews, Scotland. [2013-07-15].
- David Pingree. Census of the Exact Sciences in Sanskrit (CESS). American Philosophical Society. : p254.
- Boyer. The Arabic Hegemony. 1991: 226.
By 766 we learn that an astronomical-mathematical work, known to the Arabs as the Sindhind, was brought to Baghdad from India. It is generally thought that this was the Brahmasphuta Siddhanta, although it may have been the Surya Siddhanata. A few years later, perhaps about 775, this Siddhanata was translated into Arabic, and it was not long afterwards (ca. 780) that Ptolemy's astrological Tetrabiblos was translated into Arabic from the Greek.缺少或
- （Plofker 2007，pp.428–434）
- （Plofker 2007，pp.421–427）
- Boyer. China and India. 1991: 220.
However, here again Brahmagupta spoiled matters somewhat by asserting that , and on the touchy matter of , he did not commit himself:缺少或
- （Plofker 2007，p.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.
- Brahmagupta, and the influence on Arabia. School of Mathematical and Computational Sciences University of St Andrews. 2002-05 [2013-07-15].