Brahmagupta and the Brahmasphutasiddhanta
Brahmagupta was a seventh-century Indian mathematician and astronomer, and his Brahmasphutasiddhanta is a major early treatise, dated to 628 CE.
What it is
The work covers planetary models, the positions of the Moon and planets, and the arithmetic of the zero and negative numbers. It is among the early texts to treat zero as a number in its own right.
How it is worked out or read
Its astronomical methods influenced later Indian and Islamic astronomy. The site's calculations do not use his parameters, but the mathematical tradition is part of the background.
Where it appears on this site
Who Brahmagupta was
Brahmagupta was an Indian astronomer and mathematician of the seventh century CE. By his own account he composed the Brahmasphutasiddhanta in 628 CE, at the age of thirty, and he is associated with Bhillamala, the present Bhinmal in Rajasthan. Decades later, in 665 CE, he wrote the Khandakhadyaka, a shorter and more practical handbook for calendar calculation that remained in use for a long time.
His work belongs to the siddhanta phase of Indian astronomy, in which writers set out mathematical models for the motions of the Sun, Moon and planets, and rules for computing eclipses, conjunctions and the calendar.
What the Brahmasphutasiddhanta contains
The title means roughly the corrected or well-established treatise of Brahma, and the work presents itself as a revision of an older tradition. Its chapters cover the mean and true motions of the planets, the three questions of time, place and direction, lunar and solar eclipses, the rising and setting of planets, the Moon's crescent, conjunctions and astronomical instruments. Alongside these are chapters of pure mathematics.
Those mathematical chapters are the best known part today. They give rules for arithmetic with zero and with negative numbers, treated as quantities in their own right, together with methods for solving certain equations, including rules that later mathematicians developed further. Brahmagupta was also a sharp critic of some earlier astronomers, Aryabhata among them, and his disagreements are a useful window into the debates of the time.
Influence beyond India
In the eighth century, works in the tradition of Brahmagupta were translated into Arabic at the Abbasid court in Baghdad, where they became known under the name Sindhind. Through this route Indian astronomical tables and methods reached scholars in the Islamic world, and from there some ideas travelled further. The history is complex and the details of transmission are still studied, but Brahmagupta's place in it is well established.
Why a Jyotish reader should know the name
Every chart rests on calculation, and the siddhanta texts are where that calculation was first set out systematically in India. Knowing that Brahmagupta's methods underlie many later calendars helps a reader see that Jyotish has always depended on the best astronomy available in its time. Modern panchangs use modern astronomy instead of siddhanta tables, but they continue the same aim: to compute the positions of the sky as accurately as possible before any interpretation begins.