Bhaskaracharya and the Siddhanta Shiromani
Bhaskaracharya, also called Bhaskara II, was a 12th-century Indian mathematician and astronomer, and his Siddhanta Shiromani is a major astronomical treatise.
What it is
The work covers the mean and true planetary motion, eclipses, the mathematics of spherical astronomy and the calculations used in the calendar. It is organised in parts, including one on the mathematics of astronomy.
How it is worked out or read
Bhaskara's models were used in later Indian almanacs, and his work is one of the sources of the computational tradition. The site's calculations use modern models instead.
Where it appears on this site
See Aryabhata and astronomy and history of Jyotish.
Bhaskara II
Bhaskaracharya, often called Bhaskara II to distinguish him from an earlier astronomer of the same name, was born in 1114 CE. By his own statement he completed the Siddhanta Shiromani in 1150, at the age of thirty-six. He is associated with the town of Vijjadavida, and tradition links him with the astronomical school at Ujjain, which had earlier been associated with Varahamihira and Brahmagupta. His work is often regarded as the high point of the classical siddhanta tradition.
The four parts of the work
The Siddhanta Shiromani, meaning the crown jewel of siddhantas, is usually described in four parts. The Lilavati deals with arithmetic and measurement, and is famous for its problems written in graceful verse. The Bijaganita deals with algebra, including methods for solving certain classes of equations. The Grahaganita deals with the mathematics of planetary positions: mean and true motions, eclipses and conjunctions. The Goladhyaya deals with the sphere: the shape of the Earth, the celestial sphere, instruments and the reasoning behind the methods.
Some scholars treat the Lilavati and Bijaganita as separate works, and the Grahaganita and Goladhyaya as the Siddhanta Shiromani proper. Either way, the four together form one programme of study.
The Karanakutuhala
In 1183 Bhaskara wrote the Karanakutuhala, a practical handbook that simplified the calculations of the Siddhanta Shiromani for everyday calendar use. Works of this kind, called karana texts, start from a recent epoch so that a calculator does not have to count days from the beginning of a vast cosmic age. The Karanakutuhala remained in use for centuries for preparing almanacs, which shows how directly this astronomy fed into the panchang.
What a modern reader can take from him
Bhaskara's work shows the siddhanta tradition at its most mature: careful about method, willing to explain its reasoning and attentive to teaching. The Goladhyaya in particular insists that a student should understand why a rule works, not only how to apply it. That attitude is useful for any modern student of Jyotish who wants to know where the numbers in a chart come from before reading meanings into them.
Where to read him today
Translations of the Lilavati and of parts of the Goladhyaya are available in English and Hindi, and several older editions are in the public domain. A reader who starts with the Lilavati will meet the arithmetic that underlies calendar work, set out in problems that were meant to be enjoyed as well as solved.