Preface

The Brāhma Sphuṭa Siddhānta by Brahmagupta

When five hundred and fifty years of the Saka kings had passed, in the reign of the illustrious king Vyāghramukha, the ornament of the Chāpa dynasty:
The Brāhma Sphuṭa Siddhānta was composed by Brahmagupta, son of Jishnu, in thirty years, for the pleasure of virtuous mathematicians and astronomers.

According to this statement by the Acharya (Brahmagupta) in the Saṃjñādhyāya Chapter on Definitions of the Brāhma Sphuṭa Siddhānta, the year 520 of the Saka era marks the time of the Acharya's birth, and after thirty years had passed, he composed this astronomical treatise known as the Brāhma Sphuṭa Siddhānta. Many Western scholars have concluded that the village of Bhinmal in the Gurjara country was his birthplace. Even oral traditions of the astronomers of the Gurjara region confirm that the village now known as Bhinmal—formerly known as Bhillamala—was the birthplace of the Acharya. This village is currently famous, situated in the northwestern border of the Gurjara region, between the Malwa (Marwar) country and the south, located between Mount Abu and the Luni River, to the northwest of that mountain.

Brahmagupta composed the Brāhma Sphuṭa Siddhānta based on the Brahma Siddhānta contained in the Vishnudharmottara Purana. By correcting the ancient Brahma Siddhānta through observations made with instruments like the water-clock original: "नलिका" to ensure the calculation of planetary positions matched visual observation, Brahmagupta created the new Brāhma Sphuṭa Siddhānta.

The planetary mathematics spoken of by Brahma, which had become obscured over a great length of time,
is now being clearly spoken of by Brahmagupta, son of Jishnu.
Having perfected the mathematical foundations original: "बीज" (bīja) using instruments like the water-clock,
decisions and predictions must be made from these corrected planetary positions.

From these and similar statements, the context is clear. The commentary known as Tilaka, written by the four-veda scholar Pṛthūdaka, was famous, but it is not available in its entirety today. Dr. Colebrooke original: "कोलव्रूक" obtained that entire commentary (written by Pṛthūdaka), and on that basis, he published the English translation of the 12th and 18th chapters of this work, which are known as Vyakta Arithmetic and Avyakta Algebra, in the year 1756 of the Saka era.

1. It is the opinion of many that he was born into a Vaishya family and was the chief astronomer to the King of Rewa, Vyaghrabhateshwara.