Crown of Treatises: Chapter on Mathematics

...has merely performed a salutation. However, the complete planetary mathematicsoriginal: "Grahaganita"; the mathematical calculations used to determine the positions and motions of celestial bodies. certainly existed; otherwise, why would Aryabhata and Brahmagupta consider it the root of their own systems? The inaccuracies in the mathematics were well-known, which is why Brahmagupta explicitly wrote:

"The planetary mathematics spoken by Brahma had, over a great length of time, become decayed. Therefore, it is now being clearly stated by Brahmagupta, the son of Jishnu. Having calculated the most accurate correctionsoriginal: "Beeja"; algebraic corrections applied to astronomical formulas to match observed reality. using instruments such as the sighting-tube, the final determinations and predictions should be made from the planets thus corrected." original: "Brahmoktam grahaganitam mahata kalena yatkhilibhutam..."

From ancient times until today, four types of Brahma-Siddhanta have been known:
(1) That included within the Pancha-Siddhantika.
(2) That included within the Vishnudharmottara Purana.
(3) That included within the Shakalya Samhita. The catalog of Sanskrit manuscripts of the Bengal Asiatic Society mentions the name 'Shakalya Samhita'. Ranganatha Daivajna has quoted two or four verses from this Samhita in his commentary on the Surya Siddhanta (Chapter on Planetary Conjunctions, Verse 14). It contains 6 chapters and 764 verses. Brahma gave these instructions to Narada. Besides astronomical theory, it also covers auspicious timingoriginal: "Muhurta"; the selection of the best time to perform a specific ritual or action., hence it was named a 'Samhita'. It is based on the Pancha-Siddhantika. Mr. Dixit determines its composition date to be around 743 Saka era (821 CE).

(4) Brahmagupta’s Brahma-Sphuta-Siddhanta.

Prithudaka Swami, the ancient commentator on the Brahma-Siddhanta, wrote that "the Brahma-Siddhanta within the Vishnudharmottara Purana is the original source for Brahmagupta." The system in this Purana is likely a reflection of the extremely ancient Paitamaha Siddhanta. It should be observed that the Paitamaha Siddhanta—which Brahma extracted from the Vedas—became the root for the systems of Aryabhata, Brahmagupta, and finally Bhaskara. In this way, the Veda itself is the root of astronomyoriginal: "Jyotish"; the traditional Indian science of astronomy and astrology.. Dada Bhai, the commentator on the Surya Siddhanta, wrote in his work Kiranavali that Brahmagupta’s system is merely an expanded version of the Paitamaha Siddhanta.