The first three chapters of the Grahalāghava of Gaṇeśa Daivajña : edition, translation, and mathematical and historical analysis.

The field of history of mathematics allows mathematicians the ability to trace patterns of mathematical development throughout human history, and often reconnect them to the inspirations and motivations that led to mathematical progress. The narrative of mathematical development in India, specifically the second millennium Indian exact sciences, has only been a topic of close study in recent years. This classical era of mathematical astronomy in India featured a diverse expanse of calculatory works devoted to predictive astronomy, or finding the timings, locations, and appearances of celestial phenomena. The choice of parameters for time divisions and number of cyclic planetary revolutions for these calculations primarily differentiated the different schools during this era. One such school, the Gaṇeśapakṣa, was founded by Gaṇeśa Daivajña (b. 1507 CE) of Nandigrāma, India with the composition of his text, the Grahalāghava (“brevity [in calculations] of the planets”) (1520 CE). The text featured innovative modifications to the previously established time divisions and mean longitude calculations, as well as the ambitious removal of trigonometric computations in all stated formulas. These parameters and procedures inspired a sizable proliferation of commentaries and astronomical tables through much of the second half of the second millennium, with many extant manuscripts and much relevance to astrology in India today. In this thesis, we use critical editions and manuscripts of the Grahalāghava and earlier astronomical works to study the first three chapters of the Grahalāghava with the aim of exploring Gaṇeśa’s trigonometryapproximating techniques and tracing potential influences of earlier works to contextualize the Grahalāghava in the larger tradition