In the history of exchanges between Islamicate and Sanskrit astral sciences, Nityānanda's Siddhāntasindhu (c. early 1630s), composed at the court of the Mughal emperor Shāh Jahān (r. 1628–58), is among the earliest examples of a Persian astronomical text translated into Sanskrit. In a recent publication, Misra (2021) describes the sociohistorical context in which Nityānanda translated Mullā Farīd's Zīj-i Shāh Jahānī (c. 1629/30) into Sanskrit, and among other things, provides parallel comparative editions (accompanied by English translations) of the Persian and Sanskrit text describing the computation of true declination of a celestial object.


While Misra's paper focuses on the linguistic aspects of the translation process, the present paper studies the mathematics of the three methods of computing the true declination vis-à-vis Nityānanda's recension of his Sanskrit translations from his germinal Siddhāntasindhu to his chef d'œuvre the Sarvasiddhāntarāja (1638). The paper begins by discussing the transformation of the Sanskrit text from the Siddhāntasindhu Part II.6 to the spaṣṭakrāntyādhikāra `topic on true declination' in the gaṇitādhyāya `chapter on computations' (henceforth identified as I.spa·krā) of his Sarvasiddhāntarāja. The metrical verses of Sarvasiddhāntarāja I.spa·krā are edited and translated into English for the very first time. A large part of this paper focuses on the technical (mathematical) analysis of the three methods of true declination, and includes detailed explanatory and historical notes. The paper also includes several technical appendices and an indexed glossary of technical terms.