Geometry of prāṇakalāntara in the Lagnaprakaraṇa

The prāṇakalāntara, which is the difference between the longitude of a point on the ecliptic and its corresponding right ascension, is an important parameter in the computation of the lagna (ascendant). Mādhava, in his Lagnaprakaraṇa, proposes six different methods for determining the prāṇakalāntara. Kolachana et al. (Indian J Hist Sci 53(1):1–15, 2018) have discussed these techniques and their underlying rationale in an earlier paper. In this paper, we bring out the geometric significance of these computations, which was not fully elaborated upon in the earlier study. We also show how some of the sophisticated relations can be simply derived using similar triangles.