Textual analysis of ancient Indian mathematics (Q2813323)

This is an interesting paper on the recent analyses of Brahmagupta's discourse on the cyclic quadrilateral and Baudhāyana's approximate quadrature of the circle.NEWLINENEWLINEThe misconceptions, if any, about the ancient Indian mathematical texts such as Brahmagupta's \textit{Brāhmasphuṭasiddhānta} (BSS) or Baudhāyana's \textit{Śulbasūtra} (BSlS) need to be set aside by submitting them to a literary analysis. To understand the text, not only the content is important, but also the methodology and the reason for the usage of a specific expression.NEWLINENEWLINEThe author has taken four examples for his study. BSS \((*4.1)\) for explaining the \textit{tricaturbhuja}, BSS XII 30--31 \((*4.2)\) for the perpendicularity, BSS XII 24 \((*4.4)\) for the redundancy and BSlS I.59 \((*4.3)\) for the quadrature rule. The \textit{tricaturbhuja} BSS \((*4.1)\) is explained by taking recourse to Sanskrit grammar, considering it as a \textit{bahuvrīhi} compound. So, \textit{tricaturbhuja} would mean ``a geometric figure having sides that are three and four''. BSS XII 30--31 \((*4.2)\) is explained by the identifying segments made by the perpendicular from a vertex to the opposite diagonal, with the portions determined by the intersection of the diagonals. As far as the redundancy problem BSS XII 30--31 \((*4.2)\) is concerned, the author explains it by considering a triangle the base of which is the diameter of the circumcircle, and when a perpendicular is dropped from the vertex to the diameter, there are actually three right-angled triangles. Brahmagupta refers to all the three. For Baudhāyana's \textit{Śulbasūtra}, the author has used what he calls scale-calculus, a particular method of reasoning.NEWLINENEWLINEThe paper concludes with useful hints and guidelines for the analysis of mathematical texts. The references include many of the author's earlier works. The breach in the continuity if Indian mathematics poses many difficulties to modern authors in understanding texts such as those of Brahmagupta. A close literary analysis such as this definitely helps to understand ancient Indian texts better.