Sanskrit-Prakrit interaction in elementary mathematics as reflected in Arabic and Italian formulations of the rule of three -- and something more on the rule elsewhere (Q2928868)

In this very useful survey of the `rule of three', the author traces the use of this rule in Indian mathematics from the works of Aryabhata and some of the other mathematicians of the period. The goal was to solve a problem of the following type: if \(A\) corresponds to \(X\), then to what does \(B\) correspond to? The answer `one way or the other' according to the rule is \(Y=(B\times X)/A\), which is a shorthand version of one type of the method of cross-multiplication. The author then presents an extensive treatment of the evolution of this rule in Arabic, Latin, Italian, and Ibero-Provençal treatises through many centuries. The rule from Indian and Italian sources was mostly used for commercial benefits and normally passed down verbally. However, a more rigorous treatment of the rule could be found in some Arabic and Latin sources, which the author discusses in a succinct manner. In this survey, the author also discusses the use of this rule in the Ibero-Provençal area. But the formulation of this rule there is unlike that in the Arabic sources and no clear answer could be given as to the origin of this rule in these regions. Also, not much evidence can be found on how the rule was communicated from India to the West or whether in fact this was ever the case. The origin of this rule in China is not discussed in this survey. The bibliography is extensive and points to all the major sources pertinent to the discussion.