Different clusters of text from ancient China, different mathematical ontologies

Karine Chemla

doi:10.1086/703799

Abstract

Sources attesting to mathematical activities in ancient China form at least four distinct clusters of texts, bespeaking at least four different—though overlapping—ways of practicing mathematics. I ...

Highlights

In the different contexts in which mathematics has been practiced, we can observe a certain diversity in the types of entities actors’ work has brought into play
The way in which The nine chapters refers to multiplication cheng and division chu supports the hypothesis of the coherence of the corpus; that is, that the algorithms learned with Mathematical canon by Master Sun were those on which The nine chapters relied, and in particular, those with respect to which processes of computation described in The nine chapters likewise stated relations of similarity or opposition
Like multiplication cheng and division chu, they rely on the positions of the decimal expansion of the number, whose root is extracted. Likewise, these algorithms bring into play three main positions, called respectively “quotient,” “dividend,” “divisor.”12 In the same way as the names for the positions borrow the terms used for division in Mathematical canon by Master Sun, the elementary operations used to execute both square and cube root extractions derive for the most part from the process of division

Summary

Introduction

In the different contexts in which mathematics has been practiced, we can observe a certain diversity in the types of entities actors’ work has brought into play. The way in which The nine chapters refers to multiplication cheng and division chu supports the hypothesis of the coherence of the corpus; that is, that the algorithms learned with Mathematical canon by Master Sun were those on which The nine chapters relied, and in particular, those with respect to which processes of computation described in The nine chapters likewise stated relations of similarity or opposition.

Results

Conclusion