John Marsh and the curious world of decimal arithmetic

Duncan J. Melville

pp. 23-42

in: Maria Zack, Dirk Schlimm (eds), Research in history and philosophy of mathematics, Basel, Birkhäuser, 2018

Abstract

In the early eighteenth century, techniques of computation for decimal fractions, especially non-terminating repeating decimals, were being developed amid a debate over their utility compared to common fractions for merchants and tradesmen facing complicated metrological and currency systems. That is, we are almost exclusively concerned with procedures for manipulating decimal representations of rational numbers; irrationals get only a brief mention. The most comprehensive exploration of these arithmetical techniques was undertaken by John Marsh in his Decimal Arithmetic Made Perfect of 1742. In this paper we explain Marsh's achievement, locate his contribution in the context of earlier work, and consider his audience and its implications as evidence for the depth and spread of interest in mathematics in England