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Mathematical Treasure: Peter Barlow’s Number Theory and Dictionary

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

English mathematician and physicist Peter Barlow (1776–1862) served as assistant mathematics master at the Royal Military Academy in Woolwich from 1801 to 1847. His works included An Elementary Investigation of the Theory of Numbers (1811)—which appeared at a time when the phrase “the theory of numbers” was new in the mathematical lexicon—and A New Mathematical and Philosophical Dictionary (1814).

Title page of Peter Barlow's Elementary Investigation of the Theory of Numbers.

Table of contents, page 1, from Peter Barlow's Elementary Investigation of the Theory of Numbers.

Table of contents, page 2, from Peter Barlow's Elementary Investigation of the Theory of Numbers.

The publication of mathematical dictionaries followed a vogue taking place on the Continent; for instance, see earlier examples from Jacques Ozanam and Jean d’Alembert.

Title page for Peter Barlow's New Mathematical and Philosophical Dictionary, 1814.

An excerpt from the dictionary’s entry on fluxions:

Peter Barlow's definition of fluxions, page 1.

Peter Barlow's definition of fluxions, page 2.

Peter Barlow's definition of fluxions, page 3.

Peter Barlow's definition of fluxions, page 4.

Full digitizations of the copies owned by the University of Michigan are available at HathiTrust and in the Internet Archive.

Index of Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Peter Barlow’s Number Theory and Dictionary," Convergence (August 2021)