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Thomas Harriot's Doctrine of Triangular Numbers: the `Magisteria Magna'
Edited by: Janet Beery, University of Redlands, CA, and Jacqueline Stedall, The Queens College, Oxford, England
A publication of the European Mathematical Society.
Heritage of European Mathematics
2008; 144 pp; hardcover
Volume: 2
ISBN-10: 3-03719-059-0
ISBN-13: 978-3-03719-059-3
List Price: US$84
Member Price: US$67.20
Order Code: EMSHEM/2
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Thomas Harriot (1560-1621) was a mathematician and astronomer who founded the English school of algebra. He is known not only for his work in algebra and geometry but also as a prolific writer with wide-ranging interests in ballistics, navigation, and optics. (He discovered the sine law of refraction now known as Snell's law.)

By about 1614, Harriot had developed finite difference interpolation methods for navigational tables. In 1618 (or slightly later) he composed a treatise entitled `De numeris triangularibus et inde de progressionibus arithmeticis, Magisteria magna', in which he derived symbolic interpolation formulae and showed how to use them. This treatise was never published and is here reproduced for the first time. Commentary has been added to help the reader follow Harriot's beautiful but almost completely nonverbal presentation.

The introductory essay preceding the treatise gives an overview of the contents of the `Magisteria' and describes its influence on Harriot's contemporaries and successors over the next sixty years. Harriot's method was not superseded until Newton, apparently independently, made a similar discovery in the 1660s. The ideas in the `Magisteria' were spread primarily through personal communication and unpublished manuscripts, and so, quite apart from their intrinsic mathematical interest, their survival in England during the seventeenth century provides an important case study in the dissemination of mathematics through informal networks of friends and acquaintances.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.


Graduate students and research mathematicians interested in the history of mathematics.

Table of Contents

  • Thomas Harriot and the `Magisteria magna': A short chronology
  • Thomas Harriot's `Magisteria magna' and constant difference interpolation in the seventeenth century
  • Bibliography
  • De numeris triangularibus et inde de progressionibus arithmeticis: Magisteria magna
  • Acknowledgements
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