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Thomas Harriot’s Doctrine of Triangular Numbers: the ‘Magisteria Magna’
Heritage of European Mathematics

Thomas Harriot’s Doctrine of Triangular Numbers: the ‘Magisteria Magna’

Janet Beery (University of Redlands, USA)
Jacqueline Stedall (University of Oxford, UK)

ISBN print 978-3-03719-059-3, ISBN online 978-3-03719-559-8
DOI 10.4171/059
December 2008, 144 pages, hardcover, 17 x 24 cm.
64.00 Euro

Thomas Harriot (c. 1560–1621) was a mathematician and astronomer, known not only for his work in algebra and geometry, but also for his 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 to 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 Harriot’s method was not superseded until Newton, apparently independently, made a similar discovery in the 1660s. The ideas in the ‘Magisteria’ were spread primarily through personal communication and unpublished manuscripts, and so, quite apart from their intrinsic mathematical interest, their survival in England during the seventeenth century provides an important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.

Keywords: Harriot, seventeenth century, figurate numbers, interpolation

Further Information

Review in Zentralblatt MATH 1168.01001

Review in MR 2516550

MAA Reviews

Review in Historia Math. 38 (2011), 123–125

Review in Notes and Records of the Royal Society 64 (2010), 303–304

EMS Review