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

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*Janet Beery; Jacqueline Stedall*

A publication of the European Mathematical Society

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 Harriot's method was not superseded until Newton, apparently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communication and unpublished manuscripts, and so, quite apart from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.

#### Readership

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