Thomas Harriot's Doctrine of Triangular Numbers: the "Magisteria Magna"
This remarkable book consists of three parts. In the first part, the editors give a very short biography of Thomas Harriot (1560-1621), English mathematician, astronomer and geographer, who developed finite difference interpolation methods for the construction of navigational tables by means of constant differences. Towards the end of his life, he summarized the methods and presented them in his famous treatise entitled "De numeris triangularibus et inde de progressionibus arithmeticis: Magisteria magna" (1618). He explained his mathematical ideas (e.g. triangular numbers and the difference method), expressed the relevant formulae in something very close to modern algebraic notation and described how to use them.
The editors also give a short chronology of the way of the "Magisteria", which was lost for many years, before being rediscovered at the end of the eighteenth century and finally published at the beginning of the twenty-first century. In the second part, the editors give an overview of the contents of the "Magisteria". They explain Harriot's presentations and methods of table construction. They also analyse its influence on Harriot's contemporaries (e.g. N. Torporley, H. Briggs, W. Warner and Ch. Cavendish) and his successors (e.g. J. Pell, N. Mercartor, I. Newton and J. Gregory), who explored his methods before or independently of Newton's rediscovery of them in 1665. Harriot's original pages are published in the third part of this book in facsimile. The editors have added many commentaries helping the reader to follow Harriot's ideas. The book can be recommended to anybody interested in English mathematics of the 17th century. Everybody can find here many stimulating ideas.