Willebrord Snellius (1580-1626): a humanist reshaping the mathematical sciences

Abstract

Although Willebrord Snellius was one of the most eminent scientists of the Dutch Golden Age, never before had a substantial volume been devoted to his life and work. Liesbeth de Wreede's thesis fills this lacuna. It gives an overview of Snellius's life and work and analyses a number of case studies in depth. The focus is in particular on Snellius's development of the style of humanist mathematics and its roots, and his predilection for 'exactness', that is, a clear demarcation of allowable concepts in geometry. In the biographical part of the thesis, De Wreede discusses Snellius's life and work, and the backgrounds necessary to understand his mathematical oeuvre: Leiden University, humanist scholarship as it was practised there, mathematical practice in the rest of the Dutch Republic, the ideas of Petrus Ramus, and life and work of Willebrord's father Rudolph. Snellius (1580-1626) taught courses at the university, and was a scientific adviser for his colleagues and the government of the Dutch Republic. Moreover, he published many works, both his own books as editions and translations of works of others, all except one written in Latin. He covered almost the complete domain of the mathematical sciences: geometry, arithmetic, astronomy, navigation, surveying and optics. The first two case chapters discuss cases from mixed mathematics. The first of these is devoted to the way in which Snellius calculated the length of the circumference of the earth more precisely than his predecessors, as explained in his 'Eratosthenes Batavus'. The second discusses the patronage relationships between Landgrave Maurice of Hessen, and Rudolph and Willebrord Snellius. This study is largely based on hitherto unknown letters. The content of Willebrord Snellius's astronomical works, both dedicated to Maurice of Hessen, is related to the patronage relationship. The next three chapters discuss topics from pure mathematics. The first of these introduces the 'Fundamenta Arithmetica et Geometrica', Snellius's translation of a book by Ludolph van Ceulen. This translation is a rich source for Snellius's thoughts about acceptable mathematics, because he reacted to Van Ceulen's approach in his translations and his own commentaries, thus making the book into a dialogue between a representative of the practitioners' and one of the academic tradition. The dedicatory letter is analysed extensively, because it gives Snellius's opinion on the issue of the use of numbers in geometry, an important problem in the period, in a nutshell. The next chapter discusses Snellius's contributions to the solution of the triangle division problem, a popular geometrical problem in his period. In the last case chapter, Snellius's criticism on the traditional formulation and proof of Heron's Theorem (relating the area of a triangle to the lengths of its sides) is central. He protested against the four-dimensional magnitude that was present in the traditional approach, because such an entity could not exist in geometry. Snellius's study of the cyclic quadrilateral also receives attention. In the final chapter, all results of the previous chapters are used to sketch a complete image of Snellius's mathematics and Snellius as a mathematician.