Rodhe, S. (Author)
British Society for the History of Mathematics Bulletin
Volume: 32
Issue: 1
Pages: 75-90
Dedicated to the memory of Jacqueline Stedall - The index of a Swedish textbook from 1721 put me on the track: on page 455 we will find a theory of series by Christian Goldbach. The book, Geometria, is written by the non-academic mathematician Anders Gabriel Duhre. He was a teacher in mathematics and mechanics for the Swedish officers at a military school in Stockholm. Geometria is not another Euclid’s Elements. It deals with more modern theories as trigonometry and infinitesimal methods to find areas, but does not include Newtonian or Leibnizian theories of fluxions or differentials. Duhre and Goldbach met several times, while Goldbach stayed in Sweden for almost two years in 1718–20. According to Goldbach’s diaries they discussed series, a subject that Goldbach had a great interest in, since Nicolaus (I) Bernoulli in September 1712 had introduced him to one of the works Jacob Bernoulli left on infinite series. Duhre had studied John Wallis’ Arithmetica infinitorum, with a theory on series based on figurative numbers. He had written about it and more or less done a Swedish translation of a small part of Wallis’ text. It was printed in Duhre’s Algebra in 1718. Goldbach seems to have been impressed by Duhre’s work. Presumably Goldbach was the author of a review of the book in the Acta Eruditorum. A few months after he had left Sweden Goldbach wrote a letter to Duhre I was very pleased to read the review of your Algebra in the Acta Eruditorum; it was put into exactly the words I had hoped for. They also added specimen methodi ad summas serierum as you know. I am not quite sure who included it in these Acta, but I would have preferred it to be postponed until the method was more carefully elaborated and developed. Goldbach’s article Specimen methodi ad summas serierum (transl Example of a method for the sums of series) follows next to the review of Duhre’s book in Acta Eruditorum. It is on five pages in five paragraphs and deals with general forms for terms and sums of series, especially such that the general term is fractional with a polynomial in the denominator and a constant in the nominator. In his Geometria Duhre had written a personal translation of the first four paragraphs of the text. The fifth paragraph is quite different from Goldbach’s printed text and includes another method that Duhre explicitly states to be Goldbach’s originally.
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