an unpublished letter from henry oldenburg to johann heinrich rahn

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250 Noel Malcolm
JOHANN HEINRICH RAHN
Johann Heinrich Rahn (1622–76) was a member of a prominent Zurich family: his father
served as a city councillor for more than 50 years, and was Bürgermeister (Mayor) of
Zurich from 1655 until his death in 1669. Rahn probably acquired his special interest in
mathematics from his uncle Johann Georg Werdmüller, who was the engineer in charge
of the city’s fortifications. He himself was appointed a ‘Schützenmeister’, which meant
that he supervised shooting practice, and a ‘Zeugherr’, responsible for military supplies
and artillery. 3 His mathematical interests were stimulated in 1654 by the arrival in Zurich
of John Pell, the former Professor of Mathematics at Amsterdam and Breda (and future
FRS), who served as Cromwell’s envoy to the Protestant cantons of Switzerland from
May 1654 to June 1658. The first sign of his connection with Pell is a letter he sent, dated
4 November 1654, enclosing a short mathematical demonstration and thanking Pell for
the gift of a copy of one of Pell’s publications, his compilation of texts refuting the
Danish circle-squarer Longomontanus. 4 What further contacts they had over the next two
years is not known, but at some time in early 1657 Rahn began to receive regular weekly
tutorials from Pell. As John Aubrey would later write (summarizing what Pell had told
him), ‘Rhonius [the latinized version of ‘Rahn’] was D r Pell’s scholar at Zurich, and
came to him every friday night’; Pell himself would refer to Rahn as his ‘disciple’ and
would retain ‘coppies of the most considerable papers that he wrought in my presence or
that I gave him to transcribe’. 5
In early 1658 Rahn was appointed ‘Landvogt’ (provincial governor) of Kyburg, a district
at the northern edge of the canton of Zurich; writing to Pell from there on 3 March
1658, he remarked that his heavy administrative workload prevented him from spending
any time on mathematics, but said that he had the consolation of remembering ‘how
many very delightful hours’ they had spent together. 6 Nevertheless, during the next year
he somehow found time to compose the German-language textbook on algebra that
would make him famous: Teutsche Algebra, oder algebraische Rechenkunst, zusamt
ihrem Gebrauch (Zurich, 1659). This work was heavily indebted to Pell, and it was a debt
that Rahn was happy to acknowledge (though, probably in deference to Pell’s own habitual
modesty, without mentioning his name): Rahn explained in his preface that ‘in the
solutions, and in the arithmetic too, I make use of a completely new method … which I
first learned from an eminent and very learned person.’ This new method, he explained,
consisted in ‘a triple margin’—Pell’s system of presenting the working-out of a problem
in three columns. But that was not the only thing owed to Pell in this volume: Rahn also
introduced the division sign (which Pell had invented), and in a section on squaring the
circle he presented the theorem Pell had defended in his controversy with
Longomontanus. 7
When Rahn’s book was published, Pell was back in London, leading a somewhat
obscure existence without any public or academic position. He was no longer in touch
with Rahn, but in November 1660 he did receive a copy of Rahn’s book from his friend
Theodore Haak (the German-born scholar and translator, a man of wide scientific interests,
who would be elected FRS in the following year). 8 Other copies evidently found
their way to England, for in the early 1660s two separate translations of it were under-