**Jakob Hermann** was a Swiss mathematician who made contributions to dynamics.

- Hermann was taught mathematics by Jacob Bernoulli who, at that time, was working on infinite series.
- Four of these students were Johann Jacob Fritz, who defended his dissertation on series in 1689, Hieronymus Beck who defended his thesis in 1692, Jakob Hermann who, as we noted above, defended his dissertation in 1696, and Nicolaus Harscher who defended his thesis on series in 1698.
- It was Jakob Hermann, however, who Jacob Bernoulli considered was the best of his students and he was assigned Theses 36-46 which he defended under the title Positiones arithmeticae de seriebus infinitis earumque summa finita Ⓣ(Arithmetical results on infinite series with finite sums).
- Hermann answered Nieuwentijt's criticisms in Responsio ad clarissimi viri Beruh.
- In 1701 Hermann became a member of the Berlin Academy of Science, his election being very much due to support from Leibniz who was delighted to see the clarity with which he had defended the infinitesimal calculus.
- Despite all this mathematical activity, Hermann officially studied theology after taking his Master's degree and he took his final theology examinations in 1701.
- It was through Jacob Bernoulli that Hermann had become friendly with Leibniz and, following the death of Jacob Bernoulli in 1705, Leibniz asked Hermann to write an obituary notice for Acta Eruditorum.
- When the chair of mathematics in Padua became vacant, Leibniz wrote to Fardella, who taught in Padua from 1693 to 1709, on 7 December 1704 giving a high opinion of Hermann's abilities.
- Because of the strong recommendation, Hermann was appointed to the chair of mathematics at the University of Padua on 28 April 1707.
- This was one of the most topical subjects in the scientific literature of the time, with Newton, Bernoulli and Varignon all studying it, which is why Hermann gladly accepted the invitation of his friend and colleague Antonio Vallisneri, who, "because of his ardent desire to see the deeper sciences promoted", urged him to contribute to the Journal he had just founded with Scipione Maffei and Apostolo Zeno - the Giornale de' Letterati d'Italia.
- In fact, while in Padua, Hermann lectured on the standard topics of the day, namely classical geometry, mechanics, optics, hydraulics, and gnomonics.
- It was while he was in Padua that Hermann did most of the work on his most famous book, the Phoronomia Ⓣ(Phoronomics (the science of motion)), which is a text on mechanics.
- Hermann held his post in Padua until his contract expired on 28 April 1713.
- While in Padua he had asked Leibniz's advice about moving to a university in another country and Leibniz had suggested a position in Frankfurt-an-der-Oder, but advised Hermann to see out the six year contract he had signed with Padua.
- Although he had a very successful career in Italy, Hermann seems to have found the fact that he was a Protestant in a Roman Catholic country somewhat difficult and, of course, Germany presented a religious environment much more to his liking.
- Hermann worked on trajectory problems, algebraically squarable curves, and attraction; results on all of these topics he published in papers while in St Petersburg.
- The journal was launched with an article by Hermann taking pride of place.
- Hermann worked in mechanics and studied the 'inverse problem' where one has to determine the orbit from a knowledge of the law of force.
- In the preface, Hermann declares his intention of adhering to geometrical methods, since these seem to him more suitable for beginners.
- Hermann's 'Phoronomia' is indeed representative of the process of transition that transformed dynamics in the first decades of the 18th century.
- An example of Hermann's approach is illustrated by looking at how he proved Kepler's area law.
- Hermann, however, gave a proof in the Phoronomia in terms of differentials.
- Although his notation was rather different from modern notation, and not particularly easy to understand, Hermann reworked the same ideas into a notation which is essentially that used today and sent his new version of the proof to John Keill who published it in Journal litéraire in 1717.
- In his work on curves in space, Hermann discusses the spherical epicycloid; the problem of finding the shortest distance between two points on a given surface; and the equations and properties of various surfaces from the point of view of analytic geometry of three dimensions.
- In 1708 Hermann was elected to the Academy at Bologna and, 1733, to the Académie Royale des Sciences in Paris.

Born 16 July 1678, Basel, Switzerland. Died 11 July 1733, Basel, Switzerland.

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Geometry, Origin Switzerland, Physics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive