Phoronomia, sive de viribus et motibus corporum solidorum et fluidorum libri duo.

Amsterdam: Apud Rod. & Gerh. Wetstenios, 1716.

First edition of the first textbook on theoretical mechanics based on the Leibnizian calculus, important for containing the first published discussion of the kinetic theory of gases. “This textbook concerned advanced mechanics in the modern sense and was considered an important work, very favorably reviewed by Leibniz himself in the Acta Eruditorum” (Fellmann in DSB). “The beginning of the kinetic theory of gases is usually assigned to the year 1738, when Daniel Bernoulli's ‘Hydrodynamica’ appeared at Strasbourg. The famous tenth section of this book pursued some of the consequences of the assumption that ‘elastic fluids’ consist of innumerable tiny particles in rapid motion. [However an] earlier attempt dates from 1716, and is to be found in the ‘Phoronomia’ of Bernoulli’s compatriot Jacob Hermann … For us the importance of Hermann’s chapter XXIV is that it is, as far as I know, the first attempt to deal mathematically with the relations between heat and motion. The intuition that the speed of the particles must be squared is especially noteworthy, but perhaps not more so than the assumption that their speeds will not all be the same, so that an average must be taken” (Knowles Middleton). “In 1716, the Swiss mathematician Jakob Hermann (1678-1733) published his book on theoretical mechanics, Phoronomia, in which he proposed the first definite measure of the heat of molecular motion. In Proposition LXXXV he wrote: Calor, caeteris paribus, est in composite ratione ex densitate corporis calidi, & duplicata ratione agitationis particularum ejusdem (Heat, in bodies of similar composition, is in the composed ratio of the density of the hot body and the square of the agitation of its particles), in other words, for the first time it was being suggested that the pressure is proportional to the density and the mean square velocity of the molecules” (Wisniak).

Jakob Hermann (1678-1733) received his initial training from Jacob Bernoulli, and graduated with a degree in 1695. He became a member of the Berlin Academy in 1701. He was appointed to a chair in mathematics in Padua in 1707 (on the recommendation of Leibniz), but moved to Frankfurt an der Oder in 1713, and thence to St. Petersburg in 1724. Finally, he returned to Basel in 1731 to take up a chair in ethics and natural law. "While in Padua, Hermann lectured on the standard topics of the day, namely classical geometry, mechanics, optics, hydraulics, and gnomonics. However, his work with other scientists was almost entirely devoted to understanding, developing and applying methods in the infinitesimal calculus. It was while he was in Padua that Hermann did most of the work on his most famous book, the Phoronomia, which is a text on mechanics. Although he began writing the book in 1709, it was not published until 1716, three years after he left Italy …

“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. After leaving Padua in April, he went to Vicenza where he lived at the home of Giovanni Checozzi (1691-1756) and Sebastiano Checozzi (1693-1719) until June, after which he went first to Basel and subsequently to Frankfurt-an-der-Oder to take up his new appointment. He spent eleven years in Frankfurt-an-der-Oder, again a position which, as we have explained, was largely due to Leibniz’s recommendation. But in 1724 Peter the Great called him to Russia to found, together with a number of others, the St. Petersburg Scientific Academy. He went to Russia in 1725, meeting Christian Goldbach in Königsberg while on the journey, and held a chair of higher mathematics in the St. Petersburg Academy until 1731 …

“In 1726, the St. Petersburg Academy began to publish a journal under the title Commentarii Academiae Petropolitanae. The journal was launched with an article by Hermann taking pride of place. Leonhard Euler arrived at the Academy in 1727. This was a difficult time since, following the death of Catherine, Peter II had become tsar at the age of twelve. There was political turmoil which had a serious affect on the work of the Academy which was close to collapse. Hermann worked at the Academy through these difficult years until, with the death of Peter II in 1730, the political situation stabilised. He had wanted to return to Basel, however, and had been appointed to the chair of ethic and natural law there in 1727. He had a substitute carry out the duties involved until his contract in St Petersburg came to an end in 1731 at which time he returned to Basel to take up the chair he had formally held for four years. He had hoped that a chair of mathematics would become vacant in Basel before his contract at the St. Petersburg Academy came to an end but this did not happen.

“Hermann worked in mechanics and studied the ‘inverse problem’ where one has to determine the orbit from a knowledge of the law of force. He proposed the term ‘phoronomia’ in 1716 for the topic which was sometimes called ‘rational mechanics’ and is now called 'theoretical mechanics'. This appears in the title of his important book Phoronomia, sive de viribus et motibus corporum solidorum et fluidorum libri duo (1716) …

“An example of Hermann's approach is illustrated by looking at how he proved Kepler’s area law. This had been proved by Newton in the Principia by using an intuitive limiting geometrical process. 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” (MacTutor).

“The complexity of the process of mathematization of dynamics is particularly evident in transitional figures, such as Jakob Hermann (1678–1733). He belonged to the Basel school headed by the Bernoullis and, sharing their methodology, made important contributions to the analytical treatment of dynamics. However, he also leaned towards Newton and, on many occasions, preferred to deal with dynamical problems in terms of geometry. His methodology is thus quite eclectic … Hermann’s main work is Phoronomia, which, written during his Italian period, was published in Amsterdam in 1716. This work is devoted to the dynamics of solid and fluid bodies and covers many problems dealt with by Newton in the first two books of the Principia. In the preface, Hermann declares his intention of adhering to geometrical methods, since these seem to him more suitable for beginners [pp. vii–viii]. However, his knowledge of calculus is evident in the way in which he deals with infinitesimals. Hermann’s Phoronomia is indeed representative of the process of transition that transformed dynamics in the first decades of the 18th century” (Guicciardini).

Not in Norman, Roberts & Trent or Tomash. N Guicciardini. ‘An episode in the history of dynamics. Jakob Hermann’s proof (1716-1717) of Proposition 1, Book 1, of Newton's Principia,’ Historia Mathematica 23 (1996), pp. 167-181. W. E. Knowles Middleton, Jacob Hermann and the Kinetic Theory, British Journal for the History of Science 2 (1965), pp. 247-250. J. Wisniak, ‘Kinetic theory. From Euler to Maxwell,’ Indian Journal of Chemical Technology 12 (2005), pp. 730-742.

4to (234 x 190 mm), pp. [xxii], 401, [2], including engraved allegorical frontispiece, with 12 folding engraved plates. Title printed in red and black with engraved vignette, woodcut diagrams in text. Fine contemporary Dutch vellum, red gilt title label to spine. Ex-library stamps of the Royal Society of Edinburgh.

Item #4289

Price: $2,800.00

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