PHORONOMIA

4to, pp. [xx], 401, [2] emendata, [1] blank; with additional engraved title-page and 12 folding leaves at end, containing 160 diagrams; title-page printed in red and black with engraved vignette; repaired tear to final folding leaf, just touching one diagram, tear to head of third folding leaf, again just touching one diagram, and repaired tear to Aaa3, with text legible; otherwise, aside from occasional spotting and marginal browning, clean and fresh; in contemporary calf, rebacked preserving original panels, gilt in compartments with raised bands, morocco lettering-piece; some wear to extremities.

First edition of the Swiss mathematician Jakob Hermann's best known work.

Hermann (1678-1733) was a native of Basel, and studied at the city's university under Bernoulli, through whom he got to know Leibniz, to whom the present work is dedicated; much of his early work was devoted to a defence of Leibnizian calculus. This led to a deeper interest in mechanics, a subject to which his greatest contribution was the present work. What Hermann calls 'Phoronomia' we would now call theoretical mechanics.

Phoronomia '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. 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).

"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" (O'Connor and Robertson).

Much of Hermann's book was written while he was teaching in Padua, although by the time he published the work, had had returned to a chair in Basel, after a period in St Peterburg. He was elected to the Académie Royale des Science in Paris in 1733.

DSB VI, 304-5; Poggendorff I, 1077; 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 (2) (1996), 167-181.