The complex itinerary of Leibniz's planetary theory. Physical convictions, metaphysical principles and Keplerian inspiration (Q5971111)

Leibniz's planetary theory, composed in 1689 in response to the publication of Newton's \textit{Principia mathematica} is notoriously difficult. Leibniz rejected the presumption of an action at a distance and tried to explain the inverse square law by assuming aethereal vortices. Some of the conceptual and mathematical intricacies and possible errors were already debated in the 18th century in particular with Newtonians, and have been analysed more recently by \textit{E. J. Aiton} [The vortex theory of planetary motions. London: Macdonald \& Co (1972; Zbl 0274.01016)] and in several articles and \textit{D. B. Meli} [Equivalence and priority: Newton versus Leibniz. Including Leibniz's unpublished manuscripts on the Principia. Oxford: Clarendon Press (1993; Zbl 0792.01008)], among others. The present book attempts to give a comprehensive analysis of Leibniz's contribution to planetary theory without neglecting adjacent questions, as its relation to the concepts of inertia and gravity. While there is considerable thematical overlap in particular with Meli's work, the focus is different: Meli's aim was to investigate the relation of Leibniz's theory to Newton's work. In the present monograph, an emphasis is put on Kepler's influence. Furthermore, Leibniz's 1706 papers, in which he revisited his theory in response to criticism from the Newton camp and which have received less attention so far, are treated in detail. There is also a difference in approach: Whereas Meli gives a global view of Leibniz's theory, its context and reception, the present book offers a close reading of Leibniz's texts: each of Leibniz's contributions is treated separately and much emphasis is put on the discussion of Leibniz's terminology. For a reader trying to understand Leibniz's cosmology, the best is to study all these works in parallel. The present book is structured as follows. In a short introduction titled ``The historical-conceptual reference frame'', Leibniz's relevant papers and the author's leading research questions are presented. Besides the fundamental 1689 paper \textit{Tentamen de motuum coelestium causis}, Leibniz also published a short answer to criticism by the Newton acolyte David Gregory in 1706 [``Excerptum ex epistola G. G. L. quam pro sua hypothesi physica motus planetarii olim (Febr. 1689) his Actis inserta, ad amicum scripsit'', Acta eruditorum, October 1706, pp. 446--451 (called ``Beilage'' on p. 1, Note 1 of the present book after a 19th-century edition)] and composed several manuscripts published only in the 19th century. Chapter 2 describes ``the most important elements of Leibniz's planetary theory'', namely the decomposition of planetary motion into a ``circulatio harmonica'' and a ``motus paracentricus'', and the treatment of the inverse square law and of elliptic motion as developed by Leibniz around 1689. Chapter 3, an interlude, deals with ``Leibniz's concept of inertia'' and its relation to similar concepts by Kepler and Newton. Chapter 4, ``The final version of Leibniz's planetary theory'', treats Leibniz's 1706 papers. Chapter 5 studies the relation to Leibniz's ideas on ``gravity and cosmology''. Providing a unified theory for planetary motion and gravity, which is one of the main achievements of Newton, was beyond the scope of Leibniz's papers. However, his explanations of gravity and planetary motion via an aether are closely related. The properties and interrelations of the different aethers are one important topic of this chapter. Chapter 6 goes much beyond its subject ``Kepler's influence on Leibniz's planetary theory'' and rather tries to give a complete picture of Kepler's influence on Leibniz, devoting much attention to the metaphysical concepts of causality and harmony. As a side remark one might add that the numerous references to Kepler's \textit{Tabulae Rudolphinae} in Leibniz's correspondence (p. 134) are due to the role these tables played in the Protestant calendar reform around 1700; in this context their value and correctness was extensively discussed. Some questions addressed in the present book will certainly inspire furture research -- for instance the number and precise nature of the aethers postulated by Leibniz (pp. 90, 96) or ``how profound the knowledge Leibniz achieved of Kepler's work [\dots] was'' (p. 134). They will hopefully be further clarified once more manuscripts from Leibniz's estate are edited (for a preliminary list of relevant manuscript sources see [Meli, loc. cit., pp. 308f.]; in the present book only published sources are used). For example, in the sources cited by the author Leibniz attributes to Kepler the idea that a rotating body has the tendency to recede along the tangent, but does not give a precise reference. The author argues (p. 129) -- as had Meli [loc. cit., p. 29] -- that Leibniz is referring to a passage in the first book of Kepler's \textit{Epitome}. This can be confirmed from the manuscript LH 35, 10, 8 fol. 16, where Leibniz writes: ``Keplerus aliquoties de rejectione per tangentem. Praeclarus est locus libro primo Epitomes [\dots]'' and then cites and comments on the passage in question. For Kepler's impact on Leibniz's philosophy the manuscript LH 35, 15, 6 fol. 28f. is relevant, which begins: ``Kepleri loca sunt multa meae de Corporis constitutione Philosophiae consentanea'' and contains excerpts of Kepler's \textit{Epitome}. Excerpts also show that Leibniz -- contrary to the author's guess on p. 118 -- did read Kepler's \textit{Astronomia nova} [Meli, loc. cit., p. 27, Note 12]. The last instance is not the only one which shows that the book would have profited from a more careful preparation and editorial oversight. There are quite a few italianisms (e.g. the consistent use of ``imagine'' for ``image'') and typos. The figures -- all reproduced from other sources -- are sometimes blurred and do not always match the reasoning, which makes understanding the often complex argumentation still more challenging (e.g. p. 9, Fig. 2.1). Here, it would have been helpful if the figures were drawn from scratch as needed in the text. The book usefully contains an ``index of authors''. (The manuscript sources cited in this review are to be found in the Gottfried Wilhelm Leibniz Bibliothek in Hanover. They have recently been made available as scans [\url{http://digitale-sammlungen.gwlb.de/index.php?id=7}], consulted: 15 January 2017.)