Leibniz’S Correspondence in Science, Technology and Medicine (1676 –1701)

Home , Denis Papin

[Title page]

Leibniz’s Correspondence in Science, Technology And Medicine (1676 –1701)

Core Themes and Core Texts

James G. O’Hara

Contents

Preface

Acknowledgements

List of Illustrations or Plates

Introduction: Core Themes

1) Biographical Background (1676 –1701) 2) Mathematics 3) Natural Philosophy Dynamics Vis Viva 4) Physics The Pneumatic Engine Theory of Matter, Elasticity, Sound and Acoustics, Strength of Materials Terrestrial Magnetism Meteorology Astronomy and Celestial Mechanics Resisting Media and Motion in Resisting Media Optics: Theories of Light: Newton and Huygens Catoptrics, Dioptrics and Optical Instruments Microscopy 5) Energy Conversion, Transmission, and Storage. Power Technology Mining in the Harz Mountains Transport and Transportation The Steam Pump and Steam Engine Other Enginery 6) Engineering Ballistae – Military Engines and Engineering Civil Engineering: Urban Water Supply, Garden Design and Architecture Engineering Manufactories Process or Chemical Engineering Engineering Science: Mechanics of Fluids 7) Projects Calculating Machines Steganography and Cryptography Military-Related Projects (Submarines, et similia) Economic and Techno-Economic Projects The Organization of Science and Education 8) Alchemy and Chemistry 9) Earth Sciences: Geology, Mineralogy, Paleontology and Ethnography, Etymology 10) Biology and Life Sciences 11) Medicine: Anatomy, Physiology Pathology, Therapeutics, Pharmacology Epidemiology, Demography The Medical Profession, Mathematization and Rationalization

The Correspondence: Core Texts

Chapter 1 (1676 –June1683)

Biographical Background (1676–June 1683) Mathematics Natural Philosophy and Physics Technology: Mining in the Harz District Projects: Calculating Machines Techno-Economic Projects Projects: The Organization of Science Alchemy and Chemistry Geology, Mineralogy and Paleontology Medicine

Chapter 2 (July1683–1690)

Biographical Background (1683–1690) Mathematics: Infinitesimal Calculus and other Issues Natural Philosophy Physics: Celestial Mechanics, Mechanics, Acoustics, Optics and sundry topics Technology: Mining and Power Technology Ballistae – Military Engines and Engineering Engineering Science Projects: Economics and Administration Alchemy and Chemistry Geology, Mineralogy and Paleontology Biology and Medicine

Chapter 3 (1691–1693)

Biographical Background (1691–1693) Infinitesimal Calculus and other Mathematics Natural Philosophy and Dynamics Physics: Celestial and Terrestrial Mechanics Physics: Optics Engineering Science: Hydromechanics and Mechanics of Fluids Projects: Calculating Machines and Cryptography Projects: Experiments with Submersible Vessels Techno-Economic Projects Projects: The Organization of Science Medicine

Chapter4 (1694–June 1696)

Biographical Background (1694 – June 1696) Infinitesimal Calculus and other Mathematics Dynamics and Natural Philosophy Physics: Celestial Mechanics, Gravitation Physics: Optics Power Technology and Mining Engineering Engineering: Ballistae, Military Engines Projects: Mathematical Instruments and Calculating Machines Projects: Submersibles, Diving Vessels and Navigation Projects: Economics and Trade Projects: The Organization of Science and Education Medicine and Res Medica

Chapter 5 (July 1696–1698)

Biographical Background (July 1696 – 1698) Mathematics: The Brachistochrone and Isoperimetric Problems Mathematics: The Priority Dispute Mathematics: Criticism of the Differential Calculus Mathematics: Mathematical Textbooks and Sundry topics Natural Philosophy: The Controversy with Papin about “Vis Viva” and “Actio” Physics: Optics Power Technology Civil Engineering, Garden Design and Architecture Other Engineering Enterprises Process or Chemical Engineering Projects: Cryptography Projects: Brandy Distillation Alchemy and Chemistry Paleontology and Earth History Biology Medicine

Chapter 6 (1699–1701)

Biographical Background (1699–1701) Mathematics Natural Philosophy Physics Astronomy and Calendar Reform Power Technology Engineering: Manufactories Projects: Calculating Machines Projects: the Berlin Society of Sciences and the Organization of Science Alchemy Geology, Mineralogy, Paleontology, and Ethnography, Etymology Biology Medicine Conclusion

Epilog: Core Theses and Conclusion

The Ten Theses

1) The Field of Mathematics 2) The Field of Natural Philosophy 3) The Field of Physics 4) Energy, Power Technology, Mining, Transportation 5) Engineering and Engineering Science 6) The World of Projects and Projectors 7) The Fields of Alchemy and Chemistry 8) Geology, Mineralogy, and Paleontology 9) The Fields of Biology and the Life Sciences 10) The Field of Medicine

Conclusion and Concluding Thesis

Name Index

Subject Index

Bibliography (Works Cited)

Preface

Leibniz’s correspondence in mathematics, science and technology is being edited and published in Series III of the German Academy Edition of all of his writings and letters.1 The first volume of the third series covering the period of Leibniz’s sojourn in Paris (1672-1676) was edited by Joseph Ehrenfried Hofmann (1900-1973) and published posthumously in 1976 and in a revised form in 1988.2 Hofmann was a scholar – whose specialist interest was the development of Leibniz’s infinitesimal calculus during the Paris period – and the author of Die Entwicklungsgeschichte der Leibnizschen Mathematik während des Aufenthaltes in Paris (1672- 1676), published in 19493, and of Leibniz in Paris 1672-1676 –his growth to mathematical maturity, published in 1974 and reprinted in 2008.4 The overriding interest in mathematics in the first volume of the series meant that the systematic presentation of Leibniz’s correspondence in science, technology – a term that was used for the first time in the modern sense more than 60 years after Leibniz’s death – and medicine only began with the publication of the second volume in 1987 which covered Leibniz’s first years in Hannover from 1676 to 1679.5 Subsequent volumes of the series then appeared in 1991, 1995, 2003, 2004, 2011 and 2015, covering Leibniz’s life to the year 1701.6 The present work aims to present in English central themes and central texts from Leibniz’s correspondence in science, technology and medicine derived mainly from the first eight volumes of Series III of the Academy Edition. Chapter 1 presents key texts published (for the most part) in the first three volumes of the series. Each one of the following five chapters (Chapters 2 to 6) then presents texts published

1 Academy Edition (A) = G. W. Leibniz, Sämtliche Schriften und Briefe, published by the Prussian (Preußische) later German (deutsche), and most recently Berlin-Brandenburg Academy of Sciences (Berlin- Brandenburgische Akademie der Wissenschaften) together with the Academy of Sciences in Göttingen (Akademie der Wissenschaften zu Göttingen), Darmstadt (later Leipzig, most recently Berlin), 1923ff. To date (end of 2020) about 60 volumes in 7 series (I-IV, VI-VIII) have been published (cf. http://www.leibnizedition.de ). 2 A III,1 = Academy Edition, ser. III, vol. 1. 3 J. E. Hofmann, Die Entwicklungsgeschichte der Leibnizschen Mathematik während des Aufenthaltes in Paris (1672-1676), Munich, 1949. 4 J. E. Hofmann, Leibniz in Paris 1672-1676 – his growth to mathematical maturity, London and New York, 1974 and 2008 (reprint). 5 A III,2. 6 A III,3-8. (again for the most part) in a specific volume of the series (volumes 4 through 8). The author of the present work (writing here in the third person) has coedited the texts of (and coauthored the introductions to) the latter five volumes. The ideas and interpretations presented here in the introduction and in the text presentations are however the outcome of the joint editorial ‘spadework’ undertaken in cooperation with a range of former colleagues over a period of twenty six years spent at the ‘Leibniz-Archiv’, the editorial and research center at the ‘Gottfried Wilhelm Leibniz Bibliothek’, the State Library of the German federal state of Lower Saxony, in Hannover. A play on words, a pun around the German word ‘Band’ (meaning volume), gave rise within the editorial team to the designation ‘bandleader’ (or ‘band’ leader) for the most senior colleague working on a particular volume. In this vein then, mention must be made here of the ‘band leaders’ whose ideas and interpretations find expression in the present work (albeit in the translation by the author), namely Herbert Breger (Volume 3), Heinz- Jürgen Heß (Volumes 2, 4, 5 and 6), and Charlotte Wahl (Volume 8). The author of the present work then had the honor to act as a ‘big band leader’ for Volume 7 (with more than 1000 printed pages) covering the period of the greatest density of Leibniz’s correspondence in mathematics, science and technology, namely July 1696 to December 1698. Besides the ideas and interpretations of the ‘band leaders’ referred to, those of other former colleagues who worked on the volumes of Series III may possibly also be found in the present work, namely Ralf Krömer and Heike Sefrin-Weis (Volume 7) and Uwe Mayer (Volume 8). If the play on words or pun around the German word ‘Band’ be applied to the present volume, then the author must surely be seen in his role as a ‘broad band leader’ and architect of a volume in which there is a shift away from a predominance of mathematics with scientific subject areas now becoming more prevalent. While mathematics retains its pivotal position in many respects, nine other scientific or scholarly subject areas have been identified and included alongside mathematics. The present ‘broad band’ represents as it were a decathlon of the history of science and technology at the end of the seventeenth century with the ‘broad band leader’ assuming the role here of an editorial decathlete. The author’s penchant for a ‘broad- band’ approach is attributable, on the one hand, to a scholarly background in engineering, engineering science and the history of science and technology (rather than mathematics and history of mathematics, or philosophy and history of philosophy) and, on the other hand, to a latitudinal early academic career development (spent for the most part in western Europe along or near the 53rd parallel north or circle of latitude), specifically at the National University of Ireland, the former University of Manchester Institute of Science and Technology (UMIST), the former ‘Technische Hogeschool Delft’ and the former ‘Institut für Social- und Wirtschaftsgeschichte’, the then center for social and economic history, and history of technology, at the University of Hamburg. Although not primarily concerned with Leibniz or his correspondents, the works of a number of former mentors, influencers and colleagues are cited in the footnotes and listed in the Bibliography, including James Dooge (history of fluid mechanics after Galileo), Donald Cardwell (thermodynamics in the early industrial age), Richard Hills (history of power technology), Alan Williams (medieval and early-modern arms and armor), Emrys Evans (Celtic Studies), Olaf Pedersen and Maureen Farrell (early physics and astronomy and the historical interaction between science and religion), Volker Bialas (Kepler Edition), specialists in Christiaan Huygens studies from the years between the Huygens anniversary celebrations in 1979 and 1995 (including Henk Bos, Joella Yoder, Jan van Maanen), and Ulrich Troitzsch (technological thought in the late seventeenth and eighteenth centuries). Although not intended as a biography of Leibniz, the Introduction and the six chapters present factual and chronological biographical information intended to serve as a frame of reference for his interaction with his correspondents and which in turn may serve as a basis for Leibniz biographical studies in the future.7 The work Leibniz[.] A Biography of the historian of mathematics and physics, Eric J. Aiton (1920-1991), was for the author of the present work the first introduction to Leibniz studies.8 Having first encountered the biographer at the University of Manchester in the mid-1970s, it was a pleasure to have discussions with him in Germany at the end of the

7 cf. for example K. Müller, G. Krönert, Leben und Werk von G. W. Leibniz[.] Eine Chronik[.] Bearbeitet von Kurt Müller und Gisela Krönert, Frankfurt am Main, 1969. 8 E. J. Aiton, Leibniz[.] A Biography, Bristol and Boston, 1985 and Gottfried Wilhelm Leibniz[.] Eine Biographie, Frankfurt am Main, 1991. following decade. However, Aiton’s biography was published at the time when only the first volume of Leibniz’s correspondence in mathematics, science and technology had been published. A further issue is the fact that the sum total of Leibniz’s correspondence covers many more scholarly fields than those scientific areas treated in the present work, as for example the fields of logic, metaphysics, ethics, jurisprudence, political and social philosophy and history (to name just those alluded to by a peer reviewer of the present work) and which of course are central aspects for biographers of Leibniz like, for example, Maria Rosa Antognazza.9 At all events, the author of the present work would argue that Leibniz, following studies and academic qualification in philosophy and jurisprudence, first became a scientist – an alchemist10 or chemist who in 1667 was secretary of an alchemical society in Nuremberg11 and who contemplated at that time editing the works of renowned alchemists – before becoming a jurist, a mathematician and a philosopher. If the years 1672-1676 marked (in the words of Hofmann) Leibniz’s growth to mathematical maturity, the years 1676-1701 surely marked his growth to maturity in a range of scientific disciplines. The raison d’être then of the present work is accordingly – following in the footsteps of Eric Aiton – to lay on the foundation of Leibniz’s correspondence the groundwork for a more pronounced scientific dimension in future Leibniz biographical studies. In this sense too, the ten theses – each arising within one the ten subject areas considered – presented in the epilog should be seen. Leibniz’s correspondence reveals his fundamental standpoint that, although mathematics and the sciences are rooted in metaphysics or (to use the formulation of the author’s former colleague at the Leibniz edition, Hartmut Hecht) are within the paradigm of metaphysics12, one cannot use metaphysics to explain the physical world (or universe) and its laws. In view of the traditional proximity of paradigms and scientific revolutions13 in the history of science and mathematics14, the

9 M. R. Antognazza, Leibniz[. ]An Intellectual Biography, New York, 2008. 10 That is, prior to the denigration of alchemy, an attitude that first began to take hold in the eighteenth century; cf. p.105 in: N. Guicciardini, Isaac Newton and Natural Philosophy, London (and Chicago), 2018. 11 cf. G. MacDonald Ross, “Leibniz and the Nuremberg Alchemical Society”, Studia Leibnitiana, vol. 6(2), 1974, pp. 222-248. 12 cf. H. Hecht, Gottfried Wilhelm Leibniz[.] Mathematik und Naturwissenschaften im Paradigma der Metaphysik, Stuttgart, Leipzig, 1992. In the context of this ‘paradigm of metaphysics’, see also for example: R.T.W. Arthur, Classic Thinkers[:] Leibniz, Cambridge, UK, and Malden, MA, 2014. 13 cf. T. S. Kuhn, The Structure of Scientific Revolutions, Chicago, 1962, 1970, 1996 and 2012 (see chap. V: The Priority of Paradigms); T. S. Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, Cambridge, MA, 1957 and 1992. author of the present work suggests an alternative paradigm or framework which might be formulated as ‘Gottfried Wilhelm Leibniz’s Correspondence[.] Science, Technology and Medicine within the paradigm of the Scientific Revolution’. Leibniz’s correspondence reveals him not just as a philosopher but also as a scientist in the tradition of major figures of the Scientific Revolution of the seventeenth century which saw the replacement of qualitative scholastic Aristotelian natural philosophy by quantitative mechanistic Newtonian mathematical physics and the evolution of ‘Classical Science’.15 The Scientific Revolution likewise saw the appearance of a group of outstanding scientists and mathematicians which included Johannes Kepler, Galileo Galilei, René Descartes, Pierre de Fermat, Christiaan Huygens, Isaac Newton16, and of course Leibniz himself, and which pursued an envisioned goal – that followed from Galileo’s new conception of the task of science and that was in accordance with the explicit statement by Newton of the mathematical principles of natural philosophy (in the title of his magnum opus) – of discovering the mathematical relations that hold for the physical world (or universe).17 As regards philosophy, Leibniz appears at times to be at odds not just with Cartesian philosophy but with metaphysics as such; specifically he appears to follow in the footsteps of Galileo as an engineer and proponent of rational thought and experimental science.18 Leibniz even expressed his standpoint (in a letter to Friedrich Hoffmann on November 1, 1701) that, in higher education, a single lesson (or lecture hour) in experimental science had a greater value for him than a hundred corresponding lessons in metaphysics,

14 cf., in this context, R. C. Brown, The Tangled Origins of the Leibnizian Calculus: A Case Study of a Mathematical Revolution, Singapore, New Jersey, London, 2012; see in particular chap. 1, pp. 1-14 (Evolution or Revolution in Mathematics: The Case of Leibniz), and chap. 11, pp. 231-244 (Some Concluding Remarks on Mathematical Change). 15 cf. E. J. Dijksterhuis. De mechanisering van het wereldbeeld, Amsterdam, 1950, 1983, 1998 and 2006: E. J. Dijksterhuis (C. Dikshoorn, trans.), The Mechanization of the World Picture, Oxford, London, New York, 1961, 1969 and Princeton, 1986; see Part IV (The Evolution of Classical Science). 16 cf. for example: I. Bernard Cohen, The Newtonian Revolution with illustrations of the transformation of scientific ideas, Cambridge and New York, 1980 and 1983; H. F. Cohen, The Scientific Revolution[.] A Historiographical Inquiry, Chicago, 1994; J. Henry, The Scientific Revolution and the Origins of Modern Science, Basingstoke, New York, 1997; J. C. Boudri (S. McGlinn, trans.), What was Mechanical about Mechanics[.] The Concept of Force between Metaphysics and Mechanics from Newton to Lagrange, Dordrecht, 2002; see chap. 1, pp. 5-8 (The Horizon of the Scientific Revolution). 17 cf. M. Kline, Mathematics in Western Culture, Oxford, London, New York, 1953 and 1964; see chap. 16 (The Newtonian Influence: Science and Philosophy), in particular p. 237. 18 cf. M. Valleriani, Galileo Engineer (Boston Studies in the Philosophy of Science, vol. 269), Dordrecht, Heidelberg, London, New York, 2010. logic or ethics. Drawing inspiration from the book Christianity not Mysterious (1696) of the Irish “heretic”19, and one who fell out with the Catholic Church, then fell foul of the Irish Protestant Ascendancy and went on to become a “persona non grata” in Hannover, namely John Toland (whose opus was published five years before his first discussions with Leibniz in Hannover)20, and with the perception that Leibniz’s standpoint (namely that, although mathematics and the sciences are rooted in metaphysics, one cannot use metaphysics to explain the physical world) mirrors Toland’s deistic, rationalistic and controversial standpoint (that, although God created the world, there was no subsequent divine interaction with, or direct intervention in, that created world)21, the author of the present work coined the title ‘Science not Metaphysical’ for an earlier publication on Galileo’s influence on Leibniz which was also intended as a plea for a research and editorial approach to the edition of Leibniz’s correspondence in mathematics, science and technology within the framework of the academic field of history of science and technology and embracing the paradigm of the Scientific Revolution rather than that of 22 metaphysics. In the history of science and religion, following the triumph of 23 Copernican-Galilean heliocentrism , geological, geomorphological, cosmological and cosmogenic theorizing then served, in the time of Newton and Leibniz, to greatly undermine the strict historical veracity

19 cf. J. G. Simms, “John Toland (1670–1722), Donegal heretic”, Irish Historical Studies, vol. 16, no. 63, March 1969 , pp. 304-320; M. Brown, A Political Biography of John Toland, Oxford, New York, 2012; see chap. 1 (Ireland, 1670-1697), chap. 2 (London. 1697-1700) and chap. 3 (Hanover, 1701-1707). 20 cf. N. Gädeke, “»Matières d’esprit et de curiosité« oder: Warum wurde John Toland in Hannover zur persona non grata?”, pp. 145-166, in: W. Li, S. Noreik (eds.), G.W. Leibniz und der Gelehrtenhabitus: Anonymität, Pseudonymität, Camouflage, Köln (Cologne), Weimar, Wien (Vienna), 2016. 21 cf. J. Toland, Christianity not Mysterious, or a Treatise shewing, that there is nothing in the Gospel contrary to reason, nor above it, and that no Christian doctrine can properly be call’d a mystery, London, 1696; P. Mc Guinness, A. Harrison, R. Kearney (eds.), John Toland’s Christianity not Msterious. Text, Associated Works and Critical Essays, Dublin, 1997. Regarding Leibniz’s Thought on Divine Creation, see for example: N. G. Robertson, “The Doctrine of Creation and the Enlightenment”, pp. 425-439, in: R. D. Crouse, W. Otten, W. Hannam, M. Treschow (eds.), Divine Creation in Ancient, Medieval, and Early Modern Thought, Leiden, Boston, 2007. 22 cf. J. G. O’Hara, “Science not Metaphysical. Leibniz als Naturwissenschaftler in der Nachfolge von Galilei”, in: M. Kempe (ed.), Der Philosoph im U-Boot[.] Praktische Wissenschaft und Technik im Kontext von Gottfried Wilhelm Leibniz, Hannover: Gottfried Wilhelm Leibniz Bibliothek, Forschung, vol. 1, 2013, pp. [33]-56. 23 cf. for example: (1) O. Pedersen, Early Physics and Astronomy: A Historical Introduction, Cambridge, 1974 and 1993; see chap. 20 (The Reform of Astronomy), and in particular pp. 263-282 (Nicolaus Copernicus, and After Copernicus) (2) F. Krafft, “Die ‚Copernicanische Revolution‘”, Antike und Abendland, vol. 40, 1994, pp. 1–30 (Reprinted in: H. Kuester (ed.), Das sechzehnte Jahrhundert. Europäische Renaissance, Regensburg, 1995, pp. 181–214 ) (3) M. A. Finocchiaro, Defending Copernicus and Galileo: Critical Reasoning in the Two Affairs (Boston Studies in the Philosophy of Science, vol. 280), Dordrecht, Heidelberg, London, New York, 2010 (4) J. L. Heilbron, Galileo, Oxford, 2010. of Biblical narrative.24 And so the interaction between science and religion in the early-modern period led ultimately, in the words of Olaf Pedersen, to a “divorce of science and religion”.25 Pedersen has for example likewise described Leibniz’s meeting with the Danish physician, geologist, and Catholic theologian Nicola(u)s Steno (Niels Stensen) in Hannover, on December 7, 167726, as the meeting of a “Scientist and [a] Saint”, of a “Rationalist” and a “Faithful Observer” which was the overture perhaps to their extensive scientific, philosophical and theological exchanges.27 In the light of this divorce of science and religion, Leibniz chose, in treating the physical world, to take the low road, as it were, of enlightenment, and of rational thought and scientific rationalism28 rather than the high road, so to speak, of mysticism, religion and theology.29 In this sense then Leibniz stands apart from contemporaries like Robert Boyle, Isaac Newton, William Whiston and others who have been broadly characterized as ‘scientist-theologians’ and who were inspired by a sense of compatibility of science and religion.30 Accordingly, following the concluding thesis of this work – which underlines Leibniz’s role both in the development of rational scientific thought in the last quarter of the seventeenth century and in an adherence to the principle of the separation of science and religion – and considering also the autobiographical self-characterization of his

24 cf. I. Leask, “Constant Process: The Science of Toland’s Pantheisticon”, Eighteenth-Century Ireland/ Iris an dá chultúr [Ireland of the two cultures], vol. 34, 2019, pp. 11-27; see p. 16. 25 cf. O. Pedersen, “The divorce of science and religion: Historical interaction between science and religion”, pp. 139-160, in: J. Fennema, I. Paul (eds.), Science and Religion[.] One World – Changing Perspectives on Reality, Dordrecht, Boston, London, 1990. 26 cf. K. Müller, G. Krönert, 1969 (op. cit., note 7), p. 50. 27 cf. (1) A. Vibeke Vad, “Polidore and Théophile: The Rationalist and the Faithful Observer”, pp. 39-47 (in particular p. 39), in: K. Ascani, H. Kermit, G. Skytte (eds.), Niccolo Stenone (1638-1686)[.]Anatomista, Geologo, Vescovo, Atti del seminario organizzato da Universitetsbiblioteket i Tromsø e l’Accademia di Danimarca lunedi 23 ottobre 2000 (Proceedings of a Conference on October 23, 2000), Rome (Analecta Romana Instituti Danici, Suppl. XXXI), 2002, and (2) H. Kermit, M. Drake (trans.), Niels Stensen[,] 1638- 1686[.] The Scientist who was Beatified, Leominster, Herefordshire, UK, 2003. See also: M. Lærke, “Leibniz and Steno, 1675-1680”, chap. 3, pp. 63-84, in: R. Andrault, M. Lærke (eds.). Steno and the Philosophers[.] Edited by Raphaële Andrault[,] Mogens Lærke, Brill’s Studies in Intellectual History, vol. 276, Leiden, 2018. 28 cf. M. Dascal (ed.), Leibniz: What Kind of Rationalist? (Logic, Epistemology, and the Unity of Science, vol. 13), Dordrecht, 2009; see pp. 1-13 (Introduction) and pp. [83]-152 (Part II: Natural Sciences and Mathematics). 29 cf. for example G. MacDonald Ross, “Leibniz and the origin of things”, Part III (Theology and Mysticism), chap. 17 (pp. [241]-257) in: M. Dascal, E. Yakira (eds.), Leibniz and Adam, Tel Aviv, 1993; A. P. Coudert, R. H. Popkin, G. M. Weiner (eds.), Leibniz, Mysticism and Religion[.] International Archives of the History of Ideas, no. 158, Dordrecht, Boston, London, 1998; L. Strickland (ed.), Leibniz on God and Religion: A Reader, London, 2016. 30 cf. R. Jakapi, “Early Modern Natural Philosophy Allied with Revealed Religion: Boyle and Whiston”, part IV, chap. 19, pp. 233-244, in: M. Fuller, D. Evers, A. Runehov, K.-W. Sæther, B. Michollet (eds.), Issues in Science and Theology: Nature – and Beyond: Transcendence and Immanence in Science and Theology, Cham, Switzerland, 2020. tiger-like vivacity and sprightly manners (in his letter to Rudolf Christian von Bodenhausen on December 30, 1693), the last line of the Epilog may be seen as the unofficial title of this book.

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Acknowledgements

I wish to thank my former colleagues and the present staff of the ‘Leibniz-Archiv’, the Leibniz editorial and research center, at the ‘Gottfried Wilhelm Leibniz Bibliothek’ in Hannover for their assistance and support in the preparation of this book. I am grateful to the ‘Gottfried Wilhelm Leibniz Bibliothek’, the main repository of the literary estate of Leibniz and in particular of the manuscript letters cited and quoted in this work, for access to its historical rare book and manuscript collections over more than three decades. All of the letter texts cited, quoted and translated have been previously published or cited in the volumes of the Leibniz Academy Edition. I am grateful to the ‘Gottfried Wilhelm Leibniz Bibliothek’, and to the Leibniz Edition, for permission to cite, quote and translate the texts presented here. I am particularly grateful to Michael Kempe, the present head of the ‘Leibniz Archiv’, for his encouragement and practical support in the preparation of this volume. Among other things I am grateful for access to the retro-digitized versions of older volumes of the Leibniz Edition. An earlier version of this work was circulated among the present staff members of the series III (Correspondence in mathematics, science and technology) and series VII (Mathematical Writings) of the Leibniz Edition. I am grateful for the comments, corrections and improvement suggestions received in return, particularly from Siegmund Probst and Hartmut Hecht, the present and former heads of the series series VII and VIII (Scientific writings), respectively. I am also grateful for the encouraging and constructive comments and suggestions of the three anonymous peer reviewers, as well as those of the Editorial team at Brill in Leiden, and in particular for the editorial assistance provided by Rosanna Woensdregt and her colleagues.

Hameln, December 2020 James Gabriel O’Hara

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List of Illustrations or Plates

All of the items in the following list of illustrations (with the exception of the first and the last) have been drawn following the figures in the original manuscripts by the author using the Adobe Illustrator graphics design and drawing program. All these drawings have previously been published in the volumes of the Leibniz Academy Edition. The first and last items [possible cover illustrations] are facsimile copies taken from the Oeuvres Complètes de Christiaan Huygens and the Leibniz Academy Edition, respectively.

Image files 1-17

Chapter 3 (p. [70])

Papin’s submersible vessel (1691). Source: Denis Papin to Christiaan Huygens, August 26, 1691 (Huygens, Oeuvres Complètes, vol. 10, p.120). = Image file 1

Chapter 4 (p. [23])

Papin’s mechanical thought experiment. Source: Denis Papin to Leibniz, December 9, 1695 (A III,6, p. 561). = Image file 2

Chapter 4 (p. [25f.])

Leibniz’s engineering thought experiment. Source: Leibniz to Denis Papin, January 1, 1696 (A III,6, p. 596). = Image file 3

Chapter 4 (p. [65])

Leibniz’s sketch of a damaged rod-engine transmission line. Source: Leibniz to Johann Daniel Crafft, April 16, 1694 (A III,6, p. 51). = Image file 4

Chapter 4 (p. [71])

Leibniz’s drawing illustrating Johannes Teyler’s method of calculating the quantity of fire power in a fortification array. Source: Leibniz to Christiaan Huygens, May 6, 1694 (A III,6, p. 73). = Image file 5

Chapter 5 (p. [38])

Sketch of Papin’s thought experiment regarding the substitution of a body with a surrogate body during a two-body collision. Source: Denis Papin to Leibniz, November 15, 1696 (A III,7, p. LV and p. 172). = Image file 6

Chapter 5 (p. [39])

Another sketch of Papin’s thought experiment regarding the substitution of a body with a surrogate body during a two-body collision. Source: Denis Papin to Leibniz, November 25, 1696 (A III,7, p. 190). = Image file 7

Chapter 5 (p. [41])

Yet another sketch of Papin’s thought experiment regarding the substitution of a body with a surrogate body during a two-body collision. Source: Denis Papin to Leibniz, January 14, 1697 (A III,7, p. 261). = Image file 8

Chapter 5 (p. [42])

Sketch of Papin’s thought experiment to demonstrate the equivalence of separate collisions of a body with two other bodies. Source: Denis Papin to Leibniz, October 24, 1697 (A III,7, p. 626). = Image file 9

Chapter 5 (p. [50])

Sketch of Leibniz’s thought experiment regarding the collision of a body moving along the diameter of a square with two other bodies resting at a corner. Source: Leibniz to Denis Papin, January 26, 1698 (A III,7, p. 709, p. 724 and p. 880). = Image file 10

Chapter 5 (p. [78])

Sketch of Leibniz’s design for sealing, or making airtight, the contact between a piston and a pump cylinder. Source: Leibniz to Denis Papin, August 8, 1698 (A III,7, p. 866). = Image file 11

Chapter 5 (p. [93])

Papin’s drawing of his new blast furnace. Source: Denis Papin to Leibniz, October 9, 1698 (A III,7, p. 916). = Image file 12

Chapter 6 (p. [16])

Chapter 6 (p. [17])

Papin’s sketch of the thought experiment regarding the collision of three spheres at a corner of a square. Source: Denis Papin to Leibniz, February 23, 1699 (A III,8, p. LVII and p. 60). = Image file 14

Chapter 6 (p. [36])

Sketch of Leibniz’s physical thought experiment regarding the operating principle of the barometer. Source: Leibniz to Bernardino Ramazzini, March 18, 1700 (A III,8, p. 371). = Image file 15

Chapter 6 (p. [66])

Drawing of Francesco Maria Levanto’s reverberation furnace. Source: Magnus Gabriel Block to Leibniz, June 24, 1699 (A III,8, p. 160). = Image file 16

Chapter 6 (p. [71])

Drawing of Jobst Heinrich Voigt’s threshing-machine. Source: Cord Gabriel Plato von Gehlen to Leibniz, November 28, 1699 (A III,8, p. 251). = Image file 17