Isaac Newton and Natural Philosophy (Renaissance Lives) 9781780239064, 1780239068

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isaac newton

☞ Books in the renaissance

lives series explore and illustrate the life histories and achievements of significant artists, intellectuals and scientists in the early modern world. They delve into literature, philosophy, the history of art, science and natural history and cover narratives of exploration, statecraft and technology. Series Editor: François Quiviger Already published Blaise Pascal: Miracles and Reason  Mary Ann Caws Caravaggio and the Creation of Modernity  Troy Thomas

Hieronymus Bosch: Visions and Nightmares  Nils Büttner Isaac Newton and Natural Philosophy  Niccolò Guicciardini John Evelyn: A Life of Domesticity  John Dixon Hunt Michelangelo and the Viewer in His Time  Bernadine Barnes Petrarch: Everywhere a Wanderer  Christopher S. Celenza Rembrandt’s Holland  Larry Silver

ISA AC NEW TON and Natural Philosophy n ic c ol Ò g u ic c i a r di n i

R E A K T ION B O OK S

Published by Reaktion Books Ltd Unit 32, Waterside 44–48 Wharf Road London n1 7ux, uk www.reaktionbooks.co.uk First published 2018 Copyright © Niccolò Guicciardini 2018 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publishers Printed and bound in China by 1010 Printing International Ltd A catalogue record for this book is available from the British Library isbn 978 1 78023 906 4

cover: Anon, Sir Isaac Newton, c. 1690, oil on canvas, London, Science Museum; © akg-images/Nimatallah

contents

Introduction: Images of Newton 7 1 From Woolsthorpe to Cambridge, 1642–1664 22 2 Early Achievements, 1665–1668 42 3 A Young Professor and His Audience, 1669–1674 76 4 A Maturing Scholar, 1675–1683 102 5 Natural Philosopher, 1684–1695 143 6 The Last Years, 1696–1727 180 Chronology 233 references

237 bibliograph\ 253 acknowledgements 257 photo acknowledgements 259 index 261

introduction

Images of Newton

T

he figure of isaac newton has survived the last three centuries untarnished. Generally regarded as one of the greatest scientists in history, Newton belongs in a list that includes Archimedes, Galileo, Darwin, Einstein and few others. However, this consensus con­ceals divisions, tensions and differences of opinion. The history of Newton’s reputation is in fact a complex one, which the histo­r­ ian cannot ignore. Whoever sets out to write a short intel­lec­tual biography of this English natural philosopher has to examine not only his printed works, numerous portraits, memorabilia and millions of words of manuscripts, but a succession of ‘images’ of Newton created by scientists, writers, artists, clerics and politicians, all demanding attention (illus. 1). Even when he was still alive, Newton’s work was given widely differing interpretations. While for many contempor­ ary British mathematicians Newton discovered the ‘new analysis’, for Continental mathematicians he was considered an expert in obsolete techniques. His new theory of light and colour was not accepted as the young Lucasian Professor expected in 1672, but instead sparked a controversy that lasted for many years. Newton’s theory of gravitation was described by his supporters as the incontrovertible discovery of the 1 Eighteenth-century copy after Godfrey Kneller’s first known portrait of Isaac Newton (1689), oil on canvas. This painting was recently identified by the director of the Accademia Tadini in Lovere, Marco Albertario.

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physical cause of planetary motion, while for followers of Descartes and Leibniz it was nothing more than an interesting mathematical theory, but devoid of physical meaning. While Edmond Halley praised the Principia as a work useful to navigation, for many members of the Royal Society Newton’s masterpiece seemed difficult to reconcile with Francis Bacon’s agenda, aimed at promoting useful knowledge, and backed by influential experimental philosophers such as Robert Boyle. The conception of nature proposed in the Principia and Opticks was hailed by some as compatible with the truth revealed in the Bible. For others, Newton’s mathematical principles of natural philosophy concealed potential risks for religion, with some accusing him of opening the door to the pagan inconsistencies of natural magic, Epicurean materialism or even the occult qualities given wide currency in Renaissance natural philosophy from which the new mechanical science had only recently freed itself. Other critics accused Newton of deism, of supporting an immanent conception of God or even of defending the anti-Trinitarian heresy, namely the denial of the teaching held by the majority of Christian denominations after the fourth-century ad ecumenical councils according to which God is three distinct ‘hypostases’ or persons who are coeternal, coequal and indivisibly united in one being. One might think that these initial, contradictory, contemporary readings over time could have converged towards a more detached, consistent evaluation, but this was not to be the case. The eighteenth century is often described as the ‘century of Newton’. A philosophe of Voltaire’s calibre was among the first to popularize Newtonian philosophy as the official

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Images of Newton

position of those who rejected the ancien régime and espoused the new philosophy of the Enlightenment. The political resonances of Newtonian propaganda as promoted by Voltaire in France were explicit: Newton’s philosophy of gravitation had been developed in a country free from censorship, where the French model of absolute monarchy had been repelled. From an Enlightenment perspective, Newtonian philosophy, or rather the ‘Newtonian method’, could be applied to other disciplines, also in the social and moral sciences. Newtonian natural philosophy in the mid-eighteenth century was an almost universal benchmark for how to acquire true know­ ledge. However, the result of this affirmation of Newton’s theories and method was not convergence and consistency, but rather fragmentation, with various attempts at appropriat­ing his work by apologists of Christianity as well as by atheists, empiricists associating Newton with Bacon, and rationalists who aimed to reconcile Newton with Gottfried Wilhelm Leibniz and Christian Wolff – as did Voltaire’s brilliant partner, the Marquise du Châtelet (illus. 2). And so in the eighteenth century the figure of Newton enjoyed a success and diffusion bordering on worship. Paint­ ings and statues dedicated to the great Englishman were accompanied by a laudatory literature that became a popu­ lar genre in both major cultural centres and the provinces. These eighteenth-century images of Newton, as we shall see, were however misrepresentations of the real man. The fact is that Newton’s science became nothing short of a cultural fashion that had little to do with historical research based on his writings. The aristocracy and rich upper classes sought instructors and experimenters who could keep them

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informed on Newton’s new natural philosophy. This interest was motivated on the one hand by the belief that scientific knowledge could be of help in commerce and industry, while on the other, Newtonian philosophy made it possible to contemplate nature as a product marvellously ordered by a divine artist (illus. 3). The publication of popularizing introductions 2 Émilie du Châtelet’s posthumous French translation of Newton’s Principia (1759) was enriched by her annotations written in Leibniz’s notation. Marianne Loir, Gabrielle Émilie le Tonnelier de Breteuil, Marquise du Châtelet, c. 1745, oil on canvas.

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Images of Newton

to the Principia and Opticks met with extraordinary success throughout the Age of Enlightenment. However – a fact known only to specialists in the history of science – this concealed a profound crisis in Newtonian thought in the eighteenth century. There was indeed a crisis in Newtonian mathematics, to the extent that we may even call the 1700s the century of the decline of Newtonian mathematics. It has been observed on various occasions that it was scientists from continental Europe, such as Johann and Daniel Bernoulli, Leonhard Euler, Jean-Baptiste Le Rond D’Alem­bert, Joseph-Louis Lagrange and Pierre-Simon de Laplace, who developed calculus in the eighteenth century, intro­ducing the concept of function, the creation of the calculus of partial derivatives and the calculus of variations. More­over, these developments were based on Leibniz’s notation and following leads provided by Leibniz’s work on math­ematics, not Newton’s. The Principia were finally accepted on the Continent, but only when seen in terms of Leibniz’s math­ematical formalism. Newtonian mechanics based on the three laws or axioms of motion was soon replaced by a more general approach formulated in terms of minimum principles such as the principle of least action. The crowning glory of mathematical progress in the eighteenth century, the Traité de mécanique céleste (1799–1827) by Laplace, certainly marked the success of Newton’s ideas, being based on the theory of gravitation, but also showed their weakness: such success had been made possible using notation and concepts attributed to Leibniz and his Continental followers. This was already in evidence in François Jacquier and Thomas Le Seur’s annota­ ted edition of the Principia (Geneva, 1739–42). These two

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French Minim friars based in Rome produced their annotations in collaboration with the Genevan mathematician and moderate Calvinist Jean-Louis Calandrini. This edition is interesting because in their notes the three commentators used the Leibnizian calculus and many results achieved by Continental mathematicians, such as Johann Bernoulli and Leonhard Euler. Indeed, the Continental mathematicians were quick in rereading and adapting Newton’s magnum opus to their own mathematical language. In the image reproduced here we can see the two friars quietly collaborating in commenting on Newton’s holy text. Jacquier commissioned this painting after the death of his close friend. The painter had to rely upon a caricature of Le Seur: thus the père’s far too long nose (illus. 4). It was in the early nineteenth century that the image of Newton began to be significantly reappraised. This took place in a cultural context too complex to be sketched, even briefly, 3 In Georgian Britain, it became a popular fashion to ask itinerant lecturers to illustrate the Newtonian System of the World by means of the ‘orrery’, a mechanical model of the solar system. Joseph Wright of Derby, A Philosopher Giving a Lecture on the Orrery, 1766, oil on canvas.

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Images of Newton

in this introduction. One need only recall generally how the advent of pre-Romantic sensibilities, Naturphilosophie and a critical attitude towards the Enlightenment may have encouraged a rejection of Newton’s ideas, identified – as we shall see, wrongly – with Enlightenment ideology. Moreover, in the 4 François Jacquier and Thomas Le Seur portrayed as working on a mathematical problem. The spine of the Bible can be seen on the far left, representing the reconciliation between science and faith. Louis-Gabriel Blanchet, The Fathers François Jacquier and Thomas Le Seur Working in Their Room at Trinità dei Monti in Rome, 1772?, oil on canvas.

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purely scientific field, there was a progressive decline of the corpuscular conception of Nature, once again wrongly identified with the natural philosophy of Newton. With Thomas Young and Augustin-Jean Fresnel, wave theories of light took hold, while it was commonly thought that Newton defended the corpuscular theory of light. The theories of Hans Christian Ørsted and Michael Faraday conceived of electrical and magnetic action as caused by contact forces, that is, actions that are transmitted at a finite velocity in a medium, rather than instantaneously and at a distance, as is the case for Newtonian gravitation. The early nineteenth century is a source of great interest to the biographer of Newton. It was in this period that, as mentioned above, the image of Newton was reviewed, and the echoes of this reappraisal can still be heard today. Through­ out the eighteenth century, biographers of Newton had merely echoed the praise of Bernard Le Bovier de Fontenelle, who in turn had received information from John Conduitt, husband of a half-niece of Newton, and a close friend of Newton in his last years, who looked after a rich collection of manuscripts that Newton had left at his death. Although stereotyped, the image of Newton was not without a certain complexity. For example, it was well known that Newton, in addition to working on mathematics, the science of motion, optics and the theory of gravitation, had cultivated an interest in biblical exegesis, prophesies, alchemy and chronology. It was no secret among his contemporaries, especially his correspondents and friends, that he had embraced some form of anti-Trinitarian heresy.1 This could be gleaned in various works of his printed posthumously, such as The Chronology of

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Images of Newton

Ancient Kingdoms Amended (1728), Observations upon the Prophecies of Daniel, and the Apocalypse of St John (1733), A Dissertation upon the Sacred Cubit of the Jews (1737), the text of two letters on the Trinitarian corruptions of the New Testament (1754) and four letters addressed to the theologian Richard Bentley on the relationship between God and Nature (1756). The prevailing interpretation in Britain, a few decades after Newton’s death, when the memory of Newton in the flesh had faded, was that in addition to being a great natural philosopher, he was also a Christian in perfect harmony with Anglican orthodoxy. His view of the world would have implied, if not proven, that there was a supreme architect. Newton’s alleged heresy, which his contemporaries had to some extent suspected, was thus gradually forgotten. This reassuring vision was put into question by the gradual discovery of Newton’s private archive, which had been consulted only sporadically in the eighteenth century and the first half of the nineteenth century. Newton’s private papers reveal a man of pronounced intellectual and moral strength, engaged in research dictated by an agenda in many ways unexpectedly unrelated to the image of the scientist admired in the Enlightenment and of the devout Anglican celebrated by the Church of England. The first public opening of the archive took place in 1888 when a committee, formed by the astronomer John Couch Adams, the chemist George Downing Liveing, the medieval historian and antiquary Henry Richards Luard and the physicist George Gabriel Stokes, issued a cata­ logue of the collection of Newton’s manuscripts acquired by the University Library in Cambridge. The 5th Earl of Ports­mouth, a descendant of Catherine Barton, half-niece

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of Newton and wife of Conduitt, had decided to donate those papers of Newton in his possession ‘which related to science’. On receiving a preliminary report on the contents of the collection, Lord Portsmouth ‘expressed a wish that the papers relating to Theology, Chronology, History, and Alchemy, should be returned to him’. The committee thus retained only the manu­scripts relating to mathematics, the Principia, hydrostatics, the dispute with Leibniz, optics, astronomy, a few alchemical ones and part of the correspondence, and returned those concerning ‘non-scientific’ subjects, including biog­ raphical matter and papers concerning Newton’s activities at the Mint, considering them ‘not of much interest’.2 We here see for the first time the division between two Newtons, the scientist and the alchemist, the experimental philosopher and the heretic, which would end up dividing Newtonian scholars into opposing camps. Newton’s ‘secret’ manuscripts were later sold at public auction in 1936. While the break-up and dispersion of the Portsmouth archive may be deplored, it was precisely this sale that finally made Newton’s papers available to scholars. After many vicissitudes, the two major buyers, who managed to acquire most of the lots auctioned for a pittance, were the Semitic scholar Abraham Yahuda and the economist John Maynard Keynes. Yahuda bought manuscripts relating to chronology, church history, the Temple and the study of prophecies. The Yahuda manuscripts are now preserved at the National Library of Israel in Jerusalem. Keynes instead donated the manuscripts in his possession, mainly related to alchemy and biographical memoirs, to King’s College, Cambridge.3 Keynes was also the author of an essay entitled

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Images of Newton

‘Newton the Man’ (1945) that caused a sensation. From the study of the manuscripts in his possession Keynes had come to the surprising conclusion, so often quoted, that Newton was not the first Enlightenment scientist, but rather a follower of the great twelfth-century ad Jewish Talmud scholar, philosopher and scientist Moses Maimonides (Moshe ben Maimon): Newton would have been no less than a philosopher who tried to decode the texts of an ‘esoteric brotherhood’ active since antiquity in the Middle East. For Keynes, he was, ultimately, not a scientist but ‘the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago’. 4 Indeed, Keynes’s manuscripts cannot fail to provoke astonishment: here Newton speaks in symbols and alchemical emblems, of a vegetative spirit that pervades Nature, the transmutation of metals, Egyptian and Chaldean myths, the wisdom of Hermes Trismegistus and the philosopher’s stone. The reader of Keynes’s manuscripts will find, for example, that in the early 1690s, just after completing his masterpiece on planetary motions, the Principia (1687), Newton read French alchemical literature with the help of Nicolas Fatio de Duillier (illus. 5). It is clear that Newton was fascinated by the emblem representing the philosophers’ stone, which he reproduced in a manuscript bearing the title ‘The method of ye work’, which Keynes could acquire for about twenty pounds in 1936 (ms Keynes 21, fol. 6r (King’s College Library, Cambridge)). Who, then, was Newton? The cold mathematician who calculated the orbits of the planets, espousing a deterministic

5 Engraving from Alexandre Toussaint de Limojon de Saint-Didier’s Le Triomphe hermétique, ou la pierre philosophale victorieuse (Amsterdam, 1689).

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Images of Newton

view of nature and stripping ‘the awful rainbow’ of ‘all charms’, as John Keats complained? Or rather a heretic who, denying the tenets of orthodox Christianity, conceived of natural phil­ o­sophy as a search for the providential action of a single God pantocràtor? Or, maybe, ‘the last of the Sumerians’, a mystical restorer of the esoteric pagan wisdom of Hermes or a follower of Maimonides? We should take into account that these questions, emerging in the mid-twentieth century in the wake of the discovery of the manuscripts of the Portsmouth Collec­ tion, were posed in a cultural climate particularly sensitive to issues such as the boundary between science and non-science, debated in the philosophical field by Karl R. Popper, Paul Feyerabend and Thomas Kuhn. Historians, on the other hand, were engaged in research, undertaken by pioneers such as Walter Pagel, Paolo Rossi and Frances A. Yates, aimed at assess­ ing the role of magic and alchemy in the so-called scien­tific revolution.5 Two factions soon formed, with the defenders of Newton the scientist led by Alfred Rupert Hall, Marie Boas Hall, I. Bernard Cohen and Derek Thomas Whiteside, who tended to belittle the importance of his alchemical and theological manuscripts.6 The innovators, including Frank E. Manuel, Betty Jo Teeter Dobbs and, to some extent, Richard S. Westfall, were supporters of the ‘other’ Newton, the alchemist and theologian who would devote only a small fraction of his time and energy to mathematics and physics.7 This generation of great Newtonians has now gone, but left an important legacy. It is time for us to re-examine the issue of the two Newtons that emerged as a result of the sale of the manuscripts, but with greater serenity. Largely thanks to the historians mentioned above, we know much more about

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Newton and his time, and consequently Newton’s interests in alchemy, chronology, biblical prophecies and Church history seem less surprising to us. Newton was a man of his time, not a Sumerian, a neo-Platonic belonging to Marsilio Ficino’s Academy or a Paracelsian alchemist at the court of Rudolf ii. His passions and studies, however ill-suited to our modern image of a scientist, would not have seemed unusual to his contemporaries, although his conclusions and methods may sometimes have surprised them. He was clearly not a man who liked to repeat what he had learned from others, but an original thinker always committed to finding something new, be it a mathematical theorem or the interpretation of a biblical passage. The task we have before us is fraught with difficulties. First, we have to understand that Newton’s work is not an attempt to answer questions that came to him spontaneously, but to address those posed by his contemporaries. These questions, however, did not have a merely theoretical dimension, but existed in a political and social context beset by dramatic events that Newton, like all men and women of his time, had to deal with. We will need to examine Newton’s sources, but also his correspondence and his extremely peculiar approach to the publication and promotion of his ideas. Second, we must, in our attempt to bridge the gap between Newton the scientist and the ‘hidden’ Newton that emerges from what might be the result of too hasty a reading of the Portsmouth manuscripts, avoid the risk of a reductio ad unum, the idea that there is a key to understanding the substantial unity of Newton’s thought: the idea, for example, that we can easily draw analogies between his mathematical and

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Images of Newton

theological work. Quentin Skinner has already warned against this ‘myth­ology of coherence’, in reference to the thought of Niccolò Machiavelli and Thomas Hobbes; according to him, it is necessary to avoid seeking to artificially create con­sistency in the classics a posteriori.8 Newton’s intellectual biography is full of contradictions and fractures, as much as those of Machiavelli and Hobbes portrayed by Skinner. These contradictions must be acknowledged, provided that we do not view them in terms of disciplinary distinctions emerging many years later; that is, in terms of distinctions defined in terms of concepts such as science and non-science that were unknown to Newton and his contemporaries, who identified themselves as natural philosophers rather than scientists. Third and last, and this aspect is particularly close to my heart, we should not think that the ‘traditional’ Newton, the mathematician and physicist, is less remote to us than Newton the alchemist and theologian. In Newton’s England, astronomy, optics and even mathematics were disciplines whose aims and methods were defined in ways considerably different from the ones accepted nowadays. What matters from the point of view of this book is to understand how these scientific disciplines were conceived by Newton and his contemporaries as deeply connected to issues of great religious and philosophical reach, contrary to what happens today. Now, after this brief historiographical introduction, and having risked tiring the reader with too many caveats, it is time to meet Newton. In the next chapter we will travel to a small village of the North of England a few months after the outbreak of the Civil War between the Royalists and Parliamentarians.

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From Woolsthorpe to Cambridge, 1642–1664

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he \ears in which Newton lived (1642–1727) were beset by profound upheavals that transformed the monarchy, the Church and Parliament. In his long life, Newton witnessed the Civil Wars (1642–51) and the Interregnum (1649–60), the Restoration of the Stuarts (1660–88) and the Glorious Revolution of 1688, which placed William of Orange and Queen Mary Stuart on the throne, and finally the Hanoverian succession (1714).

political and r eligious context The Civil Wars occurred during the years of Newton’s childhood. This unprecedented military confrontation between parliament and king was incepted in 1642, causing armed conflicts in Ireland, Scotland and England. War broke out fol­lowing the unrest caused by a crippling tax policy promoted by the king. Moreover, together with the archbishop of Canterbury William Laud, the king had pursued a policy fav­ourable to the episcopal structure and rituals of the Church

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From Woolsthorpe to Cambridge

of England that was opposed by influential and well-organized religious groups, most notably the Puritans. The Puritans, influenced by the thought of John (Jean) Calvin, thought that only a few were predestined for eternal salvation, preached a rigid moral doctrine and acted with enthusiasm in the parishes to organize the communities of the faithful and godly. As they saw it, Church doctrine and the Sunday services imposed by Laud were too similar to Roman Catholicism. The language of the Puritans was inflamed by heated rhetoric, and their vision of the world was at times close to millenarianism. We should take into account the fact that since 1618 continental Europe had been in the grip of the Thirty Years War, a brutal conflict that decimated the European population, accompanied by the looting and famine so well depicted in the etchings of Jacques Callot (illus. 6). The war had broken out among Catholics, Lutherans and Calvinists, who had taken up arms against each other. What clearer sign could there be that it was urgent to identify the right cause, to be on the side of the saints in a religious war fought in the name of the Lord?

6 Jacques Callot, The Hanging, 1733, etching.

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Newton, then, spent his childhood in an England beset by civil war, culminating in the execution of the king (1649; illus. 7) and exile of his successor (1651). The family and school environment where Newton spent his childhood was, as we shall see, far from homogeneous politically and religiously: the split resulting from the civil war even crept into the provinces, dividing and tearing apart families and small commu­n­ities. It is very likely that young Isaac witnessed the divisive effects of political sectarianism and religious fanaticism. Throughout his life Newton would appreciate the beneficial effects of a political vision that tolerated religious differences (albeit with the exception of Catholics) and opposing political opinions: he entertained more than cordial correspondence with Jacobites and Whigs, Arminians and Socinians, Presbyterians 7 Execution of Charles i, from The Confession of Richard Brandon the Hangman (London, 1649).

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From Woolsthorpe to Cambridge

and Episcopalians, belying the current vision of Newton as a fanatic and misanthrope. Since 1653 the charismatic Oliver Cromwell had been head of the Commonwealth of England, Scotland and Ireland with the title of Lord Protector. By the death of Cromwell (1658), the failure of his son Richard to establish himself as a credible leader, tensions and discontent caused by another bout of economic depression and fear at the prospect of riots caused by religious groups perceived by many as ‘extrem­ists’, such as the Quakers, had paved the way for the restoration of the Stuarts. When, in 1660, Charles ii returned from exile he did nothing to hide his love for the good life and pomp, and flaunted his mistresses. A large part of English society res­ponded favourably to the new climate that promoted pleasurable entertainments, culture and theatre. However, the Stuart Resto­ration did not fail to arouse the concerns and suspicions of those who saw in the restored monarchy a reaffirmation of the rights of Catholics. Already in 1663 a Member of Parliament referred to rumours that ‘there is a design, and an intention to change the constitution of the government of this kingdom and to reduce us after the model of France, [where] they have lost all their liberties, and [are] governed by an arbitrary and military power.’1 Anti-Catholicism and anti-popery were fuelled by the fact that Charles ii seemed to nourish sympathies, confirmed by historical research, for the France of Louis xiv, where Protestants were under attack. In effect, the Treaty of Dover of 1670 established an alliance with France against the United Provinces, an alliance whose commercial viability was evident, but which contained secret clauses stipulating that Charles ii

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would declare himself a Catholic, if and when the opportunity arose, in exchange for French financial aid. The suspicions of his subjects were therefore well founded, beyond their worst expectations. The Third Anglo-Dutch War (1672–4) came to be perceived by many as a counter-reformist crusade. The year 1672 saw the promulgation of the Second Declaration of Indulgence, in which Charles ii tried to ensure religious tolerance, suspending the penal code against all those, the so-called ‘non-conformists’, who publicly did not adhere to the prayers, rites and administration of sacraments prescribed by the Church of England according to the Act of Uniformity (1662). Charles’s move was interpreted as being in favour of Catholics. In the following year Parliament forced the king to withdraw the Declaration of Indulgence, otherwise they would not vote to provide money for war, and to give his approval to a new Test Act, which affirmed the opposite principle: all holders of office were required to pass a sacramental test (that is, to take Anglican Communion) and pronounce a declaration against transubstantiation. For all those not prepared to accept the occasional conformity practised by some Protestant Dissenters, this meant remaining marginalized. In 1673, as a consequence of the new legisla­tion, the king’s brother, James, resigned as Lord High Admiral and married the Catholic Mary of Modena, nicknamed the ‘Pope’s daughter’. James, even more than Charles, was a source of acute concern for anti-Catholics. In Restoration England incendiary pamphlets, such as An Account of the Growth of Popery and Arbitrary Government in England (1677) by Andrew Marvell, were printed against the Crown, accusing it of plotting to introduce a regime of absolutist tyranny. Public opinion went

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From Woolsthorpe to Cambridge

so far as to accuse the Catholics of causing the plague (1665) and Great Fire of London (1666). The late 1670s and early 1680s, in which Newton began to be interested in the texts of heretical sects, were characterized by deep concern about the imminent restoration of Catholicism, popery and ‘arbitrary’ government. From 1679 to 1681 there was an attempt to exclude James from succession to the throne by law. One of the main defenders of the move was the patron of John Locke, Anthony Ashley Cooper, 1st Earl of Shaftesbury. In the 1690s Newton, as a friend and correspondent of Locke, thus found himself dangerously close to an environment where incendiary ideas had circulated. In Locke’s milieu it was believed that during the Restoration a Catholic conspiracy was in progress, and that it was necessary to oppose this plan; a few were prepared to envisage violence and an armed conflict against the king if necessary. As we will see later, the succession of James ii (1685) made the situation even more serious for those sharing antiCatholic feelings. While Charles ii’s agreements with Louis xiv were secret, and his suspected Cath­olicism was revealed on his deathbed when he was in a feeble state of health, the case of James ii is different. James, a self-declared Catholic, openly tried to defend the interests of his co-religionists, attempting to repeal the Test Acts and promoting Catholics to positions of leadership. Newton, as we shall see, played a role opposing this. The public, one might even say courageous, taking of sides by Newton aligned him with the Whigs, though not with the more radical fringe, and this partly explains his political fortunes after the Glorious Revolution (1688). After the events of 1688 and 1689 Newton was on the side of the

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winning faction in English politics. We will see in Chapter Six how his familiarity with the powerful Charles Montagu, first Lord Halifax, probably helped him in his London career. Throughout Newton’s lifetime extremists with deist or heretical ideas were feared, persecuted and excluded from social life in England perhaps even more than Catholics. Deists believed that the truths of religion were accessible to reason, regardless of revelation: a position that Newton most probably never shared. The heretics in Newton’s England included advocates of the anti-Trinitarian heresy, such as the Socinians, the followers of the anti-Catholic humanists Lelio and Fausto Sozzini who rejected the dogma of the Trinity. Others maintained heretical positions on many key issues, such as the existence of the Devil, and the survival of the soul over the body (the so-called ‘mortalists’, whose most famous member was John Milton). There was widespread persecution of religious minorities, such as the Quakers, not only during the Restoration but after the Glorious Revolution, with exclusions from academic office (this was the case with Newton’s friend and successor to the Lucasian Chair at Cambridge, William Whiston), arrest, torture and, in some exceptional cases, execution. We will look at the controversial issue of Newton’s ‘religion’ in greater depth later. Here we need merely observe that Newton developed, although exactly when is unclear, marked sympathies for a form of anti-Trinitarian heresy which, if it had become public, would have completely compromised his academic and political career.

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From Woolsthorpe to Cambridge

childhood And so, a few months after the outbreak of the Civil War, on 25 December 1642 according to the Julian calendar then in use in England, Isaac Newton was born in Woolsthorpe, near Grantham in Lincolnshire (illus. 8).2 He had already lost his father, also named Isaac. The Newtons were yeomen farmers, small landowners, who enjoyed a good reputation (Isaac senior was lord of a manor), but whose ranks did not boast men of letters or members of the clergy. A more important role in the cultural education of the young Isaac seems to have been played by his mother’s family. His mother, Hannah Ayscough (or Aiscough), was born in a more learned family of the minor gentry. Hannah’s brother, William, achieved a

8 Woolsthorpe Manor, near Grantham, Lincolnshire, the birthplace of Isaac Newton.

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certain success, studying at Cambridge, obtaining his ma and being ordained in the Anglican clergy. In fact, the young Isaac grew up under the care of Ayscoughs, for whom it was natural to provide an education for the family’s children. When Isaac was three, Hannah married 63-year-old Barnabas Smith, Rector of North Witham, and moved into her new husband’s house. Newton may have perceived this as an abandonment, although he was left in the hands of his grandmother, and Smith’s rectory is, according to Google Maps, just a 33-minute walk away. When the Rector died in 1653, Hannah returned to Woolsthorpe with three siblings. From these origins, humble but not poor, Newton climbed up the social ladder with a success that reveals a character ready to grasp, in a hierarchical society, any opportunities conducive to social and economic advancement. As we shall see, Newton would first obtain a professorship at Cambridge (1669), a distinction less important at the time than one might imagine today, then become a member of the Conven­ tion Parliament (1689), Warden (1696) and Master (1700) of the Royal Mint, a lucrative and prestigious post, and later be appointed President of the Royal Society (1703). In 1705 he was knighted. Engineering a successful career in the society in which Newton lived was no mean feat. On the one hand, there were undoubtedly factors of progress and social mobility. England in the seventeenth century experienced a period of marked demographic expansion, accompanied by the redistribution of wealth in terms of land, partly as a result of the expropri­ ation of the monasteries and the sale of land belonging to the Crown established under the Republic. Urban areas witnessed

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From Woolsthorpe to Cambridge

significant growth, London especially. These factors led to the emergence of new social strata among traders and the urban classes, who often ended up filling the ranks of the gentry. On the other hand, the rise in population caused many to succumb to poverty. Further, the continuous upheavals, vendettas and purges could change the fortunes of many and, in some cases, even lead to expulsion from public office or judicial persecution. In 1655 Newton began to attend the Free Grammar School in Grantham (about seven miles from Woolsthorpe), where he lodged with the town apothecary, a certain William Clark(e), who distinguished himself as one of the most eminent Puritan sympathizers of the Republican cause in the town. Until then, the young Isaac had grown up in an environment, that of the Ayscough family and their friends the Babingtons, who had, instead, royalist and Anglican inclinations. The experience of political and sectarian conflict, and of how such conflict could split a small community, or even a family (the Babing­tons were related to the Clarks), into sympathizers of opposing parties, must have been a common experience in the England of those turbulent years. Clark, in addition to having probably exposed Newton to puritanical ideas, may have had a further role in the education of young Isaac. As an apothecary, and brother of a doctor (Joseph, who had close contact with another great figure from Lincolnshire, the neo-Platonist philosopher Henry More), Clark had a good chemical (or alchemical) library and a laboratory, which may have played a role in arousing an interest in chemistry and natural philosophy in the young student.

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At the grammar school in Grantham students were taught in the traditional way, in other words in classical languages, Latin, Greek and perhaps rudimentary Hebrew. These language skills were essential for reading the Bible, and thus for the ecclesiastical career chosen by many of Newton’s contemporaries. The first readings of Newton, however, concerned not only the Sacred Scriptures but a kind of erudite entertainment that came under the label of ‘mathematical magic’ (illus. 9), which spread thanks to the publication of catalogues of inventions and contraptions. According to testi­monies collected after Newton’s death, surviving manuscripts and engrav­ings of geometrical drawings still admired today by visitors to his birthplace in Woolsthorpe, these must have aroused in the young Isaac an early taste for technical invention and manual dexterity. These were in fact qualities that characterized his later experiments, destined to change 9 ‘How to make flying Dragons’, from John Bate, The Mysteries of Nature and Art in Four Severall Parts (London, 1654). The young Newton consulted this book, in order to put his manual dexterity to good use.

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the history of optics, such as the experimentum crucis and construction of the reflecting telescope, which are still seen as milestones in the history of physics. Unfortunately, we know little of the sundials that Newton, according to oral tradition, set up in Clark’s home. studies at cambridge In 1661, thanks to intervention by his uncle William Ayscough, rector of the parish of Burton Coggles, by the headmaster in Grantham, and probably also by Humphrey Babington, brother of Clark’s wife, Isaac became the first of the Newtons to receive a university education, entering Trinity College, Cambridge. Babington, after being expelled from Trinity for his royalist sympathies, had been reinstated, and promoted Newton’s interests on various occasions. The young Newton’s assessment of the political situation in the early years of his university career is unknown, but we have enough clues to be able to speculate. In a non-technical (not theological or political) sense of the term, Newton was a puritan: he did not join in the festivities of his peers, and closed himself in his study, where he would meticulously list his sins.3 In 1663 he met John Wickins, who had entered the college early that year, with whom he became friends. Evidently, the two shared the same tastes, and we can assume that they despised the other revelling students. For twenty years Wickins remained Newton’s roommate and assistant, and occasionally aman­uensis. During his life, as far as we know, Newton remained a virgin, did not go to the theatre and rarely frequented the coffee shops that would become the

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meeting places for London’s educated society. Manuscripts survive in which Newton explains the rules for maximizing concentration in research and avoiding the temptations of worldly pleasures, which he then lists in such detail – bordering on the pornographic – that one suspects a certain inclination to voyeurism. Newton is not the only leading figure of the so-called Scientific Revolution to have behaved in this way. His friend Robert Boyle also saw asceticism as a necessary quality for the pious, Christian philosopher of nature. The historian of science Robert K. Merton even proposed a variant of the theory on the birth of capitalism published at the beginning of the twentieth century by the German sociologist Max Weber, to the effect that English Puritanism and German Pietism were a prerequisite for the development of experimental science.4 Rigid self-control, dedication to research, the serene acceptance of experimental results, the study of nature aimed at revealing the providential action of God, and an interest in the applications of the new science which could serve society, would all be elements of a scientific practice in harmony with the moral ideals of Puritanism. This influential thesis, now considered one-sided and overly generic, might how­ever capture an important aspect of Newtonian psychology, as far as we can tentatively surmise from historical evidence inscribed in his manuscripts and letters. The young Isaac matriculated as a subsizar, a poor student who served as a valet for others and who sat in separate pews in chapel during religious services. It is unlikely, however, that Newton had to submit to these humiliating tasks. He probably had other concerns, since the political situation at the

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university, and in England in general, was still unstable and in a state of flux. The Restoration of the Stuart monarchy had occurred just a year earlier and Cambridge, a hotbed of Puritan sympathizers, was under pressure. It is easy to imagine the feeling of anxiety that the young Isaac must have experienced amid such political turmoil. To Newton’s generation the future looked uncertain, since no established and recognized authority that could validate truth and guarantee justice was easily discernible. This instability also characterized the fields of natural philosophy and theology. The Aristotelian philosophy still taught at Cambridge was in disrepute. Various new philosophies were being ambitiously advanced by Bacon, Descartes, Hobbes, Spinoza and More, among others, as substitutes for the old forms of knowledge. It was perceived that a choice between them would have important theological implications, and recent European and English history had shown how easily theological debates could translate into political unrest and the miseries of war. Newton soon sought an answer to these concerns in a world on paper: in books that he could borrow or acquire, and notebooks he would fill in minute yet legible handwriting, organizing his ideas according to the genre of theological commonplace books. As we will see, certain works on math­ e­ma­tics polarized Newton’s attention with a strength that, I feel, was not due to any choice on his part but to the fact that his mind was extraordinarily equipped for mathematical inventiveness. His annotations after the winter of 1664 reveal the journey of an independent mind that took the existing literature on the most advanced mathematical topics as a springboard for creating new concepts and methods. It is

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agreed by all commentators that within the span of a few years Newton became one of the greatest mathematicians and experimental physicists of all time. Studies in British universities were still closely linked to the Aristotelian tradition that Newton was familiar with from reading compendiums of logic, rhetoric and natural philosophy. These works are commented on in a notebook (some­times called the ‘Trinity Notebook’), preserved in the Cambridge University library, that our subsizar began to write in 1661.5 Soon, however, Newton was attracted by a new ‘natural philosophy’, which questioned precisely Aristotelian philosophy, and began to read the works of Descartes. In particular, in 1664 Newton began to study in depth Geometria, a mathematical work published in French in 1637 as an appendix to the Discours de la méthode, and subsequently translated into Latin by Frans van Schooten, in which curves were represented by equations. Newton also commented on Descartes’ Principia Philosophiae (1644), the height of mechanical philoso­ phy, which is an attempt to explain all natural phenomena in terms of geometry, matter, motions and collisions. Moreover, he read the works of Boyle (he commented on his Experiments and Considerations Touching Colours (1664)), John Wallis (particularly influential on him was the Arithmetica infinitorum (1656)), Galileo’s Dialogo in the English translation (1661) by Thomas Salusbury, Hobbes’s De corpore (1655) and Walter Charleton’s Physiologia Epicuro-Gassendo-Charltoniana (1654) (a version of Pierre Gassendi’s atomism). In short, through selfstudy Newton acquired a fairly extensive knowledge of the latest developments that the new natural philosophy had to offer. These readings, it is worth mentioning, were not required

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by the university curriculum, but were engaged in out of pure personal interest. The pages of the notebook provide detailed information on the young Isaac’s readings, his initial reactions and his method of study. Particularly interesting are the pages penned in 1664–5 under the ambitious title of ‘Qu[a]estiones quae­ dam philosophiae’ (Certain Questions of Philosophy). The young student kept a commonplace book (that is, a notebook subdivided into various titled sections, each devoted to a commonly used topic: a topos in Greek, a locus in Latin, a ‘place’ in English) where he listed the subjects that interested him, and which he intended to study in greater depth – not only through the reading of Aristotelian and anti-Aristotelian texts, but by means of experiments. His method was thus analytical and comparative. Recording notes in a commonplace book was a technique in vogue in England in the seventeenth century and one which Newton had perhaps learned by imitating the theological notes of his stepfather. These can still be seen in the precious folio notebook known as the Waste Book, which once belonged to Smith, and which Newton had brought with him from Woolsthorpe.6 But Newton soon showed that he intended to contribute new ideas and new experimental results. Newton’s reading notes cover subjects from the nature of atoms and the vacuum to the cohesion of matter (typical themes of the Epicurean tradition accepted by Charleton and rejected by Descartes), the issue of the composition of the continuum and the nature of mathematical indivisibles (here we find traces of reading of the Mathesis universalis (1657) by John Wallis). They also touch on the nature of space, time and movement (here we

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see the clear influence of Descartes, whose works Newton studied, reading the Opera philosophica (1656)), the nature of stars and comets, and the composition of the universe. Newton was also interested in optical, magnetic and electrical pheno­m­ ena – Boyle’s Experiments and Considerations Touching Colours (1664) was studied carefully, while from 1665 there are traces of his reading of Robert Hooke’s Micrographia (1665). But the ‘Qu[a]estiones’ also contain theories and experiments (somewhat gruesome ones regarding the functioning of the eye) 10 Newton’s study of vision by pressing his eye with a bodkin so as to deform it (c. 1666). This experiment shows both Newton’s interest in the functioning of visual perception and the discipline he exerted upon himself.

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on sight (illus. 10) and hearing, imagination, fantasy and invention, the nature of the soul and God (and here Newton read and compared the opposing views of Hobbes’s De corpore (1655) and Henry More’s Immortality of the Soul (1659)). It is a list whose scope and apparent heterogeneity may be disconcerting for readers unfamiliar with seventeenthcentury natural philosophy. The fact is that the new natural philosophy, in all its widely varying versions (the Cartesian mechanical view, Gassendi’s atomism, the experimental phil­ o­sophy of Boyle and so on), questioned Aristotelian philosophy as a whole, and this shook one of the foundations on which scholastic philosophy was built. The enterprise undertaken by the ‘new philosophers’ involved the discussion and review of all the topics contemplated in the Aristotelian philosophical tradition. At the same time, Aristotelianism was presented as far from monolithic doctrine, since many possible readings of the Aristotelian corpus were possible. Dealing with this complex tradition meant, at the time, accepting an intellectual challenge that called into question the vision of the world, man, knowledge and ultimately of God Himself and of His relationship with Nature. Throughout his life Newton, like many of his contemporaries, would always maintain this broader view, this sense of the philosophy of nature as being based on an investigative approach that called into question philosophically and theologically challenging issues. During the years when Newton was a student, Cambridge boasted a philosopher, Henry More, who as we know was part of the entourage of the young Newton in Grantham, and a mathematician, Isaac Barrow, who in ways which are not entirely clear exerted some influence on his education. More,

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generally considered one of the leading exponents with Ralph Cudworth of ‘Cambridge Platonism’, attempted to read Cartesian mechanism as a premise for a neo-Platonic philosophy. After his initial enthusiasm for the thought of Descartes, More shared with many of his contemporaries deep concern about the potential materialistic and atheistic consequences of mechanical philosophy. In fact, according to More, Cartesian mechanism led to a conception of nature as a kind of clockwork mechanism, which worked according to the inescapable rules of impact: the natural world thus seemed independent of the providential action of God. What space was left for free will in a natural reality governed solely by the laws of the impacts between bodies? Nature cannot, according to More, be reduced to passive matter, motion and impacts between corpuscles: there is, according to the English philosopher, an immaterial element that makes Nature active and not merely passive. As we will see later, at least from the 1670s onwards, Newton also shared these theological concerns regarding the mechanical philosophy and corpuscularism. Newton’s debt to More is still the subject of debate among historians.7 We know for sure that the two exchanged ideas, but then found themselves in disagreement on a topic of common interest: the prisca sapientia of the ancient Hebrews and the hermeneutics of biblical prophecies.8 The role of Isaac Barrow in the formation of the young Newton, meanwhile, seems to be more documented.9 From 1663 onwards Barrow held the Lucasian Chair of Mathematics at Cambridge. He was a fellow of the same college as Newton, Trinity, and we know that he had a role in introducing Newton to the most sophisticated mathematical techniques. It is very

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likely that Newton attended some of Barrow’s lectures. There are strong similarities between the mathematics of Barrow and Newton’s early mathematical works. Barrow was also to ask his young colleague to oversee the publication of his lec­tures, and it was Barrow who promoted knowledge of Newton’s early mathematical discoveries in 1669 by sending one of his manuscripts to mathematicians in London. Finally, also in 1669, it was Barrow, stunned by Newton’s math­e­­ma­tical prowess, who ensured that the Lucasian Chair of Mathematics passed to his young protégé. We thus have reason to believe that Newton was not isolated in his early studies on natural philosophy and mathematics. But what were the mathematical discoveries that had so impressed Barrow? We discuss this in the next chapter. As we shall see, Newton in the mid-1660s, the so-called anni mirabiles (the marvellous years), made funda­ mental discoveries in mathematics and optics, and began thinking in an innovative way about gravitation.

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Early Achievements, 1665–1668

I

n 1665, as if england had not been sufficiently put to the test by political instability, the plague, probably coming from the United Provinces, hit London. By the summer the situation was dramatic. Owing to the lack of reliable censuses at the time, it is difficult to estimate the number of deaths. The poor in particular were decimated, and it is thought that between 1665 and 1666 about a quarter of London’s population died from the epidemic.

in the prime of the age for invention As a preventive measure, the University of Cambridge was evacuated and Newton moved to the country, isolated from the academic environment. This forced interruption of academic life is part of Newtonian mythology, since it is in this period that the famous episode of the apple is said to have taken place. The year 1665 is also referred to as Newton’s annus mirabilis. It is documented by surviving manuscripts that in 1665 and 1666 Newton achieved important results in mathematics and optics, and that he had interesting insights

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concerning uniform circular motion, the motion of the Moon, the planets and gravity. About fifty years later, this is how Newton would remember his early research: In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Binomial into such a series. The same year . . . I had the method of fluxions & the next year in January had the Theory of colours . . . And the same year I began to think of gravity extending to the orb of the Moon . . . All this was in the two plague years of 1665 and 1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then at any time since.1 This autobiographical reconstruction, so often cited, of his youthful scientific achievements is in broad outline correct, although we should extend the period to which Newton refers to the years 1665–8. It should be said that the autobiograph­ ical reports that Newton left for posterity – especially through the memoirs of confidants and friends such as John Conduitt, William Stukeley, David Gregory and Abraham De Moivre – and which constitute the material on which the first biographies of Newton were based, may not be accepted wholesale by an historian of science. However, in this chapter we will follow the course, broadly confirmed by historical research, laid by Newton himself in the above quote, and so in the next few sections we will give an outline of the young Newton’s discoveries in mathematics, optics and finally those relating to gravity.

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the methods of series and fluxions The young Newton had very few mathematical books on his desk (see Table 1).2 The new art of algebra, in which symbols for constant and variable magnitudes were manipulated by means of equations, attracted his attention. Newton was introduced to this new method by Viète’s and Oughtred’s works, but the seminal text in Newton’s mathematical formation was Descartes’ Géométrie. Descartes had proposed – or so he claimed in the opening sentence of the work – a novel method for the solution of ‘all the problems of geometry’. In the Géo­métrie Descartes had explained how ‘equations’ could be used in the process of geometrical problem solving. Indeed, problems in geometry, since Euclid’s times, had been solved by means of geo­­ metrical constructions, most notably by the intersection of curves. In the case of Euclid’s Elements, by the intersection of circles, traced by a compass, and straight lines, traced by a René Descartes, Geometria (Amsterdam, 1659–61) François Viète, Opera mathematica (Leiden, 1646) Frans van Schooten, Exercitationum mathematicarum libri (Leiden, 1656–7) William Oughtred, Clavis mathematicae, 3rd edn (Oxford, 1652) John Wallis, Operum mathematicorum Pars Altera (Oxford, 1656) John Wallis, Commercium epistolicum (Oxford, 1658) Table 1. Some of the mathematical books annotated by Newton in the 1660s.

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straight edge. Descartes’ revolutionary idea was that the curves employed in geometrical problem solving could be conceived of as loci of points (on a plane) the coordinates of which satisfy a relation expressed by a polynomial equation.3 Thus, for example, according to Descartes’ new method, 3y = ax2 is the equation of a parabola (where x and y are variables, and a is a constant). In the early seventeenth century geometry and algebra were still considered two separate disciplines, the former dealing with continuous magnitudes (such as lengths of segments, or angles), the latter with discrete magnitudes (such as the natural numbers 1, 2, 3, . . .). Therefore, in order to treat geometrical problems by algebraic means, mathematicians such as Viète, Fermat and Descartes had to overcome conceptual obstacles that should not be underestimated. By 1665 Newton had already mastered Descartes’ method. The representation and study of plane curves by means of equations was no mystery to him. Newton was particularly interested in a method for determining the tangent to a plane curve that Descartes had developed in the Géométrie and applied in the Dioptrique to devise non-spherical lenses. Simplifying somewhat, one might say that Newton became a mathematician by studying Descartes’ Géométrie. This short essay, which in its Latin edition was accompanied by a lengthy commentary by Frans van Schooten and other mathematicians, provided a systematic method for tackling geometrical problems. There were, however, lacunae and unresolved problems in the Géométrie. Most disappointingly, Descartes had confined himself to the algebraic treatment of what he called ‘geometrical’ curves (those we would identify as ‘algebraic’ curves)

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and had quite explicitly excluded ‘mechanical’ curves (‘transcendental’ curves, in modern terms) such as the spiral as lacking ‘exactness’. By this Descartes meant that these curves could not be expressed by an equation in x and y with a finite number of terms, such as x2 + y2 = 1 for the unit circle’s circumference.4 Further, Descartes had ignored a problem that was of the utmost importance: the calculation of the areas of curvilinear surfaces (for example, the calculation of the area of the circle). The most perceptive mathematicians of Newton’s generation understood that the next step in mathematical development was to devise a method for tackling the topics that Descartes had excluded from his masterpiece. Mechanical curves were interesting as objects of study for a whole series of reasons. They naturally emerged as solutions of problems concerning technology (for example, the cycloid was used by Huygens in his study of horology) and natural philosophy (for example, in his correspondence with Marin Mersenne, Descartes identified the logarithmic spiral as the solution of a problem on motion). Mechanical curves also occurred as solutions of problems concerning the area of curvilinear surfaces. Most notably, it was known that the area bounded by a hyperbola is expressed by the logarithmic curve. The calculation of logarithms – a very important issue in seventeenth-century mathematics, table-making, navigation, surveying and astronomy – was thus related to the mathematical treatment of a curve that had been excluded from Descartes’ Géométrie. We should not forget that Newton’s early mathematical discoveries were deeply motivated not only by the young student’s fascination for mathematics per se, but by practical

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applications, most notably to trigonometric and logarithmic table-making, and that Newton was soon, via John Collins, to attract the attention of mathematical practitioners, such as ‘gaugers’ engaged in calculating volumes of barrels. Too often we look at Newton as a natural philosopher whose thought flew high above the needs of mankind, and tend to under­ estimate how seriously he took the practical needs of the world of the so-called ‘mathematical practitioners’, such as gaugers and surveyors. Thus mechanical curves and the calculation of curvilinear surfaces emerged as a promising topic for young ambitious mathematicians – and Isaac Newton was certainly not lacking in ambition. But how could one deal with the above topics? It was by reading Hendrik van Heuraet and Joannes Hudde’s annotations to the Latin translation of the Géométrie (1659–61), and Wallis’s Arithmetica infinitorum (1656), and most probably by exchanging ideas and books with Barrow, that Newton found an answer: a technique he named ‘new analysis’. In early modern Europe ‘analysis’ was a term with a complex semantic stratification, as it was used in medicine, chemistry, philosophy and mathematics. To mathematicians ‘analysis’ meant the ‘art of mathematical discovery’, as outlined in Pappus’s Mathematical Collections, a fourth-century ad work whose Latin edition had appeared in 1588. What was ‘new’ in the analysis Newton was developing? To put it briefly, the use of the infinite and infinitesimal. Descartes’ method of problem solving was confined to the use of finite magnitudes (such as finite segments) expressed by ‘finite’ equations (that is, equations with a finite number of terms). Wallis, instead, had conceived finite curvilinear surfaces as composed

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of an infinite number of infinitesimal (smaller than any finite magnitude, but different from zero) component surfaces, and had calculated their areas by means of sums (or products) with an infinite number of terms (or factors). It was by following Wallis’s steps that Newton, in winter 1664–5, made his first mathematical discovery, the binomial theorem. This allowed him to approximate curvilinear areas via ‘infinite series’, that is, by summing an ever-increasing number of terms (imagine the calculation of the circle’s area by means of π, a number defined by an infinite number of decimals). The range of problems that Newton’s new art of dis­cov­ ery – the new analysis that he was soon to term the ‘methods of infinite series and fluxions’ – could broach successfully is impressive. Newton could determine tangents to all known curves. Further, he could calculate the area of surfaces bounded by curves important for astronomy, such as the ellipse, or even by mechanical curves, such as the cycloid. By means of the bi­nomial theorem, he was able to express trig­onometric magnitudes and logarithms in terms of infinite series. Indeed, the binomial theorem allows approximating the area of surfaces bounded by a circumference (hence the calculation of trig­ onometric magnitudes, such as the sine and the cosine) or bounded by an equilateral hyperbola (hence the calculation of logarithms) via infinite power series. The reader who wishes to get an idea of these approximations can think about the calculation of π as the number 3 followed by an infinite number of decimals, 3.14159 . . . The generality of this new method brought mathematics to a level that only a handful of mathe­maticians in Europe could dream of, most notably the Scots­man James Gregory, who was producing similar

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results. Newton’s ‘new analysis’ is certainly the most celebrated of his mathematical discoveries. Broadly speaking, one can say that this new technique consisted of what nowadays we call, to use Leibniz’s terminology, ‘calculus’. So it is often said that in his youth Newton ‘discovered calculus’. However, it is not trivial to say exactly what is meant by it. Historically speak­ ing, it is not a good idea to establish the mean­ing of the above expression too strictly, but rather leave the historical actors directly involved to speak and see what they meant by calculus, and how they practised it. Calculus as we know it today (and there is still ambiguity, sometimes dissent, about what it should be and how it should be taught) consists of a series of notations, concepts, methods and theor­ems that have been achieved over a long period of time; certainly it was not invented by a single man. Rather, we should conceive the discovery of calculus as a long process, at least spanning the period beginning with Pierre de Fermat and Kepler and culmin­ating with the work of Euler. Be that as it may, by the end of the 1660s, the first Lucasian Professor and, as a matter of fact, a major protagonist in the invention of cal­culus, Barrow, realized that his younger fellow in Trinity had achieved significant progress in mathematics that deserved to be known outside the confines of the University. Thus, through Barrow’s intermediation, a short manuscript tract in Newton’s hand entitled De analysi per aequationes numero terminorum infinitas (On Analysis by Means of Equa­ tions with an Infinite Number of Terms) was dispatched to London in July 1669. The addressee was Collins, an amateur mathematician who made a living, if only a modest one, out of his entrepreneurial activities in the field of mathematical

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book publishing. This sector was somewhat in crisis because of the depression in the print business caused by the Great Fire, but Collins managed to supervise the printing of several books, mostly related to algebra and navigation. In these disciplines there was a great need to update what was available on the English market. Newton devoted De analysi to his techniques for calculating the areas of curvilinear surfaces by means of infinite series. Newton was convinced that infinite series, which he called ‘infinite equations’, were the means for solving some of the most advanced unresolved issues high up on the agenda of the mathematicians of his age. When he summarized its contents for Leibniz in 1676, he stated, maybe echoing the incipit of Descartes’ Géométrie, that the ‘limits of analysis are enlarged’ by the use of ‘infinite equations’ in such a way that ‘by their help analysis reaches . . . to all problems’.5 When Collins received Newton’s tract he was thrilled, although it is debatable whether he really understood what he had in his hands (illus. 11). For Newton, getting in touch with Collins meant achieving free access to a network of mathematical correspondents, both in Britain and on the Continent, and to the bustling world of printers and booksellers active in the capital. Newton could not have been offered the option to print his method in a more conspicuous 11 Cover of the De analysi manuscript ‘Sent by Dr Barrow to Mr Collins’ on 31 July 1669. In Newton’s time mathematicians often circulated their ideas via correspondence rather than by printed publications.

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and attractive way, yet nothing came of it. One should note that Newton was not at the time extraneous to the printing business. Indeed, he busied himself in the edition of a book on geography by Bernhard Varen, which appeared in 1672, and through Collins’s instigation did a great deal of work in editing Barrow’s lectures and in updating the Latin translation of a Dutch treatise on algebra.6 The extant correspondence between Newton and Collins reveals much of Newton’s changing approach to publishing mathematics in the period from 1669 to the late 1670s. Collins had several proposals for Newton: for example, to issue De analysi together with some of Barrow’s works he was expecting to publish. While waiting for Newton’s permission, Collins made copies of De analysi, a short tract that would not have been so expensive to print, and we have good reason to think that he circulated information about this youthful work by correspondence with British and perhaps even Continental mathematicians. Reading the epistolary exchange between Newton and Collins leads the historian to follow a zigzag path: at first, Newton seems close to accepting Collins’s invitations to print De analysi, or even submit to him a more extensive treatise in which he had systematized his discoveries; but then – within a matter of weeks – we find him withdrawing his promise, much to Collins’s frustration. The new treatise was the so-called De methodis serierum et fluxionum (On the Methods of Series and Fluxions) he had almost completed in 1671.7 De methodis, a much longer treatise than De analysi, would have changed the history of mathematics if it had been printed in the 1670s. Yet this masterpiece was only published in an English translation more than sixty

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years (1736) after its composition, because of Newton’s idiosyncratic attitude towards publication, an attitude that was fuelled (as we shall see later) by the polemics surrounding the validity of the experimentum crucis in the years 1672–6 (illus. 12).8 Newton had achieved results that would have made him famous all over Europe as the most creative mathema­ tician then living. Yet in letters sent to Collins he stated his increasing reluctance to print them. By the mid-1670s Newton was adamant in not allowing his mathematical jewels to escape from his hands. To the lucky few who had corres­ponded with him on mathematical subjects and who had had access to his manuscripts he ordered silence and secrecy. What was the origin of Newton’s anxieties over printing his mathematical discoveries? Historians are still divided on this issue. In part, Newton’s attitude to the publication of his extraordinary mathematical discoveries is due to the fact that in his time mathematicians would communicate their results through the circulation of manuscripts and correspondence, rather than in printed publications. Further, we should not ignore the fact that in the late 1670s Newton began to have a critical attitude, bordering on contempt, with regard to the algebraic methods of the ‘Moderns’ and to turn his attention, which in the 1690s would become nothing short of veneration, to the geometric methods of the ‘Ancients’. According to Newton, algebra did not have the simplicity, beauty and certainty of geometry. In later life Newton would confide to the editor of the third edition of the Principia, Henry Pemberton, his regret for having begun his mathematical studies by reading Descartes rather than the works of the great geometers of ancient

12 Frontispiece from Isaac Newton, The Method of Fluxions and Infinite Series (London, 1736). Some ancient-looking mathematicians apply fluxions to help a shooter to kill two birds with one shot: his rifle is aligned along the tangent to the curve path lmn along which he is walking.

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Greece.9 Finally, as already mentioned, the frustrating and irritating controversy caused by the publication in 1672 of his early results in optical experimentation, to which we will turn in the next section, convinced him of the risks inherent in printed publication. This discovery in optics, like the methods of series and fluxions, is also closely linked to practical applications.

the prism and the telescope By now an old man, in 1726 Newton told his friend John Conduitt (husband of his half-niece Catherine Barton) that in August 1665 he had bought a glass prism ‘to try some experiments upon Descartes’ book of colours [the Dioptrique or the Météores (1637)]’.10 It thus seems that it was mainly Descartes, as in the case of mathematics, who inspired Newton. Yet we should also consider that Barrow’s lessons concerned precisely optics and mathematics, and that in Newton’s time the Aristotelian theory, according to which colours are generated by a mixture of light and darkness, was still defended by some, and certainly was critically considered by Newton. Descartes conceived of light as ‘a certain motion, or prompt and vivid action’ transmitted through a medium consisting of spherical particles. The spherical particles had a tendency to move in a straight line and a tendency to rotate on themselves. When white light, conceived therefore as the motion (or rather, a tendency to motion) of small spheres, was reflected or refracted, the spheres could acquire additional rotatory motion; it was this additional motion that generated the sensation of colour. The different texture of the surfaces

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of different bodies generated more or less rapid rotatory motions, and therefore different colours. Descartes’ theory could be used to explain optical phen­ o­mena, such as reflection, refraction and colours, in mechanical terms. Natural philosophers contemporary to Newton were uncertain of the nature of light, how it was produced and how it interacted with matter, and how to explain phenomena such as the rainbow, the formation of colour in chemical experiments, the colours produced in soap bubbles, and newly discovered phenomena such as birefringence and diffraction. Descartes had also enunciated a mathematical law on refraction (so-called Snell’s law) that could be used to study how lenses worked in telescopes. Newton soon also became aware of the alternative theories of light, such as that defended by Hooke, whereby light was a ‘quick vibratory motion’, ‘pulse’ or ‘vibration’ which propa­ gated in a medium. Hooke in Micrographia (1665) used the ana­ logy with ‘waves or rings’ propagating ‘on the surface of water’. These are so-called ‘wave’ theories as opposed to ‘corpuscular’ theories. Also according to the wave theory of Hooke, as for that of Descartes, white is the primary original colour of light, and colours are modifications of white light. Colour theories based on assumptions such as that of Descartes or Hooke are thus called ‘modificationist theories’. Pulses of white light, according to Micrographia, were deformed when they interacted with matter. It was this deformation that gene­rated the modified pulses that caused the sensation of colour. Another important source used by the young Newton was Boyle’s Experiments and Considerations Touching Colours (1664).

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Boyle felt that the explanation of the formation of colour should proceed first and foremost experimentally. The work’s subtitle is significantly The Beginning of an Experimental History of Colours, and the frontispiece bears a quotation from Bacon. Like Bacon, Boyle believed that it was first necessary to study the variety of circumstances in which natural phenomena occur. For example, Boyle studied the formation or alteration of colour due to chemical process, and focused on a great wealth of details. This led to discussion ‘of the changes of the Colour of Jasmin flowers, and Snow drops, by Alcalizate and Sulphureous Salts’ and ‘Of the Mixing and Tempering of Painters’ Pigments’, among others. In fact, the Experiments consist of a rich repertoire of experimental results followed by a discussion of the theories on the formation of colour at the time in circulation. Like everyone, Boyle adopted a modi­ ficationist theory. For him, colours were mainly the result of the modification of light when it interacted with the surface of bodies; the ‘Colour of Bodies depends chiefly on the disposition of the Superficial parts, and partly upon the Variety of the Texture of the Object’. It is of great interest that Boyle studied the spectrum of colours produced by a glass prism. Boyle also described an experiment in which he used two prisms, and this experiment might have inspired Newton in his research on light.11 In the years between 1665 and 1668 Newton thus spent his time replicating experiments already described in the available literature. Experiments with the prism were described in many works accessible to Newton; in addition to those of Descartes and Boyle, we can mention Charleton’s Physiologia and Hobbes’s De corpore.

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A decisive step came when Newton darkened his room, drilled a circular hole in the shutters of a window, and projected a beam of sunlight through a triangular glass prism. He projected the image onto a screen far away from the prism. Newton was thus able to observe the formation of the colour spectrum from red to violet, a ‘celebrated’ phenomenon, which he had already read about. But he did not see a circular image, as he might have expected. The image projected on the screen was extremely elongated. It is likely that already at this point the following insight flashed into Newton’s mind. Colours are not modifications of white light. On the contrary, white light is composed of colours. The prism does not ‘change’ white light, but divides it into its coloured components, with the red rays less deflected, and the violet ones most deflected in refraction. Before reaching this conclusion Newton reflected on the possible causes of the elongated shape of the spectrum. Was this perhaps due to defects in the glass of which the prism was made? Or to the positioning of the prism? Or the fact that the beam incident on the prism was not composed of parallel rays, because the sun fills a finite visual angle? One after the other, these explanations were disproved by careful varying of the experimental conditions. The method adopted by Newton, a combination of quantitative precision, imagination in the experimental arrangement and manual skills, progressively led to the conclusion that the beam of sunlight is composed of rays with different refractive indices, which are therefore deflected in the passage from air to glass, and then from glass to air, at different angles.12 To check this intuition Newton performed an experiment destined to become famous as the experimentum crucis (illus. 13).

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In this experiment, two prisms are used, abc and abc. After the first prism, which could rotate, he placed a first screen dge with a small hole. By rotating the prism abc Newton then projected a blue, red, or yellow beam through the small hole of the first screen, refocused it by passing it from a second screen dge and then made it hit a second fixed prism abc. Newton observed that the rays refracted at a greater/ smaller angle by the first prism were refracted at a greater/smaller angle again by the second prism.13 So white light, he claimed, was composed of rays with different refraction co­efficients. Newton’s readers have had trouble proving that the com­po­ nent rays are ‘immutable’, that is, that they are not changed by refraction. Indeed, the coloured beams passing through the second screen experience some notable chromatic dis­ pers­ion after passing through the second prism (for example, a yellow beam hitting the second prism will produce an image with green and red boundaries). The production of an (almost) homo­geneous coloured light beam was left as an open problem in the 1672 paper. Only after refining the experiment by using a lens could one verify that the second prism did not change the coloured beams leaving the first

13 Experimentum crucis. Sunlight passing through a small hole E is refracted by two prisms.

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prism, but refracted them, leaving their colour unchanged.14 Newton also performed various experiments in which he refocused the rays separated by a prism on a point, thus reobtaining a spot of white light. White light, Newton concluded, is not simple: it is an aggregate of rays characterized by different indices of refraction. These rays are simple constituents of light, since they are not altered through reflection or refraction. In his private annotations Newton interpreted this result in corpuscularist terms. That is, for him, light consisted of the emission of corpuscles. Newton observed that if light were a wave it would not propagate rectilinearly, but rather pass behind obstacles. In Huygens’s work one can find a wave model of light that shows that this Newtonian conclusion is incorrect. According to Newton’s theory, each colour was caused by particles of a different nature (for example, the corpuscles that generate the sensation of red may be faster or heavier than those that generate the sensation of violet). White light was thought to be a mixture of different corpuscles that were, by means of a mechanism of interaction between light and matter, separated by the glass prism. William Newman has seen an analogy between the language of Newton’s works on optics and those on alchemy: as an alchemist separates and then recomposes the corpuscles constituting matter, so the optician refracts white light through a prism, achieving the dispersion of the colours of the spectrum to then refocus them and once more obtain white light.15 As we will see, Newton would in any case attempt to distinguish his beloved corpuscular hypothesis of light from the result of the experimentum crucis, which simply proves that

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the components (whether corpuscles or other) of white light have different refractive indices. A practical consequence of the Newtonian theory of light regards the construction of telescopes. It was known that telescopes consisting of lenses are subject to a defect called spherical aberration in the focusing of the image. As Descartes had shown, when a collimated beam hits a spherical lens, rays which pass close to the centre of the lens are focused at a point slightly farther away than those passing through points near to the edge of the lens. This means that a monochromatic point source placed at a great distance is not focused exactly on a point. To obviate this defect, use was made of spherical lenses with the smallest possible curvature. This, how­ever, increased the focal length and meant that longer telescopes had to be made. So in the mid-seventeenth century extremely long telescopes were used; telescopes that were therefore very difficult to handle (illus. 14). One suggestion, discussed in Descartes’ Dioptrique (1637), consisted of trying to grind hyperbolic lenses, which, as shown 14 Johannes Hevelius (Jan Heweliusz) intent in making astronomical observations via a rather long refractor, from J. Hevelius, Machinae coelestis pars prior (Gdansk, 1673).

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in the Géométrie, are not subject to aberration. Descartes had been engaged, with the help of mathematicians such as Claude Mydorge, and grinders of lenses such as Jean Ferrier, in building a machine for grinding hyperbolic lenses (illus. 15). His expectations were great, and Descartes believed it would be possible to improve the performance of telescopes, thus allowing extraordinary advances in astronomy. Also in England, research in this area flourished, and the grinding of lenses not subject to aberration occupied many opticians and astronomers contemporary to Newton, whose works he read and made attentive notes on. Newton himself, in his early years of study, became interested in the construction of aspherical lenses. But having worked out his theory of colour, he became convinced that all these attempts were destined to fail. In fact, as he became convinced on the basis of the results of his experiments with glass prisms, lenses suffer from another defect: chromatic aberration. Since the various components of white light are

15 Machine for cutting hyperbolic lenses from Descartes, Dioptrique (Leiden, 1637).

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characterized by different refractive indices, a lens, however manufactured, cannot focus at the same point the different components of a point-like white light source. For Newton, it was no use struggling to grind aspherical lenses, since these would in any case be affected by chromatic aberration. However, chromatic aberration is an effect that regards refraction, not reflection: the rays of different colours are reflected in the same way. It is for this reason that Newton conceived and built a reflecting telescope. In Newton’s telescope the rays reflected by the concave mirror fall on a flat reflective surface inclined at 45 degrees (illus. 16). The image is seen through the eyepiece (a flat-convex lens) mounted with the axis perpendicular to the axis of the telescope. Newton used a spherical mirror, rather than a parabolic one: thus spherical aberration was not avoided. Further, the eye-piece lens will produce some slight chromatic dispersion. Reflecting telescopes were far from new. Most notably, the Scottish mathematician James Gregory had described one in 1663 in his Optica promota (which Newton was inspired by). It should be noted, however, that Newton was the first to provide a theoretical basis explaining the failure of

16 The structure of a Newtonian reflecting telescope consisting of a concave primary mirror and a reflecting secondary mirror (prism), from Optice (London, 1719).

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refracting telescopes; he stated that no lens system could prevent chromatic aberration. This proved to be too pessimistic, however. In 1695 David Gregory suggested, maybe after consultation with Newton himself, that the defect could be eliminated by ‘making the object lens of a different medium, as we see done in the fabric of the eye’, where the ‘crystalline humour’ is ‘by Nature who never does anything in vain’, joined with the ‘aqueous and vitreous humours’, which have a different ‘power of refracting’.16 In 1754 the Swedish mathematician Samuel Klingenstierna showed how an achromatic refractor could be constructed, and in the mid-eighteenth century the manufacturers of optical instruments, among which stand out achromatic lenses produced by John Dollond, managed to almost completely avoid chromatic aberration by combining glasses with different refractive indices. It should finally be noted that, although the idea of the reflecting telescope was not entirely new, Newton was the first to actually build one. The problems involved in the construction of the telescope were far from simple. In particu­ lar, Newton demonstrated great craftsmanship in the design of the mirror, made from an alloy of his own invention. Newton produced two prototypes of the telescope in 1668, and in 1671, at the encouragement of Barrow, he published the news and sent one to the Royal Society, which was dedi­ cated to the development of the fledgling natural philosophy. This type of discovery sat well with the technological and experimental agenda of the London society: Newton was elected a fellow in January 1672 (1671 os). However, reflecting telescopes became useful tools in astronomy only about a century later, since the mirrors, even when newly polished,

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reflected only a small fraction of the incident light and tended to tarnish rather quickly. A month later Newton published a letter entitled ‘New Theory about Light and Colours’ in Philosophical Transactions, the journal of the Royal Society, in which he set out his theory of colours. In this work, using terminology familiar to Bacon and Hooke, he called the experiment of the two prisms an experimentum crucis (crucial experiment). The idea was that there were experiments able to discriminate with certainty between two theories, making it possible to decide which was valid. Newton in fact saw the experiment of the two prisms as able to refute the modificationist theories of colour and to prove his theory beyond mere conjecture. Contrary to what Newton had expected, his article of 1672, as we shall see, was fiercely criticized in the years 1672–6.

the moon and the planets During the Middle Ages in Christian Europe (and even outside Europe, mostly in regions influenced by Islamic culture) an astronomical theory took hold that could predict, with great accuracy and economy of means, the positions of the planets. The theory in question had been invented by Claudius Ptolemy, an astronomer, astrologer and geographer who lived in Alexandria in Egypt in the second century ad. His system was based on and developed elements of Aristotle’s cosmology and physics, as well as technical aspects of theories developed by astronomers writing in Greek. The Ptolemaic system placed the Earth, unmoving, at the centre of the universe. The Moon, Mercury, Venus, the Sun,

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Mars, Jupiter, Saturn and the fixed stars orbited the Earth. Each of these celestial bodies was set in a spherical shell consisting of a solid, transparent crystalline material. So, for example, Mars was embedded in a spherical shell outside that of the Sun and inside that of Jupiter. The universe thus appeared as a kind of clock whose gears were crystalline spherical shells, called ‘celestial spheres’. The motions of the planets and stars were caused by the dance of these gears. The world of the planets and stars was also the world of perfection and immut­ability. The Earth was below the sphere of the Moon, at the centre of the universe, but was prey to incessant change, generation and corruption. There is no need here to devote too much attention to the Ptolemaic system, since at the time when Newton lived it had fallen into disrepute among the learned, although still defended officially by the Catholic Church. The major figures responsible for the fall of the Ptolemaic system were a Polish canon, Nicolaus Copernicus (Kopernik); a Danish aristocrat, Tycho Brahe; an Italian mathematician and philosopher, Galileo Galilei; and a German astronomer in the service of the Emperor, Johannes Kepler. The view of cosmology they handed over to Newton’s generation had nothing in common with that of Aristotle and Ptolemy. As Copernicus had stated in 1543, the Sun was at the centre of the planetary system, and Mercury, Venus, Earth, Mars, Jupiter and Saturn orbited around it. The stars were at immense distances, and astronomers began to suspect between the sixteenth and seventeenth centuries that they were similar to the Sun, perhaps each with a planetary system similar to our own.

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As Galileo had shown in the early seventeenth century, the Sun is disfigured by spots, the Moon’s surface is uneven, with mountains and valleys, and Jupiter has satellites. To Newton’s contemporaries it was also clear that the heavens are not solid: the planets were not carried by crystalline spheres, but moved in a fluid or in empty space. In fact, there was evidence that comets passed through the solar system. Tycho Brahe, in the second half of the sixteenth century, had shown that these apparitions, considered ill-omened by both the populace and the powerful, did not belong to the sub-lunar world, but were celestial bodies that crossed the planetary system without encountering resistance. This boundless, conceivably infinite universe, consisting of ‘infinite worlds’, perhaps populated by extra-terrestrials, so varied and full of irregularities, fascinated men and women of the seventeenth century, but posed a series of extremely difficult questions. Why do we not feel the motion of the Earth, if it is true that it rotates rapidly on its axis and orbits at great speed around the Sun? If there are no solid spheres, what holds the planets in their orbits around the Sun? It was this cosmological question, as we shall see, which was behind the purely mathematical problem that Halley submitted to Newton in 1684 and which was at the origin of the publication of Newton’s Principia. As we shall see later, Halley and Newton made reference to three observed features of planetary motion, later known as ‘laws’, set forth by Kepler in Astronomia nova (1609) and Harmonices mundi libri (1619). In order to understand the laws of Kepler, we should remember the geometric definition of an ellipse: given a plane p and

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two points F and F’ belonging to p, called foci, the ellipse is the locus of points P so that the sum of the distances to the foci is constant, that is FP + F’P = 2a (illus. 17). It should also be remembered that a is called the semi-major axis, while FP is called the radius vector. Kepler’s first law states that all planets move in ellipses, with the Sun at one focus (F or F’). Kepler’s second law states that the radius vector SP which joins the Sun to a planet sweeps out equal areas in equal times. So if a planet moves in 30 days from P1 to P2, in the following 30 days it will move to a point P3 such that the area of the focal sector SP2P3 is equal to the area of the focal sector SP1P2, and after another 30 days it will move to a point P4 such that the area of the focal sector SP3P4 is equal to the area of the focal sector SP1P2 (illus. 18). Kepler’s third law states that the period of revolution T of a planet moving around the Sun and the semi-major axis of 17 Ellipse.

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its orbit are in a relationship T2=Ka 3, where K is a constant. So, whatever the planet, once the units of measurement for time and distance have been set, if the time T (for example, expressed in days) taken by the planet to make one complete orbit around the Sun is squared, and then divided by the cube of the semi-major axis a of its orbit (for example, expressed in kilometres), one obtains the same constant K. Kepler’s three laws were not immediately accepted. Indeed, during the seventeenth century several astronomers rejected or ignored them. This is due to the fact that the orbits of the planets are nearly circular, and it is therefore very difficult to argue that the data in Kepler’s possession were necessarily in agreement with an elliptical trajectory. It is however true that Kepler, adopting the system of ellipses, obtained much more accurate predictions of planetary motions than those obtained by his predecessors who used circular orbits. Neither 18 Planet orbiting the Sun according to Kepler’s first two laws. The ellipticity is greatly exaggerated.

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the Copernican system nor that of Brahe had brought, compared to the Ptolemaic system, significant improvements in predictions. From a numerical point of view Kepler made a significant leap forward. But what about the cosmological explanations? Did Kepler’s three laws offer a way to achieve a causal explanation of planetary motions? Did they clarify what moved the planets? Kepler found an answer to this question in magnetism. William Gilbert, in a work entitled De magnete (1600), had already stated that the Earth was a giant magnet. The tendency of the Earth to rotate on its own axis and to keep it constant in orientation was, according to Gilbert, an effect of terrestrial magnetism. The Flemish mathematician and engineer Simon Stevin in his Vanden Hemelloop (On the Celestial Motions), published in 1608, had extended magnetism to cover planetary motion. Supporters of ‘magnetic philosophy’ described magnetic force as invisible, able to act at a distance and perhaps immaterial in nature. Gilbert spoke of his magnetic Earth as ‘an animated body, which mimics the soul’. Magnetic phil­ osophy was sometimes combined with a magical view of cosmology or a sort of cosmic animism. For Kepler, the Sun was the ‘divine prime mover of the Universe’. It had a soul and a magnetic polarity that extended through space. The Sun rotated on its axis (a fact confirmed by observing sunspots), and this rotation caused the planets to orbit the sun. The planets also had souls, brought to life by the Sun, just as the soul activates the movements of bodily organs, and also possessed a magnetic polarity that had the power to attract them towards the Sun for half of their orbit and to repel them for the other half.

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Kepler’s magnetic model is thus somewhat complicated: it envisages a magnetic force that causes a circular motion of revolution around the Sun, and another force that causes a radial motion (towards and away from the Sun). The composition of these two motions causes elliptical orbits. We thus have an explanation of Kepler’s first law of planetary motion (which says that the planets follow elliptical orbits around the Sun). Kepler’s second law, which provides for changes in a planet’s speed during its orbit around the Sun, also acquires a physical meaning. When the planet is closest to the Sun, the force that causes circular motion is more intense and therefore, reasoned Kepler, the planet’s speed is greater. ‘Magnetic philosophy’ was regarded with interest by many natural philosophers as late as the mid-seventeenth century, and most notably by a contemporary of Newton and fellow member of the Royal Society, Christopher Wren, whom we will meet again in the following chapters. Here we need only emphasize the fact that Kepler had conceived the idea that a nonmaterial force acting at a distance, emanating from the Sun, would cause the motion of the planets according to the first and second laws. As we will see, something of this idea would survive in Newton’s theory, according to which, however, not magnetism but the force of gravity was responsible for planetary motion. The explanation of astronomical phenomena in terms of magnetism encountered many difficulties. Magnetic force, some objected, acts only at close range and selectively, affecting only some bodies: it is not therefore plausible that is responsible for planetary motion. Magnets also lose their magnetism when heated, so how could the Sun emit a magnetic force? The latter argument was advanced by

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Newton in his correspondence with the Astronomer Royal John Flamsteed. An alternative approach was based on mechanical phil­ osophy, according to which all natural phenomena, not just astronomical ones, could be explained in terms of particles or corpuscles: in terms, that is, of form, disposition, motion and impacts between particles. Physiological phenomena such as blood circulation or perception, optical phenomena such as refraction, and astronomical phenomena such as the motion of comets, had to be explained in terms of matter, motion and impacts. The great champion of mechanical philosophy was Descartes, who defended it in Principia philosophiae (1644). There was no place in Cartesian mechanical philosophy for imponderable forces, attractions, sympathies or souls. The laws of nature therefore had to encompass on the one hand the laws of motion and impact, and on the other a number of assumptions about the shape and size of the particles of matter. In Newton’s England, as we shall see, there was a tendency to accept a particulate view of matter, but to conceive particles as endowed with ‘active principles’ that somehow reintroduced a kind of activity in matter envisaged in magnetic philosophy. In his Principia, Descartes explained planetary motion in terms of vortices constituted of very subtle matter. According to Descartes, interplanetary space was filled by a substance composed of extremely subtle particles. This fluid of particles whirled around the Sun. The planets, like twigs caught by a whirlpool, were thus dragged into their orbits. Descartes did not attempt a quantitative analysis of the motions of planets. Others after him, for example Leibniz in the late seventeenth

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and Leonhard Euler in the mid-eighteenth century, tried unsuccessfully to deduce planetary motions avoiding actionat-a-distance and starting with assumptions about planetary vortices. According to this viewpoint, planetary motions would be caused by contact actions, by impacts between the matter constituting the vortex and the planet. It is important to stress that Newton did not conceive his theory of gravitation during his youth, the so-called anni mirabiles. The legend of a falling apple inspiring a sleepy phil­ osopher to come up with the theory of universal gravitation is not particularly credible. Or rather, we may accept that this memory of his old age, which appears in the eighteenthcentury biographies, such as that by William Stukeley (1752), and has done much to define the Newtonian myth, perhaps corresponds to an event that really happened. It is not impossible that watching an apple fall inspired in Newton, during the period of university evacuation, to reflect on the possibility that the Earth’s gravity may extend for great distances. Indeed, in the years of his youth Newton achieved interesting results regarding uniform circular motion and gravity. On the very first page of the Waste Book, written around 1664, he drew a small diagram on uniform circular motion with some rough reasoning associated to it based on impacts and the geometry of composition of motion in which he concludes what we might translate into Huygens’s law for uniform circular motion (anachronistically this would be the statement that the acceleration is proportional to the square of the speed and inversely proportional to the radius). He also considered Kepler’s third law and Huygens’s law to easily deduce an inverse-square law valid for the planets. However, it seems

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to be an exaggeration to try and find the theory of universal gravitation in the youthful manuscripts of the 1660s. In one of these manuscripts Newton appears to be responding to an old anti-Copernican objection that if the Earth rotated around its own axis, then centrifugal force would fling bodies placed on the Earth’s surface upwards. Newton shows that on the Earth’s surface the tendency to recede from the centre of the Earth due to daily rotation (conatus recedendi a centro) is much smaller than the tendency to move towards the centre of the Earth due to gravity (conatus accedendi ad centrum virtute gravitatis). In a manuscript penned in the late 1660s, there is a passage in which Newton compares the acceleration of bodies on the Earth’s surface (this is a measurement of g obtained from experiments on the motion of pendulums) to the ‘fall’ of the Moon, in uniform circular motion, towards the Earth. Newton was thinking of gravity as a force whose intensity varies with the inverse square of the distance and extends from the Earth to the Moon. But we are still far from the theory of universal gravitation. One should note that in all the above papers concerning uniform circular motion, the acceleration of the Moon and planetary motions, Newton did not have any need to use ‘calculus’. No methods of series and fluxions were needed for these fragmentary studies on the motion of bodies. One might think that Newton devised the method of fluxions in order to deal with continuously varying motion, so that he could mathematize velocity, acceleration and force, and apply this mathematical knowledge to the planetary system. Yet this, as far as we can tell from the available evidence, was not the case. The only evidence from Newton’s early writings where

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a connection between the study of motion and the method of fluxions is vaguely established is a manuscript datable from the middle of the 1660s, where we read: If the body b moved in an Ellipsis then its force in each point (if its motion in that point be given) will be found by a tangent circle of equal crookedness with that point of the Ellipsis.17 One might speculate that here Newton is aware of the result according to which the calculation of curvature (certainly an element of the method of fluxions) of a plane trajectory allows the calculation of the normal component of force by locally applying Huygens’s law. This single passage is the only extant from Newton’s early papers where Newton draws a significant relationship between the method of fluxions and the study of motion in a non-trivial case. To say that during his anni mirabiles Newton had reached the conclusion that gravity is a universal force, which extends to any distance, which is valid for any body, which is proportional to the product of the masses, and which varies with the inverse square of the distance, is reading too much into the texts available to us. We should note that Newton’s early manuscripts do not mention Kepler’s second law of planetary motion and do not say that gravity is a universal force by which all bodies attract each other mutually. The dynamics of circular motion sketched out in the early manuscripts envisages (so it seems to most historians, even though there is no agreement on this issue) a tendency to recede from the centre, a sort of centrifugal force, which has no place in our

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textbooks on Newtonian dynamics, but which still survives even in Newton’s Principia (but again, there is no agreement on this). In addition, Newton, until the early 1680s, considered the possibility of the existence of planetary vortices, a conception that he would reject as clearly inconsistent with the theory of gravitation in the final pages of the second and the third books of the Principia.18 I think we can conclude that, despite the interest of these early manuscripts, in the period covered in this chapter Newton was still far from having conceived his theory of gravitation. But, as we shall see in the next two chapters, it was not only mathematics, optics and planet­ ary motions that aroused the interest of the young Newton.

three

A Young Professor and His Audience, 1669–1674

I

n the meanwhile, Newton’s university career had progressed: in 1667 he was made a fellow of Trinity and in 1668 he was awarded an ma. In 1669 Isaac Barrow resigned from the Lucasian Chair of Mathematics and most likely saw to it that his successor was the young, unknown Isaac Newton (illus. 19). The importance of this turning point in Newton’s intellectual biography cannot be overstated, since the position of professor allowed him to devote himself to research, almost undisturbed, until 1696, when he would leave Cambridge for London.

lectur es in cambridge What led Barrow to abandon the chair of mathematics? Per­ haps, as a highly devout man, he felt a contradiction between a chair requiring no pastoral duties and his ordination. After resigning, Barrow devoted the rest of his life to theological studies, attested by voluminous tomes of sermons that earned him great repute.1 We might perceive a similar tension in the life of Newton. In fact, according to the by-laws of Trinity, as a fellow of the College he was required to take holy orders

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within seven years of receiving the degree of ma. Thanks to high-level protection, perhaps guaranteed by Barrow himself (who became royal chaplain and Master of Trinity), in 1675 a royal dispensation was granted that exempted the Lucasian Professor from taking holy orders.2 Perhaps, however, Newton had deeper reasons than Barrow for refusing to become ordained. After the approval of the Test Acts in 1673, those 19 Isaac Barrow, the first Lucasian Professor of Mathematics in Cambridge, was a gifted mathematician and is ranked among the co-discoverers of calculus. David Loggan, Isaac Barrow, 1676, plumbago on vellum.

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who failed to conform to Anglican orthodoxy were banned from public office, and Newton in the mid-1670s had perhaps already adopted a conception of God in total conflict with some articles of the Church, in particular the initial ones concerning the Trinity.3 However, at a later stage in his life, Newton had no hesitation in holding public office as a warden and master of the Royal Mint. As Lucasian Professor, Newton was obliged to give a lecture every week during term, and to submit at least ten written lectures per year. It seems that as a teacher Newton did not have a large following, and it is unclear whether his lessons were actually attended by students. The legend, handed down by his aide and secretary, whereby Newton held his lectures in deserted classrooms, and ‘for want of Hearers, read to the Walls’, should, however, be partly revised.4 In fact, we have an Epitome trigonometriae by Newton, a set of lectures mostly based on Seth Ward’s introductory manual titled Idea trig­­ o­nometriae demonstratae (Oxford, 1654), existing in the form of a transcript dated 1683 and written by a student, Henry Wharton – destined to become chaplain to the archbishop of Canter­ bury, historian of the Church of England and the recipient of a funerary anthem by Henry Purcell. According to his biog­ rapher, Wharton acquired ‘no mean skill in Mathematicks . . . by the kindness of Mr. Isaac Newton . . . who was pleased to give farther instructions in that noble science, among a select Company in his own private Chamber’.5 It was customary at the time to transcribe the lectures of professors, and those who browse through the libraries of Cambridge colleges often come across transcripts, sometimes second hand, that circulated in universities and were also traded among students.

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We can thus surmise that Newton did indeed hold trigonometry lessons. The Lucasian Lectures are another matter. These were deposited in the University Library, and could be consulted publicly (although not by students), but no transcripts could be made without the author’s consent. In all, Newton deposited three series of Lucasian Lectures: in 1672 the lectures on optics, in 1683–4 those on algebra, and in the mid-1680s a preliminary partial version of the Principia. They are dated retrospectively so that they give the impression of actually having been taught on the prescribed days, but are clearly too advanced for the students, who received a very basic prepar­ ation in mathematics and science at university in Newton’s time. In short, Newton deposited writings that testify to his research activities rather than his teaching, which was perhaps almost non-existent.

submitting papers to the ro\al societ\ In 1660, a few months after the restoration of Charles ii, the Royal Society was founded in London. The founding members, who included Robert Boyle and Christopher Wren, were part of a group of ‘virtuosi’ who in the Interregnum years met in Oxford and at Gresham College in London, an institution founded in 1598 to promote the knowledge of techniques useful to trade and navigation. Thanks to the good offices of Robert Moray, a royalist and member of the Scottish Freemasonry, the king granted a royal charter in 1662 to the new society, which would have a president, two secretaries, a treasurer and a council. Some members were dangerously

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compromised by the support they had given to the Common­ wealth, such as John Wilkins, who was the brother-in-law of Oliver Cromwell. John Wallis (elected in 1663) had also dedi­cated his skills as a cryptographer to the republican cause and had been part of the Westminster Assembly. For the fledgling society, it was important on the one hand to ensure the protection of the king, and on the other to present experi­ mental activities as being unrelated to controversial issues of a religious or political nature. The society had a president, the mathematician William Brouncker, and a secretary, Henry (Heinrich) Oldenburg, whose duties consisted of engaging in correspondence with English and foreign men of science. In November 1662 an industrious associate of Boyle, Robert Hooke, was appointed curator of experiments. Hooke had met Boyle in Oxford and had become a valuable member of the Oxonian group thanks to his extraordinary skills as a mechanic, painter, builder of scientific instruments and inventor. Born in 1635, and having lost his father at an early age, Hooke had first tried his luck as an apprentice in the studio of the painter Peter Lely, then attended Westminster School and frequented the bustling world of watchmakers, instrument makers and mechanics active in London in the mid-seventeenth century. Boyle exploited Hooke’s technical expertise for the construction of the famous air pump, an essential tool for Boyle’s research on the properties of air. Later, after the Great Fire of London in September 1666, he would help Wren in his work to rebuild the capital. The figure of Hooke is interesting, occupying as he does an intermediate position between the world of artisans and that of natural philosophers. He is one of the

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characters from the scientific revolution described by Paolo Rossi and James Bennett, who have taught us not to underestimate the contribution of those engineers who worked in a period in which there emerged a vision of nature as a mechanism regulated by impacts between corpuscles.6 The tools that the engineers built were at the same time useful devices and models of the microphysical world. Hooke studied the motions of the planets by using pendulums and balls rolled over conical surfaces, and investigated the elastic properties of air by observing the behaviour of springs. He thus built real mechanical models that suggested that similar behaviour was displayed by natural phenomena. The most famous of his instruments is the microscope, using which he made a series of extraordinary observations illustrated in the tables of the aforementioned Micrographia (1665), a manifesto of the experi­mental philosophy promoted by the Royal Society (illus. 20). Hooke’s interests ranged from optics, astronomy and the construction of watches to chemistry, anatomy and the study of fossils, and much more. His ingenuity rightly led to him being called ‘London’s Leonardo’.7 Newton became a member of the Royal Society in 1672 after presenting his reflecting telescope. This innovation fitted well with the desiderata of the newly established institution, which attributed great importance to microscopy and the im­provement of telescopic observation. As we know, in 1672 Newton was to submit his famous paper on his experimentum crucis, in which he claimed to have proved a new theory concerning light and colours. For most of the Royal Society’s members, Newton’s confidence in having ‘proved’ a new physical theory was bound to sound provocatively arrogant: such

20 Louse holding a hair, from Robert Hooke, Micrographia (1665). This work is not only one of the greatest masterpieces of early microscopy, but a fine example of the art of illustration. Hooke shows here his aesthetic penchant for naturalistic description.

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statements were not expected. The theory had already received a thorough treatment in the Lucasian lectures on optics that Newton deposited in 1672 and dated retrospectively from 1670. In the third lecture, he stated that by the use of ‘geometry’ the science of colours, and natural philosophy in general, could achieve the ‘highest evidence’.8 He also expressed his annoyance with those natural philosophers who were con­ fining themselves to ‘conjectures and probabilities’. Newton might have had in mind Hooke, whose Micrographia (1665) had warned readers to consider any discourse concern­ing the ‘causes of things’ contained in the book to be simply a ‘small conjecture’, a ‘doubtful problem’ and an ‘uncertain guess’.9 Newton’s discourse against probabilism offered a view of natural phil­ o­sophy at odds with that promoted by influential members of the Royal Society, such as Boyle.10 It is a discourse intertwined with Newton’s well-known rejection of what is now known as the hypothetico-deductive method, a method that was championed by Descartes. Hooke was not unfamiliar with searching for the truth by means of mathematics, and actually pondered deeply on the idea of founding the experimental method on ‘philoso­phic algebra’, but in Micrographia he espoused the moral values of probabilism, which were deeply felt in the Royal Society. One should bear in mind that after the restoration of the Stuarts, many natural philosophers in the Royal Society wished to allay any fears that they might propose ‘unquestionable’ or ‘dogmatic’ conclusions. Politically opinionated philosophers or dogmatic theologians were not admitted in the society, which instead promoted innocuous, moderate scepticism. This might be the reason why any discourse presuming to

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certainty was looked upon with suspicion, while scepticism and probabilism were approved of in some of the most influential Royal Society manifestos, such as Hooke’s masterpiece on microscopy and Joseph Glanvill’s Scepsis scien­tifica (1665). The subtitle of Glanvill’s work was Con­fest Ignorance, the Way to Science: in an Essay of the Vanity of Dogmatizing and Confident Opinion. Glanvill publicly defended experimental philosophy as opposed to the ‘vanity’ of dogmatics, and spoke on behalf of the other members when he explicitly linked the practice of the experimental method to a distancing from religious and political sectarianism. This was a way not only to distance himself from the ‘enthusiasm’ (here used as a technical term, related to the theological debate of the time) and dogmatism of the Puritan generation; defending scepticism and probabilism could also have been seen as a way to ensure that the nascent experimental science was independent of politics and theology. We should remember that on the Continent, both the trial to which Galileo was subjected by the Inquisition and the condemnation of Cartesian ideas in the Calvinist universities of the United Provinces had shown how important it was to guarantee such independence. It is not without interest to note that Glanvill, a defender of the mitigated scepticism of experimental Baconian science, was a firm believer in poltergeists and witches, whose reality was, according to this early Fellow of the Royal Society, proved experimentally as well as implied by many passages of the Holy Writ. The complex cultural matrix linking modern science to magic could not be better illustrated (illus. 21). For Newton such beliefs were to be discarded as one of the many pernicious influences of the corruption of the rational

21 The witch of Endor, a controversial character of the Bible, as portrayed in the frontispiece to Joseph Glanvill’s Saducismus triumphatus (London, 1681). She is intent on summoning Samuel’s spirit before King Saul.

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and simple religion revealed by God to the patriarchs and prophets and re-established by Christ. In his Lucasian lectures on optics and his 1672 paper Newton broke with the code of behaviour promoted at the Royal Society by stating that the theory of colours he was proposing – a topic that he knew was regarded as ‘belonging to physics’11 – was not ‘an hypothesis but most rigid consequence’.12 Newton’s claim that he was achieving ‘the highest evidence’ in the theory of colours was targeted by Hooke in the heated debate that poisoned Newton’s life in the years following the publication of the ‘New Theory about Light and Colors’ (1672). The effect of the dispute concerning the experimentum crucis on Newton’s reluctance to print his mathematical results cannot be overestimated. Newton’s great paper of 1672 was criticized by Hooke, Huygens and a number of Jesuits, and this frustrating experience was to lead him – possibly out of spite – to avoid publishing his results in other fields of inquiry. In a letter dated 25 May 1672, concern­ing the project of printing his lectures on optics, Newton wrote to Collins: ‘I have now determined otherwise of them; Already by finding that little use I have made of the Presse, that I shall not enjoy my former serene liberty till I have done with it.’13 Newton claimed that his theory of colours possessed a greater degree of certainty compared to other accounts because it proceeded by experiments and mathematics. But in order to present himself as a philosopher whose use of mathematics could transcend the kind of probabilism defended in texts such as Hooke’s Micrographia, Newton had to avoid becoming embroiled in a further polemic concerning the certainty of mathematical methods. Newton was keenly aware

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that his method of series and fluxions was open to debate, because of the guesswork surrounding his theory of series (for example, when the coefficients of all the terms of the series are determined by discerning a pattern in the first terms) and the use of somewhat problematic concepts – such as ‘infinitesimal’ or ‘moment’ – in the method of fluxions. He knew that mathematicians who had published on the new analysis – such as Wallis, whose methods were the basis for his use of infinite series – had to withstand the criticisms of those who defended the rigour and certainty of ancient geometry. Such debate would have been lethal for Newton, a philosopher who had claimed to be able to bring evidence into natural philoso­ phy through geometry: if mathematics was to endow natural philosophy with evidence, it needed to be practised according to criteria that guaranteed the indisputability of its methods. Newton displayed annoyance with the qualitative models of mechanical philosophy: Descartes, and in general the followers of corpuscular philosophy (whether atomist or not), had attempted to explain natural phenomena in terms of impacts of invisible, hypothetical particles. Newton instead intended to ‘deduce’ the laws of nature (most eminently, the laws of optics discovered in the 1660s and the laws of gravitation in the 1680s) from measurable phenomena. Deduction led to much greater certainty than the ‘elegant perhaps and charming’ romances (as Roger Cotes would say in his preface to the second edition of the Principia (1713)) of the Cartesian corpuscularists, and was the realm of the mathematician. Many of Newton’s contemporaries did not accept his advocacy of the use of mathematics in natural philosophy. In their eyes, Newton had presented an incomplete theory of

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light in his 1672 article. He had indeed identified a math­ ematical property regarding the refraction of rays, but had not clearly explained what light was. Nor had he advanced a physical theory on what caused colours. To Hooke, like Huygens, who joined him in criticizing Newton, a mathematical property was not sufficient grounds for a philosophical explanation: the latter could be achieved only by stating what the nature of light was and how the phenomena of light were causally linked to this nature. This is what Descartes and Hooke had tried to do with their conceptions of light as composed of rotating spheres and vibrations, respectively. Newton responded to this criticism by claiming that his quest for certainty in natural philosophy required him to make a clear distinction between mathematical regularities deduced with certainty from phen­ omena and speculative hypotheses on the microphysical composition of matter or light. The following is a passage, composed in 1673, from Newton’s reply to Huygens: But to examine, how Colors may be explain’d hypothetically, is besides my purpose. I never intended to shew, wherein consists the Nature and Difference of colors, but only to shew, that de facto they are Original and Immutable qualities of the Rays which exhibit them; and to leave it to others to explicate by Mechanical Hypotheses the Nature and Difference of those qualities: which I take to be no difficult matter.14 Note the dismissive tone in which the mathematician Newton addresses Cartesian natural philosophers, whose mechanical hypotheses he does not consider a ‘difficult matter’.

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Newton ultimately felt he had provided an almost indubitable proof that sunlight is composite. But was his claim really well-founded? Was white light always of the same kind? Could not painters produce it by several combinations of a few primary colours, rather than a mixture of an infinite number of spectral components? Why, Hooke wondered, did coloured components emerging from the prism have to belong to the primary beam of sunlight hitting the prism? Moreover, was the corpuscular theory that Newton seemed to espouse the only one possible to explain the phenomenon of chromatic dispersion? And was it fair, wondered one of the Jesuits of Liège, Anthony Lucas, in 1676, to base a theory of colours on a handful of experiments? Had the ‘ingenious Mr. Boyle’, one of the tutelary deities of the Royal Society, not taught that general statements on nature must be based on data collected patiently and regarding a ‘vast number of new experiments’?15 But for Newton, a single well-conducted experiment, rather than uncertain induction, could reveal the truth thanks to a ‘deduction’ from the phenomenon in question. We can only imagine how irritating it must have been to the anti-Catholic Newton to be challenged by none other than a Jesuit who flaunted a fearsome combination of scrupulous syllogistics, Boylean rhetoric and experimental dexterity! As we shall see, in the case of his gravitational theory Newton met with similar criticism. He was accused of having mathematically proven the law of universal gravitation without providing a physical explanation of what the force of gravity is, how it acts and how it causes the phenomena of attraction between masses. In the case of the controversy over the nature of light, Newton was trying to distance himself

22 Rings produced by monochromatic light striking Newton’s experimental device, as described in the ‘Hypothesis’ (1675): a plano-convex lens placed on a flat glass surface.

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from Hooke’s criticisms, clearly stating that what his theory demonstrated with certainty had nothing to do with the nature of light, whether it was corpuscular or in the form of waves. In fact, the controversy with Hooke, Huygens and the Jesuits compelled Newton to refine and somewhat weaken his initial bold pronouncements. In the end Newton said, in essence, that what he had demonstrated, combining experience and geometry, was that sunlight was not simple but a heterogeneous mixture of an infinity of differently re-frangible and immutable rays, each ray being associated with a pure colour. It was necessary to abandon mechanical hypotheses and restrict ourselves to statements concerning the mathematical regularities exhibited by observable phenomena. Here, in a nut­shell, is Newton’s ideal of mathematical natural philosophy.

a letter on light and alchemical cosmolog\ In December 1675 Newton, spurred on by the criticisms of Hooke and Huygens and the argumentative Jesuits, sent two essays to Oldenburg, the secretary of the Royal Society. In the first, entitled ‘An Hypothesis Explaining the Properties of Light’, he undertook to explicitly reveal his more speculative ideas about the nature of light. In the second, entitled ‘Discourse of Observations’, he gave a mathematical explan­ ation for the formation of the natural colour of bodies and the colours in thin films – that is, the phenomenon consisting of the formation of coloured fringes such as those found in soap bubbles, a phenomenon whose explanation seemed, even to Newton himself, to require some periodic vibrations in a medium (illus. 22). Newton thus decided to play at his

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adversaries’ own game, or to explain apertis verbis what light was, in his opinion.16 In the first of these essays Newton took care to limit himself to talking of probable hypotheses. Interestingly, Newton always took pains to distinguish between two approaches: either stating a theory with certainty, or presenting hypotheses as pointers for future research. He wrote: ‘no man may confound this [Hypothesis] with my other discourses, or measure the certainty of one by the other.’17 In the Opticks (1704) these two approaches are kept well separated. Any speculative assumptions are in fact relegated to the Queries that conclude the work. In addition, in order to understand the way in which Newton presented his hypothesis, we should not underestimate what we could consider a certain eclecticism: namely, that Newton tries to formulate the hypothesis, in this case concerning light and colours, in as general a way as possible, in order to make it compatible both with the possible development of optical research and with various metaphysical views of nature. In his ‘Hypothesis’ Newton argues that space is pervaded by a thin ether (accompanied by other ethereal fluids), a kind of extremely elastic fluid. This fluid is not only found in space but pervades bodies, penetrating ‘the pores of chrystal, glass, water, and other Naturall bodyes’.18 In space it is however denser than in solids and liquids. In the ether, vibrations simi­ lar to acoustic vibrations are propagated, but they are ‘more swift’ and ‘minute’ (with a much shorter wavelength, we would say today). Light may be conceived as consisting of a flow of ‘multitudes of unimaginable small & swift corpuscles of various sizes’ that interact with the ether. Actually the ether is

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described as a medium offering resistance to the corpuscles ‘continually urged forward by a Principle of Motion’. This was clearly the preferred conception of Newton, who, however, was quick to add: But they, that like not this, may suppose Light any other corporeal emanation, or an Impulse or motion of any other Medium or æthereal Spirit diffused through the main body of æther, or what else they can imagine proper for this purpose. To avoid dispute & make this Hypothesis generall, let every man here take his fancy.19 When the corpuscles encounter the surface of a refracting medium they generate waves of ether like a stone falling into a pond. The ether ‘refracts light’: that is, the corpuscles tend to deflect towards areas where the ether is less dense and, given that the ether is less dense in glass than in air, the result is that the luminous corpuscles are deflected when passing through the surface separating air and glass. When passing from air to glass, Newton explains, they are accelerated in a direction perpendicular to the surface. In short, using this model Newton explains the mechanism responsible for refraction. In section 14 of Book 1 of the Principia Newton would show how it was possible to derive Snell’s law from his hypothesis of 1675 (with the important difference that in the Principia Newton would not refer to the ether, but more abstractly speak of a short-range force that deflected the luminous corpuscles in the vicinity of the surface separating two media with different refractive indices).20

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The phenomena observed in thin films (soap bubbles, mica and so on) by Hooke in Micrographia could be explained, according to Newton, by attributing periodic ‘mutual actions’ between the light corpuscles and the ether. According to Newton, on the surface of thin films the ether is periodically rarefied and condensed. Newton thus attempted on the one hand to save the corpuscular hypothesis of light, and on the other to provide an explanation of phenomena which, as we know today, clearly reveal the periodic properties of electromagnetic radiation.21 By using a plano-convex lens, Newton was able to measure the ‘bigness of the vibrations’ of the ether associated with various colours (illus. 23). Indeed, rings occur in correspondence with depths of the thin film of air between the lens and the plane, which are integral multiples of some definite length. The conclusion Newton reached was that this elementary length coincides with the length of the ‘pulse’ of a vibrating ethereal medium. For example, in the case of yellow the length of the pulsation would be 1/80,000 of an inch. Today, we interpret the results obtained by Newton 23 A plano-convex lens ABC with radius R is placed on a flat glass surface FBG. When it is lit from above, coloured rings are formed (see illus. 22).

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as a measure of the wavelength of the electromagnetic waves that cause us to perceive the various colours. That is, we interpret Newton’s rings as due to the interference of the light reflected at the limiting surfaces of the thin layer of air intercepted between the lens and the surface. According to measurements accepted today, deep violet has wavelength approximately 400 nm, and red approximately 650 nm, results that are very close to Newton’s. In the essay of 1675 the ether hypothesis is not only applied to optical phenomena, but used to explain chemical, electrical, magnetic and gravitational phenomena. Cohesion is also a phenomenon that Newton aims to understand. Indeed, corpuscular theories of matter had to explain by which means the particles could bind themselves in stable compounds. It is remarkable how Newton shows in this context an interest in visual perception. He was interested in possible analogies between sight and hearing, and wondered, since hearing is caused by acoustic vibrations transmitted through the air which hit the ear drum, whether sight was caused by luminous vibrations of the ether. Newton’s idea was that when ‘rays of light impinge’ the retina they ‘excite vibrations’, like those of sound, that ‘run along the aqueous pores or Crystalline pith of the Capillamenta through the optic Nerves into the sensorium’ located in the brain. 24 Analogy between the prismatic spectrum and the musical scale from the ‘Hypothesis’ (1675). The reader who is not familiar with the solfège system in use in Newton’s England should ignore the notes written on the right.

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Hence Newton’s idea of comparing the musical scale and the colour spectrum (illus. 24): as the harmony and discord of Sounds proceed from the proportions of the aereall vibrations, so may the harmony of some colours, as of Golden & blew, & the discord of others, as of red & blew proceed from the proportions of the æthereall. And possibly colour may be distinguisht into its principall Degrees, Red, Orange, Yellow, Green, Blew, Indigo, and deep violett, on the same ground, that Sound within an eighth is graduated into tones.22 Newton soon realized, however, that he had to be more cautious about this analogy, as he found that the ratios in consonant intervals did not correspond to those between the ‘bignesses’ (or wavelengths, as we would say nowadays) of waves propagating through the ‘animal spirit’ of the optic nerves. The supposed ratio of 1:2 for the wavelengths of the extreme colours in the spectrum (the ‘deepest violet’ and the ‘deepest scarlet’), which would have proved an analogy between the musical octave and the colour spectrum, had to be dropped. It is often claimed that the experiments Newton performed to study the analogy between the musical scale and colour spectrum reveal his adherence to a form of Pythag­ orean mysticism. Some Christian authors, from antiquity up to the seventeenth century, mused on the idea that the universe and man were the outward expression of the wisdom of the Creator who had forged them according to the same mathematical (arithmetical or geometrical) proportions and

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musical harmonies. The names of Cusanus and Kepler come immediately to mind. No doubt Newton was fascinated by the possible relation between the musical scale and the subdivision of the prismatic spectrum. However, this does not make Newton a neo-Pythagorean or a spokesman for the union between musical harmonies and the structure of the cosmos along the lines of Plato’s Timaeus, although certain sections of the Newtonian corpus certainly appear to suggest that their author embraced the concept of the harmony of the cosmos and nature, especially where he refers to the ‘ana­ logy of nature’ as a guiding principle in his research. However, what Newton had in mind in the ‘Hypothesis’ was an analogy between hearing and vision, rather than an analogy between musical and natural phenomena, without being committed to a conception of the world as being ordered according to musical harmonies. Rather, as we shall see later, in the mid1680s Newton realized that the universe could not simply be described as ‘harmonic’. While it is certainly governed by the mathematical law of universal gravitation, this very law engenders planetary motions, which are subject to deviations from any laws that might help describe them in mathematically simple terms. Newton’s cosmos, contrary to what a true neo-Pythagorean such as Kepler claimed, is not mathematically perfect; this feature, as we shall see later, is crucial for Newton’s theological views.23 In the ‘Hypothesis’ Newton, perhaps under the influence of Kenelm Digby’s work, wondered if ‘the gravitating attraction of the Earth’ could be caused by the ‘continuall condens­ ation’ of some ‘aethereal Sprit’. Already in the ‘Qu[a]estiones quaedam philosophiae’ Newton had rejected the Cartesian

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conception, whereby gravity was caused by the pressure of the subtle matter. In the Principia Descartes stated that bodies are pushed towards the centre of the Earth as a result of contact with swift vortexes of subtle matter. Such action would, Newton observed, be proportional to the surface of bodies, not to their mass. Gravity, continued Newton, did not act like the resistance provided by air to the motion of projectiles, which is a function of the surface of the projectiles, but always acted in direct proportion to the mass of the body. It is interesting to see in what terms Newton describes the ethereal spirit responsible for gravitation. This ether is very different from the subtle Cartesian matter, geometrized, mechanical and inert. The ‘spirit’ responsible for gravitation is not constituted by the ‘main body of the flegmatic aether’ but by something thin and diffuse, perhaps of an ‘unctuous, gummy, tenacious and springy nature’, that relates to the ether used to explain the phenomena of light in the same way that the vital spirit, necessary for keeping the flame alive and vital movements, relates to air. This thin, unctuous spirit descends rapidly and condenses into the pores of the Earth, becoming humid active matter, and is subsequently attracted from the vast body of the Earth towards the higher regions of the atmosphere. The rapid movement of the ether drags down the bodies that it pervades. From the ‘bowells’ of the Earth, the spirit is exhaled upwards after an underground transformation that makes it unable to penetrate the pores of the bodies and thus to exercise force on them. After this, the rapid downward motion recommences, which causes bodies to fall. Nature in fact, Newton adds, is constantly involved in a circular process of transformation. The cosmological vision propounded in

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the ‘Hypothesis’ is breathtaking for its Baroque beauty and remoteness from the cold mathematical theory Keats was to complain about and to which Newton would owe his fame: And, as the Earth, so perhaps may the Sun imbibe this Spirit copiously, to conserve his Shineing [sic], & keep the Planets from receding further from him. And they that will, may also suppose, that this Spirit affords or carryes with it thither the solary fewel & material Principle of Light; And that the vast æthereal Spaces between us & the stars are for a sufficient repository for this food of the Sunn & Planets.24 Newton’s language is not that of the mechanistic philosopher, but rather that of the chemist, or even alchemist if you prefer. Newton sees unfolding in Nature not only the mechanical, passive action of matter understood as res extensa, but the active action of a vital spirit. This Newtonian spirit would be closer, according to a thesis nowadays in disrepute that was held by scholars such as Dobbs, to the stoic pneuma, or Hylarchic Principle invoked by a neo-Platonist such as Henry More, than to the particles of Cartesian philosophy. In this regard there are many interesting passages, especially those relating to the relationship between volition and muscular motion, and those concerning the relationship between God and Nature. Newton refers to a ‘puzleing Prob­ lem’: by what means do muscles contract and dilate in order to cause motion in animals? The best known response was that of the Cartesians, who thought that the nervous system was made up of thin tubes through which the animal spirit

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– a gaseous or perhaps igneous substance – flowed, filling the nerves and the pores of the brain. Volition was explained by Cartesians by imagining a hydraulic interaction between brain, from which the fluid flows, and the limbs of the body, which are pushed by the animal fluid as it comes into contact with muscles. The hypothesis put forward by Newton is apparently similar to Descartes’: the ether with which muscles are imbued is an ‘animal spirit’ that can expand and contract. Maybe, Newton wonders, the soul has the power to fill muscles with this spirit or ‘wind’ by means of nerves. It is not necessary, adds Newton, to imagine a very large variation of density of the ether in the muscles, since, because of its great elasticity, even a slight variation in density would suffice to generate a large variation in pressure. The luminous ether mentioned by Newton in his ‘Hypoth­ esis’ is therefore responsible, thanks to its vibrations, for the formation of colours in thin films. There is also an ether which, combined with the unctuous spirit, causes gravitational phen­ omena. In addition, there are significant allusions to electrical, chemical and magnetic phenomena, and an ether conceived, with characteristic Newtonian caution, as a mediator between ‘soul’ and ‘body’. It is the latter that might allow us to explain what to many seemed incomprehensible in Cartesian dualist philosophy: the soul’s action on the body. For Newton, then, the study of gravitation and light is not separated from interests and concerns related to the living world and God’s action in Nature. This is particularly evident in the passages where Newton describes the action of a God who forges ‘the whole frame of nature’, starting with the ether, which as it condenses ‘is wrought into various formes, at first by the immediate hand

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of the Creator, and ever since by the power of Nature, which by vertue of the command Increase & Multiply, became a complete imitator of the copies sett her by the Protoplast’.25 But is Newton’s ether a material or spiritual element? Historians have often asked this question, which is difficult to answer for two reasons. First, Newton leaves, in my opinion deliberately, the question open. His agnosticism on this point has similarities with the cautious scepticism of John Locke regarding the possibility of establishing whether the soul is immaterial. Second, the ether is an instrument of mediation between God and Nature, between the soul and the body: ‘God, who gave animals self-motion beyond our understanding, is, without doubt, able to implant other principles of motion in bodies, which we may understand as little.’26 The ambiguous characterization of the ether, analogous to Gassendi’s flos materiae, as partly possessing mechanical (velocity, elasticity, thinness), in part chemical (sociability, unsociability) and in part vital (fermentative qualities able to breathe life into plants and animals) properties, allowed Newton to depict it as the mediator between body and soul, as the instrument of God’s creative action, as an element that went beyond Cartesian dualism, endowing Nature with unity, and which, precisely because of its (in part?) corporeal nature, could be subjected to experimental analysis. Newton’s natural philoso­ phy propounded in the ‘Hypothesis’ of 1675 therefore aspired to shed light on issues with far-reaching implications, without, it seems, a commitment to a metaphysical stance in regard to materialism and vitalism.

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A Maturing Scholar, 1675–1683

T

he fascinating cosmolog\ of the ether and the physiology of perception and muscular motion presented by Newton in his ‘Hypothesis’ have alchemical origins. In fact, the ‘Hypothesis’, a letter to the secretary of the Royal Society and therefore in the public domain, should be considered, together with some of the Queries to the Opticks and ‘De natura acidorum’, as Newton’s most important alchemical publication. It is often stated that Newton did not publish his alchemical studies. This is only in part true. Newton kept for himself laboratory notes, compendia of alchemical terms and excerpts from books and manuscripts he consulted. But in the above works he let others know about his speculative as well as his more positive results in the field. The idea that Newton was ‘esoteric’ about alchemy should be somewhat toned down. Nowadays, we are in the lucky position of being able to read carefully annotated transcriptions of Newton’s alchemical writings on the website The Chymistry of Isaac Newton.1

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newton the alchemist By the mid-1670s Newton was already an expert alchemist. Newton’s early interest in alchemy dated back to the late 1660s. In that period he must have dirtied his hands with experimenting on alloys for his telescope’s mirror, a research activity that should not however be understood as belonging to the Newtonian alchemical quest. In the end, alchemical research failed to bring great results (if we exclude the activities of Newton at the Mint, when his practical knowledge of metals must have been helpful): the reason of course is that Newton had set himself the task of transmuting metals, and this is not possible by heating a metal alloy gently in a hermetically sealed vessel. Besides, the theoretical and experimental research studies in the field of alchemy undertaken by Newton from the late 1660s until the first decade of the eighteenth century are attested by a large number of manuscripts, correspondence and the presence in Newton’s library of patiently annotated works on alchemy.2 The problem in the evaluation of Newton­ ian alchemical manuscripts is that in almost all cases, these are transcripts and excerpts taken from printed works and manuscripts: only a few passages of the million words constituting his alchemical corpus can be attributed to Newton. Newton was clearly interested in this literature, but the fact that he studied it does not imply that he entirely agreed with its contents, or that he adhered to the ethos of the authors whose works he annotated and transcribed. Some of these authors were Rosicrucians, convinced believers in the wisdom of the legendary Hermes Trismegistus, devotees of a Chris­ tianized or neo-Platonic Kabbalah. Yet Newton clearly and

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vocally distanced himself from the ‘Hermetick Philosophers’, abhorred the ‘Kabbalist’ and considered the early Christians to have been influenced by Jewish mysticism, Gnosticism and neo-Platonisms leading to a pagan corruption of the Christian religion. By indiscriminately associating Newton with the authors of the alchemical books that he annotated and read, we risk attributing to him positions (the mysticism of John Dee, for example) that were so alien to him as to arouse his most sarcastic and vitriolic comments. Nevertheless, the image of a ‘hermetic’ Newton has been very popular, at least since Keynes’s day. However, the figure of Newton bent over a steaming crucible in search of the philosopher’s stone and the transmutation of metals, a figure that is attested by the manuscripts, is undeniably at odds with the image received from the Enlightenment and positivist tradition of the scientist, attentive not to make assumptions unsupported by empirical evidence. As discussed in the Introduction, the paradox mainly comes from the fact that we tend to apply to Newton categor­ies of science and alchemy which would not have been shared by his contemporaries. At the time, a scientist of Newton’s calibre would rather have been called a ‘natural philosopher’ whose ambition went far beyond that of a modern-day physicist or a chemist. And yet the association between alchemy and the occult, mysticism and irrationality is a cultural phen­omenon, as William Newman and Lawrence Principe make clear in their seminal works, that occurs mainly in the last decades of the eighteenth century and in the nineteenth century in the wake of an interest in mesmerism, the emergence in Germany of Rosicrucian Masonic societies, and

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the fascination in Victorian England for poltergeists, occultism and ‘psychical research’.3 In fact, an alchemist in the seventeenth century was not, as we would now imagine, necessarily a charlatan or a mystical practitioner of the occult. The denigration of alchemy is an attitude that began to take root in the eighteenth century. In the seventeenth century alchemists were the subject of criticism and parody, and sometimes ended up in trouble with the law as counterfeiters. Not a few alchemists, after promising princes and rulers that they could transmute base metals into gold, had to spend the last days of their lives in a cell well equipped with alchemical instruments, with the chilling choice between successful transmutation and the scaffold. But apart from the charlatans, there were also alchemists dedicated to the production of drugs, pigments and dyes and the purification of metals, and their skills in metallurgy were often sought in the flourishing mines of Central Europe. It can be assumed that many philosophers of nature, such as Boyle and Newton, were interested in coming into contact with these technicians, who effectively possessed empirical know­ledge. It should be noted that these same highly skilled workers often also pursued metallic transmutation since there was no empirical reason to disbelieve in its possibility. In the seventeenth century alchemy was practised at court, in the mines, in pharmacies, in painters’ studios and dyers’ workshops, and sometimes at universities. It was a discipline integrated in the culture of the time, not necessarily prohibited or illegal and not necessarily associated with cultural movements such as Hermeticism, Rosicrucianism or neo-Platonic mysticism. Important contemporaries of Newton devoted themselves to

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alchemy, such as Locke and Boyle, two empiricist and sceptical thinkers who have little in common with Renais­sance natural magic.4 Thinkers, in other words, who have little to do with the idea that knowledge is attainable through mystical enlightenment; rather they were seeking, like Newton, to make advances in the knowledge of the subject through laboratory experiments and the study of alchemical texts. It is said that Newton had many alchemical texts in his library. The seventeenth century was, in effect, the golden era of alchemy. These texts, it should be emphasized, despite their bizarre titles (such as Arcana arcanissima), cannot be attributed to an ‘esoteric’ culture, for the simple fact that they were printed works, available at major book fairs and sold in great numbers. At the time many were attracted to such literature, some of which fell into the category of erudite amusement. Some of the books belonging to alchemical literature seem designed to elicit a smile, attract the reader’s curiosity and possibly even create a feeling of awe at being confronted with such arcane language and mysterious symbols. The same effect is created by these texts today as it was in Newton’s time. Books such as Michael Maier’s Atalanta fugiens (1618) were most probably meant to be received and read in the pursuit of moral elevation and intellectual delight. In these works the reader is presented with a baroque tapestry of enigmas and emblems that must be decoded as Christian allegories for virtues and sins. This requires a knowledge of classical languages, sometimes including some Hebrew, of music theory, of mythology, of a Christianized Kabbalah and of the Holy Bible. Library owners in the early modern period very often acquired an amateurish erudite competence, a kind of scholarship akin

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to that of twenty-first-century Internet surfers, based on the reading of anthologies of adagia from the classics and of compendia of Graeco-Roman mythology, biblical exegesis and ancient history. By leafing through a book like the Atalanta fugiens they could practice an ennobling humanistic exercise that combined brain-teasing, erudition and moral discourse. But Newton’s interest in alchemy clearly went beyond curiosity. He was convinced that by decoding the emblems and symbolic language of alchemical texts he could acquire know­ ledge about the transmutation of metals. Motivated by this con­viction Newton studied alchemical literature as extensively as he could, even devoting attention to alchemists who shared ideas (such as neo-Platonic Trinitarism or Christian Kabbalah) that he abhorred. Nonetheless, he was convinced that some down-to-earth laboratory procedure could be extracted even from texts that epitomized, in his opinion, a corrupted view of religion and philosophy, such as the corpus hermeticum. Indeed, Newton treated the language of alchemy not as allegorical or mystical, but as a code that he tried to decipher in order to obtain a plain descriptive meaning, a formula applicable in the laboratory. An analysis of Newton’s hermeneutical work on the alchemical works of renowned alchemists such as Maier and Sendivogius shows without a shred of doubt that he was searching for a recipe for making gold. As Newman has convincingly argued, the credibility of alchemy in the seventeenth century, and the interest shown in it by Newton, Leibniz and Locke, depends on at least two factors.5 First, the technicians who worked on metals in mines relied successfully on alchemical theories for purifying metals. They handed down the idea that metals were transmuted in

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the bowels of the earth and testified to the truth of the phen­ omenon of transmutation. It was thus thought that traces of gold in the silver mines were indicative of an initial natural transformation into the more noble metal. Second, the cor­ pus­cular theories of matter and cohesion in vogue in the seventeenth century made the idea that a metal could be decomposed into more elementary particles plausible. Metals, such as lead and iron, were considered compounds (not elements, as in contemporary chemistry), and therefore one could always hope to analyse them by breaking the causes of cohesion, whatever they might be, into their ultimate components and recombining these into a synthesis that would give rise to different metals. Those who cautiously adhered to a corpuscular philosophy, such as Boyle, did not need to make recourse to mystical beliefs in order to be convinced that a metal, like lead, could be dissolved into the most basic and small corpuscles constituting matter and that these could then be rearranged in order to form gold. So what was alchemy? It is not easy to answer this question, since the discipline was practised in extremely diverse contexts: embraced by a visionary hermetic such as Giordano Bruno, but also by a ‘sceptical chemist’ such as Robert Boyle. If we provide long lists of alchemists, identified according to some arbitrary criterion, then outline their relationships to each other, we end up making the period resemble a chapter in the history of magic rather than in the history of science; a chapter seamlessly spanning the ages from Para­ celsus to Newton. It is therefore appropriate, in order to avoid general­izations, to confine our attention to England in the mid-seventeenth century.

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In London during the Interregnum there was a New England alchemist by the name of George Starkey, who however used the pseudonym ‘Eirenaeus Philalethes’. Starkey was in contact with Samuel Hartlib and Robert Boyle and transmitted to England, as amply demonstrated by Newman and Principe, the ideas on matter of Jan Baptista van Helmont.6 The ideas were corpuscular, but – and this is the crucial point – this was a form of corpuscularism completely different from that of Descartes. For van Helmont, the particles had a shell structure, with outer parts and inner, much smaller, parts that could be separated and recombined in the alchemical process. It was these arrangements of the constituent particles of the most complex particles that made the transmutation of metals possible. Corpuscles, moreover, were a hotbed of activity: matter was not passive. The material cor­pus­cles were activated by tiny semina (a term perhaps taken from Lucretius) located inside them. Once liberated, the semina could give rise to vital phenomena such as fermentation and generation. Metals had curative properties thanks to the vital principles they contained. The language used by Newton in the ‘Hypothesis’ reveals interest, confirmed in the alchemical manuscripts, in the theories of Starkey and van Helmont, and in general in a corpus­cular view of chemistry that was not in line with the mechanistic notion of passive matter. Even Walter Charleton (who spread the ideas of Pierre Gassendi in England) and Nathaniel Highmore, to take two examples of Newton’s contemporaries, espoused a vision of matter as consisting of particles endowed with qualities and powers (and not only with extension, as Descartes thought). It is also worth

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mentioning Matthew Hale, who claimed that God ‘superadds an active virtue’ to matter, a notion that Newton espoused several times, making it capable of its own motion, without which it would be ‘stupid and dull’ and would move only ab extrínseco as a result of accidental impacts.7 It is to this tradition, alive in England, devoted to the defence of an anti-mechanist corpuscularism, that Newton refers in his alchemical studies. One can therefore say that, in seeing matter as consisting of particles with active powers given to them by God, Newton draws on works produced by an anti-Cartesian and anti-Hobbesian front defended by a broad and diverse spectrum of English natural philosophers, not only neo-Platonists but supporters of Gassendi or neo-Stoics, and alchemists influenced by Hel­mont’s ideas.8 Newton was still unwilling to align himself with any of these positions: his interest in alchemical practice never seemed to translate into the adoption of a philosophical or metaphysical position such as Stoicism or Platonism. The timeframe in which Newton was engaged in alchemy extends for decades. We know that in 1669 he equipped himself with furnaces to conduct experiments with metals. We have numerous manuscripts that bear witness to his laboratory research dating back to a period from the 1670s to the 1690s (illus. 25).9 From manuscript sources we can infer that Newton was particularly interested in the transmutation of metals, the ability to transform one metal into another. From some of his early manuscripts we learn that Newton shared the view that metals could ‘vegetate’, could be transformed in the belly of the Earth through processes similar to those found in plants (such as the germination of seeds): metals grew, putrefied and regenerated themselves. The study

25 Newton annotates the prices of materials bought in 1687 and in 1693. This annotation shows the public dimension of alchemy: chemicals were on sale and alchemists possessed much-admired cabinets. After Newton’s death, Thomas Pellet added ‘Not fit to be printed’.

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of metals could thus provide a key to the ‘subtle chemistry’ of the characteristic phenomena of the living world, as opposed to the ‘vulgar’ chemistry of the mechanists. According to a tradition widespread among alchemists, the vegetation of matter was due to the action of tiny seeds hidden in the minute recesses of particles of matter. While vulgar chemistry studied processes of combination between gross corpuscles of matter, subtle chemistry studied the deepest, most radical process of transmutation, a process that was involved in the vital phenomena of the generation and growth of living organisms. All metals melt at a certain temperature; one of them, mercury, is liquid at room temperature. Alchemists believed that metals contained a principle of liquidity, thus called ‘mercury’, and a principle of solidity or unctuousness, called ‘sulphur’. The alchemical doctrine of mercury and sulphur (and salt, according to Paracelsus) interacted with corpuscularism in a complex way. One of the strategies for achieving the transmutation of metals consisted of isolating the ‘mercurial’ principle from one metal to recombine it with the principle of solidity from another. Newton attributed great importance to antimony. Stibnite (a sulphide mineral with the formula Sb2S3 ) was fused with another metal to obtain a ‘regu­ lus’, a substance that formed on the bottom of the crucible. Newton was fascinated by the crystalline appearance of what he called ‘star reguli’, which he aimed to obtain. One attempt consisted in melting stibnite, iron and ores of iron, copper, tin, lead and bismuth, purified by saltpetre: in the regulus at the bottom of the crucible, Newton found a ‘Glorious Star’. ‘Star-shaped’ crystalline formations could in effect be seen.10

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Perhaps Newton hoped that this procedure would allow the production of the ‘philosophical mercury’ in which gold could vegetate. Some crystalline formations, for example dendrites (one of these, a ‘Philosophers’ Tree’, was actually described in Bate’s book on the ‘Mysteries of Nature and Art’ that the young Isaac consulted during his time in Grantham), attracted the attention of Newton. In some cases they resemble vegetal forms that seem to grow under the alchemist’s eyes as in a chemical garden that would thus reveal the contiguity between the world of metals and that of living phenomena (illus. 26). We have already discussed Newton’s interest in the living world (phenomena such as generation, fermentation and corruption) and also the questions that he posed on the relationship between body and soul (regarding perception, volition and free will). Even though the attribution of a ‘vitalist’ cosmology to Newton is not warranted by the available manuscript evidence, it is likely that the attempt to find an answer to these questions led him away from mechanism and towards alchemical literature. These interests are manifested in his early writings, and we still find them in his later writings, where we read: ‘How do the Motions of the Body follow from the Will, and whence is the Instinct in Animals?’ Or: ‘We cannot say that all Nature is not alive.’11 It is thus tempting to surmise, though scholars are divided on this issue, that Newton was interested in the powers inherent in matter that could activate interactions between the Will and the body, thus allowing a view of man as a free agent who could influence the movements of the body with the soul, and a vision of God as an agent in Nature. These virtues are not due to the ponder­able and passive matter of Cartesian mechanical

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philosophy, but rather to the action of the vital elements of which the alchemists, neo-Stoics, neo-Pythagoreans and neo-Platonists spoke. The authority of the ancients was important for Newton. He was convinced, as had been many alchemists such as Michael Maier, that ancient Greek-Roman mythology concealed instructions for alchemical recipes. The gods were associated with the planets, the planets with metals, and so it was possible for Starkey and Newton to interpret the myth of Vulcan casting his net over Venus and Mars, caught red-handed, as a recipe to obtain a crystalline formation, ‘the net’, starting with metals (copper and iron). Alchemy was not only a discipline for the experimental phil­ osopher, but the domain of the hermeneutist in possession 26 ‘Flowers of antimony’, from Henry Baker, Employment of the Microscope (London, 1753).

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of the philological tools necessary for the textual analysis of alchemical literature and the deciphering of emblems. In a youthful manuscript, one of the few among the theor­etical alchemical manuscripts in which Newton seems to express his own ideas rather than transcribing those from other authors, known as ‘Of Nature’s Obvious Laws & Pro­ cesses of Vegetation’ and followed by a short treatise in Latin whose opening words are ‘Humores Minerales’, Newton speaks of the Earth as a ‘great animall’ that inhales and exhales an ethereal spirit, vital for its ‘dayly refreshment’.12 From what emerges in the studies by William Newman, Newton’s sources were Michael Sendivogius, a Polish alchemist in the service of Rudolf ii, and Johannes Grassaeus (Grasshoff ), whose works Newton had annotated in the 1660s.13 According to this view a vital agent was responsible for the vegetation of metals in the bowels of the Earth. In the underworld there occurred metallic transmutations that the alchemist tried to reproduce in the laboratory. Newton suggested that these underground transmutations were due to ‘acid liquors’ that dissolved metals in their mercurial and sulphurous components and carried them towards the centre of the Earth. Here they met ascending fumes that recombined the components, resulting in new metals. The fumes emerging from the underworld ‘wander all over the earth’, bestowing, observed Newton, ‘life on animals and vegetables’. The importance attached by Newton to acids is attested by a manuscript entitled ‘De natura acidorum’, which Newton gave in 1692 to the Scottish physician Archi­bald Pitcairne and which was later published with the consent of the ‘illustrious author’ in the second volume of the Lexicon Technicum (1710) by John Harris. Together

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with the ‘Hypothesis’ and some of the Queries to the Opticks, this is one of the few works by Newton on alchemical research that appeared in print during the author’s lifetime. Together with ‘Of Nature’s Obvious Laws & Processes of Vegetation’ and a monumental Index chemicus, one of the most important Newtonian alchemical manuscripts is Praxis (c. 1693), a summa of Newton’s achievements on the making of gold (Babson Ms. 420). This text, as usual with Newton’s man­u­scripts, began as a set of notes on alchemical books, such as Alexandre St Didier’s Triomphe hermétique, but developed into an independent treatise in which Newton appears to be trying to expound his results in the alchemical art of metal transmutation. As Paul Greenham has recently argued, Newton’s full use of the sexual and astrological imagery of the alchemical tradition was understood by its author not in spiritual or mystical terms, but rather as a coded language translatable into down-to-earth laboratory practices. In this manuscript treatise Newton studied thoroughly the alchemical literature in order to extract from its symbolism (made out of ‘crude sperms’ and ‘menstrua’ of the ‘sordid whore’, and a ‘fascinating table of twelve alchemical symbols and their corresponding associations with pagan deities, the seven planets, four elements and the unique fifth element – earth or chaos’) a process in which a gold amalgamated with mercury could vegetate and grow.14 To repeat, such ‘vegetation’ was understood by Newton in corpuscular terms, as due to vegetative processes activated by the finest particles constituting matter. Far from being a pastime in his old age, alchemy occupied an important place in Newton’s natural philosophy. So much so that one of his main correspondents, John Collins, in a letter

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of 19 October 1675 addressed to James Gregory, des­paired of being able to interest Newton in mathematics and especially of being able to convince him to publish his mathematical studies: ‘[Newton] being intent upon Chimicall Studies and practises, and both he and Dr Barrow &c [are] beginning to thinke mathcall Speculations to grow at least nice and dry, if not somewhat barren.’15

algebr a and geometr\ It is often believed that after the creative outburst of the anni mirabiles of his youth, Newton abandoned mathematics for other interests such as alchemy, religion and natural philoso­ phy. Evidence of this can be seen in the letter quoted above. However, the extant manuscripts, distributed across the eight magnificent volumes edited by Whiteside, disprove such a view. Newton continued to be productive as a mathematician until the mid-1690s, when his move from Cambridge to London as Warden of the Mint brought a real change to his lifestyle. In this section I shall attempt to provide a survey of Newton’s mature mathematical work. Sometime between the autumn of 1683 and early winter of 1684 Newton, according to the statutes of the Lucasian Chair, deposited a set of lectures that were printed much later under the title Arithmetica universalis (1707).16 The lectures bear dates ranging from 1673 to 1683, but these were added at a later date and it is highly unlikely that they were ever delivered to Cambridge students. In the Lucasian Lectures on Algebra Newton drew on results he had obtained in the 1660s and observations he had recorded in 1670 while working

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on the project of publishing a treatise by Gerard Kinckhuysen.17 From several points of view, Newton’s professed antiCartesianism notwithstanding, these lectures can be described as a fulfilment of Descartes’ programme, since algebra is here extensively presented as the tool to be used in the resolution of geometrical problems, most notably problems concerning curves.18 However, the Lucasian Lectures on Algebra contain some critical comments on the use of algebra that are worth considering (illus. 27). In the final part Newton stated that curves must be seen as being traced by motion, rather than as defined by an equation. Newton’s passionate insistence on the idea that curves must be primarily seen as traced by motion, rather than as loci of points in a Cartesian plane satisfying an equation, as modern mathematicians following Descartes’ steps claimed, has deep roots in his conception of the relationship between geometry and mechanical practice, a conception whose impor­t­ance in Newton’s mathematized natural philosophy can hardly be overestimated. In the 1690s, in writings devoted to geometry, Newton reconsidered this issue. Here we read that the ‘species’ of a geometrical magnitude, like a sphere, a cone or a cylinder, is best revealed not by its equation but by the ‘reason for its genesis’.19 The geometer who has learned about the mech­ anical genesis of curves has an epistemological advantage over the algebraist: he knows the nature of curves because he masters their construction. Newton seems to sug­gest that we know what we can construct, not what we can calculate. Further, conceiving curves as generated by motion allows us to relate geometry to the study of objects that exist in rerum natura.

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Thus, for Newton, what is important in geometrical construction is not the equation of the geometrical magnitude, but the fact that an elegant and simple tracing mechanism is deployed. One of the reasons why Newton around the middle of the 1670s distanced himself from algebra was the fact that, in his opinion, the geometry practised by the Greek geom­eters was aesthetically more pleasing. The ancients’ geometrical method – Newton often affirmed – is ‘more elegant by far than the Cartesian one’. The enthusiastic ack­now­l­edge­ment of the elegance and conciseness of geometry compared to the ‘tediousness’ of the ‘algebraic calculus’ is a topos that recurs frequently in Newton’s mathematical manuscripts.20 The 27 In the Lucasian Lectures on Algebra, one finds a comparison between algebraic and geometrical analyses. Problem 55 requires one to find a conic passing through five given points. The geometrical solution of this problem was highly significant from Newton’s point of view.

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importance in Newton’s mindset of such aesthetic evalu­ations can hardly be overstated. It should, however, be noted that Newton, despite his admiration for the mathematical methods of the ancients, was far from thinking that there had been no progress in mathematics and that his discoveries were not real innovations. Newton, especially after writing the Principia, was well aware that he had made a unique contribution to mathematics and, in particular, to the mathematization of the world system. In a manuscript in which he gives a brief account of the Principia, Newton, speaking of himself in the third person, says: The great difficulty of this part of Mathematicks seems to be the reason that the Ancients made but little progress in it. In this last age since the revival & advancement of these studies, some able Mathe­ma­ticians as Galileo & Hugenius have carried it on further than the Ancients did. Mr Newton to advance it far enough for his purpose has spent the two first of his three books in demonstrating new Propositions about force & motion before he begins to consider the systeme of the world.21 What Newton admired in the ancients was their method, yet he was far from thinking that the only thing left to the moderns was a passive rediscovery of Greek mathematics. There was ample space for progress, but this had to be achieved not by tedious symbolical manipulations, but rather by deep geo­ metrical insights. One of these, equivalent to Steiner’s theorem, was communicated to Collins in 1672. Newton noted that if

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two angles of given magnitudes turn about their respective vertices (the poles A and B) in such a way that the point P of intersection of one pair of arms always lies on a straight line r, the point of intersection P’ of the other pair of arms will describe a conic (illus. 28). In the late 1670s, commenting upon Descartes’ solution of a geometric problem posed by the late Alexandrian mathematician Pappus, Newton stated with vehemence: To be sure, their [the ancients’] method is more elegant by far than the Cartesian one. For he [Descartes] achieved the result [the solution of the Pappus problem] by an algebraic calculus which, when transposed into words (following the practice of the Ancients in their writings), would prove to be so tedious and entangled as to provoke nausea, nor might it be understood. But they accomplished it by certain simple proportions, judging that nothing written in a different style was worthy to be read, and in consequence they were concealing the analysis by which they found their constructions.22 However, with the benefit of hindsight, we might consider Newton’s statements in favour of the ‘elegance’ of geometry as misunderstandings of the role and strength of Cartesian algebra. Of course, when algebraic symbols are translated into prose, they often lead to rather opaque mathematical demonstrations. It might be claimed that the introduction of mathematical symbols at the beginning of the seventeenth century was proposed by its defenders as a vehicle for freeing

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mathematical demonstrations from cumbersome verbal formulations. Further, only algebra could enable generalizations unthinkable in geometry. Newton was aware of the power of algebra in achieving generality, and did not want to deny this. What he insisted on is that in some problems the moderns relied on algebra when the geometrical style of the ancients could be used with greater simplicity and aesthetic beauty. One should not underestimate the values that informed Newton’s opposition to Cartesian algebra. That is, we should avoid judging – again with the benefit of hindsight – Newton’s mathematical practices and methods to be dead ends in the development of mathematics. The invectives against the use of algebraic symbols that characterize Newton’s critique of 28 Newton’s ‘organic’ construction of conic sections communicated to John Collins in a letter of 20 August 1672.

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Descartes’ analytical geometry, and that later also informed Newton’s critique of Leibnizian calculus, must be viewed as part of a wider philosophical project that he had in mind. Read­ing Newton’s defence of geometry as a backward move, and identifying algebraization as a progressive element in seventeenth-century mathematics, means failing to grasp the values that underlie the confrontation between mathematicians such as Huygens, Barrow and Newton on the one hand and Descartes, Oughtred and Wallis on the other. Newton was not alone in his defence of geometry with regard to algebra: his writings on this topic form part of a pro-classical school of mathematics that includes major geometers working in the sixteenth and seventeenth centuries. First, Newton defended visualization over algorithmic efficiency. Second, he defended geometry over algebra as better anchored to physical reality. Third, Newton in his search for a restoration of the ancient geometrical matter, as a matter of fact contributed to the devel­opment of projective geometry, a modern research field in which other seventeenth-century mathematicians, such as Blaise Pascal and Girard Desargues, excelled. Fourth, aesthetic criteria, such as conciseness and elegance, played a role in Newton’s choice to opt for the geometrical methods of the ancients. Finally, Newton’s critical attitude towards Cartesian algebra resonated with his distaste for Cartesian philosophy, and in general for the modern mechanistic view of the world. Newton’s preference in the late 1670s for a geometrical style is thus part of a broad mathematical and philosophical programme. It is the geometrical style that was to play a promin­ent role in Newton’s masterpiece, the Mathematical Principles of Natural Philosophy, to which we will turn in the next chapter.

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newton the her etic Anti-Cartesianism, and a harking back to the past that characterizes Newtonian mathematics in the mid-1670s, based on admiration for the ancients and the idea that the moderns had corrupted a simple knowledge that needed to be restored, strongly marks Newton’s view of religion. Of course, the reference to the ‘Ancients’ we find in his mathematical work has an entirely different meaning to the one we find in his religious manuscripts: referring to Euclid is not the same as referring to Moses! The former was admired for his math­ emat­ical method, the latter revered as a prophet. Nevertheless, there is a common thread linking these references despite their differences, a thread that shows the mentality of the author, taking a stance against the corruption of the moderns. There is a stylistic, rhetorical similarity that brings us closer to the feelings of a natural philosopher, theologian and mathematician who, although in very different disciplines, regarded his contemporaries with suspicion and was keen to self-fashion his work as a restoration of lost knowledge. Further, it should be noted, Pythagoras figures in Newton’s accounts of ancient history both as a sage in possession of a pristine knowledge of the cosmos and as a mathematician. To begin with a perhaps too obvious observation, for Newton, as was usual in his time, religion had enormous importance.23 As a good Protestant, Newton considered the reading and personal interpretation of the Bible as central elements of a morally godly life. Although Newton’s religious convictions evolved over time, we can say that he remained faithful to certain principles, at least from the late 1670s.

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Most notably, he believed that a simple religion revealed to patriarchs such as Noah had repeatedly been corrupted by man’s natural tendency to superstition. For example, later in his life Newton came to the conclusion that when the religion of the ancient Hebrews spread into Egypt, it was corrupted by a series of magical beliefs. Noah and his sons, and the ancient kings, were deified; their prophetic metaphorical language was interpreted so as to give souls to the stars and planets, in a sort of idolatrous cosmology. Pagan polytheism, in which the Jews themselves had fallen, had been rejected, first by Moses and then by Christ, who had restored the old religion. This simple, pristine religion consisted in recognizing a unique God as supreme Lord, and in following the commandment of mutual love. Yet after the Apostolic age, the study of early Church history showed that a great apostasy had polluted Christ’s simple message. This diabolical plan had been perpetrated by reading the coded language of the Bible in physical and metaphysical terms. The corrupters (whom Newton variously identified as neo-Platonists, Kabbalists, ‘Hermetick Professors’ and Gnostics) had ‘twisted the meaning’ of Holy Writ. Instead of reading the biblical figurative language as standing for a moral truth concerning God’s dominion on His creatures, they had interpreted it in a physical or metaphysical way: ‘The grand occasion of errors in the faith has been the turning of the scriptures from a moral & monarchical to a physical & metaphysical sense, & this has been done chiefly by men bred up in the metaphysical theology of the heathen Philoso­phers[,] the Cabbalists & Schoolmen.’24 Indeed, according to Newton, the Holy Trinity was a Christianized heretical version of the

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pagan neo-Platonic or Gnostic doctrine of emanation. A theme that recurs in Newton’s religious writing is that the heathens’ metaphysics had led them to hypostatize nonexisting entities such as the ‘consubstantiality’ of the three Godheads. According to Newton, a similar metaphysical error was at the origin of a great variety of religious monstrosities, from Egyptian polytheism to Pythagorean soul transmigration, and later the Catholic cult of saints and relics. The Roman Catholics were prone to magical rituals involving holy water and the veneration of images and to monastic practices that polluted morality and religion. Newton was here in line with Protestant rhetoric. But his religiosity was far from any of the established confessions. From reading some of the manuscripts belonging to the Newtonian corpus sold at auction in 1936 it becomes clear that Newton embraced heretical religious beliefs with regard to the figure of Christ, even though there is disagreement about the period in which this occurred. The point of greatest conflict with the position taken by the Anglican Church thus concerns the dogma of the Trinity. In his manuscripts, Newton in fact displays anti-Trinitarian beliefs, beliefs that he shared with some of his correspondents, such as William Whiston and Samuel Clarke. Newton believed that Christ was divine, but subordinate and not consubstantial with the Father. Newton accepted that it was proper to believe in Christ’s death, resurrection and ascension, and to believe that He had bequeathed to His disciples the Holy Spirit (a believer who attached such importance to a literal reading of Scripture could not think otherwise). However, Newton argued that Christ was a servant of the Father and infinitely

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less powerful than God. Therefore, he believed that worship could be directed to Christ, but not prayers (prayers were to be to the Father through Christ).25 The idea that he was consubstantial with the Father was, for Newton, a metaphysical idea that had no confirmation in Holy Scripture, which could be the only sure basis for true faith. One can even infer from the manuscripts, albeit with some uncertainty, that Newton also denied the existence of the Devil and demons, and that he did not believe that the soul survived the body (in this vision, eternal life would be granted to a select few at the Second Coming of Christ through the resurrection of the body).26 It is extremely difficult to establish a chronology for the development of Newton’s heretical beliefs. Therefore, in this section, we cannot stick too rigidly to dates, but simply say that we are talking about positions argued by Newton in the 1670s and 1680s. The manuscripts that attest heretical positions cannot always be dated with certainty. The fact that Newton in 1675 asked, as we saw earlier, dispensation from the obligation to take holy orders may be interpreted, albeit with some uncertainty, as due to an intention on his part to avoid swearing his acceptance of the Thirty-nine Articles of Anglican Church, one of which concerns precisely the Trinity. Scott Mandelbrote has studied a document from 1677 that shows how Newton came into contact with antiTrinitarian literature in the context of the theological debates that the masters of arts, as a result of the Divinity Act, had to take part in. On this occasion, Newton addressed the vexed question of the relationship between free will and divine foreknowledge.27

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In Restoration England there were numerous thinkers who turned to the anti-Trinitarian heresy, or who instead embraced deist positions, denying the necessity of revelation to achieve knowledge of God. Very distinct positions, such as deism and anti-Trinitarianism, were embraced by some as a sure antidote against the Catholic plotting of the Stuart court or against what were perceived as Romanist contaminations of the Anglican Church. In the 1670s the Protestants felt under attack in Europe. In England, the restoration of Charles ii was, to their eyes, clearly characterized by a return to a Francophile policy, hedonism and moral dissolution. It should thus not be surprising that in this political climate Newton kept his religious ideas to himself, or rather circulated them within a well-selected circle of trusted friends. Revealing them publicly would have jeopardized his career, as his successor on the Lucasian Chair, William Whiston, another anti-Trinitarian, found out when in 1710 he was ex­pelled by the University of Cambridge, without Newton raising a finger to defend him, for having publicly expressed his beliefs. In fact, even after the Glorious Revolution (1688) and the expulsion of the Stuarts, the anti-Trinitarians had to stay on the defensive. In 1697 the Blasphemy Act condemned Uni­ta­rianism as a serious offence and banned anti-Trinitarians from holding public office. However, the Arians or the Socin­ ians did not risk more serious consequences than those suffered by Whiston. Severe cases of repression against them can be counted on the fingers of one hand.28 Newton’s silence on his anti-Trinitarian convictions was therefore justified in what was a climate of effective repression. It is no surprise that Newton, the heretic, was in favour of religious toleration

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(excluding, of course, Catholics). He, moreover, had no intention of proselytizing in public, maybe only in private within a circle of biblical scholars of high moral standing. He was well aware of the horrors that could ensue from the political radicalization of religious beliefs, and politically he was a typical representative of a culture of the Restoration, tending towards sober introspection in religious matters. He was in favour of maintaining religious convictions on controversial issues not regarding the simple profession of faith of a pre-Nicene creed, professed in the apostolic age, within the sphere of private convictions. It must be said that Newton’s sympathies for some form of heresy were not actually a secret to his contemporaries. The fact that he refused the sacraments on his deathbed, his responses at social occasions, and perhaps even the language used in the General Scholium of the Principia (1713) to characterize the relationship between God and Nature,29 were enough for his contemporaries to suspect that Newton was a heretic with anti-Trinitarian sympathies who occasionally conformed to the Anglican rite. In 1705 a group of some one hundred Cambridge students was reported crying ‘no fanatic, no occasional conformity’ against Newton, who had just been knighted by Queen Anne during her visit to the university, an incident that may not necessarily reflect any rumours about Newton’s heresy.30 Obviously, at the time, to avoid trouble with the political and religious authorities it was sufficient to maintain a facade of silence, which did not rule out the possibility of revealing something of one’s beliefs through public behaviour and the linguistic style used in one’s works; nor did it stop one from sharing heretical ideas with other dissenters.

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Newton was convinced that he was part of a circle of chosen ones who were able, through their mathematical and philosophical skills, to understand the action of God in the Book of Nature and, through their knowledge of the innermost elements of the Book of Scripture, to have access to the revealed truth. Such conviction might sound veined with irrationality, and thus deliver a Janus-face image of Newton’s genius: the mathematician on one side, the religious esoteric ‘adept’ on the other. This is the ‘Da Vinci Code effect’ that creates so many hermeneutical problems for amateurs reading Newton’s texts on prophecies. Yet Newton’s conviction could be read in a historical setting that resembles little the atmosphere of Dan Brown’s thriller. Namely, Newton, being profoundly religious and living in a profoundly religious mileu, was convinced that his extraordinary mathematical prowess (something that was evident to anybody who had read his mathematical papers) was a ‘gift of God’, a ‘talent’ (Matthew 25:14–30), that he was morally called to apply to unravel the numerological and allegorical passages of the Bible. In order to extricate Newton from the plot of Brown’s mystery-detective novel, we have to consider on the one hand Newton’s religious mindset, in which the whole of human life is an expression of the will of God, and on the other the religious and erudite culture of his times, a culture in which the deciphering of prophecies was a highly valued humanistic and religious enterprise. The deepest truths of religion (‘the strong meat which belongeth to men of full age’) were not necessary for the salvation of the masses (for whom ‘milk for the babes’ sufficed), but had to be peacefully discussed by those in the

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know, the elect destined to interpret the Scriptures.31 In particular, in the mid-1670s Newton focused his attention on the Book of Revelation and, mainly in a later period, the Book of Daniel. Like many of his English contemporaries, such as the Cambridge-based Joseph Mede, whose Clavis apocaliptica (1627/ 32) he greatly admired, Newton was following an exegetical tradition embracing humanists such as Lorenzo Valla and Desiderius Erasmus and the great worthies of the Reformation, such as Philipp Melanchthon and Jean Calvin. Commenting on the complex numerology and allegorical images of the most mysterious parts of Holy Writ was the purview of a chosen few who could decipher its prophetic language. Why was that revealed language expressed in allegories and emblems? The answer of radical Protestantism was: because God wanted to test the faith of those chosen for salvation. Deciphering the Book of Revelation or the meaning of the proportions and structure of the Temple was the moral duty, a ‘duty of the greatest moment’, of those who could by identifying the anti-Christ distinguish the true Church from apostasy, read in the history of mankind the imprint of God’s providential design and ultimately prepare themselves for the Second Coming of Christ.32 Newton, as always showing his moderation and cautious approach to sacred texts, did not share the ethos of those millenarianists who predicted an imminent Second Coming of Christ (Christ, Newton quoted from the Holy Writ, ‘comes as a thief in the night’: it is not up to us to predict His coming). Thus, in two places where Newton speculates on the time of the Second Coming of Christ, he conjecturally positions it in the distant future (in order to ‘put a stop to the rash

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conjectures of fanciful men’), no sooner than the year ad 2060 (illus. 29). It is precisely from a patient exegesis of the biblical text that Newton drew an image of God as the sole supreme ruler, omnipotent and omniscient, who governs the course of natural events and human history constantly, at every instant of time, and who acts in the world as a ubiquitous presence. God is, we read in the General Scholium that concludes the second edition of the Principia, ‘all eye, all ear, all brain, all arm, all force of sensing, of understanding, and of acting’.33 The biblical God, according to Newton, is an agent who is always present in directing cosmic events. It is not the God of Descartes who, according to an interpretation that not so many Descartes scholars would accept, is the creator of a world-machine that, after creation, may do without its creator. Many contemporaries of Newton believed that man’s free will and the providential action of God would not be possible in a world-machine governed by the laws of impact between corpuscles consisting of passive matter. Mechanicism denies, according to Newton, the finality of nature, and above all denies the providential presence of God. For Newton, God governs the world according to a providential plan that the philosopher contemplates in natural phenomena. How does God act in the world? With what instrument does he manifest his providential action? Newton here wanted to avoid falling into a form of pantheism or Baruch Spinoza’s identification of God with Nature. Boyle had already stressed God’s ability to move bodies directly, just as the human mind causes movements of the limbs. Newton adopted this idea, maybe taking it in fact from Boyle,

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stressing that to do this, God has to be in every place at every moment of time. The dilemma that the natural philosophers of Newton’s times had to face was to defend the idea that the order of Nature revealed by the new mathematized science could not be the product of chance (as suggested by Epicurean­ ism) or necessity (as suggested by Spinozism), but could only be constituted by God.34 Did Newton believe that God was present through the mediation of those vegetative principles permeating space discussed in alchemical literature, as Dobbs has argued? The Newtonian manuscripts do not seem to give a clear answer to this question. Further, the great themes of free will and divine grace, which run through Reformation 29 Detail showing the future Millennium from the apocalyptic time chart in Mede’s Clavis apocaliptica (1672). Newton had a great esteem for Mede’s interpretation and followed his method respectfully.

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and Counter-Reformation theological literature, seem absent from Newton’s view, perhaps because these issues were felt by Newton to be foreign to a faithful reading of the sacred text, where such philosophical and metaphysical questions have no place. It is important to stress the fact that Newton, notwithstanding his dislike for metaphysics, did in fact endorse a metaphysical position by distancing himself from Cartesian dualism. He stated this in the manuscript known as ‘De gravitatione’ (uncertain date) and would also stress in his mature writings, such as Query 23/31 and the Opticks, that God is a powerful ever-living Agent, who being in all Places, is more able by his Will to move the Bodies within his boundless uniform Sensorium, and thereby to form and reform the Parts of the Universe, than we are by our Will to move the Parts of our own Bodies.35 God implanted in man a semblance of his ability to act voluntarily. But just as God acts in the world by being present everywhere, so the human will acts on the body not thanks to a soul separate from the body, as follows both from Cartesian dualism and Leibniz’s notion of pre-established harmony: the distinction between the ideas of thinking and extended substances cannot be so ‘lawful and perfect’, as Descartes claims, ‘so that both can pertain to the same created substance, that is, that bodies can think or that thinking substances can be extended’, we read in ‘De gravitatione’.36 Consequently, as would seem to be expressed in a memorandum penned by

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David Gregory in 1694, Newton believed that the soul perishes with the death of the body. Only with the resurrection of the body, at the Second Coming of Christ, would the soul be reborn with the body: it did not exist independently of the body.37 Probably, Newton was here influenced by the mortalist theological tradition widespread in England in the Civil War and Interregnum (the case of John Milton is well known), but we cannot rule out relations with Socinian literature.38 Newton, who exchanged these ideas with Locke, probably included mortalism in his project for the restor­ ation of the ancient Jewish religion, seeing that distinguished biblical exegetes of his time had come to the conclusion that in the Old Testament there was no trace of the idea that the soul survives the body. According to Newton the conception of God as the absolute and sole ruler of the world was corrupted in the early centuries of the Christian era by the infiltration of pagan philo­sophies, especially of a neo-Platonic, Hermetic and Gnostic nature. The original antediluvian religion, restored in more recent times by Moses, and then by Christ, was corrupted in the early councils, especially that of Nicaea (ad 325), by perverse men such as Athanasius, who, by persecuting Arius, introduced into Christian belief a real philosophical monster, the dogma of the Trinity.39 The defenders of the dogma of the Trinity, according to Newton, did not have scripture on their side, but only pagan philosophers. Christ in the Gospels reaffirms his subordination to the Father, and where the New Testament seems to offer a prop to Trinitarians, this happens because of uninspired interpolations artfully introduced by the enemies of Arius.

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Newton in particular focused on the so-called ‘Comma Johanneum’, which he interpreted as a late addition, due to Jerome’s Latin translation, to the sacred text.40 In supporting these positions, which Newton communicated to Locke in the early 1690s, originally with the intention, later retracted, of having them published anonymously in the United Provinces, Newton showed that he was influenced by a contemporary view based on a philological approach to Holy Scripture promoted by the likes of Erasmus and Richard Simon. Newton carefully studied the history of the early Church, and wrote at length, in secret, on the theological debates regard­ing Christology that took place in the early centuries of the Christian era. His writings are impressive on the one hand because of the erudition with which he analyses the texts of the Fathers of the Church, and on the other for his legalistic analysis, as if he were preparing a speech in court against Athanasius. Anti-Arian positions are disputed on a scriptural, theological and even political and moral level. Newton amassed historical evidence on the ‘conspiracy’ of Athanasius that, again according to our Lucasian Professor, plotted perverse machinations against Arius. Newton’s writings against the Trinitarian heresy are of a fierce, polemical vehemence. In the 1670s Newton also began to consider the interpretation of biblical prophecies (particularly those contained in the Book of Revelation). Just as Nature offers to the scrutiny of the alchemist, the cosmologist and the physicist signs of the purposeful and ordering intervention of God, so history reveals His providence.41 The prophecies in fact, once deciphered, are nothing but descriptions of historical events. In revealing them to the prophets, God wanted to show that

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the history of man is preordained according to a providential plan. The deciphering of the prophecies, however, was not to be undertaken for utilitarian purposes, to predict the future or to predict the Second Coming of Christ, as in the extensive millenarian literature of the time. The deciphering of prophecies served only the purpose of confirming God’s free action in human history. Just as the alchemist does not devote himself to the study of the Book of Nature to obtain gold or health, so the biblical exegete must only aim at the contemplation of God’s action in history. It thus becomes important to find a correspondence between historical events and biblical prophecies. What idea of human history had Newton acquired in his studies on biblical prophecies? Newton, at least from the mid-1680s onwards, adopted the myth, widespread from the Renaissance until at least the eighteenth century, of ‘Mosaic Philosophy’: the ancient wisdom of the Jews, wisdom that would later be corrupted by false interpreters. He was con­ vinced that the patriarchs and prophets, such as Noah and later Moses, knew truths that concerned not only God and his relationship with Creation, but Creation itself. The ancient Jews would have possessed astronomical and physical know­ ledge that Newton tried to ‘restore’ in his activities as a natural philosopher. In a Latin work of the 1680s entitled ‘Theologiae gentilis origines philosophicae’ he explicitly associated idolatry with a wrong geocentric natural philosophy. For Newton, the fact that Ptolemy was an Egyptian was significant from this point of view, since it was precisely in Egypt that the poly­ theistic corruption of Noah’s religion had taken place. Noah and his sons knew the heliocentric cosmology that Copernicus

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would have rediscovered many generations later. But this wisdom had been lost because of false interpreters. Newton also espoused the myth that Greek philosophers such as Pythagoras and Democritus had received the elements of this wisdom. In the Pythagorean and Democritean tradition there were thus still some elements of ancient Jewish wisdom: heliocentrism and the cosmology of the void and atoms. It is in this context that Newton spoke of the ancient wisdom as including a ‘rational religion’, a view of the divinity that was spread among various cultures, not just the Hebrew one. By contemplating nature, some ancient sages had reached, without revelation, an understanding of the frame of the word and of the existence of a unique divine ruler. The circular temples, or prytanea, were seats where the ancients both worshipped the only God and celebrated the heliocentric structure of the planetary system. This ancient wisdom, the prisca sapientia, was kept hidden from the common people through an esoteric language that made use of architectural proportions, textual metaphors and emblems. The belief in an original wisdom, in a prisca sapientia, is evident in many of Newton’s British contemporaries. Many of his acolytes espoused this view, which Newton had already set out in the incipit of an edition of the last book of the Principia, written in the mid-1680s, but that would be published posthumously (1728), where we read that the Coper­ nican system was known to ‘Philolaus, Aristarchus of Samo, Plato in his riper years . . . the whole sect of the Pythagoreans . . . Anaximander . . . and Numa Pompilius’. Copernicus himself, under the influence of Ficino’s neo-Platonism, had stated

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very similar ideas in De revolutionibus (1543). According to Newton it was only after Eudoxus, Callippus and Aristotle that ‘the ancient philosophy began to decline, and to give place to the new prevailing fictions of the Greeks’. 42 In the 1690s, after the composition of the Principia, Newton came to attribute to the ancient Jewish, Chaldean, Greek and Latin sages knowledge of the laws of optics and celestial mechanics that he had simply rediscovered. In manuscripts, known as the Classical Scholia, which Newton was planning to add to his Principia, but that he would not publish and which would be included in the preface to Astronomiae physicae et geometricae elementa (1702) by David Gregory, it was stated that the ancients were aware of the fact that gravitation varied with the inverse square of the distance and that they had concealed this knowledge in musical metaphors.43 Indeed, in the Classical Scholia, the Ur-mathematician Pythagoras appears intent on producing celestial harmonies by plucking the intestines of sheep and sinews of oxen by playing Apollo’s lyre. According to Newton, Pythagoras concealed in a coded musical language his knowledge of universal gravitation. However, other natural philosophers contemporary to Newton expressed some doubts regarding the myth of the prisca, as is clear from the correspondence between Christiaan Huygens and a young follower of Newton, Nicolas Fatio de Duillier (illus. 30).44 Newton’s interest in alchemical texts, which still in the 1690s he read with the help of Fatio, who translated for him from French both treaties of alchemy and the Traité de la lumière (1690) by Huygens, is part of his reverent respect for antiquity. It was not only the moderns’ theories of matter that commanded Newton’s respect, but those of

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the ancients, whose traces are discernible in alchemical texts, including texts by those alchemists who were considered by Newton as charlatans or infected by pagan or Kabbalist metaphysics. Was Newton therefore convinced that the old patriarch Noah while contemplating the rainbow, Pythagoras playing his lyre and Numa Pompilius while adoring the central fire in the Temple of Vesta were in possession of a fully fledged science so that they knew about calculus, the theory of gravitation and optical dispersion? Were they manipulating equations and performing observation to, say, calculate the Earth’s shape, the refraction of starlight in the Earth’s atmosphere or the periods of the comets? Such naivety, which might have elicited Huygens’s incredulity and some irony at the Royal Society, is improbable. What Newton most likely meant is that the ancient sages possessed a simple view of nature (they knew that planets gravitate towards a central Sun, that matter is made out of corpuscles moving in a vacuum and so on) compatible with true religion. He thought that it was our duty to deploy experimental and mathematical philosophy, instruments, laboratory tests and mathematical deductions in order to recover what was given by revelation to the ancient patriarchs. In line with Protestant doctrine, Newton thought that the age of the prophets, the period in which God spoke to mankind via the Holy Spirit, was over. After Christ, we were in the age of the interpreters, who have to busy themselves, avoiding the ‘enthusiasm’ of those who seek divine illumination as well as the hypotheses of rationalist system builders, with hard experimental, mathematical and exegetical work, in order to cancel the diabolical effects

30 In 1689 Nicolas Fatio de Duillier met Newton in London and for a few years he enjoyed Newton’s intimacy, becoming one of his closest collaborators.

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of metaphysical pagan corruptions. Mathematical natural philosophy, the ‘business of philosophy’, indeed, according to Newton, allows us to find a view of nature that is conducive to the contemplation of God’s action in Nature. We will have more to say about this in the next two chapters.

five

Natural Philosopher, 1684–1695

I

n november 1679 Hooke, recently elected as secretary of the Royal Society, wrote a brief conciliatory letter to Newton in which he expressed his intention to re-establish contact with him, putting behind them the controversy on the experimentum crucis and proposing his hypothesis on the motion of the planets.

the role of hook e and halle\ The hypothesis in question was not new: Hooke had already partly presented it at the Royal Society in 1666, and later published it in 1674 at the end of an essay entitled An Attempt to Prove the Motion of the Earth from Observations, which was dedi­ cated to his astronomical observations of stellar parallax.1 In concluding his essay, Hooke described to his readers a ‘System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Notions’.2 Hooke’s new system depended on three ‘Suppositions’. The first was that all celestial bodies ‘have an attraction or gravitating power towards their own Centers, whereby they

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attract not only their own parts . . . but that they also attract all the other Coelestial Bodies that are within the sphere of their activity’. It appears that Hooke considered this sphere of activity to be finite. The second assumption, most likely taken from Descartes’ Principia, was that all bodies moved in a straight line at constant speed ‘till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipsis, or some other more compounded Curve Line’. The third assumption was that ‘the attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers.’ Hooke described the way the planets of the solar system were attracted by the gravitational power of the Sun and how their attraction to one another influenced their motion in a ‘considerable’ way, and hoped that astronomers would dedicate themselves to establishing the law of the variation in gravitational force in order to reduce ‘all the Coelestial Motions to a certain rule’.3 From the correspondence between Hooke and Newton in 1679 and 1680 it can be seen that these three assumptions concerning planetary motions caught the Lucasian Professor totally off his guard. As we know, in the ‘Hypothesis’ of 1675 Newton had conceived of an ‘æthereal spirit’ responsible for the ‘gravitating attraction of the Earth’ and had envisioned the planetary system and the ‘vast spaces between us and the stars’ as being filled with this spirit, which is what keeps the planets in orbit around the Sun. The ether of the ‘Hypothesis’ still survives in some of the queries (21, 22) of the Opticks; its alchemical nature distinguishes it from a Cartesian planetary vortex.4 However, in his correspondence with Thomas Burnet

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and Flamsteed in the years 1680–81, Newton was considering the idea of an ethereal terrestrial and solar vortex outlined in terms that one would define as Cartesian. A terrestrial vortex responsible for the tides also appeared in Varenius’s Geographia, whose first and second editions, put together by Newton, appeared in Cambridge in 1672 and 1681.5 The comet of 1682 (later christened ‘Halley’s comet’), however, moved close to the ecliptic plane and in retrograde direction compared to the planets, and then in the opposite direction to the motion of the hypothetical planetary vortex. It is plausible that it was the observation of Halley’s comet that convinced Newton that Hooke’s theory had to be taken seriously.6 According to Hooke, indeed, the motions of the planets occurred in empty space, and were achieved by ‘compounding the celestiall motions of the planetts of a direct motion by the tangent & an attractive motion towards the central body’.7 Additionally, Hooke expressed himself in a way that seems to suggest that he considered that attraction decreases with the inverse of the square of the distance and, in January 1679/80, asked Newton to give a demonstration of the path followed by a body subject to a force of this kind, and to explain its physical cause.8 Hooke’s intuition as a physicist seems formidable, but perhaps we risk interpreting his statements, which are far from easy to decipher, in the light of the theory of gravitation developed by Newton a few years later. It seems, however, very likely that his correspondence with Hooke made the scales fall from Newton’s eyes, allowing him to see much further than before. Historians are divided on the nature of Newton’s debt to Hooke: lately, Michael Nauenberg has

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defended the thesis according to which by 1679 Newton had developed a mathematical theory of orbital motion.9 Be that as it may, it must be said that although Hooke should be given credit for having averted Newton from his youthful view of the planets, he was not the one who provided a mathematical model for the new paradigm. It is one thing to propose a qualitative hypothesis (that planets move in the void, and are subject to an inverse-square gravitational force directed towards the Sun that diverts them from their straight inertial trajectory), quite another to examine it mathematically and systematically as Newton did in the Principia. Hooke’s ‘System of the World’ was taken into careful consideration at the Royal Society. Christopher Wren, the great mathematician and architect, had considered the possibility that planets were subject to a force that varied with the inverse square of the distance. In 1684 he had challenged Hooke and Halley to produce a mathematical theory of this planetary model, promising a book worth 40 shillings to whoever succeeded. Finding a solution to Wren’s challenge proved too difficult, and it is probably for this reason that in August 1684 Halley visited Newton. The accounts of the meeting between Halley and Newton do not tell us exactly what Halley had asked Newton and how Newton replied, but their discussion certainly left its mark on Halley. It was clear that Newton had a new theory, mathematically developed, that gave a quantitative form to Hooke and Wren’s hypothesis on planetary motion. Halley returned to London with the promise that he would obtain from Newton details of the new mathematical theory of planetary motion in writing. And so, in November 1684, Halley received a brief manuscript entitled ‘De motu

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corporum in gyrum’ containing a plausible solution to the 40-shilling bet placed by Wren. Newton showed that if the planets obeyed the first two laws of Kepler, they were thus attracted towards the Sun by a force that varied with the inverse of the square. Halley was enthusiastic. He told the members of the Royal Society and simultaneously urged Newton to develop his ideas. Newton allowed himself to be influenced by this enthusiasm and set to work with a tireless intensity that stunned his assistant. He would often write standing up, leaning over his table, too engrossed even to sit down or eat. Finally, in the summer of 1687, the classic that was going to change science was in print. In those three years Halley had received from Newton hundreds of handwritten pages full of mathematical arguments, diagrams, experimental results and astronomical observations. Halley had read, corrected and patiently commented on each line. He had also maintained contact with the Royal Society, under whose auspices the Principia was published, and the printer. As if this were not enough Halley, although in financial difficulties, had footed the bill for the publication. Halley probably did not make a profit from this risky venture, but did not lose his money either.10 Without his enthusiasm and determination, the Principia would never have seen the light (illus. 31). Halley also had the role of mediating between Newton and the other members of the Royal Society. First, he had to deal with the somewhat touchy Hooke, who was offended because he believed, not without reason, that Newton should have acknowledged his contribution to the discovery of universal gravitation, and the publication of the Principia in fact

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further worsened relations between the two. In his work, the Lucasian Professor made no mention of the correspondence with Hooke and of the debt he owed to Hooke’s gravitational theory of planetary motion, a theory that, ultimately, was also published in 1674 and reviewed in the Philosophical Transactions of the Royal Society, and therefore could not be entirely ignored. In his letters to Halley, Newton made no attempts to conceal his irritation with Hooke: the latter had only been able to formulate a hypothesis, not a mathematical proof and therefore, according to Newton, did not even deserve a mention. For the rest of his life, Hooke felt cheated of the ‘greatest discovery in nature, that ever was since the world’s creation’, as his friend John Aubrey complained to the antiquarian Anthony à Wood.11 Halley had a hard time persuading Newton, who had been offended by Hooke’s insinuations, not to withdraw from print the third book of the Principia dedicated to a ‘System of the World’, a system that looked more like the one outlined by Hooke in 1674 than that described in Newton’s ‘Hypothesis’ of 1675. Halley also had to win acceptance from the Royal Society for a work that only partly represented its ideals. Newton presented a text that was difficult to read: even among the leading fellows, there were few who could understand it. The Principia contained only sporadic hints to practical applications of the mathematical propositions that filled its pages, and the experimental evidence was meagre when compared to that patiently collected over the years by researchers such as Hooke and Boyle. There was clearly little evidence of Bacon’s ideals of a natural philosophy useful to the progress of society, based on inductive evidence, accessible and open

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to the criticism of the other ‘virtuosi’ followers of the Novum organum, in Newton’s impervious, apodictic work. Halley could mention, to present the Principia to the Royal Society and before its patron James ii, the parts of the third book that could be useful for the art of navigation. Newton collected data from a network of observers spread over Europe, Africa, the Americas and Asia, on the tides, on the variation in the length of the seconds pendulum in function of latitude, and 31 Edmond Halley holding a sheet of paper with a diagram related to a fourth-degree algebraic equation. Halley had written an essay on this topic in 1687. Thomas Murray, Edmond Halley, c. 1690, oil on canvas.

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on comets. Some of these experimental data, combined with Newton’s mathematical method applied to the determination of the Moon’s motion, could potentially give important results in the field of navigation, cartography and the determination of longitude.12 The Principia have the following structure. An ‘author’s preface to the reader’ is followed by a set of definitions and a scholium to the definitions. Then there is the enunciation of three ‘axioms or laws of motion’, followed by corollaries. The work continues with three books. The first two deal mainly with mathematics, applied to the motion of bodies in a vacuum (Book i), and in media that offer resistance such as air or water (Book ii). The third book deals with the ‘System of the World’: it is here that Newton presents his cosmology based on the idea that the planets move in empty space, attracted towards the Sun by a force inversely proportional to the square of the distance. This force, gravitation, acts between all the masses of the universe, so that two point-like particles attract each other with a force whose intensity is proportional to the product of their masses and inversely proportional to the square of their distance. The ways this force acted were mysterious, and Newton was silent on its causes, a fact that, as we shall see, attracted criticism. Ultimately, Newton, according to his critics such as Huygens, repeated the mistake made in the case of colour theory: he had stated a mathematical law, but failed to explain the physical causes underpinning it. The Principia was fairly well received in England, but met with less favour on the Continent.13 It should be added that the Principia is written terribly, and this did nothing to help the reception of Newton’s magnum

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opus. Newton, working with inventive fury, ended up delivering a convoluted work to the printers, full of gaps. Anyone who has made a serious attempt to read the Principia knows how many cases there are in which a corollary is much more import­ ant than the relative theorem, and how many points there are where Newton leaves the reader, for brevity’s sake, to work out their own proofs of statements that are far from simple. A probably spurious tradition handed down in a note by John Conduitt recounts that ‘the students at Cambridge said there goes the man who has writt a book that neither he nor any one else understands.’14 The difficulty of Newton’s work lay mainly in the fact that his results had been obtained through the use of mathematical techniques understandable only to a few experts. Today we are accustomed to the fact that theoretical physicists speak a language comprehensible only to experts in the field, but in Newton’s time most cosmological texts, such as those of Galileo and Descartes, could be approached without great difficulty by a reader who was not a specialist in mathematics. Conduitt also informs us of the confusion generated by Newton’s work in the Republic of Letters. Powerful aristocrats, such as Charles Montagu, were apparently willing to pay good money to unravel the complex reasoning of the Principia: Earl Halifax [Charles Montagu] asked Sir I. N. if there was no method to make him master of his discoveries without learning Mathematicks – Sir I. said No it was impossible, but Mr Maine recommended [John] Machin to his Lordship for that purpose who have him 50 Guineas by way of encouragement. Machin

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as he told me himself tried several schemes but never any that satisfied him & gave it up in despair. [Henry] Pemberton attempted it with great emolument to himself 3000 subscriptions at a Guinea which shewed the earnest desire of all ranks &c.15

32 Frontispiece of the first edition of Isaac Newton’s Philosophiae naturalis principia mathematica.

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So, at first glance it does not seem that the work financed by Halley could become the accepted manifesto of the Royal Society. Ultimately, the Principia remained to some extent a foreign body to the Society, whose members espoused the Baconian ideal of an experimental philosophy accessible for public discussion and beneficial to human welfare. The import­ance of Newton’s work, however, was immediately recog­nized, even by most of those who were unable to read it from beginning to end (illus. 32).

the pr eface to the principia: omnis philosophiae difficultas In the Preface to the first edition of the Principia, Newton states that ‘the whole difficulty’ of natural philosophy is ‘to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces’.16 We should note the combined presence of trad­ itional and somewhat innovative elements in this statement of intent. Natural philosophy is ‘philosophy’ in the Aristotelian sense, insofar as it is a science aimed at discovering the causes of phenomena (verum scire est scire per causas). The causes are, however, sought not in the Aristotelian sense of the term, as material, formal, efficient and final causes. Not even Newton identifies the causes with the impacts between corpuscles of mechanical philosophy, the invisible operations of microscopic mechanisms.17 The causes of the phenomena of motion act at a distance, and it is this view of them that aroused criticism on the Continent, as we shall see later. The environment in which Newton was working was certainly receptive to his

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position, as we mentioned in the discussion of the English tradition of chemistry, since many saw Nature as pervaded by active principles. We cannot rule out that this cultural attitude contributed to the acceptance of Newton’s gravitational theory. It must be said that Newton’s texts show no sign of the notion of gravitation acting at a distance being based on theories of short-range interparticulate action, which would have indicated that Newton’s chemistry influenced his cosmology. However, we cannot rule out that an antimechanist English cultural climate in the field of matter theory might have offered a conceptual space in which Newton’s gravi­tational theory could be formulated and accepted more naturally than in Continental milieux dominated by Car­ tesianism. It is often the case that the attitudes, mindsets and cultural fashions of a social group play a role that is difficult to demonstrate, precisely because they act tacitly as presuppositions that determine what is to be accepted, and what rejected. In the Preface, Newton has something very interesting to tell us about the tools that he intends to use ‘to discover the forces’ using motion as his starting point. As he had said in his Lucasian lectures on optics, it is geometry that may allow the natural philosopher to achieve the ‘highest evidence’. In the Preface, Newton characterizes geometry in a rather innovative way. In fact, Newton states that geometry is subordinate to mechanics, since geometric objects are thought of as generated by motion and are thus presented to the geometer by mechanics. Mechanics, continues Newton, teaches us how to draw straight lines, circles and other curves that are the subject of geometrical study.

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It is important to understand the scope of this reversal of the traditional subalternatio of mechanics (together with music and astronomy, one of the ‘mixed mathematical disciplines’) to geometry (which, along with arithmetic, was one of the ‘pure mathematical disciplines’). In the Aristotelian tradition the mixed mathematical sciences are less perfect compared to the pure ones, because they deal with material, less perfect, objects, compared to the objects of the pure mathematical sciences. But for Newton mechanics is not less perfect than geometry, and therefore not subordinated to it, if by mech­anics we mean the ‘rational mechanics’ mentioned by Pappus, quoted by Newton, in the eighth book of the Mathematical Collec­tions. Rational mechanics teaches us how to draw curves (for example, a circle drawn by a compass, an ellipse traced by an ellipsograph); it creates them before the geometer may apply himself to studying them. Newton here between the lines seems to take a stand against Descartes, who in his Géo­métrie (1637) had characterized ‘mechanical’ curves (for example, spirals) as inexact and therefore inadmissible in geometry. When Newton wrote the Preface he had years of study behind him on what was termed ‘organic geometry’. To understand what Newton had in mind when he said that the search for the causes of motion in natural philosophy can only be per­ formed by using geometry, subordinated to rational mechanics, we need to mention the studies on geometry conducted by Newton just before the composition of the Principia. Organic geometry studies the mechanisms (the instruments, organa, in Greek) that generate plane curves. For the sake of simplicity we may think of the compass as a tool for generating a circle or the instrument devised by Newton, a tool for drawing conic

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sections (see illus. 28).18 These geometrical studies by Newton are related to contemporary developments in projective geom­ etry by Girard Desargues, Blaise Pascal and then Philippe de La Hire (whose treatise on conic sections Newton quotes in the Principia). Conceiving of curves as being plotted by an instrument and not as the result of an equation allows Newton to expand the class of geometrically admissible curves. Just because a curve, such as the spiral, does not have an algebraic equation in Cartesian coordinates, this does not mean that it is not admissible in geometry, as Descartes claimed. But what matters most in the context of this chapter is that organic geometry is by its very nature a tool suited to Newton’s natural philosophy. In a manuscript of the 1690s in which Newton reworks the Preface to the Principia, we read: ‘any plane figures executed by God, nature or any technician you will are measured by geometry in the hypothesis that they are exactly constructed.’19 Thus the curves are not plotted only by instruments handled by a human craftsman, but by God (perhaps in the Preface to be identified with ‘the most perfect mechanic of all’) and Nature. Perhaps we can say that just as the compass is in the hands of the human artificer, so force is in the hands of God? May we go as far as to say that the motions of the planets are caused by a force which in the final analysis depends on the ‘divine arm’ that draws their trajectories through the heavens? This was a highly sensitive and controversial issue, to which we will return, but let us say here that these questions seem to be beyond Newton’s mental horizon. They are metaphysical questions to which Newton does not intend to respond: we cannot stress enough the sobriety with which Newton avoids

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compromising himself in speculations concerning how God acted on Nature. Deducing forces from planetary trajectories is one of the main problems that Newton sets himself. Starting with the study of planetary motions Newton deduces the existence of an attractive gravitational force acting between the planets which varies with the inverse square of the distance and proportional to the product of their masses. Having established the existence of this force, or rather, once it has been stated using an inductive generalization that this force acts on all masses that make up the universe, he proceeds ‘to demonstrate the other phenomena’: the tides, the motions of the Moon, comets and so on. Newton’s procedure seems so natural for a modern-day physicist that we may fail to realize just how innovative the agenda outlined in the Preface actually was. Newton tells us that the main problem of natural philosophy is to start with what is observable, what appears – namely phenomena – in order to discover forces, which are the invisible causes of those phenomena. Let us imagine the trajectory of a bullet or a planet: this is a phenomenon that we can see and, what is more import­ ant, measure. This trajectory, says Newton, is generated by a force, a bit like the way a circle is traced by a compass. But while we can build and manipulate a compass, force is an element that works in Nature, which is inaccessible to our senses, and which is not the result of a human construction. We can however infer the existence of force by measuring the trajectory’s acceleration. It was said earlier that the trajectories of the planets, the starting point for the geometrical method of deduction of the

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force of gravitation outlined in the Preface, can be measured, and it is from these measurements that the discovery of universal gravitation derives. But in which frame of reference should the motions of bodies be measured? In which spatial frame of reference should the trajectories of the planets, the moon and comets be represented? And what clock should we use to measure their motions? If we do not clarify this, the deduction of forces from motions cannot be accurately defined. And it is here that Newton’s famous reflection on absolute time and space is justified.

definitions After the preface, the Principia begins with a number of definitions followed by the scholium on absolute time and space. The first definition is that of ‘quantity of matter’ measured by the product of density and volume. Density, we should remember, was measured as specific gravity. We would now refer to the first concept introduced by Newton as ‘mass’. Newtonian scholarship agrees that this first definition is an important step in the history of mechanics. Indeed, before Newton there was a great deal of ambiguity and variety of expressions: there was talk of weight, bulk and the extension of a body. Newton instead clearly distinguishes between weight and mass: the former is not invariant. The weight of an apple on Earth is different from its weight on the moon. The experiments of Jean Richer on the variation of the length of the seconds pendulum in function of latitude had dem­ onstrated that also on the Earth the weight of a body varied in function of its location. Mass, however, is an invariant

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magnitude. The meaning of the notion of mass is explained by Newton in the laws and especially in the application of the laws to concrete physical situations. For example, Newton knows that it follows from the second law that the same force applied to different bodies causes accelerations inversely proportional to their masses. It is in the Principia that we find the conceptual distinction between inertial mass and gravitational mass, followed by experimental proofs of their equivalence. The second definition regards the ‘quantity of motion’ measured by the product of velocity and the quantity of matter. This is a concept that had played a key role in the work of Des­cartes and in the studies of the impacts of bodies conducted by Huygens, Wallis and Wren. The third definition is extremely interesting and teaches us how important it is to look at Newton’s science of motion and pay attention to what distinguishes it from Newtonian mechanics as taught today. The ‘inherent force of matter’, or ‘force of inertia’ of matter, Newton says in his third defin­ ition, ‘is the power of resisting by which every body, so far as it is able, preserves in its state either of resting or of moving uniformly straight forward’. This ‘force’ occurs when an ‘impressed force’ acts on the body to make it change its state of motion.20 We can understand the ‘impressed force’ as the resultant of a system of forces acting on the body. In speaking of inertia as a ‘force’ that is activated within a body as a ‘resistance’ to the change in rectilinear uniform motion when an impressed force, for example an impact, is applied to the body, Newton seems to refer to the idea that bodies possess some form of internal activities. This is an interesting idea, which it might be tempting to relate to Newton’s marked aversion

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to the idea that matter is ‘passive’. It should be said that this interpretation seems to be belied by what Newton says in Query 31 of his Opticks (to which we will return) where he speaks of inertia as a ‘passive principle’ that alone is not able to preserve motion in Nature. The definitions continue with the setting forth of impressed force and three different measures of centripetal force. For reasons of space we will not dwell on these here.

absolute time and space Newton introduces the concepts of absolute time and space in the scholium to the definitions of the basic concepts of nat­ ural philosophy. Also in this scholium, as and more than in the Preface, Newton takes a stand against Descartes, who in the second part (sections 24–5) of the Principia philosophiae (1644) had defined motion as the translation of a portion of matter with respect to other portions of matter that are immediately adjacent to it. For Newton, instead, the motion of bodies was to be related to absolute space.21 The reasons for the rejection of Cartesian notions of movement, and the subsequent defence of absolute space and time, are at the same time meta­ physical/theological and physical/astronomical. The former are not completely explicit in the scholium to the definitions: they would be taken up once more in the famous General Scholium with which Newton would conclude the second (1713) and third (1726) edition of the Principia, and then in the correspondence between Leibniz and Clarke of 1715–16. There are a number of texts that Newton penned which have been studied as defining, albeit in a tentative way, a

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Newtonian ‘metaphysics’ or ‘theology’ of space and time: most notably, the De gravitatione (an enigmatic notebook whose dating and purpose are unclear), a short text known as ‘tempus et locus’ (early 1690s?) and a draft notice (c. 1718) that might have been intended for inclusion in a collection of letters gathered in the late 1710s by the Huguenot réfugié Pierre Des Maizeaux.22 Clearly, Newton was up to criticizing existing theories of space, time and motion, especially the Cartesian ones, as unfit to good scientific practice and even potentially dangerous from a religious point of view. It seems to me that at least one motivation behind such Newtonian forays into a philosophical terrain that was so foreign to his practically oriented mindset came from a religious concern. As we shall immediately see, Newton’s mathematical physics, more precisely the fulfilment of the ‘main problem’ of his natural philosophy as expounded in the Preface, required the assumption of very ‘real’ notions of absolute time and space, that is, the notion that they exist independent of the choice of reference or measurements of the human mind. Newton worried about the consequences for religion in positing entities that are infinite and eternal, two attributes that should pertain only to God. The risk was that of attributing divine properties to Nature, a risk that did not occur in cosmologies that regarded the universe as finite in time and space. But, Newton stated, absolute time and space are neither substances nor a property of a substance: they are real but their ontological status is weaker and inoffensive from a religious point of view. In Newton’s words, they are ‘emanative effects of the primary existing being’, God. This might be understood as implying that since God is omnipresent and eternal,

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space and time are infinite. In other words, since ‘all things are in time as regards duration of existence, and in place as regards amplitude of presence,’ the infinite time and space required by Newtonian natural philosophy are also conse­ quen­ces of the existence of God. Such positions, which were made public in the correspondence between Leibniz and Clarke, have elicited many commentaries and criticisms. Luckily for the author of this book, it is not his duty to elucidate such thorny questions in these pages.23 In the scholium to the definitions Newton explains that ‘absolute, true, and mathematical time’ in itself, and by its nature without relation to anything external, ‘flows uniformly’. Also absolute space is ‘without reference to anything external’.24 It is with respect to absolute time and space, says Newton, that we must speak of the position and motion of bodies. But how can we identify absolute space and time? Which of the bodies that surround us is at rest or moves according to uniform rectilinear motion, with respect to absolute space? The difficulty inherent in this question is increased by the fact that the laws of Newtonian physics do not vary from one reference system to another moving with uniform rectilinear motion with respect to the former. As Galileo had already stated, it is not possible to establish on the basis of physical experience whether our laboratory is stationary or moving uniformly in a straight line. Newton believed that it was possible to distinguish relative motion from absolute motion according to the ‘effects’ caused by rotation. Newton provides two examples. The first is the famous one of the rotating bucket. Newton asks us to imagine a bucket filled with water and hanging from a ‘cord’. This is clearly

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aimed at refuting Descartes, who defined motion as a shift between two adjacent bodies. Yet, says Newton, the relative motion of the walls of the bucket compared to the water it contains is irrelevant for defining the state of the water’s motion. If we twist the rope from which the bucket is hanging and then let the rope unravel, initially we will have relative motion between two adjacent bodies, the walls of the bucket and the water, and the surface of the water will be flat. Then we will have an annulment of the relative motion between the walls and the water, and the surface of the water will be curved. If we then suddenly grab the bucket with our hands we will have relative motion between the walls and the water, but the surface will continue to be curved. Then, gradually, the relative motion between the walls and the water will diminish and the surface will return flat. The definition of motion given by Descartes, according to Newton, does not allow us to provide a causal explanation of the phenomenon. The relative motion of the water with respect to the bucket has no stable relationship with the curvature of the surface of the water. Newton explains this by saying that the curvature of the surface of the water is an effect of the rotation of the water with respect to absolute space, regardless of the motion of the water with respect to adjacent bodies. This was Newton’s reasoning, and it would not be overcome until over two centuries later, when Albert Einstein’s theory of relativity deeply changed the intuitive notions of time, space and motion on which Newton’s scholium rested. In the second example proposed by Newton we have two ‘balls’ joined by a ‘cord’ in an empty space: there are no other bodies against which to measure the system’s motion made up of the two balls and a cord. If a tension is

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measured in the cord, then the balls are rotating with respect to absolute space. If we know the coefficient of elasticity of the cord we can determine the velocity of rotation. This is the effect by which we can determine the status of rotatory motion with respect to absolute space. Newton believed that in reference frames accelerated with respect to absolute space, accelerations are measured which do not correspond to real forces. To ensure that the science of motion deduces forces that actually exist we need to consider the ‘absolute’ motion of bodies; that is, accelerations are to be measured with respect to absolute space and time. In short, if the task of natural philosophy is to discover forces starting with motions, such motions are to be measured with respect to absolute space and time, to ensure that the deduction will lead us to identify real and not fictitious forces – ‘fictitious’ insofar as they depend on the choice of the frame of reference. Above we have considered examples related to the space reference frame. Let us consider now time measurements. Let us imagine that we all agree in using the same space reference frame (for example, a frame at rest or moving uniformly rela­ tive to the fixed stars: this was Newton’s choice, after all). Let there be two observers in this system who measure the motion of a body. Let us suppose that they agree that motion is along a straight line. Yet the two observers use two different clocks. According to observer 1, the body covers equal spaces in equal times. According to observer 2, the body is retarded (let us say, it covers 1 m in the first second, 0.9 m in the following second, 0.8 m in the third second, and so on). The deduction of forces is consequently different. The first observer will

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claim that the total force acting on the body is equal to zero, presumably because the body travels in a void where no gravi­ tational force is present. The second observer will deduce that presumably there is a medium exerting a drag force which retards the motion of the body. Newton thought that the two observers could not both be right. According to Newton, natural philosophy must lead to the discovery of true forces, and therefore we need to calculate, as best as we can, true accel­erations. We will never be able to do so with absolute pre­ cision, since we do not know how to identify absolute space and absolute time, relative to which true motions are measured, but we can approximate true, absolute and mathematical time and space. In his claims in the Scholium to the definitions, Newton introduced overly stringent requirements. The assumption of absolute space is too stringent, because Newton’s laws require only an equivalence class of inertial frames (to use an anachron­ ism), rather than a single privileged resting frame. To put it another way, absolute velocity is a meaningless notion for Newtonian mechanics (as Newton himself proved in the corollaries to the laws). So, in a way, by referring to absolute space as a privileged resting frame, Newton made an unnecessarily stringent assumption. His notion of absolute time is, instead, more justified from the point of view of Newtonian mechanics (whereas it is not from the point of view of special rela­tivity).25 Indeed, the structure of absolute time is the right one for Newtonian mechanics: we can approximate absolute time by getting nearer to an un-accelerated or un-retarded motion, or to an isolated rotating rigid body, but the laws of motion provide no criterion at all for approximating ‘true

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velocity’. The essential aspect of absolute time, ‘equable flow’, or absolute equality of time-intervals (more generally, absolute ratio of time-intervals) was not, contrary to the notion of an absolute resting frame, a concept that Newton was introducing unnecessarily, but a notion that is implicit in the laws of motion. Newton thought that astronomers, through their practice, had already taught us how to approximate absolute time, by correcting solar time with the ‘equation of time’, so as to determine sidereal time.26 It is important to stress the fact that Newton’s defence of absolute space and absolute time is based on his conviction that these notions are presupposed by good scientific practice. Immanuel Kant would have much to say about this a century later. To recapitulate: employing a good clock and a good space reference frame means that one measures accelerations that are as close as possible – judging from what technology and scientific knowledge are available – to true accelerations. From these accelerations we can deduce forces that are, in terms of direction and magnitude, as close as possible to the true forces acting in rerum natura. A last question must be answered: How can we tell a true force from an apparent one? According to the third law of motion, a true force applied to a body A – which may be a contact force or a force acting at a distance – is caused by another body B, which in turn is accelerated by an equal and opposite reaction force exerted by A (according to the third law of motion). A true force is always an interaction between two bodies:

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to speak of separate impressed forces acting on two bodies, which happen to come in an action-reaction pair, is misleading. The ‘force’ corresponds to a mutual interaction between bodies that is not broken down into separate ‘actions’ and ‘reactions’, except in our descriptions of it.27 In the case of the planetary system, by assuming a reference frame at rest relative to the fixed stars and a time determined by the Earth’s rotation, Newton demonstrated in Book 3 of the Principia that the planets and the Sun interact on each other via equal and opposite gravitational forces decreasing with the square of the distance. He was able to determine the relative masses of the planets and the Sun and to show that the centre of mass of the planetary system is always very close to the Sun. In his mind, Newton had thus brought the great Copernican debate to a close: he could proudly state that he had solved the ‘the main difficulty of philosophy’ by measuring the true motions and the true forces acting in the planetary system. Newton’s concepts of absolute time and space left some of his contemporaries sceptical, especially Huygens, Leibniz and George Berkeley. Their criticisms have a depth that cannot be underestimated. A formidable critique of the concepts of absolute time and space would be proposed by Ernst Mach in the late nineteenth century. Einstein, as mentioned above, would permanently change, with the theory of relativity, the concepts of space and time.

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the thr ee laws of motion The Principia are based on three ‘axioms or laws of motion’, as follows: 1. Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed. 2. A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed. 3. To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction.28 Newton was not aware of the innovative nature of his laws. In fact, he attributed the first two (incorrectly) to Galileo, and did not mention Descartes, to whom he had a debt. There is a manuscript where Newton attributes the first law of inertia to the ancients, and he enumerates Lucretius, Anaxagoras and Aristotle in this regard.29 Once more, we see the latitudinarian reference to ancient science that occurs in Newton’s writings. The atomism of Democritus propounded in De rerum natura is certainly a philosophical alternative to Aristotelianism, yet Newton does not seem to be concerned with these philosophical distinctions when referring to the ancient tradition. As for the third law, Newton attributed it to Wren, Wallis and Huygens. The fact that each force corresponds to an

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equal and opposite force is essential to the understanding of Newton’s cosmology. The supporters of magnetic philosophy, such as Kepler, had said that the Sun exerts a force on the planets. Newton tells us that this (gravitational) force of the Sun on any planet must correspond to an equal and opposite force of the planet on the Sun. The Sun cannot therefore be considered as a motionless body that exerts its action on the Earth and other planets. The Sun also undergoes a force caused by the action of the planets, a force that then causes an acceleration of the Sun. It is only the extra mass of the Sun compared to that of the Earth and the other planets that ensures that it may be regarded, with good approximation, as immobile. Finally, we should observe that the three laws of motion allow the deduction of forces starting with the phenomenon of the motion of bodies (as Newton requires in the Preface), provided that the measurements are performed in function of absolute space and time: that is, that they are performed in a reference frame approximately at rest or in uniform rectilinear motion with respect to absolute space, and using a ‘good’ clock. The first law allows us to establish that if a body is not at 33 Diagram for proposition 6, book 1 of the Principia. A body moves in a void along the trajectory APQ under the action of a centripetal force directed towards S. The deviation RQ from inertial motion (because of the second law of motion) measures the intensity and direction of the centripetal force.

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rest or moving with uniform rectilinear motion the resultant of the forces acting on it is non-zero. The second law allows measuring the intensity and direction of this force. It is the deviation from the inertial trajectory that the body would follow if forces did not act on it that provides a measurement of the resultant force (illus. 33). The third law allows us to conceive of a force as an interaction between two bodies. Real forces are always interactions between two bodies, unlike fictitious forces, which are measured in reference frames that are accelerated with respect to absolute space, or using clocks not synchronized with absolute time.

the s\stem of the wor ld The first two books of the Principia are occupied by a large number of theorems and mathematical problems concerning, with a few notable exceptions (for example, experiments on fluid resistance and the speed of the propagation of sound), the motion of bodies considered abstractly. It is only in the third book that Newton applies some of these theorems to the study of natural phenomena. In fact, in the third book of the Principia Newton abandons the abstractly mathematical approach prevailing in the first two books to address in concrete terms the study of the ‘System of the World’: In the preceding books I have presented principles of philosophy that are not, however, philosophical but strictly mathematical . . . It still remains for us to exhibit the system of the world from these same principles.30

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The astronomical phenomena related to planetary motion are the starting point that allows Newton to apply some of the mathematical results set out in the first two books to infer the existence of an attractive force acting between all the planets and the Sun, whose intensity varies with the inverse square of the distance, proportional to the product of the masses, and which he then identifies with the force of gravitation. Newton, by means of an inductive generalization, states that gravitational force acts between all the masses of the universe: this is the origin of the theory of universal gravitation. Two things are striking about this theory. First, the level of quantitative precision that Newton claimed, sometimes wrongly, he had achieved. Second, the Principia sets forth a unified mathematical theory of the phenomena of Nature. The motion of a stone thrown by a sling, the flow and ebb of the sea, the motion of the Moon, the planets and more distant comets were attributed to the same cause: gravitational force. This latter feature is illustrated in the simplest way in a famous illustration taken from The System of the World, a brief essay published posthumously in 1728 that Newton had initially conceived as the last book of the Principia (illus. 34). Here we see a cannon placed on top of an extremely high mountain. If the cannon fires a shell on the level, with a low initial speed, then the shell’s motion, owing to the composition of the inertial rectilinear motion and the accelerated motion caused by gravity, will approximately follow the para­ bolic trajectory envisaged by Galileo. If, however, we decide to gradually increase the speed with which the shell leaves the cannon, we will observe increasingly long trajectories, until the shell enters into orbit around the Earth. The message,

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even for readers with scant mathematical knowledge, is clear: the same force studied by Galileo, the familiar force of gravity, is responsible for the motion of the Moon around the Earth. This surprising unification of terrestrial and celestial phen­ omena is obtained on the basis of the astronomical pheno­m­ ena (Phenomena 1–6) that form the basis of the deduction of the force of gravitation, and of brief demonstrations (Propositions 1–8) in which, using some results from the first book, consequences are drawn starting with the phenomena themselves. Remember that in the Preface Newton had stated that the aim of natural philosophy is to investigate the forces acting in nature, starting from phenomena. 34 Setting a satellite into orbit. After Isaac Newton, A Treatise of the System of the World, 2nd edition (London, 1731).

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Once the existence of gravitational force has been established, Newton develops the second part of the agenda he had set in the Preface: deducing the phenomena from this force. The success of the theory of gravitation comes to depend on its predictive effectiveness when it is applied to the phenomena observed by astronomers, and this success is even greater if the theory is able to predict phenomena not yet observed, that is, if it has the capacity to extend our knowledge. We see, in a nutshell, the extent of the success of the theory of gravitation set forth later in the third book of the Principia. This magnificent deduction can be divided into various topics: (i) characteristics of planetary motion (Propositions 10–17) (illus. 35), (ii) the figure of the Earth (18–20) and of the Moon (38), (iii) inequalities of the Moon’s motion (22–35), (iv) precession of the equinoxes (21, 39), (v) tidal motions (24, 36–7), and (vi) trajectories of comets (40–42). From this list, the magnitude of the results obtained by Newton is clear. A single force, the familiar gravitation responsible for the fall of bodies towards the centre of the Earth, is able to explain a large number of terrestrial and celestial phenomena. It is possible to consider this force in terms of mathematics, which becomes the language that allows us to understand the causes of a wide range of phenomena. And it is the mathematization of gravitational force which made it possible to solve the greatest enigmas of the time concerning ‘System of the World’: are there reasons for preferring the Copernican system over the geocentric one? And, if the planets orbit the Sun, what holds them in their orbits? Nevertheless, the solution of these enigmas offered in the Principia, despite its magnificence, is beset by difficulties of

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both a technical and foundational nature. Many topics covered in the second and third book (the motion of fluids, the propagation of sound, the motion of the lunar apogee, the shape of the Earth, the tides, the precession of the equinoxes) are addressed by Newton with physical and mathematical tools that, in hindsight, may seem to us inadequate. Indeed, Newton made recourse to geometrical methods that soon became obsolete. The use of calculus is noticeably absent in the Principia, so much so that, as we have seen above, the second law of motion is not written as a formula, F = ma. It would be the task of mathematicians such as Johann Bernoulli, Clairaut, Daniel Bernoulli, Euler, D’Alembert, Lagrange and Laplace, to name but a few, to develop the dynamics of fluids and rigid bodies, the calculus of variations and the theory of partial differential equations, the principles of least action, elliptic integrals and many other techniques that would make the solution of the problems dealt with inadequately in the Principia possible. While noting the inadequacies found in the Principia we must not however underestimate the positive results achieved, nor the progressive nature of Newton’s aim. For instance, the theory of planetary perturbations, addressed by Newton in a still highly unsatisfactory way, would lead to important developments in mathematical physics as late as the early twentieth century. 35 Diagram for Proposition 66, book 1. Newton studies three bodies in gravitational interaction. This proposition is fundamental for the treatment of the precession of equinoxes, tides and planetary motions.

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The greatest success obtained by Newton’s planetary theory lies in the fact that for the first time there had been achieved a union between the needs of mathematical prediction and those of causal explanation. In systems prior to that of Newton there had been predictive but not explanatory mathematical models (for example, Kepler’s three laws allowed the construction of accurate astronomical tables, but said nothing conclusive about what caused planetary motion). Or systems which were explanatory, but not mathematicized (for example, the Cartesian theory of vortices attributed to the subtle matter in motion around the Sun the role of causing planetary motion, but it was not a mathematized theory). Newton’s ‘System of the World’, however, specifies a cause of planetary motion, the force of gravity, but at the same time provides it with a mathematical formulation that allows predictions of a precision previously unheard of. It is a system that achieves that ideal union between geometry and philoso­ phy that Newton had proposed in his earlier study on optics, where he expressed his hope that the ‘conjectures and probabilities’ of natural philosophy could be superseded thanks to the application of geometry. However, Newton’s predictions are only approximate. There are discrepancies between theory and observational data, and it is a merit of Newton and his contemporaries that they did not turn a blind eye to these anomalies, even though they were in some cases very small discrepancies by the standards of the time. The development of mechanics and math­ematics in the eighteenth century, mentioned above, depended largely on trying to resolve these anomalies, the small (and sometimes not so small, as in the case of the

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motion of the lunar apogee) discrepancies between theory and observations found in the second and third books of the Principia. In a nutshell, the Principia is a repertoire of successes, but also of unsolved issues. It is thus a work that indicates the way forward for further research. The great strength of Newton’s work lies in its progressive nature, the fact that it is an open work that contains not only solutions and successes, but problems and lacunae, which channelled the research of generations of mathematicians and physicists. As the eminent cosmologist Hermann Bondi said, the greatness of a scientist is to be seen not only in the answers he provides, but in the problems he poses. These must belong to a difficult category to distinguish: neither insoluble nor trivial.31 As said above, the Principia contains not only technical difficulties but those of a foundational nature. For many contemporaries of Newton, the Principia was a mathematically sublime work, but one that was unsatisfactory in terms of physics. This judgement was expressed as soon as the Principia was published. Natural philosophers of the Cartesian school were bound to react in this way since, for them, providing a physical explanation meant presenting a mechanical model. And what physical model did Newton propose to explain gravitational force? In the Principia, Newton did not provide a physical explanation of what gravitation is, of how it acts between bodies in such a way that they attract each other at a distance, with no time delay. This kind of criticism against Newton had already been raised during the debate in the 1670s on the experimentum crucis. According to his critics, Hooke and Huygens, Newton described the mathematical regularity characterizing the chromatic dispersion of white light, but did

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not explain what light was and how it physically generated colours. Similarly, in the Principia he formulated a mathematical theory of gravitation without illustrating the physical nature of this force. The reaction of a great Cartesian such as Huygens to the Principia is interesting, since his view was initially shared by most natural philosophers on the Continent. On the one hand, Huygens did not cease to praise Newton’s work in mathematics. On the other, he expressed his scepticism with regard to Newtonian physics. Huygens wrote: I am dissatisfied also with all the other theories which he [Newton] bases on the principle of attraction, which seems to me absurd . . . And I was often surprised to see how he could make such an effort to carry on so many researches and difficult calculations which have as foundation this very principle.32 The absurd principle was that two masses could attract each other at a distance, instantly, and in a void. Huygens adhered to a Cartesian mechanical philosophy, according to which natural phenomena were to be studied in terms of contact, such as the impact between particles and the propagations of waves in a medium. An action at a distance such as gravitation was not acceptable, and was not part – as Huygens repeated on several occasions – of ‘sound philosophy’. Many on the Continent shared the scepticism of Huygens. Newton was accused of having introduced an incomprehensible principle. This principle seemed to many to be a return to the occult qualities of Renaissance philosophy; and it

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was precisely in antithesis to this tradition that mechanical philosophy was born. There was also the suspicion that these ideas of Newton placed the author of the Principia within the tradition of natural magic, according to which Nature is subject to non-material forces, mysterious ‘sympathies’ and ‘antipathies’. What is most striking is the frequency with which, in French- and German-speaking countries, Newton’s Principia was seen as a work that displayed shortcomings in terms of physics. In 1712 Pierre Rémond de Montmort wrote to Johann Bernoulli praising the new edition of De la Recherche de la vérité by Nicolas Malebranche, which developed the theory of Cartesian vortices, expressing his hope that Newton could read it before publishing the second edition of the Principia. In his reply Bernoulli agreed that as far as regards gravity, Newton had only proposed a ‘supposition’.33 Newton took these objections very seriously. In a sense he agreed with them. In a letter to Richard Bentley in 1693 he wrote that it was ‘unconceivable’ to think that ‘inanimate brute matter should (without the mediation of something else which is not material) operate upon and affect other matter without mutual contact’. According to Newton the objections of Huygens and Continental astronomers were thus legitimate, but only within a mechanistic conception according to which matter is inanimate.34 In the next chapter we will see how Newton’s mature years and old age were spent in debates with his peers on the Continent in which he attempted to defend the method adopted in his study of optics and gravitation. This involved mathematical, physical, methodological and finally even theological arguments, as can be inferred from the passage just quoted.

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In fact Newton, in his correspondence and in significant additions to the subsequent editions of the Principia, the ‘rules for the study of natural philosophy’ and the General Scholium, was led to face thorny philosophical problems concerning scientific method, causation and the nature of absolute space and time. Indeed, these writings belong to the canon of eighteenth-century philosophy: they made a pro­ found impact on the philosophes of the Enlightenment until Immanuel Kant, and even later; they deserve much more attention than the one given to them in this short introductory book.35 The greatness of Newton as a scientist made his philosophical pronouncement related to the Principia immensely authoritative. For the biographer of Newton it is interesting to note that his involvement in philosophical issues was defensive in nature. It does not seem that these writings stemmed from a genuine interest on the part of Newton, but were rather caused, as first happened in the 1670s in the context of the polemic on his theory of colours, by his need to defend his mathematical and experimental edifice from criticisms, above all those levelled by a major philosopher, Gottfried Leibniz. The debates concerning the Principia belong to a period of Newton’s life in which he became an important figure in London’s political and scientific life. We turn to Newton as a public figure in the next chapter.

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T

he publication of the Principia projected Newton into the public sphere. After 1687 Newton was no longer a solitary Cambridge professor whose mathematical feats were known to a few initiates; he became one of the best-known natural philosophers of his time. Newton was now a public figure who had to affirm his ideas, defend them from critics and make them look attractive even to those who, like John Locke, Richard Bentley and Samuel Clarke, did not have the mathematical background to understand them fully. In the last years of his life, the discussions, and often arguments, that Newton engaged in with his contemporaries led him to explain and hone many ideas that he had previously kept to himself. It is in this context that Newton entered the European philosophical debate. We get the impression that philosophy was for Newton a necessity rather than a vocation, a defensive strategy rather than a chosen line of research. In short, Newton dealt with issues such as causality and explan­ation to fend off attacks from phil­osophers such as Leibniz, rather than out of genuine interest, and he never wrote systematically about philosophy.1

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newton the public figur e It was in 1689 that Newton met a young scholar from Geneva, Nicolas Fatio de Duillier, with whom he would forge a close, albeit short friendship (see illus. 30). Fatio was interested in the new natural philosophy and had already met several eminent scientists, most notably Giovanni Domenico Cassini, Astronomer Royal in Paris, and the great Huygens in Holland. But it was Newton who, in the years 1689–93, became his mentor. Fatio conversed with Newton on alchemy, maintained contact with Huygens, contributed to the study of the quadrature of curves, and proposed a theory on the causes of gravitation based on the ether, which enjoyed some currency, especially in Geneva. For a while, Fatio thought about editing and commenting on a new edition of the Principia, suggesting to Huygens that he should help him in the task. It is clear that Newton was charmed by this talented young man and that Fatio had a flair for winning the sympathies of some of the greatest natural philosophers of his time. In 1693 the collaboration between Newton and Fatio ended for unexplained reasons, and it is interesting to note that in the same year Newton suffered from a serious nervous breakdown, his letters revealing considerable psychological distress. Much has been said on the causes of this, and various hypotheses have been put forward: the most picturesque, although un­ proven, is that he was poisoned by the mercury he handled with few precautions in his alchemical laboratory. Fatio would subsequently join the sect of the Camisards, the ‘prophets of the Cévennes’, who, animated by deep religious fanaticism, had taken up arms against Louis xiv after the revocation of the Edict of Nantes in 1685, an event that caused the exodus

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of many Huguenots. After this move, Fatio, who in 1707 was placed in the pillory at Charing Cross, was no longer someone whom Newton, always attentive to his political career, could be seen to associate with.2 The years immediately following the publication of the Principia, 1688 and 1689, were marked by a political earthquake known as the ‘Glorious Revolution’, with James ii forced to take refuge in France, throwing the Great Seal of the Realm into the River Thames, owing to the invasion by William of Orange, who landed in Torbay at the head of a powerful army. The invasion was promoted by important sectors of the English political class and the Church of England. As already mentioned, James ii’s ascent to the throne in 1685 had exacerbated religious tensions existing during the reign of his elder brother. The revocation of the Edict of Nantes heightened anti-Catholic feelings and caused thousands of Huguenots to seek refuge in London: they brought with them horrific stories about the persecution of Protestants under Louis xiv. In these troubled circumstances James stubbornly made no attempt to hide his sympathies for Catholicism, and the suspicion that there could be a restoration of the rights of Catholics inflamed tempers. Already in 1678–81 dozens of innocent people had been tried and executed because of the hysteria caused by the accusations made by a figure of dubious morality, a dissenter named Titus Oates. He had convinced the public by means of a series of false statements that there was a conspiracy, known as the ‘Popish Plot’, to assassinate Charles ii with the help of the Jesuits and establish Roman Catholicism. We do not know if Newton was convinced by these rumours, but it

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is certain that in 1687 he suspended the writing of Principia to take an active role in the university’s opposition to the king’s request that Sidney Sussex College confer the title of Magister Artium on a Benedictine monk. Newton and other delegates of the university confronted the Lord Chancellor, George Jeffreys, a man with very few moral scruples who had been in charge of putting down the rebellion led by the Duke of Monmouth against the Catholic king (1685), and did so with great severity. The university was able to defend its case and the degree was never conferred. A similar campaign was fought in Oxford, where James forced Magdalen College to appoint a Catholic as president. When Parliament was called after the escape of James ii the situation could not have been more dramatic, nor more conducive to sudden political fortunes. In January 1689 England no longer had a legitimate sovereign, and supporters of the Whig party, which had backed the invasion of William of Orange as a champion of the defence of Protestantism against Stuart ‘popish’ ambitions, had to justify the legality of the invader’s sovereignty. The debate concerning the accession to the throne of the new king engendered a crisis that raised deep moral and political sentiments. In 1689 Newton was elected a member of the ‘Convention Parliament’ as a representative of the University of Cambridge. He was to sit in Parliament again in 1701. The Glorious Revolution had consequences for English history that it is hard to overstate. The result in dynastic terms was the rise to the throne of William and his wife, Mary, the daughter of James, and an end to the possibility of having a Catholic monarch on the throne of England. It

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was established by law that succession to the throne would have Protestantism as a requirement. In the absence of any heirs of William and Mary, and of Anne as well, the Act of Settlement (1701) established that the crown had eventually to pass to the Electress Sophia of Hanover and her nonRoman Catholic heirs. According to some, the course of events from the Glorious Revolution to the Hanoverian succession was set for purely human reasons, not imposed by divine right. Others wished to present this as the result of divine Providence. And then there were those who found it difficult, or openly refused, to depart from obedience to the Stuarts. The Act of Toleration (1689) confirmed the supremacy of the Church of England but allowed some dissenting Protestant denominations freedom of worship (but not access to public office or the universities). Catholics, Jews, atheists and anti-Trinitarians, like Newton, were meanwhile excluded from toleration, and had to be wary. As mentioned above, Newton’s successor to the Lucasian Chair, William Whiston, was deprived of his academic post as a result of his professed anti-Trinitarian faith. Newton deftly managed to prevent his religious convictions from hindering his career. He was, of course, in favour of toleration within a broad spectrum of Protestant confessions. After election to the Convention Parliament, in fact, Newton felt he had joined the political elite, and harboured an ambition to leave Cambridge and head for London in search of a well-paid, prestigious position. The opportunity pre­sented itself in 1696, apparently through the good offices of Locke and Charles Montagu, Chancellor of the Exchequer, with his appointment as Warden and then Master (late 1699),

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of the Royal Mint. In 1703 Newton was appointed President of the Royal Society, and in 1705 he was knighted. His remarkable political ascent made him influential and wealthy. In London Newton lived with his niece Catherine Barton (daughter of a half-sister), who belonged to the social entourage, and was perhaps temporarily the mistress at one time, of his old fellow student the powerful Montagu. It seems that this friendship decisively favoured Newton’s career in London. His appointment to the Mint, however, turned out to be anything but a sinecure, given that British finances were crippled by the costs of William’s military campaigns in the war against France. The foundation of the Bank of England (1694) and the re-coinage of new money were decisions taken to counter a dramatic financial crisis. Newton was primarily responsible for re-coining new money, a position in which his knowledge of metals acquired in years of experimentation with the alchemic laboratory furnace may have proved useful. Newton devoted himself to the fight against counterfeiters, showing unexpected investigative skills for an introverted mathematician and natural philosopher, as well as displaying considerable courage, albeit, according to some, combined with a morbid pleasure in sending counterfeiters to the gallows.3 In 1703 Newton was elected President of the Royal Society (illus. 36). This position allowed him to state the math­ema­ tization of natural philosophy, which had interested him since youth, in one of Europe’s most important scientific institutions. He followed this agenda not without encoun­ter­ing opposition from naturalists, physicians, botanists, antiquaries and experimental philosophers, who eyed the mathematical language of the Principia with suspicion. This opposition would

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become more acute immediately after the death of Newton in the competition for succession to the Presidency. 4 Newton exercised his power acquired as President not by removing the portraits of Hooke hanging on the walls, as has often been claimed, but in gaining the upper hand in a heated dispute with Flamsteed the Astronomer Royal, who had refused to grant Newton free access to the astronomical data collected at Greenwich. Newton needed these data because he was still intent upon completing his theory of the Moon. As we know, the Principia contains many gaps and imperfections (even in its third and last edition). The largest concerns predicting the motion of the Moon. Newton’s theory of the Moon expounded in the third book of the Principia and in a short 1702 essay suffered from many shortcomings, which was particularly frustrating for Newton given that a solution would allow him to develop a method for determining longitude 36 A 19th-century reconstruction of a meeting of the Royal Society. The President, Sir Isaac Newton, is seated and holding a gavel. On the table in front of him lies the Society’s mace. Woodcut engraving by John Arthur Quartley.

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using astronomical instruments. The problem of establishing longitude was extremely important for the science of navigation. Equipped with lunar tables, a sailor on the high seas would be able to proceed as follows. First, observe the position of the Moon relative to the fixed stars. Then on the basis of this observation, read Greenwich Mean Time on the tables and, by comparing this with the local time, determine longitude. Newton became a member of the Parliamentary Committee for the Board of Longitude in 1714, which established that a prize would be awarded to those who could solve the problem of longitude with the required precision. Newton and Flamsteed deeply disagreed over who could claim the intellectual property of the astronomical data collected at the Royal Observatory. The Astronomer Royal, who had financed the manufacture of many instruments from his own pocket? Or the President of the Royal Society, supported by the husband of Queen Anne, and in 1710 awarded the title of ‘Constant Visitor’ to the Observatory? Flamsteed felt little warmth for the theoretician anxious for data that could confirm his mathematical theories, while the mathematician was bound to be irritated by the pedantic precision with which the astron­ omer believed that his data was not yet ready for publication. In the end Newton forcibly took possession of the papers kept in Greenwich and entrusted them to Flamsteed’s archenemy, Edmond Halley. The Historia coelestis saw the light in 1712, but two years later, with the ascension to the throne of George i, the wind turned in favour of the astronomer, who was able to take possession of as many copies as possible of the Historia to burn them in a bonfire ‘as a sacrifice to Heavenly Truth’. During his long presidency Newton acted

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as an absolute monarch, whose wishes the other members of the Royal Society could only obey, and above all promoted research on electrical phenomena inspired by his idea that electric force could play a key role in optical, chemical and vital phenomena. Another intellectual endeavour that occupied Newton during his years in London was chronology. The object of this discipline consisted in writing a grandiose history of human civilization by comparing Hebrew history as set forth in the Bible with the histories of other ancient peoples such as the Egyptians, the Assyrians, the Babylonians, the Medes, the Persians, the Greeks and the Romans, handed down in the historical works of authors such as Manetho, Josephus and Herodotus. The problem that fascinated so many erudite scholars, such as Isaac and Gerard Vossius, Joseph Scaliger, Denis Pétau, Samuel Bochart and John Marsham, was a synchronization of the events occurring in different civilizations, in such a way that biblical history could be accommodated in a large picture of Middle East ancient history. This interest occurred in a turbulent age of dissent in which there was growing awareness of the complex history of the transmission of the Bible, so that establishing the most authoritative version and confirming the truth of the his­tor­ical books of the Holy Writ was a moral duty for men of Newton’s religious temper. Newton aimed at disproving the authority of the pagan histories compared to the narrative provided by the Bible. In his opinion the heathen had exag­ger­ated the antiquity of their civilizations. It is also im­portant to add that Newton’s England saw the beginnings of an interest in demog­raphy and annuities. Biblical

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and pagan ancient histories and myths had to fit with the accepted knowledge about population growth. In a few words, a disci­pline now as foreign to us as chron­ology intersected with intellectual en­deavours that spanned philology, biblical her­me­neutics, archaeology, ancient history, geography, mythology, demography and, as we shall see, astronomy. Long genealogies of kings, reigns, prophets and battles gave rise to tables that distinguished one chronologer from another (illus. 37). The issues at stake were theologically dangerous. Were the Jews the most ancient civilization? What was the relationship between ancient civilizations? How were ancient knowledge and rituals transmitted from one people to another and, possibly, corrupted in the process? As Isaac La Peyrère famously put into question, was Adam the first man? When did the creation of the world happen? If this occurred a few thousand years before Christ, how could the Earth be populated by so many human beings? Most probably, Newton’s interest in chronology stemmed in part from his research on prophecies: since he believed that prophecies referred to real historical events, it became impor­tant for him to acquire a more precise knowledge of ancient history. Newton, like many other chronologers who opposed themselves to millenarian fanatics, showed little interest in establishing the date of creation or predicting the end of the world, even though two manuscript fragments (one dating after 1704) survive in which he speculated that the Second Coming of Christ and the establishment of the Kingdom of God on earth could occur no sooner than the year ad 2060. His work on chronology rather reveals a genuine interest in what nowadays we would call prehistory and

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ancient history, since he concentrated, as Marsham had done, on postdiluvian events. It also seems that Newton, by now a London celebrity, valued the prestigious status conferred on practitioners in such an erudite field and perhaps was also somewhat fascinated by its esoteric genre. His ideas on the corruption of the ancient religion found corroboration in the history of the ancient cultures that he composed in the last years of his life. But Newton brought to chronology methodological innovations that depended upon his expertise in natural philosophy. As Buchwald and Feingold have shown in their monumental study, Newton dealt with numerical, astronomical and demographic data in ways that were innovative in chronology, so much so that when an unauthorized French translation of a draft of his chronology was published in Paris it received sharp criticisms from the humanists of the Académie des inscriptions et belles-lettres, who thought that the discipline should be founded on antiquarian and textual evidence. Newton instead resorted to a complex argument in which the hermen­ eutics of classical sources were mingled with astronomical calculations on the precession of the equinoxes, according to the predictions studied in the Principia. Newton, of course, was not unique in using astronomical knowledge in the field of chronology, yet his status of eminent cosmologist and his skill in mathematical astronomy brought chronology to an unprecedented level of mathematical sophistication. Thanks to philological and historical analysis which today may only appear bizarre, Newton argued, on the basis of the testimony taken from several ancient sources, such as fragments from the Titanomachy and a commentary by Hipp­archus

37 Newton owned the 1676 edition and made much use of this erudite tome in order to synchronize the Hebrew chronology with the history of the Egyptians and Greeks. John Marsham, Chronicus canon Ægyptiacus Ebraicus Græcus et disquisitiones (London, 1672).

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of Aratus’ Phaenomena, that Chiron the Centaur and Musaeus (according to Newton these were mythological names for renowned ancient astronomers) had prepared for the Argo­ nauts a celestial sphere in which the equinoxes fell in different constellations from those of today. In the Principia Newton had provided a quantitative prediction of the phenomenon known as ‘precession of the equinoxes’, the slow motion of the equinoxes caused by the cyclic precession of Earth’s axis of rotation. Thus Newton could deduce the year in which Jason and his band had sailed on the ship built by Argus equipped with the celestial sphere made by Musaeus. Dating the voyage of the Argonauts (Newton, again, believed that the myth con­ cealed an historical event, namely a Greek expe­dition aimed at convincing the other peoples of the Mediterranean Sea to join forces against Egypt) allowed a new dating of the Trojan War and, therefore, of all ancient history.5 According to Newton’s chronology the Temple of Solomon, whose pro­ portions Newton studied carefully, was built before the Trojan War, and not much later as was generally believed. This is just an example of how Newton attempted to shorten the antiquity of pagan civilizations. Newton’s historical research confirmed him in his conviction that cultural transmission went from the land of Noah to the land of the Pharaohs, and that it was in Egypt that the primitive monotheistic religion had been corrupted into polytheistic idolatry. In some of Newton’s manuscripts relating to the Temple we find evidence of his beliefs regarding the harmony between sacred architecture and the structure of the cosmos. We know that Newton believed that the structure of pagan temples proved the survival of heliocentric cosmology also

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among the Gentiles. Newton’s interest in the proportions of the Tabernacle and Temple of Jerusalem, and thus in establishing the measurements of the sacred cubit, is motivated by his belief that the Temple was a prophetic figure for the New Jerusalem, that it is the place where Revelation was staged and where important aspects of the worship of the ancient Hebrews were encoded, and that, lastly, it reflected the separation of the elect from the rest of the people.6 As far removed from our scientific sensitivity as this ‘historical’ research by Newton may be, his literary style is clearly in line with that studied quantitative precision that charac­ terizes his work in alchemy and astronomy. This is seen in the scrupulousness – or presumed scrupulousness – with which Newton deals with the description of the Temple in the book of Ezekiel, the ancient history handed down in the Chronicle of Eusebius of Caesarea or the Judean Antiquities by Flavius Iosephus (Yosef ben Matityahu). It is also seen in his use of astronomy, demographic theories and mathematics to interpret the sources and ancient chronologies. In 1704 Newton published the Opticks in English, a work that also appeared two years later in a Latin translation. In this treatise, certainly more widely read than the Principia and an equally great masterpiece, Newton published his research on refraction (the experimentum crucis and its variants which we discussed earlier) and interference (the observations on rings from the 1670s), and added new studies on diffraction. In an appen­dix, Newton published the Tractatus de quadratura curvarum, a work dedicated to the quadrature of curves (integral calculus), and Enumeratio lienearum tertii ordinis, a work dedi­ cated to the classification of cubic curves. We should note that

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while in the 1670s Newton attributed responsibility for the phenomena of interference to the vibrations of a luminous ether, in Opticks he abandons the ether and rather speaks of forces acting at close range on the luminous corpuscles. The Opticks ends with a series of sixteen Queries which would under­ go interesting variations and increase in number in the Latin edition (1706) and then in the English second edition (1717– 18), where there are 31 Queries. It is interesting to observe how here, too, Newton tries to separate clearly the parts of his work in which, ‘following the method of analysis and synthesis of the mathematicians’, results are ‘derived’ with certainty from phenomena, and those parts in which he sets forth conjectures and hypotheses that may guide future research but which are not established with certainty. The Queries are among the passages most widely read by Newtonian scholars; and rightly so, since they contain insights into chemistry, electricity and magnetism that would inspire research in these areas throughout the eighteenth century. The Queries also contain important statements regarding Newtonian assumptions about cosmology, the relationship between God and nature, and the scientific method. In 1707 William Whiston took the initiative, it is unclear whether or not with Newton’s consent, of publishing Newton’s lectures on algebra under the title Arithmetica universalis. This is one of the first printed publications of Newtonian mathematics and was highly successful, also owing to the didactic nature of certain sections. Here, Newton reveals his extraordinary ability as an algebraist, but in the final appendix (as we know) he makes a series of pronouncements against algebra and in favour of geometry, which appear incongruous in a

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work dedicated precisely to the algebraic method. Only those familiar with Newton’s mathematical manuscripts can see in this asymmetry between the body and appendix of the Arith­metica universalis a trace of Newton’s polemic against the math­ematics of the moderns, and what Descartes had proposed in the Géométrie, a trace of the passion with which Newton stated his intention to adopt as a model the example of Huygens and the ancient geometers who, according to Newton, exceeded the moderns in elegance and conciseness. Conversely, some problems (for example, drawing a conic passing through five given points) are solved using geometrical methods precisely in order to demonstrate the superiority of geometry over algebraic symbolism. These are issues that Newton would return to in the debate with Leibniz.7 A violent dispute broke out with Leibniz regarding who should be given the credit for inventing calculus. In 1699 Fatio, in his Lineae brevissimi descensus investigatio geometrica duplex, accused Leibniz of having published under the name of ‘differential and integral calculus’ a mathematical method that, according to Fatio, was discovered by Newton. It should be stated clearly that the study of the manuscripts that Leibniz penned during his stay in Paris (1672–6) has proven that he formulated his calculus independently from Newton. Further, Leibniz’s calculus has foundational as well as algorithmic features that set it apart from Newton’s method of series and fluxions. With a certain amount of diplomacy Hans Sloane and John Wallis calmed the waters, arguing in letters promptly sent to Leibniz that Fatio had obtained the imprimatur of the Royal Society by means of a subterfuge, but the differences became unbridgeable in 1708 when the Scottish mathematician John Keill, in

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the Philosophical Transactions of the Royal Society, accused Leibniz of having plagiarized Newton’s method of series and fluxions. Newton’s supporters blamed Leibniz for having acquired information on Newton’s invention through correspondence and during two visits to London in 1673 and in 1676, and of having then published the Newtonian method in 1684, simply changing the notation. This was a very serious accusation, and had been made in the official publication of the Royal Society, of which Newton was President. Leibniz, who was a fellow of the Society, called for an official retraction. In 1711 and in 1713 two publications inspired by this con­ troversy were published. The first was a collection of Newton’s youthful mathematical writings (the De analysi, in which Newton had developed his method of series back in 1669, is published here for the first time) and some of his letters.8 This elegant little book was edited by William Jones, a maths teacher with a prominent place in Newton’s circle of friends, as well as a great collector of books and mathematical manu­ scripts (illus. 38). Jones was tutor to George Parker, son of Thomas (in 1721 appointed 1st Earl of Macclesfield), and had 38 This engraving is a headpiece in a collection of Newton’s mathematical tracts edited by William Jones (1711). Minerva and the putti display several diagrams from the Principia.

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purchased the papers of John Collins, correspondent and admirer of Newton in the 1670s. These papers would turn out to be extremely important for the production of Commercium epistolicum, a publication edited by a Royal Society committee set up to respond to the request made by Leibniz for Keill to withdraw his accusations. The Commercium, like the anonymous ‘Account of the Book entituled Commercium Epistolicum’ published in 1715 on the Philosophical Transactions, was actually studied in detail by Newton himself. Distributed free in early 1713, the Commercium predictably sided with Keill. Leibniz was once again accused of plagiarism, and this time the charge was more serious, since the Commercium was the result of an investigation by a committee that had the official approval of the Royal Society. This marked the beginning of an all-out war between Newton and Leibniz. The communities of Continental and British mathematicians clashed in a dispute that did not end even with the death of Leibniz in 1716. In 1713 the second edition of the Principia was published. It differs in many technical details from the first (while the third edition of 1726 contains few variations). With the help of Roger Cotes, a brilliant young professor of astronomy at Cambridge, many errors were eliminated in the 1713 edition (some noted by the pro-Leibniz mathematician Johann Ber­ noulli). The most significant changes are a methodological preface by Cotes and a General Scholium that concludes the work.9 In these two new additions Newton and Cotes deal with criticism from the Continental philosophers, who were far from convinced by the concept of gravitational force, a concept that seemed incomprehensible to many, and more a mathematical artifice than a real physical explanation. Indeed,

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in his work Newton tries to define a new way of understanding natural philosophy, a new concept that would have a great success in England but would encounter strong resistance on the Continent.

divine providence In England the first public affirmation of Newton’s natural philosophy originated with the preaching of a fine classicist and theologian, Richard Bentley. Bentley had been appointed by the committee (the trustees) in charge of choosing the preacher for a series of sermons funded by a bequest established in the will of Robert Boyle. The great experimental phil­­osopher, correspondent of Newton and Hooke’s patron, had died in 1691, expressing his will to establish public sermons in London churches which, putting aside any division between the various Christian denominations, would defend the truth of Christianity against ‘notorius infidels’ such as ‘Atheists, Theists, Pagans, Jews and Mahometans’. The Boyle Lectures became a powerful vehicle for the spread of Newton­ianism. In fact Bentley decided to defend Christianity relying not only on Scripture but on natural philosophy. This apologetic genre, so-called ‘physico-theology’, would become very popu­lar. Moreover, this attitude could be directly based on the tradition of the Psalms, where a description of the wonders of Creation was often followed by praise of the creator. In this sense the naturalist John Ray in The Wisdom of God Manifested in the Works of Creation of 1691 had already argued that in the perfection of the inanimate and animate worlds it was possible to detect the work of a skilled craftsman. This is the

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well-known teleological argument, or ‘Argument from Design’, according to which Nature reveals to the philosopher a purpose that cannot be attributed to natural laws, but rather to the design of a providential architect. Bentley decided to turn to the by now famous natural philosopher, author of the Principia, to whom he wrote a letter in 1692. Newton’s four answers to Bentley, penned between December 1692 and February 1693 and published in 1756, reveal much of Newton’s view of religion. Newton apparently responded with enthusiasm to the young theologian and stated that the results of his Principia could be exploited to defend the existence of a divine architect. However, we may perhaps observe in Newton’s answers a certain anxiety. For Newton, in search of a prestigious appointment in London, Bentley’s acquaintance was an opportunity not to be missed. Bentley was in fact associated with influential circles in the Anglican Church, being a protégé of the powerful theologian Edward Stillingfleet, and his questions may also be seen as dictated by a desire to explore the theological dangers that may have been concealed in Newton’s text. Ultimately, the cosmology of the Principia was based on infinite space, the void and the atoms, on the existence of a natural law that regulates deterministic interactions between corpuscles, and God is hardly mentioned in the first edition. A Lucretian and Epicu­rean interpretation of Newtonian cosmology could not be ruled out, which would have brought the Principia closer to a phil­ osophy notoriously oriented towards atheism and irreligion.10 Moreover, the ode by Halley that opened the work effectively displayed Epicurean tones that were amended in the second edition.11 It is not by chance that the Italian refugee Giovan

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Francesco Salvemini, then suspected of atheism, premised a quotation of Lucretius’ ode to Epicurus in De rerum natura to his collection of Newtonian essays.12 Newton reassured Bentley that the mechanistic cosmogony of the Cartesian Principia may be excluded on a scientific basis. Descartes had argued that it was possible to imagine the formation of the stars, planets and even of the solar system and the Earth as the result of collisions, governed by the laws of impact between corpuscles of passive matter. On the contrary, Newton stated that it was ‘absurd [to imagine] the growth of new systems out of old ones without the mediation of a divine power’.13 The planets orbit the Sun in nearly circular trajectories. Newton was well aware that to put a planet into circular orbit it was necessary to calibrate very carefully the initial velocity transverse to the radius vector drawn from the Sun to the planet. A lower or higher velocity, or a slightly different initial direction of projection, would generate a non-circular (elliptical, parabolic or hyperbolic) orbit, which might lead the planet to approach and to move away from the Sun in a way more similar to that of a comet: in these conditions, life would not be possible. Newton adds: ‘I do not know any power in nature which could cause this transverse motion without the divine arm.’14 Indeed, in the correspondence with Bentley, Newton claims that the order and stability of the planetary system, namely, the fact that planets move in the same direction, roughly in the same plane and in nearly circular orbits, reveal the existence of a ‘cause’ that is not ‘blind and fortuitous, but very well skilled in Mechanics and Geometry’. And he concludes: ‘I am compelled to ascribe the frame of this [planetary] Systeme to an intelligent agent.’15

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In other texts, such as the last query of the Latin version of the Opticks (1706), Newton will repeat this thesis. Another serious problem in the Principia regards stars. It is often said with some emphasis that Newton unified celestial and terrestrial physics. But in heaven there are not only the planets, but stars. For Newton, like all his contemporaries, these celestial bodies fully deserved the name of ‘fixed stars’. For Newton and Bentley the stars were unmoving, and did not change position. Bentley thus asked Newton a difficult question: if there is a force of attraction that extends to infinity, what prevents the stars from attracting each other and collapsing in their centre of mass? Bentley’s query proved to be a difficult hurdle for Newton, and in this case the theo­ lo­gian proved himself to be a better mathematician than the Lucasian Professor. Newton began by saying that the stars were infinite and distributed evenly. Since each star was attracted in every direction by an infinite number of stars, the system was is in a state of equilibrium. It could be objected, how­ever, that the Earth should also be in equilibrium: it too would be drawn in every direction by an infinite number of stars! Newton and Bentley had stumbled on the so-called cosmolo­ gical paradox. The solution lay in realizing that the stars are not ‘fixed’, but attract each other and follow trajectories in the same way as planets and comets. The idea that the stars are ‘in motion’ was accepted only in the eighteenth century.16 At a certain point in the correspondence between Bentley and Newton we see a curious role reversal: Bentley poses math­ ematical and cosmological problems, and Newton becomes a theologian. Assuming that the stars are in equilibrium on account of their infinite number and uniform distribution,

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how can we assess the probability of this configuration being created? It is as difficult, Newton observed, as making an infinite number of needles stand upright on a mirror. It was here that Newton once again invoked divine Providence. The stars were in equilibrium because God had placed them at a great distance from one another and distributed them in the most appropriate way to prevent the gravitational collapse feared by Bentley. Newton writes: And much harder it is to suppose that all the particles in an infinite space should be so accurately poised one among another as to stand still in a perfect equilibrium. for I reckon this as hard as to make not one needle only but an infinite number of them (so many as there are particles in an infinite space) stand accurately poised upon their points. Yet I grant it possible, at least by a divine power; & if they were once so placed I agree with you that they would continue in that posture without motion for ever, unless put into new motion by the same power.17 As Newton had already stated in the Principia, after creating the universe, God intervenes with a ‘continuous miracle’ to stop the stars from falling, albeit over immense time spans, onto each other. God’s providential intervention is also invoked to ensure the stability of the solar system. This concept is made clear in particular in Query 23 in the Latin version of the Opticks published in 1706.18 As we know, the planetary system of the Principia is subject to the mutual perturbations of the planets.

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This system, left to itself, according to Newton, is doomed to destruction. The mutual interaction of planets and comets would end up causing impacts between the various bodies of which the solar system is composed. The regularity of the cosmos of Ptolemy, Copernicus and even Kepler is lost in the Newtonian system of interacting masses. The regularity that we observe in the planetary system is not guaranteed, according to Newton, by natural causes but by supernatural causes, by a ‘divine reformation’ that allows our planet to avoid the long-term destructive effects of gravitation. The ‘won­ derful Uniformity in the Planetary System’ can only be the ‘Effect of Choice’. In fact, according to Newton, the reciprocal gravitational action of the planets and comets would generate irregularities which over time accumulate until the system requires a ‘Reformation’ guaranteed by the providential, continuous intervention of God. It is in this context that Newton speculated about the role comets might play in the divine plan of cyclical world reformation. The matter dispersed by comets’ tails brings life to planets, and when a comet falls on a star it causes an increase in heat that is seen in the phenomenon of novae stellae observed by astronomers in 1572 and 1604. In his old age Newton played with the idea that the fall of the 1680 comet on the Sun would destroy life on Earth, according to the divine will.19 The God of which Newton speaks in Query 23/31, as we have observed, is not the creator of a Nature that may exist under necessary laws, or be based on ‘blind Fate’. He is an ‘in­ tel­­­ligent agent’ who applies order to a fragile Nature in need of divine intervention. Query 23/31 contains some im­port­ant statements about the mode of action of this ‘powerful

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ever-living Agent’; statements that would later re-emerge in the General Scholium concluding the second edition of the Principia.20 Recalling ideas already expressed in ‘De gravitatione’, Newton says that God, being in all Places, is more able by his Will to move the Bodies within his boundless uniform Sensorium, and thereby to form and reform the Parts of the Universe, than we are by our Will to move the Parts of our own Bodies. And yet we are not to consider the World as the Body of God, or the several Parts thereof, as the Parts of God. He is an uniform Being, void of Organs, Members or Parts, and they are his Creatures subordinate to him, and subservient to his Will; and he is no more the Soul of them, than the Soul of Man is the Soul of the Species of Things carried through the Organs of Sense into the place of its Sensation, where it perceives them by means of its immediate Presence, without the Intervention of any third thing. The Organs of Sense are not for enabling the Soul to perceive the Species of Things in its Sensorium, but only for conveying them thither; and God has no need of such Organs, he being every where present to the Things themselves.21 Absolute space thus becomes the theatre of Newtonian cosmology. Newton had to define his theological position, being careful not to fall into a form of immanentism. Indeed, the Deus pantokràtor described in the General Scholium is omnipresent and intervenes directly in Nature.

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Does the force of gravitation, an instantaneous action between distant bodies, thus ultimately originate in God? Newton’s position on this issue is highly nuanced. Newton had no doubt that the force of gravitation is, like all nat­ural phenomena, ultimately in God’s hands. God is the prime cause of all natural phenomena. However, this does not imply that we cannot investigate ‘secondary causes’, to use an Aristotelian term that also seems applicable to the analysis of Newtonian texts: namely, that we can not try to identify the material mechanisms that mediates the force of gravitation. Newton wrote to Bentley: You sometime speak of gravity as essential & inherent to matter: pray do not ascribe that notion to me, for the cause of gravity is what I do not pretend to know . . . Tis unconceivable that inanimate brute matter should (without the mediation of something else which is not material) operate upon & affect other matter without mutual contact; as it must if gravitation in the sense of Epicurus be essential & inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate inherent & essential to matter so that one body may act upon another at a distance through a vacuum without the mediation of any thing else by & through which their action or force may be conveyed from one to another is to me so great an absurdity that I believe no man who has in philosophical matters any competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly

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according to certain laws, but whether this agent be material or immaterial is a question I have left to the consideration of my readers.22 There has been much discussion on this statement. Is the agent responsible for gravitation therefore ‘material’ or ‘im­material’ for Newton? We can address this question by noting that already in the ‘Hypothesis’ of 1675, the agent that causes gravitation is not identified with ‘brute and inanimate’ matter (such a ‘mechanical cause’, observes Newton in the General Scholium of the Principia, acting on bodies would produce an action proportional to their surface, not to their mass),23 but with matter possessing active principles (and therefore with ‘something else that is not material’). The notion of an ether possessing active principles was familiar to Newton and his contemporaries, and had been discussed within a long, conso­lidated tradition, including alchemists and scholars of chem­ istry, critical of Cartesian mechanism; neo-Stoics and neo-Platonists, critical of Hobbes’s De corpore; and followers of Gassendi and Charleton’s Christianized version of Epicur­eanism. A large and varied group of thinkers believed in the presence in matter of ‘active principles’, and not merely of passive inertia. It is impossible, and perhaps pointless, to try to associate Newton with one of these schools of thought.24 We should lastly note the alarmed reference to Epicurus. Newton is clearly worried about the prospect that his phil­osophy may in some way be associated with Epicurean atom­ism; with some form of pagan philosophy in which matter by its very essence possesses active principles, whereas these can be given to matter only by God. This is what

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Newton seems to suggest to the young theologian, who must surely have understood the strength of that ‘reason’ that drove Newton to ‘pray’ Bentley not to attribute to him the idea that nature could be active per se, that it could have a vital principle independent of the will of its Creator. Newton argues that without the presence of ‘active principles’ it would not be possible to explain either the origin of ‘motion’ in the universe, or its preservation over time. Motion, due to friction, non-elastic collisions and so on, is bound to decline, as Newton had studied in the Principia by defining what is known today as ‘coefficient of restitution’. He carried out experiments on this coefficient, measuring the ratio of speed of separation to speed of approach in a head-on collision between two objects. As usual, Newton distances himself from Descartes, who instead had seen the conservation of motion (that Descartes defined, again allowing ourselves a somewhat misleading anachronistic terminology, as a scalar mv) as a fundamental principle of Nature (metaphysically grounded on God’s immutability). Leibniz, instead, stated the conservation of vis viva, mv2, as the fundamental law of mechanics. It is interesting to hear Newton’s own words, and quote once again from Query 23 of 1706 (in its English version, 1717/18): The Vis inertiæ is a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in pro­ portion to the Force impressing it, and resist as much as they are resisted. By this Principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into

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Motion . . . Motion may be got or lost. But by reason of the Tenacity of Fluids, and Attrition of their Parts, and the Weakness of Elasticity in Solids, Motion is much more apt to be lost than got, and is always upon the Decay. For Bodies which are either absolutely hard, or so soft as to be void of Elasticity, will not rebound from one another. Impenetrability makes them only stop. If two equal Bodies meet directly in vacuo, they will by the Laws of Motion stop where they meet, and lose all their Motion, and remain in rest, unless they be elastick, and receive new Motion from their Spring.25 On the Continent, meanwhile, Descartes, and then Leibniz, expressed the belief that in Nature there exist conservation laws, but Newton once again rejected their view, arguing for the inevitable decay of the motion of passive matter. For Newton, the active principles present in matter were responsible for the conservation of motion, but could also be used to explain gravitation, fermentation and the cohesion of bodies. In fact, he continues: It seems to me farther, that these Particles [created by God in the Beginning] have not only a Vis inertiæ, accompanied with such passive Laws of Motion as naturally result from that Force, but also that they are moved by certain active Principles, such as is that of Gravity, and that which causes Fermentation, and the Cohesion of Bodies.26

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It must be emphasized that for Newton the arguments derived from natural philosophy (the stability and order of the system of stars and planets, the conservation of motion, the proportions observed in the animal world) are not meant to belittle the central role played by revelation for the know­ ledge of true religion. What Newton seems to be saying is that his natural philosophy restores a vision of Nature, known to the ancient Jews, that is compatible with revelation. Newton’s observations on divine providence are intended to show how the Newtonian natural philosopher contemplates Nature in a way that makes the existence of the God of the Bible who rules the universe plausible. In other manuscripts, however, he contemplated the existence of a ‘most rational’ religion amongst the Gentiles, an ‘astronomical theology’, based on a wise knowledge of Nature. In the early 1690s he wrote: ‘So then the first religion was the most rational of all others till the nations corrupted it. ffor there is no way (without revelation) to come to the knowledge of a Deity but by the frame of Nature.’27 As we have seen in this section, in the letters to Bentley of 1692–3 Newton expresses ideas that were proclaimed from the pulpits of London churches. These ideas would be stressed and honed in Query 23 of the Latin Optice (1706) and in the General Scholium to the Principia (1713). According to Newton, his natural philosophy implied the omnipresence in infinite space and time of a providential agent. He believed that the existence of gravitational force, a non-mechanical active principle, could be deduced from phenomena with mathematical certainty, but that the cause of gravitation was not yet known. That cause could be the direct intervention of God, or the

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effect of a natural cause as yet to be discovered. Certainly, the causal chain that the philosopher of nature patiently tries to unravel is bound to end in a prime cause that can only be the Divine Architect. In the General Scholium, Newton states his famous motto ‘hypotheses non fingo’, in which he clearly marks the boundary between what is firmly established in his natural philosophy and what instead was still beyond its possibilities of analysis. This famous passage is worth quoting in full: Hitherto we have explain’d the phænomena of the heavens and of our sea, by the power of Gravity, but have not yet assign’d the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centers of the Sun and Planets, without suffering the least diminution of its force; that operates, not according to the quantity of the surfaces of the particles upon which it acts, (as mechanical causes use to do,) but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides, to immense distances, decreasing always in the duplicate proportion of the distances. Gravitation towards the Sun, is made up out of the gravitations towards the several particles of which the body of the Sun is compos’d; and in receding from the Sun, decreases accurately in the duplicate proportion of the distances, as far as the orb of Saturn, as evidently appears from the quiescence of the aphelions of the Planets; nay, and even to the remotest aphelions of the Comets, if those aphelions are also quiescent. But hitherto I have not

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been able to discover the cause of those properties of gravity from phænomena, and I frame no hypoth­eses. For whatever is not deduc’d from the phænomena, is to be called an hypothesis; and hypo­theses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferr’d from the phænomena, and afterwards render’d general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough, that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.28 Before looking, in brief, in the next section at the reaction of the champion of Continental philosophers, Leibniz, to Newton’s natural philosophy, it is appropriate to examine the reasons for its success in England. As we know, Newton was celebrated in England as the greatest philosopher of all time. Halley’s ode and the famous couplet by Alexander Pope, the portraits and the high positions he held are all evidence of the triumph of Newtonian philosophy in England. It should be noted that this philosophy, in its technical details, was well beyond the comprehension of the vast majority of Newton’s contemporaries. It is therefore legitimate to ask why Newton­ian natural philosophy enjoyed almost immediate and unanimous acceptance in England. This is a question to which there is no simple, unequivocal answer, and sociologists and

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historians of science have proposed various interpretations. It is not my intention here to examine this fascinating historical debate, and I will restrict myself to highlighting some aspects of English culture and politics that seem to have provided fertile ground for such an overwhelming cultural phenomenon. First, we can observe how Newtonian natural philosophy can be seen as a response to the dangerous metaphysical and theological implications that were perceived in the thinking of the great supporters of the new science, such as Descartes, Hobbes and Spinoza. The new mechanical philosophy had come into conflict with religion and had been rejected by people of faith from almost all religious denominations. Nor should we forget that in the early decades of the seventeenth century Galilean science had provoked a resounding religious conflict. The men of Restoration England were emerging from a period of intense, violent political clashes fuelled by bitter sectarian divisions. It therefore seems reasonable to surmise that many in Newton’s generation felt a particularly acute need to avoid the disruptive effects of religious intolerance in the name of the common good. The Puritan ambition to create a nation of godly men was replaced by that of building a society that was tolerant, but ruled by religious values shared by the majority of subjects. Many scientists thus tried to present the study of nature as a practice compatible with religion. Newton’s natural philosophy – with its marked anti-mechanism, based on an idea of matter as animated by imponderable active principles, open to the prospect that God intervened providentially and continuously in nature, characterized by prudent modesty on the limits of human reason to understand first

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causes – lent itself to being exploited in the extensive apologetic literature promoted by dominant factions within the Anglican Church. Bentley would be the first in a long list of physico-theologians, ending with William Paley at the end of the eighteenth century, to combine religion and Newtonian philosophy. After Newton’s death, religious Newtonianism, indeed, was accepted on the Con­tin­ent too, by thinkers with Calvinist as well as Catholic convictions. Furthermore, the divine providence to which Newton frequently refers is – as noted by Gerald Straka – an extremely popular theme in Anglican apologetic literature after the Glorious Revolution. Had William’s invasion not been fav­ oured with a ‘Protestant wind’, which had carried the fleet of the future king towards England, while preventing James’s fleet from going out to sea? Had the succession established by the Convention Parliament of 1689 not interfered in an unaccustomed way with the system of hereditary succession, manifesting God’s providential intervention in history? The affirmation of Newtonian philosophy after the publication of the Principia owes something not only to its mathematical and predictive success, but to the characteristic religious mindset of the Restoration and the Glorious Revolution. Newton, a convinced anti-Trinitarian who cleverly exploited Nicodemism to conceal beliefs that would have excluded him even from the wider reach of religious tolerance after 1689, took advantage of this cultural climate.29 The reaction on the Continent, as we shall see in the next section, was completely different, and many of the issues discussed in the correspondence with Bentley re-emerged in a polemical context with religious and political overtones.

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the controvers\ with leibniz The controversy with Leibniz, which broke out following Keill’s allegations, led to the publication of Commercium epistolicum (1712), and a series of letters, articles and pamphlets that impassioned the European Republic of Letters.30 It is often claimed that two parties were formed: the Newtonian party in England and Scotland, with footholds in the United Provinces, and a prevailing Leibnizian party on the Continent, with important centres in Basel and Paris. The dispute between Newton and Leibniz over the invention of calculus actually divided European mathematicians in a more complex way, with many trying to weigh into the controversy revealing intentions that went well beyond defending either of the two protagonists. For example, Johann Bernoulli clearly claimed that his own role in the invention of calculus had been as important as Leibniz’s, Pierre Varignon was interested in mediating between the two, and Keill himself was engaged in a parallel argument with Christian Wolff on the structure of matter and on medicine that intersected with the math­ ematical controversy. The two contenders who clashed in an all-out war were both outstanding mathematicians; they had discovered the ‘same’ algorithm, yet had very different visions of mathematics, its role and the significance of their personal contribution to the development of mathematical thought. Indeed, as I wrote earlier, the notion that Newton and Leibniz discovered the ‘same’ mathematical theory, the ‘calculus’, is a very problematic one. There are equivalences between the two algorithms (indeed, it was easy for the mathematicians of the early eighteenth century corresponding from the two

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sides of the Channel to switch from Leibniz’s ds to Newton’s dots), but also differences in notation and conception. Besides, both Newton and Leibniz offered several versions of their mathematical theories – changing notations, developing new methods, refining their concepts and, from a certain moment onwards, certainly influencing each other. In his ‘Account’ of 1715 Newton argued that the difference with Leibniz lay in the fact that while Leibniz’s calculus allowed symbols that did not correspond to anything real (infinitesimal magnitudes), in the geometric method favoured by Newton magnitudes were real, and were always visible, just like in the geometry of the ancients. Newton thus tried to contrast his geometrical method, allegedly in harmony with that of the ancients, to the symbolic, modern one promoted by Leibniz. Leibniz for his part was happy to point out the importance of his algorithm in freeing the mind from the ‘burden of imagination’. Reducing mathematics to a ‘blind use of reasoning’ was an ideal for the German philosopher, who tried to reduce reasoning even in philosophy to an algebraic manipulation of symbols. Yet Leibniz’s foundational reflections on the nature to the calculus, unknown to Newton, in several ways answered Newton’s desiderata of intelligibility and rigour. Further, the mathematics of the Principia was less classical than Newton would have liked to admit, for two reasons. First, the Newtonian method allowed limit procedures not envisaged in classical geometry, and which were conceivable only by a mathematician who had practised calculus. Second, in some advanced parts of the Principia Newton failed to conceal the use of fairly sophisticated techniques of quadrature

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(integration), of which only the author of De quadratura would be capable. In particular, some propositions (for example, Proposition 41 of the first book) start with the admission that a method for the ‘quadrature of curvilinear figures’ must be granted. In these propositions Newton reduces a problem to quadrature, but says nothing about how to perform such quadrature. To his acolytes who, perplexed, asked to be enlightened, Newton responded by translating the geometry of the Principia into algebraic language and offering refined solutions consisting in the integration of what were highly difficult functions for the time.31 But this method of discovery, essential for carrying out demonstrations of the Principia, was revealed by Newton in the year 1690 in correspondence, or in some cases, while talking to students who respectfully visited the now famous natural philosopher. Basically, it seems that Newton was inclined to using a private register to communicate algebra and calculus, and a public register to express his natural philosophy in a style resembling that of Archimedes. He himself confided to Gregory: ‘algebra is fit enough to find out, but entirely unfit to consign to writing and commit to posterity.’32 Moreover, the outdated style and geometry of the Principia gave the opportunity to Leibniz and Johann Bernoulli, who knew nothing of Newton’s private correspondence and his peculiar strategy for the publication of his mathematical discoveries, to argue that Newton in 1687 had no notion of calculus: if he had, would he not have perhaps used it in the Principia, where we do not find differential equations? But the question bluntly posed by Leibniz and Bernoulli requires an effort of interpretation on the part of the historian

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of mathematics. An example will suffice – I hope – to illustrate this aptly. In a note concerning central force motion written in the early 1690s, Newton approaches the problem by mathematizing in algebraic terms displacement, time, velocity and ‘gravity’ (illus. 40). What he attempts to write is the equation of motion for central force motion. With reference to the simple case of rectilinear free fall towards the force centre, he writes that the second fluxion ÿ of the distance from the centre of force (the altitudo or distantia, y), denoted by the characteristic double dot over the y, is proportional to the ‘body’s gravity’. Newton is here very close to broaching central forces with methods that belong to the eighteenth-century analytic mechanics of the Bernoullis and Euler, or at least he is close to performing an initial experiment in this direction. The manuscript ends abruptly, and one can only guess whether its author continued somewhere else the calculation under the condition ‘should the body move obliquely off ’. I should make it clear that I am not drawing attention to this page because I wish to claim that I have found proof of the fact that Newton could write F = ma. There has been a somewhat vacuous debate among historians of mathematics and physics on Newton’s way of mathematically expressing the second law of motion. As we know, in the Principia there is no second law expressed in calculus terms. So the (vexed) question has been: could Newton write F = ma? And if not: who was the first to do so? Historians of mathematics often focus on straightforward questions such as those of credit and priority, which all too often become a real obsession. Perhaps we should settle the question by acknowledging that the formulation of the second law of motion is a process that began

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with Huygens and ended with Euler, and that Newton too played a role – an important role – in this process. Further, while it is wrong to say that Newton could write F = ma (in this manuscript he does not), it is equally wrong to say that he could not relate his fluxional calculus to the science of motion, to ‘rational mechanics’, as he called it. Here, in this note, we find Newton doing exactly that: he writes that ‘gravitas’, the central force, is proportional to the second fluxion of radial displacement. But here, what we are above all interested in is one aspect of this page that is related not to its content, but to its form. When we look for texts in which Newton approaches rational mechanics in terms of 39 The last portrait of Newton, taken one year before his death. The sitter is proudly holding a copy of the 3rd edition of the Principia. Unknown artist after Enoch Seeman, 1726, oil on canvas.

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calculus, we should not read the printed texts or the manuscripts prepared for a public audience. Rather, we must wrack our brains over scraps of paper, such as this bifolium, jotted down in a quick hand. What is so important for us today, when looking back at the history of mathematical physics, is part of Newton’s private mathematical workshop, not of the image he so carefully presented to the public. Understanding Newton the mathematician is very much a matter of guesswork, of reading between the lines of his frequently terse language, in an attempt to catch a glimpse of the mind of a practitioner who was resorting to both tools that would soon become obsolete and methods that would shape eight­eenthcentury mathematics. All of these issues emerged in the context of the controversy with Leibniz regarding who was the first to invent calculus. The two mathematicians not only accused each other, but did not share the philosophical agendas in which they situated their mathematical discoveries. Not only was Newton convinced that the German philosopher was plagiarizing his method (and we should stress this accusation is false),

40 Newton’s attempts to write the equation of motion for central force trajectories in terms of the calculus of fluxions (early 1690s).

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he also believed that Leibniz, a typical representative of the mathematics and philosophy of the moderns, had developed a calculus that lacked elegance and beauty, that used empty symbols, that did not refer to anything real. In addition, Newton showed little interest in Leibniz’s innovations in the field of notation, which were crucial to the latter, who attached great importance to the invention of symbols and rules for algorithmic manipulation. It is interesting to note how Newton structured the Com­ mercium epistolicum in order to confirm Keill’s allegations of plagiarism. The Commercium gives an account of the results obtained by Newton in the 1660s in the field of the quadrature of curves by means of infinite series. Leibniz’s reaction was one of shocked amazement. From his point of view the Commercium did not contain a single word on calculus! Where, he wondered, were the basic rules of the calculus (the rules for the differentiation of the sum, the product, the power and the quotient of two variable magnitudes)? For Leibniz, a master of symbolic logic, ‘discovering the calculus’ meant determining an algorithm based on simple rules applicable to the elementary cases to which the most complex cases are reducible. For Newton, one of the greatest solvers of complex mathematical problems in history, ‘discovering calculus’ meant being able to solve challenging problems. For him it was natural not to devote any attention in the Commercium to those simple rules so important for Leibniz and which even today calculus textbooks begin with.33 The mathematical controversy with Leibniz that we outlined above soon developed into a wide-ranging philosophical controversy. Towards the end of the same anonymous ‘Account’

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in which Newton reviewed the Commercium we read that: ‘It must be allowed that these two Gentlemen differ very much in Philosophy.’34 In 1715 these philosophical differences had significant political repercussions. The political arena in which Leibniz and Newton each took on a leading role also fuelled the dispute, and this in part explains why the abstractions of mathematics could ignite so much fury. As we know, Newton belonged to the entourage of Lord Halifax, and was very close to factions in the Church of England that had promoted the Glorious Revolution. Leibniz, meanwhile, had become an advisor of the Emperor and the Tsar, and was in the service of the Duke of Hanover (illus. 41). It was in part thanks to Leibniz’s diplomatic efforts that the House of Hanover had obtained imperial electoral status and his patron acceded to the throne of Great Britain and Ireland in 1714 as George i.35 The prospect of having Leibniz – a towering diplomat and metaphysician who actively pursued an ecumenical policy of reconciliation between the Christian Churches – as Royal His­torian in London must have been a daunting one for Newton’s entourage, in which anti-Catholic feelings prospered. Indeed, in his numerous political writings Leibniz had revealed a pro-Habsburg political agenda addressed at transcending denominational differences under the patronage and guide of the Emperor and even the Pope. Leibniz’s defence of a res publica christiana and of federalism in the Reich were motivated by interests typical of Central European intellectuals. These interests were remote from those of many English­men, who with William had experienced how a foreign monarch could launch England into an expensive foreign policy, the meaning and interests of which were better understood on

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the other side of the Channel. Leibniz could gain approval not only in German-speaking mileux, such as the Catholic Court in Vienna and the Lutheran University of Helmstedt, but in England, where the Earl of Macclesfield cited the words of praise addressed to the German diplomat by Bishop Gilbert Burnet. Thus Leibniz became politically dangerous for the many who saw the Hanoverian succession, in the spirit of the Bill of Rights, as a bulwark against Catholicism. The priority dispute also served the purpose of discrediting Leibniz at the Royal Court.36 It might be contended that the anxieties and passions surrounding Newton’s thought on mathematical method that we have looked at in this chapter were determined by the fact that mathematics played such a prominent role in his broad-ranging philosophical agenda – one polemically oriented against the theological heresies of the ‘mechanical philosophy’ promoted by the Cartesians and by Hobbes, the probabilism in vogue at the Royal Society, and the ecumenism defended by the diplomatic endeavours of Leibniz. The greatest mathematician since Archimedes’ time, like the Syra­cusan geometer and mechanic himself, used mathematics for bellig­erent purposes. It might be contended that during the calcu­lus controversy Leibniz was portrayed by Newton as a kind of revenant metaphysical Cabbalist who relied upon symbols and a blind use of reasoning (the cogitatio caeca), hypo­statizing non-existent entities, such as vortices and infinitesimals, that Newton spurned.37 Leibniz’s modern and ontologically un­grounded mathematics was thus depicted as somehow related to Leibniz’s false philosophy, and this last as a metaphysics dangerously similar to the ‘Mystery

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of Iniquity’ that had polluted the Church in the third and fourth centuries (Second Letter to the Thessalonians 2:7). Newtonian drafts on early Church history written during the priority controversy are extant.38 Following Manuel’s, Westfall’s and Iliffe’s perceptive observations, it might be worth devoting more attention to textual concordances between these manuscripts, in which Newton pro­vides an erudite historical account of how ‘men skilled in the learning of heathens’, immoral Cabbalists, Schoolmen and Gnostics 41 Andreas Sheits, Gottfried Leibniz, 1703, oil on canvas.

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had corrupted the original religion of the ancient Hebrews, ‘straining the scriptures from a moral to a metaphysical sense’,39 and the contemporaneous Newtonian writings on the heresies implied by the metaphysics propounded by an immoral plagiarist such as Leibniz. Such textual evidence suggests that in Newton’s mind his own biased history of the discovery and plagiarism of calculus was related to the narrative of revelation, corruption and recovery that structures his writings on chronology and the history of religion. 40 The Princess of Wales, Caroline, would definitely have been happy to receive at court a man she trusted on philosophical and theological matters, but this would not happen thanks to a barrage from the Newtonians, who made a concerted effort to convince Caroline of the worth of Newtonian philosophy. Leibniz had, in fact, written in November 1715 to the princess fearing the presence in London of Newtonian philosophers able to subvert the principles of religion. Leibniz was obviously trying to launch a ‘devastating attack’, to quote Bertoloni Meli, ‘with very serious consequences’: if he was right, Newton and his acolytes held a heretical philosophy. 41 It is worth quoting from Leibniz’s letter in full: Natural religion itself, seems to decay (in England) very much. Many will have human souls to be material: others make God himself a corporeal being. Mr. Locke, and his followers, are uncertain at least, whether the soul be not material, and naturally perishable. Sir Isaac Newton says, that the space is an organ, which God makes use to perceive things by. But, if God stands in need of any organ to perceive things by, it will follow,

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that they do not depend altogether upon him, nor were produced by him. Sir Isaac Newton, and his followers, have also a very odd opinion concerning the work of God. According to their doctrine, God Almighty wants to wind up his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion. Nay, the machine of God’s making, is so imperfect, according to these gentlemen; that he is obliged to clean it now and then by an extraordinary concourse, and even to mend it, as a clockmaker mends his work; who must consequently be so much the more unskilful a workman, as he is oftener obliged to mend his work and to set it right. According to my opinion, the same force and vigour remains always in the world, and only passes from one part of matter to another, agreeably to the laws of nature, and the beautiful preestablished order. And I hold, that when God works miracles, he does not do it in order to supply the wants of nature, but those of grace. Whoever thinks otherwise, must needs have a very mean notion of the wisdom and power of God.42 This letter, in which Leibniz summarizes some of the reasons for his disagreement with Newton, is at the basis of the famous correspondence, published shortly after the death of Leibniz in 1716, between Leibniz and the theologian Samuel Clarke, who defended Newton. It is unclear to what extent Clarke, and before him Cotes in the preface to the second edition of the Principia (1713), faithfully represented

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the ideas of their master. The issues addressed by Leibniz and Clarke include the nature of space and time, vacuum, the relationship between God and Nature, providence and divine omniscience, the principle of sufficient reason and the identity of the indiscernibles, the existence of atoms and the conservation laws in physics. The correspondence is a master­piece that profoundly influenced eighteenth-century European philosophy. In the correspondence Leibniz reiterated his criticism of Newton’s theory of gravity. Invoking an action at a distance between the bodies, without explaining the mechanism of this interaction, meant either invoking a perpetual miracle, or reintroducing into natural philosophy the occult qualities of Aristotle, such as the ‘dormitive virtue’ of opium mocked by Molière. This last criticism had led to an outraged reaction from Cotes, who devoted a fair part of his Preface to the Principia (1713) to the issue. Newton’s own answer is contained in a manuscript in which he commented on a letter sent by Leibniz to the Dutch polymath Nicolaas Hartsoeker and published in 1712. Leibniz went so far as to say that resorting to gravity as the cause of planetary motion was tantamount to invoking the supernatural as an explanation of natural phenomena.43 All in all, Leibniz’s invective was well argued, given Newton’s ideas on divine providence discussed in the previous section. Newton, however, was convinced that he had shown that gravity exists: more precisely, that he had ‘deduced from phenomena’ that two bodies of masses m1 and m2 attract each other with a force that varies with the inverse of the square of the distance and proportional to the product of the masses. In his reply addressed to the editors of the

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journal in which Leibniz had published his criticism of the theory of gravitation, Newton wrote: And to understand this without knowing the cause of gravity, is as good a progress in philosophy as to understand the frame of a clock & the dependence of the wheels upon one another without knowing the cause of the gravity of the weight which moves the machine is in the philosophy of clockwork, or the understanding the frame of the bones & muscles by the contracting or dilating of the muscles without knowing how the muscles are contracted or dilated by the power of the mind is [in] the philosophy of animal motion.44 This reply by Newton paves the way for his famous motto, ‘hypotheses non fingo’ (I do not feign hypotheses), contained in the General Scholium to the second edition of the Principia (1713). Notice how Newton’s methodological attitude does not deny to hypotheses a heuristic role. They may be formulated (as Newton did, for example, in the Queries to the Opticks), but must be distinguished from what is known with certainty. In the case of gravity, according to Newton, we know for sure that it exists, but we do not yet know the cause. Newton does not deny that in the future it will be possible to determine the cause of gravity; he simply says that he does not yet have the tools to be able ‘to deduce such a cause from phenomena’. Leibniz was instead a supporter of the Cartesian theory of the vortices, and attributed the acceleration of the planets towards the Sun to the action of an interplanetary ether. For Newton, instead, accepting the

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existence of this interplanetary ether led to the error that he had denounced since he had been a young man in his Optical Lectures: reducing natural philosophy to a ‘romance’, relying on the action of particles whose existence is only hypothesized but not proven. We may perhaps say that distinguishing hypotheses from certainties was one of Newton’s great ambitions. That this ambition had been achieved was affirmed with conviction by the vast majority of English natural philosophers, and with equal conviction denied, at least initially, by most on the Continent. When Newton died in 1727 he was mourned in London with a devotion that amazed Voltaire, who, according to his probably spurious account, was present at the funeral. Few of his English supporters could have imagined that after a few decades of Cartesian resistance in France and other countries of the Continent, Newtonianism would have been affirmed, albeit in a form that had little to do with the natural philosophy that we have tried to present in these pages. The Newton we have studied was not a Sumerian walking in the streets of Restoration England, as Keynes suggested. Neither was he the Paracelsian or Pythagorean magus that so fascinates the media. Mostly he was a problem-solver, proud of being so effective in handling the technicalities of math­ ematics, alchemy and biblical hermeneutics. He rejoiced in castigating – on the basis of his technical expertise – the ‘romances’ of system builders, rationalists and enthusiasts. His anti-philosophical stance, which makes it a hopeless task to attempt to define him as a Platonist or empiricist, a Socinian or a deist, stemmed both from his pride of belonging to highly specialized guilds of practitioners and from the religious

42 Newton’s monument in Westminster Abbey (1731). Newton is resting on four books of the disciplines to which he devoted his life.

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minimalism that he endorsed. Keeping his distance from the ‘hot and superstitious part of mankind’, he conceived religious life as based on adherence to a plain reading of the Holy Writ and to moral norms which could be reduced to the two ‘greatest commandments’. Yet he was a practitioner with great ambitions, capable of embarking on philosophical and metaphysical controversies when it came to themes relevant to his natural philosophical agenda. Moreover, he conceived his natural philosophy and his biblical and early Church studies as decisive for mankind’s salvation. Newton’s was a majestic programme: an all too grandiose plan compared to those drawn even by the most speculative twenty-firstcentury cosmologists and string-theorists. The successes and failures of his scientific work, the divergences between his scientific agenda and practice, and his peculiar reading of the troubled political tensions of his own times through the lens

43 The broad spectrum of Newton’s interests displayed in this detail of his monument. On the fore-edges of the four books one can read ‘Divinity’, ‘Chronology’, ‘Opticks’, ‘Philo[sophiae] Prin[cipia] Math[emathica]’. Newton’s religious and historical works were seen as based upon his scientific achievements.

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offered by a biased evaluation of the events surrounding the early councils of the Church, characterize an intellectual biography that is fragmented and contradictory, and impossible to pigeonhole into any one philosophical or confessional sect. Studying Newton’s life gives us access to the complex cultural world of the ‘other present’ of our precursors – a past age that the historian experiences, once again, as a ‘foreign country’.

Chronology

Dates according to the Gregorian calendar 1643

Born on 4 January in Woolsthorpe, Lincolnshire (on 25 December 1642 according to the Julian Calendar) 1654/5 Enrols at the Free Grammar School in Grantham. Lodges with the town apothecary 1661 Enters Trinity College, Cambridge, as a subsizar 1664 Probably begins studying mathematics under Isaac Barrow. Begins to write ‘Qu[a]estiones quaedam philosophiae’ 1664–5 Annotations to Wallis’s Arithmetica infinitorum (1656). Discovery of the binomial theorem 1665 Graduates ba 1665–6 The marvellous years. Method of fluxions. Experimentum crucis. Studies on circular motion and hypothesis on gravity extending to the Moon 1667 Elected Fellow of Trinity College 1668 Awarded an ma. Begins alchemical experiments 1669 Writes De analysi and Barrow sends it to John Collins. Elected Lucasian Professor of Mathematics 1670–71 Writes De methodis serierum et fluxionum 1670–72 Optical Lectures 1671 Sends the reflecting telescope to the Royal Society 1672 Elected Fellow of the Royal Society. Polemic about ‘New Theory about Light and Colors’ begins 1673 Receives a copy of Huygens’s Horologium oscillatorium

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Sends the ‘Hypothesis Explaining the Properties of Light’ to the Royal Society. Phenomena of interference. Royal dispensation granted exempting the Lucasian Professor from taking holy orders Sends to Oldenburg two mathematical letters for Leibniz 1676 1679–80 Correspondence with Hooke on planetary motions 1683–4 The Lucasian Lectures on Algebra deposited at the University Library 1684 Halley visits Newton. ‘De motu corporum in gyrum’ 1685–7 Writes the Principia Opposition to the king’s request that Sidney Sussex 1687 College confer the title of Magister Artium on a Benedictine monk. Newton and other delegates of the University confront the Lord Chancellor, George Jeffreys. Principia published Elected to the Convention Parliament 1689 1692–3 Correspondence with Bentley on the relationships between natural philosophy and religion 1693 Nervous breakdown 1696 Moves to London as Warden of the Mint Fatio accuses Leibniz of having plagiarized the calculus 1699 1701 Elected mp 1702 The Theoria lunae is published 1703 Elected President of the Royal Society 1704 Opticks published Knighted by Queen Anne 1705 1706 New Quaestiones added to the Latin edition of the Opticks 1707 Whiston publishes the Lucasian lectures on algebra with the title Arithmetica universalis ‘De natura acidorum’ published in Harris, Lexicon technicum, 1710 vol. ii. Volume of Philosophical Transactions published in which appears the 1708 issue in which John Keill accused Leibniz of plagiarism 1711 Newton’s mathematical writings edited by Jones 1713 The Commercium epistolicum is distributed for free. Second edition of Principia, edited by Cotes, published. General Scholium

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1715 1715–16 1717 1725 1726 1727

Chronology

Anonymous ‘Account’ of the Commercium epistolicum Leibniz–Clarke correspondence Second English edition of the Opticks (new Queries added). Reissued in 1718 Unauthorized publication of Abrégé de la chronologie de M. le Chevalier Newton Third edition of the Principia, edited by Pemberton, published Dies on 31 March, refusing the last rites

references

Abbreviations Correspondence = The Correspondence of Isaac Newton, ed. H. W. Turnbull, J. F. Scott, A. R. Hall and L. Tilling, 7 vols (Cambridge, 1959–77) mp = The Mathematical Papers of Isaac Newton, ed. D. T. Whiteside, 8 vols (Cambridge, 1967–81) Optical Papers = The Optical Papers of Isaac Newton, vol. i: The Optical Lectures, 1670–1672, ed. Alan E. Shapiro (Cambridge, 1984) Opticks = Opticks, or a Treatise of the Reflections, Refractions, Inflections and Colours of Light, 4th edn (London, 1730/New York, 1979) Principles = The Principia: Mathematical Principles of Natural Philosophy . . . Preceded by a Guide to Newton’s Principia by I. Bernard Cohen, trans. I. B. Cohen and A. Whitman, assisted by J. Budenz (Berkeley, ca, 1999)

Introduction: Images of Newton 1 Stephen Snobelen, ‘Isaac Newton, Heretic: The Strategies of a Nicodemite’, British Journal for the History of Science, xxxii (1999), pp. 381–419. 2 A Catalogue of the Portsmouth Collection of Books and Papers Written by or Belonging to Sir Isaac Newton: The Scientific Portion of Which Has Been Presented by the Earl of Portsmouth to the University of Cambridge Drawn Up by the Syndicate Appointed the 6th November, 1872 (Cambridge, 1888), p. x.

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3 On Netwon’s manuscripts, see Sarah Dry, The Newton Papers: The Strange and True Odyssey of Isaac Newton’s Manuscripts (Oxford, 2014). A transcription of the manuscripts and works of Newton is available on the website of The Newton Project, whose main editors are Rob Iliffe and Scott Mandelbrote (see www.newtonproject.ox.ac.uk, accessed 27 May 2017), The Newton Project Canada, edited by Stephen Snobelen (see www.isaacnewton.ca, accessed 1 July 2015), and on the website The Chymistry of Isaac Newton directed by William R. Newman (see http://webapp1.dlib.indiana.edu/newton, accessed 1 July 2015). 4 John Maynard Keynes, ‘Newton the Man’, The Royal Society Newton Tercentenary Celebrations, 15–19 July 1946 (Cambridge, 1947), p. 27. On the changing images of Newton, see Rebekah Higgitt, Recreating Newton: Newtonian Biography and the Making of Nineteenth-century History of Science (London, 2007); Patricia Fara, Newton: The Making of Genius (London, 2002). 5 Walter Pagel, From Paracelsus to Van Helmont: Studies in Renaissance Medicine and Science (London, 1986); Paolo Rossi, Francis Bacon: From Magic to Science (London, 1968); Frances A. Yates, Giordano Bruno and the Hermetic Tradition (London, 1964). 6 See A. Rupert Hall, Isaac Newton: Adventurer in Thought (Cambridge, 1992); I. Bernard Cohen, The Newtonian Revolution: With Illustrations of the Transformation of Scientific Ideas (Cambridge, 1980); Derek Thomas Whiteside’s introductions to The Mathematical Papers of Isaac Newton (Cambridge, 1967–81) (cited as mp). 7 See for example Betty J. T. Dobbs, The Janus Faces of Genius: The Role of Alchemy in Newton’s Thought (Cambridge, 1991); James E. McGuire and Piyo M. Rattansi, ‘Newton and the “Pipes of Pan”’, Notes and Records of the Royal Society, xxi (1966), pp. 108–43; Richard S. Westfall, ‘Newton and Alchemy’, in Occult and Scientific Mentalities in the Renaissance, ed. B. Vickers (Cambridge, 1984), pp. 315–35; Richard S. Westfall, Never at Rest: A Biography of Isaac Newton (Cambridge, 1980); Frank E. Manuel, The Religion of Isaac Newton (Oxford, 1974). 8 Quentin Skinner, ‘Meaning and Understanding in the History of Ideas’, History and Theory, viii (1969), pp. 3–53.

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References

1 From Woolsthorpe to Cambridge, 1642–1664 1 Quoted in J.C.D. Clark, English Society, 1660–1832 (Cambridge, 2000), p. 66. 2 According to the Gregorian calendar Newton’s date of birth is 4 January 1643. 3 On the non-technical characterization of the term ‘puritan’ attributable to Newton, see Robert Iliffe, Newton: A Very Short Introduction (Oxford, 2007), p. 13, a work to which I am deeply indebted in this chapter. 4 Robert K. Merton, Science, Technology and Society in Seventeenth-century England (Bruges, 1938). 5 Steffen Ducheyne, ‘Newton’s Training in the Aristotelian Textbook Tradition: From Effects to Causes and Back’, History of Science, xliii (2005), pp. 217–37. 6 The ‘Quaestiones’ have been transcribed with an extensive and learned commentary in J. E. McGuire and M. Tamny, Certain Philosophical Questions: Newton’s Trinity Notebook (Cambridge, 1983). 7 For two different points of view, see A. Rupert Hall, Henry More: Magic, Religion, and Experiment (Oxford, 1990) and James McGuire, ‘Force, Active Principles and Newton’s Invisible Realm’, Ambix, xv (1968), pp. 154–208, as well as John Henry’s essay ‘Henry More and Newton’s Gravity’, History of Science, xxxi (1993), pp. 83–97. 8 As evidence of Newton’s knowledge of so-called Cambridge Platonism we may also cite a manuscript dating back to the early 1680s, entitled ‘Out of Cudworth’, which proves the attention dedicated by Newton to the study of the True Intellectual System of the Universe (London, 1678) by Ralph Cudworth, but it certainly does not imply that Newton accepted the ideas it contained. 9 Mordechai Feingold, ‘Newton, Leibniz, and Barrow Too: An Attempt at a Reinterpretation’, Isis, lxxxiv (1993), pp. 310–38.

2 Early Achievements, 1665–1668 1 Add. 3968.41, fol. 85r (Cambridge University Library) (c. 1718). I. B. Cohen, Introduction to Newton’s Principia (Cambridge, 1971), p. 291. This passage, which I have greatly streamlined, is from the

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draft of a letter that Newton apparently intended for Pierre Des Maizeaux. It is discussed in Richard Westfall, Never at Rest: A Biography of Isaac Newton (Cambridge, 1980), p. 143. 2 On Newton’s early mathematical studies, see the transcriptions, translations and commentaries by D. T. Whiteside in mp, 1. 3 To avoid anachronism. Descartes did not have ‘Cartesian axes’, but he used what we know as ‘Cartesian coordinates’. For example, given an ellipse, he defined y as the abscissa measured from the vertex, and x as the corresponding ordinate, so that the ellipse’s equation was x2 = ry – (r/q)y2, with r and q constants. See René Descartes, The Geometry of René Descartes with a Facsimile of the First Edition, ed. and trans. D. E. Smith and M. L. Latham (New York, 1954), pp. 95–6. 4 Henk Bos, Redefining Geometrical Exactness: Descartes’ Transformation of the Early Modern Concept of Construction (New York, 2001). 5 Correspondence, ii, p. 29. 6 Bernhardus Varenius (Varen), Geographia Generalis (Amsterdam, 1650). Newton’s notes on Gerard Kinckhuysen’s Algebra are edited in mp, ii, pp. 295–447. 7 mp, iii, pp. 32–328. 8 Isaac Newton, The Method of Fluxions and Infinite Series (London, 1736). 9 Henry Pemberton, A View of Sir Isaac Newton’s Philosophy (London, 1728). 10 ms Keynes 130.10, ff. 2v–3v (King’s College, Cambridge). 11 Robert Boyle, Experiments and Considerations Touching Colours (London, 1664), pp. 21, 219, 225–7, 263. J. E. McGuire and M. Tamny, Certain Philosophical Questions: Newton’s Trinity Notebook (Cambridge, 1983), p. 440. 12 Simon Schaffer, ‘Glass Works: Newton’s Prisms and the Uses of Experiment’, in The Uses of Experiment: Studies in the Natural Sciences, ed. David Gooding, Trevor Pinch and Simon Schaffer (Cambridge, 1989), pp. 67–104. 13 It is likely that the two prisms used by Newton had different angles and different optical indices. If one uses two identical prisms, as it can be done today in the classroom, then rays with the same colour are refracted at the same angle in the first and in the second prism.

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References

14 See Yoshimi Takuwa, ‘The Historical Transformation of Newton’s Experimentum Crucis: Pursuit of the Demonstration of Color Immutability’, Historia Scientiarum, xxiii (2013), pp. 113–40; and Opticks, p. 69. 15 William R. Newman, ‘Newton’s Early Optical Theory and its Debt to Chymistry’, in Lumière et vision dans les sciences et dans les arts, de l’Antiquité du xviie siècle, ed. Michel Hochmann and Danielle Jacquart (Geneva, 2010), pp. 283–307. 16 David Gregory, Catoptricae and diptricae elementa (1695), p. 98. 17 Add. 4004, fol. 1r (Cambridge University Library), mp, i, p. 456. 18 See the correspondence with Thomas Burnet and John Flamsteed in Correspondence, ii, pp. 319, 322, 340–47.

3 A Young Professor and His Audience, 1669–1674 1 Mordechai Feingold, ‘Isaac Barrow: Divine, Scholar, Mathematician’, in Before Newton: The Life and Times of Isaac Barrow, ed. M. Feingold (Cambridge, 1990), pp. 1–104 (on pp. 79–80). 2 We know that Newton went to London in the spring of 1675 to ask for a dispensation from the Secretary of State Joseph Williamson. 3 Evidence in favour of this interpretation comes from two facts. There is plausible evidence of Newton’s application for another Fellowship, one dedicated to the study of law and exceptionally exempted from the ordination obligation and that had unex­ pectedly become available. The other is the message which Newton sent to Oldenburg in 1675, just before his ordination was due, to inform him that he expected shortly to part with his fellowship. I thank Floris Cohen for bringing the above points to my attention (both are included in Richard S. Westfall, Never at Rest: A Biography of Isaac Newton (Cambridge, 1980), pp. 330–33). 4 ms Keynes 135, fol. 2 (King’s College, Cambridge). 5 mp, iv, p. 11, p. 188. Newton’s trigonometry lessons are in mp, iv, pp. 116–202. The testimony of another of Newton’s mathematics students, Thomas Parkyns, seems less relevant. See Westfall, Never at Rest, p. 210. 6 Paolo Rossi, Philosophy, Technology, and the Arts in the Early Modern Era (New York, 1970). James A. Bennett, ‘The Mechanics’ Philosophy

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and the Mechanical Philosophy’, History of Science, xxiv (1986), pp. 1–28. 7 Richard Nichols, The Diaries of Robert Hooke, the Leonardo of London, 1635–1703 (Lewes, 1994). James A. Bennett, Michael Cooper, Michael Hunter and Lisa Jardine, London’s Leonardo: The Life and Work of Robert Hooke (Oxford, 2003). 8 Optical Papers, pp. 86, 88 and 436, 438. 9 Robert Hooke, Micrographia (London, 1665), Preface. 10 Steven Shapin, ‘Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice’, Science in Context, ii (1988), pp. 23–58. 11 Optical Papers, pp. 87 and 439. 12 Correspondence, i, pp. 96–7. This passage was censored by Henry Oldenburg, the secretary of the Royal Society. 13 Correspondence, i, p. 161. 14 Philosophical Transactions, xcvii (6 October 1673), p. 6109, in Papers and Letters, p. 144; Correspondence, i, p. 264. 15 Correspondence, ii, p. 105. 16 Ibid., i, pp. 362–86. Newton had been working on these essays since 1672. 17 Ibid., p. 364. 18 Ibid., p. 367. 19 Ibid., p. 370. 20 Snell’s Law, which is named after Willebrord Snel van Royen and also appeared in Descartes’ Dioptrique, states that when light passes from a medium with a refractive index n1 to another medium with a different refractive index n2, the relationship between the sine of the angle of incidence and the sine of the angle of refraction is the inverse of the relationship between the refractive indices of the two media. 21 To be fair, after the affirmation of quantum mechanics, the conception of light accepted today allows both a corpuscular and wave interpretation to be valid. 22 Correspondence, i, p. 376. 23 Niccolò Guicciardini, ‘The Role of Musical Analogies in Newton’s Optical and Cosmological Work’, Journal of the History of Ideas, lxxiv/1 (2013), pp. 45–67.

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References

24 Newton, Correspondence, i, p. 366. 25 Ibid., p. 364. 26 Ibid., p. 370.

4 A Maturing Scholar, 1675–1683 1 I have profited from the free accessibility of the alchemical manuscripts at The Chymistry of Isaac Newton, http://webapp1. dlib.indiana.edu/newton (accessed 22 May 2016), and I should also mention the importance for writing this section of the works by Newman, Principe and Clericuzio, cited in references. 2 At this point Newton may have been farming out the experimentation (Bill Newman, private correspondence, 2 October 2016) . 3 See L. M. Principe and W. R. Newman, ‘Some Problems with the Historiography of Alchemy’, in Secrets of Nature: Astrology and Alchemy in Early Modern Europe, ed. W. R. Newman and Anthony Grafton (Cambridge, ma, 2011), pp. 385–431. Lawrence M. Principe, The Secrets of Alchemy (Chicago, il, 2013), pp. 83–106. This book is an excellent historical introduction to alchemy. 4 Peter Anstey, ‘John Locke and Helmontian Medicine’, in The Body as Object and Instrument of Knowledge: Embodied Empiricism in Early Modern Science, ed. C. T. Wolfe and O. Gal (Dordrecht, 2010), pp. 93–120. 5 William Newman, ‘Why Did Isaac Newton Believe in Alchemy?’, presentation at the Perimeter Institute, 2 October 2010. See video at www.perimeterinstitute.ca (accessed 20 May 2016). 6 William R. Newman and Lawrence M. Principe, Alchemy Tried in the Fire: Starkey, Boyle, and the Fate of Helmontian Chymistry (Chicago, il, 2002). 7 Matthew Hale, Observations Touching the Principles of Natural Motions (London, 1677), p. 8. 8 See Antonio Clericuzio, Elements, Principles and Corpuscles: A Study of Atomism and Chemistry in the Seventeenth Century (Dordrecht and London, 2000). 9 The most important are kept in the University Library of Cambridge as Add. 3973 and Add. 3975.

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10 Newman writes: ‘Antimony metal can be made to form a visibly crystalline structure by slowly cooling the molten antimony beneath a thick layer of slag. The antimony is reduced from stibnite by heating it with iron and saltpeter until fusion ensues. The antimony initially reduced must be further purified by repeated fusion with additional saltpeter before the star can be produced.’ See The Chymistry of Isaac Newton/Educational Resources/Chymical products at http://webapp1.dlib.indiana.edu/ newton (accessed 17 July 2015). 11 We quote from Query 28 of the second English edition of the Opticks (1717/18) and from a draft of the Latin edition of Quaestio 23 (1706): ms Add. 3970, fol., 620v (Cambridge University Library). 12 ms Dibner 1031b (Smithsonian Institution, Washington, dc, usa). 13 See William R. Newman, ‘Geochemical Concepts in Isaac Newton’s Early Alchemy’, in The Revolution in Geology from the Renaissance to the Enlightenment, ed. G. D. Rosenberg (Boulder, co, 2009), pp. 41–9. 14 Paul T. Greenham, ‘A Concord of Alchemy with Theology: Isaac Newton’s Hermeneutics of the Symbolic Texts of Chymistry and Biblical Prophecy’, PhD, University of Toronto (2015), p. 80. 15 Correspondence, i, p. 356. 16 The manuscript deposited by Newton (probably in 1683–4) bears no title. See mp, v, pp. 54–491. 17 The notes on Kinckhuysen’s Algebra are in mp, ii, pp. 277–447. 18 Jacqueline Stedall, From Cardano’s Great Art to Lagrange’s Reflections: Filling a Gap in the History of Algebra (Zürich, 2011). 19 mp, vii, p. 291. 20 See, for example, mp, iv, p. 277. 21 ms Add. 4005, fol 41r (Cambridge University Library). In S. Ducheyne, The Main Business of Natural Philosophy: Isaac Newton’s Natural-philosophical Methodology (Dordrecht, Heidelberg, London, New York, 2012), p. 297. 22 mp, iv, p. 277. Translation by D. T. Whiteside. 23 Our understanding of Newton’s religious views has advanced a great deal lately thanks to the studies of the manuscripts freely available at the website of the Newton Project. In writing

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this section I have profited immensely from the works of Rob Iliffe, Scott Mandelbrote and Stephen Snobelen cited below. Iliffe generously allowed me to read a preliminary version of his masterpiece Priest of Nature: The Religious Worlds of Isaac Newton (Oxford, 2017). See also The Newton Project, www. newtonproject.ox.ac.uk (accessed 23 May 2016). 24 Newton, ‘Drafts on the History of the Church’. Yahuda ms 15.5, fol. 97r (The National Library of Israel). 25 See Keynes ms 8 (King’s College Library, Cambridge). 26 Stephen Snobelen, ‘Isaac Newton, Heretic: The Strategies of a Nicodemite’, British Journal for the History of Science, xxxi (1999), pp. 381–419. 27 Scott Mandelbrote, ‘Becoming Heterodox in Seventeenth-century Cambridge: The Case of Isaac Newton’ (forthcoming). 28 In 1697 an Edinburgh student was hanged, in 1703 Thomas Emlyn was imprisoned, and in 1724 Edward Elwell was tried. These seem to be the most serious cases of repression against the Arian heresy in the period we are dealing with. See Jonathan C. D. Clarke, English Society, 1660–1832 (Cambridge, 2000), pp. 330–33, and Stephen Snobelen, ‘Isaac Newton, Heresy Laws and the Persecution of Religious Dissent’, Enlightenment and Dissent, xxv (2009), pp. 204–59. 29 Stephen Snobelen, ‘“God of Gods, and Lord of Lords”: The Theology of Isaac Newton’s General Scholium to the Principia’, Osiris, xvi (2001), pp. 169–208. 30 A. Rupert Hall, Isaac Newton: Adventurer in Thought (Cambridge, 1992), p. 323. 31 Keynes ms 3, (e.g. fol. 3 and 39) (King’s College, Cambridge) and Newton ms, Ch. 2, fol. 20 (Martin Bodmer Foundation, Geneva). These terms can be found in Maimonides, but also in Hebrews 5: 12–14, from which Newton quotes. 32 Scott Mandelbrote, ‘“A Duty of the Greatest Moment”: Isaac Newton and the Writing of Biblical Criticism’, British Journal for the History of Science, xxvi (1993), pp. 281–302. Stephen Snobelen, ‘“A time and times and the dividing of time”: Isaac Newton, the Apocalypse and 2060 ad’, Canadian Journal of History, xxxviii (2003), pp. 537–51.

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33 Principles, p. 942. 34 Eric Schliesser, ‘On Reading Newton as an Epicurean: Kant, Spinozism and the Changes to the Principia’, Studies in History and Philosophy of Science, xliv/3 (2013), pp. 416–28. 35 Isaac Newton, Opticks (London, 1717/18), p. 379. 36 Add. ms 4003, fol. 26 (Cambridge University Library) in Philosophical Writings, p. 31 (translation slightly adapted). 37 Correspondence, iii, p. 336. 38 On Socinianism in Newton see Stephen Snobelen, ‘Isaac Newton, Socinianism and “the One Supreme God”’, in Socinianism and Cultural Exchange: The European Dimension of Antitrinitarian and Arminian Networks, 1650–1720, ed. Martin Mulsow and Jan Rohls (Leiden 2005), pp. 241–293. 39 ‘Paradoxical Questions Concerning the Morals and Actions of Athanasius and His Followers’, ms n563m3 p222 (William Andrews Clark Memorial Library (ucla)). Robert Iliffe, ‘Prosecuting Athanasius: Protestant Forensics and the Mirrors of Persecution’, in Newton and Newtonianism: New Studies, ed. J. Force and S. Hutton (Dordrecht, 2004), pp. 113–54. 40 For Newton, the Trinitarian corruptions regard John 1.5:7 and Timothy 1.3:16. 41 Scott Mandelbrote, ‘Isaac Newton and the Exegesis of the Book of Daniel’, in Die Geschichte der Daniel-Auslegung in Judentum, Christentum und Islam, ed. K. Bracht and D. S. du Toit (Berlin and New York, 2007), pp. 351–75. 42 The System of the World in Principles, pp. 549–50. 43 James E. McGuire and Piyo M. Rattansi, ‘Newton and the “Pipes of Pan”’, Notes and Records of the Royal Society, xxi (1966), pp. 108–43. 44 Correspondence, iii, p. 193, p. 196.

5 Natural Philosopher, 1684–1695 1 Robert Hooke, An Attempt to Prove the Motion of the Earth from Observations (London, 1674), reprinted in Robert T. Gunther, Early Science in Oxford (Oxford and London, 1931), viii, pp. 1–28. Hooke’s Attempt was read at the Royal Society in 1670. 2 Ibid., p. 27.

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3 Ibid., p. 28. 4 Correspondence, i, pp. 365–6. 5 Newton refers to a planetary vortex also in a manuscript datable to the early 1680s, where we read ‘Materiam coelorum fluidam esse [et] circa centrum systematis cosmici secundum cursum Planetarum gyrare.’ Newton continues saying that the matter of the heavens revolves in the direction of the course of the planets. Add 3965, 14, f, 613r (Cambridge University Library). 6 N. Kollertsrom, ‘How Newton Failed to Discover the Law of Gravity’, Annals of Science, lvi (1999), pp. 331–56. 7 Correspondence, ii, p. 297. 8 Ibid., pp. 309, 313. 9 According to Michael Nauenberg, by 1679 Newton had already developed a sophisticated mathematical theory of central force motion, based on the decomposition of motion into tangential and normal components. The calculation of the radius of curvature of the trajectory and the application of Huygens’s law to the normal component of force allowed Newton to approximate orbits by a graphical method. It is the correspondence with Hooke, based on decomposition of motion into tangential and radial components that made Newton aware of the fact that for central force motion the area law is valid. This insight allowed Newton to mathematize central force in a much more successful way. See Michael Nauenberg, ‘Robert Hooke’s Seminal Contributions to Orbital Dynamics’, Physics in Perspective, vii (2005), pp. 4–34. 10 Alan Cook, Edmond Halley: Charting the Heavens and the Seas (Oxford, 1998), p. 155. 11 Correspondence, iii, p. 42. The letter to Aubrey dated 15 September 1689 was written with Hooke’s own contribution. 12 Simon Schaffer, ‘Newton on the Beach: The Information Order of Principia Mathematica’, History of Science, xlvii (2009), pp. 243–76. 13 A very good introduction to the Principia is provided in the opening essay by I. B. Cohen in Principles. 14 ms Keynes 130.05, fol. 2r (King’s College, Cambridge) available at www.newtonproject.ox.ac.uk. 15 Ibid., fol. 3v–4r.

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16 Principles, p. 382. On the Praefatio ad lectorem see Mary Domski, ‘The Constructible and the Intelligible in Newton’s Philosophy of Geometry’, Philosophy of Science, lxx (2003), pp. 1114–24. 17 This concept, often repeated in critical literature, should however be mitigated to some extent, taking into account the fact that in the second book of the Principia Newton uses corpuscular models to explain the macroscopic properties (inertia, viscosity and so on) of fluids. 18 Newton, inspired by the work of Jan de Witt and Van Schooten, had invented an instrument for the mechanical generation of conic sections. The operation of Newton’s ‘compass’ is, in fact, based on the understanding of Steiner’s theorem on conics. 19 mp, vii, pp. 287, 289, trans. D. T. Whiteside. 20 Principles, pp. 404–5. 21 On absolute time and space in Newton, see Robert DiSalle, Understanding Spacetime: The Philosophical Development of Physics from Newton to Einstein (Cambridge, 2006). 22 J. E. McGuire, ‘Existence, Actuality and Necessity: Newton on Space and Time’, Annals of Science, xxxv (1978), pp. 463–508. 23 For the most lucid account of Newton’s engagement with philosophical issues the reader should consult A. Janiak, Newton as Philosopher (Cambridge, 2008). 24 Principles, p. 408. 25 Albert Einstein, as is well known, rejected the notion of absolute simultaneity. This is an assumption that even the staunchest critics of absolute time, such as Gottfried Wilhelm Leibniz and George Berkeley, accepted; or, more precisely, they did not even seem to be aware that this was a crucial assumption. 26 Principles, p. 410. 27 Chris Smeenk and Eric Schliesser, ‘Newton’s Principia’, in Oxford Handbook for the History of Physics, ed. Jed Buchwald and Robert Fox (Oxford, 2013), pp. 109–65 (on p. 121). 28 Principles, pp. 416–17. 29 ms Add. 3970, fol 652a (Cambridge University Library) in A. Rupert Hall and Marie Boas Hall, Unpublished Scientific Papers of Isaac Newton (Cambridge, 1962), p. 309. 30 Principles, p. 793.

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31 Hermann Bondi, ‘Newton and the Twentieth Century, a Personal View’, in Let Newton Be! A New Perspective on His Life and Works, ed. J. Fauvel, R. Flood, M. Shortland and R. Wilson (Oxford, 1988), p. 242. 32 C. Huygens, Oeuvres (The Hague, 1888–1950), ix, p. 538. 33 Letter from Pierre Rémond de Montmort to Johann Bernoulli (5 December 1712), letter from Bernoulli to Montmort (2 February 1713). University Library of Basel, l ia 665, Nr.6* and l ia 665, Nr.3. 34 Correspondence, iii, pp. 253–4. 35 The General Scholium appeared in the second (1713) edition. The rules appeared because of a radical restructuring of the opening of the third book in the second edition. The first two belonged to a list of ‘hypotheses’ in the first edition, the third was added in the second edition. The fourth rule was added in the third edition (1726). For a lucid discussion of the rules and the Scholium, see Andrew Janiak, Newton as Philosopher (Cambridge, 2008), and Newton: Philosophical Writings, ed. A. Janiak (Cambridge, 2004). The talks delivered at a symposium devoted to the General Scholium can be accessed at https://isaacnewton.ca/generalscholium-symposium (accessed 29 May 2016).

6 The Last Years, 1696–1727 1 The best account of this aspect of Newtonian thought is Andrew Janiak, Newton as Philosopher (Cambridge, 2008). 2 On Fatio, see Scott Mandelbrote, ‘The Heterodox Career of Nicolas Fatio de Duillier’, in Heterodoxy in Early Modern Science and Religion, ed. J. Brooke and I. MacLean (Oxford, 2005), pp. 263–96. 3 Thomas Levinson, Newton and the Counterfeiter: The Unknown Detective Career of the World’s Greatest Scientist (Boston, 2009). 4 Mordechai Feingold, ‘Mathematicians and Naturalists: Sir Isaac Newton and the Royal Society’, in Isaac Newton’s Natural Philosophy, ed. J. Z. Buchwald and I. B. Cohen (Cambridge, ma, 2001), pp. 77–102. 5 Jed Z. Buchwald and Mordechai Feingold, Newton and the Origin of Civilization (Princeton, nj, 2013).

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6 See Raquel Delgado Moreira, ‘“What Ezekiel Says”: Newton as a Temple Scholar’, History of Science, xlviii (2010), pp. 153–80. 7 See my Isaac Newton on Mathematical Certainty and Method (Cambridge, ma, 2009). 8 Isaac Newton, Analysis per Quantitatum, Series, Fluxiones, ac Differentias: Cum Enumeratione Linearum Tertii Ordinis, ed. W. Jones (London, 1711). 9 On the General Scholium, see Steffen Ducheyne, ‘The General Scholium: Some Notes on Newton’s Published and Unpublished Endeavours’, Lias: Sources and Documents Relating to the Early Modern History of Ideas, xxxiii/2 (2006), pp. 223–74. 10 Eric Schliesser, ‘On Reading Newton as an Epicurean: Kant, Spinozism and the Changes to the Principia’, Studies in History and Philosophy of Science, xliv/3 (2013), pp. 416–28. 11 W. R. Albury, ‘Halley’s Ode on the Principia of Newton and the Epicurean Revival in England’, Journal of the History of Ideas, xxxix/1 (1978), pp. 24–43. 12 Isaac Newton, Opuscula Mathematica, Philosophica et Philologica, ed. Castiglione (Giovan Francesco Salvemini) (Lausanne and Geneva, 1744). 13 Correspondence, iii, p. 253. 14 Ibid., p. 240. 15 Ibid., pp. 235, 240. 16 Michael Hoskin, ‘Newton, Providence and the Universe of Stars’, Journal for the History of Astronomy, viii (1977), pp. 77–101. 17 Correspondence, iii, p. 238. 18 This would become Query 31 in the English edition of 1717/18 from which we quote. 19 David Kubrin, ‘Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy’, Journal of the History of Ideas, xxviii (1967), pp. 325–46; Stephen Snobelen, ‘The Unknown Newton: Cosmos and Apocalypse’, The New Atlantis: A Journal of Technology and Society, xliv (2015), pp. 76–94. 20 Isaac Newton, Opticks (1717/18), pp. 378, 379. 21 Ibid., p. 379, Opticks, p. 403. 22 Correspondence, iii, pp. 240, 253–4. 23 Principles, p. 943.

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24 We have already discussed the Newtonian ether possessing active principles in the concluding section of Chapter Three and the first section of Chapter Four. 25 Isaac Newton, Opticks (London, 1717/18), pp. 372–4, Opticks, pp. 397–8. 26 Ibid., p. 376. 27 ms Yahuda 41, 7r (National Library of Israel, Jerusalem, Israel). See the ‘Theologiae Gentilis Origines Philosophicae’ (a treatise which survives in several drafts, esp., ms Yahuda 16.2). The best guide to Newton’s religion is Robert Iliffe, Priest of Nature: The Religious Worlds of Isaac Newton (Oxford, 2017). I thank the author for allowing me to read a draft of his book, to which I am deeply indebted. See also Richard S. Westfall, ‘Isaac Newton’s Theologiae Gentilis Origines Philosophicae’, in The Secular Mind: Transformations of Faith in Modern Europe. Essays Presented to Franklin L. Baumer, ed. W. W. Wagar (New York, 1982), pp. 15–34. 28 Isaac Newton, The Mathematical Principles of Natural Philosophy, trans. A. Motte (London, 1729), p. 392. 29 Gerald M. Straka, Anglican Reaction to the Revolution of 1688 (Madison, wi, 1962). 30 On the Newton-Leibniz controversy, see A. R. Hall, Philosophers at War: The Quarrel between Newton and Leibniz (Cambridge, 1980). A fine biography is Maria Rosa Antognazza, Leibniz: An Intellectual Biography (Cambridge, 2009). On the reception of Newtonianism in France, see John B. Shank, The Newton Wars and the Beginning of the French Enlightenment (Chicago, il, and London, 2008). 31 Niccolò Guicciardini, ‘Lost in Translation? Reading Newton on Inverse-cube Trajectories’, Archive for History of Exact Sciences, lxx/2 (2016), pp. 205–41. 32 mp, vii, p. 196. Translation by D. T. Whiteside. 33 For further details on the issues dealt with in this section, see my Isaac Newton on Mathematical Certainty and Method (Cambridge, ma, 2009). 34 Philosophical Transactions of the Royal Society, xxix/342 (1715), pp. 173–224 (on p. 224) 35 It is also thanks to Leibniz’s genealogical research on the House of Hanover that in 1692 the status of Elector was awarded to Duke

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36 37 38

39 40

41

42 43

44

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Ernst August. Leibniz’s intervention in the Hanoverian succession is particularly evident in his activities when William visited Celle in October 1698. On Leibniz’s political views, see Friedrich Beiderbeck, ‘Leibniz’s Political Vision of Europe’, in The Oxford Handbook of Leibniz, ed. Maria Rosa Antognazza (Oxford, online 2015). Domenico Bertoloni Meli, ‘Caroline, Leibniz, and Clarke’, Journal of the History of Ideas, lx (1999), pp. 469–86. Some of these themes occupy also Cotes’s Preface and the General Scholium in the second edition of the Principia (1713). Rob Iliffe, Newton: A Very Short Introduction (Oxford, 2007), p. 127. The manuscripts are ‘Of the Church’ (Bodmer Library) and drafts on the history of the church Yahuda ms 15. I thank Rob for a very informative email on this (6 February 2016). Yahuda ms 15.5, f. 97r. F. Manuel, A Portrait of Isaac Newton (Cambridge, ma, 1968), p. 339; R. Iliffe, Priest of Nature, Ch. 10; Richard S. Westfall, Never at Rest: A Biography of Isaac Newton (Cambridge, 1980), pp. 822–3. Domenico Bertoloni Meli, ‘Newton and the Leibniz-Clarke Correspondence’, in The Cambridge Companion to Newton, 2nd edn, ed. Robert Iliffe and George Smith (Cambridge, 2016), pp. 586–96 (on p. 589). The Leibniz-Clarke Correspondence, ed. H. G. Alexander (Manchester, 1956), pp. 11–12. Leibniz’s letter (published in 1712) and Newton’s reply are in Isaac Newton, Philosophical Writings, ed. Andrew Janiak (Cambridge, 2004), pp. 109–17. Correspondence, v, p. 300.

bibliograph\

Works by Newton Available Online A transcription of a large number of the manuscripts and the works of Newton is available on the website of The Newton Project, whose main editors are Rob Iliffe and Scott Mandelbrote (see www.newtonproject.ox.ac.uk, accessed 5 June 2017), The Newton Project Canada, directed by Stephen Snobelen (see www.isaacnewton.ca, accessed 1 July 2015), and on the website The Chymistry of Isaac Newton, directed by William R. Newman (see http://webapp1.dlib.indiana.edu/newton, accessed 1 July 2015). Digitized images of the Yahuda Collection are available via the webpage of the National Library of Israel, http://web.nli.org.il/sites/ nli/English/collections/Humanities/Pages/newton.aspx (accessed 6 September 2013). The Cambridge Digital Library has completed the digitization of the Newton manuscripts from the Portsmouth Collection held in the University Library at Cambridge, http://cudl.lib.cam.ac.uk/collections/ newton (accessed 6 September 2013).

A Selection of Works by Newton (in English or English Translation) Certain Philosophical Questions: Newton’s Trinity Notebook, ed. James E. McGuire and Martin Tamny (Cambridge, 1983) The Chronology of Ancient Kingdoms Amended, ed. John Conduitt (London, 1728)

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The Correspondence of Isaac Newton, ed. H. W. Turnbull, J. F. Scott, A. R. Hall and L. Tilling, 7 vols (Cambridge, 1959–77) Isaac Newton’s Papers and Letters on Natural Philosophy, ed. I. B. Cohen and R. E. Schofield (Cambridge, ma, 1958) The Mathematical Papers of Isaac Newton, ed. D. T. Whiteside, 8 vols (Cambridge, 1967–81) The Mathematical Works of Isaac Newton, 2 vols, ed. D. T. Whiteside (New York, 1964, 1967) Observations upon the Prophecies of Daniel, and the Apocalypse of St John, ed. Benjamin Smith (London and Dublin, 1733) The Optical Papers of Isaac Newton, vol. i: The Optical Lectures, 1670–1672, ed. Alan E. Shapiro (Cambridge, 1984) Opticks: or, A Treatise of the Reflections, Refractions, Inflections and Colours of Light. Based on the Fourth Edition (London, 1730), with a preface by I. B. Cohen, a foreword by Albert Einstein, an introduction by E. T. Whittaker, and an analytical table of contents by Duane H. D. Roller (New York, 1952/1979) Philosophical Writings, ed. Andrew Janiak (Cambridge, 2004, 2nd edn 2014) The Principia, Mathematical Principles of Natural Philosophy: A New Translation, trans. I. Bernard Cohen and Anne Whitman, with the assistance of Julia Budenz, preceded by ‘A Guide to Newton’s Principia’ by I. B. Cohen (Berkeley, ca, 1999) A Treatise of the System of the World (London, 1728) Two letters of Sir Isaac Newton to Mr. LeClerc: the former containing a dissertation upon the reading of the Greek text, I John, v. 7: the latter upon that of I Timothy, iii 16, published from authentick mss in the Library of the Remonstrants in Holland (London, 1754) Unpublished Scientific Papers of Isaac Newton: A Selection From the Portsmouth Collection in the University Library Cambridge, ed. A. Rupert Hall and Mary Boas Hall (Cambridge, 1962)

Suggested Reading on Newton Bertoloni Meli, Domenico, Equivalence and Priority: Newton versus Leibniz (Oxford, 1993)

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Bibliography

Buchwald, Jed Z., and Mordechai Feingold, Newton and the Origin of Civilization (Princeton, nj, 2013) Cohen, I. B., The Newtonian Revolution (Cambridge, 1980) —, and G. Smith, The Cambridge Companion to Newton (Cambridge, 2002), 2nd edn ed. R. Iliffe and G. Smith (Cambridge, 2016) Craig, John, Newton at the Mint (Cambridge, 1946) Dobbs, Betty Jo Teeter, The Foundations of Newton’s Alchemy, or ‘The Hunting of the Greene Lyon’ (Cambridge, 1975) —, The Janus Faces of Genius: The Role of Alchemy in Newton’s Thought (Cambridge, 1991) Dry, Sarah, The Newton Papers: The Strange and True Odyssey of Newton’s Manuscripts (Oxford, 2014) Ducheyne, Steffen, The Main Business of Natural Philosophy: Isaac Newton’s Natural-Philosophical Methodology (New York, 2012) Feingold, Mordechai, The Newtonian Moment: Isaac Newton and the Making of Modern Culture (New York and Oxford, 2004). Figala, Karin, ‘Newton as Alchemist’, History of Science, xv (1977), pp. 102–37 Goldish, Matt, Judaism in the Theology of Sir Isaac Newton (Dordrecht and Boston, ma, 2010) Guicciardini, Niccolò, Isaac Newton on Mathematical Certainty and Method (Cambridge, ma, 2011) —, Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736 (Cambridge, 1999) Harper, William L., Isaac Newton’s Scientific Method: Turning Data into Evidence about Gravity and Cosmology (Oxford, 2011) Iliffe, Rob, Newton: A Very Short Introduction (Oxford, 2007) —, Priest of Nature: The Religious Worlds of Isaac Newton (Oxford, 2017) Jacob, Margaret C., The Newtonians and the English Revolution, 1689–1720 (Hassocks, Sussex, and Ithaca, n\, 1976) Janiak, Andrew, Newton as Philosopher (Cambridge, 2008) Koyré, Alexandre, Newtonian Studies (Cambridge, ma, and London, 1965) Levenson, Thomas, Newton and the Counterfeiter: The Unknown Detective Career of the World’s Greatest Scientist (London, 2009) Mandelbrote, Scott, ‘“A Duty of the Greatest Moment”: Isaac Newton and the Writing of Biblical Criticism’, British Journal for the History of Science, xxvi (1993), pp. 281–302

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—, ‘Isaac Newton and the Exegesis of the Book of Daniel’, in Die Geschichte der Daniel-Auslegung in Judentum, Christentum und Islam, ed. K. Bracht and D.S. du Toit (Berlin, 2007), pp. 351–75 Nauenberg, Michael, ‘Newton’s Early Computational Method for Dynamics’, Archive for History of Exact Sciences, xlvi (1994), pp. 221–52 Newman, William R., Gehennical Fire: The Lives of George Starkey, an American Alchemist in the Scientific Revolution (Cambridge, ma, 1994) Pourciau, Bruce, ‘Radical Principia’, Archive for History of the Exact Sciences, xliv (1992), pp. 331–63 Principe, Lawrence, ‘The Alchemies of Robert Boyle and Isaac Newton: Alternate Approaches and Divergent Deployments’, in Rethinking the Scientific Revolution, ed. M. Osler (Cambridge, 2000), pp. 201–20 Schaffer, Simon, ‘Comets and Idols: Newton’s Cosmology and Political Theology’, in Action and Reaction: Proceedings of a Symposium to Commemorate the Tercentenary of Newton’s Principia, ed. Paul Theerman and Adele F. Seef (Newark, London and Toronto, 1993), pp. 206–31 —, ‘Glass Works: Newton’s Prisms and the Uses of Experiment’, in The Uses of Experiment: Studies in the Natural Sciences, ed. D. Gooding, T. Pinch and S. Schaffer (Cambridge, 1989), pp. 67–104 Shapiro, Alan E., Fits, Passions, and Paroxysms: Physics, Method, and Chemistry and Newton’s Theories of Colored Bodies and Fits of Easy Reflection (Cambridge, 1993) Smith, George E., ‘The Newtonian Style in Book ii of the Principia’, in Isaac Newton’s Natural Philosophy, ed. Jed Buchwald and I. Bernard Cohen (Cambridge, ma, 2001), pp. 249–313 Snobelen, Stephen, ‘“God of Gods, and Lord of Lords”: The Theology of Isaac Newton’s General Scholium to the Principia’, Osiris, xvi (2001), pp. 169–208 —, ‘Isaac Newton, Heretic: The Strategies of a Nicodemite’, British Journal for the History of Science, xxxii (1999), pp. 381–419 Westfall, Richard S., Never at Rest: A Biography of Isaac Newton (Cambridge, 1980)

acknowledgements

This book is a shortened and updated version rewritten in English of my Newton (Rome, 2011). I owe a great debt to several Newton scholars with whom I have corresponded in these last twenty years. Most notably, I should acknowledge that I have learnt a great deal about Newton’s mathematics from Tom Whiteside and Michael Nauenberg, Newton’s natural philosophy from Bernard Cohen and George Smith, Newton’s optics from Alan Shapiro, Jed Buchwald and Franco Giudice, Newton’s alchemy from Bill Newman and Larry Principe, Newton’s religion from Scott Mandelbrote, Rob Iliffe and Stephen Snobelen, Newton’s chronology from Jed Buchwald and Moti Feingold, and Newton’s philosophy from Mary Domski, Steffen Ducheyne, Andrew Janiak and Eric Schliesser. Raquel Delgado Moreira, Franco Giudice, Dmitri Levitin, Bill Newman, Larry Principe, Stephen Snobelen and Yoshimi Takuwa have provided useful comments on sections of this book. I thank them, as well as the series editor François Quiviger, of the Warburg Institute, for their kind help. I have profited immensely from the transcription of Newton’s manu­ scripts made available online by The Newton Project (directed by Rob Iliffe and Scott Mandelbrote – www.newtonproject.ox.ac.uk), The Chymistry of Isaac Newton project (directed by William Newman – http://webapp1. dlib.indiana.edu/newton) and The Newton Project Canada (directed by Stephen Snobelen – www.isaacnewton.ca). I thank Cambridge University Press for allowing me to draw upon my chapter ‘A Brief Introduction to the Mathematical Work of Isaac Newton’, in The Cambridge Companion to Newton, 2nd edn, ed. Robert Iliffe and George E. Smith (Cambridge, 2016), pp. 382–420, in Chapter Two (section on ‘The Methods of Series and Fluxions’) and Chapter Four (section on ‘Algebra and Geometry’).

photo acknowledgements

The author and publishers wish to express their thanks to the below sources of illustrative material and/or permission to reproduce it. Galleria dell’Accademia Tadini, Lovere, Bergamo (photo Studio Fotografico Da Re 2015 © Accademia Tadini, Archivio Fotografico): 1; collection of the author: 22; © Biblioteca Civica Angelo Mai e Archivi storici comunali, Bergamo: 33; © Biblioteca Nazionale Braidense, Milan and Ministero dei Beni e delle Attività Culturali e del Turismo: 15, 16; © Biblioteca Nazionale Marciana, Venice and Ministero dei Beni e della Attività Culturali e del Turismo: 38; © Bibliothèque de Genève: 30; © Bibliothèque Nationale de France, Paris: 5; photos Compomat s.r.l./ © Niccolò Guicciardini: 13, 17, 18, 23, 28 (courtesy Massimo Galuzzi), 34, 35; reproduced by kind permission of the Syndics of Cambridge University Library: 7 (xxi.41.14), 9 (le.5.24), 10 (Add. 3975, f. 15), 12 (m.4.31), 14 (Qq*.1.61 (A)), 20 (U*.4.35(C)), 21 (Williams 504), 25 (Add. 3975, f. 174v), 26 (Hh.15.44), 27 (m.6.11), 29 (Yorke. a. 31), 37 (n.9.19), 40 (Add. 3965, f. 39r); © Dean and Chapter of Westminster: 42, 43; photo Derby Museum Collection: 3; © Herzog August Bibliothek, Wolfenbüttel: 41; from Isaac Newton, Philosophiae Naturalis Principia Mathematica (London, 1687): 32; © Musée des Beaux-Arts, Bordeaux: 2; © Musée des Beaux-Arts, Nantes: 4; © National Portrait Gallery, London: 19, 39; © Royal Society Library, London: 11, 31, 36; from H. W. Turnbull, ed., The Correspondence of Isaac Newton, vol. i (Cambridge, 1959): 24; © Victoria and Albert Museum, London: 6.

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index

Illustration numbers are indicated by italics. Act of Toleration 184 Act of Uniformity 26 Adams, John Couch 15 alchemy 31, 103–17 Anaxagoras 168 Anaximander 138 ancient wisdom (prisca sapientia) 137–40 Anglo-Dutch War 26 Anne, Queen 129, 184, 187, 233 Anti-Christ 131 anti-Trinitarians 126–9 antimony 26 apple (falling in Newton’s garden) 72 Aratus 192 Archimedes 7, 216, 222 Argonauts 192 argument from design 199 Aristarchus of Samo 138 Aristotelianism causes 153, 205, 226 colours 54 cosmology 64, 65, 139 laws of motion 168 mathematical sciences 155



studied at Cambridge 35, 36, 37, 39 Arius 135–6 Ashley Cooper, Anthony, 1st Earl of Shaftesbury 27 Athanasius, St 135–6 Aubrey, John 148 Ayscough, Hannah 29–30 Ayscough, William 29, 33 Babington (family) 31 Bacon, Francis 8, 9, 35, 56, 64, 84, 148, 153 Baker, Henry, ‘Flowers of antimony’ 26 Bank of England 185 Barrow, Isaac geometry 123 Loggan, David, Isaac Barrow 19 and Newton’s De analysi 49–51 Newton’s mentor 39–41, 47, 63, 76–7, 232 optics 54 tired of mathematics 117 Barton, Catherine 15, 54, 185 Bate, John 32, 113, 9

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Bennett, James 81 Bentley, Richard 15, 178, 180, 198–213, 233 Berkeley, George 167 Bernoulli, Daniel 11, 174, 217 Bernoulli, Johann 11, 12, 174, 178, 197, 214, 216, 217 Bill of Rights 222 binomial theorem 43, 48–9 Blanchet, Louis-Gabriel, The Fathers François Jacquier and Thomas Le Seur 4 Blasphemy Act 128 Board of Longitude 187 Boas Hall, Marie 19 Bondi, Hermann 176 Boyle lectures 198 Boyle, Robert alchemy 105–6, 108–9 colours 36, 38, 55–6 experimental philosophy 39, 148 religion 34, 132–3, 198 and the Royal Society 8, 79–80, 83, 89 Brahe, Tycho 65, 66, 69 Breteuil le Tonnelier, Gabrielle Émilie de (Marquise du Châtelet) 9, 2 Brouncker, William 80 Brown, Dan 130 Bruno, Giordano 108 Buchwald, Jed 190 bucket (mental experiment) 162–3 Burnet, Gilbert 222 Burnet, Thomas 145

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Calandrini, Jean-Louis 12 Callippus 139 Callot, Jacques 23 The Hanging 6 Calvin, John (Jean) 23, 131 Caroline of Brunswick, Princess of Wales 224 Cassini, Giovanni Domenico 181 Charles i, King 22–4, 7 Charles ii, King 25–7, 79, 128, 182 Charleton, Walter 36, 37, 56, 109, 206 Chiron 192 chronology 188–93 civil wars 22–4 Clark(e), William 31, 33 Clarke, Samuel 126, 160, 162, 180, 225–6, 234 coefficient of restitution 207 Cohen, I. Bernard 19 Collins, John and ‘gaugers’ 47 and Newton’s alchemy 116 and Newton’s geometry 120, 122, 28 and Newton’s optics 86 papers 197 receives Newton’s work on series and fluxions 49–52, 232, 11 Comma Johanneum 136 Commonwealth of England 25 Conduitt, John 14, 16, 43, 54, 151 conservation laws 207 Convention Parliament 30, 183 Copernican system 66, 167, 173, 203

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Copernicus, Nicolaus (Mikołaj Kopernik) 65, 137, 138 corruption (of original religion) 125–6, 135–6 Cotes, Roger 87, 197–8, 225–6, 234 counterfeiters 185 Cromwell, Oliver 25, 80 Cromwell, Richard 25 Cudworth, Ralph 40 D’Alembert, Jean-Baptiste le Rond 11, 174 Da Vinci Code, The 130 Daniel (Book of ) 131 Darwin, Charles 7 De Moivre, Abraham 43 Declaration of Indulgence (second) 26 Dee, John 104 deism 28, 228 Democritus 138, 168 dendrites 113, 26 Des Maizeaux, Pierre 161 Desargues, Girard 123, 156 Descartes, René hypothetico-deductive method 83 laws of motion 144, 159–60, 163, 168, 207–8 mathematics 36, 44–7, 50, 52, 118, 121, 123, 155–6, 195 mechanical philosophy 35, 37–8, 40, 71, 87–8, 98, 109, 151, 132, 212 muscular motion (volition) 100, 134

Index



optics 54–6, 60–61 planetary system 8, 71–2, 75, 144, 175, 178, 227 Devil, the (and demons) 127 Digby, Kenelm 97 Dobbs, Betty Jo Teeter 19, 99, 133 Dollond, John 63 Edict of Nantes 181–2 Einstein, Albert 7, 163, 167 epicureanism 8, 37, 133, 199–200, 205–6 Erasmus, Desiderius 131, 136 ether 92–101 Euclid 44, 124 Eudoxus 139 Euler, Leonhard 11, 12, 49, 72, 174, 217, 218 Eusebius of Caesarea 193 experimentum crucis 33, 52, 57–9, 64, 81, 86, 143, 176, 193, 232, 13 Faraday, Michael 14 Fatio de Duillier, Nicolas 17, 139, 181–2, 195, 233, 30 Feingold, Mordechai 190 Fermat, Pierre de 45, 49 Ferrier, Jean 61 Feyerabend, Paul 19 Ficino, Marsilio 20, 138 Flamsteed, John 71, 145, 186–7 fluxions 43, 49–54, 73–4 Fontenelle, Bernard le Bovier de 14 Freemasonry 79, 104 Fresnel, Augustin-Jean 14

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Galilei, Galileo conflict with the Church 84, 212 Dialogo 36, 151 as an icon of science 7 laws of motion 162, 168, 171–2 mathematics 120 planetary system 65–6 Gassendi, Pierre 36, 39, 101, 109, 110, 206 geometry 117–23 George i, King 187, 221 Gilbert, William 69 Glanvill, Joseph 84, 21 Glorious Revolution 27–8, 128, 182–4, 213, 221 gnosticism 104, 125–6, 135, 223 Grassaeus, Johannes (Grasshof ) 115 gravity 72–3, 89–91, 98, 143–53, 170–79 Great Fire of London 27, 50, 80 Greenham, Paul 116 Gregory, David 43, 63, 135, 139, 216 Gregory, James 48, 62, 117 Gresham College 79 Hale, Matthew 110 Hall, Alfred Rupert 19 Halley, Edmond August 1684 visit to Newton 66, 233 comet 145 and Flamsteed 187 Murray’s portrait 31

264

ode 199, 211 and the Principia 146–50 and the Royal Society 8, 153 Hanoverian Succession 184, 222 Harris, John 115, 233 Hartlib, Samuel 109 Hartsoeker, Nicolaas 226 Hermes Trismegistus 17, 19, 103–4, 105, 107, 125, 135 Hevelius, Johannes (Jan Heweliusz) 14 Highmore, Nathaniel 109 Hipparchus 190 Hobbes, Thomas 21, 35, 36, 39, 56, 206, 212, 222 Hooke, Robert Micrographia 38, 55, 81, 94, 20 optics 55, 64, 80–84, 86, 88–9, 91, 94, 176–7 portraits 186 theory of planetary motion 143–8, 233 Hudde, Joannes 47 Huygens, Christiaan gravitation 150, 176–8 horology 46, 233 law for uniform circular motion 72, 74 laws of motion 159, 168, 218 mathematics 120, 123, 195 and Nicolas Fatio de Duillier 181 optics 59, 86, 88, 91 and the prisca sapientia 139, 140 time and space 167 Hylarchic principle 99 hypotheses non fingo 210–11, 227

265

idolatry 125 Iliffe, Robert 223 inertia 159–60, 206–7 interference of light 91–5, 22 Jacquier, François 11, 12, 4 James ii, King 26, 27, 149, 182–3, 213 Jason 192 Jeffreys, George 183, 233 Jones, William 196, 233, 38 Josephus (Titus Flavius Iosephus = Yosef ben Matityahu) 188, 193 Kabbalah 103–4, 106, 107, 125, 140, 223 Kant, Immanuel 166, 179 Keats, John 19, 99 Keill, John 195–7, 214, 220, 233 Kepler, Johannes harmony of the world 97 laws of planetary motion 66–70, 72, 74, 147, 175 mathematics 49 planetary system 65, 68–9, 169, 203 Keynes, John Maynard 16–17, 104, 228 Kinckhuysen, Gerard 118 Klingenstierna, Samuel 63 Kneller, Godfrey, Isaac Newton 1 Kuhn, Thomas 19 La Hire, Philippe de 156 La Peyrère, Isaac 189

Index

Lagrange, Joseph-Louis (Giuseppe Luigi) 11, 174 Laplace, Pierre-Simon de 11, 174 Laud, William 22–3 laws of motion 168–70, 217–18, 40 Le Seur, Thomas 11, 12, 4 Leibniz, Gottfried Wilhelm alchemy 107 controversy with Newton 16, 50, 179, 180, 195–7, 207–8, 211, 214–28 correspondence with Samuel Clarke 160, 162 gravitation 8 and Madame du Châtelet 9 mathematics 11, 49 planetary system 71–2 pre-established harmony 134 Sheits, Andreas, Gottfried Leibniz 41 time and space 160, 162, 167 Lely, Peter (Pieter van der Faes) 80 Limojon de Saint-Didier, Alexandre Toussaint de 116, 5 Liveing, George Downing 15 Locke, John 27, 101, 106, 107, 135, 136, 180, 184, 224 Loir, Marianne, Gabrielle Émilie de Breteuil 2 Louis xiv, King of France 25, 27, 181, 182 Luard, Henry Richards 15 Lucas, Anthony 89

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Lucasian Chair of Mathematics 7, 28, 40–41, 76–9, 117, 128, 184 Lucretius (Titus Lucretius Carus) 109, 168, 200 Mach, Ernst 167 Machiavelli, Niccolò 21 Machin, John 151 magnetic philosophy 69–70 Maier, Michael 106, 107, 114 Maimonides, Moses (Moshe ben Maimon) 17, 19 Malebranche, Nicolas 178 Mandelbrote, Scott 127 Manuel, Frank Edward 19, 223 Marsham, John 188, 190, 37 Marvell, Andrew 26 Mary ii, Queen 22, 183–4 Mary of Modena, 2nd wife of James ii 26 mass 159 mathematical magic 32 mechanical philosophy 40, 87 Mede, Joseph 131, 29 Melanchthon, Philipp (Philipp Schwartzerdt) 131 mercury poisoning 181 Mersenne, Marin 46 Merton, Robert King 34 mesmerism 104 millenarianism 23, 131–2, 137, 189, 29 Milton, John 28, 135 Mint, Royal 185 Molière (Jean-Baptiste Poquelin) 226

266

Montagu, Charles, 1st Lord Halifax 28, 151, 184–5, 221 Montmort, Pierre Rémond de 178 Moray, Robert 79 More, Henry 31, 35, 39–40, 99 Moses 124, 125, 135, 137 Murray, Thomas, Edmond Halley 31 Musaeus 192 muscular motion 99–100 musical scale 95–6 Mydorge, Claude 61 Nauenberg, Michael 145 neo-Platonism 40, 103, 105, 107, 110, 114, 125–6, 135, 138, 206 nervous breakdown 181 Newman, William Royall 59, 104, 107, 109, 115 Nicaea (council) 135 Noah 125, 137, 140, 192 Numa Pompilius 138, 140 Oates, Titus 182 Oldenburg, Henry (Heinrich) 80, 91 organic geometry 155–6 Ørsted, Hans Christian 14 Oughtred, William 44, 123 Pagel, Walter 19 Paley, William 213 Pappus (Pappos) 47, 121, 155 Paracelsus (Theophrastus von Hohenheim) 20, 108, 112, 228

267

Parker, George, 2nd Earl of Macclesfield 196 Parker, Thomas, 1st Earl of Macclesfield 196, 222 Pascal, Blaise 123, 156 Pellet, Thomas 25 Pemberton, Henry 52, 152, 234 Pétau, Denis 188 Philolaus 138 Pitcairne, Archibald 115 plague 27, 42–3 Plato 97 poltergeist 84, 105 Pope, Alexander 211 Popish Plot 182 Popper, Karl R. 19 Principe, Lawrence 104, 109 priority controversy on calculus (with Leibniz) 196–7, 214–20 probabilism 83–4 prophecies 16, 20, 40, 130, 136–7 Ptolemaic system 64–5 Ptolemy, Claudius (Klaúdios Ptolemaîos) 64–5, 137, 203 Purcell, Henry 78 Pythagoreanism 96–7, 114, 124–6, 138–40, 228 quantity of motion 159 Ray, John 198 Restoration 25–7, 35, 79, 83, 128–9, 212–13 Revelation (Book of ) 131 Richer, Jean 158 Rossi, Paolo 19, 81

Index

Royal Society 63, 79–80, 83–6, 185–7, 36 Rudolf ii, Emperor 20, 115 Salvemini, Giovanni Francesco (aka Jean de Castillon) 200 Scaliger, Joseph 188 Scott, James, 1st Duke of Monmouth 183 Second Coming of Christ 131–2, 189–90 Seeman, Enoch (atelier of?), Sir Isaac Newton 39 Sendivogius, Michael (Michał Se˛dziwój) 107, 115 sight (sense of ) 39, 63, 95–6, 10 Simon, Richard 136 Skinner, Quentin 21 Sloane, Hans 195 Smith, Barnabas 30, 37 Snell’s law 55, 93 Socinianism 24, 28, 128, 135, 228 Sophia of Hanover, Electress 184 Sozzini, Fausto 28 Sozzini, Lelio 28 Spinoza, Baruch 35, 132–3, 212 stability of planetary system 203 of stars 201–2 Starkey, George (aka Eirenaeus Philalethes) 109, 114 Steiner’s theorem 120, 28 Stevin, Simon 69 stibnite 112, 26 Stillingfleet, Edward 199 stoicism 99, 110, 114, 206 Stokes, George Gabriel 15

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Straka, Gerald 213 Stukeley, William 43, 72 telescope 60–63, 81, 16 Temple of Jerusalem 131, 138, 192–3 temples (pagan) 138, 140 Test Act (1673) 26, 27 Thirty Years War 23 three-body problem 174, 35 Treaty of Dover 25–6 Trojan War 192 Valla, Lorenzo 131 Van Helmont, Jan Baptista 109, 110 Van Heuraet, Hendrik 47 Van Schooten, Frans 36, 44, 45 Varen, Bernhard (Varenius) 51, 145 Varignon, Pierre 214 Viète, François 44, 45 viv viva 207 Voltaire (François-Marie Arouet) 8, 9, 228 vortex theory of planetary motions 71–2, 75, 145, 175, 178, 227 Vossius, Gerardus (Gerritt Vos) 188 Vossius, Isaac (Vos) 188 Wallis, John laws of motion 159, 168 mathematics 36, 37, 44, 47–8, 87, 123, 195, 232 and the Royal Society 80

268

Ward, Seth 78 Weber, Max 34 Westfall, Richard Sam 19, 223 Westminster Assembly 80 Westminster School 80 Wharton, Henry 78 Whiston, William 28, 126, 128, 184, 194, 233 Whiteside, Derek Thomas 19, 117 Wickins, John 33 Wilkins, John 80 William iii of Orange-Nassau, King 22, 182–4, 185, 213, 221 witches 84, 21 Wolff, Christian 9, 214 Wood, Anthony à 148 Woolsthorpe 29–33, 8 Wren, Christopher 70, 79, 80, 146–7, 159, 168 Wright of Derby, Joseph, A Philosopher Giving a Lecture on the Orrery 3 Yahuda, Abraham 16 Yates, Frances Amelia 19 Young, Thomas 14