Adriaen Verwer (1654/5–1717) and the first edition of Isaac Newton's Principia in the Dutch Republic

Abstract

The Amsterdam-based merchant and mathematics enthusiast Adriaen Verwer (1654/5–1717) was one of the few in the Dutch Republic to respond to the first edition of Newton's Principia (1687). Based on a close study of his published work, his correspondence with the Scottish mathematician and astronomer David Gregory (1659–1708), and his annotations in his own copy of the first edition of the Principia, I shall scrutinize the impact of Newton's ideas on Verwer's thinking. The proposed analysis, which will add nuance to earlier findings, also has broader implications for our understanding of the introduction of Newton's ideas in the Dutch Republic, as will be shown.

Preamble: one of Newton's ‘most valiant soldiers’?

When the main character of this essay, Adriaen Verwer (1654/5–1717), was buried in the Oude Kerk in Amsterdam,¹ the Rotterdam poet Jan Suderman (1680–1724),² who was married to Verwer's niece, wrote the following verses on the occasion of his uncle's death:

Oh, eternal honour of the English,

Oh, great Newton, who carries the torch of that knowledge for others,

Whose wisdom supports Christ's religion,

You lose, now Verwer is buried,

One of your most valiant soldiers.³

In these verses, Suderman presents Isaac Newton as an important figure whose natural philosophy buttressed Christian faith, and Verwer as one of Newton's most ardent supporters. Was it the case, one might ask, that Verwer was one of Newton's ‘most valiant soldiers’? Does Suderman's poem indeed coincide with historical reality, and, moreover, what was the impact of Newton's work, and especially the first edition of the Principia,⁴ on Verwer's intellectual project? In this essay, I seek to provide answers to these questions.

In a seminal paper, Rienk Vermij argued that, ‘mainly under the influence of informal contacts with David Gregory and his circle’, ‘Newtonian ideas’ were put to use by a group of ‘mathematical amateurs’ in Amsterdam of which Verwer was part, to ‘demonstrate the fallaciousness of Spinoza's geometrical method and uphold revealed religion’.⁵ The group was, in Vermij's view, united in their endeavour to respond to ‘the challenge of Spinozism’.⁶ The members of this group were extremely unhappy that ‘the mathematics they cherished as a way to truth should really lead to unacceptable conclusions’, as became clear from Baruch Spinoza's (1632–77) Ethica ordine geometrico demonstrata (Ethics Demonstrated in Geometrical Order), which was published as part of his Opera posthuma (1677). According to Vermij, Newton's work did not radically transform Verwer's thought; rather, the latter picked up elements that fitted well with his own ‘frame of mind’ so that Newton's ideas, which spread, ‘not over ideological interest-groups, but by way of existing scholarly networks’, were fitted ‘into Verwer's preconceived world view’.⁷

Eric Jorink and Huub Zuidervaart, who have picked up on Vermij's idea of the ‘use(fulness)’ of Newton, have gone so far as to claim that ‘Newton became so successful not because he was right, but because he was useful’ for responding to local needs, such as providing a response to Spinoza's thought.⁸ Recently, Emma Mojet has tried to provide substance to Jorink and Zuidervaart's claim by looking at Verwer's case. Based on new sources—namely Verwer's copy of the first edition of the Principia, which contains numerous annotations made by him,⁹ and his correspondence with David Gregory—she has concluded that, ‘In order to refute Spinoza, Verwer searched for a different mathematics and a better mathematical method, and he found models of it in Newton's Principia.’ Moreover, ‘With Newton's example of proper mathematical reasoning, Verwer could argue that there was indeed an active God in the universe, thereby refuting Spinoza’,¹⁰ which suggests that Newton's Principia was significant for Verwer's project, and especially for his criticism of Spinoza. In this essay, I would like to add nuance to these earlier findings. In addition, by contextualizing Verwer's theological views, I shall shed new light on his work.

Verwer's case is significant, because he was one of the few in the Dutch Republic who studied the first edition of the Principia. Therefore, he is vital for our understanding of early responses to Newton's work in the Republic. Once the Principia came off the press in July 1687, Christiaan Huygens (1629–1695) and Burchard de Volder (1643–1709) each received a presentation copy.¹¹ Although de Volder never endorsed nor taught Newton's natural philosophy, he is reported to have intensely studied the Principia after its publication.¹² Jean Le Clerc (1657–1736), the Swiss polymath, theologian and professor of philosophy, Hebrew and classics at the Remonstrant Seminary in Amsterdam, also studied the first edition, as we will see in what follows.¹³

Huygens, who joined the Royal Society in 1663, was very knowledgeable about the Principia. He encountered Newton's work early on: in 1672, the secretary of the Royal Society, Henry Oldenburg (c.1618–1677), informed Huygens about Newton's reflecting telescope, and shortly afterwards about his new theory of light and colours.¹⁴ Huygens’ response to Newton's telescope was favourable, and he deemed Newton's theory of light ‘very plausible’, although he raised several issues of concern.¹⁵ As a result of the exchange of thought between Huygens and Newton, through letters sent via Oldenburg, Newton modified certain claims relating to his theory of the heterogeneity of white light in 1673.¹⁶ In the same year, Huygens’ Horologium oscillatorium was published, a work which Newton greatly admired.¹⁷ Also in 1673, a letter by Huygens on Newton's telescope appeared in a volume of the Journal des sçavans, which was published in Amsterdam.¹⁸

When Nicolas Fatio De Duillier (1664–1753) reported that Newton's Principia was about to be published, Huygens wrote back stating that he wanted to see it, but hoping that it would not contain the supposition of attraction.¹⁹ A year later, Huygens told his brother Constantijn that he wanted to meet Newton, and that he admired the ‘inventions’ in the Principia.²⁰ In June 1689, he travelled to England to visit his brother. During his trip, he met Newton on several occasions, and he gave an account of his Traité de la lumière … avec un discours de la cause de la pesanteur (1690) at the Royal Society.²¹ Although, as is well known, to Huygens the notion of attraction seemed unintelligible and ‘absurd’,²² he was genuinely impressed by many of the results obtained in the Principia, and he endorsed the inverse-square law, at least for celestial bodies, which indicates that Huygens was critical of universal gravitation.

However, it is important to note that Huygens offered empirical arguments against universal gravitation. He tried to marshal evidence for his own spherical vortex theory by drawing on measurements with seconds-pendulums taken during an expedition on the Alcmaer from the Cape of Good Hope to Texel in 1687. He wrote a report on the measurements that were collected during the expedition to the directors of the Dutch East India Company, which he later mentioned in Traité de la lumière.²³ Whereas, in Huygens’ account, variation of gravity with latitude results only from the centrifugal forces produced by the earth's rotation, according to Newton it results from both centrifugal forces and gravitational forces on a non-spherical earth. As a result, the variation of surface gravity with latitude is larger according to Newton's theory than it is according to Huygens’. Having determined that the centrifugal effect of the earth's rotation is 1/289th of the force of gravitation at the equator,²⁴ Huygens could calculate how much seconds-pendulums needed to be shortened at different latitudes. He then compared the results of his calculations with Newton's and with the observed measurements. Although based on a limited set of data, the measurements collected on the Alcmaer favoured Huygens’ theory.²⁵

Huygens sent the report to both Johannes Hudde (1628–1704) and de Volder for review, which means that they may have been aware of the importance of the empirical argument that Huygens was putting forward against universal gravitation. Hudde, who was indisposed owing to a fever, replied that he had no time to study the report in detail.²⁶ De Volder sent a generally positive report on Huygens’ results to the directors of the Dutch East India Company, in which, however, he cast doubt on Huygens’ value for the difference in longitude between the Cape of Good Hope and Texel.²⁷ The Scottish mathematician and astronomer David Gregory (1659–1708), to whom we will return in what follows, was fully aware of the significance of Huygens’ argument, as is clear from a memorandum he composed on 11 November 1691.²⁸

Little is known about the distribution of the first edition of the Principia in the Dutch Republic. Once it had appeared in early July 1687, Edmond Halley (1656–1742), who published Newton's magnum opus at his own expense, made over a portion of the edition to the London bookseller Samuel Smith (1658–1707). Many of these ‘Smith’ copies were exported to the Continent.²⁹ In a letter in 1687 from the Amsterdam-based publisher and bookseller Johannes Janssonius van Waesberge II (1644–1705) to Smith, an order of ‘100 Newton’ is mentioned, at a total cost of £966 10s.³⁰ The high price might be an indication that the books ordered were copies of the Principia.³¹ There is no way of telling how many of these copies were sold, nor when or to whom. In the summer of 1687, Smith visited the Dutch Republic in August and Flanders in the first half of September, and he may have sold copies of the Principia during his trip.³² Two or three years after the publication of the Principia, the Leiden publisher and bookseller Pieter van der Aa (1659–1733) returned to Smith seven of the 12 copies of the Principia that he had tried to sell in Frankfurt.³³ In a letter of 1690 from the Rotterdam-based publisher Reinier Leers (1654–1714), whom Verwer called a ‘friend’,³⁴ to Smith, Leers mentioned the possibility of returning ‘some copies of Newton’, which may have been copies of the Principia, as a way of paying Smith.³⁵

A Mennonite merchant in Amsterdam

Adriaen (Pieterszoon) Verwer was born in Rotterdam in 1654 or 1655.³⁶ His father, the merchant Pieter (Adriaenszoon) Verwer, was a deacon of the Mennonite congregation of the Waterlanders in Rotterdam. The Waterlanders derived their name from Waterland, a region in the north of the Dutch Republic. They were more liberal and progressive than other Mennonites, and they did not have a negative attitude towards worldly affairs. They began calling themselves ‘Waterlanders’ (‘doopsgezinden’) in order to distinguish themselves from other Mennonite parties.³⁷ Many Mennonites were economically active, and interested in cultural and scientific matters.³⁸ In 1655 five Rijnsburg Collegiant teachers were admitted to the congregation of the Waterlanders, including the surgeon Jacob Ostens (1630–1678).³⁹ Adriaen's father and others supported the admittance of these Rijnsburg Collegiants. Given their liberal and tolerant stance, Collegiants openly discussed Socinianism, millenarianism and chiliasm, and the teachings of René Descartes (1596–1650) and Spinoza.⁴⁰ Collegiants, who were characterized by an anti-clerical, anti-confessional and anti-formalist attitude, endorsed ‘free prophecy’, namely the interpretation of the Scriptures by the individual believer, and freedom of speech during their meetings (‘colleges’), which were held in the vernacular language; and they practised charity, tolerance and piety. They promoted a return to the original apostolic church and they were particularly averse to churches, dogma and clerical supervision.⁴¹ The Rijnsburg principles, however, came into conflict with the views of the more conservative members of the Mennonite congregation, which resulted in tensions. Eventually, the two parties split and went their own ways.

Pieter Verwer was also a member of an Erasmus-inspired, irenic and tolerant circle of friends who met regularly from 1656 to discuss literary, political, philosophical and religious issues.⁴² The group was composed of individuals from different confessional and professional backgrounds, including the Collegiant tile manufacturer and poet Joachim Oudaen (1628–1692); the translator, publisher and bookseller Frans van Hoogstraten (1632–1696), who was drawn to Jansenism; the Remonstrant publisher Isaac Naeranus (?–1717); the Collegiant poet Joost van Geel (1631–98); the Remonstrant regent Adriaen Paets (1632–1686); the Walloon Reformed painter and poet Heijmen Dullaert (1636–1684); the Remonstrant preacher Gerard Brandt de Jonge (1657–1683); Herman van Zoelen (1625–1702), who was a member of the Rotterdam city council; the Remonstrant merchant and poet Frans de Haes (1656–1690); the Collegiant wine merchant and weaver Johannes Bredenburg (1643–91); Oudaen's brother-in-law; and the surgeon Ostens. Very little is known about Verwer's early years and his education, but Oudaen, who gave philological instruction to some of the younger members of the Erasmus-inspired circle, seemed to have played a significant role in his education.⁴³ While initially being receptive to Spinoza's earlier work, Oudaen vehemently opposed the Ethics, ⁴⁴ and in 1683 he sent a letter to Verwer in which he expressed his doubts about the successful outcome of his refutation of the Ethics, ’t Mom-aensicht der atheistery afgerukt (The mask of atheism torn off) (1683), to which we will return later.⁴⁵

The first traces of Adriaen Verwer in our historical records appear in a professional context. Between 1676 and 1678, he worked as a servant for the Rotterdam merchant Willem Pedy (c.1636–1710), who initiated him into the world of sea trade and maritime law.⁴⁶ Verwer rapidly acquired expertise in maritime law and, because of this expertise, he was consulted during the preparation of the Ordonnance de la marine (1681), which was established under Jean-Baptiste Colbert's administration during the reign of Louis XIV.⁴⁷ Later Verwer published a treatise on maritime law, average and bottomry.⁴⁸ In 1680, he moved to Amsterdam ‘because of the trade’ (‘om den Koophandel’), where he would die on 23 March 1717.⁴⁹

In 1680 the Amsterdam population had grown to approximately 210,000–220,000 inhabitants.⁵⁰ During the Dutch Golden Age in the seventeenth century, Amsterdam was one of the wealthiest cities in the world, one of the most important centres of (transit) trade, a site of information exchange⁵¹ and conspicuous consumption,⁵² and an important centre for the production of luxury goods and books in Europe, ‘boasting over 270 booksellers and printers in the period between 1675 and 1699’.⁵³ The principal seat of the Dutch East India Company, which was founded in 1602, was in Amsterdam. Although during the second half of the seventeenth century the Amsterdam trade continued to grow, it did so to a lesser degree than it had done during the first half. And even in Amsterdam, one of Holland's most tolerant cities, there were clear limits to what could be uttered and published.⁵⁴

Verwer embodied what the humanist Casparus Barlaeus (Caspar van Baerle; 1584–1648) had called the mercator sapiens in the inaugural address which he delivered in 1632 on the occasion of the foundation of the Athenaeum Illustre of Amsterdam.⁵⁵ Barlaeus argued that commerce, wealth and learning could and should go hand in hand, thereby promoting the ideal of the mercator sapiens, a hybrid figure who was to be well versed both economically and intellectually. More importantly, Barlaeus tried to free commerce from the religious suspicion and moral anxieties that it incited; in his mind ‘the merchant could do good even when keeping the benefit of his activities rather than only by giving away his wealth; commerce could itself be among the best pursuits of human life’.⁵⁶

In 1688 Verwer married Hester Pellewijk, with whom he had three children: Elisabeth (b. 1691), Jo(h)anna (b. 1694) and Pieter (b. 1696).⁵⁷ The Verwer family is known to have lived in Keizersgracht at what is now no. 232.⁵⁸ Verwer and his wife were baptized on 9 February 1689 in the Mennonite congregation of the Lamb and Tower (Lam en Toren).⁵⁹ He also served as a deacon for the Lamb and Tower between 1697 and 1702.⁶⁰ Verwer's Inleiding tot de christelyke Gods-geleertheid (Introduction to Christian theology) appeared in 1698.⁶¹

In 1707 Verwer published a linguistic study of the Dutch language and its grammar.⁶² According to him, the Dutch language was originally characterized by regularity; an important part of his linguistic project was therefore to uncover the rules underlying Dutch grammar. He argued that analogy (‘analogie’) was one of the methodological tools to accomplish this, and that it was founded on ‘the natural axiom’ according to which ‘like arises from like’.⁶³ Jan Noordegraaf has claimed that this axiom finds its origin in Newton's second regula philosophandi, ⁶⁴ according to which ‘the causes assigned to natural effects of the same kind are the same’.⁶⁵ However, in linguistics, analogy had been in use long before the Principia became available,⁶⁶ and refers to an agreement between words, on the basis of which existing words can take on a different form or new words can be formed. Analogy in linguistics has little to do with the contents of the second regula philosophandi, which stipulates that causes that have been shown to be necessary and sufficient for their effects should be minimized as far as possible.⁶⁷ The claim that it finds its origin in Newton's second regula philosophandi, which Verwer did not mention in his published work, is therefore to be dismissed as speculation. Verwer's linguistic studies did not embody what has been called ‘linguistic Newtonianism’.⁶⁸

Chaining the hellhound

When in 1677 Spinoza's Ethica was published, many of Verwer's contemporaries were outraged, and as a consequence Spinoza's claims were vehemently attacked. The Dutch Reformed authorities took action, and managed to convince the Supreme Court of Holland, Zeeland and West Friesland to place an embargo on the Opera posthuma in 1678, which was shortly afterwards also put on the index of forbidden books by Rome.⁶⁹ Verwer's contemporaries were appalled by the claims which Spinoza defended, inter alia his credo ‘Deus, seu Natura’, his necessitarian thesis in Proposition 33 of Part 1 according to which ‘things could not have been produced by God in any other order than is the case’,⁷⁰ and his attack on final causes in the appendix to Part 1, by which he undermined the foundations of physico-theology.⁷¹ They were especially incensed by the geometrical order, i.e. by its ‘intimidating array of definitions, axioms, propositions, demonstrations and corollaries’,⁷² which Spinoza used to demonstrate his ideas, because this gave the impression to its readers that they were established demonstratively with absolute certainty.⁷³

In his Dictionaire historique et critique (1697), the Rotterdam-based philosopher Pierre Bayle (1647–1706) described Spinoza as ‘the first to have reduced atheism to a system and to have made a doctrine out of it that is connected and bound together in the ways of the geometers’.⁷⁴ In Wederlegging van de Ethica of Zede-Kunst (Refutation of Ethics or Morality), the Dordrecht-based grain-broker Willem van Blijenbergh (1632–1696) warned that many of the readers of the Ethics, especially the unskilled, would be inclined to endorse the claims developed in it because it had the appearance of a mathematical work.⁷⁵ In 1678, the apostolic vicar of the Dutch Mission, Jan van Neercassel (1625–1686), reported to Rome that Dutch non-Catholics were enticed by Spinoza's ‘philosophy and the hollow fallacy according to the teaching of geometrical people’.⁷⁶

A first strategy for refuting the Ethics was to take issue with Spinoza's definitions and axioms. This strategy was followed, for instance, by the Socinian Frans Kuyper (1629–1691), who anonymously published a repudiation of the Ethics in which he called the veracity of Spinoza's key definitions and axiom into question. His refutation was appended to the Dutch translation of Henry More's (1614–1687) criticism of Spinoza's concept of substance.⁷⁷ Kuyper vehemently rejected the idea that Spinoza had proven ‘his atheistic theses mathematically, that is infallibly’.⁷⁸ Another strategy to counter the Ethics was to argue that the very method which Spinoza used was fundamentally flawed. As we will see in what follows, this was the strategy followed by Verwer.

Three years after his arrival in Amsterdam, Verwer's ’t Mom-aensicht der atheistery afgerukt (The Mask of Atheism Torn Off) was published; according to Jonathan I. Israel, it ‘provides an intriguing glimpse into the fraught world of amateur philosophical debate in Amsterdam in the early 1680s’.⁷⁹ It contains a refutation of Spinoza's Ethics (1677).⁸⁰ Oudaen's accompanying poem, which he sent on 5 July 1683, after having received a copy of ’t Mom-aensicht, as Verwer recorded at the end of a letter which Oudaen sent on 2 July,⁸¹ stated that, in this work, Verwer had ‘chained the hellhound [i.e. Spinoza] and subdued its barking from three throats’.⁸² Verwer was exposed to Spinoza's writings for the first time in 1682, upon which he immediately started working on ’t Mom-aensicht, which he finished shortly thereafter, according to his own testimony.⁸³ He came to know Spinoza's work through contact ‘with some wise men, now mostly deceased’.⁸⁴ According to Verwer, in his Ethics Spinoza ‘tricked the entire world’, because he demonstrated the consequences of certain hypotheses without proving these very hypotheses.⁸⁵ Followers of Spinoza blindly endorsed Spinoza's unproven suppositions.⁸⁶

Verwer argued that all demonstrations of the truth of a proposition are based on principles (gronden) that are grounded either in entia realia, i.e. in things that actually exist and that can only be known a posteriori,⁸⁷ or in entia rationis, i.e. things that are simply presupposed by our reason (verstand). If a demonstration is based on entia realia, which is the case in physics for instance, then the conclusion derived from this demonstration—supposing that the conclusion is inferred correctly—will make a truthful statement about the world. If, however, a demonstration is based on entia rationis, which is the case in mathematics, then the conclusion derived from this demonstration—again, supposing that the conclusion is inferred correctly—will simply deduce the consequences of what is being presupposed. Whereas demonstrations based on entia realia have ‘an undeniable persuasiveness for any intellect’, demonstrations based on entia rationis have no such persuasiveness.⁸⁸ This epistemological distinction testifies to Verwer's empirical bent. He did not criticize the usefulness of mathematics as such; rather he wanted to convey that mathematics cannot provide us with truths about the actual world. Correspondingly, he advocated the idea that, if we wish to obtain real knowledge, we should rely on ‘pure natural reasoning’ (‘suyvere’ or ‘bloote nateurlijke redenering’), i.e. on reasoning drawn from phenomena, and thus freed from the yoke of arbitrary suppositions. If we rely on ‘natural’ reasoning, we will be able to uncover both eternal and temporal truths, he asserted.⁸⁹

In ’t Mom-aensicht, Verwer tried to show that the doctrine of dependence (dependentie), according to which creation depends on God, is correct, while the doctrine of independence (independentie), according to which creation is independent from God, is mistaken. He pointed out that the doctrine of independence is endorsed by atheists (God-verloochenaers) such as Niccolò Machiavelli, Lucilio Vanini, Thomas Hobbes and Spinoza.⁹⁰ In order to prove the doctrine of dependence ‘by means which our opponents approve in their own writings’,⁹¹ Verwer argued that local motion (motus localis) is not essential to bodies. If it were essential to bodies, then there would be no bodies at rest. He also argued that the first cause of local motion is to be found in a cause that is different from and external to matter, and that this cause is God.⁹² Verwer used proofs grounded in what he believed to be empirical considerations to argue for God's existence. Immediately before providing the proofs for these claims, he pointed out that the figments of the defenders of independence are shattered ‘against the firm-standing wall of experience’.⁹³ His proofs are structured as follows. First, there is a statement of the proposition (voorstel) that needs to be proved; second, there is a demonstration (betooging) of that proposition; and, third, there is a concluding scholium (leering) explicating the broader significance or implications of what has been proved. Verwer's proofs are structured ‘mathematically’, i.e. they follow the format propositio–demonstratio–scholium, but the premises used are drawn from phenomena, showing yet again that there is a significant empirical orientation in his thinking. He remarked that his conclusion that God is the direct or indirect cause of local motion, and other conclusions concerning God's attributes, are ‘obtained solely from natural reason’.⁹⁴

Verwer referred to Johannes Bouwmeester's Dutch translation of Philosophus autodidactus (1671), which contained the story of a fictitious feral child living alone on a deserted island who through critical inquiry acquires knowledge about himself, nature and God ‘without any human interaction or divine revelation’.⁹⁵ When this individual finally enters the civilized world at an adult age, he notices that the knowledge he has acquired through critical inquiry corresponded to the ideas expressed in the Qur'an. Verwer pointed out that, when Bouwmeester's translation appeared, some fanatics used this story ‘to prove that through reason one could rise as high as through the revelations in our New Testament’.⁹⁶ Therefore, contrary to what has been claimed,⁹⁷ Verwer did not endorse the view according to which all religious truths can be learned through natural reason.

After having summarized the main theses developed in Spinoza's Ethics,⁹⁸ which is written in ‘an order that is common in mathematics’,⁹⁹ Verwer painstakingly analysed Spinoza's argumentation. Without going into further detail, the upshot of his analysis is that Spinoza's Ethics assumes independence rather than proving it:

When one realizes that this [doctrine of] independence, which is the only bedrock of Spinoza's philosophy, is not only presupposed but also by its very nature devoid of any proof so that it is and will be impossible for him or anyone else ever to substantiate it, and, moreover, when one has already learned that the [doctrine of] dependence is on solid ground, what can be concluded about the entire building that is based on independence? Nothing else than that it will crumble down in an instant as soon as the storms and winds of dependence strike it with force.¹⁰⁰

It has been claimed that Verwer's opinion of Spinoza's analysis of the passions is positive.¹⁰¹ However, he clearly rejects Spinoza's treatment of the passions insofar as it is ‘grounded in independence’.¹⁰² In ’t Mom-aensicht, he offers ‘mathematical’ demonstrations, in the sense that his proofs are structured according to the scheme propositio–demonstratio–scholium, a scheme that structurally corresponds to the form of argumentation of Spinoza's Ethics.¹⁰³ However, epistemologically there is a major difference between Verwer and Spinoza, for the former urges that proper knowledge about the world is to be based, not on entia rationis, but on entia realia.

Entering the Republic of Letters

Verwer corresponded with David Gregory,¹⁰⁴ who studied mathematics at the University of Leyden and left his position as professor of mathematics at the University of Edinburgh to become Savilian Professor of Astronomy at the University of Oxford in December 1691. Newton had recommended Gregory for the professorship in July;¹⁰⁵ the two men frequently corresponded, and Gregory became one of Newton's intimi. Only two letters from Verwer to Gregory have been preserved,¹⁰⁶ and it is unclear how frequently they corresponded. It has been observed that letters helped ‘to create a community of learned persons inside and outside universities, who were interested in the advance of knowledge’.¹⁰⁷ In May and June 1693, Gregory made a visit to the Dutch Republic, during which he met Hudde and Frederik Ruysch (1638–1731) in Amsterdam, and Huygens, with whom he corresponded, at Hofwijck in Voorburg and Leyden.¹⁰⁸ In a memorandum which was written in Leyden and dated 29 June 1693, Gregory created a to-do list which contains the following items: ‘To talk with M^r Huygens about his Dioptricks and mine’ and ‘To settle a correspondence with Volder, Leers Verwer, vander Aa’.¹⁰⁹

In a letter written in August 1691, Verwer provided an overview of the state of the art of Dutch mathematics. He told Gregory that Hudde was heavily distracted by his duties as a member of the Amsterdam vroedschap, and that it was unlikely that he would return to his mathematical studies.¹¹⁰ He also informed Gregory that he was unaware of what Huygens had been up to since the publication of Traité de la lumière (1690), but that it did not seem that he had said farewell to his scholarly pursuits. He reported, moreover, that de Volder, who seems to have only occasionally visited Amsterdam as reported by Le Clerc,¹¹¹ was affected by the censorship installed by the orthodox Calvinist Frederic (Friedrich) Spanheim the Younger (1632–1701) at the University of Leyden.¹¹² In passing, he mentioned some of Gerard Kinckhuysen's (c.1625–1666) contributions to mathematics, and he noted that Abraham de Graaf (1635–1717), whom he knew personally, had not been very active mathematically since the publication of his De beginselen van de algebra of stelkonst (Principles of Algebra) (1672).¹¹³

Verwer thanked Gregory for sending him a copy of his Excercitatio de geometrica de dimensione figurarum (1684), and asked him to thank Archibald Pitcairne (1657–1713), who would briefly become professor of medicine at the University of Leyden between 1692 and 1693, where he had little impact on the spread of Newton's ideas in the Dutch Republic,¹¹⁴ for sending a copy of a book which Verwer characterized as an ‘epicheirema’.¹¹⁵ He also told Gregory that he had communicated his letters, which are now lost, to his friend the broker Jan Makreel, ‘a man most skilled in analytic studies’ to whom he did not dare to compare himself.¹¹⁶ The enigmatic Makreel was an acquaintance and correspondent of E. W. von Tschirnhaus (1651–1708), and he brought Bernard Nieuwentijt's (1654–1718) mathematical work to the attention of G.W. Leibniz (1646–1716), who soon disagreed with its contents.¹¹⁷ Makreel was also an acquaintance of Hudde, who gave him a single-lens microscope.¹¹⁸ Nieuwentijt was also on familiar terms with Hudde.¹¹⁹ In addition, Verwer informed Gregory that one of the editors of the Bibliothèque universelle et historique (1686–1693; which played a significant role in the diffusion of English learning¹²⁰), Le Clerc, whom he identified as a ‘friend of ours (nobis amicus)’, would be willing to publish Gregory's work, should he have any plans to publish in the Dutch Republic.¹²¹

Le Clerc, another savant who studied the first edition of the Principia, took issue with the introduction of metaphysics into theology by Descartes, Spinoza and Bayle, as a result of which they corrupted religion.¹²² Having settled in Amsterdam in 1683, in the mid 1680s he met John Locke (1632–1704), who was in voluntary exile in the Dutch Republic between 1683 and 1689,¹²³ through Philipp van Limborch (1633–1712), who had been professor of theology at the Remonstrant Seminary since 1668.¹²⁴ In order to conceal his identity, Newton planned to anonymously publish a French version of A Historical Account of Two Notable Corruptions in Scripture in the Dutch Republic in the early 1690s. Locke asked Le Clerc to translate it into French. By the time that the translation was finished, Newton had cold feet and he instructed Locke to annul all plans to publish it.¹²⁵ In 1688, a brief and descriptive review of Newton's Principia appeared in Le Clerc's journal.¹²⁶ It has been suggested the author of the review was Locke or de Duillier.¹²⁷ However, in Le Clerc's own review of the second edition of the Principia he noted that ‘The first edition of this book appeared in 1687, and we have published a small extract composed by Mr. Locke in the eighth tome of the Bibliothèque universelle.’¹²⁸

In his 1696 physics textbook, Le Clerc reported that, according to Newton, the primary and secondary planets are maintained in their orbits by a force ‘which he does not define (quod non definit)’, and that this force is ‘inversely proportional to the square of the distances between their centres’. He also pointed out that the ‘most sharp-minded (acutissimus)’ Newton had concluded that the hypothesis of vortices conflicted with astronomical observation.¹²⁹ Here Le Clerc referred to the scholium to Proposition 53 in Book II of the Principia,¹³⁰ which he quoted in extenso.¹³¹ Given Newton's demonstration in this scholium, ‘it is difficult for the intellect [to understand] in what way the fluid matter, which encircles the sun, in no way affects [the regular motion of] the planets that float in it’.¹³² It has been claimed that Le Clerc described the force of gravity ‘as inversely proportional to the distance (rather than to its square)’,¹³³ which might lead readers to believe that Le Clerc's understanding of the Principia in the Physica was not up to scratch. However, the source consulted in order to support this claim was a later edition of Le Clerc's Physica that is affected by a typographical error.¹³⁴ Le Clerc also remarked that, according to Newton, the weights of the planets are proportional to their masses, and he called attention to Newton's statement that ‘God placed the planets at different distances from the sun so that each one might, according to the degree of its density, enjoy a greater or smaller account of heat from the sun’.¹³⁵ Although Le Clerc was clearly not a skilled mathematician, he was well informed about the main tenets developed in the Principia around 1696.

In the bulk of his letter to Gregory, Verwer discussed a number of mathematical problems, some of which he discussed with Makreel, namely the determination of the centre of gravity, the properties of different sorts of curves, and the catenary.¹³⁶ He also confided to Gregory that the mind sees poorly if it loses track of the connection between all sciences, and that, if we study sciences such as mathematics, philosophy, theology and jurisprudence separately, we are like pagans who worship several deities individually. In this context, he revealed his endeavour to connect mathematics ‘to the whole of knowable topics (cum materiae scibilis toto)’.¹³⁷ Although Verwer's plans were extremely sketchy, it is clear that he identified mathematics as the discipline that would connect different scientific branches.

Verwer as a reader of the first edition of the Principia

Verwer's copy of the first edition of Newton's Principia has recently been discovered. It contains his own annotations and a set of annotations that signalled differences with the second and third editions of the Principia (1713 and 1726).¹³⁸ Verwer seems not to have been the author of this second set of annotations, because close inspection reveals that they were written by a later, unknown hand (see figures 1 and 2). There are therefore no indications that Verwer ever read the second edition of the Principia. Moreover, it cannot be inferred from his copy when exactly he studied the Principia. Verwer referred to the Principia in his 1698 Inleiding tot de christelyke Gods-geleertheid. From a letter to Gregory, we also know that he was studying the Principia in early 1703.¹³⁹ It seems that he studied it at least until 1713, because his copy contains a couple of references to his own, now lost, ‘mechanical notes’ (adversaria mechanica) of 1713.¹⁴⁰

Figure 1.

An annotation in an unknown hand. (From MAG: Rariora Qu 291, p. 30, Utrecht University Library. By permission of Utrecht University.) (Online version in colour.)

Figure 2.

Annotations in Verwer's own hand. (From MAG: Rariora Qu 291, p. 37, Utrecht University Library. By permission of Utrecht University.) (Online version in colour.)

Verwer's annotations show that he quite systematically studied the first edition of the Principia.¹⁴¹ The majority of his annotations occur in Book I, paying special attention to Laws 1–3 and Corollary 2 to the laws; Definitions 1–4, 7 and 8; Lemmas 1, 5, 6, 10, 11 and 14; the scholium to Section 1; and Propositions 1, 4 (and its scholium), 5, 6, 8, 9, 11, 13–17, 36, 38, 43–44 and 66. He also paid attention to Book II, Proposition 2, the scholium to Proposition 4, Proposition 24, the scholium generale, and Propositions 49, 51 and 52; and to Book III, Hypotheses 5–7, Corollaries 2–4 to Proposition 6, and Propositions 19 and 28.¹⁴² On some unnumbered pages at the end of his copy, he also summarized some of the key tenets developed in Books II and III. All in all, it was especially Book I that drew his attention.

Verwer's annotations show that he was actively engaged with Newton's Principia.¹⁴³ His annotations roughly fall into eight categories: cross-references, which serve the purpose of making sense of certain statements in the Principia by referring back to material that has already been explained; references to literature, which allowed Verwer to understand or deepen his understanding of Newton's arguments,¹⁴⁴ or, in a minority of cases, to signal points of (dis)agreement;¹⁴⁵ explanatory notes, in which Verwer spelled out the meaning of statements developed in the Principia in his own words—these notes also include formalizations of statements which Newton expressed in words rather than with the aid of mathematical symbols;¹⁴⁶ calculations, whereby Verwer recalculated Newton's results in order to fully grasp them; occasional corrections; indices, which provide an overview of certain claims in the Principia; summaries, which give a rundown of specific sections in the Principia, ¹⁴⁷ or provide a synthesis of results which Verwer found important; and, finally, comments, in which Verwer reflected on the broader implications of certain passages in the Principia.¹⁴⁸

In what follows, I will focus on how Verwer responded to the Principia by concentrating on a number of important comments in the sense characterized above. After the second occurrence of the word ‘force’ in the excerpt ‘a body exerts this force [i.e. the force of inertia] during a change of its state, caused by another force impressed upon it’,¹⁴⁹ which is a fragment from Newton's comment to Definition 3, Verwer inserted an asterisk which was accompanied in the margin by the statement ‘an argument for the existence of God’.¹⁵⁰ Hereby, he was implying that, according to Newton's Definition 3, bodies are impressed upon by God. This claim reminds us of Verwer's argument for the existence of God in ’t Mom-aensicht, according to which the first cause of local motion is to be found in God. Verwer therefore saw confirmed in Definition 3 of the Principia what he already believed. In a comment at the end of his copy, he stated that Newton's finding that God arranged the distances of the planets from the sun according to their densities, which is in fact the only reference to God in the first edition of the Principia, testifies to ‘God's most perfect science’.¹⁵¹ In his 1696 Physica, Le Clerc had already drawn attention to the physico-theological significance of Newton's claim on the matter.

The same page at the end of Verwer's copy contains a comment that has not surfaced in the literature. Here he draws attention to Newton's statement that in the Principia he did not consider ‘the physical causes and sites of forces’ and related statements.¹⁵² This is then followed by a reference to Ecclesiastes 8:16–17, in which the crucial sentence is: ‘Then I beheld all the work of God, that a man cannot find out the work that is done under the sun: because though a man labour to seek it out, yet he shall not find it; yea further; though a wise man think to know it, yet shall he not be able to find it’ (KJV). From this Verwer concluded that ‘the causes of phenomena … are hidden’.¹⁵³ It is unclear whether he endorsed the idea that both the proximate and the remote cause of gravity are hidden.¹⁵⁴ In contrast to other compatriots, like Huygens for instance, Verwer did not believe that Newton's methodological strategy to remain neutral with respect to the cause of gravity constituted a major natural philosophical flaw. On the contrary, the fact that Newton did not succeed in uncovering the cause of gravity contains a message of epistemological humility that fitted well with Verwer's religious beliefs. Without referring to Newton, Verwer used Ecclesiastes 8:16 in his Inleiding as part of an argument that intended to show that humans cannot penetrate the inner workings of nature.¹⁵⁵ What needs to be emphasized here is that, among the hundreds of annotations in his copy of the first edition of the Principia, only in the three abovementioned instances did Verwer point to the theological repercussions of Newton's magnum opus. For the most part, he focused on the technical aspects of the Principia.

The foundations of Christian faith and natural reason

Verwer's Inleiding tot de christelyke Gods-geleertheid (Introduction to Christian Theology) appeared in 1698. He published it with the hope that the ‘systematic reasoning’ (cogitatio systematica) that it contained would serve as ‘instruction and guideline for the education of our own children’.¹⁵⁶ The ‘main disagreements and schisms’ in religion emerge when too much or too little is believed. Correspondingly, Verwer sought to find a middle way between these extremes, so that disagreement and schism could be avoided. Superstition (bygeloof) occurs when too much is believed; it is ‘childish or slavish, and it never advances to full-grown freedom’.¹⁵⁷ Disbelief (on-geloof) occurs when too little is believed. A disbeliever who lapses into ‘a sweet-delusional slumber dream’ is not interested in uncovering truth but only in ‘extenuating his deeds and opinions’.¹⁵⁸ Religion (godsdienst) aims to realize eternal bliss so that in the afterlife humans can attain a state that is equal to God's.¹⁵⁹ In order to counter superstition and disbelief, Verwer sought to provide a systematic demonstration of the foundations of Christian faith. These are threefold:¹⁶⁰ first, that there is a God, who is perfect, incorruptible, ‘existing separately from all other beings’, necessary, supremely wise, almighty, one, eternal, unchangeable and ‘the first and supreme cause of things’;¹⁶¹ second, that there is an eternal bliss that cannot be attained in this life, but only in the afterlife by those who have practised Christian virtues (e.g. humble and respectful worship of God, prudence, valour, moderation, mercifulness, endurance, and endorsement of the golden rule) during their mortal life;¹⁶² third, that there is an eternal unhappiness that awaits those who have not lived in a Christian way.

Verwer endorsed a form of cessationism, since he was convinced that, after the early centuries, miracles had ceased, and he furthermore believed that from then on worldly temptations had arisen that negatively affected religiosity. Protestants believed that miracles ceased after the Apostolic Age or once Christianity was firmly established.¹⁶³ In order to restore Christian faith after the era of miracles, God supplied us with the ability to reason.¹⁶⁴ According to Verwer, once miracles had ceased, the foundations of the Christian faith could be learned and known ‘only by that ingenious ability and by that strength of reason by which God almighty has desired to endow humans in particular at his creation’.¹⁶⁵ Verwer did not endorse the view according to which all religious truths can be known through reason, for the truths of the New Testament can only be learned through divine revelation. But why is it the case that after the early centuries the three foundations of the Christian faith can be known only by natural reason? Here Verwer's reference to Romans 1:20 is highly significant.¹⁶⁶ According to him, this verse reveals that everyone can learn at least some things about God from his creation, namely the fundamentals of the Christian faith, and that those who do not arrive at these straightforward conclusions about God from his creation by their reason are simply without excuse.¹⁶⁷ In other words, God can hold the unwilling accountable given that he has provided natural reason to every human. Verwer's concept of ‘reason’ was thus not a secular one, but a divinely supplied ability that offered every human being the opportunity of learning the foundations of the Christian faith. He underscored that the ‘word of faith’ is superior to the ‘wisdom of reasoning’.¹⁶⁸

Verwer wrote to Gregory in 1703 that he had handed over two copies of his Inleiding to Willem (Gulielmus) Moncrief (or Moncreif), a Scottish law student at the University of Leyden, who would send one to Gilbert Burnet (1643–1715), the Bishop of Salisbury, who read Dutch fluently, and the other to Newton.¹⁶⁹ In the same letter, he stated that he devoted his ‘spare hour to Newton's book [i.e. the Principia]’ and that he was ‘amazed by the marvellous genius of this man’.¹⁷⁰ Initially, he planned to order his exposition entirely ‘mathematically’, but he ultimately decided to compose parts of it ‘in a general ongoing style’ because the ‘mathematical order’ had an unintended consequence, in that it distracted ‘the unaccustomed and simpleminded’.¹⁷¹ Once he had introduced and discussed the three foundations of the Christian faith ‘in a general ongoing style’,¹⁷² Verwer reordered his argumentation ‘in geometrical order’ (geometrico ordine),¹⁷³ in such a way that, in his opinion, it did not suffer from the unintended consequence just mentioned. He followed a mathematical order, structuring his argumentation in the form propositio–demonstratio–consectarium/a–scholium, because he intended to demonstrate the Christian fundamentals beyond all possible doubt.¹⁷⁴ The structure of his argument in the Inleiding is thus similar to that of his ’t Mom-aensicht.

At the very end of the Inleiding, Verwer added what he called a ‘geometrical analysis’ of his demonstrations in the form of a cryptic Latin formula, which ‘in the Newtonian form of speech’ reads ‘eternal felicity is proportional to pious works and inversely proportional to divine grace’.¹⁷⁵ In a letter to David Gregory on 25 January 1703, in which he summarized the contents of the Inleiding, and explained the meaning of his formula, Verwer stated that he tried to mathematically demonstrate this formula ‘in a way that would be certain and infallible, and would not contain anything superfluous’.¹⁷⁶ He represented his formula as follows: (Dh)/f is to (Dhm)/ef × G (or: (Dh)/f – (Dhm)/ef × G ∝ 0), where D stands for the name of God, h for man, f for God's felicity, m for means, e for end and G for God's grace. He took (Dh)/f to represent man's eternal felicity, which stands ‘as h to D to f’, and (Dhm)/ef to represent pious works, which stand ‘to man's eternal felicity as m to e’, i.e. as a means to an end.¹⁷⁷ From this result, he inferred D × hef – D × hmf × Geff ∝ 0, by multiplication with eff. Verwer seems to have been very serious about this formula, since he sought to bring it to Newton's attention.¹⁷⁸ He also thought that it could put an end to religious disputes.¹⁷⁹

In order to understand the meaning of Verwer's formula, we need to pay attention to his theological views, and more precisely to his views on the conditions under which one can receive eternal felicity. In the second scholium to the fourth proposition of his Inleiding, he states that only those who have ‘unwavering faith’ and who have ‘perfectly fulfilled the duties of good works’ can hope to receive eternal felicity,¹⁸⁰ which implies that only a minority is able to receive it, as is clear (Verwer points out) from Matthew 20:16 and 22:14.¹⁸¹ Nevertheless, by calling on, for instance, Ephesians 2:10 (‘For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them’; KJV) and 1 John 1:7 (‘But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin’; KJV), Verwer argued that true Christians ought to perform as many pious works as possible in order to receive eternal felicity. Therefore, eternal felicity is proportional to pious works, which corresponds to what is expressed in his formula. Furthermore, God is able to ‘give some men, even if they have stumbled and fallen, eternal felicity’, if he so chooses.¹⁸²

In his 1703 letter to Gregory, Verwer stated: ‘More clearly expressed, it is to be said that eternal happiness really is acquired by good works and by divine grace jointly, so that indeed a defect or weakness in good works is compensated by divine grace.’¹⁸³ The idea is that a lack of good works can be compensated for by divine grace, or, put differently, that, when the quantity of good works is low, the quantity of divine grace can be increased so that eternal felicity can be acquired. This is the case, not when eternal felicity is proportional to pious works and inversely proportional to divine grace, but only when eternal felicity is proportional to pious works and divine grace jointly.¹⁸⁴ Given what Verwer wanted to convey theologically, it is mathematically required that eternal felicity is proportional to pious works and divine grace. That eternal felicity is proportional to divine grace is expressed as such in his formula. However, it is contrary to his explanation of his formula which he provided in the Inleiding. This is not the first time that attention has been called to the discrepancy between Verwer's formula and his explanation. It has been claimed previously that his formula is incorrect, whereas his explanation is sound.¹⁸⁵ Here I have argued the opposite: his formula is correct, but his explanation is unsound.¹⁸⁶

Inleiding tot de christelyke Gods-geleertheid contains a reference to Newton's Principia. Verwer wrote that, by considering ‘the daily course and arrangement of visible things’, the existence of God can be demonstrated in several ways.¹⁸⁷ As a simple example, he pointed out that the motions of the heavenly bodies do not follow a circular but an ‘oval’ trajectory, which, he added, is accepted by the most distinguished astronomers, such as Johannes Kepler, Ismaël Boulliau, Giovanni Domenico Cassini, John Flamsteed, Huygens and Newton. He concluded that it is impossible ‘that an oval rotation can be performed and kept going somewhere without the ministry of a ruler who exists outside of things’. He then recommended Newton's Principia to those interested in understanding the ‘oval’ trajectory of the celestial bodies.¹⁸⁸ In 1703, Verwer described the motions of the planets as ‘elliptic’.¹⁸⁹ The words ‘oval’ and ‘elliptical’ were used interchangeably.¹⁹⁰

Verwer frequently used Gregory's 1702 Astronomiae physicae & geometricae elementa, ‘the first thorough mathematical introduction to the Principia’,¹⁹¹ to help him understand the claims developed in the Principia,¹⁹² and in his 1703 letter he wrote to Gregory that he had duly studied his ‘astronomical work’ and that it ‘pleases both him and others’.¹⁹³ It might have been the case that Verwer only started seriously studying the Principia once Gregory's Astronomiae was available, which would help to explain why he stated in 1703 that he was devoting his ‘spare hour to Newton's book’. This contention must, however, remain speculative in view of the available sources. In his second letter to Gregory, Verwer remarked that, in order to strengthen the existence of a divine mover, he did not rely on the argument drawn from local motion, as he had done in ’t Mom-aensicht, but instead on an argument drawn from the ‘elliptical’ motion of the planets, suggesting thereby that the latter was an alternative to the former.¹⁹⁴ Verwer found in Newton's Principia an instance of an argument of the kind he had put forward in earlier work. Although he might not have fully digested the Principia at the time when he published Inleiding tot de christelyke Gods-geleertheid, and although Newton was only one of the astronomers whom he mentioned, Verwer was one of the first in the Dutch Republic who could be seen by others to have publicly mobilized the Principia for physico-theological purposes.

In Conclusion

Verwer's ’t Mom-aensicht testifies to the empirical bent in his thinking. In order to disprove the patrons of ‘independence’, he put forward an argument which was, according to his own understanding, grounded in phenomena to demonstrate that God is the first cause of local motion. His fondness for this line of reasoning made him receptive to the physico-theological arguments that he later found in the first edition of Newton's Principia. In Definition 3 of the Principia, Verwer saw an echo of his own argument according to which God is the first cause of local motion. He furthermore considered Newton's statement that God arranged the distances of the planets from the sun according to their densities as having important physico-theological significance, and he regarded the elliptical motion of the planets which he found in the work of Newton and others as an indication of divine intervention. Moreover, he thought that Newton's statement that he did not consider ‘the physical causes and sites of forces’ contained an important message of epistemological humility that fitted well with his religious beliefs.

In contrast to the second edition of the Principia (1713), which contained the famous General Scholium and Roger Cotes’ (1682–1716) lengthy editorial introduction in which he emphasized that Newton's Principia ‘will stand as a mighty fortress against the attacks of atheists’ and that ‘nowhere you will find more effective ammunition against that impious crowd’,¹⁹⁵ the physico-theological implications of the Principia were hardly spelled out in its first edition. That task was left to its readers. Together with Le Clerc, Verwer was one of the first in the Dutch Republic to clearly see the physico-theological potential of the Principia. However, as a mathematics enthusiast he spent most of his time mastering the mathematical technicalities of the Principia. That Newton was successful in the Dutch Republic simply because he was useful, and not because he was right, is misleading, because Dutch scholars were genuinely interested in his mathematical and natural philosophical work in its own right. The claim that the group of enthusiasts of which Verwer was a member were united in their endeavour to refute Spinoza is also somewhat misleading, since nearly all of its members were interested in mathematics, and only Verwer, Le Clerc and later Nieuwentijt are known to have criticized Spinoza's work.

Finally, there is no evidence in support of the claim that ‘In order to refute Spinoza, Verwer searched for a different mathematics and a better mathematical method, and he found models of it in Newton's Principia.’¹⁹⁶ Verwer never compared Newton's method to Spinoza's; more specifically, he never used arguments grounded in the nature of Newton's physico-mathematics qua mathematics in order to refute Spinoza's Ethica. In his posthumously published Gronden der zekerheid (Foundations of Certitude), the Purmerend-based physician, local politician and experimental philosophy and mathematics enthusiast Nieuwentijt argued for the superiority of Newton's mixed-mathematical method over Spinoza's hypothetical pure-mathematical method,¹⁹⁷ but this was not an argument of the kind ever put in writing by Verwer. To claim otherwise is, in my opinion, to read the extant sources in the light of later developments. I hope to have contributed to a more nuanced understanding of Newton's significance for the Amsterdam merchant on whom we have focused throughout this essay, and also of the piecemeal appropriation of Newton's ideas in the Dutch Republic.