Presents Newton's unifying idea of gravitation and explains how he converted physics from a science of explanation into a general mathematical system.

Aside from the Principia and occasional appearances of the Opticks , Newton' writings have remained largely inaccessible to students of philosophy, science, and literature as well as to other readers. This book provides a remedy with wide representation of the interests, problems, and diverse philosophic issues that preoccupied the greatest scientific mind of the seventeenth century. Grouped in sections corresponding to methods, principles, and theological considerations, these selections feature explanatory notes and cross-references to related essays.

Motus quidem veros corporum singulorum cognofcere , & ab apparentibus actu diícriminare, difficillimum est ; propterca quod partes ípatij illius immobilis in quo corpora vere moventur, non incurrunt in sensus.

In his monumental 1687 work, _Philosophiae Naturalis Principia Mathematica_, known familiarly as the _Principia_, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space (...) vehicles. This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the _Principia_ also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system. The translation-only edition of this preeminent work is truly accessible for today's scientists, scholars, and students. (shrink)

Sir Isaac Newton (1642-1727) left a voluminous legacy of writings. Despite his influence on the early modern period, his correspondence, manuscripts, and publications in natural philosophy remain scattered throughout many disparate editions. In this volume, Newton's principal philosophical writings are for the first time collected in a single place. They include excerpts from the Principia and the Opticks, his famous correspondence with Boyle and with Bentley, and his equally significant correspondence with Leibniz, which is often ignored in (...) favor of Leibniz's later debate with Samuel Clarke. Newton's exchanges with Leibniz place their different understandings of natural philosophy in sharp relief. The volume also includes 'De Gravitatione', offered here in a corrected translation, which is crucial for understanding Newton's relation to his great predecessor Descartes. In a historical and philosophical introduction, Andrew Janiak examines Newton's philosophical positions and his relations to canonical figures in early modern philosophy. (shrink)

In view of the presertt state of development of non cktssicallogic, especially of paraconsistent logic, a new stand regardmg the relatzons between logtc and ontology is deferded In a parody of a dicturn of Quine, my stand may be summarized as follows To be is to be the value of a vanable a specific language with a given underlymg logic Yet my stand differs from Qutne's, because, among other reasons, I accept some first order heterodox logIcs as genutne alternatwes to (...) ciassical logic I aiso discuss some questions of non classical logic to substantzate my argument, and suggest that rny position complements and extends some uleas advanced by L Apostei. (shrink)

The aim of this paper is twofold: (1) to show the principal aspects of the way in which Newton conceived his mathematical concepts and methods and applied them to rational mechanics in his Principia; (2) to explain how the editors of the Geneva Edition interpreted, clarified, and made accessible to a broader public Newton’s perfect but often elliptic proofs. Following this line of inquiry, we will explain the successes of Newton’s mechanics, but also the problematic aspects (...) of his perfect geometrical methods, more elegant, but less malleable than analytical procedures, of which Newton himself was one of the inventors. Furthermore, we will also consider the way in which Newtonianism was spread before in England and afterwards on continental Europe. In this respect the Geneva Edition plays a fundamental role because of its complete apparatus of notes, and because it appeared only thirteen years after the publication of the third edition of the Principia (1726). Finally, we will also confront some problems connected to the metaphysics of calculus. Therefore, the case of Newton is one of those in which, starting from mathematics applied to physics, it is possible to connect an impressive series of fundamental arguments such as the role of mathematics in science; the comparison between Newton’s geometrical methods and analytical methods; the way in which Newtonianism was spread as well as the philosophical implications of Newton’s mathematical concepts. (shrink)

This paper has the aim to provide a general view of the so called Jesuit Edition (hereafter JE) of Newton’s Philosophiae Naturalis Principia Mathematica (1739–1742). This edition was conceived to explain all Newton’s methods through an apparatus of notes and commentaries. Every Newton’s proposition is annotated. Because of this, the text – in four volumes – is one of the most important documents to understand Newton’s way of reasoning. This edition is well known, but systematic (...) works on it are still missing. We are going to fill this gap by means of a project exposed in the final remarks of this paper. In this paper we will: A) expound the way in which the notes and the additions to the JE were conceived by the commentators; B) provide some pieces of information about the commentators; C) summarize the most important of their notes; D) examine closely their notes as to a particularly important question: the so called "inverse problem of the central forces". (shrink)

I discuss some questions of quantum physics, for instance the validity and limitations of the basic language of set theory to deal with problems related to elementary particles. I also present a sketch of a formalization of a “metaphysics of structures”, which might be useful for a kind of “ontic structural realism”, and briefly review the concept of quasi-truth, which underlies my way of understanding scientific theories and the scientific activity.

In view of the present state of development of non classical logic, especially of paraconsistent logic, a new stand regarding the relations between logic and ontology is defended In a parody of a dictum of Quine, my stand May be summarized as follows. To be is to be the value of a variable a specific language with a given underlying logic Yet my stand differs from Quine’s, because, among other reasons, I accept some first order heterodox logics as genuine alternatives (...) to classical logic I also discuss some questions of non classical logic to substantiate my argument, and suggest that may position complements and extends some ideas advanced by L Apostel. (shrink)

Newton certainly regarded his second law of motion in the Principia as a fundamental axiom of mechanics. Yet the works that came after the Principia, the major treatises on the foundations of mechanics in the eighteenth century—by Varignon, Hermann, Euler, Maclaurin, d’Alembert, Euler (again), Lagrange, and Laplace—do not record, cite, discuss, or even mention the Principia’s statement of the second law. Nevertheless, the present study shows that all of these scientists do in fact assume the principle (...) that the Principia’s second law asserts as a fundamental axiom in their mechanics. (For what that second law asserts, we rely on Newton’s own testimony.) Some, like Varignon and Hermann, assume the axiom implicitly, apparently unaware that any assumption is being made, while others, like Maclaurin and Euler, assume the axiom explicitly, apparently unaware that the assertion assumed is the second law as Newton himself understood it. But in every case these scientists employ the principle asserted by the Principia’s second law fundamentally, unaware that they should be citing Neutonus, Prin., Phil. Nat. Math., Lex II. (shrink)

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying Newton’s methods in Principia is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right space-time structure for Newton’s Principia requires the notion of parallelism of spatial directions at different times and nothing more. Only relative motions are definable (...) in this framework, never absolute ones. (shrink)

This paper is a summary of a lecture in which I presented some remarks on Gödel’s incompleteness theorems and their meaning for the foundations of physics. The entire lecture will appear elsewhere.

Newton rested his theory of mechanics on distinct metaphysical and epistemological foundations. After Leibniz's death in 1716, the Principia ran into sharp philosophical opposition from Christian Wolff and his disciples, who sought to subvert Newton's foundations or replace them with Leibnizian ideas. In what follows, I chronicle some of the Wolffians' reactions to Newton's notion of absolute space, his dynamical laws of motion, and his general theory of gravitation. I also touch on arguments advanced by (...) class='Hi'>Newton's Continental followers, such as Leonhard Euler, who made novel attempts to defend his mechanical foundations against the pro-Leibnizian attack. This examination grants us deeper insight into the fate of Newton's mechanics on the Continent during the early eighteenth century and, more specifically, sheds needed light on the conflicts and tensions that characterized the reception of Newton's philosophy of mechanics among the Leibnizians. (shrink)

The first proposition of the Principia records two fundamental properties of an orbital motion: the Fixed Plane Property (that the orbit lies in a fixed plane) and the Area Property (that the radius sweeps out equal areas in equal times). Taking at the start the traditional view, that by an orbital motion Newton means a centripetal motion – this is a motion ``continually deflected from the tangent toward a fixed center'' – we describe two serious flaws in the (...) Principia's argument for Proposition 1, an argument based on a polygonal impulse approximation. First, the persuasiveness of the argument depends crucially on the validity of the Impulse Assumption: that every centripetal motion can be represented as a limit of polygonal impulse motions. Yet Newton tacitly takes the Impulse Assumption for granted. The resulting gap in the argument for Proposition 1 is serious, for only a nontrivial analysis, involving the careful estimation of accumulating local errors, verifies the Impulse Assumption. Second, Newton's polygonal approximation scheme has an inherent and ultimately fatal disability: it does not establish nor can it be adapted to establish the Fixed Plane Property. Taking then a different view of what Newton means by an orbital motion – namely that an orbital motion is by definition a limit of polygonal impulse motions – we show in this case that polygonal approximation can be used to establish both the fixed plane and area properties without too much trouble, but that Newton's own argument still has flaws. Moreover, a crucial question, haunted by error accumulation and planarity problems, now arises: How plentiful are these differently defined orbital motions? Returning to the traditional view, that Newton's orbital motions are by definition centripetal motions, we go on to give three proofs of the Area Property which Newton ``could have given'' – two using polygonal approximation and a third using curvature – as well as a proof of the Fixed Plane Property which he ``almost could have given.''. (shrink)

Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravitation. It is very much more than a demonstration that 'to us it is enough that gravity really does 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 the sea'. It is important to us as a model of all mathematical physics.Representing a decade's (...) work from a distinguished physicist, this is the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Professor Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breath-taking economy of Newton's methods.Subrahmanyan Chandrasekhar is one of the most reknowned scientists of the twentieth century, whose career spanned over 60 years. Born in India, educated at the University of Cambridge in England, he served as Emeritus Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics at the University of Chicago, where he has was based from 1937 until his death in 1996. His early research into the evolution of stars is now a cornerstone of modern astrophysics, and earned him the Nobel Prize for Physics in 1983. Later work into gravitational interactions between stars, the properties of fluids, magnetic fields, equilibrium ellipsoids, and black holes has earned him awards throughout the world, including the Gold Medal from the Royal Astronomical Society in London, the National Medal of Science in the United States, and the Copley Medal from the Royal Society. His many publications include Radiative transfer, Hydrodynamic and hydromagnetic stability, and The mathematical theory of black holes, each being praised for its breadth and clarity. Newton's Principia for the common reader is the result of Professor Chandrasekhar's profound admiration for a scientist whose work he believed is unsurpassed, and unsurpassable. (shrink)

Newton’s Principia reconceptualizes rational mechanics and physics, and offers a novel unification of these heretofore distinct disciplines. In this paper, I argue for a reading of the Principia that insists on a strict distinction between the rational mechanics (in Books 1 and 2) and the physics (in Book 3), in which the Definitions and the Axioms/Laws play a surprising dual role that both distinguishes the rational mechanics from the physics and unifies them into a single project: a (...) philosophical mechanics. (shrink)

SummaryThis contribution examines the circumstances of composition of the annotated edition of Newton's Principia that was printed in Geneva in 1739–1742, which ran to several editions and was still in print in Britain in the mid-nineteenth century. This edition was the work of the Genevan Professor of Mathematics, Jean Louis Calandrini, and of two Minim friars based in Rome, Thomas Le Seur and François Jacquier. The study of the context in which this edition was conceived sheds light on (...) the early reception of Newtonianism in Geneva and Rome. By taking into consideration the careers of Calandrini, Le Seur and Jacquier, as authors, lecturers and leading characters of Genevan and Roman cultural life, I will show that their involvement in the enterprise of annotating Newton's Principia answered specific needs of Genevan and Roman culture. The publication and reception of the Genevan annotated edition has also a broader European dimension. Both Calandrini and Jacquier were in touch with the French république des lettres, most notably with Clairaut and Du Châtelet, and with the Bernoulli family in Basel. Therefore, this study is also relevant for the understanding of the dissemination of Newton's ideas in Europe. (shrink)

Newton described his Principia as a work of ‘experimental philosophy’, where theories were deduced from phenomena. He introduced six ‘phenomena’: propositions describing patterns of motion, generalised from astronomical observations. However, these don’t fit Newton’s contemporaries’ definitions of ‘phenomenon’. Drawing on Bogen and Woodward’s distinction between data, phenomena and theories, I argue that Newton’s ‘phenomena’ were explanatory targets drawn from raw data. Viewed in this way, the phenomena of the Principia and the experiments from the Opticks (...) were different routes to the same end: isolating explananda. (shrink)

The Oxford Handbook of the History of Physics brings together cutting-edge writing by more than twenty leading authorities on the history of physics from the seventeenth century to the present day. By presenting a wide diversity of studies in a single volume, it provides authoritative introductions to scholarly contributions that have tended to be dispersed in journals and books not easily accessible to the general reader. While the core thread remains the theories and experimental practices of physics, the Handbook contains (...) chapters on other dimensions that have their place in any rounded history. These include the role of lecturing and textbooks in the communication of knowledge, the contribution of instrument-makers and instrument-making companies in providing for the needs of both research and lecture demonstrations, and the growing importance of the many interfaces between academic physics, industry, and the military. (shrink)

Leibniz's dispute with Newton over the physico-mathematical theories expounded in the Principia Mathematica have long been identified as a crucial episode in the history of science. Dr. Bertoloni Meli examines several hitherto unpublished manuscripts in Leibniz's own hand illustrating his first reading of and reaction to Newton's Principia. Six of the most important manuscripts are here edited for the first time. Contrary to Leibniz's own claims, this new evidence shows that he had studied Newton's masterpiece (...) before publishing An Essay on the Causes of Celestial Motions. This article, representing his response to Newton, is included here in English translation. Dr. Bertoloni Meli analyses the important implications of this episode on a variety of themes ranging from priority claims to the mathematization of nature in the seventeenth century. Besides providing a careful study of Leibniz's style and strategy, the author examines how our perception of Newton's achievement is affected and the reception of the rival theories by the mathematical community around 1700. "Bertoloni's book provides a very detailed and deep analysis of Leibniz's calculus and dynamics by focusing on a consistent and important set of previously unknown manuscripts..." Niccolo Guicciardini, Universita de Bologna "...Equivalence and Priority is a major contribution to our understanding of the development of mathematical physics in the late seventeenth and early eighteenth century." Daniel Garber, University of Chigago. (shrink)

ABSTRACTThe worksheets that presumably contained Newton's early development of the fundamental concepts in his Principia have been lost. A plausible reconstruction of this development is presented based on Newton's exchange of letters with Robert Hooke in 1679, with Edmund Halley in 1686, and on some clues in the diagram associated with Proposition 1 in Book 1 of the Principia that have been ignored in the past. A graphical construction associated with this proposition leads to a rapidly (...) convergent method to obtain orbits for central forces, which elucidates how Newton may have have been led to formulate some of his most fundamental propositions in the Principia. (shrink)

SUMMARYThis paper provides an account of Chinese translations of Newton’s Principia produced over the past century and a half within the larger context of the dissemination of Newtonian philosophy in China. Given its fundamental importance in the history of science, the Principia, originally penned in Latin, has been translated into a number of other languages. While in all these languages no more than two full translations have appeared, as many as four complete versions in Chinese have been (...) produced since the 1850s, when first attempts were made to translate the Principia in late imperial China. They include a 1931 version in semi-classical Chinese completed during the Republican era and three rival versions in modern Chinese published in contemporary China. This rich history of translating the Principia into Chinese, which remains little known to scholars in the West, is for the first time reconstructed and presented in English. This account is based on a meticulous scrutiny of manuscripts, historical records, secondary literature and interviews with some of the contemporary translators. It demonstrates that Chinese translation of the Principia is a complex process that involves scientific traditions, linguistic peculiarities, translators’ subjectivity, readers’ expectations and even the role of the market. (shrink)

In this essay I argue against I. Bernard Cohen's influential account of Newton's methodology in the Principia: the 'Newtonian Style'. The crux of Cohen's account is the successive adaptation of 'mental constructs' through comparisons with nature. In Cohen's view there is a direct dynamic between the mental constructs and physical systems. I argue that his account is essentially hypothetical-deductive, which is at odds with Newton's rejection of the hypothetical-deductive method. An adequate account of Newton's methodology needs (...) to show how Newton's method proceeds differently from the hypothetical-deductive method. In the constructive part I argue for my own account, which is model based: it focuses on how Newton constructed his models in Book I of the Principia. I will show that Newton understood Book I as an exercise in determining the mathematical consequences of certain force functions. The growing complexity of Newton's models is a result of exploring increasingly complex force functions (intra-theoretical dynamics) rather than a successive comparison with nature (extra-theoretical dynamics). Nature did not enter the scene here. This intra-theoretical dynamics is related to the 'autonomy of the models'. (shrink)

Recent findings on Newton's heretical beliefs in the five draft versions of the General Scholium, which was added to the second edition of the Principia in 1713, are discussed here. We shall use these snapshots as a tool to gain understanding into the process of composition of the theological material from the General Scholium.

In his Essay concerning Human Understanding, John Locke explicitly refers to Newton’s Philosophiae naturalis principia mathematica in laudatory but restrained terms: “Mr. Newton, in his never enough to be admired Book, has demonstrated several Propositions, which are so many new Truths, before unknown to the World, and are farther Advances in Mathematical Knowledge” (Essay, 4.7.3). The mathematica of the Principia are thus acknowledged. But what of philosophia naturalis? Locke maintains that natural philosophy, conceived as natural science (...) (as opposed to natural history), would give us demonstrations of the necessary connection between the (ultimately, simple) ideas constitutive of our complex ideas of various natural kinds of substances (e.g., gold). Indeed Locke goes so far as to suggest that a completely adequate natural science would also realize (perhaps, per impossibile) the goal of transforming the corpuscularian hypothesis into knowledge by demonstrating the necessary connection between the ‘microstructure’ (primary qualities of insensible corpuscles) of a particular natural kind of substance (e.g., gold) and the ideas of secondary qualities constitutive of the complex idea of that kind of substance. Locke’s conclusion concerning the possibility of the development of a natural science thus conceived is pessimistic: In vain therefore shall we endeavor to discover by our Ideas, (the only true way of certain and universal knowledge,) what other Ideas are to be found constantly joined with that of our complex Idea of any Substance: since we neither know the real Constitution of the minute Parts, on which their Qualities do depend; not, did we know them could we discover any necessary connexion between them, and any of their Secondary Qualities: which is necessary to be done, before we can certainly know their necessary co-existence (Essay, 4.3.14). It is understandable that, with such a conception of the science of nature, Locke found little of it in Newton’s Principia. In this paper, I further explore what might, perhaps with some hyperbole, be termed Locke’s ‘disappointment’ with the Prinicipia as a contribution to natural science. In particular, I argue that Locke’s adherence to the idealist epistemology of the Way of Ideas entails that mathematics cannot lend its certainty as a scientia to natural philosophy. Consequently, he finds more mathematics than natural philosophy in the Principia. (shrink)

In this paper, I discuss how Newton’s inductive argument of the Principia can be defended against criticisms levelled against it by Duhem, Popper and myself. I argue that Duhem’s and Popper’s criticisms can be countered, but mine cannot. It requires that we reconsider, not just Newton’s inductive argument in the Principia, but also the nature of science more generally. The methods of science, whether conceived along inductivist or hypothetico-deductivist lines, make implicit metaphysical presuppositions which rigour requires (...) we make explicit within science so that they can be critically assessed, alternatives being developed and assessed, in the hope that they can be improved. Despite claiming to derive his law of gravitation by induction from phenomena without resource to hypotheses, Newton does nevertheless acknowledge in the Principia that his rules of reasoning make metaphysical presuppositions. To this extent, Newton has a more enlightened view of scientific method than most 20th and 21st century scientists and historians and philosophers of science. (shrink)

As the seventeenth century progressed, there was a growing realization among those who reflected on the kind of knowledge the new sciences could afford (among them Kepler, Bacon, Descartes, Boyle, Huygens) that hypothesis would have to be conceded a much more significant place in natural philosophy than the earlier ideal of demonstration allowed. Then came the mechanics of Newton's Principia, which seemed to manage quite well without appealing to hypothesis (though much would depend on how exactly terms like (...) "force" and "attraction" were construed). If the science of motion could dispense with causal hypothesis and the attendant uncertainty, why should this not serve as the goal of natural philosophy generally? The apparent absence of causal hypothesis from the highly successful new science of motion went far towards shaping, in different ways, the account of scientific knowledge given by many of the philosophers of the century following, notable among them Berkeley, Hume, Reid, and Kant. This "Newtonian" interlude in the history of the philosophy of science would today be accounted on the whole a byway. The Principia, despite its enormous achievement in shaping subsequent work in mechanics, was from the beginning too idiosyncratic from an epistemic standpoint to serve as model for the natural sciences generally. (shrink)

In this research, we present the most important characteristics of the so called and so much explored Jesuit Edition of Newton’s Philosophi? Naturalis Principia Mathematica edited by Thomas Le Seur and Fran?ois Jacquier in the 1739-1742. The edition, densely annotated by the commentators (the notes and the comments are longer than Newton’s text itself) is a very treasure concerning Newton’s ideas and his heritage, e.g., Newton’s geometry and mathematical physics. Conspicuous pieces of information as to (...) history of physics, history of mathematics and epistemology can be drawn from it. This paper opens a series of study concerning Jesuit Edition, whose final scope is to put in evidence all the conceptual aspects of such edition and its role inside the spread of scientific ideas and inside the complex relation science, popularization & society. (shrink)

The first edition of Isaac Newton's famous Principia mathematica (1687) contains only one reference to the Scriptures and one mention of God and natural theology. Thus, there is superficial evidence to suggest that this pivotal work of physics is a mostly secular book that is not fundamentally associated with theology and natural theology. The fact that the General Scholium – with its overt theological and natural theological themes – was only added to the Principia a quarter-century later (...) with the second edition of 1713 may also suggest that this theology came as an afterthought and is therefore not integral to the conceptual structure of the Principia . Moreover, the relative paucity of theology in the first edition, combined with the evidence of the appended General Scholium of 1713, could be used as evidence of a ‘theological turn’ in Newton's thought after 1687. This article uses evidence from Newton's private manuscripts to argue that there is more theology in all three editions of the Principia than a simple reading of the published text would imply. This article also demonstrates that the seeds of Newton's theological conception of Nature and the cosmos – conceptions that can be found in manuscripts beginning in the early 1690s, and that are acknowledged in the General Scholium of 1713 – are already present in Newton's private papers prior to 1687. Newton engaged in a great deal of theological writing after 1687, but the period of the composition of the Principia only marks the end of the first third of Newton's six-decade intellectual career and thus it should not be surprising to find more theology after the Principia than before. Nevertheless, there are important theological writings going back to the 1660s that show that Newton's strongly biblical and providentialist theology pre-dates the Principia and, crucially, that his theological conception of the cosmos does as well. The first edition of the Principia , therefore, was composed after Newton had begun to formulate his theology and theological understanding of the cosmos. (shrink)

Comment caractériser les méthodes de démonstration mathématique utilisées dans les Principia de Newton? Ni géométrie à l'antique ni véritable «calcul différentiel», le raisonnement s'appuie sur les figures, mais en supposant qu'elles bougent et se déforment. Les situations infinitésimales sont traitées comme stade ultime de configurations finies, grâce à certains procédés de représentation (témoins finis de l'infinitésimal). Le temps intervient sous deux modes différents dans ces procédés. Les exemples sont pris dans les lemmes de la section I (proportions ultimes) (...) et dans la démonstration de la proposition 48-49 du livre I (rectification de l’épicycloïde). (shrink)

Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the putting-together in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity is ultimately related (...) to spatial extension. I use this conception of Newton’s project to explain the organization and proofs of the first theorems of mechanics to appear in the Principia. The placementof Kepler’s rule of areas as the first proposition, and the manner in which Newton proves it, appear natural on the supposition that Newton seeks a measure, in the sense of a moveable spatial quantity, of time. I argue that Newton proceeds in this way so that his reasoning can have the ostensive certainty of geometry. (shrink)

In this article, we document how, in the public arena, British readers of the first edition of Isaac Newton's Philosophiae naturalis principia mathematica (1687) tried to make sense of the relation between gravity, matter, and divine and natural causation—an issue on which Newton had remained entirely silent in the first edition of the Principia. We show that readers attached new meanings to the Principia so that parts of it migrated to a different intellectual debate. It (...) will be shown that one particular result Newton obtained in the Principia, namely the rejection of a vacuum in Corollary 3 to Proposition 6 in Book 3, was the most important locus in debates on the relation between gravity, matter, and causation. (shrink)

This article examines the text of Principia Mathematica to discover the extent to which Newton's claims about his own contribution to it were justified. It is argued that for polemical reasons the General Scholium, written twenty-six years after the first edition, substantially misrepresented the methodology of the main body of the text. The article discusses papers of Wallis, Wren and Huygens that use the third law of motion as set out by Newton in Book 1. It also (...) argues that Newton's use of induction is quite different from and subtler than the ‘logical’ and ‘probabilistic’ notions of induction discussed and then rejected by a number of twentieth-century philosophers. (shrink)