of the intellectual movement we call the scientific revolution of the seventeenth century, and that recognition defines the task I have set myself in this paper—to give an account first of the scientific revolution and then of the relation of Newton and hisPrincipia to it.

Beyond the ranks of historians of science, in my opinion, the scientific revolution is frequently misunderstood. A vulgarized conception of the scientific method, which one finds in elementary textbooks, a conception which places overwhelming emphasis on the collection of empirical information from which theories presumably emerge spontaneously, has contributed to the misunderstanding, and so has a mistaken notion of the Middle Ages as a period so absorbed in the pursuit of salvation as to have been unable to observe nature. In fact, medieval philosophy asserted that observation is the foundation of all knowledge, and medieval science (which certainly did exist) was a sophisticated systematization of common sense and of the basic observations of the senses. Modern science was born in the sixteenth and seventeenth centuries in the denial of both.

Consider astronomy for example. Nearly everyone takes Copernicus as the beginning of the scientific revolution, and developments in astronomy foreshadowed the course of the scientific revolution as a whole.² Medieval astronomy rested on two basic propositions: that the motions observed in the heavens actually take place there, and that we must accept the validity of the basic observation each of us makes every moment, to wit, that we live on a stable earth. Geocentric astronomy followed directly from these premises, a complex system of circles on circles, of deferents, epicycles, and eccentrics, which provided a reasonable account in theory of the observed celestial phenomena.

Early in the sixteenth century, Nicholas Copernicus became dissatisfied with the system. It contained arbitrary elements. For example, in geocentric astronomy the sun was only one planet among seven, and yet the sun was involved in the theories of all the others except the moon. Mercury and Venus never depart far from the sun; they are seen in the west in the evening after sunset, or in the east in the morning before dawn, but never in the midnight sky. In order to make the theories of Mercury and Venus work, the centres of their epicycles had always to lie on the line between the sun and the Earth. Mars, Jupiter, and Saturn, on the other hand, go through their retrogressions when they are in the opposite part of the heavens from the sun; each of them, in the middle of its retrogression, crosses the meridian precisely at midnight. To make their theories correspond to the heavens it was necessary that the radii vectors of their epicycles always be parallel to the line between the sun and the Earth. Why was this so? How was it possible that the sun be merely one planet and yet participate in the theories of the others? Moreover, the geocentric system contained no necessary criteria for orbital size; as long as deferent and epicycle maintained the necessary proportion to each other established by observation, they could be of any size. Hence the planets had no necessary order. The Ptolemaic order was commonly accepted, but only on the basis of ad hoc assumptions that had no intrinsic relation to the system; there was no conclusive argument why Saturn, for example, could not be closer to the Earth than Mercury. And the so-called system did not appear to be a system at all to Copernicus. Consider the order of motions, in the Ptolemaic arrangement, as Copernicus would have known them. The Earth stood motionless in the centre. The moon circled the Earth with a period of one month. Beyond the moon were Mercury, Venus, and the sun, all with periods (for Mercury and Venus, average periods), in the Ptolemaic system, of one year. Then Mars, two years, Jupiter, twelve years, Saturn, thirty years, and beyond all the planets the sphere of the fixed stars with a period of one day in the opposite direction. In Copernicus's eyes, this was not an ordered system, it was chaos.

Copernicus saw that he could remove all of the arbitrary elements and solve all of the problems by the simple expedients of putting the Earth into motion, with both a diurnal rotation and an annual revolution around the sun, and of treating most of the motions in the heavens as mere appearances resulting from the motions of the Earth. All that was necessary was to put the Earth in motion; this was an incredible thought, fundamentally at odds with all experience and with the dictates of common sense. And yet, by accepting that premise, he could arrive at a system that presented a spectacle of mathematical order and harmony not to be found in Ptolemy. For Ptolemaic, geocentric astronomers, each planet was a separate problem. For Copernicus and heliocentric astronomers, system was foremost. In the heliocentric system, the orbits are measurable in terms of the astronomical unit (the distance, not well measured in terrestrial units in Copernicus's age, between the Earth and the sun). Hence they had a necessary order, and that order corresponded to a harmonious system of motions in which periods decreased with distance from the sun, and the fixed stars at the periphery stood motionless. Copernicus threw common sense to the winds in order to pursue the arcane satisfactions of mathematical harmony (Copernicus, Revolutions)³

Copernicus was only the beginning. If he challenged some of the assumptions of common sense, he was unable to recognize the others to which he still clung. Foremost among these was the conviction that only circular motions can be found in the heavens and thus that astronomy can employ only circles in its account of heavenly phenomena. To the ancient Greeks, the circle had represented the perfect figure, that path in which a body can move forever without altering its relation to the centre, and the perfection of the circle had seemed to correspond to the perfection and immutability of the heavens. Copernicus was as wedded to the notion that the circle was the sole device of astronomical theory as the ancient Greeks, but circles obstructed the pursuit of a mathematically simple and harmonious system. It remained for Johannes Kepler, two generations later, to challenge their role. As Kepler began to propose that the planets move in non-circular orbits, he received a letter of protest from another astronomer who insisted that he was destroying the very foundation of astronomy. In a witty reply, Kepler referred to circles as voluptuous whores enticing astronomers away from the honest maiden Nature (Kepler, "Letter" 205). He knew whereof he spoke, for it had taken Kepler years to escape the attractions of the enchantress. His elliptical orbits, together with his two other quantitative laws of planetary motion, which yielded a system breathtaking in its mathematical simplicity, was another victory of abstract reason over assumptions accepted for centuries as the very embodiment of common sense.⁴

Kepler's three laws did nothing, however, to make the proposition that the Earth is in motion one whit less incredible than it seemed to virtually everyone. Here we confront the phenomena of moving objects, especially falling objects, on an Earth said to be rotating on its axis. The objections raised were by no means silly, and once again they sprang from common sense itself and from the observations all of us constantly make. If the Earth is moving as Copernicans claimed, surely we would perceive the motion. The size of the Earth was known then with sufficient accuracy to make the point. If it is rotating on its axis, we are, at this moment, moving from west to east at approximately a thousand miles per hour. To put the dilemma in twentieth-century terms, which make the problem considerably less difficult than seventeenth-century conditions, we ride in our cars every day, and we never fail to perceive the motion. Is it possible that we are cruising down the cosmic highway at a rate well over ten times the highest speed we ever go in our cars and are yet unaware of the motion? Or drop a stone from the top of a tall building with a flat side. Ballantine Hall on the campus of Indiana University—the twentieth-century example in this case differs from a seventeenth-century one only in the style of the architecture—is nine storeys tall; it takes a stone roughly two and a half seconds to fall from the top to the ground. A thousand miles per hour is equivalent to more than a thousand feet per second. During the time the stone is falling, Ballantine Hall moves more than half a mile to the east. How is it possible that a stone dropped one foot out from the eastern wall of Ballantine falls parallel to its side and lands very nearly one foot from the base of the wall?

The problem of motion on a moving Earth defined the major work of Galileo, who rethought the very conception of motion in order to justify the assertion that the Earth is turning on its axis. Motion, Galileo decided, is not, as Aristotle had thought, a process whereby entities realize their being. Motion is merely a state in which a body finds itself, a state that alters nothing in a body, a state to which a body is indifferent. Hence we are unable to perceive uniform motions in which we participate along with everything around us. When motion is understood in these terms, stones can fall parallel to the vertical walls of buildings when the Earth is in motion as well as they would if the Earth were at rest. Contrary to the central assertion of Aristotle's analysis, uniform motion understood in Galileo's terms requires no cause. As I hold the stone before I drop it from the top of Ballantine Hall, the stone is moving from west to east at the same rate as the building and I. The stone's horizontal motion continues unaffected; the eastern wall of Ballantine does not catch up with the stone. We perceive only the vertical drop in which we do not participate. As Descartes, who shared the new conception, put it, philosophers have been asking the wrong question. They have been asking what keeps a body in motion. The correct question is why does it not continue to move forever (Oeuvres). We know the new conception of motion as the principle of inertia. Although Galileo did not use that term, he made the concept the corner-stone of a new science of motion (or mechanics, as physicists call it) which became the central edifice in the whole new complex of modern science, and philosophers of science today agree that the principle of inertia is the basic concept on which the science we know rests.⁵

With Galileo the Copernican universe became believable, but was it true? Or to rephrase the question, what evidence was there in its favour in the early decades of the seventeenth century? As soon as one puts the question in those terms, one is forced to concede that the evidence in its favour was almost precisely the advantage that Copernicus, and Copernicans after him, had pursued, that is, mathematical harmony and simplicity. For the truth is that there was precious little other evidence to support it. Galileo's new science of motion answered the major objection against the system, but it did not count as evidence for it. To be sure, late in 1609 the same Galileo had turned his newly improved telescope on the heavens, but neither Galileo nor anyone else could look through a telescope and see the Earth moving around the sun and rotating on its axis. Galileo did observe the mountainous surface of the moon, the spots on the sun from the motion of which he inferred the rotation of the sun on its axis, and the satellites of Jupiter. These phenomena all fit more smoothly into the Copernican picture of the universe, but they did not demonstrate that it was true. Especially Galileo observed the phases of Venus which did demonstrate that Venus (and by implication Mercury) revolves around the sun and were then logically incompatible with the Ptolemaic system, but the phases of Venus did not demonstrate that the Copernican system is true.⁶ One forgets all too easily another observation that Galileo did not make, stellar parallax. If the Earth is moving around the sun in an immense orbit, then if we observe the angle at which some fixed star appears in the middle of the summer and again six months later in the middle of the winter, after the Earth has moved an immense distance, surely the two angular locations will differ. To the naked eye the angles appeared identical. Alas, they also appeared identical through early telescopes. Today we know why: the fixed stars are so far removed that it was well into the nineteenth century before telescopes powerful enough to distinguish the two angles were developed. Such distances were inconceivable to most people in the early seventeenth century. At the least, the failure to observe stellar parallax offset the positive observation of the phases of Venus. Primarily for the ethereal advantages of mathematical harmony and simplicity early scientists asked mankind to surrender the most obvious evidence of the senses and the manifest dictates of common sense. They did not ask in vain. During the seventeenth century a new school of natural philosophers who were ready and indeed eager to accept the invitation appeared until, by the end of the century, none of them could imagine how anyone had ever believed otherwise.

Observe the process that I describe. From Copernicus's question about the order of the universe there spread out an expanding domain of discussion that grew ever broader. It does not appear to me to have been spurred on by issues of practical utility as so much scientific investigation in our age is, but rather by the pursuit of Truth. (I capitalize "truth" as I am convinced sixteenth- and seventeenth-century natural philosophers would have done.) Johannes Kepler, a man without personal resources, who was dependent for his livelihood on the favours of patrons and, conscious as he was of the current patron's mortality, always on the look-out for the next, was willing to live teetering on the brink of oblivion if he could demonstrate the correct pattern of the heavens. Galileo was willing to dare the fury of the Inquisition because it mattered to him whether the universe was geocentric or heliocentric.

The next major step was taken by a Frenchman, René Descartes, to whom such issues also mattered. Instructed in part by Galileo's debacle, he chose to live in exile in the Netherlands in order that he might more freely pursue his thoughts. Descartes universalized the tendencies inherent in the scientific movement. It is not only the heavens that are not as they seem to be, and not only motion. The whole universe is not as it seems to be. We see about us a world of qualities and of life. They are all mere appearances. Reality consists solely of particles of matter in motion. Some of the particles impinge on our senses and produce sensations, but nothing similar to the sensations exists outside ourselves. Reality is quantitative, particles characterized solely by size and shape, and of course motion. The picture of nature that I am describing so briefly was known in the seventeenth century as the mechanical philosophy; it provided the philosophic framework of the scientific revolution. The world was not like a living being, it was like a great machine. Things such as plants and animals, said to be living—human beings, with their capacity for rational thought were partial exceptions—were only complicated machines. Thus the ultimate implication of the movement Copernicus initiated proved to be much wider than Copernicus had imagined. Humankind was not merely displaced from the centre. It was displaced entirely. Its presence was irrelevant to the universe; the universe was not created for human benefit: it would have been almost entirely the same whether humankind was there or not.⁷

Isaac Newton arrived on the scene after the early stages of the scientific revolution. He was born in 1642, the year Galileo died, twelve years after Kepler died, two years before Descartes published his Principles of Philosophy. Everything that I have discussed contributed to his intellectual inheritance. The scientific revolution was a complex movement of many dimensions. For my purposes in this paper, let me summarize it under three major themes, all of crucial importance to Newton. The scientific revolution presented a new picture of the universe, heliocentric rather than geocentric. It presented a new image of nature as inert particles in motion, the mechanical philosophy. And it presented a new vision of reality in terms of quantity rather than quality, so that increasingly science would express itself through mathematical demonstrations. Though implicit in the pursuit of mathematical harmony and simplicity, the third theme has not been explicit in the examples I have cited. To insist on its centrality, let me quote two representative statements. "Geometry," said Kepler, "being part of the divine mind from time immemorial, from before the origin of things, being God Himself (for what is in God that is not God Himself?), has supplied God with the models for the creation of the world and has been transferred to man together with the image of God. Geometry was not received inside through the eyes."⁸ The same vision was shared by Galileo, who brought geometry down from the heavens, and building with it on the foundation of his new conception of motion, created what had heretofore appeared to be a contradiction in terms, a mathematical science of terrestrial motion. "Philosophy," said Galileo, "is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it …" (Discoveries 237-8). The new vision of reality, the conviction that the world is structured mathematically, was perhaps more basic to the scientific revolution than anything else.

When Newton enrolled in Cambridge in 1661, none of the early work of the scientific revolution had penetrated the standard curriculum. Despite some superficial changes, the university remained still in its medieval mould, and the philosophy of Aristotle continued to be the focus of the studies it prescribed. Newton was not a docile student, however, and sometime around 1664 he undertook a new programme of study. The record of his reading survives.⁹ It contains no suggestion of tutorial guidance; on the contrary, it strongly implies that Newton struck out on his own. First, apparently, he discovered mathematics. In this he may have been influenced by the inaugural lectures of Isaac Barrow in the newly created Lucasian Professorship of Mathematics. Barrow was not Newton's tutor, however, and the two men became close only five years later. The seventeenth century was the most creative period in mathematics since the age of ancient Greece; in the short space of twelve to fifteen months, during what was also his final year as an undergraduate, Newton, by himself, absorbed the entire prior achievement of seventeenth-century mathematics and began to move beyond it towards the calculus. He set down the definitive statement of what he called the fluxional method in October 1666, about one and a half years after he had taken his Bachelor of Arts degree.¹⁰ Mathematics was not all he discovered. He also found the new natural philosophy, especially the writings of Descartes and Pierre Gassendi (whose revival of ancient atomism offered an alternative mechanical philosophy). Within the context of natural philosophy, he came upon the problem of colours. When he was less than a year beyond his BA degree, Newton set down in the same notebook in which he recorded his reading in natural philosophy as a whole the first suggestion of the central concept to which all of his work in optics would be devoted, that light is not homogeneous as everyone had heretofore believed, but a heterogeneous mixture of difform rays that provoke different sensations of colour.¹¹ During much the same period, Newton also discovered the science of mechanics.¹² One of the best known Newtonian stories, which is drawn from a passage he composed toward the end of his life, claims that he developed the concept of universal gravitation at this time. Newtonian scholars no longer believe that story. Nevertheless, it is clear that he entertained vague thoughts about the dynamics of the heavens at this time, and that he later drew upon and amplified these thoughts (Herivel 183-98).

Later Newton found other interests as well, primarily chemistry/alchemy, and theology, which together largely dominated his time and consciousness from the late 1660s. In August 1684, as even people only vaguely informed about Newton know, he received an unexpected visit from Edmund Halley, who bluntly asked him what would be the shape of the path followed by a body orbiting another that attracted it with a force that varied inversely as the square of the distance. We cannot follow in any depth the psychology of Newton's response to Halley's question. We can only say that somehow the question reawakened earlier interests long dormant, so that late in the same year Newton sent Halley a tract of ten pages, which is known by the title De motu.

De motu was a short treatise on orbital dynamics that demonstrated the relation of Kepler's three laws of planetary motion to an inverse square attraction (Herivel 257-92). Although the demonstrations in De motu later became part of the Principia, they did not rest on a solid foundation in the early tract, for it presented only a primitive and crude science of dynamics. It did not accept the principle of inertia, and it did not state any general force law. Moreover, the defects of De motu were not so much the shortcoming of Newton as the limitations of the science of his day. In 1684, no one had constructed a satisfactory science of dynamics that corresponded to the new conception of motion. In Kepler's conclusions about planetary motion and in Galileo's science of uniformly accelerated motion, mechanics had arrived at kinematic laws, but as yet no dynamics to support the kinematics existed. Newton's first task, as he set out to expand and elaborate De motu, was to create a workable science of dynamics.

Those papers also survive (Herivel 292-320). They show that during the months following the composition of De motu Newton carried out an intense investigation of the fundamental concepts of the science of mechanics. Partly this was a work of definition, and as he proceeded, Newton provisionally defined no less than nineteen different concepts, of which five definitions survived into the Principia. From the investigation emerged the three laws of motion that still introduce courses in physics just as they introduced the Principia three centuries ago, three laws that constitute a quantitative science of dynamics from which both Galileo's kinematics of uniformly accelerated motion and Kepler's kinematics of planetary motion follow as necessary consequences. Thus Newton's science of dynamics bound celestial mechanics together with terrestrial mechanics, and for this reason people frequently refer to it as the Newtonian synthesis.

As an expression of Newtonian dynamics, the Principia was also a synthesis of the major themes of the scientific revolution. It supplied the final justification of the heliocentric system of the universe, in its Keplerian form, by providing its dynamic foundation. It raised the mathematical vision of reality to a new level of intensity. The Principia was a book of mathematical science, modelled on Euclid; more than any other work of the scientific revolution, it established the pattern that the whole of modern science has striven to fill in. The third theme that I singled out, the mechanical image of nature, is perhaps less obvious in the Principia; nevertheless, the book is unintelligible apart from it. Like every mechanical philosopher in the seventeenth century, Newton looked upon nature as a system of material particles in motion. To the astringent ontology of the prevailing mechanical philosophy, which ascribed to particles only size, shape, and motion, and insisted that all the phenomena of nature are produced by impact alone, Newton added a further category of property—forces of attraction and repulsion—whereby particles and bodies composed of particles act upon other particles and bodies at a distance.¹³ The Newtonian conception of attractions also formed an essential dimension of Newton's mathematical view of reality, for the forces were mathematically defined. For example, the gravitational attraction of bodies for each other varied inversely as the square of the distance.

The structure of the Principia reflects its dynamic foundation. Book I is all abstract mathematical dynamics of point masses moving without resistance in various force fields. While Newton consistently explored the consequences of different force laws in the problems to which Book I devoted itself, he focussed his attention primarily upon the inverse square attraction and the phenomena of motion it entails. Book II considered the motion of bodies through resisting media and the motions of such media, reaching its climax with the examination of the dynamic conditions of vortical motion. That is, Book II was primarily an attack on the natural philosophy of Descartes and the prevailing mechanical picture of nature he had inspired. Newton demonstrated that vortices are unable to sustain themselves without the constant addition of new energy (or "motion," in the language of the seventeenth century) and are unable to yield Kepler's three planetary laws.

With the alternative system discredited, Book III returned to the demonstrations of Book I, which it applied to the observed phenomena of the universe. Newton's first law states that bodies in motion, undisturbed by any external influence, tend to move in straight lines. Planets move in closed orbits, and in their motions they observe Kepler's second law, the law of areas. For both reasons it follows from Book I that the planets must be attracted toward a point near the centre of their orbits where the sun is located. For the same reasons, the satellites of Jupiter and Saturn must be attracted toward those planets. Moreover, planets travel in ellipses with the sun at one focus, and their lines of apsides (the major axes of the ellipses) remain stable in space. The orbits of the system also obey Kepler's third law. It follows from the demonstrations of Book I that the attraction toward the sun must vary inversely as the square of the distance, and since the satellites of Jupiter conform to Kepler's third law, they too must be attracted by such a force. Furthermore, because the planetary system observes Kepler's third law, the attraction of the sun for each of the planets must be proportional to its quantity of matter. Again, the same holds for the attraction of Jupiter for its satellites, and since the satellites move in orbits that are nearly concentric with Jupiter as it orbits the sun, the attraction of the sun for both Jupiter and its satellites must be proportional to their several quantities of matter.

The Earth also has a satellite, the moon, which constantly accompanies it and does not fly off into space along a straight line; therefore the Earth must attract the moon to hold it in its orbit. Unlike Jupiter, the Earth has only one satellite, and that one with an orbit so highly irregular as not to appear truly elliptical; from such a satellite alone one cannot reason to an inverse square force. However, on the Earth there is a substitute for additional satellites. Heavy bodies fall to its surface where we can experiment with them. Hence the importance of the correlation between the motion of the moon and the measured acceleration of gravity on the surface of the Earth. How far from the Earth is a heavy body we drop—or, to speak in terms of the famous myth, how far is an apple from the Earth? Whether it was an apple or an experimental weight, any body that a seventeenth-century scientist could handle was at most a few feet from the surface of the Earth. Newton's correlation demanded that it must be roughly four thousand miles from the Earth; that is, the crucial distance was not to the surface but to the centre. To put it this way is to insist on the importance of the demonstration at which Newton arrived some time in 1685, that a homogeneous sphere, composed of particles that attract inversely as the square of the distance, itself attracts other bodies, no matter how close they may be, with forces that are inversely proportional to the bodies' distances from the sphere's centre. With the crucial demonstration about spheres, Newton could further demonstrate that the attraction that causes heavy bodies to fall toward the Earth is quantitatively identical to the attraction that holds the moon in its orbit. The critical correlation between the motion of the moon and the acceleration of gravity was the single strand that connected the cosmic attraction, shown to be necessary to hold the solar system together, with terrestrial phenomena, thus allowing him to apply to the attraction the ancient word gravitas, heaviness. From the motions of pendulums he could show that heaviness on Earth also varies directly in proportion to the quantity of matter. Thus Newton was brought to state what is perhaps the most famous generalization of modern science, that "there is a power of gravity pertaining to all bodies, proportional to the several quantities of matter which they contain" (Mathematical Principles 414).

The principle of universal grativation, which I have just quoted, appeared early in Book III as Proposition 7, derived from the sharply limited number of phenomena I cited. The rest of the book then applied the principle to a number of other phenomena that had not contributed to its derivation. Recent European expeditions, especially a French expedition to the northern coast of South America, had revealed that the length of a pendulum that completes a swing in one second varies with the latitude. Near the equator a seconds pendulum needs to be shorter than it is in Europe. Newton was able to demonstrate that the shorter length of the pendulum is due to the decrease in the intensity of gravity near the equator because of the oblate shape of the Earth.

He turned from the shape of the Earth to the perturbations of the moon. Over the centuries astronomers had empirically established a number of anomalies in the moon's motion. Newton now showed that all the known perturbations are dynamic effects of the attraction of a third body, the sun. He applied the same analysis of the effects of a third body to the shape of a ring of water treated as a satellite circling the Earth and being perturbed by the combined effects of the moon and the sun, and he arrived at the explanation of the tides. When the "satellite" was the bulge of matter around the equator, the same analysis yielded the conical motion of the Earth's axis known as the precession of the equinoxes. In a final tour de force, Newton reversed a tradition as old as astronomy itself and, treating comets as planet-like bodies subject to the same orbital dynamics as planets, he succeeded in describing observed locations of the great comet of 1680-81 in terms of a parabolic orbit.

It would be difficult to overestimate the impact of the Principia. As I insisted, there has never been a time since the day of its publication when it was not perceived as a monumental achievement. Take its treatment of the moon as an example. The Principia suggested for the first time the cause of the moon's known anomalies, and in so doing inaugurated a wholly new chapter in lunar theory. Much the same can be said of the tides, the precession of the equinoxes, comets, and, of course, the book's central problem, planetary motion. Moreover, all of these phenomena were reduced to a single causal principle, and all was done with a degree of mathematical precision that made it impossible for anyone who understood the mathematics to doubt the theory. In the words of David Gregory, who had just finished reading the Principia in the late summer of 1687, Newton taught the world "that which I never expected any man should have knwon" (Correspondence 2: 484). In the more recent language of Thomas Kuhn, the Principia established the paradigm which modern science in its various dimensions has been attempting to emulate ever since.

The Principia was published three hundred years ago. In comparison to the total population of Europe, it was, to be sure, only a handful who recognized its significance. Nevertheless, its appearance was the most important event of 1687. I am not exactly an impartial judge, but let me state forthrightly that I am not aware of any event to match its impact on western civilization during the intervening three centuries.

Notes

¹ J. T. Desaguliers stated that he had heard this story from Newton. John Conduitt was also familiar with the story, and we can assume with confidence that he got it from the same source (King's College, Keynes mss. 130.6, Book 2: 130.5, Sheet 1). Newton undoubtedly learned it from Locke himself.

² For more detailed treatment of the astronomical revolution see Koyré, Astronomical Revolution and Kuhn.

³ For short statements of the system see Copernicus's Commentariolus or Rheticus's Narratio prima in Copernicus, Three Treatises.

⁴ See especially Kepler's Astronomia nova, the work of 1609 in which he announced his first two laws, and his summary statement of his work in The Epitome of Copernican Astronomy in the Gesammelte Werke. Books IV and V of the Epitome have been translated into English by C. G. Wallis in vol. 16 of Great Books.

⁵ For Galileo's discussion of the problem of motion on a moving Earth see primarily the Second Day of his Dialogue. For his science of mechanics as a whole, see his Two New Sciences. There is an enormous literature on Galileo and his new science of motion. The basic work that shaped our present understanding of Galileo is Koyré, Galileo Studies. See also Clavelin.

⁶ Galileo's accounts of his observations appear in The Starry Messenger (1610), the opening passage of the Discourse on Bodies in Water (1612), and the Letters on Sunspots (1613). Translations of the first and the third can be found in Discoveries. Drake has also edited a seventeenth-century translation of the second, published as a separate volume, and more recently included his own translation of it in Galileo, Cause.

⁷ See especially Descartes's Principles and also the shorter exposition of his natural philosophy in Le monde. For discussions of the mechanical philosophy see Hall, Harré, and the relevant chapter of Collingwood.

⁸Harmonices mundi, IV, in Gesammelte Werke, 6: 223. I quote the translation in Caspar, 271.

⁹ See his undergraduate notebook, although it contains the record only of his philosophical studies; the records of his work in mathematics and mechanics are in McGuire and Tamny.

¹⁰ The record of Newton's early studies in mathematics, up to the tract of October 1666, makes up the first volume of Mathematical Papers. In the notes to this edition and in other writings, D. T. Whiteside is also the leading commentator on Newton's mathematics.

¹¹ For Newton's early work in optics see Shapiro and my own article. Shapiro is currently editing a full publication of Newton's optical papers. Volume one, which has appeared, contains the early Lucasion lectures on optics. Volume two will contain the material I am now discussing.

¹² His early notes on mechanics, mostly in another notebook that Newton called the "Waste Book," are published and discussed in Herivel, 121-82.

¹³ Scholars argue about whether Newton meant to ascribe forces to bodies or understood that they were caused by some "mechanical" device (in the seventeenth-century meaning of "mechanical") such as a particulate aether. For the view that Newton understood forces as real entities in nature, see McGuire, "Forces," 154-208. For the argument that he understood gravity, for example, to be caused by a material medium, see Cohen, Newtonian Revolution. Home, 95-117, vigorously defends the position that Newton never understood electrical and magnetic forces as actions at a distance. I have generally taken the side that Newton did accept forces as real entities in nature, but the argument of this paper does not depend on that position. Whatever Newton thought about the ontological status of forces, the Principia proceeded in terms of attractions and repulsions acting at a distance.

WORKS CITED

Caspar, Max. Kepler. Trans. C. Doris Hellman. New York: Abelard-Schuman, 1959.

Clavelin, Maurice. The Natural Philosophy of Galileo. Trans. A. J. Pomerans. Cambridge, MA: MIT Press, 1974.

Collingwood, R. G. The Idea of Nature. Oxford: Clarendon, 1945.

Cohen, I. Bernard. "Isaac Newton, Hans Sloane and the Académie des Sciences." Mélanges Alexandres Koyré. 2 vols. Paris: Hermann, 1964. 2:61-116.

——. The Newtonian Revolution. Cambridge and New York: Cambridge UP, 1980.

Copernicus, Nicholas. On the Revolutions. Trans. Edward Rosen. Baltimore: Johns Hopkins UP, 1978.

——. Three Copernican Treatises. Trans. Edward Rosen. New York: Dover Publications, 1939.

Desaguliers, J. T. Preface A Course of Experimental Philosophy. 2 vols. London, 1734-44.

Descartes, René. Le monde, ou traité de la lumière. Trans. Michael Mahoney. New York: Abarus Books, 1979.

——. Oeuvres de Descartes. Ed. Charles Adam and Paul Tannery. 12 vols. Paris: L. Cerf, 1897-1910.

——. Principles of Philosophy. Trans. V. R. and R. P. Miller. Dordrecht: Kluwer, 1983.

Fatio de Duillier, Nicholas. Letter to Christiaan Huygens, 14 June 1687. Christiaan Huygens. Oeuvres complètes. 22 vols. The Hague, 1888-1950. Vol. 9.

Galileo. Cause, Experiment, and Science. Trans. Stillman Drake. Chicago: U of Chicago P, 1981.

——. Dialogue Concerning the Two Chief World Systems–Ptolemaic and Copernican. Trans. Stillman Drake. Berkeley: U of California P, 1962.

——. Discoveries and Opinions of Galileo. Trans. Stillman Drake. Garden City, NY: Doubleday, 1957.

——. Two New Sciences. Trans. Stillman Drake. Madison: U of Wisconsin P, 1974.

Great Books of the Western World. Ed. Robert M. Hutchins. 50 vols. Chicago: W. Benton, 1952.

Gregory, David. Letter to Newton. 2 September 1687. Newton, Correspondence.

Hall, Marie Boas. "The Establishment of the Mechanical Philosophy." Osiris 10 (1952): 412-541.

Harré, Rom. Matter and Method. London: Macmillan; New York: St Martin's, 1964.

Herivel, John. The Background to Newton's Principia. Oxford: Clarendon Press, 1965.

Home, R. W. "Force, Electricity, and the Powers of Living Matter in Newton's Mature Philosophy of Nature." Religion, Science, and Worldview. Ed. Margaret J. Osier and Paul L. Farber. Cambridge and New York: Cambridge UP, 1985.

Kepler, Johannes. Gesammelte Werke. Ed. Walther von Dyck and Max Caspar. 19 vols. Munich, 1937-83.

——. Letter to Fabricius. 10 November 1608. Kepler. Gesammelte Werke. Vol. 16.

Koyré, Alexandre. The Astronomical Revolution. Trans. R. E. W. Maddison. Ithaca: Cornell UP; Paris: Hermann, 1973.

——. Galileo Studies. Trans. John Mepham. Hassocks [Engl.]: Harvester Press, 1978.

Kuhn, Thomas. The Copernican Revolution. Cambridge, MA: Harvard UP, 1957.

McGuire, J. E. "Forces, Active Principles, and Newton's Invisible Realm." Ambix 15 (1968): 154-208.

McGuire, J. E., and Martin Tamny. Certain Philosophical Questions: Newton's Trinity Notebook. Cambridge and New York: Cambridge UP, 1983.

Newton, Isaac. The Correspondence of Isaac Newton. Ed. H. W. Turnbull. 7 vols. Cambridge UP, 1959-77.

——. The Mathematical Papers of Isaac Newton. vols. Ed. D. T. Whiteside. Cambridge and New York: Cambridge UP, 1967-81.

——. The Optical Papers of Isaac Newton. Ed. Alan E. Shapiro. 3 (projected) vols. Cambridge and New York: Cambridge UP, 1984.

——. [Principia.] Sir Isaac Newton's Mathematical Principles of Natural Philosophy and his System of the World. Ed. Florian Cajori. Trans. Andrew Motte. Berkeley: U of California P, 1934.

Rev. of Principia. Philosophical Transactions of The Royal Society of London 16 (1686-87): 291-97.

Shapiro, Alan E. "The Evolving Structure of Newton's Theory of White Light and Color." Isis 71 (1980): 211-35.

Westfall, Richard S. "The Development of Newton's Theory of Colors." Isis 53 (1962): 339-58.