In this study, we test the security of a crucial plank in the Principia’s mathematical foundation, namely Newton’s path leading to his solution of the famous Inverse Kepler Problem: a body attracted toward an immovable center by a centripetal force inversely proportional to the square of the distance from the center must move on a conic having a focus in that center. This path begins with his definitions of centripetal and motive force, moves through the second law of (...) motion, then traverses Propositions I, II, and VI, before coming to an end with Propositions XI, XII, XIII and this trio’s first corollary. To test the security of this path, we answer the following questions. How far is Newton’s path from being truly rigorous? What would it take to clarify his ambiguous definitions and laws, supply missing details, and close logical gaps? In short, what would it take to make Newton’s route to the Inverse Kepler Problem completely convincing? The answer is very surprising: it takes far less than one might have expected, given that Newton carved this path in 1687.Keywords: Isaac Newton; Principia; Centripetal force; Second law of motion; Conic orbits; Inverse Kepler Problem. (shrink)

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 was one of the greatest scientists of all time, a thinker of extraordinary range and creativity who has left enduring legacies in mathematics and physics. While most famous for his Principia, his work on light and colour, and his discovery of the calculus, Newton devoted much more time to research in chemistry and alchemy, and to studying prophecy, church history and ancient chronology. This new edition of The Cambridge Companion to Newton provides authoritative introductions to these (...) further dimensions of his endeavours as well as to many aspects of his physics. It includes a revised bibliography, a new introduction and six new chapters: three updating previous chapters on Newton's mathematics, his chemistry and alchemy and the reception of his religious views; and three entirely new, on his religion, his ancient chronology and the treatment of continuous and discontinuous forces in his second law of motion. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:120 HISTORY OF PHILOSOPHY Opera theologica quae latine edidit, 3 vols. (Roterodami, 1651-1660). His religious polemics with Amyrault and Grofius were famous. Paul Dibon, professor at the Ecole Pratique des Hautes Etudes, is the most prominent contemporary historian of seventeenth-century Dutch philosophy and intellectual life; he is perfectly aware of the fact that genuine history can only be founded on solid erudition, and this inventory is a first-class contribution (...) to it. Only those who ignore the difficulties of this kind of research will underestimate the enormous effort it involves--an effort which is, much more than a pedantic and mechanical listing of data, a kind of venatio, requiring a continuous alertness, a surprising amount of imagination and intelligence, a painstaking precision, and an enormous background of knowledge. The letters are arranged in chronological order (with the exception of a few which are undated). Each entry lists the date, the names and locations of the sender and addressee, and the opening words of the letter. The status of the letter (original/ minute/copy/printed) is indicated, as is the library in which the letter is located (and the call number), and/or, if the letter was published, the printed source. Thirty-two libraries were explored. GIORGIO TONELLI State University o/ New York at Binghamton Introduction to Newton's Principia. By I. Bernard Cohen. (Cambridge, Mass.: Harvard University Press, 1971. Pp. xxx+380. $30.00) Over the past dozen years or so Newtonian scholarship has burgeoned as never before, and a first and fundamental result has been the publication of more and more of the wealth of manuscript material and letters that Newton left as a legacy of potential insight and confusion to future scholars. To date, the most imposing of the undertakings in publication have been The Correspondence (1959- ), begun under the editorship of H. W. Turnbull and continued more recently under that of J. F. Scott, and the Mathematical Papers (1967- ), started and continuing under the editorship of D. T. Whiteside. Selected documents of importance have been published by I. Bernard Cohen, assisted by Robert E. Schofield, in Isaac Newton's Papers and Letters on Natural Philosophy... (1958), by A. R. Hall and Marie Boas Hall in Unpublished Scientific Papers o/ Isaac Newton (1962), and by J. W. Herivel in The Background of Newton's Principia (1965); additional documentary material has appeared in studies by Alexandre Koyr6, I. Bernard Cohen, Johannes A. Lohne, D. T. Whiteside, Richard S. Wesffall, J. E. McGuire and P. M. Rattansi, and still others--a full bibliography would run to considerable length. Nor, although the uncertainties in the interpretation of the documents are sometimes overwhelming, has this spate of publication merely served to replace one set of scholarly puzzles by another. The traditional, monolithic and impenetrable image of Newton "with his prism and silent face, / The marble index of a mind for ever / Voyaging through strange seas of Thought, alone..." has lost something of its hypnotic hold, and we begin to discern some of the steps, not to say jogs and leaps, in Newton's actual journey of thought and discovery. The volume here under review introduces another major enterprise in Newtonian scholarship, a "variorum" edition of the Principia. The edition itself, which has yet to appear, will consist primarily of a facsimile reproduction of the third edition (1726)-the last edition that Newton himself supervised----collated line by line with the variant readings in the two prior editions and in a manuscript of the first edition, and with the BOOK REVIEWS 121 corrections, improvements, and additions that Newton entered into copies of the first and second editions. This textual part of the edition was delivered to the press in 1966; additional parts are in various stages of preparation. There is to be a Commentary dealing with the prefaces, definitions, laws of motion, and the first three sections of Book I and most of Book III, along with English versions and modern analytical paraphrases of the sections dealt with, a glossary, and a number of short essays on such topics as the astronomical and physical data used by Newton, the mathematical background to the understanding of the Principia, and the analysis of... (shrink)

This collection of specially commissioned essays by leading scholars presents research on Isaac Newton and his main philosophical interlocutors and critics. The essays analyze Newton's relation to his contemporaries, especially Barrow, Descartes, Leibniz and Locke and discuss the ways in which a broad range of figures, including Hume, Maclaurin, Maupertuis and Kant, reacted to his thought. The wide range of topics discussed includes the laws of nature, the notion of force, the relation of mathematics to nature, Newton's argument (...) for universal gravitation, his attitude toward philosophical empiricism, his use of 'fluxions', his approach toward measurement problems and his concept of absolute motion, together with new interpretations of Newton's matter theory. The volume concludes with an extended essay that analyzes the changes in physics wrought by Newton's Principia. A substantial introduction and bibliography provide essential reference guides. (shrink)

If you were to list the perennial issues in philosophy, the nature of time would no doubt be on that list. The essays in the present volume all touch upon the problem of time. The volume includes four contributions from different perspectives within the history of philosophy of time.Jani Hakkarainen and Todd Ryan delve into David Hume's account of time. Hume thinks there can be no time without succession. Consequently, unchanging, steadfast objects do not have a duration. They are stationary, (...) not subject to any change. Although they lack a duration, they coexist with a temporal succession. This introduces a problem: What is the relation between unchanging objects and time? Hakkarainen and Ryan draw on what they call Hume's Principle of Quantitative Comparison. Each indivisible temporal extent is equal to any other temporal extent; differences in duration are due to the different number of temporal parts. Steadfast objects may be thought to undergo a certain number of calculable changes when they are compared to ordinary successions we experience. This experience is provided, for example, by the ticking of a clock. We have the capacity to think that steadfast objects have precise durations. We humans nevertheless cannot give any deep explanation as how we come to this conclusion.Emily Thomas focuses on the graphic representation of time. Whereas the visual representation of time has typically been done with matrices or grids, Joseph Priestley represented time in a line in 1765. Priestley's line divides time “by an equal scale” into centuries. Many have interpreted this as being evidence of a Newtonian influence, as if there is an absolute time flowing equably. Thomas situates Priestley's position in the modern debates on the nature of our ideas. She argues that the absolutist reading does not have merit. Thomas thinks rather that Priestley sides with David Hartley, who explained how we acquire the ideas of duration and time from sensation. Thomas's essay advances our understanding of the history of space-time parallelism. With timelines, the analogy between time and space becomes a possibility. In my essay I assess Ernst Mach's criticism of Isaac Newton's substantivalist account of time. Newton's argument for absolute time relates to his mathematical-empirical physics and theology. In his Science of Mechanics, Mach largely neglects the laws of motion, calculus and the omnipresence theology that is at the background of Newton's concept of time. Mach did however criticize Newton's absolutist argument on the basis that the self-existing flow cannot be observed, measured, or experimented with, and he provided an alternative relational account of time. I point out that this was not only extreme positivism or phenomenalism, but an epistemology and ontology suited for the subsequent physical theories of relativity. Finally, I argue that Mach's denial of the independent atomic structure of matter should not be entirely assimilated to his denial of substantivalism about time. The two phenomena are different, so we should evaluate Mach's reasoning concerning them accordingly. Matyáš Moravec and Peter West go through Susan Stebbing's criticism of Arthur Eddington's popular account of the passage of time. Stebbing's target, Moravec and West argue, is Eddington's largely Bergsonian view on time. She objects to the view that our minds have “a private door” to the physical reality which no measurements can disclose. Stebbing believes that our experience of the passage of time belongs to our ordinary, every-day experience, and she thinks Eddington mystifies the whole idea by leaning on a peculiar form of introspection. Moravec and West build a case for Bergson's influence on Eddington, arguing that Bergson probably did contribute to Eddington's idea of “the intuition of becoming.” Both seem to think that we may access the dynamic temporal reality in ways not captured by scientific investigation, by means of an introspective internal experience of duration. As a final remark, I think I should note, with regret, that out of the six authors in this volume only one is a woman. Let the reader know that as an editor I tried to strike a better balance. I still trust that the quality of the articles is high, and most importantly, worthwhile for readers interested in the history of philosophy of time. (shrink)

Sir Isaac Newton, writing in Latin, defined his celebrated laws of motion verbally. When the laws of motion are read as relating to his arithmetic and his calculus, division by zero is undefined so his physics fails at mathematical singularities. The situation is unchanged in modern real arithmetic and real calculus: division by zero is undefined so both Newtonian Physics and its modern developments fail at mathematical singularities. However, when Newton’s text is (...) read as relating to transreal arithmetic and transreal calculus, division by zero is defined and we show that the resulting Transreal Newtonian Physics does operate at mathematical singularities. We hold out the hope that the whole of modern physics may be similarly extended. We use the new physics to predict a convection current at the singularity in a black hole and suggest experiments in astronomy and high energy physics that might confirm or rebut our predictions. Thus our exegesis of Newton’s text extends mathematical physics and may, in future, extend experimental physics. (shrink)

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 illuminating Guide to Newton's _Principia_ by I. Bernard Cohen makes this preeminent work truly accessible for today's scientists, scholars, and students. (shrink)