Philosophiae Naturalis Principia Mathematica

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Title page of Newton's Philosophiae Naturalis Principia Mathematica from 1687

Philosophiae Naturalis Principia Mathematica, often also called Principia Mathematica or simply Principia , is Isaac Newton's main work . The Latin title translated means The Mathematical Foundations of Natural Philosophy. The work was first submitted as a manuscript to the Royal Society in 1686 , received permission to print from Samuel Pepys on July 5, 1686, and was published in Latin in 1687. Again and again encouraged by Edmund Halley , the initiator of the work and organizer of the first edition, Newton wrote one of the most influential books on physics and astronomy of all time.

History and Editions

Newton's personal copy ( Cambridge University Library ) of the first edition with personal notes for the second edition

The real impetus for the book came when Edmund Halley visited Newton in Cambridge in August 1684 and mentioned a discussion between him, Christopher Wren, and Robert Hooke in January of that year in which Hooke claimed that the Kepler laws were derived from an inverse-square approach Distance to have derived decreasing gravitational force. Hooke had already made such a force law responsible for the planetary motion in (published) letters to Newton in 1674, as a balancing force for centrifugal force , and Halley had also come to this conclusion, but could not derive the Kepler laws from it. Newton replied to Halley in Cambridge in 1684 that he had already succeeded in doing this, but that he could not find the documents. In November 1685 he sent Halley the derivation in a treatise "De motu corporum in gyrum" (On the movement of bodies in an orbit). There he not only derived the Kepler laws (elliptical trajectory), but also trajectories on other conic sections (hyperbolas, parabolas) and treated the movement of a body in a medium with resistance. Halley reported this to the Royal Society in December 1685 and urged Newton to publish his results. During this time Newton also had contacts to the Royal Astronomer John Flamsteed , who provided him with observation data of the planets. In April 1686 the final manuscript of the Principia was presented to the Royal Society, which (after disputes over priority with Hooke) approved publication on June 30th. The cost of printing took Halley, as the Royal Society their budget for printing costs with the publication of of Francis Willughby originating and John Ray finished work De Historia Piscium, had a natural history of the fish consumed.

Beginning in 1709, Newton worked with substantial assistance from the Plumian Professor of Astronomy at Trinity College , Roger Cotes , on a second edition of the Principia, which was published in 1713, with an extensive and enlightening foreword by the editor Cotes, coordinated with Newton. At that time Newton was employed as head of the Royal Mint and otherwise involved in various priority disputes, especially with Leibniz . In a “General Scholium” at the end of Book 3 in this second edition, he criticizes Descartes and Leibniz. Here you can also find his famous sentence that he would not form hypotheses (“ Hypotheses non fingo ”). The third edition appeared on March 25, 1726 with the collaboration of Henry Pemberton (Newton mentioned in the foreword this time with praise).

From 1739 to 1742 an edition of the 3rd edition with detailed commentary (almost line by line) was published in Geneva , edited by the Franciscans Thomas Le Seur and François Jacquier (but other scientists also worked on it), in which they also used the more modern Leibniz calculus Calculus used. This so-called Jesuit edition was recommended in 1980 by the Newton biographer Richard Westfall as one of the best-commented editions of the Principia. Newton himself had avoided infinitesimal calculus and arithmetic equations in his Principia and presented his mathematical derivations as geometrical proportions. This was based on the classical form of the representation of mathematics since ancient Greece ( Euclid's elements ).

Between 1745 and 1749, Émilie du Châtelet , a friend of Voltaire , wrote a translation into French together with Alexis-Claude Clairaut . It was also Voltaire who circulated the famous tale of the discovery of gravity by an apple falling on Newton. In France, Newton's theories, which by no means met with approval from all contemporaries, only found acceptance in the form of translation and analytical commentary by du Châtelet. Gottfried Wilhelm Leibniz and Christiaan Huygens , two great contemporary scientists on the “continent”, were and remained skeptical until their deaths.

The first German-language complete edition was published in 1872 by Jakob Philipp Wolfers .

The main inner belt asteroid (2653) Principia was named after the plant.


Newton derived the law of gravity in the Principia . He combined Galileo Galileo's research on acceleration and Johannes Kepler's research on planetary motions ( Kepler's laws ) into a unified theory of gravitation and laid the foundations of classical mechanics by formulating the three basic laws of motion . He also introduced the concepts of absolute time , absolute space (based on his famous bucket experiment ), action at a distance and thus indirectly the concept of determinism , all of which have been used for the scientific worldview of many generations up to Albert Einstein's theory of relativity and quantum mechanics were formative.

The roughly 600-page work is divided into three books, the first of which mainly contains the mathematical derivations of Newton's famous laws of motion ( dynamics and gravitation ), while the second, also very mathematically oriented, deals with body movements in viscous liquids. The second book ends with the refutation of the hypothesis that the movements of the planets and their satellites are caused by eddy movements of an ethereal fluid that fills the whole universe . Thus Newton's Principia mathematica from 1687 represents, among other things, an answer to Descartes' Principia philosophiae from 1644, where Descartes tried to justify this in detail in the third section From the visible world in a fluid-mechanical way . With the theory of an infinitely extensive etheric fluid, Descartes had convinced most of the scholars of the time. ( Newton later criticized the ether fluid again in his very influential book Opticks from 1704.)

The third book, entitled About the World System, concerns the application of the knowledge gained in the first two books to the actual movements of celestial bodies, whereby Newton compares his calculations with a large number of measurement data from other naturalists and in this way proves the correctness of his theoretical derivations. With this in mind, Newton introduces the third book with the following words:

“In the previous books I presented principles for physics, but not physical, but only mathematical, namely so that physical things can be treated on the basis of these principles. ... It now remains for us to explain the structure of the world system on the basis of these principles. On this subject I have written the third book in a generally understandable form so that it can be read by quite a few ... "


Newer editions of the Latin original

  • Isaac Newton's Philosophiae Naturalis Principia Mathematica, the 3rd Edition with Variant Readings. Editors Alexandre Koyré , I. Bernard Cohen (with assistance from Anne Whitman). Harvard University Press, Cambridge / Mass. 1726 and Cambridge University Press, Cambridge 1972. ISBN 0-674-66475-2 .

German translations

  • Sir Isaac Newton's Mathematical Principles of Natural Science. With comments and explanations. Edited by Prof. Dr. J. Ph. Wolfers . R. Oppenheim, Berlin 1872, online.
  • Mathematical foundations of natural philosophy. Selected, translated, introduced and edited by Ed Dellian. Meiner, Hamburg 1988. (Philosophical Library; Volume 394), ISBN 3-7873-0764-8 ; New edition 2007 by Academia Verlag Sankt Augustin; 4th edition 2016.
  • The mathematical principles of physics. Translated and edited by Volkmar Schüller, de Gruyter, Berlin (among others) 1999. ISBN 3-11-016105-2 (following the third edition, with additional material such as reviews of the three editions during Newton's lifetime and texts deleted by Newton from the first edition ).

English translations

  • Andrew Motte (translator): The mathematical principles of natural philosophy. London 1729 (translation of the 3rd edition from 1726). Reprinted by Amherst, 1995.
  • Florian Cajori using Motte's translation: Sir Isaac Newton's Mathematical Principles of Natural philosophy and his system of the world. University of California Press, Berkeley 1934 (with the original draft of Book 3 "System of the World" ).
  • I. Bernard Cohen, Anne Whitman: The Principia. Mathematical Principles of Natural Philosophy. A New Translation. With an introduction "A Guide to Newton's Principia" by IB Cohen, University of California Press, Berkeley 1999.


  • Isaac Newton : Philosophiae Naturalis Principia Mathematica . 1st edition. Jussu Societatis Regiae ac typis Josephi Streater, London 1687 ( [accessed July 30, 2017]).
  • Isaac Newton : Philosophiae Naturalis Principia Mathematica . 3. Edition. Innys, Regiae Societatis typographos, London 1726 ( [accessed July 30, 2017]).
  • S. Chandrasekhar : Newton's Principia for the Common Reader. Clarendon Press, Oxford 1995, ISBN 0-19-851744-0 . (The book is a precise mathematical analysis of the Principia for the modern reader, rather than a historical analysis. Books 1 and 3 are treated fairly completely, Book 2 only in parts).
  • John Herivel : The Background to Newton's Principia. A study of Newton's dynamical researches in the years 1664-1684. Clarendon Press, Oxford 1965.
  • I. Bernard Cohen : Introduction to Newton's "Principia". Cambridge University Press, Cambridge 1971, ISBN 0-521-07648-X .
  • Niccolò Guicciardini : Reading the Principia. The Debate on Newton's Mathematical Methods for Natural Philosophy from 1687 to 1736. Cambridge University Press, Cambridge et al. a. 1999, ISBN 0-521-64066-0 .
  • Niccolò Guicciardini: Philosophia Naturalis Principia Mathematica. In: Ivor Grattan-Guinness (Ed.): Landmark Writings in Western Mathematics. 1640-1940. Elsevier, Amsterdam a. a. 2005, pp. 59-87.
  • The Preliminary Manuscripts for Isaac Newton's 1687 Principia, 1684-1686. Facsimile of the original autographs, now in Cambridge University Library. With an introduction by DT Whiteside . Cambridge University Press, Cambridge u. a. 1989, ISBN 0-521-33499-3 , ( Cambridge University Library Newton Manuscripts 2), (facsimile edition of Newton's manuscripts in preparation for the Principia).
  • William Harper: Isaac Newton's Scientific Method: Turning Data into Evidence about Gravity and Cosmology. University Press, New York, Oxford (Sept.) 2011.

Individual evidence

  1. ^ Title page of the 1st edition ( picture of the title page of Newton's Philosophiae Naturalis Principia Mathematica )
  2. ^ Richard Westfall: Never at Rest. A Biography of Isaac Newton. Cambridge University Press, p. 882.
  3. Principes mathématiques de la philosophie naturelle. 2 volumes, Paris 1756, reprint Paris 1966.
  4. ^ Lutz D. Schmadel : Dictionary of Minor Planet Names . Fifth Revised and Enlarged Edition. Ed .: Lutz D. Schmadel. 5th edition. Springer Verlag , Berlin , Heidelberg 2003, ISBN 978-3-540-29925-7 , pp. 186 (English, 992 pp., [ONLINE; accessed on September 2, 2019] Original title: Dictionary of Minor Planet Names . First edition: Springer Verlag, Berlin, Heidelberg 1992): “1964 VP. Discovered 1964 Nov. 4 at the Goethe Link Observatory at Brooklyn, Indiana. ”
  5. René Descartes: Principia philosophiae. Elzevier Verlag Amsterdam 1644, German: The principles of philosophy. Felix Meiner Verlag, Leipzig 1922, Section 3: “From the visible world” - online at
  6. Schüller-Translation (1999), p. 379.
  7. Guicciardini (review in The British Journal of the History of Science, Volume 38, 2005, pp. 366-368) highlights the usefulness of Chandrasekhar's mathematical analysis, closely following Newton, for today's readers in explaining the structure of the Principia understand, but also points out that, according to his own statements, Chandrasekhar himself refrained from using secondary literature on a larger scale and also does not have the reference to Newton's contemporaries and predecessors, i.e. the historical embedding, in mind. According to Guicciardini, he also has a tendency to ignore Newton's possible errors and mistakes and to interpret Newton in terms of much later modern mathematical and physical insights.

Web links

Commons : Philosophiae Naturalis Principia Mathematica  - collection of images, videos and audio files
Wikisource: Philosophiae Naturalis Principia Mathematica  - Sources and full texts (English)