Philosophiæ Naturalis Principia Mathematica

, Often called Philosophiae Naturalis Principia Mathematica also Principia Mathematica or simply Principia, is the main work of Isaac Newton. The Latin title translates as Mathematical Principles of Natural Philosophy. The Principia was first proposed in 1686 as a manuscript of the Royal Society and published on July 5, 1687 in Latin. From Edmund Halley, who was the initiator of the work and the first edition organized, encouraged again and again, Newton wrote one of the greatest physical and astronomical books of all time.

History and expenditure

The real impetus for the book came when Edmund Halley Newton visited in August 1684 in Cambridge, and a discussion between him, Christopher Wren and Robert Hooke in January of the same year mentioned in the Hooke claimed that the Kepler laws from a recognition of a reversed to the square of to have derived distance decreasing gravitational force. Such a power law Hooke had already in 1674, blamed for the planetary motion in (published) letters to Newton, as a balancing force to the centrifugal force, and Halley had come to this conclusion, but could not derive the Kepler laws from it. Newton replied in 1684 in Cambridge over Halley, it was him this already been done before, but he could not find the documents. November 1685 he sent Halley in the derivation of a treatise " De motu corporum in gyrum " (On the motion of bodies in an orbit ). He headed there not only the Kepler laws from ( elliptical orbit ), but also tracks on conics ( hyperbolas, parabolas ) and treated the motion of a body in a medium with resistance. Halley reported it in December 1685 at the Royal Society, and urged Newton to publish his results. During this period Newton also had contacts with the Royal Astronomer John Flamsteed, who provided him with observations of the planets. April 1686 the final manuscript of the Principia was presented to the Royal Society, which ( according to priority disputes with Hooke ) agreed on 30 June of publication. The cost of printing took over Halley, as the Royal Society had their budget for printing costs with the publication of originating by Francis Willughby and completed by John Ray work De Historia Piscium, a natural history of the fish consumed.

From 1709 Newton worked with major support from the Plumian Professor of Astronomy at Trinity College, Roger Cotes, on a second edition of the Principia, published in 1713 (without any mention of Cotes ). Newton was at this time 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. This is also where his famous sentence, he would not invent hypotheses ( " Hypotheses non fingo "). The third edition was published on 25 March 1726 at the collaboration of Henry Pemberton ( the Newton this time praised in the preface mentioned).

1739-1742 appeared in Geneva edition of the 3rd edition with detailed ( almost line by line ) comment, issued by the Franciscan Thomas Le Seurat and François Jacquier (but also other scientists were working with ), in which it also the more modern Leibniz used calculus calculus. This so-called Jesuit edition was in 1980 recommended by Newton biographer Richard Westfall as one of the best annotated editions of the Principia. Newton himself had shown in his Principia avoided the calculus actually used by him and his mathematical derivations given a geometric shape.

Between 1745 and 1749 the Marquise du Chatelet, a friend of Voltaire, together with Alexis -Claude Clairaut wrote what the drawbacks of strictly geometric version of the original diminished greatly by a translation into French, which was provided with very good and modern integral calculus -use comments and those interested in more detail brought.

It was Voltaire who brought the famous story of the discovery of gravitation in circulation by a falling on Newton 's apple. Especially in France learned Newton's theories, which by no means found approval among all his contemporaries, from the beginning of their greatest acceptance. Gottfried Wilhelm Leibniz and Christiaan Huygens, two great scientist - contemporaries on the " continent", were and remained until her death, however, skeptical.

Content

Newton introduced into the Principia from the law of gravity. He combined so that the researches of Galileo Galilei and Johannes Kepler to accelerate the planetary motions ( Kepler's laws ) to a unified theory of gravitation and laid the foundations of classical mechanics by formulating the three laws of motion. He also introduced here the concepts of absolute time, absolute space (based on his famous bucket experiment), the distance effect and thus indirectly the concept of determinism one, which all of the scientific worldview of many generations up to the Theory of Relativity Albert Einstein and quantum mechanics were formative.

The 600 -page book is divided into three books, the first of which contains mainly the mathematical derivations of the famous Newton's laws of motion ( dynamics and gravity ), while the second, also very mathematically oriented book of body movements is in viscous liquids. The second book ends with the refutation of the hypothesis that the movements of the planets and their satellites are due to eddy motions of the universe fulfilling essential fluid caused. Thus Newton's Principia mathematica of 1687 provides, among other things, a response to Descartes ' Principia Philosophiae from 1644 is where Descartes in the third section attempted to justify exactly this in detail in a fluid- mechanical nature of the visible world. With the theory of an infinitely extended Ätherfluidums Descartes had convinced the majority of former scholars. (Later Newton criticized the Ätherfluidum again in his very influential book Optics by 1704. )

The third book entitled On the world system concerns the application of work done in the first two books of knowledge on the actual movements of celestial bodies, Newton compares its calculations with a variety of measurement data from other naturalists, and thus proves the correctness of the theoretical derivations. In this sense, Newton introduces the third book in the following words:

"In the previous books, I have set out principles for physics, but not physical, but only mathematical, namely so on the basis of physical things can be treated. There ... now remains for us to explain to on the basis of these principles, the structure of the world system. On this subject I have written the third book in general terms so that it can be read by quite a lot ... "

Expenditure

Recent editions of the Latin original

• Isaac Newton 's Philosophiae naturalis principia mathematica / the 3d ed, with variant readings, editor Alexandre Koyré, I. Bernard Cohen ( with the assistance of Anne Whitman ). ( Facsimile of the ed.) 1726 - Cambridge - Mass. : Harvard University Press, and Cambridge: Cambridge University Press, 1972 - ISBN 0-674-66475-2.

German translations

• Mathematical Principles of Natural Philosophy, with observations and comments published by Jacob Philipp Wolfers. - Berlin: Verlag von Robert Oppenheim, 1872 Online.
• Mathematical foundations of natural philosophy; selected, translated, introduced and edited by Ed Dellian. - Hamburg: Meiner, cop. 1988th ( Philosophical Library, Volume 394), ISBN 3-7873-0764-8; New edition 2007 Academia Verlag, Sankt Augustin.
• The mathematical principles of physics; translated and edited by Volkmar Schüller. - Berlin [ etc.]: de Gruyter, 1999 ISBN (following the third edition, with additional material such as reviews of the three editions of Newton's lifetime, and painted by Newton texts from the first edition ) 3-11-016105-2 - Online.

English Translations

• Andrew Motte ( Translator ): The mathematical principles of natural philosophy, London 1729 ( translation of the 3rd edition of 1726) reprint Amherst 1995
• Florian Cajori using of 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, Berkeley: University of California Press, 1999.