Philosophiæ Naturalis
Contents 1 Contents 1.1 Expressed aim and topics covered
1.2
2 Writing and publication 2.1 Halley and Newton's initial stimulus 2.2 Preliminary version 2.3 Halley's role as publisher 3 Historical context 3.1 Beginnings of the Scientific Revolution 3.2 Newton's role 3.3 Newton's early work on motion 3.4 Controversy with Hooke 4 Location of early-edition copies 5 Later editions 5.1 Second edition, 1713 5.2 Third edition, 1726 5.3 Annotated and other editions 5.4 English translations 5.5 Homages 6 See also 7 References 8 Further reading 9 External links 9.1
9.1.1
9.2 English translations 9.3 Other links Contents[edit] Expressed aim and topics covered[edit] Sir
In the preface of the Principia, Newton wrote:[11] [...] Rational Mechanics will be the sciences of motion resulting from any forces whatsoever, and of the forces required to produce any motion, accurately proposed and demonstrated [...] And therefore we offer this work as mathematical principles of his philosophy. For all the difficulty of philosophy seems to consist in this—from the phenomenas of motions to investigate the forces of Nature, and then from these forces to demonstrate the other phenomena [...] The Principia deals primarily with massive bodies in motion, initially under a variety of conditions and hypothetical laws of force in both non-resisting and resisting media, thus offering criteria to decide, by observations, which laws of force are operating in phenomena that may be observed. It attempts to cover hypothetical or possible motions both of celestial bodies and of terrestrial projectiles. It explores difficult problems of motions perturbed by multiple attractive forces. Its third and final book deals with the interpretation of observations about the movements of planets and their satellites. It shows: how astronomical observations prove the inverse square law of
gravitation (to an accuracy that was high by the standards of Newton's
time);
offers estimates of relative masses for the known giant planets and
for the Earth and the Sun;
defines the very slow motion of the
The opening sections of the Principia contain, in revised and extended
form, nearly[12] all of the content of Newton's 1684 tract De motu
corporum in gyrum.
The Principia begin with "Definitions"[13] and "Axioms or Laws of
Motion",[14] and continues in three books:
Newton's proof of Kepler's second law, as described in the book. If an instantaneous centripetal force (red arrow) is considered on the planet during its orbit, the area of the triangles defined by the path of the planet will be the same. This is true for any fixed time interval. When the interval tends to zero, the force can be considered continuous. (Click image for a detailed description). The second section establishes relationships between centripetal
forces and the law of areas now known as Kepler's second law
(Propositions 1–3),[16] and relates circular velocity and radius of
path-curvature to radial force[17] (Proposition 4), and relationships
between centripetal forces varying as the inverse-square of the
distance to the center and orbits of conic-section form (Propositions
5–10).
Propositions 11–31[18] establish properties of motion in paths of
eccentric conic-section form including ellipses, and their relation
with inverse-square central forces directed to a focus, and include
The quantity of matter is that which arises conjointly from its density and magnitude. A body twice as dense in double the space is quadruple in quantity. This quantity I designate by the name of body or of mass. This was then used to define the "quantity of motion" (today called momentum), and the principle of inertia in which mass replaces the previous Cartesian notion of intrinsic force. This then set the stage for the introduction of forces through the change in momentum of a body. Curiously, for today's readers, the exposition looks dimensionally incorrect, since Newton does not introduce the dimension of time in rates of changes of quantities. He defined space and time "not as they are well known to all". Instead, he defined "true" time and space as "absolute"[44] and explained: Only I must observe, that the vulgar conceive those quantities under no other notions but from the relation they bear to perceptible objects. And it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common. [...] instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical discussions, we ought to step back from our senses, and consider things themselves, distinct from what are only perceptible measures of them. To some modern readers it can appear that some dynamical quantities
recognised today were used in the Principia but not named. The
mathematical aspects of the first two books were so clearly consistent
that they were easily accepted; for example, Locke asked Huygens
whether he could trust the mathematical proofs, and was assured about
their correctness.
However, the concept of an attractive force acting at a distance
received a cooler response. In his notes, Newton wrote that the
inverse square law arose naturally due to the structure of matter.
However, he retracted this sentence in the published version, where he
stated that the motion of planets is consistent with an inverse square
law, but refused to speculate on the origin of the law. Huygens and
Leibniz noted that the law was incompatible with the notion of the
aether. From a Cartesian point of view, therefore, this was a faulty
theory. Newton's defence has been adopted since by many famous
physicists—he pointed out that the mathematical form of the theory
had to be correct since it explained the data, and he refused to
speculate further on the basic nature of gravity. The sheer number of
phenomena that could be organised by the theory was so impressive that
younger "philosophers" soon adopted the methods and language of the
Principia.
Rules of Reasoning in Philosophy[edit]
Perhaps to reduce the risk of public misunderstanding, Newton included
at the beginning of
Newton's own first edition copy of his Principia, with handwritten corrections for the second edition. The process of writing that first edition of the Principia went
through several stages and drafts: some parts of the preliminary
materials still survive, while others are lost except for fragments
and cross-references in other documents.[59]
Surviving materials show that Newton (up to some time in 1685)
conceived his book as a two-volume work. The first volume was to be
titled De motu corporum, Liber primus, with contents that later
appeared in extended form as
Titlepage and frontispiece of the third edition, London, 1726 (John Rylands Library) It is not known just why Newton changed his mind so radically about
the final form of what had been a readable narrative in De motu
corporum, Liber secundus of 1685, but he largely started afresh in a
new, tighter, and less accessible mathematical style, eventually to
produce
Italian physicist
The foundation of modern dynamics was set out in Galileo's book
Artist's impression of English polymath
Hooke published his ideas about gravitation in the 1660s and again in
1674. He argued for an attracting principle of gravitation in
A page from the Principia Since only between 250 and 400 copies were printed by the Royal Society, the first edition is very rare. Several rare-book collections contain first edition and other early copies of Newton's Principia Mathematica, including:
In 2016, a first edition sold for $3.7 million.[91]
A facsimile edition (based on the 3rd edition of 1726 but with variant
readings from earlier editions and important annotations) was
published in 1972 by
Book: Isaac Newton Atomism Elements of the Philosophy of Newton References[edit] ^ "The Mathematical Principles of Natural Philosophy", Encyclopædia
Britannica, London
^ Among versions of the Principia online: [1].
^ a b Volume 1 of the 1729 English translation is available as an
online scan; limited parts of the 1729 translation (misidentified as
based on the 1687 edition) have also been transcribed online.
^ Newton, Isaac. "Philosophiæ Naturalis Principia Mathematica
(Newton's personally annotated 1st edition)".
^ a b [In Latin] Isaac Newton's Philosophiae Naturalis Principia
Mathematica: the Third edition (1726) with variant readings, assembled
and ed. by
[1] Further reading[edit] Alexandre Koyré, Newtonian studies (London: Chapman and Hall, 1965). I. Bernard Cohen, Introduction to Newton's Principia (Harvard University Press, 1971). Richard S. Westfall, Force in Newton's physics; the science of dynamics in the seventeenth century (New York: American Elsevier, 1971). S. Chandrasekhar, Newton's Principia for the common reader (New York: Oxford University Press, 1995). Guicciardini, N., 2005, "Philosophia Naturalis..." in Grattan-Guinness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 59–87. Andrew Janiak, Newton as Philosopher (Cambridge University Press, 2008). François De Gandt, Force and geometry in Newton’s Principia trans. Curtis Wilson (Princeton, NJ: Princeton University Press, c1995). Steffen Ducheyne, The main Business of Natural Philosophy: Isaac Newton’s Natural-Philosophical Methodology (Dordrecht e.a.: Springer, 2012). John Herivel, The background to Newton's Principia; a study of Newton's dynamical researches in the years 1664–84 (Oxford, Clarendon Press, 1965). Brian Ellis, "The Origin and Nature of Newton's Laws of Motion" in Beyond the Edge of Certainty, ed. R. G. Colodny. (Pittsburgh: University Pittsburgh Press, 1965), 29–68. E.A. Burtt, Metaphysical Foundations of Modern Science (Garden City, NY: Doubleday and Company, 1954). Colin Pask, Magnificent Principia: Exploring Isaac Newton's Masterpiece (New York: Prometheus Books, 2013). External links[edit] Wikimedia Commons has media related to Philosophiae Naturalis Principia Mathematica.
Second edition (1713)[edit] ETH-Bibliothek Zürich. ETH-Bibliothek Zürich (pirated Amsterdam reprint of 1723). Third edition (1726)[edit] ETH-Bibliothek Zürich. Later
Principia (in Latin, annotated). 1833 Glasgow reprint (volume 1) with
Books 1 and 2 of the
English translations[edit]
Andrew Motte, 1729, first English translation of third edition (1726) WikiSource, Partial
Google books, vol.1 with
Robert Thorpe 1802 translation N. W. Chittenden, ed., 1846 "American Edition" a partly modernised English version, largely the Motte translation of 1729. Wikisource Archive.org #1 Archive.org #2 eBooks@Adelaide eBooks@Adelaide Percival Frost 1863 translation with interpolations Archive.org Florian Cajori 1934 modernisation of 1729 Motte and 1802 Thorpe translations Ian Bruce has made a complete translation of the third edition, with notes, on his website. Other links[edit] David R. Wilkins of the School of Mathematics at
v t e Isaac Newton Publications
Other writings Notes on the Jewish Temple
Quaestiones quaedam philosophicae
Discoveries and inventions Calculus Fluxion Newton disc Newton polygon Newton–Okounkov body Newton's reflector Newtonian telescope Newton scale Newton's metal Newton's cradle Sextant Theory expansions Kepler's laws of planetary motion Problem of Apollonius Newtonianism Bucket argument Newton's inequalities Newton's law of cooling Newton's law of universal gravitation Post-Newtonian expansion Parameterized post-Newtonian formalism Newton–Cartan theory Schrödinger–Newton equation Gravitational constant Newton's laws of motion Newtonian dynamics
Gauss–Newton algorithm Truncated Newton method Newton's rings Newton's theorem about ovals Newton–Pepys problem Newtonian potential Newtonian fluid Classical mechanics Newtonian fluid Corpuscular theory of light Leibniz–Newton calculus controversy Newton's notation Rotating spheres Newton's cannonball Newton–Cotes formulas Newton's method Newton fractal Generalized Gauss–Newton method Newton's identities Newton polynomial Newton's theorem of revolving orbits Newton–Euler equations Newton number Kissing number problem Power number Newton's quotient Newton–Puiseux theorem Solar mass Dynamics Absolute space and time Finite difference Table of Newtonian series Impact depth Structural coloration Inertia Spectrum Phrases "Hypotheses non fingo" "Standing on the shoulders of giants" Life Cranbury Park
Woolsthorpe Manor
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Friends and family Catherine Barton John Conduitt William Clarke Benjamin Pulleyn William Stukeley William Jones Isaac Barrow Abraham de Moivre John Keill Cultural depictions Newton (Blake) Newton (Paolozzi) In popular culture Related Writing of Principia Mathematica List of things named after Newton
Elements of the Philosophy of Newton
Authority control WorldCat Identities VIAF: 184313227 LCCN: n85003718 GND: 4232118-9 SUDOC: 027580040 ^ (Chapter 2 written by S |