(English: The Mathematical Principles of Natural Philosophy), often called simply the (), is a book by Sir Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation.
The Principia is written in Latin and comprises three volumes, and was authorized (imprimatur) by Samuel Pepys, then-president of the Royal Society on 5 July 1686 and first published in 1687. After annotating and correcting his personal copy of the first edition, Newton published two further editions, one of 1713 with errors in the 1687 version corrected, and another, improved one translate.google.co.uk : "améliorée" of 1726.
The forms a mathematical foundation for the theory of classical mechanics, and is generally considered to be one of the most important works in the history of science.J. M. Steele, University of Toronto, (review online from Canadian Association of Physicists) of N. Guicciardini's "Reading the Principia: The Debate on Newton's Mathematical Methods for Natural Philosophy from 1687 to 1736" (Cambridge UP, 1999), a book which also states (summary before title page) that the "Principia" "is considered one of the masterpieces in the history of science". It has been referred to as "the greatest scientific work in history" and "the supreme expression in human thought of the mind's ability to hold the universe fixed as an object of contemplation".
Recent research has challenged the long-held view that the Principia had only a limited initial readership, suggesting that its early influence on Enlightenment science was substantially greater than previously recognized.
In formulating his physical laws, Newton developed and used mathematical methods now included in the field of calculus, expressing them in the form of geometric propositions about "vanishingly small" shapes. In a revised conclusion to the , Newton emphasized the empirical nature of the work with the expression Hypotheses non fingo ("I frame/feign no hypotheses"). Among other achievements, Newton provides an explanation for Johannes Kepler's laws of planetary motion, which Kepler had obtained empirically.
Contents
Expressed aim and topics covered
The Preface of the work states:From Motte's translation of 1729 (at 3rd page of Author's Preface); and see also J. W. Herivel, The background to Newton's "Principia", Oxford University Press, 1965.
Newton situates himself within the contemporary scientific movement which had "omit[ed] substantial forms and the occult qualities" and instead endeavoured to explain the world by empirical investigation and outlining of empirical regularities.
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.
The book: shows how astronomical observations verify 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 motion of the Sun relative to the Solar System barycenter; shows how the theory of gravity can account for irregularities in the motion of the Moon; identifies the oblateness of the shape of the Earth; accounts approximately for marine tides including phenomena of spring and neap tides by the perturbing (and varying) gravitational attractions of the Sun and Moon on the Earth's waters; explains the precession of the equinoxes as an effect of the gravitational attraction of the Moon on the Earth's equatorial bulge; and gives theoretical basis for numerous phenomena about comets and their elongated, near-parabolic orbits.
The opening sections of the Principia contain, in revised and extended form, nearlyThe De motu corporum in gyrum article indicates the topics that reappear in the Principia. all of the content of Newton's 1684 tract De motu corporum in gyrum.
The Principia begin with "Definitions" and "Axioms or Laws of Motion", and continues in three books:
Book 1, De motu corporum Book 1, subtitled De motu corporum (On the motion of bodies) concerns motion in the absence of any resisting medium. It opens with a collection of mathematical lemmas on "the method of first and last ratios", a geometrical form of infinitesimal calculus.
The second section establishes relationships between centripetal forces and the law of areas now known as Kepler's second law (Propositions 1–3), and relates circular velocity and radius of path-curvature to radial forceThis relationship between circular curvature, speed and radial force, now often known as Huygens' formula, was independently found by Newton (in the 1660s) and by Huygens in the 1650s: the conclusion was published (without proof) by Huygens in 1673.This was given by Isaac Newton through his Inverse Square Law. (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 establish properties of motion in paths of eccentric conic-section form including ellipses, and their relationship with inverse-square central forces directed to a focus and include Newton's theorem about ovals (lemma 28).
Propositions 43–45 are demonstration that in an eccentric orbit under centripetal force where the apse may move, a steady non-moving orientation of the line of apses is an indicator of an inverse-square law of force.
Book 1 contains some proofs with little connection to real-world dynamics. But there are also sections with far-reaching application to the solar system and universe:
Propositions 57–69 deal with the "motion of bodies drawn to one another by centripetal forces". This section is of primary interest for its application to the Solar System, and includes Proposition 66 along with its 22 corollaries: here Newton took the first steps in the definition and study of the problem of the movements of three massive bodies subject to their mutually perturbing gravitational attractions, a problem which later gained name and fame (among other reasons, for its great difficulty) as the three-body problem.
Propositions 70–84 deal with the attractive forces of spherical bodies. The section contains Newton's proof that a massive spherically symmetrical body attracts other bodies outside itself as if all its mass were concentrated at its centre. This fundamental result, called the Shell theorem, enables the inverse square law of gravitation to be applied to the real solar system to a very close degree of approximation.
Book 2, part 2 of De motu corporum Part of the contents originally planned for the first book was divided out into a second book, which largely concerns motion through resisting mediums. Just as Newton examined consequences of different conceivable laws of attraction in Book 1, here he examines different conceivable laws of resistance; thus Section 1 discusses resistance in direct proportion to velocity, and Section 2 goes on to examine the implications of resistance in proportion to the square of velocity. Through Book II, Newton was an important pioneer of fluid mechanics, and a later analysis showed that of its 53 propositions almost all are correct, with only two or three open to question. Book 2 discusses (in Section 5) hydrostatics and the properties of compressible fluids; he also derives Boyle's law (incorrectly; for an ideal gas is not like an elastic fluid). The effects of air resistance on pendulums are studied in Section 6, along with Newton's account of experiments that he carried out, to try to find out some characteristics of air resistance in reality by observing the motions of pendulums under different conditions. Newton compares the resistance offered by a medium against motions of globes with different properties (material, weight, size). In Section 8, he derives rules to determine the speed of waves in fluids and relates them to the density and condensation (Proposition 48; this would become very important in acoustics). He assumes that these rules apply equally to light and sound and estimates that the speed of sound is around 1088 feet per second and can increase depending on the amount of water in air.
Less of Book 2 has stood the test of time than of Books 1 and 3, and it has been said that Book 2 was largely written to refute a theory of Descartes which had some wide acceptance before Newton's work (and for some time after). According to Descartes's theory of vortices, planetary motions were produced by the whirling of fluid vortices that filled interplanetary space and carried the planets along with them.Eric J Aiton, The Cartesian vortex theory, chapter 11 in Planetary astronomy from the Renaissance to the rise of astrophysics, Part A: Tycho Brahe to Newton, eds. R Taton & C Wilson, Cambridge (Cambridge University press) 1989; at pp. 207–221. Newton concluded Book 2 by commenting that the hypothesis of vortices was completely at odds with the astronomical phenomena, and served not so much to explain as to confuse them.
Book 3, De mundi systemate Book 3, subtitled De mundi systemate (On the system of the world), is an exposition of many consequences of universal gravitation, especially its consequences for astronomy. It builds upon the propositions of the previous books and applies them with greater specificity than in Book 1 to the motions observed in the Solar System. Here (introduced by Proposition 22, and continuing in Propositions 25–35) are developed several of the features and irregularities of the orbital motion of the Moon, especially the variation. Newton lists the astronomical observations on which he relies, and establishes in a stepwise manner that the inverse square law of mutual gravitation applies to Solar System bodies, starting with the satellites of Jupiter and going on by stages to show that the law is of universal application. He also gives starting at Lemma 4 and Proposition 40 the theory of the motions of comets, for which much data came from John Flamsteed and Edmond Halley, and accounts for the tides, attempting quantitative estimates of the contributions of the Sun and Moon to the tidal motions; and offers the first theory of the precession of the equinoxes. Book 3 also considers the harmonic oscillator in three dimensions, and motion in arbitrary force laws.