# Philosophiæ Naturalis Principia Mathematica

Philosophiæ Naturalis Principia Mathematica (English: The Mathematical Principles of Natural Philosophy — often referred to as simply the Principia) is a famous book by Isaac Newton. The book established the foundations of classical mechanics and gives the physics and mathematics of Newton's laws of motion and his law of universal gravitation based on Kepler's laws of planetary motion. The Principia is written in Latin and comprises three volumes. The 1st edition was published in 1687 with a 2nd edition in 1713 and a 3rd edition in 1726.

## Quotes

* Definition IVAn impressed force is an action exerted upon a body, in order to change its state, either of rest, or of uniform motion in a right line. This force consists in the action, only, and remains no longer in the body when the action is over. For a body maintains every new state it acquires, by its inertia only. But impressed forces are of different origin, as from percussion, from pressure, from centripetal force.
** Newton's Principia for the Common Reader. Oxford University Press. 2003. p. 19. ISBN 019852675X. (analysis and commentary, with translation from the Latin, by Subrahmanyan Chandrasekhar; 1st edition 1995)
* In the publication of this work, Edmond Halley, a man of the greatest intelligence and of universal learning, was of tremendous assistance, not only did he correct the typographical errors and see to the making of the woodcuts, but it was he who started me off on the road to this publication. For when he had obtained my demonstration of the shape of the celestial orbits, he never stopped asking me to communicate it to the Royal Society, whose subsequent encouragement and kind patronage made me begin to think about publishing it.
** "Author's Preface to the Reader". The Principia: Mathematical Principles of Natural Philosophy. University of California Press. 2014. pp. 381–383. ISBN 9781322192215. (quote from p. 383; translated from the 3rd edition of the Latin original by I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz)

### Book I

    Quotes are from (1729) edition as translated by Andrew Motte, unless otherwisee indicated.
* I. Absolute, True, and Mathematical Time, of it self, and from its own nature flows equably without regard to any thing external, and... is called duration...
* Relative, Apparent, and Common Time is some sensible and external (whether accurate or unequable) measure of Duration by the means of motion, which is commonly used instead of True time...
* II. Absolute Space, in its own nature, without regard to any thing external, remains always similar and immoveable.
* Relative Space is some moveable dimension or measure of the absolute spaces; which our senses determine, by its position to bodies; and which is vulgarly taken for immoveable space...
* Such is the dimension of a subterraneous, an aereal, or celestial space, determin'd by its position in respect of the Earth.
* Absolute and Relative space, are the same in figure and magnitude; but... not... always numerically the same.
* [I]f the Earth... moves; a space of our Air, which relatively and in respect of the Earth, remains always the same, will at one time be one part of the absolute space into which the Air passes; at another time it will be another part... and so, absolutely... it will be perpetually mutable.
* III. Place is a part of space... a body takes up, and, is according to the space, either absolute or relative.
* I say, a Part of Space, not the situation, nor the external surface of the body. For the places of equal Solids, are always equal; but their superficies, by reason of their dissimilar figures, are often unequal.
* Positions properly have no quantity, nor are they so much the places themselves, as the properties of places.
* The motion of the whole is the same thing with the sum of the motions of the parts, that is, the translation of the whole, out of its place, is the same thing with the sum of the translations of the parts out of their places; and therefore the Place of the whole, is the same thing with the Sum of the places of the parts... it is internal, and in the whole body.
* IV. Absolute motion, is the translation of a body from one absolute place into another; and Relative motion, the translation from one relative place into another. Thus in a Ship under sail, the relative place of a body is that part of the Ship, which the Body possesses... which... moves together with the Ship: And Relative rest, is the continuance of the Body in the same part of the Ship.... But Real, absolute rest, is the continuance of the Body in the same part of... Immoveable space...
* [I]f the Earth... moves... and if the body moves also relatively in the Ship; its true motion will arise, partly from... motion of the Earth, in immoveable space, and partly from the relative motions... of the Ship on the Earth... [and] of the Body in the Ship... As if that part of the Earth where the Ship is, was truly mov'd toward the East, with a velocity of 10010 parts; while the Ship itself with a fresh gale... is carry'd towards the West, with a velocity... 10... parts; but a Sailor walks... towards the East, with 1 part... then the Sailor will be moved... absolutely in immoveable space towards the East with a velocity of 1001 parts, and relatively...[to] the Earth towards the West, with... 9... parts.
* Absolute time, in Astronomy, is distinguish'd from Relative, by the Equation or correction of the vulgar time. For the natural days are truly unequal, though they are commonly consider'd as equal, and used for a measure of time: Astronomers correct this inequality for... accurate deducing of the celestial motions.
* It may be, that there is no such thing as an equable motion, whereby time may be accurately measured. All motions may be accelerated and retarded, but the True, or equable progress, of Absolute time is liable to no change.
* The duration or perseverance of the existence of things remains the same, whether the motions are swift or slow, or none at all: and therefore it ought to be distinguish'd from what are only sensible measures thereof; and out of which we collect it, by means of the Astronomical equation. The necessity of which Equation, for determining the Times of a phaenomenon, is evinc'd as well from the experiments of the pendulum clock, as by eclipses of the Satellites of Jupiter.
* As the order of the parts of Time is immutable, so also is the order of the parts of Space.
* All things are placed in Time as to order of Succession; and in Space as to order of Situation.
* It is from their essence or nature that they are Places; and that the primary places of things should be moveable, is absurd.
* These are therefore the absolute places; and translations out of those places, are the only Absolute Motions.
* But because the parts of Space cannot be seen, or distinguished from one another by our Senses therefore in their stead we use sensible measures of them.
* For from the positions and distances of things from any body consider'd as immoveable, we define all places: and then with respect to such places, we estimate all motions...
* And so instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs: but in Philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures... For it may be that there is no body really at rest, to which the places and motions of others may be referr'd.
* But we may distinguish Rest and Motion, absolute and relative, one from the other by their Properties, Causes and Effects.
* It is a property of Rest, that bodies really at rest do rest in respect of one another.
* And therefore as it is possible, that in the remote regions of the fixed Stars, or perhaps far beyond them, there may be some body absolutely at rest; but impossible to know from the position of bodies to one another in our regions, whether any of these do keep the same position to that remote body; it follows that absolute rest cannot be determined from the position of bodies in our regions.
* It is a property of motion, that the parts, which retain given positions to their wholes, do partake of the motions of those wholes.
* For all the parts of revolving bodies endeavour to recede from the axe of motion; and the impetus of bodies moving forwards, arises from the joint impetus of all the parts.
* Therefore, if surrounding bodies are mov'd, those that are relatively at rest within them, will partake of their motion.
* Upon which account, the true and absolute motion of a body cannot be determin'd by the translation of it from those which only seem to rest: For the external bodies ought not only to appear at rest, but to be really at rest.
* For otherwise, all included bodies, beside their translation from near the surrounding ones, partake likewise of their true motions; and tho' that translation was not made they would not be really at rest, but only seem... so.
* For the surrounding bodies stand in the like relation to the surrounded, as the exteriour part of a whole does to the interiour, or as the shell does to the kernel; but, if the shell moves, the kernel will also... as being part of the whole, without any removal from near the shell.
* [I]f a place is mov'd, whatever is placed therein moves... with it; and therefore a body, which is mov'd from a place in motion, partakes also of the motion of its place.
* [E]ntire and absolute motions can be no otherwise determined than by immoveable places... but relative ones to moveable places.
* [N]o other places are immoveable, but those that, from infinity to infinity, do all retain the same given positions one to another... ever... unmov'd... immoveable space.
* The Causes by which true and relative motions are distinguished... are the forces impress'd upon bodies to generate motion.
* True motion is neither generated nor alter'd, but by some force impress'd upon the body moved: but relative motion may be generated or altered without any force impress'd upon the body.
* The Effects which distinguish absolute from relative motion are, the forces of receding from the axe of circular motion.
* For there are no such forces in a circular motion purely relative, but in a true and absolute circular motion, they are greater or less, according to the quantity of the motion.
* If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then fill'd with water, and held at rest together with the water; after by the sudden action of another force, it is whirl'd about the contrary way, and while the cord is untwisting it self, the vessel continues for some time in this motion; the surface of the water will at first be plain, as before the vessel began to move: but the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little from the middle, and ascend to the sides of the vessel, forming it self into a concave figure... and the swifter the motion becomes the higher will the water rise, till at last, performing its revolutions in the same times with the vessel, it becomes relatively at rest in it.
* This ascent of the water shews its endeavour to recede from the axe of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, discovers it self, and may be measured by this endeavour. At first, when the relative motion of the water in the vessel was greatest it produc'd no endeavour to recede from the axe: the water shew'd no tendency to the circumference, nor any ascent towards the sides of the vessel, but remain'd of a plain surface, and therefore its True circular motion had not yet begun.
* But afterwards, when the relative motion of the water had decreased, the ascent thereof towards the sides of the vessel, prov'd its endeavour to recede from the axe; and this endeavour shew'd the real circular motion of the water perpetually increasing, till it had acquir'd its greatest quantity, when the water rested relatively in the vessel.
* And therefore this endeavour does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defin'd by such translations.
* There is only one real circular motion of any one revolving body, corresponding to only one power of endeavouring to recede from its axe of motion, as its proper and adequate effect: but relative motions in one and the same body are innumerable, according to the various relations it bears to external bodies, and like other relations, are altogether destitute of any real effect, any otherwise than they may perhaps participate of that one only true motion.
* And therefore in their system who suppose that our heavens, revolving below the sphere of the fixt Stars, carry the Planets along with them; the several parts of those heavens, and the Planets, which are indeed relatively at rest in their heavens, do yet really move. For they change their position one to another (which never happens to bodies truly at rest) and being carried together with their heavens, participate of their motions, and as parts of revolving wholes, endeavour to recede from the axe of their motions.
* Wherefore relative quantities, are not the quantities themselves, whose names they bear, but those sensible measures of them (either accurate or inaccurate) which are commonly used instead of the measur'd quantities themselves.
* And if the meaning of words is to be determin'd by their use; then by the names Time, Space, Place and Motion, their measures are properly to be understood; and the expression will be unusual, and purely Mathematical, if the measured quantities themselves are meant. Upon which account, they do strain the Sacred Writings, who there interpret those words for the measur'd quantities. Nor do those less defile the purity of Mathematical and Philosophical truths, who confound real quantities themselves with their relations and vulgar measures.
* It is... a matter of great difficulty to discover, and effectua'ly to distinguish, the True motions of particular bodies from the Apparent: because the parts of that immoveable space in which those motions are perform'd, do by no means come under... observation...
* Yet... we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions.
* For instance, if two globes kept at a given distance one from the other, by means of a cord that connects them, were revolved about their common centre of gravity, we might, from the tension of the cord, discover the endeavour of the globes to recede from the axe of their motion, and from thence we might compute the quantity of their circular motions. And then if any equal forces should be impress'd at once on the alternate faces of the globes to augment or diminish their circular motions; from the encrease or decrease of the tension of the cord, we might infer the increment or decrement of their motions; and thence would be found, on what faces those forces ought to be impress'd, that the motions of the globes might be most augmented, that is, we might discover their hindermost faces, or those which, in the circular motion, do follow.
* But the faces which follow being known, and consequently, the opposite ones that precede, we would likewise know the determination of their motions.
* And thus we might find... the quantity and the determination of this circular motion, ev'n in an immense vacuum, where there was nothing external or sensible with which the globes could be compar'd.
* But now if in that space some remote bodies were plac'd that kept always a given position to one to another, as the Fixt Stars do in our regions; we could not... determine from the relative translation of the globes among those bodies, whether the motion did belong to the globes or to the bodies.
* But if we observ'd the cord, and found that its tension was that very tension which the motions of the globes required, we might conclude the motion to be in the globes, and the bodies to be at rest; and... from the translation of the globes among the bodies, we should find the determination of their motions. But how we are to collect the true motions from their causes, effects, and apparent differences; and vice versa, how from the motions, either true or apparent, we may come to the knowledge of their causes and effects, shall be explain'd more at large in the following Tract, For to this end it was that I compos'd it.

## Quotes about Newton’s Principia

* Isaac Newton's Principia Mathematica is indisputably one of the important and influential books ever written, yet it is scarcely read. Latin is not the problem, for translations in English and French have done little to expand its readership. Those who have attempted to read the Principia quickly recognize the problem: The geometrical style of mathematics is almost opaque to the modern reader.
** Alan E. Shapiro, (November 1996)"Translating, Elucidating and Explaining the Mathematics of Newton's Principia". Physics Today 49 (11): 81–82. DOI:10.1063/1.881562.
* The first edition of Isaac Newton's famous Principia mathematica (1687) contains only one reference to the Scriptures and one mention of God and natural theology. Thus, there is superficial evidence to suggest that this pivotal work of physics is a mostly secular book that is not fundamentally associated with theology and natural theology. The fact that the General Scholium – with its overt theological and natural theological themes – was only added to the Principia a quarter-century later with the second edition of 1713 may also suggest that this theology came as an afterthought and is therefore not integral to the conceptual structure of the Principia. Moreover, the relative paucity of theology in the first edition, combined with the evidence of the appended General Scholium of 1713, could be used as evidence of a ‘theological turn’ in Newton's thought after 1687. This article uses evidence from Newton's private manuscripts to argue that there is more theology in all three editions of the Principia than a simple reading of the published text would imply.
** Stephen D. Snobelen, (2010). "The theology of Isaac Newton's Principia Mathematica: A preliminary survey". Neue Zeitschrift für Systematische Theologie und Religionsphilosophie: 377–412. DOI:10.1515/nzst.2010.023.

## External links

* Andrew Motte (1729) 1st English translation of Newton's 3rd (1726) edition
** Vol. 1, Book 1, & Vol. 2, Books 2 & 3. @Archive.org
** Vol. 1, Book 1. @GoogleBooks
* "American Edition" (1846) ed. N. W. Chittenden, partly modernized Motte's 1729 translation.
** Copies 1 & 2 @Archive.org
** eBooks@Adelaide eBooks@Adelaide @WayBack Machine
* Percival Frost translation (1863) Setions 1-3 with notes, illustrations & problems @Archive.org
* Ian Bruce translation of 3rd ed. with notes.