The Laws of Motion and the Rules of Reasoning in Philosophy
Original title: Philosophiæ Naturalis Principia Mathematica: Axiomata, sive Leges Motus; Regulæ Philosophandi (Latin)
Isaac Newton (1643–1727)
Translated by Andrew Motte (1696–1734), 1729
1687; Rules in their final form 1726

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Rights: Latin original 1687–1726; Newton died in 1727. The translator, Andrew Motte, died in 1734; the translation was published in 1729. The Rules of Reasoning are on Wikisource at The_Mathematical_Principles_of_Natural_Philosophy_(1729)/Rules_of_Reasoning_in_Philosophy. Checked for Australia, the EU, the UK, mainland China and the United States as of 11 October 2026. Guidance, not legal advice.
Source: Wikisource, https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1729)/Axioms,_or_Laws_of_Motion (retrieved 2026-10-11)
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Axioms, or Laws of Motion


Law I

*Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impress'd thereon.*

Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve the motions both progressive and circular for a much longer time.


Law II

*The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.*

If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impress'd altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force) if the body moved before, is added to or subducted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joyned, when they are oblique, so as to produce a new motion compounded from the determination of both.


Law III

*To every Action there is always opposed an equal Reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.*

Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend it self, will draw the horse as much towards the stone as it does the stone towards the horse and will obstruct the progress of the one as much as it advances that of the other. If a body impinge upon another, and by its force change the motion of the other; that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, towards the contrary part. The changes made by these actions are equal, not in the velocities, but in the motions of bodies; that is to say, if the bodies are not hinder'd by any other impediments. For, because the motions are equally changed, the changes of the velocities made towards contrary parts are reciprocally proportional to the bodies. This law takes place also in Attractions, as will be proved in the next Scholium.


Rules of Reasoning in Philosophy


Rule I

*We are to admit no more causes of natural things, than such as are both true and sufficient to explain their appearances.*

To this purpose the philosophers say, that Nature do's nothing in vain, and more is in vain, when less will serve; for Nature is pleas'd with simplicity, and affects not the pomp of superfluous causes.


Rule II

*Therefore to the same natural effects we must, as far as possible, assign the same causes.*

As to respiration in a man, and in a beast; the descent of stones in Europe and in America; the light of our culinary fire and of the Sun; the reflection of light in the Earth, and in the Planets.


Rule III

*The qualities of bodies, which admit neither intension nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.*

For since the qualities of bodies are only known to us by experiments, we are to hold for universal, all such as universally agree with experiments; and such as are not liable to diminution, can never be quite taken away. We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising; nor are we to recede from the analogy of Nature, which uses to be simple, and always consonant to itself. We no otherwise know the extension of bodies, than by our senses, nor do these reach it in all bodies; but because we perceive extension in all that are sensible, therefore we ascribe it universally to all others also.

That abundance of bodies are hard we learn by experience. And because the hardness of the whole arises from the hardness of the parts, we therefore justly infer the hardness of the undivided particles not only of the bodies we feel but of all others. That all bodies are impenetrable, we gather not from reason, but from sensation. The bodies which we handle we find impenetrable, and thence conclude impenetrability to be an universal property of all bodies whatsoever. That all bodies are moveable, and endow'd with certain powers (which we call the vires inertiae) of persevering in their motion or in their rest, we only infer from the like properties observ'd in the bodies which we have seen. The extension, hardness, impenetrability, mobility, and vis inertiae of the whole, result from the extension, hardness, impenetrability, mobility, and vires inertiae of the parts: and thence we conclude the least particles of all bodies to be also all extended, and hard and impenetrable, and moveable, and endow'd with their proper vires inertiae. And this is the foundation of all philosophy.

Moreover, that the divided but contiguous particles of bodies may be separated from one another, is matter of observation; and, in the particles that remain undivided, our minds are able to distinguish yet lesser parts, as is mathematically demonstrated. But whether the parts so distinguish'd, and not yet divided, may, by the powers of nature, be actually divided and separated from one another, we cannot certainly determine. Yet had we the proof of but one experiment, that any undivided particle, in breaking a hard and solid body, suffer'd a division, we might by virtue of this rule, conclude, that the undivided as well as the divided particles, may be divided and actually separated to infinity.

Lastly, If it universally appears, by experiments and astronomical observations, that all bodies about the Earth, gravitate towards the Earth; and that in proportion to the quantity of matter which they severally contain; that the Moon likewise, according to the quantity of its matter, gravitates towards the Earth; that, on the other hand, our Sea gravitates towards the Moon; and all the Planets mutually one towards another; and the Comets in like manner towards the Sun; we must, in consequence of this rule, universally allow, that all bodies whatsoever are endow'd with a principle of mutual gravitation. For the argument from the appearances concludes with more force for the universal gravitation of all bodies, than for their impenetrability; of which among those in the celestial regions, we have no experiments, nor any manner of observation. Not that I affirm gravity to be essential to bodies. By their vis insita I mean nothing but their vis inertiae. This is immutable. Their gravity is diminished as they recede from the Earth.


Rule IV

*In experimental philosophy we are to look upon propositions collected by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.*

This rule we must follow that the argument of induction may not be evaded by hypotheses.