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History and Philosophy of Science

Newton's Regulae Philosophandi


Regulae Structural Changes

Rule I

Rule II

Rule III

Rule IV


The revisions:



Principia (1687)

Hypoth. III. Every body can be transformed into body of any other kind, and can assume successively all intermediate degrees of quality.


1690s Revisions

Hypoth. III. The laws {and properties} of all bodies on which experiments can be made are laws {and properties} of all bodies whatsoever.

For the properties of bodies become known only by means of experiments, and consequently all those are to be declared general which in general agree with experiments. Certainly in opposition to the tenor of experiments, imaginary ideas [literally ‘dreams’] must not be rashly invented, nor must we withdraw from the analogy of nature, since that is commonly simple and always in harmony with itself. The extension of bodies becomes known only by means of the senses, but is not perceived in all cases, yet because it applies to all perceptible things it is affirmed of all things whatsoever. The greater number of bodies we find by experience to be hard or solid, and therefore the particles not of these only but also of all others, we with good reason conclude are hard. From these properties of perceptible bodies we conclude that all bodies are mobile and impenetrable, and that they by certain forces continue in motion or at rest. That the divided parts of bodies can be separated one from the other, we know from the phenomena; and that the indivisible parts can by reason be distinguished into small parts, is certain from mathematics. But whether the parts distinguished can be separated from each other by the forces of nature, is uncertain: yet if even by one single experiment it were established that by the fraction of some one undivided particle a hard body suffered division, we should by force of this hypothesis reach a general conclusion that not only were the divided parts separable but also that all the indivisible parts could be divided ad injinitum.


Draft 1: (p. 241) _THIS IS ERRATA sheet at the end. (p.68), annotated copy, Trinity. (MS ERRA) Earliest, according to Cohen p.25 Intro. McGuire: N. Q. 16.200 Trinity College. Draft 1 on annotated errata sheet copy with some relation to Huygens. Full version in Volume X of Opera Omnia of Huygens p.47-55.

Hypoth III. The properties qualities of bodies that cannot be intended and remitted and that belong to all bodies on which experiments can be made are qualities of all bodies universally.

Draft I.0 - on the margin of the page. E1a Second. Draf N. Q. 16.200 Trinity College .

Hypoth III. The qualities of bodies that cannot be intended and remitted and that belong to all bodies on which experiments can be made are qualities of all bodies universally. The same is to be understood of qualities of all bodies of the same kind. This evidently is the Foundation of all Philosophy. For otherwise one could not derive the qualities of insensible bodies from the qualities of sensible [ones].

Hypoth IV. Things which agree as to all their known qualities with other kinds of things are not to be considered as new kinds of things.


Hypoth IV. Every body can be transformed into body of any other kind, and can assume successively all intermediate degrees of quality.


U. L. C. Add. 3965.6, Folio 256‘. In McGuire, p. 74; actually folio 266r. In Cohen's hypothesis paper, 176


Axiom 4. The qualities of bodies which are perceptible and which cannot be intended and remitted, as far as can be [known] in experience belong to all bodies, must be regarded as the properties of all bodies, are the properties of all bodies.
Qualities which are intended (and remitted such as motion and rest,) heat and cold, wet and dry, light and darkness, colour and blackness (opacity and transparency, a good smell and a bad smell) acidity, bitterness and sweet- ness, volatility and immovability, (liveliness, health and sickness), these things do not come in for consideration here. The things which cannot be intended and remitted such (bulk) impenetrability (solidity) and motion [something scored out which is illegible] and that inertia which causes a resistance to motion and to changes of motion (solidity and extension) are usually con- sidered to be the properties of all bodies. And the reason is because a quality which cannot be remitted cannot be taken away (from the whole); and on the other hand that which can be taken away, if it were to be taken away from some parts of the whole, it could be remitted in the whole. Impenetrability indeed is usually described as the essence of bodies and is hence attributed to all of them; but the essential properties of bodies do not become known by the light of nature. We gather (only) from the senses the fact that the bodies which we touch (all tangible things) arc impenetrable and we (conclude that) because this quality (in these things) is not intended or remitted (conclude that) we attribute to all bodies alike, no less to the heavenly bodies and to bodies imperceptible to the senses than to those bodies which we touch: and that too with an argument which we think so strong (that nothing in the whole nature of things) that this quality is taken to be the essence of bodies and is therefore considered to be the firmest foundation of all philosophy. there- fore the axiom on the strength of which we gather this property of bodies must not be repudiated. Of the same kind is the argument for the inertia and (mobility and force of resistance) of matter. In (only) a few bodies we gather by experiments that this (force of inertia) is proportional [to the quantity] of matter and the mobility inversely propor- tional to the same without perceptible intension and remission and thence [we attribute it] to all [bodies]. Because . . . projectiles [move] in straight lines uniformly except in so far as they are impended by the air or gravity [there is a large tear in the manuscript] we attributed this law of motion to all bodies. [At this point, because of the tear at the bottom of the page, nothing more can be conjectured with any degree of certainty. There is also a tear at the top of the sheet which affects the deciphering of the remarks on the verso side. It begins:] . . . cannot be brought into a smaller space . . . but can . . . their least particles [yield] to compression. However from the compression of other bodies cannot be [rightly] (necessarily) inferred the compression of the least parti- cles . . . we gather from [a word missing] do not yield to compression because the [least] particles of all bodies (be compressed) cannot be reduced to a smaller space by compression. (The foundation therefore) Therefore this axiom is the foundation of all philosophy. At all events nature would not be suffi- ciently simple and consistent with itself [unless] the qualities of bodies on which it is allowed to make experiments, as many of them as arc found to be immutable, apply in common to all bodies.

Draft 2: (p. 242-4) -- U. L. C. Ad. 4005.15 Folio 81r. Found on loose manuscript sheet.

Draft 3: U.L.C Adv b. 39. I. p.402a.
E1ii (or E1i, as in Cohen intro p.26). First is written the old version, as in E1a and Locke's copy, then changed to Regulae and added the last clause. in the interleaved first edition. (p.241, contains the change from hypothesis to Rule. Substantially the same as that published in 1713.


Principia (1713)


1710s Revisions




Principia (1727)


Rule III. Those quanlities of bodies that cannot be intended and remitted and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally.

For the qualities of bodies can be known only through experiments; and therefore qualities that square with experiments universally are to be regarded as universal qualities; and qualities that cannot be diminished cannot be taken away from bodies. Certainly idle fancies ought not to be fabricated recklessly against the evidence of experiments, nor should we depart from the analogy of nature, since nature is always simple and ever consonant with itself. The extension of bodies is known to us only through our senses, and yet there are bodies beyond the range of these senses; but because extension is found in all sensible bodies, it is ascribed to all bodies universally. We know by experience that some bodies are hard. Moreover, because the hardness of the whole arises from the hardness of its parts, we justly infer from this not only the hardness of the undivided particles of bodies that are accessible to our senses, but also of all other bodies. That all bodies are impenetrable we gather not by reason but by our senses. We find those bodies that we handle to be impenetrable, and hence we conclude that impenetrability is a property of all bodies universally. That all bodies are movable and persevere in motion or in rest by means of certain forces (which we call forces of inertia) we infer from finding these properties in the bodies that we have seen. The extension, hardness, impenetrability, mobility, and force of inertia of the whole arise from the extension, hardness, impenetrability, mobility, and force of inertia of each of the parts; and thus we conclude that every one of the least parts of all bodies is extended, hard, impenetrable, movable, and endowed with a force of inertia. And this is the foundation of all natural philosophy. Further, from phenomena we know that the divided, contiguous parts of bodies can be separated from one another, and from mathematics it is certain that the undivided parts can be distinguished into smalled parts by our reason. But it is uncertain whether those parts which have been distinguished in this way and not yet divided can actually be divided and separated from one another by the forces of nature. But if it were established by even a single experiment that in the breaking of a hard and solid body, any undivided particle underwent division, we should conclude by the force of this third rule not only that divided parts are separable but also that undivided parts can be divided indefinitely.

Finally, if it is universally established by experiment and astronomical observations that all bodies on or near the earth gravitate toward the earth, and do so in proportion to the quantity of matter in each body, and that the moon travitates toward the earth in proportion to the quantity of its matter, and that our sea in turn gravitates toward the moon, and that all planets gravitate toward one another, and that there is a similar gravity of comets toward the sun, it will have to be concluded by this third rule that all bodies gravitate toward one another. Indeed, the argument from phenomena will be even stronger for universal gravity than for the impenetrability of bodies, for which, of course, we have not a single experiment, and not even an observation, in the case of the heavenly bodies. Yet I am by no means affirming that gravity is essential to bodies. By inherent force I mean only the force of inertia. This is immutable. Gravity is diminished as bodies recede from the earth.

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