Newton: PHILOSOPHIÆ NATURALIS PRINCIPIA MATHEMATICA

Hypothesis vorticum multis premitur difficultatibus. Ut planeta unusquisque radio ad solem ducto areas describat tempori proportionales, tempora periodica partium vorticis deberent esse in duplicata ratione distantiarum a sole. Ut periodica planetarum tempora sint in proportione sesquiplicata distantiarum a sole, tempora periodica partium vorticis deberent esse in sesquiplicata distantiarum proportione.

The hypothesis of vortices is pressed by many difficulties. In order that each planet, with a radius drawn to the sun, may describe areas proportional to time, the periodic times of the parts of the vortex would have to be in the duplicate ratio of the distances from the sun. In order that the periodic times of the planets be in the sesquiplicate proportion of the distances from the sun, the periodic times of the parts of the vortex would have to be in the sesquiplicate proportion of the distances.

Ut vortices minores circum saturnum, jovem & alios planetas gyrati conserventur & tranquille natent in vortice solis, tempora periodica partium vorticis solaris deberent esse æqualia. Revolutiones solis & planetarum circum axes suos, quæ cum motibus vorticum congruere deberent, ab omnibus hisce proportionibus discrepant. Motus cometarum sunt summe regulares, & easdem leges cum planetarum motibus observant, & per vortices explicari nequeunt.

In order that the lesser vortices, gyrated around Saturn, Jupiter & the other planets, be preserved & float tranquilly in the solar vortex, the periodic times of the parts of the solar vortex ought to be equal. The revolutions of the sun & of the planets about their own axes, which ought to be congruent with the motions of the vortices, are discrepant from all these proportions. The motions of comets are exceedingly regular, & they observe the same laws as the motions of the planets, & they cannot be explained by vortices.

Feruntur cometæ motibus valde eccentricis in omnes coelorum partes, quod fieri non potest, nisi vortices tollantur.

Comets are carried by very eccentric motions into all parts of the heavens, which cannot happen unless the vortices are abolished.

Projectilia, in aëre nostro, solam aëris resistentiam sentiunt. Sublato aëre, ut sit in vacuo Boyliano, resistentia cessat, siquidem pluma tenuis & aurum solidum æquali cum velocitate in hoc vacuo cadunt. Et par est ratio spatiorum coelestium, quæ sunt supra atmosphæram terræ. Corpora omnia in istis spatiis liberrime moveri debent; & propterea planetæ & cometæ in orbibus specie & positione datis secundum leges supra expositas perpetuo revolvi.

Projectiles, in our air, sense only the resistance of the air. The air being removed, as in the Boylean vacuum, the resistance ceases, since a light feather & solid gold fall with equal velocity in this vacuum. And the same reasoning holds for the celestial spaces which are above the atmosphere of the Earth. All bodies in those spaces ought to be moved most freely; & therefore the planets & comets in orbits of given form & position, according to the laws set forth above, revolve perpetually.

Perseverabunt quidem in orbibus suis per leges gravitatis, sed regularem orbium situm primitus acquirere per leges hasce minime potuerunt.

They will indeed persevere in their orbits by the laws of gravity, but by these laws they could by no means acquire, in the beginning, the regular disposition of the orbits.

Planetæ sex principales revolvuntur circum solem in circulis soli concentricis, eadem motus directione, in eodem plano quamproxime. Lunæ decem revolvuntur circum terram, jovem & saturnum in circulis concentricis, eadem motus directione, in planis orbium planetarum quamproxime. Et hi omnes motus regulares originem non habent ex causis mechanicis; siquidem cometæ in orbibus valde eccentricis, & in omnes coelorum partes libere feruntur.

The six principal planets revolve around the sun in circles concentric with the sun, with the same direction of motion, in nearly the same plane. Ten moons revolve around the earth, Jupiter, & Saturn in concentric circles, with the same direction of motion, in planes of the orbits of the planets as nearly as possible. And all these regular motions do not have their origin from mechanical causes; since comets are carried in very eccentric orbits, and are borne freely into all parts of the heavens.

Quo motus genere cometæ per orbes planetarum celerrime & facillime transeunt, & in apheliis suis ubi tardiores sunt & diutius morantur; quam longissime distant ab invicem, ut se mutuo quam minime trahant. Elegantissima hæcce solis, planetarum & cometarum compages non nisi consilio & dominio entis intelligentis & potentis oriri potuit. Et si stellæ fixæ sint centra similium systematum, hæc omnia simili consilio constructa suberunt Unius dominio: præsertim cum lux fixarum sit ejusdem naturæ ac lux solis, & systemata omnia lucem in omnia invicem immittant.

By which kind of motion the comets pass through the orbits of the planets most swiftly & most easily, & at their aphelia, where they are slower & linger longer, they are as far as possible distant from one another, so that they draw one another as little as possible. This most elegant structure of the sun, planets, & comets could have arisen only by the counsel & dominion of an intelligent & powerful being. And if the fixed stars are the centers of similar systems, all these, constructed by like counsel, will be subject to the dominion of the One: especially since the light of the fixed stars is of the same nature as the light of the sun, & all the systems send light into all others mutually.

Et ne fixarum systemata per gravitatem suam in se mutuo cadant, hic eadem immensam ab invicem distantiam posuerit.

And lest the systems of the fixed stars fall into one another by their own gravity, he has set those same at immense distances from one another.

Hic omnia regit non ut anima mundi, sed ut universorum dominus. Et propter dominium suum, dominus deus

He governs all things not as the soul of the world, but as the lord of all things. And on account of his dominion, the lord god

1 [“Pantokrator” litteris Graecis: Pantokrátwr] dici solet. Nam deus est vox relativa & ad servos refertur: & deitas est dominatio dei, non in corpus proprium, uti sentiunt quibus deus est anima mundi, sed in servos. Deus summus est ens æternum, infinitum, absolute perfectum: sed ens utcunque perfectum sine dominio non est dominus deus.

1 ["Pantokrator" in Greek letters: Pantokrátwr] is commonly said. For "god" is a relative term and is referred to servants; and "deity" is the dominion of God, not over a proper body, as those think for whom God is the soul of the world, but over servants. The highest God is an eternal, infinite being, absolutely perfect; but a being, however perfect, without dominion, is not the Lord God.

Dicimus enim deus meus, deus vester, deus Israelis, deus deorum, & dominus dominorum: sed non dicimus æternus meus, æternus vester, æternus Israelis, æternus deorum; non dicimus infinitus meus, vel perfectus meus. Hæ appellationes relationem non habent ad servos. Vox deus passim

For we say my god, your god, the god of Israel, the god of gods, & the lord of lords: but we do not say my eternal, your eternal, the eternal of Israel, the eternal of gods; we do not say my infinite, or my perfect. These appellations have no relation to servants. The word god commonly

2 significat dominum: sed omnis dominus non est deus. Dominatio entis spiritualis deum constituit, vera verum, summa summum, ficta fictum. Et ex dominatione vera sequitur deum verum esse vivum, intelligentem & potentem; ex reliquis perfectionibus summum esse, vel summe perfectum.

2 signifies a lord: but not every lord is a god. The dominion of a spiritual entity constitutes a god—true a true one, supreme a supreme one, feigned a feigned one. And from true dominion it follows that the true god is living, intelligent, & powerful; from the remaining perfections, that he is supreme, or supremely perfect.

Æternus est & infinitus, omnipotens & omnisciens, id est, durat ab æterno in æternum, & adest ab infinito in infinitum: omnia regit; & omnia cognoscit, quæ fiunt aut fieri possunt. Non est æternitas & infinitas, sed æternus & infinitus; non est duratio & spatium, sed durat & adest. Durat semper, & adest ubique, & existendo semper & ubique, durationem & spatium constituit.

Eternal & infinite, omnipotent & omniscient, that is, he endures from eternity to eternity, & is present from infinity to infinity: he rules all things; & he knows all things which are done or can be done. He is not eternity & infinity, but eternal & infinite; he is not duration & space, but he endures & is present. He endures always, & is present everywhere, & by existing always & everywhere, he constitutes duration & space.

Cum unaquæque spatii particula sit semper, & unumquodque durationis indivisibile momentum ubique, certe rerum omnium fabricator ac dominus non erit numquam, nusquam. Omnis anima sentiens diversis temporibus, & in diversis sensuum, & motuum organis eadem est persona indivisibilis. Partes dantur successivæ in duratione, coexistentes in spatio, neutræ in persona hominis seu principio ejus cogitante; & multo minus in substantia cogitante dei. Omnis homo, quatenus res sentiens, est unus & idem homo durante vita sua in omnibus & singulis sensuum organis.

Since every particle of space is always, & every indivisible moment of duration is everywhere, surely the maker and lord of all things will not be never, nowhere. Every soul that feels, at different times, & in different organs of the senses & of motions, is the same indivisible person. Parts are given successive in duration, coexistent in space, but neither in the person of man or in his thinking principle; & much less in the thinking substance of God. Every man, inasmuch as a sentient thing, is one & the same man during his life in all & each of the organs of sense.

Deus est unus & idem deus semper & ubique. Omnipræsens est non per virtutem solam, sed etiam per substantiam: nam virtus sine substantia subsistere non potest. In ipso

God is one & the same God always & everywhere. He is omnipresent not through power alone, but also through substance: for power cannot subsist without substance. In him

3 continentur & moventur universa, sed sine mutua passione. Deus nihil patitur ex corporum motibus: illa nullam sentiunt resistentiam ex omnipræsentia dei. Deum summum necessario existere in consesso est: Et eadem necessitate semper est & ubique. Unde etiam totus est sui similis, totus oculus, totus auris, totus cerebrum, totus brachium, totus vis sentiendi, intelligendi, & agendi, sed more minime humano, more minime corporeo, more nobis prorsus incognito.

3 the universe is contained and moved, but without mutual passion. God suffers nothing from the motions of bodies: they perceive no resistance from the omnipresence of God. That the supreme God necessarily exists is in common agreement: and by the same necessity he is always and everywhere. Whence also he is wholly like unto himself, all eye, all ear, all brain, all arm, all power of sensing, understanding, & acting, but in a manner by no means human, by no means corporeal, in a manner utterly unknown to us.

Ut cæcus non habet ideam colorum, sic nos ideam non habemus modorum, quibus deus sapientissimus sentit & intelligit omnia. Corpore omni & figura corporea prorsus destituitur, ideoque videri non potest, nec audiri, nec tangi, nec sub specie rei alicujus corporei coli debet. Ideas habemus attributorum ejus, sed quid sit rei alicujus substantia minime cognoscimus.

As a blind man has no idea of colors, so we have no idea of the modes by which the most wise God senses & understands all things. He is utterly destitute of every body & of corporeal figure, and therefore he can neither be seen, nor heard, nor touched, nor ought he to be worshiped under the species of any corporeal thing. We have ideas of his attributes, but what the substance of any thing is we do not at all know.

Videmus tantum corporum figuras & colores, audimus tantum sonos, tangimus tantum superficies externas, olfacimus odores solos, & gustamus sapores: intimas substantias nullo sensu, nulla actione reflexa cognoscimus; & multo minus ideam habemus substantiæ dei. Hunc cognoscimus solummodo per proprietates ejus & attributa, & per sapientissimas & optimas rerum structuras & causas finales, & admiramur ob perfectiones; veneramur autem & colimus ob dominium. Colimus enim ut servi, & deus sine dominio, providentia, & causis finalibus nihil aliud est quam fatum & natura.

We see only the figures & colors of bodies, we hear only sounds, we touch only the external surfaces, we smell odors alone, & we taste savors: the inmost substances we know by no sense, by no reflex action; & much less have we an idea of the substance of God. Him we know only through His properties & attributes, & through the most wise & best structures of things & final causes, & we admire on account of perfections; we venerate moreover & worship on account of dominion. For we worship as servants, & God without dominion, providence, & final causes is nothing other than fate & nature.

A cæca necessitate metaphysica, quæ utique eadem est semper & ubique, nulla oritur rerum variatio. Tota rerum conditarum pro locis ac temporibus diversitas, ab ideis & voluntate entis necessario existentis solummodo oriri potuit. Dicitur autem deus per allegoriam videre, audire, loqui, ridere, amare, odio habere, cupere, dare, accipere, gaudere, irasci, pugnare, fabricare, condere, construere.

From a blind metaphysical necessity, which indeed is the same always and everywhere, no variation of things arises. The whole diversity of created things according to places and times could have arisen only from the ideas and will of the necessarily existing being. Moreover, God is said by allegory to see, hear, speak, laugh, love, hold in hatred, desire, give, receive, rejoice, be angry, fight, fashion, found, construct.

Nam sermo omnis de deo a rebus humanis per similitudinem aliquam desumitur, non perfectam quidem, sed aliqualem tamen. Et hæc de deo, de quo utique ex phænomenis disserere, ad philosophiam naturalem pertinet.

For all discourse about God is derived from human affairs by some likeness, not indeed a perfect one, but nevertheless a partial one. And so much on God; to discourse about him from the phenomena pertains to natural philosophy.

Hactenus phænomena cælorum & maris nostri per vim gravitatis exposui, sed causam gravitatis nondum assignavi. Oritur utique hæc vis a causa aliqua, quæ penetrat ad usque centra solis & planetarum, sine virtutis diminutione; quæque agit non pro quantitate superficierum particularum, in quas agit (ut solent causæ mechanicæ) sed pro quantitate materiæ solidæ; & cujus actio in immensas distantias undique extenditur, decrescendo semper in duplicata ratione distantiarum. Gravitas in solem componitur ex gravitatibus in singulas solis particulas, & recedendo a sole decrescit accurate in duplicata ratione distantiarum ad usque orbem saturni, ut ex quiete apheliorum planetarum manifestum est, & ad usque ultima cometarum aphelia, si modo aphelia illa quiescant.

Thus far I have set forth the phenomena of the heavens & of our sea by the force of gravity, but I have not yet assigned the cause of gravity. This force indeed arises from some cause which penetrates to the very centers of the sun & the planets, without diminution of its virtue; and which acts not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes are wont to do) but according to the quantity of solid matter; and whose action extends on every side to immense distances, always decreasing in the duplicate ratio of the distances. The gravity toward the sun is compounded from the gravities toward the several particles of the sun, & in receding from the sun it decreases exactly in the duplicate ratio of the distances as far as the orbit of Saturn, as is manifest from the quiescence of the aphelia of the planets, & as far as the utmost aphelia of comets, provided only that those aphelia are at rest.

Rationem vero harum gravitatis proprietatum ex phænomenis nondum potui deducere, & hypotheses non fingo. Quicquid enim ex phænomenis non deducitur, hypothesis vocanda est; & hypotheses seu metaphysicæ, seu physicæ, seu qualitatum occultarum, seu mechanicæ, in philosophia experimentali locum non habent. In hac philosophia propositiones deducuntur ex phænomenis, & redduntur generales per inductionem.

But the rationale of these properties of gravity I have not yet been able to deduce from the phenomena, and I feign no hypotheses. For whatever is not deduced from the phenomena is to be called a hypothesis; and hypotheses, whether metaphysical, or physical, or of occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy propositions are deduced from the phenomena, & rendered general by induction.

Sic impenetrabilitas, mobilitas, & impetus corporum & leges motuum & gravitatis innotuerunt. Et satis est quod gravitas revera existat, & agat secundum leges a nobis expositas, & ad corporum cælestium & maris nostri motus omnes sufficiat.

Thus the impenetrability, mobility, & impetus of bodies, & the laws of motions & of gravity have become known. And it is sufficient that gravity truly exists, & acts according to the laws set forth by us, & suffices for all the motions of the celestial bodies & of our sea.

Adjicere jam liceret nonnulla de spiritu quodam subtilissimo corpora crassa pervadente, & in iisdem latente; cujus vi & actionibus particulæ corporum ad minimas distantias se mutuo attrahunt, & contiguæ factæ cohærent; & corpora electrica agunt ad distantias majores, tam repellendo quam attrahendo corpuscula vicina; & lux emittitur, reflectitur, refringitur, inflectitur, & corpora calefacit; & sensatio omnis excitatur, & membra animalium ad voluntatem moventur, vibrationibus scilicet hujus spiritus per solida nervorum capillamenta ab externis sensuum organis ad cerebrum & a cerebro in musculos propagatis. Sed hæc paucis exponi non possunt; neque adest sufficiens copia experimentorum, quibus leges actionum hujus spiritus accurate determinari & monstrari debent.

It would now be permissible to add some things about a certain most subtle spirit pervading gross bodies, & lying hidden in the same; by whose force & actions the particles of bodies at the smallest distances mutually attract one another, & being made contiguous cohere; & electric bodies act at greater distances, as well by repelling as by attracting neighboring corpuscles; & light is emitted, reflected, refracted, inflected, & heats bodies; & all sensation is excited, & the limbs of animals are moved at will, namely by the vibrations of this spirit propagated through the solid capillary threads of the nerves from the external organs of the senses to the brain & from the brain into the muscles. But these things cannot be set forth in a few words; nor is there present a sufficient store of experiments, by which the laws of the actions of this spirit ought to be accurately determined & shown.

F I N I S

E N D

1. Id est Imperator universalis.

1. That is, the universal Emperor.

2.Pocockus noster vocem dei deducit a voce Arabica du, (& in casu obliquo di,) quæ dominum significat. Et hoc sensu principes vocantur dii, Psalm. lxxxiv. 6. & Joan. x. 45. Et Moses dicitur deus fratris Aaron, & deus regis Pharaoh (Exod. iv. 16. & vii 1.) Et eodem sensu animæ principum mortuorum olim a gentibus vocabantur dii, sed falso propter defectum dominii.

2.Pocockus of ours derives the word god from the Arabic du, (& in the oblique case di,) which signifies lord. And in this sense princes are called gods, Psalm.84. 6. &John.10. 45. AndMoses is called a god of his brother Aaron, and a god of King Pharaoh (Exod.4. 16. & 7 1.) And in the same sense the souls of dead princes were formerly called gods by the nations, but falsely on account of a defect of dominion.

3. Ita sentiebant veteres, utPythagoras apud Ciceronem, de Natura deorum, lib.1.Thales, Anaxagoras, Virgilius Georgic. lib. iv. v. 220, & Æneid. lib.6. v. 721.

3. Thus the ancients thought, asPythagoras in Cicero, On the Nature of the Gods, book1.Thales, Anaxagoras, Virgil Georgics, book 4, v. 220, & Aeneid, book 6, v. 721.

Philo Allegor. lib.1. sub initio.Aratus in Phænom.

Philo, Allegories, book 1, at the beginning. Aratus, in the Phaenomena.

sub initio. Ita etiam scriptores sacri ut Paulus in Act. xvii.

at the beginning. Thus also the sacred writers, as Paul in Acts 17.

27, 28. Johannes in Evang. xiv. 2. Moses in Deut.

27, 28. John in the Gospel 14. 2. Moses in Deuteronomy.

iv. 39. & x. 14. David Psal. cxxxix. 7, 8, 9. Solomon 1 Reg.

4. 39. & 10. 14.David Psalm 139. 7, 8, 9. Solomon 1 Kings.

viii. 27. Job xxii. 12, 13, 14. Jeremias xxiii.

8. 27.Job22. 12, 13, 14.Jeremiah23.

23, 24. Fingebant autem idololatræ solem, lunam, & astra, animas hominum & alias mundi partes esse partes dei summi & ideo colendas sed falso.

23, 24. But the idololaters imagined the sun, the moon, & the stars, the souls of men, & other parts of the world to be parts of the supreme God, & therefore to be worshipped, but falsely.