Denique si corpora omnia in circuitu terrae gravia esse in terram, idque pro quantitate materiae in singulis, Et lunam gravem esse in terram pro quantitate materiae suae, Et vicissim mare nostrum grave esse in lunam, Et planetas omnes graves esse in se mutuo, Et cometarum similem esse gravitatem in solem, per experimenta et observationes astronomicas universaliter constet: Dicendum erit per hanc regulam quod corpora omnia in se mutuo gravitant. Nam et fortius erit argumentum ex phaenomenis de gravitate universali, Quam de corporum impenetrabilitate: De qua utique in corporibus coelestibus nullum experimentum, Nullam prorsus observationem habemus. Attamen gravitatem corporibus essentialem esse minime affirmo. Per vim insitam intelligo solam vim inertiae. Haec immutabilis est. Gravitas recedendo a terra diminuitur. Finally, if it is universally established by experiments 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 gravitates 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 each other, 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.

(Corol. 1) Hinc pondera corporum non pendent ab eorum formis et texturis. Nam si cum formis variari possent; Forent majora vel minora, Pro varietate formarum, In aequali materia: Omnino contra experientiam. (Corol. 2) Corpora universa, quae circa terram sunt, Gravia sunt in terram; Et pondera omnium, Quae aequaliter a centro terrae distant, Sunt ut quantitates materiae in iisdem. Haec est qualitas omnium in quibus experimenta instituere licet, Et propterea per regula III de universis affirmanda est. (Corol. 3) Spatia omnia non sunt aequaliter plena. Nam si spatia omnia aequaliter plena essent, Gravitas specifica fluidi quo regio aëris impleretur, Ob summam densitatem materiae, Nil cederet gravitati specificae argenti vivi, vel auri, Vel corporis alterius cujuscunque densissimi; Et propterea nec aurum neque aliud quodcunque corpus in aëre descendere posset. Nam corpora in fluidis, nisi specifice graviora sint, minime descendunt. Quod si quantitas materiae in spatio dato per rarefactionem quamcunque diminui possit, Quidne diminui possit in inifinitum? (Corol. 4) Si omnes omnium corporum particulae solidae sint ejusdem densitatis, Neque sine poris rarefieri possint, vacuum datur. Ejusdem densitatis esse dico, Quarum vires inertiae sunt ut magnitudines. (Corol. 5) Vis gravitatis diversi est generis a vi magnetica. Nam attractio magnetica non est ut materia attracta. Corpora aliqua magis trahuntur, alia minus, plurima non trahuntur. Et vis magnetica in uno et eodem corpore intendi potest et remitti, Estque nonnunquam longe major pro quantitate materiae quam vis gravitatis, Et in recessu a magnete decrescit in ratione distantiae non duplicata, Sed fere triplicata, Quantum ex crassis quibusdam observationibus animadvertere potui. Corollary 1 Hence, the weights of bodies do not depend on their forms and textures. For if the weights could be altered with the forms, they would be, in equal matter, greater or less according to the variety of forms, entirely contrary to experience. Corollary 2 All bodies universally that are on or near the earth gravitate toward the earth, and the weights of all bodies that are equally distant from the center of the earth are as the quantities of matter in them. This is a quality of all bodies on which experiments can be performed and therefore by rule 3 is to be affirmed of all bodies universally. Corollary 3 All spaces are not equally full. For if all spaces were equally full, the specific gravity of the fluid with which the region of the air would be filled, because of the extreme density of its matter, would not be less than the specific gravity of quicksilver or of gold or of any other body with the greatest density, and therefore neither gold nor any other body could descend in air. For bodies do not ever descend in fluids unless they have a greater specific gravity. But if the quantity of matter in a given space could be diminished by any rarefaction, why should it not be capable of being diminished indefinitely? Corollary 4 If all the solid particles of all bodies have the same density and cannot be rarified without pores, there must be a vacuum. I say particles have the same density when their respective forces of inertia are as their sizes. Corollary 5 The force of gravity is of a different kind from the magnetic force. For magnetic attraction is not proportional to the matter attracted. Some bodies are attracted more, and others less, while most bodies are not attracted. And the magnetic force in one and the same body can be intended and remitted and is sometimes far greater in proportion to the quantity of matter than the force of gravity; and this force, in receding from the magnet, decreases not as the square but almost as the cube of the distance, as far as I have been able to tell from certain rough observations.

Jupiter utque respectu fixarum revolvitur horis 9 56’ (novem et quinquaginta sex minutis) mars horis 24 39’ (vigintiquatuor et triginta novem minutis), venus horis 23 (vigintitres) circiter, terra horis 23 56’ (vigintitres et quinquaginta sex minutis), sol diebus 25 1/2 (vigintiquinque et dimidium) et luna diebus 27 (vigintiseptem) horis 43’ (quadraginta tres minutis). Haec ita se habere ex phaenomenis manifestum est. Maculae in corpore solis ad eundem situm in disco solis redeunt diebus 27 1/2 (vigintiseptem et dimidium) circiter, Respectu terrae; Ideoque respectu fixarum sol revolvitur diebus 25 1/2 (vigintiquinque et dimidium) circiter. Simili motu extimus saturni satelles circa axem suum revolvi videtur, Eadem sui facie saturnum perpetuo respiciens. Nam circum saturnum revolvendo, Quoties ad orbis sui partem orientalem accedit, Aegerrime videtur et plerumque videri cessat: Id quod evenire potest per maculas quasdam in ea corporis parte quae terrae tunc obvertitur, ut Cassinus notavit. Simili etiam motu satelles extimus jovialis circa axem suum revolvi videtur, propterea quod in parte corporis jovi aversa maculam habeat quae taquam in corpore jovis cernitur ubicunque satelles inter jovem et oculos nostros transit. With respect to the fixed stars Jupiter revolves in 9 hours 56 minutes, Mars in 24 hours 39 minutes, Venus in about 23 hours, the earth in 23 hours 56 minutes, the sun in 25 1/2 days, and the moon in 27 days 7 hours 43 minutes. That these things are so is clear from phenomena. With respect to the earth, the spots on the body of the sun return to the same place on the sun’s disc in about 27 1/2 days; and therefore with respect to the fixed stars the sun revolves in about 25 1/2 days. The outermost satellite of Saturn seems to revolve about its own axis with a motion similar to our moon’s, constantly presenting the same aspect toward Saturn. For in revolving about Saturn, whenever it approaches the eastern part of its own orbit, it is barely seen and for the most part disappears from sight; and possibly this occurs because of certain spots in that part of its body which is then turned toward the earth, as Cassini noted. The outermost satellite of Jupiter also seems to revolve about its own axis with a similar motion, because in that part of its body turned away from Jupiter it has a spot which, whenever the satellite passes between Jupiter and our eyes, appears as if it were on the body of Jupiter.

Sic spatio viginti quatuor horarum aqua non bis ut fieri solet sed semel tantum perveniet ad maximam altitudinem et semel ad minimam; Et altitudo maxima, si luna declinat in polum supra horizontem loci, Incidet in horam vel sextam vel tricesimam ab appulsu lunae ad meridianum, Atque luna declinationem mutante mutabitur in defluxum. Quorum omnium exemplum in portu regni Tunquini ad Batsham sub latitudine boreali 20˚ 50’. Halleius ex nautarum observationibus patefecit. Ibi aqua die transitum lunae pere aequatorem sequente stagnat, Dein luna ad boream declinante incipit fluere et refluere, Non bis, ut in aliis portubus, Sed semel singulis diebus; Et aestus incidit in occasum lunae, Defluxus maximus in ortum. Thus in the space of twenty-four hours, the water will only once reach its greatest height, not twice as usually happens, and will only once reach its least height; and the greatest height, if the moon is declining toward the pole above the horizon of the place, will occur at either the sixth or the thirtieth hour after the appulse of the moon to the meridian; and when the moon changes its declination, this flood tide will be changed into an ebb tide. And example of all these things has been given by Halley, on the basis of sailors’ observations, in Batsha harbor in the kingdom of Tonkin at the latitude of 20˚50’ N. There the water stays still on the day following the transit of the moon over the equator; then, when the moon declines toward the north, the water begins to ebb and flow—not twice, as in other harbors, but only once every day; and the flood tide occurs at the setting of the moon, and the greatest ebb tide at its rising.

Haec disputavimus non considerando obscurationem cometarum per fumum illum maxime copiosum et crassum, Quo caput circundatur, Quasi per nubem obtuse semper lucens. Nam quanto obscurius redditur corpus per hunc fumum, Tanto propius ad solem accedat necesse est, Ut copia lucis a se reflexae planetas aemuletur. Inde verisimile fit cometas longe infra sphaeram saturni descendere, Uti ex parallaxi probavimus. Idem vero quam maxime confirmatur ex caudis. Hae vel ex reflexione fumi sparsi per aethera vel ex luce capitis oriuntur. Priore casu minuenda est distantia cometarum, Ne fumus a capite semper ortus per spatia nimis ampla incredibili cum velocitate et expansione propagetur. In posteriore referenda est lux omnis tam caudae quam capillitii ad nucleum capitis. Igitur si concipiamus lucem hanc omnem congregari et intra disum nuclei coarctari, Nucleus ille jam certe, quoties caudam maximam et fulgentissimam emittit, Jovem ipsum splendore suo multum superabit. In treating these matters, we have not been considering the obscuring of comets by that very copious and thick smoke by which the head is surrounded, always gleaming dully as if through a cloud. For the darker the body is rendered by this smoke, the closer it must approach to the sun for the amount of light reflected from it to rival that of the planets. This makes it likely that the comets descend far below the sphere of Saturn, as we have proved from their parallax. But this same result is, to the highest degree, confirmed from their tails. These arise either from reflection by the smoke scattered through the aether or from the light of the head. In the first case the distance of the comets must be diminished, since otherwise the smoke always arising from the head would be propagated through spaces far too great, with such a velocity and expansion as to be unbelievable. In the second case, all the light of both the tail and the coma must be ascribed to the nucleus of the head. Therefore, if we suppose all this light is united and condensed within the disc of the nucleus, then certainly that nucleus, whenever it emts a very large and very bright tail, will far surpass in its brilliance even to Jupiter itself.

Elegantissima haecce solis, planetarum et cometarum compages non nisi consilio Et dominio entis intelligentis et potentis oriri potuit. Et si Stellae fixae sint centra similium systematum, Haec omnia simili consilio constructa suberunt Unius dominio: Praesertim cum lux fixarum sit ejusdem naturae ac lux solis, Et systemata omnia lucem in omnia invicem immittant. Et ne fixarum systemata per gravitatem suam in se mutuo cadant, Hic eadem immensam ad invicem distantiam posuerit. Dominatio entis spiritualis deum consituit, Vera verum, summa summum, ficta fictum. Et ex dominatione vera sequitur deum verum esse vivum, Intelligentem et potentem; Ex reliquis perfectionibus summum esse, Vel summe perfectum. Aeternus est et infinitus, omnipotens et omnisciens, Id est, durat ad aeterno in aeternum, Et adest ab infinito in infinitum: Omnia regit; et ominia cognoscit, Quae fiunt aut fieri possunt. The most elegant system of the sun, planets, and comets could not have arisen without the design and dominion of an intelligent and powerful being. And if the fixed stars are the centers of similar systems, they will all be constructed according to a similar design and subject to the dominion of One, especially since the light of the fixed stars is of the same nature as the light of the sun, and all the systems send lights into all the others. And so that the systems of the fixed stars will not fall upon one another as a result of gravity, he has placed them at immense distances from one another. The lordship of a spiritual being constitutes a god, a true lordship constitutes a true god, a supreme lordship a supreme god, an imaginary lordship an imaginary god. And from true lordship it follows that the true God is living, intelligent, and powerful; from the other perfections, that he is supreme, or supremely perfect. He is eternal and infinite, omnipresent and omniscient, that is, he endures from eternity to eternity, and he is present from infinity to infinity; he rules all things, and he knows all things that happen or can happen.