(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.