Propositions 18
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Table of contents
 Proposition 1 Theorem 1
 Proposition 2 Theorem 2
 Proposition 3 Theorem 3
 Proposition 4 Theorem 4
 Scholium
 Proposition 5 Theorem 5
 Scholium

Proposition 6 Theorem 6
 Corollary 1: Hence the weights of bodies do not depend on their forms and textures.
 Corollary 2: Universally, all bodies around the earth gravitate towards the earth. The weights of all gravitate at equal distances from the earth s centre depending on the quantities of matter in them.
 Corollary 3: All spaces are not equally full.
 Corollary 4: If all the solid particles of all bodies are of the same density, nor can be rarefied without pores, a void, space, or vacuum must be granted.
 Corollary 5: The power of gravity is of a different nature from the power of magnetism
 Proposition 7 Theorem 7
 Proposition 8 Theorem 8
 Corollary 1
 Corollary 2
 Corollary 3
Proposition 1 Theorem 1
The same thing affects those that are affected by Saturn.
The former part of this Proposition appears from Pham. I, and Prop. to Jupiter s centre
Proposition 2 Theorem 2
Proposition 3 Theorem 3
Proposition 4 Theorem 4
The moon gravitates towards the Earth
The mean distance of the moon from the earth in the syzygies in semidiameters of the earth is:
 60 to Vendelin and Huygens
 60 1/2 to Copernicus
 60 2/5 to Street
 60 1/2 to Brahe when corrected
One revolution of the moon takes 27d 7h 43'.
 Earth’s circumference is 123,249,600 Paris feet.
If the moon, deprived of all motion, fell to the Earth, it will fall by 15.. Paris feet in a minute.
Scholium
Assume:
 many moons revolve around the Earth
 the smallest one would be nearest the Earth as to touch the mountaintops
If its centrifugal force stops, then it will fall to the Earth with the same velocity as bodies on mountains.
Proposition 5 Theorem 5
The circumjovial planets gravitate towards Jupiter. The circnntsaturnal gravitate towards Saturn. The circumsolar gravitate towards the sun.
By their gravity, they are maintained in curvilinear orbits.
Scholium
We shall call the centripetal force which retains the celestial bodies in their orbits as gravity since it is a gravitating force.
The cause of that centripetal force which retains the moon in its orbit will extend itself to all the planets, by Rule 1, 2, and 4
Proposition 6 Theorem 6
All bodies gravitate towards every planet. The weights of bodies towards any the same planet, at equal distances from the centre of the planet, are proportional to the quantities of matter which they contain.
Heavy bodies fall from equal heights at equal times. This is proven by pendulums. I have tried gold, silver, lead, glass, sand, eommpn salt, wood, water, and wheat.
I took two equal round wooden boxes.
 I filled one with
Corollary 1: Hence the weights of bodies do not depend on their forms and textures.
This is because if the weights were changed with the forms, they would change according to the variety of forms while their mass staying the same. This is against experience.
Corollary 2: Universally, all bodies around the earth gravitate towards the earth. The weights of all gravitate at equal distances from the earth s centre depending on the quantities of matter in them.
If the aether were void of gravity, or were to gravitate less in proportion to its quantity of matter, then, because (according to Aris totle, Des Carles, and others) there is no difference between that and other bodies but in mere form of matter, by a successive change from form to form, it might be changed at last into a body of the same condition with those which gravitate most in proportion to their quantity of matter.
On the other hand, the heaviest bodies, acquiring the first form of that body, might gradually lose their gravity. Therefore the weights would depend on the shapes of bodies, and with those shapes might be changed. This is contrary to what was proved in Corollary 2.
Corollary 3: All spaces are not equally full.
If all spaces were equal, then the specific gravity of the fluid which fills the region of the air, on account of the extreme density of the matter, would fall nothing short of the specific gravity of quicksilver, or gold, or any other the most dense body.
Therefore, neither gold, nor any other body, could descend in air.
Bodies do not descend in fluids, unless they are specifically heavier than the fluids.
If the quantity of matter in a given space can, by any rarefaction, be diminished, what should hinder a diminution to infinity ?
Corollary 4: If all the solid particles of all bodies are of the same density, nor can be rarefied without pores, a void, space, or vacuum must be granted.
Bodies of the same density means bodies whose inertia are proportional to their sizes.
Corollary 5: The power of gravity is of a different nature from the power of magnetism
Magnetic attraction does not depend on matter. Some bodies are attracted by magnets, some are not.
Magnetism in a body can be increased or reduced, sometimes stronger than gravity.
Going away from the magnet does not reduce the magnetism by half.
Proposition 7 Theorem 7
A power of gravity tends to all bodies, proportional to the quantities of matter which they contain.
All the planets mutually gravitate one towards another. This gravity is the square of the distance of places from the centre of the planet. It follows (by Prop. 69, Book 1) that gravity in all the planets is proportional to the matter which they contain.
All the parts of any planet A gravitate towards planet B, just as planet B gravitates towards A.
Corollary 1: Total attraction in gravity and electromagnetism is made up of all of the partial attractions.
Corollary 2: The force of gravity towards the several equal particles of any reciprocally as the square of the distance of places from the particles, as appears from Book 1 Cor. 3, Prop. 69
Proposition 8 Theorem 8
In two spheres gravitating towards the other, if the matter in places on all sides round about and equidistant from the centres is similar, the weight of either sphere towards the other will be reciprocally as the square of the distance between their centres.
Corollary 1
We can use this to find the weights of planets. The weights of bodies orbiting planets are (by Cor. 2, Prop. 4, Book I) as the diameters of the circles directly and the squares of their periodic times reciprocally.
Their weights at the surfaces of the planets, or at any other distances from their centres, are (by this Prop.) greater or less in the reciprocal duplicate proportion of the distances.
Thus, from the orbital period of:
 Venus is 224d 16 3/4h
 outermost moon of Jupiter is 16d 16 h
Corollary 2
This is also the way to find the quantity of matter [mass] in the planets. This is because the quantities of matter are as the forces of gravity at equal distances from their centres.
In the sun, Jupiter, Saturn, and the earth respectively are: 1, 1/xxxx, 1/xxxx, and 1/xxxxx
If the parallax of the sun is taken greater or less than 10" 30" , the quantity of matter in the earth must be augmented or diminished in the triplicate of that proportion.
Corollary 3
This is how we find the densities of the planets. According to Book 1 Prop 72, the weights of equal bodies Spheres are, at the surfaces of those spheres, as the diameters of the spheres 5 and therefore the densities of dissimilar spheres are as those weights applied But the true diameters of the Sun, .Jupiter to the diameters of the spheres.
Saturn, and the earth, were one to another as 10000, 997, 791, arid 109; and the weights towards the same as 10000, 943, 529, and 435 re and therefore their densities are as 100. 94, 67, and 400. The spectively density of the earth, which comes out by this computation, does not depend upon the parallax of the sun, but is determined by the parallax of the moon, and therefore is here truly defined.
The sun, therefore, is a little denser than Jupiter, and Jupiter than Saturn, and the earth four times denser than the sun for the sun, by its great heat, is kept in a sort of a rarefied The moon state. is denser than the earth, as shall appear after
Corollary 4
The smaller the planet, and the nearer to the sun, the more dense it is.
The gravity on the surface come nearer to equality.
 Jupiter is denser than Saturn
 Earth is denser than Jupiter
placed at different distances from the sun, that, according to their degrees of density, they might enjoy a greater or less proportion to the sun s heat.
Earth’s water would be converted to:
 ice if it were transferred to Saturn.
 vapor if it were transferred to Mercury from boiling