Examples that the said stone could not stop, by its impetus, at that centre of the world.

If bodies were perfectly spherical and of equal material, they would have a single centre; but this seems impossible to be, because matter is unequal.

Define whether the place of the common centre draws heavy bodies to itself, and whether the light parts drive them away or not.

The centre of the true gravity of bodies is unique and single, and without place it resides in the middle of bodies, leaving around itself circularly an equal weight of the body that clothes it, so that as many times as one could imagine dividing that body with a single cut whose line touched the centre, so many times would you find that weight divided into two parts of equal weight. So that if it could be divided innumerable times by a straight cut ... The second centre is unique and single, and without place (I said without place because, if it occupied place, it would not be indivisible), enclosed in the middle of the natural gravity of bodies, where it is always surrounded and clothed by equal weight on every side; and if the body where it resides is divided by an equal cut over that centre, the separated parts will always be of equal weight. This is the centre that seems to be the soul and life of heavy bodies, and the part where it dwells makes itself the guide of the motions of those bodies. This centre dwells in all heavy bodies and does nothing in any of them. Only the universal heaviness of the earth keeps its content in the middle of the elements, though it is always in continuous motion; by it moves not only the centre ...

I said 'on every side' and not 'on every part' and not 'through every diameter' of that body, because 'side' means all that part which is from the centre outward, or inward, or upward or downward. Had I said 'part', those go almost to infinite number in every direction, for you cannot show a piece so small that it is not called a part of that body; so if 'part' had been named, the manner of the statement would be false, because there could be a hole from the surface of that body whose bottom approached its centre, while on the opposite side it would stand out like a column as much as the hole is hollow, so that the weight from the surface of that bottom to the opposite surface would not hold the centre of the universal weight in its middle. Whence of necessity one says 'side' and not 'diameter' or 'part'. And it often happens that such a centre is outside the bodies, that is, not touching the heavy matter but in the air.

The common centre is that from which the sphere of air is equally remote, and [likewise] the sphere of fire. The common centre is that which every gravity desires equally to surround. I do not mean that such desire is however in such a body. No part of the air, being lighter than it, can make resistance to it.

The common centre and the centre of the earth are different. It is not necessary that the common centre lie more in earth than in water or air, because that centre is not its own but belongs to the air and the fire; for if it were ever its own it would change place in that earth, as necessity often moves it; rather, always changing, the earth would carry that centre with it, as it carries the centre of its own gravity. But that centre resides in the middle of the said elements, alone, without place; and if it were possible to make the earth into minute parts and bring them in various places to the element of fire in the manner of the stars in the sky ...

In the way that the stars of the sky show themselves, and were one to leave one of the said particles from such a site, certainly that gravity would not stop at once at the common centre, but by its impetus would pass on almost to the other side of the element, and there, still finding no rest, would take again the same road as before and return near the place whence it parted; and beyond the first motion made, it would remake the second by the same path with a shorter course, and then return, and so do very many times, like a weight fixed to the end of a cord which, pulled aside and let go, moves many times to and fro, ever diminishing its courses, until at last it stops beneath the fixed point of the cord that suspends it; so that in this way that weight would run many years up and down through the air. But if from such a height of element you let all the said particles of the world fall at one time, and they were of equal figure and weight, at one single time they would stop around the horned [common] centre. And if such descent were made at different times, certainly for many years this air would be full of motions and pieces, broken by the striking and colliding of such weights that would go to pieces, and each would sometime reach its centre with the common centre. And should you say that the single piece mentioned first suddenly ... no, because that piece does not desire that place, nor does that place, being indivisible, have power to draw it to itself; rather it is that such weight, in every light part ...

And these pieces of the world, passing to the common centre, would not find it, otherwise ... would make the ... [torn] ... in the houses.

a - m n p - o

When m is at n, a is at o, and when o returns to n, m is near p.

* It resides unique and single, surrounded and clothed circularly by equal weight.
* It resides unique, without place, and single in the middle of bodies, where in sum it is always surrounded and clothed by equal weight.
* It resides unique and single in the middle of the natural gravity of bodies, where without place equally always ...
* Unique and single, without place, it resides in the true middle of the natural gravity of bodies, where it is always surrounded and clothed by equal weight, so that as many times as the body it is enclosed in could be cut by a straight cut over that centre, always the body would be found in two parts of equal weight.
* In the middle of the gravity of bodies it is enclosed.
* Unique and single and without place, it is enclosed in the middle of the natural gravity of bodies, where it is always surrounded and clothed by equal weight, so that however many times it were divided over itself by a single cut, so many times you would find the parts of equal weight. This ...
* So that however many times its body could be divided over itself by a single cut, so many times you would find the divided parts to be of equal weight among themselves. In such a way ...
* And if the body where it resides is divided by a single cut over that centre, the 2 parts will always be equal among themselves.

The common centre and the centre of the earth are not one and the same; rather they are very dissimilar and various in nature, because the common centre does not move, the site of air and fire not changing, whereas the centre of the earth is unstable and in continuous change, for it changes as often as the winds carry the water of the seas, covering or uncovering various shores by their surging. Whence, taking weight from one part of the earth and carrying it to another where such weight is lacking, the centre becomes more remote, and as the weight increases it approaches; and so, as many changes as the weight of the waters makes upon their beds, so many changes the centre of the earth makes about the common centre. And if it were possible to remove the earth from its site and draw it aside so that the common centre remained well outside the earth, and one let a stone fall in the middle of that air interposed between the common centre and the centre of the earth, certainly that stone would without doubt descend to the common centre by the shortest way.

c b a

The weight arrived at the centre loses its heaviness. Let a be the centre of the elements, that is the common centre; c the centre of the world; b the place where the stone is left in the air at equal distance from the two centres. I say that the stone b will descend to a, the common centre, and will not rise up to the centre of the earth.

Those circles will be called lower which are nearer to the common centre, and conversely those higher which are more remote from that centre. Whatever removes from the common centre by any line is said to rise toward the sky, and whatever departs from the sky is said to descend toward the centre. The impetus made by the motion of heavy bodies makes them wandering and not knowers of the place where they move, whence their coming to rest is much delayed.

* The universal centre of the elements is the centre of none of them, because, having no stability, they cannot have a single centre. There are some who hold that the element of fire is driven by the sun in a straight line of the solar rays. This is denied, alleging that, fire being corporeal, it cannot move from its site to us without time, as the solar ray does.
The centre of the universe is the centre of no element, because the continuous revolution and various accidents born of continuous celestial influences keep those elements in continuous change of site, inasmuch as the earth, largely clothed by the sphere of water, makes one same body with that water and, like a ball, stays suspended in the air; and the centre of the sphere of water is not the centre of its gravity, and the centre of its gravity is not the centre of the gravity of the earth, but rather quite remote, whence the surface of the sphere of water is not equally distant from its centre nor from the ...

... to the men who lie upon the bottom of the sea ...
The motion made by heavy bodies toward the horned centre is not from any desire the body has in itself to find that centre, nor from attraction the centre makes, like a magnet drawing that weight to itself, but rather from the supreme contrariety of the elements; for fire, as lighter, stays higher and circularly remote from the heavier, which is the earth; the air, having more conformity with fire, comes nearer, still circularly, whence the two heavier elements embrace and join together, and the two lighter do the same, and such proportion is imagined from the heaviness of earth to that of water as of the lightness of fire to that of air, and of air with water. Whence, that element of air being spherical and the fire spherically circumscribing it, a centre must be common to both, which we shall name the common centre, c; and if by some accident some part of the air rises within the element of fire, it will fall back by the shortest way into its element. That shortest way being perpendicular toward the centre, water does the like in the air, descending by a straight line into its element, and earth the like upon water, still by the shortest way; whence a stone being let fall ...

The common centre and the centre of the sphere of water are not one and the same, because the common centre does not change site, the sphere of fire not moving, while the centre of the earth and that of the water are always in continuous change about that common centre. Also the centre of the air is not the same, because that part of the air which borders the earth receives in itself as many concavities as there are humps the earth makes where it uncovers itself outside the sphere of water; and that part of the air which borders and unites with the sphere of fire keeps a more perfect sphericity than where it borders the earth. Moreover that upper sphericity of the air, being perpendicular to the sun's course, because that air holds moisture, and the sun's heat added to the element of fire draws higher the air mixed with the moisture beneath it and raises it like a mountain, whence the air has nowhere an extremity equidistant from the centre. But the upper part of the sphere of fire has a single centre equidistant from every part of itself, because in that site there is no humid matter, for at such a site it could not sustain itself and could not pass through so great a thickness of element without the fire resolving it into itself; whence, receiving no change, that upper part resides stable and firm, keeping by every straight line an equidistant space between itself and its centre. This is the centre that stands in the middle of all the centres of the 3 other elements, which we shall name the universal centre, and the other centres around it we shall call improper centres, since, the water being attached to the earth, it impedes the true site of the centre of that earth.

Also the sphere of water, being neither of equal thickness nor of equal roundness: for although around its centre it were of equal weight, it would not be of equal distance, because the meridional part of the sphere is warmer, hence lighter and more distant from its centre than the northern part, which is denser and heavier.

m n a