The earth moves toward the centre of the elements, which motion is caused by the weight generated in it from every side. And this motion is straight, made toward the centre; and because in united bodies the part cannot move without the whole, it is necessary that the excess which the heavy body gives of itself to any hemisphere have the centre of its gravity at the surface-centre of that hemisphere, and that the centre of the acquired gravity be at the beginning of the diametral line of that earth, and that the far end of that diametral line terminate at the centre of the opposite hemisphere, there being made in that centre as much weight as was the weight given in our hemisphere.
First define gravity and its nature.
The motion the earth makes to destroy any gravity generated upon it is straight, along the diametral line, and never by any accident can it partake of a revolving motion. And such motion arises because no gravity has permanence except where it dies.
Conception.
No part united to its whole will move without the motion of its whole.
Gravity is an accident generated in bodies placed above the light medium by a liquid or flexible body lighter than itself.
What is a mathematical point.
A mathematical point is that which has no middle, and nothing in nature is smaller than it, and for this reason it is indivisible.
What is the natural point.
The natural point is that impression which the tip of some iron leaves of itself upon a place, and this is divisible to infinity.
What difference is there between centre and mathematical point.
The centre and the mathematical point are one and the same thing, but they differ only by the place where they are joined, for the centre is placed at the middle of the quantity or gravity of anything, while the point is the termination of a line or of any angle.
What difference is there between the centre of the balance and the centre of the world.
The centre ...
Of the inequality of the weight given by the ebb and flow of the sea, which comes from the sum of the rivers.

From the mathematical to the mechanical there is infinite variety, which makes the one incorporeal, indivisible, and for this reason it remains indivisible. But we shall say that there is a medium interposed between the extremity of the mathematical line and the air that faces it. Therefore it is neither part of the line nor part of the air, whence it is companion of nothing; but the mechanical point is the front of the mechanical line and is part of that line.

From the mechanical point to the mathematical there is infinite variety, because that mechanical point is visible and consequently has continuous quantity, and every continuous quantity is divisible to infinity, etc.
From the mechanical point to the mathematical point there is infinite variety, because the mechanical has continuous quantity and every continuous thing is divisible to infinity, while the mathematical is not visible, nor has any quantity, and where there is no quantity there is no division.

h - S; d n - o r f T - t - v
Of the 4 greatest portions of the right and left circle no account is taken, but only of the remainder of these circles. To the remainder is added, to the right circle, 4 portions similar to the h, and to the right circle are added 8 of the value of these 4 right ones; and those figures that receive them, the right and the left, are of equal value. From the left is cleared of its portions the smaller upper circle, and its value is rendered in f; the same is done with the smaller lower circle in that left circle, and there remains the larger triangle f, which exceeds the crescents. The left and right circle are equal between themselves, and from each are removed the 4 greatest portions, and in the right circle they remain equal, but the right remains a square, and the left thus (a figure follows) of equal value.
And to the right square is left a void for the departure of a circle surrounded by it, and to the left are removed two circles of value equal to the right circle, and that right circle is filled with 4 portions, and the two left circles are filled with 8 portions of value equal to the 4 right ones. But the 4 portions of the upper right circle are removed from their place and put back into a single portion f on the outer side, whence the void of that circle remains void and the rest remains as before, but a large triangle has been made.

I want to remove n o d r and render it in f, and I shall have made the triangle f r t v, and I have not varied the value of the whole, by the third conception; and I shall do the same on the right side and shall have made two triangles of the whole, and they would be equal to the 4 triangles of the right circle S, if they did not lack four crescents (a figure of a crescent follows) similar to the crescent o, which is similar to the portion d that is in contact with it.
Therefore I shall make a square of the two triangles of the left circle, and I shall make another square of the four triangles of the right circle S, which is greater by the 4 crescents e; and, that left square being taken from the right, there will remain of that right a square part, equal to the four crescents of the left circle, etc.