That is said to be nothing which partakes of no thing; therefore the surface, line and point are nothing, because they are not part of their whole, for they occupy nothing of that whole; and all things that occupy nothing are equal among themselves, and all together equal to one, and one to all. Therefore here the part is equal to the whole and the whole to the part, the divisible to the indivisible, the finite to the infinite.

For what cause the percussion is somewhat more powerful when a little more remote from its mover than when near. This is known: that a shot at every degree of motion acquires degrees of weakness, and its impetus increases through the wave of air that flees.

a pushes inward

The two portions a m n and a f n have their two triangles a m n and a f n equal, being on a common base.

When you have suspended the semicircle f g b at such a point that the line f g is perpendicular, then subtract from it its greater triangle f g b, and give it at the third the centre of its gravity, that is at t, and you will then know with your balance, by rule, whether t is found so far this side of n that it is a sub-double space. But to say it better, take the third of the line b f, the side of the triangle, and attach to it one of the pendants of the balance, and then go on attaching the second pendant, and you will know that the pole of the balance is the centre of gravity of that half-ball.

If the boundaries of bodies are not part of them, but beginnings of the other bodies contiguous to them, and thus reciprocally one becomes the boundary of the other without any interval; then this boundary, not being part of any thing, occupies nothing. Since no vacuum is given in nature, no body can exist without the contact of another, whence reciprocally the boundary of one body is the beginning of another, whence it is manifest that these boundaries are not part of the bodies. The boundary of one body becomes the beginning of another; beginnings and ends are of equal nature; therefore beginnings are not part of any body. The boundaries of bodies are not part of those bodies. That is nothing which partakes of no thing; therefore, the boundaries of bodies being no part of them, but reciprocally the beginning of one another, these boundaries are nothing, and by this the surface too is nothing. Air is joined with water, and the boundary of the one is common to the other, so that it may be called a continuous quantity in that they are attached together, and discontinuous in that they are of two natures. Two things that are contiguous will have a single boundary, which will not be part of the things that touch.