1. The surface is the boundary of the body.

2. The boundary of a body is not part of that body.

3. That is nothing which is not part of anything.

That is nothing which occupies nothing.

4. The boundary of one body is the beginning of another.

If a single point placed in the circle can be the beginning of infinite lines, and the ends of infinite lines separated from that point are infinite equal points, which, brought together, return into one; here it follows that the part is equal to the whole.

If the boundary of a body is not part of that body, but is immediately the beginning of another, and so conversely, the beginning of the other body will also be its boundary and not its part.

If a makes a weight of a thousand and the wheel m weighs two thousand.

Which cord sustains more, and by how much.

All the things that can be extended have thickness, which diminishes in the same proportion as it grows in its extension.

The point is the boundary of the line, and nothing else can be smaller. The line is the boundary of the surface, and no length can be thinner. The surface is the boundary of the body, and no breadth can be of less depth.

Because the boundary of one thing becomes the beginning of another.

All the boundaries of things are no part of those things, but are the beginning of another.

Therefore, since the boundaries of things are not part of those things, nor of those which they touch, these boundaries occupy nothing, and all the things that occupy nothing are equal among themselves, and all together equal to each of those, and each of those equal to all. Whence in this case it follows that the part will be equal to the whole and the whole to the part, the divisible to the indivisible, the finite to the infinite. Therefore, by what has been said, the surface, the line, the point is nothing, because it occupies nothing, and all the nothings are equal to all, and all to one, as is proved in arithmetic.

The body is clothed with several surfaces, and the surfaces are surrounded by lines, and the lines are terminated by points.

All motions are caused by abundance or scarcity, and where there is the greater excess, there the movement will be greater.

All the things that occupy nothing are equal among themselves, and all together joined will be equal to one, and each by itself equal to all. This shows that the part is equal to the whole, the whole to the part, the divisible to the indivisible, the finite to the infinite.

The point, being indivisible, occupies nothing.

All the things that occupy nothing are nothing.

The boundary of one thing is the beginning of another.

That which is not part of anything occupies nothing, and that is said to be nothing which is not part of anything.

Whatever has no boundary has no figure whatever.

The boundaries of 2 bodies joined together are reciprocally the surface of one another, like water with air.

All points are equal to all, and all to one.

If in a circle there is only one point to which infinite lines converge, and between every 2 lines an angle is included, and each separate angle terminates in a point; then many angles have many points which, returned into the circle, are equal to one sole point, the centre of that circle. Whence it is manifest that many points are equal to one and one to many, which cannot happen except in the nothing. Therefore, by what has been said, the point is nothing, and it is nothing because it occupies nothing.