The point is that which occupies no place, and nothing can be smaller.

The point is that of which nothing can be said to be smaller; therefore it has no length, breadth, or depth.

The line has only length, and a length made by the motion of the point; it follows that it has neither breadth nor depth, and its ends are points.

The surface is a space occupied by the transverse motion of the line; it follows that it has no depth, and its ends are lines.

The body is a space penetrated by the motion of the surface; it follows that it has breadth, length, and depth.

The line has only length without breadth or depth, and its ends are points.

The line is an extension made by the motion of the point, and is born and dies between the points.

The line is a length born from the motion of the point, and its ends are two points.

The line is a length born from the motion of the point, and its ends are points, than which nothing can be said to be narrower.

The surface is a length that has breadth and is born from the transverse motion of the line; its ends are lines, and nothing can be said to be thinner.

The body is a length that has breadth with depth, born from the declining motion of the surface, and its ends are surfaces.

The centre is a point which is equally distant from the opposite extremes, and from the opposite natural and accidental weights of any ponderable body.

Of things that sustain themselves within the water without motion, no part of them that rises above the water has weight in itself. It is proved: if immobile water has no weight in itself, and the things sustained by it lose their weight together with the weight of the water (as shown before), how do we wish that immobile water without weight should sustain the weight? And if it sustains the bodies, it does not sustain their consumed weight, because such weight ends together with the motion of the penetration that it made into that water.

The point situated in the middle, at equal distance from the opposite extremes and weights of anything that has weight or body, without weight or levity, changes its name and is called the centre.

If a thing that is a cord will be set ..... the point on the surface of a body suspended in the middle ..... every body has quantity, but does not always have weight.

First book of the waters.

1st. The lowest depth of the elements is their centre. The common centre is that which is equally remote from the extremes or from the opposite weights of the elements, and nothing can be imagined smaller than the centre; and this is what by the mathematicians is called the point.

2nd. Lowness and height.

That thing is said to be lower which is nearer to the centre of the elements; it follows that higher is that which is more remote from that centre.

3rd. Gravity.

Gravity is an accident generated by the violence of one element drawn or pushed into another.

4th. Levity.

Levity is said to be that thing which is less heavy, because in the elements all is heaviness, but one is more or less heavy than another.

5th. Elements.

No part of an element has gravity or levity in the same element.

6th. Water acquires no gravity unless it joins with an element or another liquid lighter and lower than itself.

Water of itself does not move unless it descends; it follows that, if it moves, it descends, and this happens by the 6th. And if you should say that in the reflex motion it makes after its descent it rises upward by cause of itself, this is not true, for it is by cause of the weight it acquires, which is an accident, as is proved in the 3rd of this - which accident is no part of the water, nor has any likeness with it, nor remains with it, because it is of short life.

Water of itself does not stop unless it is contained or held with equal height.

Centre is that which is equally remote from the opposite extremes of anything. The centre is not a part. Centre is that which occupies no place nor is part of any. The centre is that which is equally remote from the opposite extremes and opposite weights of anything, and nothing can be smaller.

The point is that of which nothing can be smaller. And its breadth, length, and depth is nothing, and nothing are its ends.

The solid is made by the motion of the surface toward that part which is seen. Its space and its ends are surfaces, than which nothing can be thinner.

The body is made by the motion that the space of the surface has, and this has breadth, length, and depth, and its ends are surfaces.

The line is made by the motion of the point, and this has length without breadth and depth, and its ends are two points.

The point has no middle, and its ends are nothing.

The line is made by the motion of the point.

The line is a length made by the motion of the point, and its ends .....

The line is a length.