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, nor depth.

The line has only length, 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 bounds 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 it is born and dies between 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, and its bounds are lines, than which 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 bounds 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 weighted body.

Of the things that support themselves within water without motion, no part of them that rises above the water has weight in itself. It is proved. If motionless water has no weight in itself, and neither do the things it sustains, it is proved by the foregoing that its weight failed together with the weight of the water; how then would we have motionless water, without weight, sustain weight? And if it sustains bodies, it does not sustain their consumed weight, because such weight ends together with the motion of the penetration it made in 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 there be placed a thing that is a cord ..... the point on the surface of a body suspended in the middle ..... every body has quantity, but does not always have weight.

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First Book of 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 is called a point by the mathematicians.

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 thrust into another.

4th. Levity. Levity is said of that which is less heavy, for 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 within the same element.

6th. Water does not acquire gravity unless it joins with an element or another liquid lighter and lower than itself.

Water by 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 reflected 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 not part of the water nor has any likeness to it, nor does it remain with it, because it is short-lived.

Water by itself does not stop unless it is contained, or is held at equal height.

The centre is that which is equally remote from the opposite extremes of anything. The centre is not a part. The 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 are nothing, and nothing are its bounds.

That which is made by the motion of the surface toward the part that is seen: its space and its bounds 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 bounds 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 bounds 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.