Principles of Capacity
1. Capacity is what enables nature to receive and contain the things that can be received and
contained.
2. Space and concavity are the principles of capacity.
3. No point that has the capacity to contain an angle is without quantity.
4. The point's capacity is entirely due to the circle or the angle.
5. All right angles have capacity for containing width, and all acute angles have capacity for
containing length.
6. No line can have the capacity to contain an angle without being divided into parts.
7. No "now" has any capacity to be divided.
8. Because the circle has more concavity than the square or triangle, the circle has greater
containing capacity than the square or the triangle.
9. In the generation of things, in the fusion of metals, in the mixture of water with wine, and of
flour with water, parts have the capacity to be within one another.
10. If parts had no capacity to be within each other, there could be no true mixture or succession.
Corollaries to the Principles of Capacity
1. It was said that capacity is what enables nature to receive and contain the things that can be
received and contained. Hence, we can conclude that in nature there is space for circles and
angles.
2. It was said that space and concavity are the principles of capacity. Hence, we can conclude
that surface and capacity have the same end.
3. It was said that no point that has the capacity to contain an angle is without quantity. Hence,
we can conclude that some point has quantity.
4. It was said that the point's capacity is entirely due to the circle or the angle. Hence, we can
conclude that in some point there is concavity.
5. It was said that all right angles have capacity for containing width, and all acute angles have
capacity for containing length. Hence, we can conclude that continuation proceeds more through
width than through length.
6. It was said that no line can have the capacity to contain an angle without being divided into
parts. Hence, we can conclude that there is no line without points.
7. It was said that no "now" has any capacity to be divided. Hence, we can conclude that time is
not made of parts.
8. It was said that because the circle has more concavity than the square or the triangle, the
circle has greater containing capacity than the square or the triangle. Hence, it follows that the
circle contains more with a shorter line than do the square or the triangle.
9. It was said that in the generation of things, in the fusion of metals, in the mixture of water with
wine, and of flour with water, parts have the capacity to be within one another. Hence, we conclude
that corporeal essences have reciprocal containing capacity.
10. It was said that without the capacity of parts to be within each other, there can be no true
mixture or succession. Hence, we can conclude that one compound capacity can be made of
several simple capacities.