Pneumatithmie

Pneumatithmie demonstrates, by closed hollow geometric figures (regular and irregular), the strange properties (in motion or rest) of water, air, smoke, and fire in their continuity, and as they are joined to the elements next them. This art is very profitable to the natural philosopher, to prove that a vacuum, or emptiness, is not in the world; and that all nature abhors it so much that, contrary to ordinary law, the elements will move or stand. Thus water will ascend, rather than leave between it and the air a space or place more than that quantity of air naturally requires or can fill. Again, water will hang and not descend, rather than leave emptiness behind it by descending. The same is true of fire and air: they will descend rather than have their continuity dissolved, or their next element forced away from them. And as they will not be extended to discontinuity, so they will not, nor can they by any human force, be pressed or pent into a space not sufficient and answerable to their bodily substance. Great force and violence will they use to enjoy their natural right and liberty.

To go to the bottom of the sea without danger.

Hereupon, two or three men together, by keeping air under a great cauldron and forcing it down in order, may descend without harm to the bottom of the sea, and stay there for a time, etc. Where note how the thicker element, as water, gives place to the thinner, as is the air, and receives violence from the thinner in like manner, etc. Pumps and all manner of bellows have their ground in this art, and many other strange devices; as hydraulica, organs worked by water, etc. Of this feat, commonly called Pneumatica, goodly works are extant, both in Greek and Latin. With old and learned schoolmen it is called the Science of the Full and the Empty.

Pneumatithmie shows, by closed hollow geometric figures, regular and irregular, the strange properties of water, air, smoke, and fire, in motion or at rest, within their own continuity and as they are joined to the elements next to them. This art is very useful to the natural philosopher, because it proves that a vacuum, or empty space, does not exist in the world. It also shows that all nature dislikes it so much that, contrary to ordinary law, the elements will move or stand still. Water rises rather than leave a space between itself and the air, more than that quantity of air naturally requires or can fill. Again, water hangs and does not fall rather than fall and leave emptiness behind it. Fire and air act the same way: they will descend rather than let their continuity be broken or the element next to them be forced away. And just as they will not stretch into discontinuity, so they will not, and no human force can, be pressed or cramped into a space too small and unfit for their bodily substance. They will use great force and violence to keep their natural right and freedom.

(Going to the bottom of the sea without danger.)

On this basis, two or three men together can keep air under a great cauldron, press it down in order, and descend to the bottom of the sea without harm, staying there for a time, and so on. Note how the thicker element, water, gives way to the thinner, the air, and in turn takes force from the thinner, and so on. Pumps and all kinds of bellows are founded on this art, along with many other strange devices, such as hydraulica, organs driven by water, and so on. Fine works on this subject, commonly called pneumatics, exist in both Greek and Latin. Old and learned scholars call it the Science of the Full and the Empty.