NOW THE PROPOSITIONS.

I. DEMONSTRATION.     I. PROPOSITION.

THE placed water holds every place that one gives it within water.

GIVEN. Let the water in the surface vessel A be the placed water in the water B C. REQUIRED. We must prove that water A will remain in that place. PROOF. And let water A (if it were possible) not hold its place, but let it have descended to where D is; This being allowed, the water that has then come into the place of A will, for the same reason, also descend to the place of D, which will then also be done by another similar one, in such a way that this water (because the reason is always the same) will make an eternal movement, which is impossible. Likewise it will also be shown that A cannot rise, or betake itself to any other side. It appears also that if one placed A within the water at the place of D, E, F, or G, that for the aforementioned reasons, it would remain at each of those places, and everywhere one sets it in B C.

A hydrostatic diagram shows a container of water labeled B C. Within it are smaller square segments labeled G, E, A, D, and F, illustrating the equilibrium of water parcels within a body of water.

CONCLUSION. The placed water, then, holds every place one gives it within water, which we had to prove.

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II. DEMONSTRATION.     II. PROPOSITION.

A solid body lighter than water does not sink entirely underneath, but a part remains sticking out.

GIVEN. Let the solid body A be lighter than the water B C, whose surface is B D. REQUIRED. We must prove that A, placed in the water B C, will not sink entirely underneath, but that a part will remain sticking out above the water. PREPARATION. Let E F be a surface vessel, whose part that is within the water and filled with water is G F, equal in size and identical to A, and its surface G H will be in the surface B D, since the surface vessel E F is neither light nor heavy.

A hydrostatic diagram shows a body of water B C with surface B D. On the right is a solid body A. In the center is a theoretical vessel E F partially submerged, containing a volume of water G F with its surface G H at the same level as the surrounding water surface B D.

PROOF. Since A is lighter by the given than the water...