The Elements of Hydrostatics

18

REQUIRED. We must prove that A placed in the water B C, will there be so much lighter than in the air, as the weight of the water equal in size to it. PREPARATION. Let D be a surface vessel full of water, even and equal to A. PROOF. The surface vessel D full of water, is in the water B C neither light nor heavy, for it holds there every shape that one gives it, by the 1st proposition, therefore the water D poured out, the surface vessel will be lighter in weight of the water than it was in its first state, that is, of so much perfectly light: Let us now lay in it the body A, the same will fit therein exactly, because they are even and equal by the stated. And the surface vessel with the body A so therein, will weigh the weight of A with its aforesaid lightness, that is the weight of A minus the weight of the water that was first poured out, but that water is equal in size to A, Therefore A placed in the water B C, is therein so much lighter than in the air, as the weight of the water equal in size to it.

A geometric diagram representing a displacement experiment. A large rectangle represents a vessel of water labeled 'B' and 'C' at the corners. Inside is a square labeled 'D'. To the right of the vessel is a square labeled 'A', identical in size to 'D'.

CONCLUSION. Every solid body's weight then, is so much lighter in the water than in the air, as the weight of the water equal in size to it, which we had to prove.

II DEMAND. IX PROPOSITION.

BEING GIVEN THE RATIO OF THE WEIGHT OF THE WATER, AND A SOLID BODY, AND THE SOLID BODY'S WEIGHT: TO FIND ITS APPARENT WEIGHT IN THE WATER.

1st EXAMPLE where the solid body is lighter than water.

GIVEN. Let A B be a water, and C a solid body weighing 2 lb, and the weight of the water, to the weight of the solid body be as from 5 to 1. REQUIRED. We must find the solid body C's apparent weight in the water A B. WORK. One shall see how much a body of water equal in size to C, would weigh, is found 5 times 2 lb, that is 10 lb, the same subtracted from 2 lb of the solid body C, remains minus 8 lb, that is light or lifting-weight 8 lb for C in the water A B.

A geometric diagram showing a vessel labeled 'A' and 'B' at the corners. A square labeled 'C' is placed inside the vessel, representing a solid body submerged in water.