It is impossible that a thick body of water should push a thin water higher than itself, they being joined in one and the same pipe. It is impossible that the greater water, joined with the lesser in one and the same pipe, can raise that lesser water higher than itself. The quantity of water that is raised is thinner than that which raises it in the same proportion as it has greater motion than that which moves it. The proportion of the motions and that of their thicknesses is one and the same, but it is inverse: that is, the greater has the lesser thickness, and the lesser has the greater thickness. No weight of water that pushes another water up through a pipe will raise the water of a thinner pipe higher than itself. The descent of no quantity of water will raise water higher than itself which is joined with it in the same conduit. The water that rises has as much motion as that which pushes it, but they are contrary motions. The motion of the water that rises bears to the motion of the water that pushes it the same proportion as that of their thicknesses, but inverse. The water that descends will never raise water joined to it in the same conduit higher than itself, even though their thicknesses were of immense variety.

Definition of the balance.

Real appendices on potential arms.

The straight lines of the potential appendices are always in a right-angled junction with the real arms of the balance, and the potential arms are in a right-angled junction with the real appendices of that balance. Never naturally will the real appendices and the real arms be found in the balance at one and the same time; but if you wish to calculate the real arms together with the weights sustained by the appendices, then necessity constrains you to employ the potential appendices; and if you wish to calculate with the real appendices, then you need the potential arms. The breaking-up which the water descending through the air makes of itself arises from the inequality of the motion of its whole, whereby the natural tenacity of the water is overcome by the power of the acquired weight. The varieties which the motion of a liquid has in itself are derived from the various obliquities which the surfaces of its sides have.

The water b o n will remain, after the water f n b has been taken away, the obliquity of the water that enters the channel s n being equal to the obliquity of the water that pours out n g. And this comes about because, at equal obliquity L b, n g, they being of equal widths, of necessity equal water passes there in equal time.

When the two motions of two wheels are one against the other on their upper parts, then they will go on wearing one against the other with useful wear, because they always draw together, and the hollows of the notches wear as much as the points of the teeth; but the teeth always grow thinner and the notches grow wider. But when the teeth of the lower parts are one against the other, then the wheels will always go on drawing apart from one another with useless wear, because the teeth themselves will wear their own points.