Double pump.

The hub n has a double set of teeth which, taken together, form a toothed rim occupying the whole circle at the face of that hub. And when one semicircle has raised its hammer m, the other toothed semicircle releases its own hammer, and by this the beam is always loaded with one and the same weight.

The hub m is fixed between the shaft of the pump and the little ladder below, and everything is joined together; and their motion is made at the same time in one and the same direction, that is, in descending it presses the water and in rising it takes up as much again.

The water that pours out of the pump weighs less than the water lying in the sheath of the hub, because in the hub's descent it pours out the water found in the space between the sheath and the hub through which it descends, which is made as narrow as possible.

9th: the proportion that the thickness of the water pressed downward bears to the thickness of the water rising upward is the same that the weight of the rising water bears to the power that makes it rise.

A thing placed in water is lighter than in air by as much as air is lighter than water. The friction of a weight resists the motion of the thing rubbed.

Whether it is better for the water to go up all at once or in two [stages]. I answer that at one time the wheel could not sustain all the water it raises in two, because in a half turn of the wheel it would raise 100 pounds and no more, and if it had to raise 200 pounds in a whole turn it could not, unless the wheel doubled its diameter; and by doubling the diameter it would double the time. Therefore it is better and more economical to make such a wheel sub-double rather than double, etc.

The descent of the hub does not sink as far as the surface of the water, because on touching the water it would lessen its weight.

The hub must weigh somewhat more than the water remaining in the pump together with the water standing in its sheath, for if the water weighed as much as the hub, the hub would not raise it.

And if, on the contrary, the water-driver were made ten times thicker than the pipe of the escaping water, and given ten times less motion than this, what would its office be? I answer, by the 9th of this, that the water would rise a tenth part of what it rose before in the height of that pipe from which it first rose.

On the nature of gravity.

Gravity is an accident conjoined to bodies removed from their natural place.

On the nature of levity.

Levity conjoined with gravity, as are unequal weights joined in a balance, or light liquids placed beneath [heavier] liquids, or other dense [bodies] heavier than it that...

Of the water that descends through a reversed siphon composed of tubes of various widths: if the water of the larger tube has a higher surface than the water of the smaller tube, only that water of the larger tube will have gravity in itself, namely the part that in its lower reach is joined with the water of the smaller tube.

1st. Waters joined together do not come to rest unless their surface is, in every part, equally distant from the centre of the world.

Therefore, in the reversed siphon a c p d t, being full of water in a c and full of air in t d, if the tubes are in triple proportion of capacity one to another, the water that rises through the tube d t will have triple the motion of the water that descends through the tube a b; and by the first [proposition] of this, the two surfaces of the waters will remain at equal heights.

The concavities a b receive within them the fingers of the hand in descending the spiral staircase: that is, the channel a receives the four smaller fingers, and b receives the thumb; and the channels c d do the same in going up, holding the four smaller fingers in channel c and the thumb in d. The rib n m receives within it the axis f o, which is the front edge of the step.

The wall of this spiral staircase is square, being made in a corner of the house.