Here the wheel of 8 spokes.

e d c b a — a b c d e are vessels.

Little tongue [tongue-valve].

Floats [bladders].

Adversary [objection]. Only the water that is poured out acquires power, like an equal amount of water of similar height and thickness, and all the rest of the water of the vessel continuous with it feels no change of that weight.

a d – b e – c – f – g. Until the water has filled a b, the water e g must weigh more than all the water that a b can hold, otherwise it could not draw out all the air that remains in that a b; and when such a pipe fills above at d, and with a greater length of water than the space a b, then the water f g is no longer worth [enough]. Therefore it is concluded that the pipe d g must be capable of as much water as fits in a b, and then of as much air, and as much more as fills a part of the pipe equal to the space a b; if not, it does not work.

a – air – p n – m – b. Whether the water a b will pour from the pipe open below at b. — It will not pour unless it first draws with it all the air that borders on it; and that air will not depart unless the water n rises to restore the vacuum from which that air departs; and that water will not rise to such a height unless the water outside a b weighs more than that which must be raised inside. Therefore the pipe a b must be of such a length that it can hold 3 times more water than the water the vacuum of the air can hold, because, once all the air in the basin has come into the outer pipe, there must be beneath that air enough water to act like an equal amount of water.

air – m n; sand – vat – n (m) – p m; sand – m m a – f p n. When the ... [falls] as ..., the weight must be heavy and thin, because the vat, having to stand above the weight of the millstone, and the height of the water having to occupy the height of the millstone and of the vat, it would be necessary that the millstone and vat be half a braccio, which would achieve nothing. Therefore set the root lower than the bottom of the pump, and (small figure) make an iron, as you see marked, on which at p is the bottom of the vat, and on which stands firm the piston [scanduppo] that drives the water of the pump. Inequality is the cause of all local motions. No rest is without equality. The air always rests between equal powers of that water which is enclosed with it.

d – a – f c a – b. If the water a b does not pour, its mouth being open below at b, what sustains it? It is the air a d c; and this air, being at the confine with the level of the water of the basin a c f, comes to give no weight to the opposite part of the air at c. And this is impossible by the fifth [proposition] of the ninth [book], which says: 'no rest is without equality', because such air sustains at a all the water a b, and at c sustains nothing. Therefore, this not being able to be, it is necessary that as much water be raised above c as is the weight of the water a b, and then that rest of the parts is caused.