If water issues from a full pipe and pours out, it will fall equal in thickness and without any intersection, and will be swift in its motion.

A vessel from whose bottom a vein of water issues. In...

Pyramided water: whoever believes so makes two errors. First, that the pyramid comes to nothing; besides this, that it would become so light that it would have no motion.

Water of continuous thickness and increasing motion. In this it happens that at the foot it would be of such velocity that 100 vessels would be filled in the time in which one is poured out above. And this is impossible.

Water of continuous thickness and equal motion. This would give the same percussion at the beginning as at the end, and would be against the maxim that a weight which descends more becomes heavier and swifter.

Here the weight makes it return to its perpendicular. The more even in bore the pipe or channel that pours is, the longer the pyramid made by the pouring water will be before it reaches the intersection; and conversely it will be shorter the more tapered the pipe or channel is. 125 / 250 thousand / 500 thousand / a million / 1 2 4 8 16 3. Here a doubt arises in the descent of discrete quantity, that is of the balls let fall at equal degrees of time. This is: if you want the increments to be of continuous arithmetic proportion, the second ball will exceed the first by double the space made by the motion, and the hundredth will exceed only by a hundredth of an interval. And if you want those increments to be of continuous geometric proportion and you made a descent of a million miles, you would see the time of the last not answer the time of the first with equal intervals.

The pipes that pour water are of 3 kinds: that is, wide at top and not at bottom, wide at bottom and not at top, and even; and there are 2 mixed kinds, that is one thick in the middle and thin at the ends, and one wide at the ends and thin in the middle.

1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536. A million braccia is 333 miglia (miles).

a1-b1-c2-d3-4-e4-f 5 8-g 6-h 7-16-i 8. Experiment. Drive 25 blowpipe balls of equal weight into a barrel so they stand one above the other perpendicularly, and set them in a high place, and release with a string, and stand below. But the motion will not let you discern the equal spaces. Test. Definition. If a b has made one degree of descent in one degree of time, b c, being swifter by the fifth [proposition], will have made one degree of motion and something more. And so d, being swifter than c; and so it continues. But know finally that if in every degree of time you give motion to one of these balls, likewise in every degree of time the motion of the last other one ends.

A group of lines of dense writing. If you pour a jug of water thinly, at every point of the water's descent a jug like the one poured will be filled, in the same time in which the first jug emptied. Therefore the water everywhere will be of equal velocity.

In equal time, an equal quantity of water passes at every part of the descent. Seventh: that water will be of swifter descent which is poured from a more even and long pipe or channel. Eighth: and conversely it will be slower which is poured from a more uneven and short channel. You who make mills, before the water descends, make it pass through a long and even channel. And let the water that strikes the wheels have a square shape, that is, as high as it is wide. And although the upper part approaches the center of the wheel, still it is better than if it spread out in great width and struck the wheels far from their center, because it would weigh little and strike little; and likewise, it is true, make it very wide, it will move little, because it will be very thin; and make it very high and narrow, it will be of little effect, because it would strike the wheel toward the center.

a-b 1-c 2-d 4-e 8. If the 10 balls that are let fall in 10 degrees of time are at the foot of double velocity, it will happen that the balls let fall from above in the said 10 degrees of time would be gathered in 5 degrees. And this is impossible, because 10 balls would be gathered before 5 had been let fall.