If two balls strike each other at a right angle, the one will depart from its begun course by so much more than the other as it is smaller than the other.

That rod or cord which is shaken with speed will appear to be doubled.

Motion of a knife fixed upon a table, which will appear as two.

This happens when a knife is fixed and, being forced, is pulled by its head to one of the sides and let go, so that it shakes many times. The same happens in the string of a lute when one tests whether it is good; and the doubling happens because the motion made up to the extreme of the course of the moving thing is much faster than at the extreme, for that extreme, when it has gone as far as it wants, stops and turns back, and stopping at one and the other extreme of the motion it is necessary that the eye imprint two likenesses of one and the same moving thing. But tell me: why does a false lute-string, in shaking, make two and three likenesses, and sometimes four?

Of water.

No part of the aquatic element will raise itself or make itself more distant from the common center except by violence.

No violence is durable.

a b c d

a: it is a straight canal of water of equal width, depth and slope, which moves one mile per hour.

b: let the bank of this canal be widened to double width, with the bottom of equal slope to the first. It is asked what motion the water will make which ordinarily and continuously passes through this canal.

Let the bank of this canal be narrowed in subdouble proportion, and say what motion its water will make per hour.

Let this canal be deepened to double, for the two middle of the four parts of its length, and say the motion of the water.

Let this canal be made of a serpentine and winding course, and it is asked what it runs per hour.

Let the bottom of the first canal be raised for three of the four parts of its length.

Of the rebound of water falling upon a whirlpool.

Of weighing water to work mills.

Of raising water by means of its fall.

Of the siphon.

4 2 — And let the weights be lead.

On the proof of how much more the water resists than the air.

Let there be two canals of equal width, current and depth, that intersect at right angles. Let these rivers be intersected at various acute or obtuse angles. Let one be double as wide as the other. Let the narrow one be double as swift as the wide one. Let one river receive another with every variety of angle, current, width and depth. Let one river have silt, mud, floated wood, gravel, sand, turbid matter, timber and branches mixed with its course. Let there be a river with cavernous and blunted banks, and stones, plants, grasses and rushes. Let this river have great stones. Let there be wind against it, as much as the river itself, in all degrees of more and less. Let there be in the river various motions and lineaments of water. It is asked, from the surface, the knowledge of the bottom. Let defenses be made against the ruin of the bank. Let the banks be made to collapse. Let mud, sand, wood or stones be placed on this bank. Let the river be made to cut a ditch. Let it be made to twist of itself. Let the twisted be made straight.

Let the water enter this canal with percussion. Let it enter crosswise. Let it enter by two canals and be made into one. Let the canal divide in the middle into two and then rejoin. Let there be made in this canal humps in the bottom, and pits and rounded elbows in the bank, and elbows of various angles, and bottoms with shoals, the bottom varied now here and now there from the bank. Let pits be made facing each other between one bank and the other, with the bottom high in the middle. Let the contrary be made. Let stones be placed near the surface. Let stones be placed that rise above the water. Let ramparts with sluices be placed.

Let two waters joined at a floodgate strike together and fall down below, intersected together. From the bottom of a canal let water be drawn: I ask what it does at the surface and what at the bottom, and from what place this water comes. Of a water that runs and has a hole beneath it. Water that runs below and not above. Water that runs above and not below.

Water that runs in the middle and not below or above. Water of equal course. Water that makes eddies above and not below. Water that makes eddies below and not above. Water that runs in the middle of rivers and not at the side, and that runs at the side and not in the middle.

If one water, intersecting another, mixes with it, being of equal course and power.