On weights.

a b c

Every weight desires to fall to the centre by the shortest way.

Weights.

The longest line that will be found in a falling weight will be the one that aligns itself with the line of the course of that weight, when the weight is uniform in itself.

Weights.

A falling weight of unequal proportion and heaviness will direct, along the line of its fall, the centre of the heavier part beneath the centre of the lighter part.

m n, x, d a, z, b c h, r f, t, S

The water that runs through a canal of equal width and depth will strike with more powerful percussion an object opposed to it across its middle than one near its banks.

If you set a piece of wood upright at f, the water struck against that obstacle will rebound only a little above the surface of the water, as appears in experiment S. But if you set that wood at a, the water will rise high, touching with its rebound the opposed object along its whole height, as is shown at t. And the reason is this. Look at the two lines m a, n a, which strike at that point a with equal distance and force. Then consider r f and x f, how much lesser a length the two lines together make up. And if you were to say to me: 'the line x f is so much longer than the line x h that, according to what you show me in the thirteenth proposition on motion — that the more a thing moves along its natural course the faster it becomes, and the greater will be the percussion at its obstacle' — as to this the reason you allege will not be denied, but upon it it will indeed be shown that a thing which moves by nature or by violence, however long and swift its course, the more resistance is opposed to its course, the more it tires and the more it is slowed. If the line x f runs with fury as far as the middle of the canal a and there makes a great percussion, when it has reached f it will have met so many cross-currents of oncoming water, or of water rebounded from the opposite bank, that this water comes to weaken its course so much that the percussion of the line x f will be no more powerful than that of the line r f. And that this is true, make the test by opposing something to its course. You will see the water rebound along the length of the object opposed, standing upright; and if the line x f were more powerful than the line r f, the water after the percussion would rebound toward the bank of r, and since it rebounds no more this way than that, the forces of the lines and their percussions are therefore equal among themselves.

If two streams of water running through two canals of equal width and depth but of unequal length come together upon one and the same object, the rebound of that part of the water after its percussion will incline and fall upon the side of the canal of lesser length.