4 [carried over from fol. 144 recto]

...each one so much greater than the other as they are more distant from the pole, so that for them all to be finished at one time, it would be necessary that little by little the water should be of swifter course, the more it pushes such a bridge in a part more distant from its pole. And we find that the straight courses of rivers are more sluggish toward the banks than in the middle, whence the bridge will be pushed sooner in the middle than at the end. And if it is not of strong construction, that bridge will break in the middle.

But if the rivers are twisted, here the nature of power in the motion of the waters changes.

a

If you shoot an arrow in a straight line toward the sky, you will find that the centre of natural motion and the centre of accidental motion are one and the same. And with the said centre will be found the centre of the arrow's weight in every part of its motion, both accidental and natural.

a is the middle of the descent, and therefore the arrow is equally balanced.

The more powerful the cause that drives the ponderous thing from itself, the sooner that thing, thus driven, will make its heavier part the guide of its motion. And conversely, driven by a weaker power, it will turn more slowly.

Example.

Let an arrow be shot by hand with little force, and let the feathers be sent forward. You will see that at the end of the motion the iron will not have made itself the guide of the motion, as the heavier part of the arrow, but rather will remain behind. And if you then shoot it again with great force, still feathers-first, you will see that at once it turns and puts the iron ahead in its motion.