Water. How rivers widen the valleys and consume the roots of the lateral mountains.

The sinuous motion of rivers through their valleys strikes and consumes the roots of the lateral mountains.

The meanders that rivers make through their valleys, rebounding from one mountain to the other, make the bank sinuous; and this sinuosity moves together with the course of the water and, over a length of time, works its way through the whole valley if it is not impeded, increasing it in length and depth while diminishing it in width.

Let the valley be a c k h, in which the meandering river a c e g k flows. I say that the banks have the same sinuosity as the river and move together with the course of the water: that is, its part a c will consume the bank below as far as b d, and likewise the bank c e as far as d f, and e g as far as f h; and by this rule such meandering will have worked through the whole valley and will increase it in length and depth, because the river continually consumes the root of the mountain where it enters the valley, and deepens it, because it carries with it the earth that clouds it; and it narrows the floor of the valley, because, in deepening, the lateral material of the mountains falls back to the foot of the undercut hills, and the lighter parts flee away together with the water while the heavier ones settle at the sides of that valley.

On the motion of the waves of the bank following the course of the river.

When the first wave of the bank departs toward the beginning of the river, immediately the second wave is generated, following the first, and so does the third and the fourth successively; as if to say, when the wave of the shore c e has descended to d f, immediately the wave a c has descended to b d, and so they do in succession.

How the cutting of Abila and Calpe in the Strait of Gades.

The cutting of Abila and Calpe in the Strait of Gades greatly diminished the rivers that descend from the Alps and run to the north. And this is proved, because before that cutting of the Gaditan mountains was made, the Mediterranean Sea was of a very high surface, which surpassed three quarters of the height of those Alps, and the penetration that this sea made through the channels and veins of the earth was very high and abundant; whereas after that Gaditan cutting the Mediterranean Sea lowered its surface, and the aforesaid high channels remained empty of their waters, and the rivers lost the abundance of their courses.

Water. How rivers widen their valleys and consume the roots of their lateral mountains.

The bases of the hills, as their valleys deepen, bend back following the flight of the river, as though they wished to ask back from the swift river the earth that it takes from them.

This arises from the 19th proposition of this book, which says: the course of the river consumes on one side of the base of the mountain, where it strikes, and gives back on the opposite side where it rebounds.

The river of great valleys changes its bed.

The rivers of great valleys make the greater changes of their beds the more remote they are from the roots of the mountains. It is proved by the 9th proposition of this book, which says: the greatest rivers run through the greatest valleys created by them, and by their magnitude they continually consume the waves of their banks, always carrying them back following the course of the river. The rest will be told in its place, etc.

On the changes of the mouths of rivers.

The mouths of rivers continually bend and descend following the course of their greatest river, and this arises from the above proposition, which says: the water takes from the wave of the bank where it strikes, and gives back on the opposite side where it rebounds.

The valleys continually deepen.

The valleys continually widen and deepen, and the rivers continually change their location.