...[?] element ... one lighter than fire and one heavier than earth. Now let us place the quintessence, lighter than fire, above the fire itself, and in it we shall assign, after our own manner, weights to the four elements. And likewise, below our degrees of earth, we shall place a liquid heavier than earth, such as molten gold; and within this we shall assign the various degrees of lightness of the four elements. And so, beginning above with the heavy elements, we shall reckon gravity successively with respect to the first and lightest; and beginning below with the heaviest, we shall reckon the lightness of the elements with respect to the heaviest, and so on. We shall say that in the quintessence, which is one degree of lightness, giving one degree in equal measure to each element weighed within it, one measure of fire weighs 2, one of air 4, one of water 8, one of earth 16, and one of gold 32. Now I draw one degree of quintessence, which is one degree of lightness, into the fire, which by its lightness cannot rest there except by forced stability; therefore I lend it 3 degrees of air, of which two stand equal to the two degrees of the fire's weight, and one of gravity destroys the one of lightness of that quintessence. Then I draw the measure of fire, which has two of lightness, that is half again lighter than air; and this two, drawn into the air, which is 4, needs 6 of water lent to it, of which 4 are made equal to the 4 of the air, and 2 of heaviness that remain destroy the lightness of the fire. There follows the air, which is 4, drawn into the water, which is 8, and here 12 of earth are needed, with which 8 remain equal to the 8 of the water, and 4 of heaviness destroy 4 of the air's lightness. There follows the water, which is 8, placed into the earth, which is 16: 24 of gold are needed, of which 16 are made equal to the weight of the water, and 8 of the earth's gravity destroy 8 of the water's gravity. Now the reverse. I wish to raise the gold, which is 32, into the earth, which is 16: I shall lend it 32 of water enclosed in its vessel, and thus I shall have consumed its heaviness, and the weight of the gold is destroyed within the earth liquefied like quicksilver. Then the earth, which is 16, within the 8 of water: 16 of air must be lent to it, and the lightness of the air has destroyed the heaviness of the earth. Experiment. Take 3 liquids that can be weighed in air, that is distilled oil of turpentine, water, and quicksilver, which cannot be mixed together, and weigh an equal quantity of each in air, each in a like vessel filled with it, and you will find that in equal quantities there are different weights. Then, placed in the parallel-sided vessel drawn here in the margin, you will see that, one being above the other, their thicknesses stand in the same proportion as their weights, but inversely: that is, the quicksilver will be of as much less thickness than the water as it is heavier. Then, wishing the quicksilver to remain within the water, add enough oil that it stays afloat. And in this way you will weigh the air, which, put in place of the oil, will be so much greater ...

Fire. The light element mixed with a heavy liquid will not submerge within that same heavy thing. Quicksilver. The light element diminishes the weight of the heavier by as much as its own weight. Add light to light, it makes lighter. Add heavy to heavy, it makes heavier. No heavy element, mixed with the light, will keep the whole of that light thing submerged by itself, except with the aid of something heavier than the submerger. With a weight equal to water you will never submerge enclosed air, except with the aid of a body heavier than water. And no body lighter than air will descend to earth, except with the aid of a body heavier than air. No liquid heavier or lighter than another comes to rest within those heavier or lighter than it; no liquid comes to rest in a liquid heavier or lighter than itself.

P. p: a pig's bladder, wetted and stretched over the end of a rod one inch thick and left to dry; then strip the stick out of it and cut it in the manner of drinking-glasses, and then varnish it with amber varnish within and without ... times, thinly.

Book of the percussions of waters against various objects.

Book. Encounters of waters with standing objects of various shapes that rise above the water. Encounters of waters with immobile objects covered by the waters. Encounters of waters with movable objects covered by the waters. Encounters of waters with standing objects that rise above the waters. Encounters of waters with bendable objects overtopped by the waters. Encounters of waters with bendable objects that rise above the waters. Encounters of waters with objects that yield with a circular motion, such as the wheels of water-driven machines.

Book. Encounters of waters with various shapes of objects, resisting and overtopped by the waters.

Book. Encounters of waters upon beds of various loose materials, such as sand, gravel, mud and earth and the like. Encounters of waters against the banks of rivers. Encounters of the sides of rivers with the slope of their shores. Encounters of waters against banks undermined below, which cause them to collapse.

30 in the rivers. Encounters of waters in the collapses of their earthen banks.

Of royal rivers and common rivers and torrents. Of making the river hollow out its middle in width throughout. Of the collapses of the banks of rivers. Collapses of the weirs and transverse dikes of rivers. Where the great depths of rivers are generated. Of the currents that consume and hollow out the foundations of the bank. Of the various currents that make different hollows in the beds of rivers. Of the different depths made by one and the same current. Of the things uncovered by the currents of the waters. Of great stones moved by small torrents. Of calculating the impact of different but equal waters meeting into one by equal obliquity. Of the impact of water divided into parts of different powers meeting at one site by equal obliquity. How united water is more powerful in impact than divided water, being of equal obliquity. Of the impact of equal waters and equal obliquity through various lengths of course. Of the impact of equal courses and equal waters meeting at one same end with various obliquities. Of the impact of various thicknesses of water at equal obliquity upon one same object. Of the meeting of waters various in thickness and in obliquity. Of the impact of scattered waters. Impact of the straight motion of water. Impact of curved motion. Of the impact of broad and shallow waters. Of the impact of narrow and thick waters. Of impacts against dense objects.

Of the impact against porous objects. Of the impact against perforated objects. Of the perpendicular fall of water. Of the fall of water sustained through various obliquities. Of the fall from various heights. Of the fall upon an object set at various obliquities. Of the fall upon different objects. Of the fall that makes no rebounding motion.

Weir of Ognissanti. Of the fall that does no harm to the object. Of the blow of the sea that should scour the harbours. Of the fall of the droplet through the air. Of the fall of water through the air. Of the fall of water that touches the channel. Waters striking objects of double obliquity. Difference between rivers that run broad and those that run narrow in their impacts. Difference of the falls of rivers that run full and those that run thin. Difference of the beds of rivers of great slope and those of slow motion. Difference of beds in rivers that run narrow between the solid rocks of the mountains. What difference there is between the bed of the wave that comes and goes, like that of the sea shores, and that which goes only one way. Of the collapses of mountains struck and undermined by the courses of waters. Various beds generated by different currents. Where the fall consumes the foundation of the place whence it falls. Of the falls that pile up the place from which they descend. Water does not follow its course after the falls in the same straightness of its descent; rather it makes there a bank of the material dug out of the place where it struck, and the more so the more directly it falls.