Fire.

Of the boilings of water.

The water that is in contact with the bottom of the fired (heated) vessel immediately converts into air mixed with fire. It is proved by the preceding proposition which said: that part of the air rises most which partakes most of heat. Therefore the exhalation of the water penetrates above the low region of the air that is in contact with it, being mixed with the element of fire, which carries it with itself in returning to its sphere.

Rings for the arms of such a mixture, and the gold clasp with jewels.

Why the bubbles leap out of the vessel where the water boils.

The bubbles of water are driven with impetus from their vessel by the weight of the water that rests upon them. Which impetus is so much swifter than the simple air that rises from the bottom of the marshes, as it is in greater quantity and of greater heat.

Which resists more under one same depth of water, the little air or the much?

Water rises from the bottom of the river in three ways, that is: either it rises with slow birth, or it is thrust up by a bellows, or it is thrust up by the fire that heats it from below and makes it vaporize with continual birth.

When c is at a, a is at c, and thus the wheel and the moving body have made half a turn.

The levelness of the surface of a motionless liquid will not differ from the levelness of the surface of the liquid heavier than it, which surrounds it with its contact.

Of the smoke of the extinguished candle.

The smoke of the extinguished candle has its edges denser than the middle, because it refracts toward the middle, fleeing from the impediment of the cold air, where it strikes in its dilation; and because it can rarefy and condense, it becomes dense at its ends; and in this case it does not do as water, which, being unable of itself to rarefy or condense, is compelled so that its part reflected from the site of the percussion makes a wave that moves upon the coming of the water in a contrary motion.

The point is said to have no part, and from this it follows that it is indivisible; and indivisible things have no middle, and what has no middle is bounded by nothing. Therefore the point is nothing, and upon nothing no science can be begun. And to flee such a principle we will say: the point is that than which nothing can be smaller, and the line is created by the motion of the point, than which nothing can be narrower or thinner, and its ends are two points; and the surface is generated by the transverse motion of the line, and nothing can be thinner, and its ends are the lines; and the body is made by motion.

Another way.

The point has no middle, and its ends are nothing.

The line is a length made by the motion of the point, and its ends are two points, and the ends of its width and depth are nothing.

The surface is created by the transverse motion of the line, and its ends are the lines, and the depth is nothing.

The body is generated by motion.

The converse: the point is generated where the length of the line ends; the line arises where the width or length of the surface ends; and the surface is created at the boundary of the width, length and depth of the body.

The point is the common boundary between nothing and the front of the line, nor is it part of the line, nor part of nothing, nor does it occupy place between nothing and the line. Therefore the end of nothing and the beginning of the line are in contact with each other without any other interval following.

If the surface is not part of a body nor part of the air with which it terminates, nor part of the body which it surrounds, and no other thing interposes between the air and the body, what can we say such a surface to be other than nothing? If the surface is not part of the body it clothes nor part of the air by which it is surrounded?

Nothing is born at the boundary of the thing.

Where nothing ends, the thing is born, and where the thing fails, nothing is born.