Aristotle · a new plain-English translation from the original language
1| BOOK 16. PROBLEMS CONCERNING LIFELESS THINGS. Why are the bases of bubbles white in water? And if they are set in the sun, they cast no shadow, but while the rest of the bubble casts a shadow, the base does not, but is lit all around by the sun. What is still more remarkable is that not even if a piece of wood is put into the water in the sun is it cut off by the water in this way. Is it that no shadow is formed there, but the shadow has been divided by the sun? If, then, a shadow is that which is not seen, then the bulk of it would be seen all around by the sun. But that this is impossible is shown in the works on optics; for it is not possible for even the smallest thing to be wholly seen round by the largest.
2| Why are bubbles hemispheres? Is it because they are carried upward toward the air alike in every direction, as if from a center? And this must be a hemisphere. The lower hemisphere is cut off by the plane surface of the water, in which the center lies. Why is it that with bodies of unequal depth, if one moves the lighter one, the thing thrown travels round in a circle — as happens with knucklebones weighted with lead, if one throws the lighter part turned toward oneself? Is it because the heavier part cannot travel at an equal speed with the lighter part, when thrown by the same force? Since it is necessary that it move altogether, but impossible that it move from an equal starting condition, then if the two parts moved at the same speed they would travel the same line, but since one part necessarily moves faster than the other, it must travel in a circle, since it is only in this figure that points which correspond to each other in this way traverse unequal lines in the same time.
3| Why do things falling to the ground and bouncing off make equal angles with the plane on either side of the point at which they struck the plane? Is it because everything by nature travels toward a right angle? Now things that fall onto a level surface, striking the plane along the perpendicular and the diameter, make, in bouncing off, angles of that same size, because the diameter divides equal parts; but things that fall obliquely, striking the surface not at the perpendicular but at a point above the perpendicular, are in turn driven off, thrust by the place struck, to travel in the opposite direction — round objects, since as they travel they unroll in the direction opposite to the thrust, whether their center remains still or also changes place; straight-edged objects, because the perpendicular itself, having been carried forward, is knocked out, just as happens to men whose legs are shaved from under them, and to those whose supports are snatched away. For all these fall in the opposite direction and backward. This is because the perpendicular is made equal to them, and they become airborne and are knocked forward; for it is clear that the opposite effects will occur behind it and below it, and things traveling downward would be heavier. So what is a fall for these is, for the bouncing bodies, a case of travel occurring. Neither of them, then, bounces off at a right angle, because the perpendicular divides the moving bodies' weight in half, and there cannot be several perpendiculars to the same plane cutting across each other; but this is what would happen to these bodies if, a perpendicular being formed at the point of rebound where the moving body struck the plane, that body were in turn bisected by it — so that the original perpendicular by which it was carried would necessarily be cut by it. Since, then, it will travel in the opposite direction, but will not travel at a right angle, it remains that the angle at the other side of the point where it struck the plane is acute; for the right angle is the boundary of the contrary angles.
4| Why does a cylinder, when pushed, travel in a straight line and trace straight lines with the circles that bound it, while a cone travels round in a circle, its apex remaining fixed, and traces a circle with the circle that bounds it? Both travel in a circle, but on the plane the cylinder traces straight lines while the cone traces circles, because the circles in the cone are unequal, and the larger of those around the same center always travels faster. Since all the circles in the cone travel at unequal speeds simultaneously, it follows that the outermost ones travel over the greatest place and line in the same time; hence they also travel in a circle. For all are traced by the same straight line, and while that straight line travels in a circle, not all the points on it trace an equal line in the same time, but traveling in a straight line it carries an equal line. But since all the circles of the cylinder are equal and around the same center, it follows that the points of the plane touched by them all together, as they roll, travel at equal speed because the cylinders — that is, the circles — are equal, and each one, having rolled out its own circle, arrives back at the plane simultaneously, so that the straight lines on the plane also become equal; for by their point of contact they traced them, being equal and equally fast. And the lines traced by the same line traveling in a straight direction turned out to be straight, so that by means of these the cylinder is carried in a straight line. For it makes no difference whether one drags the cylinder along the plane by the line at which it first touched the plane, or rolls it; for an equal and similar line of those on the cylinder will always be found touching the plane, whether the cylinder is dragged or rolled.
5| Why is it that the cut of scrolls, being a plane and straight cut, if one cuts along the base, becomes a straight line when unrolled, but if one cuts at a slant, becomes crooked? Is it because, the circles in the one cut lying in the same plane, it turns out that the slanted cut is not parallel to them, but is at a greater distance from it in one place and a lesser in another, so that as it is unrolled, the circles that lie in the same plane, and have their starting point in the same plane, will produce, as they unroll, the line arising from themselves? For the line produced comes from the circles that are in the same plane, so that it is also straight, being in a plane. But the line of the oblique cut, as it is unrolled — not being parallel to the first cut, but standing apart from it more in one place and less in another, because the cut stands in that relation to it — will not be in a plane, and so will not be straight either; for it is not possible for one part of a straight line to be in one plane and another part in another. Why do all magnitudes appear smaller than the whole when they are divided up? Is it because when divided they all have number, but in magnitude are less than the one? For a thing is called great in virtue of being continuous and a certain great quantity, whereas every number is greater than the number of any magnitude. Hence it is reasonable that the whole should appear greater when its parts are divided; for though these are the same things, the whole, being continuous, has more the nature of magnitude, while the parts have the nature of number.
6| Of what happens with the water-clock (klepsydra), the cause as a whole seems to be as Anaxagoras says: for the air is the cause, being trapped inside it, of the water not entering when the tube is stopped up. Yet it is not simply the cause: for even if one puts the water-clock into the water at a slant, with the tube stopped, the water still gets in. That is why the way in which it is a cause is not adequately stated by him. The cause is the air, as has been said; but this air, when pushed and moving on its own and not being forced, is naturally disposed to move in a straight line, just like the other elements. So when the water-clock is dipped at a slant, the air, staying on a straight course, goes out through the holes that are opposite the ones under the water, being pushed out by the water, and as it withdraws the water enters. But when the water-clock is dipped straight down into the water, the air, unable to withdraw straight upward because the top is blocked, stays near the first holes; for it is not its nature to be thrust into itself. A sign that motionless air is capable of keeping out the water is what happens with the water-clock itself. For if one fills the bulb itself with water, stops the tube, and turns it upside down onto the tube, the water does not travel down through the tube to the opening.
7| And when the opening is unstopped, it does not flow out at once down through the tube, but a little later, as though it were not at the mouth of the tube but only travels through it after the opening is made. But when the water-clock is full and standing upright, once the tube is unstopped it flows at once through the strainer, because the water is in contact with the strainer but not with the ends of the tube. So the water does not enter the water-clock for the reason already stated, but it goes out when the tube is unstopped, because the air inside it, moving up and down, creates a large emptying-out of the water in the water-clock. Being pushed downward and itself also inclined into it, it reasonably flows out, forcing back the air outside the water-clock, which is in motion and equal in power to the air pushing it on, but weaker than it in resistance, because, flowing as it does through the narrow tube, it flows faster and more violently, and strikes against the water. The cause of the water not flowing together when the tube is capped is that the water entering the water-clock forcibly pushes the air out of it. A sign of this is the wind and the gurgling noise that occurs in it.
8| As the water enters, forcing its way in, it falls together with the air into the tube, and just as pieces of wood squeezed in, or bronze pressed in by being wedged apart, stay in place without any other fastening until it is knocked out from the opposite side, as men knock out broken pegs in pieces of wood, so it happens here. This happens, when the tube is unstopped, because of what has already been said. So either it is reasonable that the water does not flow out for these reasons, or because the air going out is forceful and turned into wind. The noise shows that the water is drawn upward by the current of air, as happens in many other cases. Being drawn up and continuous with itself, all the water stays there, pressed by the air, until it is pushed back again by it. And with the beginning of it staying in place, the rest of the water hangs from it as one continuous whole. It is reasonable that this happens: for it belongs to the same power both to move something out of its own proper place and to hold it there, as it held it there before, only for a longer time, provided that what holds and what is held are equal in power, or that the holder is stronger — which is what happens here, since air is stronger than water in power.
9| Why are the parts of plants and animals, all those that are not instrumental parts, round — in plants the trunk and the shoots, in animals the shins, thighs, arms, chest — while nothing, whether whole or part, is triangular or many-sided? Is it, as Archytas used to say, because the proportion of the equal is present in natural motion (for all things move proportionally), and this proportion alone bends back into itself, so that it produces circles and round shapes, whenever it comes to be present? Why does roundness always occur at the extremities? Is it because nature, out of what is possible, makes everything as good and as fine as it can, and this shape is the finest, being most like itself throughout? Why, when a disk is thrown, does it at first trace a straight line, but as it slows down trace a spiral, until it falls? Is it that at first it traces a straight line because the air holds it upright equally on this side and that? Since the tendency is equal on both sides, the line it traces must also be of a kind that divides the space equally on both sides — and such a line is straight. But when it tips down to one side because of unevenness in the air surrounding it, it no longer traces an equal path on the inner and outer sides, but of necessity traces a curved one.
10| Why, with bodies whose depth is unequal, if one sets the lighter part in motion, does the thing thrown travel round in a circle — as happens with knucklebones weighted with lead, if one throws them turning the lighter part toward himself? Is it because the heavier part cannot travel at the same speed as the lighter part when thrown by the same force? Since it must move, but cannot move evenly and in a straight line, it must, in moving toward the inner part, move in a circle. For example, if some part of it were altogether motionless in the middle because of its weight, the part near the thrower would move forward, while the part beyond that would move back toward the thrower. But since the whole is in motion, while it has its weight carried in the middle, it must do this very same thing.
11| Why do moving things, when they strike against an obstacle, rebound in the direction opposite to their natural motion, and at equal angles? Is it because the thing moves not only with the motion proper to its own nature, but also with the motion produced by the one who threw it? Now the natural motion ceases when the thing comes to its own proper place (for everything comes to rest when it reaches the place to which it moves by nature); but as regards the motion that is not its own, it must still be in motion, and since it is prevented from going forward, it must go either sideways or straight back. All things rebound at equal angles because they move in the direction that the motion produced by the one who let them fly carries them; and it turns out that they move there at an acute or a right angle. Since, then, the obstacle that is struck prevents the motion in a straight line, it likewise prevents the moving body and checks its motion. Just as in mirrors, the end point of the straight line at which the line of sight arrives is where the image appears, so in the case of moving bodies, the opposite result occurs in the same way; for it is pushed off at an angle equal to the vertical angle formed. For one must conceive the angle and the motion as shifted. Once this is granted, it is clear that the rebound must occur at equal angles.