by Aristotle
[35] 7 · Why, though the moon is spherical, do we see it straight when it is half-full? Is it because our vision and the circumference of the circles which the sun [912a1] makes when it falls upon the moon are in the same plane? Whenever this happens, the sun appears as a straight line; for since that which casts its vision on a sphere must see a circle, and the moon is spherical, and the sun looks down upon it, there [5] must be a circle which is caused by the sun. When therefore this is opposite to us, the whole is visible and the moon appears to be full; but when it changes owing to the altered position of the sun, its circumference becomes on a plane with our sight and so it appears straight, and the rest appears circular, because a hemisphere is [10] opposite our vision, and this has the appearance of a semicircle; for the moon is always facing our vision, but when the sun sheds its rays we do not see it. And after the eighth day it begins to fill out from the middle, because the sun as it passes on makes the circle incline more towards us; and the circle being thus presented to view [15] resembles the section of a cone. It assumes a crescent-like appearance when the sun changes its position; for when the circle of the sun reaches the extreme points, which make the moon seem half-full, the circumference of the circle appears; for it is no longer in a straight line with the vision, but passes beyond it. When this happens and the circle passes through the same points, it must necessarily appear to have a [20] crescent shape; for a part of the circle is directly on a plane with the eye (a part of the circle, that is, which was formerly opposite to us), so that part of the brightness is cut off. Then the extremities too remain in the same position, so that the moon must have a crescent shape to a greater or less extent according to the sun’s movement; for when the sun changes its position, the circle upon which it looks also [25] turns, remaining on the same points; for it might assume an infinite number of inclinations, since an infinite number of the largest circles can be described through the same points.
8 · Why is it that the sun and moon, which are spherical, have the appearance of being flat? Is it because all things of which the distance is uncertain [30] seem to be equidistant, when they are more or less distant? And so in a single body composed of parts, provided that it is uniform in colour, the parts must necessarily appear equidistant, and the equidistant must appear to be uniform and flat.
9 · Why does the sun make long shadows as it rises and sets, and shorter when it is high in the heavens, and shortest of all at midday? Is it because, as it rises, [35] it will at first make a shadow parallel to the earth and cast it to an infinite distance,11 and then make a long shadow, which grows ever less because the straight line from the higher point falls within that from the lower point. Let AB be the gnomon, and C and D two positions of the sun. The ray from C, the line CF, will fall outside the line DE;12 and the shadow BE is formed when the sun is higher in the [912b1] heavens, and BF when it is lower, and it will be shortest when13 the sun is at its highest and over our head.
10 · Why are the shadows thrown by the moon longer than those thrown by the sun, though both are thrown by the same perpendicular object? Is it because the [5] sun is higher than the moon, and so the ray from the higher point must fall within that from the lower point? Let AD be the gnomon, B the moon, and C the sun. The ray from the moon is BF, so that the shadow will be DF; but the ray from the sun is CE, and its shadow therefore will necessarily be less, viz. DE. [10]
11 · Why is it that during eclipses of the sun, if one views them through a sieve or a leaf—for example, that of a plane-tree or any other broad-leaved tree—or through the two hands with the fingers interlaced, the rays are crescent-shaped in the direction of the earth? Is it because, just as, when the light shines through an aperture with regular angles, the result is a round figure, namely a cone (the reason [15] being that two cones are formed, one between the sun and the aperture and the other between the aperture and the ground, and their apexes meet), so, when under these conditions part is cut off from the orb in the sky,14 there will be a crescent on the other side of the aperture from the illuminant, that is, in the direction of the earth (for the rays proceed from that part of the circumference which is a [20] crescent)? Now as it were small15 apertures are formed between the fingers and in a sieve, and so the phenomenon can be more clearly demonstrated than when the rays pass through wide apertures. Such crescents are not formed by the moon, whether in eclipse or waxing or waning, because the rays from its extremities are not clearcut, but it sheds its light from the middle, and the middle portion of the [25] crescent is but small.
12 · Why does the parhelion not occur either when the sun is in mid-heaven or above the sun or below it, but only at the side of it? Is it because the parhelion is produced when our visual ray to the sun is refracted, and this stationary condition of [30] the air, on the occasion of which the vision is refracted, cannot occur either near the sun or far away from it? For, if it is near, the sun will dissolve it, whereas, if it is far away, the sight will not be refracted; for, if it is strained to a distance, it is weak when refracted from a small refractor. (So too a halo does not form.) If then a [35] refractor forms opposite the sun and near to it, the sun will dissolve it, whereas if it be far away, the incidence of the sight upon it will be too weak. If, however, it forms at the side of the sun, it is possible for the refractor to be at such a distance that neither does the sun dissolve it nor does the sight ascend weakened16 by passing under the earth. It does not form below the sun because, being near the earth, it [913a1] would be dissolved by the sun; whereas, if it were above the sun when the sun is in mid-heaven, the sight would be distracted. And it cannot form at all even at the side of the sun when it is in mid-heaven, because, if the sight is directed too far under the earth, very little of it will reach the refractor, so that, when it is refracted, it will be very weak.
[5] 13 · Why does the extremity of the shadow caused by the sun seem to tremble? For it is not due to the fact that the sun is travelling along; for it is impossible for it to move in contrary directions, and it is of such motion that trembling consists. (Moreover it is uncertain why a shadow changes its position, as also why the sun itself moves.) Is it due to the movement of the so-called motes in [10] the air? These can be seen in the rays which enter through a window; for they move even when there is no wind. These then being constantly carried from the shadow into the light and from the light into the shadow, the common boundary between the light and the shadow is seen to move similarly. For changing17 from side to side of it, these motes cause as it were shadow in one place and light in another; so that the [15] shadow appears to move, though it is not really it but the motes which move in this way.18
BOOK XVI
PROBLEMS CONNECTED WITH INANIMATE THINGS
1 · Why is it that the bases of bubbles in water are white, and if they are [20] placed in the sun they do not make any shadow, but, while the rest of the bubble casts a shadow, the base does not do so but is surrounded on all sides by sunlight? And, what is still more wonderful, even if a piece of wood is placed on the water in the sunlight, the shadow is cut off by the water at that point.1 Is no shadow really formed? Is the shadow dissolved by the sun? If then a shadow is to be defined as [25] anything which is not visible to the sun, the whole mass of the object all round must be visible to the sun; but the impossibility of this has been demonstrated in the treatises on optics, for even the largest optical system cannot see the whole circumference of the smallest visible object.
2 · Why are bubbles hemispherical? Is it because the radii between the centre and the outer air extend in every direction upwards to the same distance and thus necessarily produce a hemispherical form? The corresponding hemisphere [30] below is cut off by the watery surface in which the central point is situated.
3 · Why is it that in magnitudes of uneven weight,2 if you set the lighter part of them in motion, the object thrown revolves in a circle, as happens, for example, with loaded dice if you throw them with the unweighted side turned towards you? Is [35] it because the heavier part
cannot travel at the same speed as the lighter when hurled with the same force? Now the object must travel as a single whole, but cannot move alike in all its parts; therefore if the parts were moved with equal speed [913b1] they would move in the same line, while since one part travels more quickly than the other, the object necessarily revolves as it moves; for it is only in this manner that the parts which are always opposite one another can follow unequal paths in the same time. [5]
4 · Why is it that objects which fall to the earth and rebound describe similar angles to the earth’s surface on either side of the point at which they touch the surface? Is it because all things naturally tend to travel at right angles to the earth? Objects, therefore, which fall upon the ground at right angles, striking the surface perpendicularly and diametrically, when they rebound, form angles of that size, [10] because the diameter divides the angle at the surface into equal parts. But objects which fall obliquely, since they do not strike the ground perpendicularly but at a point above the perpendicular, when they are thrust back by that against which they strike, travel in the opposite direction. This in the case of round objects is due to the [15] fact that, striking against it in their course, they revolve in an opposite direction to that in which they are thrust back, whether their central point is at rest or changes its position. In the case of rectilinear objects it is due to the fact that their perpendicular is thrown backwards after being brought forward;3 just as happens to those whose legs are sheared away from under them or whose scrotum is pulled [20] downwards, for such persons always fall in a contrary direction and backwards, because their perpendicular is raised above the ground4 and then thrust forward. For clearly the opposite of perpendicularity will be to fall backwards and downwards, and objects carried downwards would be heavier. That, therefore, which in these persons involves a fall, becomes movement in rebounding objects. [25] Neither round nor rectilinear objects therefore rebound at right angles, because the perpendicular divides the objects in motion into two parts depthways,5 and there cannot be several perpendiculars to the same plane surface cutting one another, [30] which will happen if a perpendicular is formed at the moment of their impact at the point where the object in motion strikes the plane surface;6 so that the original perpendicular along7 which it travelled must necessarily be cut by the new perpendicular. Now since the object will be borne back, but will not be borne back [35] at a right angle, it remains that the angle on either side of the point of impact with the plane surface must be an acute angle; for the right angle forms the division between the opposite angles.
5 · Why is it that a cylinder, when it is set in motion, travels straight and describes straight lines with the circles in which it terminates, whereas a cone revolves in a circle, its apex remaining still, and describes a circle with the circle in [914a1] which it terminates? Both move with a circular motion, but the cylinder describes straight lines on the plane surface, while the cone describes circles because the circles which compose the cone are unequal and the greater circle always moves more quickly than the less about the same centre. Now since all the circles [5] composing the cone move at different rates, it results that the outermost circles travel over most space and describe the longest line in the same time (hence they must move in a circle); for all the circles are described by the same straight line, and when the straight line revolves the various points on it do not describe an equal line [10] in the same time, but can travel along an equal line only if they proceed in a straight direction. But in the cylinders, since all the circles are equal and about the same centre, the result is that, since they touch the plane surface at all the points on them at the same time, as they roll they travel at a uniform speed (because cylinders are [15] uniform throughout), and reach the plane surface again simultaneously when each has completed its own circuit; thus the straight lines described on the plane surface are also equal, for the circles describe them by contact, since they both are equal and travel at the same speed. Now the lines described by the same line travelling in a straight direction are straight, and so the cylinder would travel straight along [20] them; for it makes no difference whether you drag the cylinder over the plane surface at the line where it first8 touched the plane surface, or whether you roll it over it; for the result will always be that an equal and similar line made up of points on the cylinder will touch the plane surface, both when the cylinder is dragged and when it is rolled along.
[25] 6 · Why is it that if a scroll is cut level and straight, then if you cut it parallel to the base, the edge becomes straight when unrolled, but if it is cut obliquely, the edge becomes crooked? Is it due to the fact that, since the circles in the first section are in the same plane, the result is that the oblique section is not parallel but is [30] partly more and partly less distant from the first section, so that, when the roll is unfolded, the circles, which are in the same plane and have their origin in the same plane, assume, when unrolled, the line which they themselves form? For the resulting line is formed from the circles which are in the same plane, so that the line, being on a plane, is also straight. But the line of the oblique section when it is [35] unrolled, not being parallel to the first section, but partly more and partly less distant from it (this being the position of the section relative to it), will not be on a plane and therefore not straight either; for part of a straight line cannot be in one plane and part in another.
7 · Why is it that magnitudes always appear less when divided up than when [914b1] taken as a whole? Is it because, though things which are divided always possess number, in size they are smaller than that which is single and undivided? For that which is great is said to be great owing to its continuity and because it is of a certain size, but the number of its parts is always greater than the number of any undivided [5] magnitude. So it is only natural that the whole should appear greater than the parts into which it is divided; for, though the whole and its parts are identical, the whole, being continuous, possesses more of the quality of magnitude, while the parts have more of the quality of number.
8 · Of the phenomena which occur in the water-clock the cause seems to be in general that ascribed by Anaxagoras; for the air which is cut off within it is the [10] cause of the water not entering when the tube has been closed. The air, however, by itself is not the cause; for if one plunges the water-clock obliquely into the water, having first blocked up the tube, the water will enter. So Anaxagoras does not adequately explain how the air is the cause; though, as has been said, it certainly is [15] the cause. Now air, whether impelled along or travelling of itself without any compelling force, naturally travels in a straight line like the other elements. When therefore the water-clock is plunged obliquely into the water, the air preserving its straight course is driven out by the water through the holes opposite to those which [20] are in the water, and, as it goes out, the water flows in. But if the water-clock is plunged upright into the water, the air not being able to pass straight up, because the upper parts are closed, remains round the first holes; for it cannot contract into itself.9 The fact that the air can keep out the water by its immobility can be [25] illustrated by what happens with the water-clock itself. For if you fill the bulb itself of the water-clock with water, having stopped up the tube, and invert it with the tube downwards, the water does not flow along the tube to the outlet. And when the outlet is opened, it does not immediately flow out along the tube but only after a moment’s interval, since it is not already at the outlet of the tube but passes along it [30] afterwards, when it is opened. But when the water-clock is full and in an upright position, the water passes through the strainer as soon as ever the tube is opened, because it is in contact with the strainer, whereas it is not in contact with the extremities of the tube. The water does not, therefore, flow into the water-clock, for [35] the reason already mentioned, but flows out when the tube is opened because the air in it being set in motion up and down causes considerable movement10 in the water inside the water-clock. The water then, being thrust downwards and having itself
also a tendency in that direction, naturally flows out, forcing its way through the air [915a1] outside the water-clock, which is set in motion and is equal in force to the air which impels it but weaker than it in its power of resistance, because the interior air, since it passes through the tube, which is narrow, flows more quickly and violently and forces the water on. The reason why the water does not flow when the tube is closed [5] is that the water on entering into the water-clock drives the air forcibly out of it. (That this is so is shown by the breath and noise engendered in it.) As the water enters, driving the air forcibly along, it rushes into the tube itself, and11 like wedges of wood or bronze driven in by cleavage, remains in position without anything else to [10] hold it together, until it is expelled from the opposite direction, as pegs which are broken in wood are knocked out. This occurs when the tube is opened for the reasons already mentioned. If this is the reason, it is only natural that it should not flow out or make its way forth, since the air forcibly prevents it and becomes inflated.12 (The [15] noise which is made shows that the water is drawn up by the air, and this is a common phenomenon.) All the water then, being drawn up and being in itself continuous, remains in the same position under the pressure of the air, until it is thrust away again by it; and, since the first part of the water remains in the same position, the rest of the water is dependent from it in one continuous mass. It is only [20] natural that this should be so; for it is the property of the same thing to move something from its own place and to hold it when it has moved it,13 and to do so for a longer time, if that which holds and that which is held are of equal force, or if that which holds is stronger, as occurs in the present case; for air has greater force than water.