Epitome Astronomiae Copernicanae: Liber I, part 6
Part IV. Of the place of the Earth in the world, and its proportion to the world
If the whole world is enclosed by a round surface, in what place of the world, then, do you put the globe compacted of earth and water and clothed with air? It will be proved above from sight that the Earth with the whole movable world is within the embrace of the vaulted cavity formed by the firmament or fixed stars. But since this cavity, empty of fixed stars, is most ample and so inestimable, it is not yet known from what has been said hitherto in what place of this hollow space the Earth is placed, whether in the very centre of the world, or in some other place in this cavity, a little outside the centre. It will be proved, however, chiefly in the fourth book: first, that the Sun is in the very centre of the world, wherefore the Earth must be outside the centre; second, that the Earth goes with an annual motion from place to place in a circle, and so cannot be in the centre of the world; third, as regards the planets, that the Earth is hidden within the circuits of Saturn, Jupiter and Mars, but goes round about the circles of Venus and Mercury and the body of the Sun, which occupies the innermost place in these circles; and in turn is gone round by the Moon, her companion, with a winding motion.
But these things have nothing to do with the first motion, since here we are dealing with principles necessary only for the explanation of that first motion. It suffices, therefore, for the explanation of the first motion that we place the Earth at the centre of that motion, even if it is not at the centre of the whole universe. For the Earth could be the centre of the first motion even if it were not enclosed within that hollow vault of the fixed stars, but stood plainly among the fixed stars themselves.
Whence do you know that the space within the hollow sphere of the fixed stars is so great? Because, since the semidiameter of the Earth contains a little less than nine hundred German miles, yet this whole length is as nothing beside the huge distance of the fixed stars from the Earth and does not fall upon the senses, so that not only the centre of the body of the Earth, but any eye on the surface of the Earth, distant almost nine hundred miles from the centre, may be taken for the centre of the first motion, and the whole Earth itself, a body of so great an amplitude, for a mere point.
Prove that the semidiameter of the Earth vanishes in the first motion. First, the transverse diameter of the body of the Sun, which is much nearer the Earth than any fixed star, is found by instruments no greater in the middle of the heavens than when the Sun is seen to rise; although the eye, placed on the surface of the Earth, is nearer by the interval of a whole semidiameter to the culminating Sun than to the rising. Hold the same of the angle of distance of two fixed stars rising together. But by as much as culminating stars approach us more than when they rise, by so much does their distance appear greater when culminating than rising. Since, therefore, the distance between two culminating stars is not increased to sense, neither will the approach be increased to sense, and so the true approach by 900 miles will not be sensible, compared with the huge interval between them and the Earth.
If AD, or AC, BC, and DO, DP be equal, CO, CP are shorter by one semidiameter DC. If, then, AB and OP are the same constellation, the angles BCA and ODP will be equal, and consequently OCP greater, since it is equal to the two CDP and CPD.
Second, if the first motion is uniform and circular, as will be taught in the following part, and if the centre of the first motion and of the body of the Earth is the same, which we now follow, a star seen to move in the middle circle of the first motion must lie hidden so much the longer and be seen so much the shorter, as, when it is seen in the middle of the heavens, it is nearer than when it is not seen above the horizon. But the days of the stars under the equator, so to speak, are found equal to sense to the nights; the distance, therefore, of a star is equal to sense, whether it shines in the middle of the heavens or is sunk below the horizon, and consequently, compared with the distance of the star from the Earth, the greater approach of the same star culminating than rising, which is of one semidiameter of the Earth, is not sensible.
Let the Earth, or the eye on its surface, move about the centre A, and let F be a near star and at rest: F will then be seen to rise when the eye is at B, to culminate when the eye approaches it at C, to set when the eye is at D, B and D being the points at which the straight lines from F touch the Earth. It is plain, therefore, that F is seen while the eye is moved through the shorter arc BCD, and is hidden through the remaining much longer arc, and that because the star F is so near.
Let, on the contrary, the fixed star move about the centre A and the Earth rest, or the eye in it at the point C, whose horizon is ECG: the star will then be seen to rise at G, to culminate at F, to set at E, and again the arc GFE of the star, through which it appears, will be shorter, the remaining arc, through which the star is hidden, longer.
Third, finally, in whatever place of the surface two stars are seen diametrically opposite, so that as one rises the other sets and conversely, they so appear opposite in all other places of the surface of the Earth. And in the same place suppose the eye found in the straight line which joins the two fixed stars placed diametrically, so that both can be seen at once in the opposite parts of the horizon; after that hemisphere has hidden the greater part of itself and the remaining hemisphere has appeared, and the star which was at setting has come to rising, that which was before at rising will again at the same moment be seen at setting. The whole Earth must therefore be smaller than the fixed stars themselves.
But if the Earth is greater than a body that appears so small, it must be removed by a very great interval, or by innumerable diameters of the Earth.
Let AC be the Earth, BAD the horizon of the place A, EOF the horizon of the opposite place C: if, then, each falls upon the stars B and D, so that both can be seen as well from A as from C, BE or DF must be greater bodies than AC itself.
Does not this constant quantity of the appearance of the constellations teach us that the Earth is in the very middle also of all the constellations, and so of the whole world, as is commonly argued? The argument does not hold simply of the very middle of the world, but thus: first, because at all hours of one night the same quantity of each constellation is found by instruments, one of two things follows: either the Earth is at the centre of each of the circles through which the constellations are moved by the diurnal motion, or, if she herself, the fixed stars remaining at rest, produces this apparent motion, that her distance from the stars then remains invariable, without regard to where she is situated, at the centre of the universe or outside.
Second, because this quantity of appearance lasts through all parts of the year, it is further demonstrated that the Earth throughout that whole time recedes nothing, in comparison with the distance, that can be noted by sense from any of the fixed stars, and approaches nothing to it. But whether the Earth recedes by some interval which, though great enough in itself, is insensible in respect of the huge distance of the fixed stars, is not made clear by this argument. As, on the contrary, because the planets do not always, nor in all parts of the year, appear of the same quantity, it is plain from this that the interval between these and the Earth certainly varies. But whether the Earth approaches the planets, or they the Earth, or both approach and recede from each other, remains undecided by this reasoning and is left to be examined by the theoretical doctrine. For it matters nothing to the spherical doctrine, however this may be arranged, since this change of apparent magnitude does not occur within one day, which measure of time is prescribed to the first motion, the subject of the spherical doctrine.
The great circles of the sphere are divided by the terrestrial horizon into two equal parts, for always the middle part of each can be seen, and of the equator always the middle part rises in 12 hours, as appears at the equinoxes, when the Sun is in the equator. Does this suffice to assert that the Earth is the centre of the world? This indeed proves that the Earth is the centre of the great circles of the sphere which the eye imagines to itself at any time. Meanwhile, by this argument that sight may be outside the centre of the whole universe. For the circles of the sphere would exist in the imagination of sight even then, if the Earth were exiled far from her place, or if the sight were in the Moon or Jupiter or another planet, as we shall hear.
Things proportional to the circles of the heavens and of the Earth occur both in length and in breadth. For everywhere 15 German miles on the Earth make one degree in the heavens, everywhere an hour on the Earth makes 15 degrees in the heavens; their centre, therefore, must be the same, the centre namely of the Earth, so that straight lines drawn out from it cut off proportional arcs. The conclusion is conceded, because it speaks not of the centre of the machine of the world, but only of the circles of the sphere which the eye imagines to be set around it, and by that very fact places itself in the centre of it, and would do the same to whatever place of the world it were transferred. Although the form of the inference is preposterous, for the Earth is not at the centre of all the circles because proportional things occur in the circles of the Earth and of the heavens, but on the contrary proportional things occur in the circles of the Earth and the heavens because sight and reasoning describe the celestial circles from the centre of the Earth.
If the Earth were not in the middle, there would seem to be no equinoxes, when the Sun comes into the middle circle. Surely from the equinoxes it is proved that the Earth is in the common section of the zodiac with the equator, and so in the plane of both and in the centre of the equator, as will appear from the spherical doctrine. But it is not necessary that the Earth be therefore in the centre of the whole universe. For even so she will be in the plane of the zodiac, if by her own motion about the Sun (and so outside the centre of the world) she describes the zodiac under the fixed stars by imagination; even so she will be in the plane of the equator, if by the diurnal motion of her body about her axis she describes by imagination circles parallel under the fixed stars and their middle, the equator, in whatever place of the world she is so rotated. For if the Earth, in some other region of the world, were both rotated about her axis and carried about the Sun, these circles also would be carried through other fixed stars by the imagination.
If the Earth were not in the middle, at the centre of the whole world, the precise middle part of the zodiac or of the world would never be seen above the horizon, but either more or less, except only at the moment when the centre of the zodiac or of the world rises. As if NM or CE be lines of the horizon, they will cut the world into unequal parts; but if IA, then into equal, because the centre A falls on the horizon. What is objected is true, but it has nothing absurd, nothing contrary to manifest experience. For who has ever measured that which he takes in of the world at one view? Yet however great a portion of the world is seen at any time, it is accounted, by the imagination of a sphere described about the sight and bisected by the circle of the horizon, a perfect hemisphere.
Suppose the Earth O to be at a middle place between I, the extremity of the true zodiac or of the fixed stars, and the centre A: then COE, which is at right angles to AI, will cut off from CIE a third part, and the arc CNE will be double the arc CIE. But nonetheless the sight placed at O would take the arc CIE as a semicircle, no less than the arc CNE. For it would transfer all the fixed stars into ICN by straight lines drawn out from O onto the smaller circle described from O.
The two signs, in one of which the Moon is seen eclipsed, in the other the Sun, would not be seen from the Earth opposite one another, if the Earth were not in the middle. Truly if the Earth did not come between the Sun and Moon, she would not see the luminaries in opposite places. But when the Moon is eclipsed, the Earth is placed between the luminaries, because it is the Earth itself that wraps the Moon in the shadow of her body. It is necessary, therefore, that the eclipsed Moon be seen opposite the Sun, wherever you shall have set the eclipsing Earth with the eclipsed Moon.
Whenever the Moon rises eclipsed the Sun sets, and rises when she sets eclipsed, and this over the whole circuit of the Earth, wherever the eclipse falls on the horizon. Is it not proved from this that the Earth is in the middle of the world? This does not follow, but only that the Earth is in the same straight line with the luminaries when the Moon is eclipsed. But the same could happen if the Earth with the orb of the Moon were placed next to the fixed stars themselves. And the same appears of necessity also on the globe of Jupiter, supposing observers of the stars to be on it, when the four little Jovial moons are eclipsed by it, notwithstanding that Jupiter goes round very far outside the middle of the world.
The Earth is neither in the plane of the equator outside the axis of the world, nor in the axis of the world outside the plane of the equator, nor outside both at once, as is gathered from many signs or effects and appearances: therefore she will be in both at once and so in the middle of the world, or at the centre. The enumeration of the parts is good, but more is inferred than the premises demand. Truly the Earth is both in the axis and in the plane of the equator, and so at the centre of the sphere imagined around the sight, but nothing follows hence as to the very middle of the world, since the figure of the world may be one, the figure of the imagined sphere another, both indeed round, but differing in number and position. But in particular, if Copernicus places the Earth outside the middle of the world, and therefore attributes to her a twofold motion, of which in the following part, there is no longer need to confirm the position of the Earth in the middle of the sphere by signs, effects or appearances, but rather we hold it a priori and from causes. For the Earth is in the axis of the world for this reason, that the axis of the world is nothing other than the axis of the body of the Earth, about which she is whirled round by the diurnal motion like a top, continued by imagination on both sides to the fixed stars. The Earth is in the plane, and so in the centre, of the equator, because the equator is nothing other than the greatest circle of the Earth, midway between the poles, its plane being continued by imagination to the fixed stars.
Perhaps, then, it can be proved by physical arguments that the Earth holds the middle place of the world. For this is the nature of heavy things, that they are borne to the centre of the world, if they are outside it. If, then, the Earth were outside the centre, since she is a heavy body, she would fall back into the centre most swiftly, or heavy things loosed from her on the other side of the Earth, which inclines toward the centre of the world, would be carried from the Earth to the centre, which is repugnant to experience; for on every side heavy things fall toward the Earth, which, being round, the centre of the world must therefore be within the body of the Earth. The antecedent is denied. For this is not the nature of heavy things, that they are borne to the centre of the world as the centre, but this, that each is borne to the centre of its own body, whether that be in the centre of the world or elsewhere, and this then, if the heavy thing proposed is near that body and less than it. But if any one of the heavy bodies were posited separately, outside the drawing powers of its own body, as if any one of the world’s globes were placed in any place of the world whatever, so that it cannot be attracted by a stronger magnetic power, in this case heavy things cease to be heavy, for they lack motion in any direction, and are so equipped by nature as to resist in some measure a motion brought upon them from outside.
How do you prove that heavy things are not borne to the centre of the world? By reason and by experience.
Prove it by reason. If it were true that heavy things are borne to the centre of the world, the cause of this motion would be either outside the heavy things or within them. If outside, then it would be either natural, residing either in the very centre of the world or in the extremities, or violent, on account of the motion of the world. Again, if the cause of the motion were internal, it would be either the appetite of the centre or flight from the extremities of the world. But since none of these can be, it remains that the motion of heavy things is not to the centre of the world.
Why cannot the centre of the world attract, or the extremity repel, heavy things? Because the centre is nothing but a mathematical point, and in a non-body there is no power to bring motion. And since of quantities there is no efficacy, much less will there be any efficacy of a point, which is not even a quantity, but at most the bound of a line, the slightest of quantities. In the same way the extremity of the world is nothing but a spherical surface, which, so far as it is the extremity of the figure of the world, lacks all efficacy.
Prove that neither can heavy things be thrown to the middle by the violence of the world’s motion. In violent circular motion, if any things seek the middle of the whole moving thing, they must be lighter than the thing moved itself, as in whirlpools wood and chaff are lighter than the water itself turned in a circle; for there a greater impression of the rotation is made on the body of the water, which is heavier, so that it rushes with impetus and, aiming at straightness, seeks the outermost parts of the circle and as it were drains the centre; whereupon the lighter things floating on it, being forsaken on account of the lesser impression of motion on them and their slower motion, and driven inward by the swifter waters, then also on account of the slope of the centre flow naturally into the middle. But if we suppose the world to be rotated, in which is the aethereal breeze and the bodies wandering through it, the Earth at any rate will not be lighter than the aethereal breeze. The violent motion of the world, therefore, will have no right over the Earth and heavy things, to thrust them into the centre.
On the contrary, a violent motion parallel to the horizon, when it has seized heavy things, is wont to urge them, if loosened from the wheel, and to throw them off in a straight line from the circumference of the circle. Wherefore, if the violence of the world’s motion flowed over upon the Earth and heavy things, it would rather eject them from the middle toward the extremes; for the Earth is supposed to be a heavy body. Add that if the diurnal motion were in the whole world, it could not be called violent, both on account of its perpetuity and on account of its simplicity, with which a violent motion cannot stand. For a motion is violent because it conflicts with another motion which is natural to the movable thing: bodies placed on a whirl or wheel have gravity, by which they incline away from those places of theirs and away from the line of the violent motion, toward the centre of the Earth: there is therefore a place of conflict between motions toward different places, the one in a circle, the other downward, whence arises a shaking. But it is not so with the Earth, whose motion is either to the very centre of the world, as the objection would have it, and so there will be no need for that violent thrusting into it, or she seeks no quarter of herself, and so that violent seizure will not exist, since it is contrary to no natural motion of the Earth.
It is also an insufficient cause. For granting that heavy things are driven to the middle of the circle, it will not yet follow that the Earth is in the middle of the whole world, but well that she is in the axis, in which are ordered the centres of all the parallels. Finally, things unconceded are assumed, namely that the diurnal motion is in the world itself, which in the following part will be denied.
Shall we say, then, that the cause of this motion of heavy things to the centre of the world is internal, and that heavy things themselves seek the centre, or flee from the extremities? It would accordingly have to be said just as much how they seek the centre of the world or flee from the extremes, and why. For the centre is a mathematical point, described at equal distance from the extremes of a round body. Since, then, heavy things are something corporeal, while centre and extremes are grasped by the intellect alone, which heavy things, as heavy, lack, they cannot, therefore, seek the centre by their motion, as the centre, or as the inmost point of the world, nor flee from the surface, as from the extremity of the sphere; and if they could, there would still be no cause why they should flee this rather than seek that, than the contrary.
The manner in which heavy things might tend to the centre or be driven there could be this: if a body placed at the extremity of the world sent forth a power as far as the heavy things, which either drove the heavy things or was fled by them? But it is not reasonable that the corporeal force of the outermost sphere should stretch itself so far and be so exact in the least things that, with diameters exactly equal on every side, it could expel toward the middle; and as soon as a heavy thing had receded a foot’s breadth from the centre of the world, the outermost little portion of the starry sphere toward which the heavy thing inclines would feel the force done to it and the burden coming on, and gird itself to repel it, and contend with the other portions of the sphere in forces in expelling the burden and thrusting it back and forth. Much more absurdly will so great subtlety be attributed to the heavy things themselves, of distinguishing this power and its rays, from where each has descended and which of them is longer, in so great a length of all. For magnetic powers have their orbs proportioned according to the density of the bodies from which they flow, so that they do not extend to infinity.
The flight of bodies, also, is in itself contrary to nature, if it be not for the sake of something else; but the mutual appetite of bodies, or union, the rudiment of preservation, is rather agreeable to nature. He philosophizes more rightly, therefore, who defines the motion of heavy things by the force of union of bodies like one another, than he who defines it by flight of contraries.
But if the matter is turned back to powers emitted from bodies, then this cause of the motion of heavy things being at hand in the body near the Earth, there is no need to summon another from the most remote celestial body. And such a power in the body of the Earth, of attracting heavy things, being granted, the motion of heavy things to the centre of the Earth is defended, even if the Earth were not at the centre of the world but in any other place of the world.
But will not heavy things flee from the extremes, as from a nobler place, and pass to the inmost, as to a less noble place, by the genius of nature? This reason also was refuted above, for either this nobility consists in bodies, and so in an emitted power, or in figure. Not in bodies and their power, as has now been proved; not in figure, because figure has no efficacy without regard to body, and because heavy things, as such, lack intellect by which to perceive figure.
Heavy things, then, are borne to the centre of the world by accident, because by natural mutual attraction they are borne to the Earth, which is at the centre? Plainly the question is begged. The place of the Earth had to be proved from the motion of heavy things; now the motion of heavy things is deduced from the place of the Earth, as though established. Surely heavy things are borne to the Earth by a natural attractive power and that mutual, but this happens with no regard to place, for it could happen if the Earth were at the centre of the world, and it can while the Earth is outside the centre.
Aristotle proved that the motion of heavy things tends to the centre of the world from this, that the motion of light things is toward the surface of the world, since the motions of heavy and light things tend to contrary quarters. Heavy and light things are so called only by comparison, not absolutely. If fire or smoke were absolutely light bodies, they would fly away from the Earth upward as far as the outermost heaven. But clouds of smoke, when they have passed this dense air, are seen to rest hanging, which is an argument that they do not of themselves by their own nature seek either the outermost parts of the world or flee even from the centre of the Earth, but are pressed by heavier things and yield to them, like the scales of a balance, each heavy, yet the one seeks the upper regions, drawn by the heavier. It is false, therefore, that heavy things of themselves seek the higher places, false that they seek the outermost surface of the world itself.
But although it is true that on the other side the motion of light things is as if toward the outermost surface of the world, yet this is by accident, and happens even when the Earth is not placed at the centre, where on the opposite side the motion of light things tends plainly toward the centre of the world, if that be placed above the zenith, and that also by accident, on account of the situation of the Earth and the regions. Yet light things do not therefore descend from that quarter into the heavens, nor heavy things ascend toward the lower parts of the Earth, or the centre, but they ascend toward their own regions, because to ascend is to flee from the centre of the Earth (not from the centre of the world), to descend is to seek the centre of the Earth (not the centre of the whole world). Wherefore, as it does not follow: light things on one side are borne toward the centre of the world, therefore heavy things are borne from its centre, so neither does the contrary follow: light things on the other side are borne from the centre of the world to the surface, therefore heavy things to the centre of the world.
Prove now also by experience that certain heavy things are not borne to the centre of the world, though they are borne to the centre of their own body. This is plain to the eye in the globe of the Moon, which, being of the same nature as the Earth in this, that on its outer surface it has mountains and valleys, continents and seas, and yet the Moon is not in the centre of the world, as all grant, nevertheless heavy things, such as the waters of the Moon, fall neither to the Earth nor to the middle of the world, but betake themselves to the places nearest the centre of the lunar globe.
Whence can we know that in the Moon there are high and depressed places, and in the depressed ones waters? First, optics teaches, with the aid of the Belgic telescope and by a plainly necessary demonstration, that the luminous parts of the Moon are raised and stand out from the centre of her globe and are very rough; but the spotted and darkish parts are also depressed and plane, as a continuous plain. For the bright parts are seen to be illuminated both sooner than the spots, and very unequally, or in scattered fashion, among themselves. For in the middle of the shadowed parts there arise certain luminous points, as it were, whose light increases until at length all the intervening shadows are eliminated by the continuation of the bright parts. On the contrary, the spotted parts are illuminated more slowly, and the boundary of light and shadow (when the Moon is bisected) passes through them in an even straight line, with no variety or mixture of light and shadow. These things, then, are most certain from optics, that the dark matter is of an even surface in the lower parts of the Moon, or the hollows.
Now, next, taking these things so optically demonstrated as physical, and comparing them with what is similar with us on the Earth, from the height, roughness and brightness of the parts of the lunar globe he reasons to dry or arid land, namely continents and mountains illuminated by the Sun; from the spots or blackness and evenness, to moist things or waters; from the depression, finally, to gravity or inclination toward the centre of the globe.
To the Earth, the most ignoble body of the whole world, a place also ignoble is fitting. Will it, then, be in the centre of the world? The argument labours under many faults. First, it is not necessary that places correspond to bodies in nobility, if use demands otherwise. Next, the Earth is not the most ignoble body, but at least equals the body of the Moon, if she does not surpass it, since the body of the Moon is much rougher than the body of the Earth. And what if there are many other globes of this kind among the planets and the fixed stars? The body of Jupiter certainly casts a shadow as the Earth and Moon do; the body of Venus lacks light on the side turned from the Sun, as the Earth and Moon do.
Third, it is plainly false that the place of the centre is ignoble, since in the shadowing forth of the Holy Trinity the very first person, God the Father, the fountain of Divinity, is represented by it. Therefore, even if places ought altogether to correspond to bodies, to the Earth, which is held ignoble and which is at least more ignoble than the globe of the Sun, the place of the centre will not be due. But of this argument more below in the theoretical doctrine.
But since in the revolution of the globe the centre remains in its place, to the Earth surely, as a heavy body and inert to motion, the place of the centre will be due at least on account of the reasons of motion? Again the argument is faulty in more than one respect. First there is assumed what is not conceded, that the diurnal motion is in the whole machine of the world, the Earth alone being at rest; which in the following part will be overturned. But with the motion of the whole globe of the world taken away, that privilege of the centre falls. Next, the Earth is not heavy as a whole, so far as she is a whole, because there is nothing outside the Earth to attract her, from which attraction she might be called heavy. Third, the Earth is indeed inert to motion and in some measure resists a motion brought on her from elsewhere, but all bodies are such, so far as they are bodies; the Earth does not merit, therefore, above other bodies the place of the centre by this inertia. Finally, in the theoretical doctrine it will be proved that the Earth is transferred from place to place; which being posited, the argument is inverted, so that the Earth, by this very fact that she changes place, cannot be in the centre. At least for the present, this motion remaining in doubt, even the necessity of the argument is dissolved by its proceeding from her rest to a place in the centre.