Epitome Astronomiae Copernicanae: Liber IV, part 4
Part Two of Book IV. Of the Motion of the Bodies of the World
I. How many and of what kind the motions are.
What does Copernicus hold concerning the motion of bodies, what is moved, what is at rest? Local motion is of two kinds: for either the whole is turned remaining in its place, the parts succeeding one another, which motion may be called rotation, from the likeness of the lathe or the whirl, or turning, from the instrument, the pivot; or the whole itself is carried from place to place in a circle, which motion the Greeks call periphora, the Latins for the most part circuit or circumlation or compass, but both commonly call it revolution.
Copernicus therefore places the Sun as standing at the centre of the world, immovable as to the whole, that is in centre and axis; yet that he is turned, as to the parts of his body, about his own centre and axis we have discovered within a few years by sense, as I had long since asserted by reasons; with so great a speed that one rotation is completed in the space of 25 or 26 days.
Now the nearer each of the primary planets is to the Sun, the shorter the period in which it is carried around the Sun, under the same common circle of the zodiac, and all toward the same quarter toward which the parts of the body of the Sun go forward: Mercury in the space of 3 months, Venus 8 and a half, the Earth with the heaven of the Moon 12, Mars 22 and a half, or less than two years, Jupiter 12, Saturn 30 years. The sphere of the fixed stars is for Copernicus wholly immovable. The Earth meanwhile revolves also about her own axis, and about the Earth the Moon, again both toward the same quarter, if you look to the outside of the world, toward which all the primary planets go.
All the motions, however, for Copernicus are only direct and continuous; there is with him in the truth of the thing no station, no retrogradation.
By what arguments is it proved that the sphere of the fixed stars does not move? That it is not turned about a centre and axis was shown in book I. For whatever of this strikes the eyes, all that we attribute to the Earth. Let the other arguments be sought there, folio 168 ff. Let us repeat only two proper to this place. One from the speed. For if the outermost sphere has at least 4000000 diameters of the Sun in its diameter, the circumference will be 12566370: which, if it is revolved entire within 24 hours, then in one hour 523600 will be revolved, in one minute 8727, in one second, which nearly equals the pulse of a man, 145 diameters of the Sun will pass, each not less than 13 thousand German miles: so that in the space of time in which the artery is once dilated and again contracted by a double beat, about seventy-five hundred thousand miles of the greatest circle would be revolved, and Saturn, in an orbit two thousand times narrower, would still traverse about 4000 miles.
The other argument destroys altogether every motion of the sphere of the fixed stars: for it does not appear for what good, since there is nothing outside, from which or toward which it might be transferred so as to vary its situation and appearances, and it obtains by rest whatever it could gain by any motion. For from its rest the motions of all bodies are understood, and unless it afforded place, which it does most rightly by resting, nothing could be moved.
How does the proportion of the periodic times, which you have assigned to the movables, stand to the proportion already set forth of the orbs in which they are carried? The proportion of the times is not equal to the proportion of the orbs, but greater than it, and in the primary planets precisely the sesquialter of it. That is, if of the years of Saturn, 30, and of Jupiter, 12, you take the cube roots and multiply them as squares, in these square numbers will lie the genuine proportion of the orbs of Saturn and Jupiter. So it is also if you compare orbs not nearest to each other. For example Saturn has 30 years, the Earth one year. The cube root of 30 is 3 and about 11 hundredths, but the cube root of 1 is 1; the squares of these roots are 9 and 672 thousandths, and 1. Therefore the orb of Saturn is to the orb of the Earth as 9672 to 1000, and a more accurate number results if you take more accurate times.
What is gathered from this? The planets are not all carried with the same speed, as Aristotle held, otherwise the times would be as the orbs and their diameters; but the higher each is and the more remote from the Sun, the less space it traverses in one hour by mean motion: Saturn (according to the magnitude of the sphere of the Sun believed by the ancients) 240 German miles, Jupiter 320, Mars 600, the centre of the Earth 740, Venus 800, Mercury 1200. Although, according to the interval of the Sun demonstrated by me above, the number of miles must everywhere be tripled.
II. Of the causes of the motion of the planets.
State the opinion of the ancient astronomers, how they think the planets are moved. The most ancient, Eudoxus and Calippus, and Ptolemy who followed them, went no further than the circles by which they were accustomed to demonstrate the phenomena, unconcerned how the stars accomplished these circles. For so Ptolemy writes in book XIII of the great work, chapter II:
Let no one think these implications of circles which we suppose difficult, because he sees that among us men their imitation by hand is very perplexed. For it is not fair to compare our human things with the immortal gods, and to seek the credibility of sublime things from examples of things most unlike.
For what is more unlike to what, than those things which always hold in the same manner to those which never remain consistent, and those which on every side cannot be hindered by any, to those which cannot be hindered even by themselves? Rather we must take pains that, if it can be done, the simplest suppositions be fitted to the celestial motions, and if this does not succeed, then such as can. For if by the consequence of these hypotheses only all that appears in the heavens is supplied, it is by no means fitting to wonder further that implications of this kind can befall those motions of the celestial bodies: since in them there is no nature that hinders motion, but one which is by nature apt to yield and to give place to the natural motions of each globe, even if those happen to be contrary to one another: so that all things can be penetrated by all things simply, no less easily than they can be seen through. Nor is this facility to be used only about single circles, but also about whole spheres and about the axes of curved and enclosed surfaces. For although of these also, on account of the different motions, the various implications and insertions of some in others are, in the examples of theories which are wont to be prepared by human hand, very difficult, and do not easily succeed so that the motions are in nowise hindered: yet in the heavens we see that so manifold a concourse of motions by no means prevents the single ones from taking place. Nay, not even this very thing, what is simple in celestial matters, ought to be judged by examples of those things which seem simple among us: since not even here on Earth does the same thing seem equally simple to all. For it will easily happen that he who wishes so to estimate celestial things will recognise nothing of what happens in the heavens as simple, not even the invariable constancy of the first motion: because this very thing (that there be something which holds itself always in the same manner) is among men not only difficult to find but altogether impossible. Judgment is therefore to be formed not from things of our own country, but from the very natures of the things which are in the heavens, and from the immutable tenor of the motions themselves. So it will come about that in this way all motions will appear simple and much simpler than those which seem such among us: for we can suspect no labour, no difficulty in their circuits. So far Ptolemy.
What do you desire in this opinion of Ptolemy? Although it is true that the facility of celestial motions is not to be estimated from the difficulty of elementary motions, for very many reasons; yet it does not yet follow that there are no near examples of celestial motions on Earth; and Ptolemy seems to extend this excuse too far, so that he pierces through the whole astronomical reason, and so satisfies neither astronomers, nor philosophers, nor can it be tolerated even in Christian doctrine.
For as to astronomy, it brings all hypotheses whatever under suspicion of falsity, while it presses so strongly the difference of celestial and terrestrial things, that even reason itself is supposed to err in judging what is geometrically simple. For if what seems to our reason compounded in the heavens, as made up of circles, is simple in the heavens themselves, then in the heavens there are no circles compounded one with another to effect a single motion: the astronomer therefore supposes what is false, and, what is most wonderful, draws the true from merely false things. This, however, is to destroy the honour of astronomy, which Aristotle asserted in the books of the Metaphysics, thinking that astronomers are to be heard upon the form and disposition and motions of the celestial bodies. Nay, Ptolemy betrays what he wishes: for he bids us frame hypotheses as simple as possible, if it can be done. So if anyone shall have framed simpler ones than he, understanding geometrically, Ptolemy will not defend his own compound ones against him by this excuse, but will bid him bring forward those which will seem to us, men of the Earth, simpler, even if we use terrestrial examples.
As to philosophy, philosophers will deny that it suffices that the matter of the celestial body be liquid and permeable by the globes and so not resist the motions of the globes through it; for they will ask what that is which carries the globe itself round, especially if it be agreed that the matter of the globes resists the movers; they will ask by what force the mover moves the body from place to place, no immovable ground underlying, since the round body has no aid of feet or wings, by whose movement animals may carry this their body through the ethereal air, as birds through the air, by a certain effort and counter-effort of that air; they will ask by what light of mind, by what means the mover either perceives or forms the centres of the circles and the orbits cast about them. Finally, neither theology nor the nature of things allows that Ptolemy, imbued with pagan superstition, should make the stars visible gods (inferring immortal life from their eternal motion) and should grant them more than God the Maker himself has, namely that geometrical reasons which are in truth compound should be simple to them, the understanding of which God willed to be common to man, his image, with himself.
State also the opinion of Aristotle, how he thinks the planets go round. Aristotle, believing the heaven to be packed with solid orbs (though of an equivocal matter), and the later philosophers, whom the Arabs seem to have followed, and after them Purbach, the writer of the Theorics, these, I say, first believed the astronomers about the number of circles necessary for demonstrating the appearances; so Aristotle believed Eudoxus and Calippus about 25 orbs. To these he attributes as many moving intelligences, which by mind should carry round the time of the period and the quarter of the world toward which the motion was to tend. Since, however, it was probable that all look to the same principle, Aristotle judged that to these 25 orbs another 24 were to be interposed, which he called unrolling or revolving: so that each lower orb, by that rapture which it was to suffer from the upper on account of the contiguity of the surfaces, might be freed by the interposed revolving orb, which strives in an equal time against the upper and by this counter-effort presents the appearance of one at rest, on which as on an immovable place the lower, leaning, might complete its own peculiar period. So the mover of each orb was held to impart to its own orb and to all the lower which it embraced a most uniform motion in the upper orb which touched it nearest. And since it pleased that philosopher that motion is from eternity, he held the movers also eternal and immaterial, because material things were not capable of infinity: it followed, therefore, that the movers are separate and immovable principles. Since, however, this eternal duration of the celestial essence seemed to him the goodness and perfection of the whole world, being opposed to destruction, which was an evil: to those principles also he assigned the highest perfection and understanding of it, and from the understanding of the good the will to pursue it, lest it should not do well what is good: in which way he introduced to us separate minds and finally gods, no less than Ptolemy, the ministers of the perennial motion of the heavens. Nay, even Scaliger, a Christian by profession, and other followers of Aristotle dispute that this motion of the orbs is voluntary, and that the principle of will in those movers is understanding and desire. And indeed if the world were eternal, as Aristotle had contended, at least the fixed quarter toward which a planet is revolved would bear witness to understanding. For we Christians cannot deny that the highest wisdom presided over the institution of the motions, by which each was impelled toward its own quarter and as it were let out from the barriers into its own courses: this office, however, Aristotle transferred to the movers themselves, as eternal. Moving souls also were added, more closely bound to the orbs themselves and informing them, so that the intelligence only stood by, either because it seemed necessary that the first mover and the movable should meet in some third, or because the power of motion was finite with respect to the space to be traversed, nor was the motion of infinite speed, but described in time, measured to the space: which was an argument that the proportion of the moving power to the movable body and to the spaces is certain and measured. By this solidity of the orbs, therefore, and by the constant strength of the moving power, provision was made for all celestial motions or appearances whatever, so that, the principle of motion once given, all the variety of motions thereafter proceeded from the disposition and plurality of the orbs, without labour or solicitude of the intelligence; and the orbs were moved on resting poles in much the way in which in book I the body of the Earth was said to be rotated on its axis and poles; and by that motion each orb (which some make wholly adamantine, so that they by no means yield to any body) carried round its own planet bound to a fixed place, the one sustaining the other, as was said above, nor was there fear that either globes or orbs should fall, being so bound to one another.
What do you think of this philosophy? Again I object to it not so much the authority of Christian doctrine as the very absurdity of the dogma, which feigns gods whose offices are from the works of nature, and meanwhile ascribes to them from eternity such things as must necessarily have proceeded from the one first principle of all things at the beginning of time. As this reasoning could not lack such a theology, the gods being denied, the whole falls. Then neither can solid orbs be conceded, as was proved above. And again this philosophy rests on solid orbs, and they being overthrown it falls. For Aristotle would readily concede that a body cannot be transported by its soul from place to place if it be destitute of the instrument of an orb, extended to complete the whole circuit, and likewise if there be absent an immovable body on which the orb may lean. Then, if we should concede solid orbs, yet there lie immense intervals between the orbs. These will either be full of a useless orb contributing nothing to the circumstance of motions, which is most absurd, or if through those intervals there are no solid orbs, the spheres therefore do not touch or bear one another. Finally, this reasoning deserts itself, providing for the orbs how each should lean on another, but forgetting the lowest. For granting that orbs are sustained by orbs and are contiguous to one another, what then sustains the last orb of the Moon, or on what pillars does it rest upon the Earth, as they suppose, at rest, when over the whole surface of the Earth round about no solidity occurs, winds, clouds, birds going freely and most easily in every direction? Why does not the immense weight of the heavens sometimes settle down upon us, especially the denser parts of the orbs approaching our vertex? Or if there is no weight in the heavens, what need have we of orbs to carry the globes of the planets?
If there are no solid orbs, intelligences will seem so much the more needed to administer the motions of the heavens, though they be not gods; for let them be angels or some other rational creature. Nor are these needed, as will be proved, nor is it possible that a planetary globe be carried round by intelligence alone. For first, mind, destitute of animal power sufficient to impart motion, possesses no moving force in a mere nod, nor can it be heard and perceived by a brute globe, nor, if it were perceived, would a material globe have the faculty of obeying and moving itself. Now it was said before that no animal force suffices to transfer its body from place to place unless instruments be present and some resting body on which the motion is made; the matter therefore falls back to what was said above. On the contrary, the natural powers inherent in the bodies themselves of the planets can accomplish this, that the planet be transferred from place to place.
But granting that it suffices for motion that the intelligence will to move toward this or that quarter, the invention of the figure in which the line of motion is ordered will now become absurd. For we are convinced by astronomical observations rightly treated that the path of the planet is as nearly as possible circular and indeed eccentric, that is, its centre is not in the centre of the world or of any body, and that besides it passes in the succession of ages from place to place. As many arguments, however, can be brought against the invention of such an orbit as there are parts of it already described.
For first, the orbit of a planet is not a perfect circle, and if a mind effected it, it would certainly order it into a perfect circle, whose is mental beauty and perfection. On the contrary, the elliptical figure of the planetary path and the laws of motions by which such a figure is effected savour rather of the nature of the balance, or material necessity, than of the conception and destination of a mind, as will appear below. Next, granting that some other idea than that of the circle shines in the moving mind, it is asked by what means the mind can apply either this or that to the regions of the world. A circle is described about some one centre, but an ellipse, the figure of the orbits of the planets, about two centres.
What seat, then, will you give the mind that it may measure out a circle or an elliptical orbit in the liquid fields of the ether? Will you place it in that centre? You place it, then, in ethereal air, which differs in nothing from all the rest of the space of the world, since the orbit of the planet is eccentric to the body of the Sun. But this is very absurd, since elsewhere the principle of the individuation of souls is ascribed to matter and the body to which the soul is added, which differs in place and time and many other marks from the remaining matter of the world. Certainly to soul and mind no other situation belongs than through its body, which it informs. And by what force will the mind be moved from place to place in a small circle about the centre of the world, as happens with the centres of the planetary orbits in the succession of ages, if the mind lacks a body, if, as it is locatable, so it is not itself movable? By what means will the mind maintain its situation, its distance from the centre of the world? Granted that provision be made for it of a seat in the centre, how now will it bring it about that the planet, being very far absent, ordains its orbit about this centre? If it had the planet bound by a cord, he would perhaps fly round, from the centre of the tie; the mind looking out from the centre might perhaps be able to perceive whether the planet went in a circle, if, namely, it were always seen at an equal angle: but when it strayed from the orbit, by what way would it bring it back, if it did not see the orbit itself of itself? And how will the mind understand an orbit which is not particularly marked by any body? For here the discourse is not of the intellectual idea of a circle, in which there is no distinction of great and small, but of the real path of the planet, which besides the idea has also a certain quantity. But if you place the moving mind outside the centre of the orbit, its condition will be worse. For either it will be in the body that holds the centre of the world, and so all the minds will be in the same body and the difficulties above will remain of retaining the planet in its orbit and of the invention of that orbit. Or the mind will be in the globe of the planet itself: then in either case it is asked by what means the mind knows where the centre is about which the orbit of the planet is to be ordered, and how far it with its globe is distant from that point. For Avicenna rightly judged that the mover of the planet, if it is a mind, needs knowledge of the centre and of its own distance from it. For a circle is defined and perfected by the same things, a centre and an equal curvature about it, that is an equal distance of the circumference from it: so, however much you exalt the moving mind, the circle is not, even for God, anything else than what has been said; and the same must be understood of the elliptical figure in its own measure.
Why do you say that a celestial body, constant in its matter, cannot be carried round by a mere nod? But the celestial things are neither heavy nor light, but most apt for circular motion, and therefore do not resist the moving mind. Although a celestial globe is not so heavy as a stone on Earth is called heavy, nor so light as fire among us, it has nevertheless by reason of its matter a natural power of passing from place to place, it has a natural inertia or rest by which it rests in every place where it is placed alone. To remove it from its situation and rest, there is need of some power which is something more than its matter and bare body, and which overcomes this natural inertia of it. For such a faculty is already above the genius of nature, an offspring of form or an index of life.
Whence do you prove that the matter of the celestial bodies resists its movers and is overcome by them, as in a balance the weights by its moving faculty? This is proved first from the periodic times of the revolution of the several globes about their axes, as of the Earth in a diurnal time, of the Sun in a time of about 25 days. For if there were no inertia in the matter of the celestial globe, which is to it as a kind of weight, there would also be no need of any virtue for moving the globe: and the least virtue of moving being posited, there would be no cause why the globe should not be turned in a moment. But since the revolutions of the globes take place in a certain time, longer in one planet, shorter in another, hence it appears that the inertia of matter is not to the moving virtue as nothing to something. There is not, therefore, no inertia, and so no resistance of celestial matter.
The same is proved secondly from the circumlation of the globes about the Sun, considered together. For a single mover by a single rotation of himself moves six globes, as we shall hear below. But if the globes had not a natural resistance of a certain proportion, there would be no cause why they should not follow most exactly the whirling of their mover and so be turned with him in one and the same time. Now all indeed go toward the quarter toward which the mover is whirled, yet none attains fully the speed of its mover, and one follows more sluggishly than another. They mingle, therefore, with the speed of the mover their own inertia of matter in a certain proportion.
The proportion of the periodic times seems to be the work of mind, not of material necessity. The very tempering of the extreme motions, of the slowest and swiftest, in any one planet is a most exquisitely harmonic work of the supreme and adorable creating mind or wisdom: but the lengths of the periodic times, if they were the work of mind, would have something of beauty, such as are the expressible proportions: double, triple and the like. Now the proportions of the periodic times are inexpressible (commonly called irrational) and so partake of infinity, in which there is no mental beauty, because there is no definition. Secondly, these times cannot be the work of mind (I speak not of the Creator, but of the nature of the mover), because the times of one period are gathered from unequal delays in different parts of the circle. Those unequal delays, however, as will be said below, arise from material necessity and as it were from the principle of the balance.
By what force, then, do you suspend the globes, as you will, material, the Earth especially, so that each remains within the bounds of its region, though destitute of those solid bonds of orbs? Since it is certain that there are no solid orbs, it is necessary that we have recourse to this inertia of matter, by which it comes about that a globe, placed in any place of the world outside the moving virtues, rests naturally in that place, for this very reason, that matter, as such, has no faculty of transferring its body from place to place.
What is it, then, that makes the planets go round the Sun, each within the bounds of its region, if the orbs are not solid, nor can the globes themselves do anything but stick fixed, nor can they without solid orbs be moved from place to place by any soul? Although things most remote from us and without a genuine example have difficult explanations and make the judgment very slippery, as Ptolemy truly warned, yet if we follow probability, careful that we establish nothing contrary to ourselves, it cannot be obscure that neither is any mind to be introduced which by the dictate of reason and as it were by a nod carries the globes round, nor is a soul to be set over this circumlation which, as happens in the rotation about an axis, makes an impression on the globes by an equable contention of forces, but that there is only and solely the solar body, situated in the middle of the whole universe, to which this motion of the primary planets about the body of the Sun can be ascribed.
III. Of the revolution of the solar body about its own axis and its effect on the motion of the planets.
By what causes are you led to make the Sun the moving cause, or fountain of motion, of the planets? 1. Because it appears that the farther each planet is distant from the Sun than the others, the more sluggishly it advances, so that the proportion of the periodic motions is sesquialter to the proportion of the distances from the Sun. From this, therefore, we reason that the Sun is the fountain of motion. 2. That the same happens in the several planets, we shall hear below, so that the more any one planet at any time approaches the Sun, the more it is carried on faster than itself in a most exact double proportion.
3. Nor does the dignity or aptitude of the solar body disagree, which is most beautiful and of most perfect roundness, and also greatest, and the fountain of light and heat, whence all life in vegetables springs: so that heat and light can be reckoned as certain instruments, suited to the Sun for imparting motion to the planets.
4. Above all, the rotation of the Sun in his own space about an immovable axis toward the same quarter toward which all the planets follow, and in a shorter period than Mercury, the nearest to him and swiftest of all, fills up all measures of probability.
For that which today is discovered by the telescope and may be seen daily, that the body of the Sun teems with spots, which within 12, 13 or 14 days cross the disc of the Sun or its lower hemisphere, slowly at the beginning and end, swiftly in the middle (which is an argument that they stick on the surface of the Sun and turn with it), that this must necessarily so happen was proved by me, by reasons drawn from this very motion of the planets long before it was established concerning the spots of the Sun, in the Commentaries on Mars, chapter XXXIV.
What, then, do you think is to be held concerning the body of the Sun, by what force is it turned about its axis? It was said in book one that this body, and any other that revolves about its axis, was not only in the very beginning of things driven into a rotation by the creating omnipotence, but also seems to continue this motion by the presidency of a moving soul. For although this motion can be continued also in another way, explained there, yet the duration and perennity of this motion, in which the life of the whole world consists, is more rightly obtained by the presidency of a soul.
Have you also other arguments besides motion, by which it becomes probable that a soul is in the body of the Sun? 1. A great argument will be drawn from the matter of the solar body and its illumination, which seems to be a quality in the body of the Sun arising from a most powerful information by a soul, since its matter, as was said above, is consonantly the densest of the bodies of the whole world: the greatest forces, therefore, it is fitting to believe are present to that soul which so masters and inflames so stubborn a matter. See Optics, chapter VI. (Vol. II, p. 269)
2. A soul, however, I think is rather to be posited than an inanimate form, because from the origin and dispersal of the spots in the Sun, and from the unequal illumination of its different parts at different times, it appears that there is not one continuous and perpetually uniform energy in all the parts of the solar body, but that it admits motion and variation and vicissitudes, and that such things happen in the globe of the Sun as in the globe of the Earth, with the necessary changes; so that from its inmost bowels here and there images of clouds (which are perhaps black soots) breathe out, and their matter being consumed, the light of the parts which before were covered by those spots becomes brighter: which vicissitudes, since they are perennial, savour rather of the presidency of a soul than of a simple form.
3. Light itself also is of itself something cognate to soul, no less than was proved above in book I concerning heat. For nothing among us is inflamed, that is made luminous, which has not been generated by some soul in the body: as wood by the soul of the plant, spirit of wine by the vegetating soul of the vine, sparks from iron and stones, which things are cooked in the bowels of the Earth by the soul of the Earth. That light is something cognate to our flames is plain from this, that light condensed by hollow mirrors or convex glasses sets on fire like flames and coals. So it is consonant that the body of the Sun, in which light sits originally, be endowed with a soul which may be the author, guardian and continuer of that inflammation.