Great Throughts Treasury

"If there should be any [persons], who though ignorant in Mathematics, yet pretending a skill in those Learnings, should dare, upon the authority of some place of Scripture wrested to their purpose, to condemn and censure my Hypothesis, I value them not, but shall slight their inconsiderate judgment."

"After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formally used, if some assumptions (which are called axioms) were granted me. They follow in this order. There is no one center of all the celestial circles or spheres. The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere. All the spheres revolve about the sun as their mid-point, and therefore the sun is the center of the universe. The ratio of the earth's distance from the sun to the height of the firmament is so much smaller than the ratio of the earth's radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament. Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth's motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged. What appears to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve about the sun like any other planet. The earth has, then, more than one motion. The apparent retrograde and direct motion of the planets arises not from their motion but from the earth's. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens."

"Among the authorities it is generally agreed that the Earth is at rest in the middle of the universe, and they regard it as inconceivable and even ridiculous to hold the opposite opinion. However, if we consider it more closely the question will be seen to be still unsettled, and so decidedly not to be despised. For every apparent change in respect of position is due to motion of the object observed, or of the observer, or indeed to an unequal change of both. "

"Since, then, there is no objection to the mobility of the Earth, I think it must now be considered whether several motions are appropriate for it, so that it can be regarded as one of the wandering stars. For the fact that it is not the centre of all revolutions is made clear by the apparent irregular motion of the wandering stars, and their variable distances from the Earth, which cannot be understood in a circle having the same centre as the Earth. "

"The two revolutions, I mean the annual revolutions of the declination and of the centre of the Earth, are not completely equal; that is the return of the declination to its original value is slightly ahead of the period of the centre. Hence it necessarily follows that the equinoxes and solstices seem to anticipate their timing, not because the sphere of the fixed stars moves to the east, but rather the equatorial circle moves to the west, being at an angle to the plane of the ecliptic in proportion to the declination of the axis of the terrestrial globe."

"Then if the first argument remains secure (for nobody will produce a neater one, than the length of the periodic time is a measure of the size of the spheres), the order of the orbits follows this sequence, beginning from the highest: The first and highest of all is the sphere of the fixed stars, which contains itself and all things, and is therefore motionless. It is the location of the universe, to which the motion and position of all the remaining stars is referred. For though some consider that it also changes in some respect, we shall assign another cause for its appearing to do so in our deduction of the Earth's motion. There follows Saturn, the first of the wandering stars, which completes its circuit in thirty years. After it comes Jupiter which moves in a twelve-year long revolution. Next is Mars, which goes round biennially. An annual revolution holds the fourth place, in which as we have said is contained the Earth along with the lunar sphere which is like an epicycle. In fifth place Venus returns every nine months. Lastly, Mercury holds the sixth place, making a circuit in the space of eighty days. In the middle of all is the seat of the Sun. For who in this most beautiful of temples would put this lamp in any other or better place than the one from which it can illuminate everything at the same time? Aptly indeed is he named by some the lantern of the universe, by others the mind, by others the ruler. Trismegistus called him the visible God, Sophocles' Electra, the watcher over all things. Thus indeed the Sun as if seated on a royal throne governs his household of Stars as they circle around him. Earth also is by no means cheated of the Moon's attendance, but as Aristotle says in his book On Animals the Moon has the closest affinity with the Earth. Meanwhile the Earth conceives from the Sun, and is made pregnant with annual offspring. We find, then, in this arrangement the marvellous symmetry of the universe, and a sure linking together in harmony of the motion and size of the spheres, such as could be perceived in no other way. For here one may understand, by attentive observation, why Jupiter appears to have a larger progression and retrogression than Saturn, and smaller than Mars, and again why Venus has larger ones than Mercury; why such a doubling back appears more frequently in Saturn than in Jupiter, and still more rarely in Mars and Venus than in Mercury; and furthermore why Saturn, Jupiter and Mars are nearer to the Earth when in opposition than in the region of their occultation by the Sun and re-appearance. Indeed Mars in particular at the time when it is visible throughout the night seems to equal Jupiter in size, though marked out by its reddish colour; yet it is scarcely distinguishable among stars of the second magnitude, though recognized by those who track it with careful attention. All these phenomena proceed from the same course, which lies in the motion of the Earth. But the fact that none of these phenomena appears in the fixed stars shows their immense elevation, which makes even the circle of their annual motion, or apparent motion, vanish from our eyes. "

"I have no doubt that certain learned men, now that the novelty of the hypotheses in this work has been widely reported—for it establishes that the Earth moves, and indeed that the Sun is motionless in the middle of the universe—are extremely shocked, and think that the scholarly disciplines, rightly established once and for all, should not be upset. But if they are willing to judge the matter thoroughly, they will find that the author of this work has committed nothing which deserves censure. For it is proper for an astronomer to establish a record of the motions of the heavens with diligent and skilful observations, and then to think out and construct laws for them, or rather hypotheses, whatever their nature may be, since the true laws cannot be reached by the use of reason; and from those assumptions the motions can be correctly calculated, both for the future and for the past. Our author has shown himself outstandingly skilful in both these respects. Nor is it necessary that these hypotheses should be true, nor indeed even probable, but it is sufficient if they merely produce calculations which agree with the observations... For it is clear enough that this subject is completely and simply ignorant of the laws which produce apparently irregular motions. And if it does work out any laws—as certainly it does work out very many—it does not do so in any way with the aim of persuading anyone that they are valid, but only to provide a correct basis for calculation. Since different hypotheses are sometimes available to explain one and the same motion (for instance eccentricity or an epicycle for the motion of the Sun) an astronomer will prefer to seize on the one which is easiest to grasp; a philosopher will perhaps look more for probability; but neither will grasp or convey anything certain, unless it has been divinely revealed to him. Let us therefore allow these new hypotheses also to become known beside the older, which are no more probable, especially since they are remarkable and easy; and let them bring with them the vast treasury of highly learned observations. And let no one expect from astronomy, as far as hypotheses are concerned, anything certain, since it cannot produce any such thing, in case if he seizes on things constructed for another other purpose as true, he departs from this discipline more foolish than he came to it."

"Those who knew that the judgements of many centuries had reinforced the opinion that the Earth is placed motionless in the middle of heaven, as though at its centre, if I on the contrary asserted that the Earth moves, I hesitated for a long time whether to bring my treatise, written to demonstrate its motion, into the light of day, or whether it would not be better to follow the example of the Pythagoreans and certain others, who used to pass on the mysteries of their philosophy merely to their relatives and friends, not in writing but by personal contact, as the letter of Lysis to Hipparchus bears witness. And indeed they seem to me to have done so, not as some think from a certain jealousy of communicating their doctrines, but so that their greatest splendours, discovered by the devoted research of great men, should not be exposed to the contempt of those who either find it irksome to waste effort on anything learned, unless it is profitable, or if they are stirred by the exhortations and examples of others to a high-minded enthusiasm for philosophy, are nevertheless so dull-witted that among philosophers they are like drones among bees. "

"I myself consider that gravity is merely a certain natural inclination with which parts are imbued by the architect of all things for gathering themselves together into a unity and completeness by assembling into the form of a globe. It is easy to believe that the Sun, Moon and other luminaries among the wandering stars have this tendency also, so that by its agency they retain the rounded shape in which they reveal themselves, but nevertheless go round their orbits in various ways. If then the Earth also performs other motions, as for example the one about the centre, they must necessarily be like those which are similarly apparent in many external bodies in which we find an annual orbit. "

"In the midst of all dwells the Sun. For who could set this luminary in another or better place in this most glorious temple, than whence he can at one and the same time brighten the whole."

"Astronomers of my day are so inconsistent in these [astronomical] investigations ... that they cannot even explain or observe the constant length of the seasonal year. With them, it is as though an artist were to gather the hands, feet, head and other members for his images from diverse models, each part excellently drawn, but not related to a single body, and since they in no way match each other, the result would be monster rather than man. "

"To know that we know what we know, and to know that we do not know what we do not know, that is true knowledge."

"Finally we shall place the Sun himself at the center of the Universe. All this is suggested by the systematic procession of events and the harmony of the whole Universe, if only we face the facts, as they say, 'with both eyes open'. "

"For a long time then, I reflected on this confusion in the astronomical traditions concerning the derivation of the motions of the universe's spheres. I began to be annoyed that the movements of the world machine, created for our sake by the best and most systematic Artisan of all, were not understood with greater certainty by the philosophers, who otherwise examined so precisely the most insignificant trifles of this world. For this reason I undertook the task of rereading the works of all the philosophers which I could obtain to learn whether anyone had ever proposed other motions of the universe's spheres than those expounded by the teachers of astronomy in the schools. And in fact I found in Cicero that Hicetas supposed the earth to move. Later I also discovered in Plutarch that certain others were of this opinion. . . . Therefore, having obtained the opportunity from these sources, I too began to consider the mobility of the earth."

"For I am not so enamored of my own opinions that I disregard what others may think of them. I am aware that a philosopher's ideas are not subject to the judgment of ordinary persons, because it is his endeavor to seek the truth in all things, to the extent permitted to human reason by God. Yet I hold that completely erroneous views should be shunned. Those who know that the consensus of many centuries has sanctioned the conception that the earth remains at rest in the middle of the heaven as its center would, I reflected, regard it as an insane pronouncement if I made the opposite assertion that the earth moves."

"I am aware that a philosopher's ideas are not subject to the judgment of ordinary persons, because it is his endeavour to seek the truth in all things, to the extent permitted to human reason by God."

"The earth together with its surrounding waters must in fact have such a shape as its shadow reveals, for it eclipses the moon with the arc of a perfect circle."

"We regard it as a certainty that the earth, enclosed between poles, is bounded by a spherical surface."

"The massive bulk of the earth does indeed shrink to insignificance in comparison with the size of the heavens."

"Moreover, since the sun remains stationary, whatever appears as a motion of the sun is really due rather to the motion of the earth."

"At rest, however, in the middle of everything is the sun. For, in this most beautiful temple, who would place this lamp in another or better position than that from which it can light up the whole thing at the same time? For, the sun is not inappropriately called by some people the lantern of the universe, its mind by others, and its ruler by still others. The Thrice Greatest labels it a visible god, and Sophocles' Electra, the all-seeing. Thus indeed, as though seated on a royal throne, the sun governs the family of planets revolving around it."

"Yet if anyone believes that the earth rotates, surely he will hold that its motion is natural, not violent."

"I shall now recall to mind that the motion of the heavenly bodies is circular, since the motion appropriate to a sphere is rotation in a circle."

"If perchance there should be foolish speakers who, together with those ignorant of all mathematics, will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgment as rash. For it is not unknown that Lactantius, the writer celebrated in other ways but very little in mathematics, spoke somewhat childishly of the shape of the earth when he derided those who declared the earth had the shape of a ball. So it ought not to surprise students if such should laugh at us also. Mathematics is written for mathematicians to whom these our labors, if I am not mistaken, will appear to contribute something even to the ecclesiastical state the headship of which your Holiness now occupies"

"For a traveler going from any place toward the north, that pole of the daily rotation gradually climbs higher, while the opposite pole drops down an equal amount."

"For when a ship is floating calmly along, the sailors see its motion mirrored in everything outside, while on the other hand they suppose that they are stationary, together with everything on board. In the same way, the motion of the earth can unquestionably produce the impression that the entire universe is rotating."

"To know the mighty works of God, to comprehend His wisdom and majesty and power; to appreciate, in degree, the wonderful workings of His laws, surely all this must be a pleasing and acceptable mode of worship to the Most High, to whom ignorance cannot be more grateful than knowledge."

"So far as hypotheses are concerned, let no one expect anything certain from astronomy, which cannot furnish it, lest he accept as the truth ideas conceived for another purpose, and depart from this study a greater fool than when he entered it."

"1) There is no one center in the Universe. 2) The Earth's center is not the center of the Universe. 3) The center of the universe is near the Sun. 4) The distance from the Earth to the Sun is imperceptible compared with the distance to the stars. 5) The rotation of the Earth accounts for the apparent daily rotation of the stars. 6) The apparent annual cycle of movements of the Sun is caused by the Earth revolving around it, and, 7) the apparent retrograde motion of the planets is caused by the motion of the Earth from which one observes."

"The strongest affection and utmost zeal should, I think, promote the studies concerned with the most beautiful objects. This is the discipline that deals with the universe's divine revolutions, the stars' motions, sizes, distances, risings and settings . . . for what is more beautiful than heaven?"

"How could anyone observe the mighty order with which our God governs the universe without feeling himself inclined… to practice all of virtues, and to the beholding of the Creator Himself, the source of all goodness, in all things and before all things?"

"All the spheres revolve about the sun as their mid-point, and therefore the sun is the center of the universe."

"Although all the good arts serve to draw man's mind away from vices and lead it toward better things, this function can be more fully performed by this art, which also provides extraordinary intellectual pleasure."

"Every observed change of place is caused by a motion of either the observed object or the observer or, of course, by an unequal displacement of each."

"First of all, we must note that the universe is spherical."

"For it is not unknown that Lactantius, otherwise a famous writer but a poor mathematician, speaks most childishly of the shape of the Earth when he makes fun of those who said that the Earth has the form of a sphere."

"Accordingly, since nothing prevents the earth from moving, I suggest that we should now consider also whether several motions suit it, so that it can be regarded as one of the planets. For, it is not the center of all the revolutions."

"Assumed by contemporary readers to be written by Copernicus himself, this preface suggested the earth's motion was merely a mathematical device and not to be taken seriously."

"Hence the earth too is evidently enclosed between poles and is therefore spherical."

"I can easily conceive, most Holy Father, that as soon as some people learn that in this book which I have written concerning the revolutions of the heavenly bodies, I ascribe certain motions to the Earth, they will cry out at once that I and my theory should be rejected."

"I therefore took this opportunity and also began to consider the possibility that the Earth moved. Although it seemed an absurd opinion, nevertheless, because I knew that others before me had been granted the liberty of imagining whatever circles they wished to represent the phenomena of the stars, I thought that I likewise would readily be allowed to test whether, by assuming some motion of the Earth's, more dependable representations than theirs could be found for the revolutions of the heavenly spheres."

"In so many and such important ways, then, do the planets bear witness to the earth's mobility."

"For it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study."

"Let no one expect anything of certainty from astronomy, lest if anyone take as true that which has been constructed for another use, he go away... a bigger fool than when he came to it."

"Mathematics is written for mathematicians."

"Let us put these new hypotheses [in] public appearance among the old ones which are themselves no more probable, especially since they are wonderful and easy and bring with them a vast storehouse of learned observations."

"In the first book I shall describe all the positions of the spheres, along with the motions which I attribute to the Earth, so that the book will contain as it were the general structure of the universe. In the remaining books I relate the motions of the remaining stars, and all the spheres, to the mobility of the Earth, so that it can be thence established how far the motions and appearances of the remaining stars and spheres can be saved, if they are referred to the motions of the Earth."

"Near the sun is the center of the universe."

"More stars in the north are seen not to set, while in the south certain stars are no longer seen to rise."

"Moreover, there is no difference between the earth's centers of gravity and magnitude."