This translation adheres to scholarly standards for Renaissance Latin, specifically the scientific prose of Nicolaus Copernicus. Technical terms (such as scrupulus and erraticarum) have been translated according to their 16th-century astronomical context.

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OF NICOLAUS COPERNICUS OF TORUŃ

SIX BOOKS ON THE REVOLUTIONS of the Celestial Spheres.

You have in this work, now recently born and published, diligent reader, the motions of the stars—both the fixed and the wandering—restored from both ancient and recent observations: and moreover adorned with new and admirable hypotheses. You also have most efficient Tables, from which you will be able to calculate these same motions for any time with the greatest ease. Therefore buy, read, and enjoy.

"Let no one untrained in geometry enter"

Nuremberg, at the house of Johannes Petreius,
In the Year 1543.

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PAGE 22

The printed work having been reviewed and compared again with the autograph [manuscript], you shall take care to correct the following. The first number is of the leaves [folios], while the second is of the lines. The dots added denote the faces of the leaves: one for the first [recto], and two for the second [verso].

Folio 4, line 10, read posset. 6. 33. agitentur. 7. 19. terræ. 8: 14, quiddam. 13: 18, circulum. 20: 12: quam. 22. 7. Si ex K signo. 22. 20. duplam. 23. 14. rectum E angulum. 23. 15. where it has E, delete E. 23: 9, for B I, read E I. 26. 35. subtendentis duplum. 30. for K in the south pole, replace with H, of the first figure. 30: 30: for 19 replace with 29. 31: 1: in the first of the differences for 55. 50. 45. 40. 35. 3. put 0 for each. 35: 13, for perpendiculare, put ad angulos rectos [at right angles]. 45: 15, compertam. 50. 29. minor. 50. 35. for $1\frac{1}{2}$ read $0\frac{1}{2}$. 50: 20, for $20\frac{1}{2}$ read $29\frac{1}{2}$. 51. 17. for [p] 5. read 3. 54: 23, maior adijciat. In the same place, line 25. for [p] 269 $\frac{1}{2}$ read 169 $\frac{1}{2}$. 55. 6. for 165 $\frac{1}{2}$ read 165 $\frac{1}{12}$. 55: 16. for 124 read 327 $\frac{1}{6}$. 61. 22. for 196 $\frac{1}{8}$ read 186 $\frac{1}{6}$. 61. 32. for 41$\frac{1}{3}$ read 40$\frac{1}{3}$. 65. 30. whenever you see Albategnius, understand it to be Machometus Aracensis [al-Battani]. 66: 35: unitur l medio. 72: 26: for quibus, read Nam hic. These things which follow up to Sed quoniã, folio 73, line 13, are to be rejected to the end of the seventh chapter; the rest are consequently to be corrected thus. 72: 33: for dextantes graduum [ten-twelfths of a degree], read 1 degree and a sextant [one-sixth]. 72: 34, for one part and 40 scruples, read two parts and 20 scruples. 73. 9. for [p] 50 scruples, read 70. 73 11. for [p] 20 scruples, read 28. 73. 13. for [p] 20 scruples, read 28. 74. 14. for [p] 28. read 48. 75: 1: existit. 77. 9. for [p] 101 days, read 106. [Note: Latin C I S often denotes 106 in specific contexts or is a correction to CIS]. 77. 32. for [p] V of anomaly, read LV. 79. 26. quadrãs. 84. 29. read Homocentricos A B C. 86: 20, for E D B read E D F. 87: 4, pars dici, read partibus. 90. 31. loca, æquinoctialium. 91. in this figure join D I and O I with straight lines. 93: 35: read coagmentatos. 96: 2: for sunt read fiunt. Same place, line 10, for motu pertransire, read motu composito pertransire. 96. 18. naturalium, 100: 11: autem atq; in F. read autem in F. 101. 31. ipsis. 102. 8. for CLXVIII. read CXLVIII. Same place, line 12. for in read non. Same place, line 22. abundant. 106. 18. for XXXIII. read XXXIIII. 107: 21: for B C, C D, read B E, C E. Same place, line 24. for E C read B C. 108: 3: for 2 scruples, 1. Same place, line 33. read quod sub F. 109. 4. for D F L, read D E L. Same place, line 12. for G B C, read G C B. Same place, line 24 for motus read locus. Same place, line 26. for CLXX. read CLXXVII. Same place, line 29. longitudinis et anomaliæ. 109: 5: four of one degree. 110. 20. for XXXIX, read XXXVIII. 111. in this figure let E M and E L be connected with straight lines. 116: 18: for XI. read XVI. of Scorpio. 117. 6. for 56 scruples, read 55. 119. 18. for autem read etiam. 119: 12: read eius à uertice. 120. 4. for XII. read VII. 121. 19 for quo read qua. 121: 13: first to the scruples. 122: 22, read 1000000. Same place, line 32, read 1000000. 123: 24, 32 seconds of a scruple. 124 line 27. for differentiæ quinto, read differentias, quibus. 125. in this figure the circumference R E was to be taken from the right. 127: 17. read, Luna filitudinis. Same place, line 26. read D B E et sumpta. Same place, line 33. read, breuiora angulos. 128. 25. for A B, D A recto, read A B D à recto. 129. 4. read in fine horæ. 130: 35, for horarium, read horarum. 131: 11, for illic read hic. 134. 17. read reperiuntur. 134: 3, read for [p] LXIX, LIX. Same place, line 19 read diei scrupulus. Same place, line 21. for XXI, read XXXI. Same place, line 32. for IIII. read XL. 140: 29, read fin deferentis. Same place, line 32. read, at iam in Mercurio, ac magis accidere. 141. 30. read addet medio. 142. in this figure for T, read R. 142: 12, read differentia tamen insensibili. Same place, line 27. for erit read erat. 144: 3, for 864, read 854. Same place, line 18. for XX VI read XXXVI. 145. 1. read perueniret. 145: 13. for [p] CCLXXII, read CCLXXIII. Same place, line 7. for A D E, read A E D. Same place, line 18. for LXXVIII. read LXVIII. Same place, line 25. for ei, read fi, for dimetientis, read dimetiens. 146. 30. read quod sub G D, D H, sed quod sub G D. Same place, line 36. for S T read F D.

NICOLAUS

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FIRST BOOK OF THE REVOLUTIONS

OF NICOLAUS COPERNICUS.

That the universe is spherical. Chapter I.

FIRST we must observe that the universe is globular, either because that very form is the most perfect of all, needing no joint, being a complete whole; or because it is the most capacious of figures, which most suits that which is to contain and preserve all things; or even because the most absolute parts of the universe—I mean the Sun, the Moon, and the stars—are observed in such a form; or because all things seek to be bounded by this form, which appears in drops of water and other liquid bodies, when they desire to be bounded by themselves. Therefore, no one should doubt that such a form has been attributed to the celestial bodies.

That the earth also is spherical. Chapter II.

The Earth also is globular, since from every part it rests upon its center. Although a perfect sphere is not immediately seen in such great height of mountains and descent of valleys, these nevertheless vary the universal roundness of the earth the least bit. This is manifest thus: for to those traveling toward the North from any direction, that pole of the diurnal revolution is gradually raised, while the other is lowered by just as much on the opposite side, and more stars about the North are seen not to set, and in the South certain stars no longer rise. Thus Italy does not see Canopus, which is visible to Egypt. And Italy sees the last star of the River [Eridanus], which our region of a colder climate does not know. On the contrary, to those passing toward the South, those stars are raised, while those which are high to us sink. Meanwhile, the very inclinations of the poles have the same ratio everywhere relative to the measured spaces of the earth, which happens in no other figure than a spherical one. From which it is manifest that the earth also is enclosed by poles, and for this reason is globular. Add also, that the evening eclipses of the Sun and Moon are not perceived by the inhabitants of the East, nor the morning ones by those living in the west; while those in the middle see them, the former indeed later, the latter truly earlier. Navigators also perceive that the waters rest upon the same form, since land which is not seen from a ship is frequently viewed from the top of the mast. And conversely, if something shining is placed on the top of the mast, as the ship moves away from land, it seems to those remaining on the shore to gradually descend, until at last it is hidden as if setting. It is also certain that waters, flowing by their nature, always seek lower places—the same as the earth—and do not strive further from the shore than its convexity allows. For which reason, it follows that the earth is so much higher wherever it rises out of the Ocean.

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NICOLAUS COPERNICUS

How the earth with water forms one globe. Chapter III.

Therefore the surrounding Ocean, pouring forth seas everywhere, fills its deeper descents. And so it was necessary that there be less water than earth, so that the water would not absorb the whole earth—both contending toward the same center by their weight—but so that it might leave some parts of the earth for the safety of living things, and so many islands open here and there. For what else is the continent itself and the world of lands but an island larger than the others? Nor should certain of the Peripatetics be heard, who declared that the universal water is ten times greater than the whole earth. Namely, because in the transmutation of elements, ten parts of water are made from the resolution of one part of earth; taking this conjecture, they say that the earth juts out to some extent because, being cavernous, it is not balanced everywhere according to its weight, and that the center of gravity is one thing, and the center of magnitude another. But they are deceived by ignorance of the geometric art, not knowing that water cannot be even seven times greater so that some part of the earth might remain dry, unless the earth vacated the center of gravity entirely and gave place to the waters as being heavier than itself. Since spheres are to one another in the triple ratio of their diameters [i.e., volume is proportional to the cube of the diameter]. If therefore the earth were the eighth part to seven parts of water, its diameter could not be greater than that which extends from the center to the circumference of the waters; much less could the water be even ten times greater. That there is also no difference between the center of gravity of the earth and the center of its magnitude can be taken from this: that the convexity of the earth extending from the ocean does not continually swell in its withdrawal, for otherwise it would keep back the sea waters as much as possible, and would in no way allow the internal seas and such vast gulfs to break in. Again, the increased depth of the abyss would not cease as one moves from the shore of the ocean, whereby neither an island, nor a rock, nor any bit of land would be encountered by sailors who had progressed further. Now indeed it is certain that between the Egyptian Sea and the Arabian Gulf, scarcely fifteen stadia remain in almost the middle of the world. And conversely, Ptolemy in his Cosmography extended the habitable land to the middle circle [the equator], leaving moreover unknown land, where more recent authors have added Cathay and very ample regions even to 60 degrees of longitude: so that now the earth is inhabited for a greater longitude than what remains for the ocean. This will be clearer if the islands found in our age under the Princes of Spain and Portugal are added, and especially America—named after the ship's captain who discovered it—which they consider to be another world of lands because of its size still unknown, whereby we should even less wonder that there are Antipodes or Antichthones. For geometric reason compels us to believe that America itself is diametrically opposite to that part of India on the Ganges, based on its location. From all these things at last, I think it is manifest that the earth and water together rest upon one center of gravity, and that there is no other center of magnitude for the earth; which [earth], since it is heavier, has its gaping parts filled with water, and therefore the water is modest in comparison with the earth, even if perhaps more water appears on the surface. For it is necessary that the earth with the surrounding waters have such a figure as its shadow shows: for it makes the Moon fail [in eclipse] with the circumferences of a perfect circle. Therefore the earth is not flat, as Empedocles and Anaximenes thought; nor drum-shaped, as Leucippus; nor boat-shaped, as Heraclitus; nor hollow in another way, as Democritus. Nor again cylinder-shaped as Anaximander; nor extending from its lower part with an infinite thickness of roots, as Xenophanes, but with an absolute roundness, as the Philosophers believe.

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NICOLAUS COPERNICUS

That the motion of the celestial bodies is uniform, circular, and perpetual, or composed of circular motions. Chapter IIII.

After these things we shall recall that the motion of the celestial bodies is circular. For the mobility of a Sphere is to be turned in a circle, expressing its form by that very act, in the simplest body, where it is not possible to find a beginning nor an end, nor to distinguish one from the other, while it moves through the same things into itself. There are, however, several motions according to the multitude of orbs. The most manifest of all is the daily revolution, which the Greeks call nychthēmeron, that is, the space of a day and night. By this, the whole universe is thought to glide from east to west, the earth excepted. This is understood as the common measure of all motions, since we also measure time itself chiefly by the number of days. Then we see other revolutions as if struggling against it, that is, from west to east—namely, those of the Sun, the Moon, and the five wandering stars. Thus the Sun dispenses the year to us, and the Moon the months, the most common times; so each of the other five planets makes its own circuit. They are nevertheless in manifold difference: first, because they are not turned around the same poles as that first motion, running through the obliquity of the zodiac [signiferi]. Then, because in their own circuit, they are not seen to be carried uniformly; for the Sun and Moon are detected to be sometimes slow, sometimes swifter in their course. The other five wandering stars, however, we see sometimes even to go backward, and to make stations here and there. And while the Sun always proceeds on its own direct path, they wander in various ways, straying now to the South, now to the North, whence they are called "planets." Add also that sometimes they become nearer to the earth, and are called Perigee, at other times more remote, and are called Apogee. One must nevertheless confess that the motions are circular, or composed of several circles, because these types of inequalities observe a certain law and fixed restitutions, which could not happen if they were not circular. For it is the circle alone that can bring back what has been completed, just as, for example, the Sun, by a motion composed of circles, brings back to us the inequality of days and nights and the four seasons of the year.

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REVOLUTIONS LIB. I.

In which [the year] several motions are understood. Since it cannot be that a simple celestial body moves irregularly in a single orb. For that would have to happen either because of the inconstancy of the moving power—whether it be derived from without or from an intimate nature—or because of a disparity in the revolved body. Since the intellect shrinks from both, and it is unworthy that such a thing be imagined in those things which are constituted in the best order: it is consistent that their uniform motions appear to us as irregular, either because of the different poles of those circles, or even because the earth is not in the middle of the circles in which they revolve; and to us looking from the earth, it happens because of the unequal distances of these stars that the things nearer to themselves seem larger than those more remote (as is demonstrated in optics); thus in equal circumferences of an orb, because of the different distance of sight, the motions will appear unequal in equal times. For which cause I think it is necessary above all that we carefully observe what the relationship [habitudo] of the earth to the heaven is, lest while we wish to scrutinize the highest things, we are ignorant of those closest to us, and by the same error attribute to celestial things that which belongs to the earth.

Whether circular motion belongs to the earth, and concerning its location. Chapter V.

Now because it has been demonstrated that the earth also has the form of a globe, I think we must see whether motion also follows its form, and what place in the universe it occupies, without which it is not possible to find a certain reason for the appearances in the heaven. Although it is generally agreed among authors that the earth rests in the middle of the universe, so that they think it unthinkable and even ridiculous to feel the contrary. If nevertheless we consider the matter more attentively, it will be seen that this question is not yet settled, and for that reason is by no means to be despised. For every change of place that is seen is either because of the motion of the thing observed, or of the observer, or certainly a disparate change of both. For between things moved equally toward the same things, motion is not perceived—I mean between the thing seen and the observer. The earth, however, is that from which that celestial circuit is viewed and reproduced to our sight. If therefore some motion is assigned to the earth, it will appear the same in all things which are outside it, but in the opposite direction, as if they were passing by; such is the daily revolution first of all. For this seems to snatch the whole universe, except for the earth and those things which are around it. But if you allow the heaven to have nothing of this motion, but that the earth revolves from west to east, if you seriously consider it as far as the apparent rising and setting in the Sun, Moon, and Stars, you will find these things to be so. Since it is the heaven which contains and covers all things, the common place of the universe, it does not immediately appear why motion should not be attributed to the thing contained rather than the container, the located rather than the locater. Certainly Heraclides and Ecphantus the Pythagoreans were of this opinion, and Nicetas of Syracuse in Cicero, revolving the earth in the middle of the universe. For they thought that the stars set by the obstruction of the earth, and rose by its withdrawal. This being assumed, there follows also another, and no less a doubt concerning the location of the earth, although it has now been received and believed by almost everyone that the earth is the middle of the universe. Because if someone denies that the earth occupies the middle or center of the universe, yet does not confess that the distance is so great that it would be comparable to the sphere of the non-wandering stars [fixed stars], but is significant and evident to the orbs of the Sun and other stars, and thinks for that reason their motion appears different, as if they were regulated to another center than the center of the earth, he might perhaps be able to bring forth a not inept reason for the different apparent motion. For that the wandering stars are seen nearer to the earth and the same ones further away, necessarily proves that the center of the earth is not the center of those circles. Whereby it is even less clear whether the earth approaches and recedes from them, or they from the earth. Nor would it be so surprising if someone, besides that daily revolution, should imagine another motion for the earth; namely, that the earth revolves, and even wanders with several motions, and is one of the stars, as Philolaus the Pythagorean is said to have felt—a mathematician of no common sort, since for the sake of visiting him, Plato did not delay to seek Italy, as those who wrote the life of Plato relate. Many indeed have thought it could be demonstrated by geometric reason that the earth is in the middle of the universe, and like a point to the immensity of the heaven, occupying the role of the center, and for that reason is immobile, because when the universe is moved, the center remains unmoved, and those things which are nearest to the center are carried slowest.

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REVOLUTIONS LIB. I.

On the immensity of the heaven compared to the size of the earth. Chapter VI.

That so great a mass of the earth, however, has no estimation compared to the magnitude of the heaven can be understood from this. Since the limiting circles (for so horizontes are interpreted among the Greeks) bisect the whole sphere of the heaven, which could not happen if the size of the earth were significant compared to the heaven, or its distance from the center of the universe. For a circle bisecting a sphere passes through the center of the sphere, and is the greatest of the circumscribable circles. For let the horizon be the circle A B C D, while the earth from which our sight is, be E, and let E itself be the center of the horizon in which the visible things are defined from the non-visible. Let there be observed through a Dioptra or a Horoscopium, or a Chorobates placed in E, the beginning of Cancer rising at point C, and at that moment the beginning of Capricorn appears to set at A. Since therefore A E C were in a straight line through the Dioptra, it is certain that it is the diameter of the zodiac, because six Signs terminate a semicircle, and the center E is the same as that of the horizon. Again, the revolution being changed, so that the beginning of Capricorn rises in B, then also the setting of Cancer will be seen in D; and B E D will be a straight line and itself the diameter of the zodiac. Now indeed it has appeared that A E C is also a diameter of the same circle; it is clear therefore that in the common section, that E is the center. So therefore the horizon circle always bisects the zodiac, which is the greatest circle of the sphere. But in a sphere, if a circle bisects any of the greatest circles, it is itself also a greatest circle; therefore the horizon is one of the greatest circles, and its center the same as that of the zodiac, as it appears, although it is nevertheless necessary that the line which is from the surface of the earth be different from that which is from the center; but because of the immensity with respect to the earth, they become in a certain way similar to parallels, which because of excessive distance of the limit appear to be one line, when the mutual space which contains them is made incomparable to their length in sense, in the way that is demonstrated in Optics.

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NICOLAUS COPERNICUS

By this argument it appears clearly enough that the heaven is immense compared to the earth, and presents the appearance of infinite magnitude, but by the estimation of the senses the earth is with respect to the heaven as a point to a body, and the finite to the infinite in magnitude, nor does it seem to have demonstrated anything else. For it does not follow that the earth must rest in the middle of the universe. Rather, we might even more wonder if such a vastness of the universe should revolve within the space of 24 hours, instead of its smallest part, which is the earth. For as they say the center is immobile, and those things nearest to the center move less, this does not prove that the earth rests in the middle of the universe: no differently than if you say that the heaven revolves but the poles rest, and those things nearest to the poles move least. Just as Cynosura [the Little Bear] is seen to move much more slowly than Aquila or Canicula [Sirius], because it describes a smaller circle nearest the pole; since all those things belong to one sphere, whose mobility ending at its own axis does not allow an equal motion for all its parts, which nevertheless the revolution of the whole brings back in equality of time but not equality of space. To this, therefore, the reason of the argument leans: as if the earth were a part of the celestial sphere, and of the same species and motion, so that being nearest the center it would move little. It will therefore be moved itself, being a body, and not the center, in the same time through similar circumferences of the celestial circle, although smaller. How false this is, is clearer than light: for it would be necessary that it always be noon in one place, and always midnight in another, so that neither the daily risings nor settings could happen, since there would be one and inseparable motion of the whole and the part. But of those things which the difference of nature separates, the reason is far different, so that those which are enclosed in a shorter circuit are revolved more quickly than those which encompass a larger circle. Thus Saturn, the highest of the wandering stars, is revolved in the thirtieth year; and the Moon, which is undoubtedly nearest to the earth, completes its monthly circuit; and finally the earth itself will be thought to circle in the space of a day and night. Therefore the same doubt about the daily revolution will rise again. But even its location is still sought, even less certain from the things said above. For that demonstration contains nothing else than the indefinite magnitude of the heaven to the earth. But to what extent this immensity extends is by no means certain.