Three Treatises on Copernican Theory

By Nicolaus Copernicus

Universally regarded as a founder of modern astronomy, Copernicus wrote in Latin, and his works were unavailable in English until the publication of this 1939 translation. A three-part collection, it consists of the "Commentariolus," Copernicus' sketch of his hypotheses for the heavenly motions; "Narratio Prima," Georg Joachim Rheticus' popular introduction to Copernican theory; and "The Letter Against Werner," Copernicus' refutation of the views of one of his contemporaries.
The historical relevance of the "Commentariolus" and "Narratio Prima" is hard to overstate; these are the works that launched a revolution in the scientific perception of the universe. The inclusion of "The Letter Against Werner" offers an item of intrinsic interest that sheds light on the development of the great astronomer's thought. This revised edition of the original translation features extensive editorial apparatus, including an Introduction with biographies of Copernicus and his disciple, Georg Joachim Rheticus; background information on each treatise; and an index.

• Language: English
• Publisher: Dover Publications
• Release date: Oct 17, 2018
• ISBN: 9780486835334

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THREE TREATISES ON COPERNICAN THEORY

Nicolaus Copernicus

The Commentariolus of Copernicus

The Letter against Werner

The Narratio prima of Rheticus

Translated with Introduction and Notes by

Edward Rosen

Revised Second Edition

DOVER PUBLICATIONS, INC.

MINEOLA, NEW YORK

DOVER THRIFT EDITIONS

GENERAL EDITOR: SUSAN L. RATTINER

EDITOR OF THIS VOLUME: JIM MILLER

Copyright

Copyright © 1939, 1959 by Edward Rosen

All rights reserved.

Bibliographical Note

This Dover edition, first published in 2018, is a republication of the 1959 Dover revised second edition of Three Copernican Treatises, originally published in 1939 by the Columbia University Press, New York. The annotated Copernicus Bibliography, 1939–1958, from the 1959 edition is available online at: www.doverpublications.com/0486827755.

Library of Congress Cataloging-in-Publication Data

Names: Copernicus, Nicolaus, 1473–1543, author. | Rosen, Edward, 1906– editor, translator.

Title: Three treatises on Copernican theory : the Commentariolus of Copernicus : the Letter against Werner : the Narratio prima of Rheticus / Nicholas Copernicus; translated with an introduction and notes by Edward Rosen.

Other titles: Commentariolus. English

Description: Second edition, Dover edition [2018 edition]. | Mineola, New York : Dover Publications, Inc., 2018. | Originally published as thesis of Edward Rosen (Ph. D.)—Columbia University, 1939. | Republication of: New York : Dover Publications, 1959, revised second edition. | Includes bibliographical references and index.

Identifiers: LCCN 2018023411| ISBN 9780486827759 | ISBN 0486827755

Subjects: LCSH: Astronomy—Early works to 1800. | Werner, Johannes, 1468-1528. De motu octavae sphaerae. | Copernicus, Nicolaus, 1473–1543. Epistola Coppernici contra Wernerum. English. | Rhèaticus, Georg Joachim, 1514–1576. De libris revolutionum Nicolai Copernici narratio prima. English.

Classification: LCC QB41 .C84 2018 | DDC 520—dc23

LC record available at https://lccn.loc.gov/2018023411

Manufactured in the United States by LSC Communications

82775501 2018

www.doverpublications.com

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PREFACE

IT IS a matter of amazement and regret to many persons interested in the history of civilization that the writings of Copernicus, universally regarded as the founder of modern astronomy, have not yet been made available in the English language. When Professor Frederick Barry suggested that I might attempt to satisfy this need, he pointed out that the Commentariolus and the Narratio prima are better suited to convey Copernicus’s ideas to the general reader than is his classic work De revolutionibus orbium caelestium. For these treatises are briefer, and they are relatively free from the extensive calculations necessarily included in the volume that established the heliocentric system. There is, moreover, a historical reason for reproducing the Commentariolus and the Narratio prima; for it was by these papers from the hands of the rebel cosmic architect and his first disciple that the learned world was first apprised of the revolution in the conceptual structure of the universe.

The Letter against Werner possesses intrinsic interest of its own. It throws light on the development of Copernicus’s thought. The letter and the Commentariolus constitute his minor astronomical works. For these reasons it was included in this book.

I desire to record my gratitude to Professor Austin P. Evans for his editorial guidance. To the many friends and colleagues who have cheerfully given me of their special knowledge I express heartfelt thanks. For the errors that nevertheless appear—and it is rash to hope that a book of this sort can be entirely free from error—full and sole responsibility rests upon the author.

E. R.

College of the City of New York

September 4, 1939

CONTENTS

INTRODUCTION

Nicolaus Copernicus

George Joachim Rheticus

The Commentariolus

The Letter against Werner

The Narratio prima

The Doctrine of the Spheres

The Title of the Commentariolus and the Views of Copernicus concerning the Nature of Astronomical Hypotheses

Deferent and Epicycle, Eccentric and Equant

COMMENTARIOLUS

Assumptions

The Order of the Spheres

The Apparent Motions of the Sun

Equal Motion Should Be Measured Not by the Equinoxes But by the Fixed Stars

The Moon

The Three Superior Planets

Venus

Mercury

LETTER AGAINST WERNER

NARRATIO PRIMA

The Motions of the Fixed Stars

General Consideration of the Tropical Year

The Change in the Obliquity of the Ecliptic

The Eccentricity of the Sun and the Motion of the Solar Apogee

The Kingdoms of the World Change with the Motion of the Eccentric

Special Consideration of the Length of the Tropical Year

General Considerations regarding the Motions of the Moon

The Principal Reasons Why We Must Abandon the Hypotheses of the Ancient Astronomers

Transition to the Explanation of the New Hypotheses

The Arrangement of the Universe

The Motions Appropriate to the Great Circle and Its Related Bodies

Librations

The Second Part of the Hypotheses

The Motions of the Five Planets

The Hypotheses for the Motions in Longitude of the Five Planets

The Apparent Deviation of the Planets from the Ecliptic

In Praise of Prussia

BIBLIOGRAPHICAL NOTE

INDEX

ABBREVIATIONS

In references to texts the page number is followed by a period and the line number: e.g., Th 447.8.

In references to books which are numbered by leaf, not by page, r stands for recto, and v for verso: e.g., Conrad Gesner, Bibliotheca universalis, Appendix, p.5v.

In references to early printed books which are numbered by signature, the citation gives the page number within the signature: e.g., Augustinus Ricius, De motu octavae sphaerae, fol. e6r.

INTRODUCTION

NICOLAUS COPERNICUS

NICOLAUS COPERNICUS was born in 1473 at Thorn on the banks of the Vistula. His father was a prosperous merchant and municipal official in the old Hansa town. But he died when Nicolaus was only ten years old; and it was the boy’s good fortune to have for maternal uncle Lucas Watzelrode, who became Bishop of Ermland in 1489. The uncle took a fatherly interest in the nephew, guiding his way and smoothing his path. While Copernicus was still a young man, Bishop Lucas designated him a canon of the Cathedral of Frauenburg. ¹ He enjoyed the income from this ecclesiastical post until his death (May 24, 1543) at the scriptural age of seventy; and before he was thirty years old, he received in addition an appointment to a sinecure at Breslau.

Copernicus had his elementary schooling in his native city and entered the University of Cracow in 1491. After several years of attendance at the renowned Polish center of learning, he journeyed to Italy in 1496. At Bologna and Padua he studied the liberal arts, medicine, and law, obtaining the doctor’s degree in canon law at Ferrara in 1503.

Shortly after his return from Italy his first published work appeared from the press, a translation of an inferior Greek epistolographer into Latin. But it was not only in this concern with classical antiquity that Copernicus showed himself a man of the Renaissance. He also strove to achieve the many-sided accomplishments of that humanistic ideal, the universal man. He was competent in canon law; he practiced medicine; he wrote a tract on coinage; he served his cathedral chapter as an administrator and diplomatic representative; he painted his own portrait; he made many of his own astronomical instruments; and he established the heliocentric system on a firm basis.

Germans and Poles have bitterly disputed the question of Copernicus’s ethnic origin, each national group claiming the distinguished astronomer for its own. Where does the truth lie in this controversy? Politically, Copernicus was a subject of the king of Poland; he remained loyal to the Roman Catholic church; and he wrote chiefly in Latin, but a few of his private letters were composed in German.

GEORGE JOACHIM RHETICUS

George Joachim was born on February 16, 1514, at Feldkirch in the ancient Roman province of Rhaetia. In conformity with the strong classical tradition of his day he assumed the surname Rheticus. He was apparently reared in comfortable circumstances, for his parents took him in his youth to Italy.

After studying at Zürich, in 1532 he entered the University of Wittenberg, where he obtained his degree. He continued his studies at Nuremberg and Tübingen and then received an appointment as professor of mathematics at Wittenberg. He began his teaching during the academic year 1536–37.

Reports concerning Copernicus’s innovations in astronomy had reached the young man, and he was filled with great eagerness to become acquainted with the new system. But how was he to do this? Copernicus had published nothing. Rheticus resolved to seek out the aged scholar at Frauenburg and to master the new astronomy at its source.

Accordingly he set out for Prussia in the spring of 1539. Copernicus received him cordially and was his host for more than two years despite religious difficulties. Rheticus came from the principal stronghold of Protestantism, and there was bitter anti-Lutheran feeling in official Ermland. In this atmosphere of religious animosity the Protestant professor lived with the Catholic canon and studied his system with enthusiasm.

But Rheticus did not confine his studies to astronomy. On the basis of extensive travel during his stay in Prussia, he prepared a map of the region. Though the map has not been preserved, an accompanying essay on the methods of drawing maps is extant.² Two other works written during this period have both disappeared. The one was devoted to proving that the new astronomy did not contradict Scripture; the other was a biography of Copernicus. The loss of the latter is particularly unfortunate, for an account written by one so close to the great astronomer would undoubtedly throw valuable light on many obscurities in the life of Copernicus.

Rheticus left Prussia at the end of September, 1541.³ He returned to Wittenberg, resumed his teaching, and served as dean of the arts faculty in the early months of 1542. He also supervised the separate printing of the trigonometrical portion of Copernicus’s De revolutionibus orbium caelestium.

He left Wittenberg in 1542 and went to Nuremberg, where the great work was being printed. The early sections were set up under his supervision; but after his departure for Leipzig his place was taken by Andreas Osiander, of whom we shall hear more below.

Rheticus taught at the University of Leipzig from 1542 to 1551. Before he resigned, he published an ephemeris for 1551. After his resignation he devoted himself principally to the calculation of an extensive set of trigonometric tables, for which he has an independent place in the history of mathematics. In this work he received welcome financial assistance from the Emperor Maximilian II and several Hungarian nobles.

It is a curious circumstance that Rheticus was requited for the support and encouragement he brought to the old age of Copernicus. The closing years of his own life were brightened by the interest taken in his project by a young man, Lucius Valentine Otho. The tables on which he worked for a quarter of a century were finally printed in 1596, twenty years after his death, as the Opus palatinum de triangulis, begun by George Joachim Rheticus and completed by L. Valentine Otho.

THE COMMENTARIOLUS

Some years before Copernicus consented to the publication of his large work De revolutionibus orbium caelestium, he wrote a brief sketch (commentariolus) of his astronomical system. The Commentariolus was not printed during the life of its author; but a number of handwritten copies circulated for a time among students of the science,⁴ and then disappeared from view for three centuries. A copy found in Vienna was published by Maximilian Curtze in 1878.⁵ A second copy found in Stockholm was published in 1881.⁶ On Curtze’s collation⁷ of these two manuscripts Leopold Prowe based the text⁸ from which the present translation was made. A third manuscript⁹ is believed to exist in Leningrad; so far as I know, it has never been published.

The opening section of the Commentariolus was translated by Prowe.¹⁰ L. A. Birkenmajer published a partial translation of the work into Polish.¹¹ The only complete translation previous to the present one was done in German by Adolf Müller.¹²

The date of composition of the Commentariolus cannot be precisely determined.¹³ But an examination of its contents shows conclusively that the Commentariolus expounds a heliocentric system which differs in several essential features from the system taught by the mature Copernicus in the De revolutionibus. The earlier view may be called concentrobiepicyclic, and the later eccentrepicyclic; the meaning of these terms will be made clear later on. To Ludwik Birkenmajer must be assigned the credit for first pointing out that the two systems are independent, or rather that the Commentariolus is a first stage in the development of the heliocentric theory in the mind of Copernicus.

THE LETTER AGAINST WERNER

John Werner, a figure of some importance in the history of mathematics, published in 1522 at Nuremberg a collection of papers on mathematics and astronomy.¹⁴ One of these, the De motu octavae sphaerae tractatus primus, was sent to Copernicus by Bernard Wapowski, who had been his fellow student at the University of Cracow and was now a canon at Cracow and secretary to the king of Poland. Wapowski requested Copernicus to pass judgment on Werner’s contentions. Copernicus complied, sending to Wapowski under date of June 3, 1524, the Letter against Werner, a vigorous attack upon Werner’s position. In an age when scientific periodicals had not yet come into existence, such letters served the function now performed by articles and extended book reviews. The Letter against Werner, taken together with the Commentariolus, may be said to constitute the minor astronomical works of Copernicus; for besides the De revolutionibus we have nothing else on astronomy from his pen.

Handwritten copies of the Letter against Werner circulated for a time;¹⁵ and from a copy preserved in Berlin the first printed edition was made. It was included in Jan Baranowski’s edition of the De revolutionibus.¹⁶ Although the text of this edition was obviously faulty, it was reproduced by Hipler and Prowe.¹⁷ Then Maximilian Curtze found a second manuscript of the Letter against Werner in Vienna; he collated both manuscripts and published a critical text.¹⁸

The present translation was made from Curtze’s text. So far as I know, there have been two earlier translations, both into Polish, and both on the basis of the Berlin manuscript alone.¹⁹

THE NARRATIO PRIMA

It will be recalled that Rheticus left the University of Wittenberg in the spring of 1539 and set out for Prussia to study with Copernicus. In the middle of May he reached Posen, and from there he sent a letter to John Schöner, with whom he had studied at Nuremberg. In this letter he promised to inform Schöner as soon as possible whether the achievement of Copernicus justified his reputation.

Within a short time after his arrival Rheticus became aware that his host was a genius of the first rank. But Copernicus, for reasons which will be stated below, was reluctant to publish his astronomical work. The young professor added his voice to the chorus of friends who were urging Copernicus to release his manuscript for publication. In order to test public reaction to the innovations introduced by Copernicus, Rheticus rapidly wrote a survey of the principal features of the new astronomy. He cast it in the shape of a letter to his former teacher Schöner²⁰ and had it printed at Danzig in 1540.

The response was so favorable that a second edition of the Narratio prima was brought out in 1541 at Basel. It is altogether likely that the welcome accorded to the Narratio prima was the clinching argument that finally persuaded Copernicus to put his manuscript into the hands of a printer.

The reader of the Narratio prima (First Account) will notice that Rheticus speaks of his intention to compose a Second Account (Narratio secunda, Narratio altera). But Rheticus never wrote the Second Account. The Narratio prima was important, for it was the only book to which astronomers could turn for information about Copernicus’s system. But by preparing the way for the publication in 1543 of Copernicus’s own work, the De revolutionibus orbium caelestium, it made any Second Account superfluous.

When the second edition of the De revolutionibus appeared in 1566 at Basel, it included the Narratio prima. Rheticus’s work was printed a fourth and a fifth time as a companion piece to Kepler’s Mysterium cosmographicum (Tübingen, 1596; Frankfurt, 1621). It received its sixth printing in the Warsaw edition (1854) of the De revolutionibus and its seventh in the Thorn edition (1873). Finally Prowe printed it for the eighth time.²¹ The present translation was made from Prowe’s text.

The Warsaw edition included a translation into Polish, which is, so far as I know, the only one previous to the present.²²

THE DOCTRINE OF THE SPHERES

The ancient Greek astronomer Eudoxus (about 408–355 B.C.) introduced imaginary spheres into astronomical theory for the purpose of representing the apparent motions of the planets.²³ These spheres were invisible, and the observable planet was regarded as situated, like a spot or point, on the surface of the invisible sphere. The planet was deemed to have no motion of its own, but simply to participate in the motion of the sphere to whose surface it was attached. Now the observed movements of any planet are so complicated that a single sphere, moving at a uniform rate always in the same direction, could not produce the observed phenomena. Hence it became necessary to devise for each planet a set of spheres. These remained an integral part of astronomical theory until Kepler (1571–1630) banished them by demonstrating the ellipticity of the planetary orbits.

Copernicus used these spheres (orbes) throughout his work. He avoided taking sides in the controversy over the question whether the spheres were imaginary or real,²⁴ whether, that is, they were simply a mathematical means of representing the planetary motions and a convenient geometrical basis for computing the apparent paths, or whether they really had a physical existence in space and like a piece of machinery produced the observed phenomena.²⁵ But whether the planets were carried by material balls or hoops or by imaginary spheres or circles through a medium of whatever type, the resultant computation of the actual planetary courses was the same. From Copernicus’s language it sometimes appears that he regarded the planet as attached to a three-dimensional sphere; but more often a two-dimensional great circle of the sphere²⁶ was the geometrical figure to which he affixed the planet. For astronomical, as opposed to cosmological or astrophysical, theory it was a matter of indifference whether a planet was thought to be attached to a sphere or to a great circle thereof.

This repeated shift from sphere to circle and back again is, I believe, the root of some troublesome difficulties in Copernicus’s terminology. Consider first the ambiguity of the word orbis, a term of central importance and frequent occurrence in his writings.²⁷ Now orbis may mean either a three-dimensional sphere or a two-dimensional circle;²⁸ and in fact it is constantly used by Copernicus in both senses, being interchangeable at times with sphaera and more frequently with circulus.

An example of equivalence between orbis and sphaera occurs in the first Assumption of the Commentariolus: Omnium orbium caelestium sive sphaerarum unum centrum non esse;²⁹ "There is no one center of all the celestial spheres [orbium sive sphaerarum]." For a second instance of interchangeability of orbis with sphaera we turn to the section of the Commentariolus entitled "The Order of the Spheres [orbium]"; Orbes caelestes hoc ordine sese complectuntur. Summus est stellarum fixarum immobilis et omnia continens et locans;³⁰ "The celestial spheres [orbes] are arranged in the following order. The highest is the immovable [sphere] of the fixed stars, which contains and gives position to all things. We may properly hold that for the sphere of the fixed stars" Copernicus wrote here stellarum fixarum orbis,³¹ while the expression he regularly employs (in the De revolutionibus) is stellarum fixarum sphaera or non errantium stellarum sphaera³² These phrases do not occur anywhere else in the Commentariolus; for that paper, devoted almost entirely to planetary theory, seldom refers to the sphere of the fixed stars, and on those occasions it uses firmamentum.³³ On the other hand, in the Letter against Werner, which is concerned exclusively with the fixed stars, their sphaera is mentioned twice.³⁴ It is of interest to note that, although enormous differences in the distances of stars were demonstrated centuries ago, present-day textbooks of elementary astronomy still retain, for the purposes of preliminary exposition, the concept of an imaginary sphere of the fixed stars, a concept adequate enough for ordinary astronomical work.

We have seen that at times orbis means a three-dimensional sphere, sphaera.³⁵ We shall next examine some passages in which orbis is equivalent to circulus, a two-dimensional circle.

Following the ancient and medieval tradition, Copernicus devises for each of the planets a set of geometrical figures, designed to account as accurately as possible for the observed movements of the planet or, in the familiar phrase, to save the appearances.³⁶ These geometrical figures are regularly referred to in the Commentariolus as orbes; in fact orbis occurs there most frequently in two senses: (a) orbis magnus, the path of the earth’s annual revolution about the sun;³⁷ (b) the deferent of the moon, Saturn, Jupiter, Mars, Venus, and Mercury.³⁸ But in the closing paragraph of the Commentariolus, where Copernicus summarizes the plan of the solar system elaborated in that paper, he refers to these same geometrical figures as circuli.³⁹

A second example of equivalence between orbis and circulas is a sentence from the Commentariolus in which these two terms stand in juxtaposition as synonyms: Quantitates tamen semidiametrorum orbium in circulorum ipsorum explanatione hic ponentur, e quibus mathematicae artis non ignarus facile percipiet quam optime numeris et observationibus talis circulorum compositio conveniat;⁴⁰ "But in the explanation of the circles [circulorum] I shall set down here the lengths of the radii of the circles [orbium]; and from these the reader who is not unacquainted with mathematics will readily perceive how closely this arrangement of circles [circulorum] agrees with the numerical data and observations."

A striking illustration, drawn also from the Commentariolus, may serve as a third example : I gitur centro terrae in superficie eclipticae semper manente, hoc est in circumferentia circuli magni orbis. . . .⁴¹ Literal translation is of course impossible here; for those unfamiliar with Latin I give the following rendering, necessarily awkward: "Therefore, while the center of the earth always remains in the plane of the ecliptic, that is, in the circumference of the orbis magnus, which is a circle. . . ."⁴² We may conclude this discussion of the equivalence between orbis and circulus with Copernicus’s definition of the nodes in his section on The Superior Planets. The nodes are defined as . . . sectiones circulorum orbis et eclipticae . . .,⁴³ the intersections of two circles: (1) the deferent (orbis) of the planet, and (2) the ecliptic.

Although Copernicus wrenched astronomy loose from its geocentric past, his sentences abound in language that presupposes the earth to be in the center of the universe. The revolution in ideas did not at once precipitate a complete transformation of the terminology.⁴⁴ Consider, for example, his use of ecliptic, the geocentric name for the sun’s annual circuit of the heavens, a motion demonstrated by Copernicus to be not real but only apparent. In the place of ecliptic, as we saw just above, Copernicus introduced orbis magnus as the heliocentric term for the path of the earth’s real annual revolution about the sun.⁴⁵ So far as I know, no systematic examination has yet been undertaken of the remains of geocentric language in the writings of Copernicus; such a study might well yield fruitful results.

The reader who is familiar with the theory of relativity will note that the distinction made in the preceding paragraph between the real motion of the earth and the apparent motion of the sun is part of the world-view of Copernicus and Newton⁴⁶ and is itself an example of terminological lag behind a revolutionary change in fundamental ideas. For according