What Did Copernicus Write in De Revolutionibus?

De Revolutionibus Orbium Coelestium — “On the Revolutions of the Celestial Spheres” — is the book that put the heliocentric theory on the European table. Copernicus had been working on it, in one form or another, for more than three decades before it was published in Nuremberg in 1543. It is a long, technical, mathematically demanding work, modeled on Ptolemy’s Almagest of the second century AD. It is not an easy book to read, and it was almost certainly not read carefully by most of those who reacted to it. But it is the foundation of modern astronomy, and it is worth knowing what is in it. This page looks at the contents and structure of De Revolutionibus — its six books, the seven “postulates” that open Book I, the cosmological principles that animate the work, and the famous unsigned preface that the Nuremberg theologian Andreas Osiander added without Copernicus’s knowledge. For the broader life of Copernicus, see the Copernicus page. For the consequences of the heliocentric theory, see How Did Copernicus Change Astronomy? and Why Was Copernicus’s Theory Controversial?. For the empirical challenge the De Revolutionibus ultimately set up, see Kepler’s three laws of planetary motion.

Publication and Printing

De Revolutionibus was printed in Nuremberg by Johannes Petreius in 1543, in an edition of perhaps four hundred copies. The book had been through several drafts. The young Georg Joachim Rheticus, a Wittenberg professor who had visited Copernicus at Frombork in 1539, was largely responsible for the publication. Rheticus entrusted the final stages to Andreas Osiander, a Nuremberg Lutheran pastor with an interest in astronomy, while he himself was calleded away to take up a position at the University of Leipzig. Osiander added the famous preface addressed “to the reader concerning the hypotheses of this work,” and the book was printed with it. Copernicus received a copy, perhaps on his deathbed, on 24 May 1543; he is generally said to have died that same day. The first edition of De Revolutionibus is a folio volume of about 400 pages, written in Latin. It contains, in addition to the main text, several prefaces and dedicatory letters, a brief introduction by Rheticus to the reader, and various tables and diagrams. The book is dedicated to Pope Paul III, in a preface in which Copernicus explains that he has delayed publication for many years, and that he now dedicates the work to the pope in the hope that papal authority might protect it from the attacks of those who would not understand it. The dedication is itself a clue to the anxieties that surrounded the publication.

Book I: The Heliocentric Theory Stated

The first book of De Revolutionibus is the most famous. It begins with a long preface, a brief acknowledgment of the work’s debt to previous astronomers, and a “Preface to Book I” addressed to the reader. It then sets out, in Chapter 7 of Book I, the seven “postulates” or assumptions of the heliocentric theory. These are, in the standard translation:

1. The celestial spheres do not have a single common center.
2. The center of the Earth is not the center of the universe, but only the center of the lunar sphere.
3. All the spheres revolve around the Sun, which is therefore the center of the universe.
4. The ratio of the Earth’s distance from the Sun to the height of the firmament is less than the ratio of the Earth’s radius to its distance from the Sun, so that the firmament’s distance is immeasurably great.
5. Whatever motion appears in the firmament belongs not to the firmament but to the Earth. Thus the Earth and its contents perform a complete rotation on its fixed poles in a daily motion, while the firmament remains immovable.
6. Whatever motions appear to us in the Sun belong not to the Sun but to the Earth and the sphere we share with it. The Earth, with its attendant sphere, revolves around the Sun in a yearly motion, in such a way that the Sun occupies the center of its revolution.
7. The apparent retrograde and direct motions of the planets belong not to them but to the Earth. The motion of the Earth alone suffices to explain the apparent irregularity of the planets. These seven postulates are the foundational claim of the book. The fourth postulate is the most conceptually daring: it asserts that the celestial sphere is so far away that the Earth’s orbit shrinks to a point in comparison. This is the claim that makes the absence of observed stellar parallax intelligible — if the stars are unimaginably far away, then the Earth’s motion around the Sun would produce a stellar parallax too small to detect with the naked eye. The first postulate is also a significant break with the Aristotelian tradition, which had assumed that the universe had a single, well-defined center. After the postulates, Book I goes on to address a series of objections that Copernicus knew would be raised. He argues that the apparent vertical motion of falling bodies is consistent with a rotating Earth, because the bodies share the Earth’s motion. He argues that the apparent horizontal motion of clouds is also consistent, for the same reason. He argues that the Earth’s rotation is a “natural” rather than a “violent” motion, and that bodies outside the Earth have their own natural motions. These arguments are detailed and, in some places, technically astute. They are not, by modern standards, conclusive — the conservation of momentum was not understood, and the laws of falling bodies were still those of Aristotle — but they are the first serious attempt to construct a physics of a moving Earth.

Books II through VI: The Mathematics of the New System

The remaining five books of De Revolutionibus are technical. They take up, in roughly the same order as Ptolemy’s Almagest, the mathematical description of the motions of the Sun, Moon, and planets in a heliocentric system. The structure is the following: Book II is concerned with spherical astronomy — the geometry of the celestial sphere, the motion of the Earth, the determination of the lengths of the seasons, the construction of tables of solar declination, and so on. It is the most traditional part of the book, drawing heavily on Greek and Arabic sources. Book III deals with the precession of the equinoxes and the apparent motion of the Sun. Copernicus’s treatment of precession is original; he attributes the precession of the equinoxes, traditionally considered a motion of the eighth sphere, to a slow conical motion of the Earth’s axis, with a period of about 26,000 years. His treatment of the apparent motion of the Sun is a fairly direct transcription of Ptolemy’s, with the Earth and Sun exchanged. Book IV is on the Moon. Copernicus used Ptolemy’s lunar theory largely as he found it, since the Moon’s motion around the Earth was not, of course, changed by the heliocentric shift. The book contains one of the most famous observational errors in this history: a misquoted observation of a lunar distance at quadrature, which Kepler was later to puzzle over and, in his own way, partly to correct. Book V treats the planets. It is here that the heliocentric system really differs from the geocentric, because the apparent motions of the planets — the retrograde loops, the varying brightnesses, the irregular spacings of conjunctions — are all explained in terms of the Earth’s motion relative to the planets. Copernicus still used Ptolemy’s toolkit of epicycles, eccentrics, and equants, but he reorganized them around the Sun. The mathematical details are intricate; the visual diagrams in the printed book are striking. Book VI is on the latitudes of the planets — that is the fact that the planets do not move exactly in the plane of the ecliptic, but deviate from it by small but measurable amounts. The book also contains extensive star catalogs, drawing on the observations of Hipparchus and Ptolemy and adding a few of Copernicus’s own.

The Cosmological Principles

Underneath the mathematics, De Revolutionibus is animated by a small set of cosmological principles. They are not stated as axioms; they are used as working assumptions, and they shape the way the mathematics is constructed. The first principle is that the celestial motions are circular, or composed of circles. This was the standard principle of all pre-Keplerian astronomy, going back to Plato and Aristotle. Copernicus did not break with it, although Kepler eventually would. The use of uniform circular motion is, in fact, one of the most conservative features of De Revolutionibus. Copernicus does, however, restrict the use of the equant, a device Ptolemy had used to account for the variation in the angular speed of a planet along its orbit. The Maragha astronomers of the thirteenth and fourteenth centuries had also attacked the equant, and Copernicus seems to have been influenced by their work. The second principle is that the celestial bodies are spheres. This too was standard. The third, and most important, principle is that the Sun is at the center of the universe. The argument for this is, in Book I, a mixture of the aesthetic and the quasi-physical. Copernicus notes that the Sun is the brightest of the heavenly bodies; that it is the source of light and heat for the Earth; and that the relative ordering of the planets — Mercury closest to the Sun, then Venus, then Mars, Jupiter, and Saturn — falls out naturally from the periods of their revolutions. The Earth, no longer privileged, takes its place among the planets as the third from the Sun. The fourth principle is the immensity of the celestial sphere, asserted in the fourth postulate. This is the most striking conceptual move in the book, and it is the one that made the heliocentric theory difficult to disprove observationally. If the stars are so far away that the Earth’s annual orbit is a point, then the absence of observed stellar parallax is exactly what one would expect. (Stellar parallax was not, in fact, successfully observed until 1838, by Friedrich Bessel, against the bright star 61 Cygni.) The principle also made the universe, in a sense, infinite — or at least, indefinitely large — and so opened the way for the speculations of Bruno and others about an infinite universe full of other worlds.

The Osiander Preface

The most famous single passage in De Revolutionibus, and one of the most famous in this history, is the unsigned preface. It is now universally attributed to Andreas Osiander, the Nuremberg pastor who oversaw the printing of the book while Rheticus was away. The preface reads, in part:

“It is the duty of an astronomer to compose the history of the celestial motions through careful and expert study. He has no business, in doing so, to suppose that they are caused by any cause whatsoever, nor to feign fictions or to be tempted to put forward the true cause, since he could not lay claim to the true cause in any case… It is not necessary that these hypotheses should be true, or even probable; it is sufficient that they lead to a computation which agrees with the observations.” Osiander’s purpose seems to have been to defuse the controversy that he thought the heliocentric theory would provoke, by presenting it as a useful but not necessarily true calculating device. The preface was added without Copernicus’s knowledge, or at least without his explicit consent, and Copernicus’s friends and collaborators were angry when they discovered it. The preface delayed the full reception of the heliocentric theory in two ways. It gave cautious readers a pretext for not committing to it. And it provoked defenders of the heliocentric theory into a sharper defense of its physical truth than they might otherwise have made. By 1610, with Galileo, the question of whether the heliocentric theory was physically true or merely mathematically convenient had become unavoidable. The story is told in the Galileo page and in Why Was Galileo Put on Trial?.

The Long Afterlife of De Revolutionibus

After 1543, De Revolutionibus had a long, complicated history. It was read, quoted, taught, edited, and eventually put on the Index. The second edition appeared in 1566, in Basel, edited by Achilles Pirmin Gasser; this edition simply reprinted the first, including the Osiander preface, with minor corrections. A third edition appeared in 1617, in Amsterdam. In 1616 the Catholic Church placed the book on the Index of Forbidden Books, pending “corrections” — corrections that, ironically, were never actually made, because the theologians of the Sacred Congregation could not agree on what the right corrections were. The book was eventually removed from the Index in 1758, when the Index was revised to remove treatises that the Church no longer considered erroneous. In the Protestant world, De Revolutionibus was treateded more variably. Luther had dismissed Copernicus in a famous table-talk of 1539 as “the fool who wishes to reverse the entire science of astronomy; but sacred scripture tells us that Joshua commanded the sun, not the Earth, to stand still.” Melanchthon, the humanist reformer, was more nuanced but also skeptical. The Wittenberg astronomers, as noted, used the De Revolutionibus for its tables while keeping their distance from the cosmology. By the seventeenth century, the heliocentric theory was widely accepted in Protestant lands, and the index of works defending it grew rapidly. Kepler, Galileo, Descartes, and Newton all took it for granted. The story of how the heliocentric theory came to be the consensus view of European natural philosophy is the central narrative of the Scientific Revolution. It is told in summary in the page on the key figures and in detail across the heliocentrism and astronomy section.

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