SOURCE: "Copernicus the Economist" and "De Revolutionibus" in Copernicus: Scholar and Citizen, Interpress Publishers, 1972, pp. 83-115.

Copernicus the Economist

Copernicus was for many years in Warmia engrossed in economic matters and monetary questions. He introduced many new and stimulating ideas into economics, some of them much ahead of his time, and hence did not always meet with understanding. But it is worth looking closer at his practical measures and theoretical writings in this field for it forms a separate and important chapter in his life.

Among the economic problems which were examined by Copernicus that of the Prussian coinage occupies pride of place.

This problem first attracted his attention in 1510. Working in the administration and becoming acquainted with the realities of everyday life provided him with valuable experience which, with the help of source materials from Warmian archives, later (after 1517) made it possible for him to carry out an expert analysis of the monetary situation in Royal Prussia.

At the beginning of the 16th century, Royal Prussia went through a monetary crisis brought about by depreciation. The coins struck since 1457 by the Gdansk and Torun mints with royal permission, and by Elblag without such permission (the basic unit was the shilling) had a steadily diminishing silver content. Apart from the local and Crown coins, there were also several other kinds of money minted in foreign countries and cities in western Europe. These coins, together with Royal Prussian shillings, were constantly driven out by coins from the Prussia of the Teutonic Order where shillings and grosze of ever poorer quality were struck in the mint belonging to the Grand Masters. Better money disappeared from the market, for it was taken out of the country or melted down by local goldsmiths and silversmiths. All this caused considerable losses, especially among the knights, peasants and merchants, in all deals in which money was used. It had also an adverse effect on the value of rents paid by the peasantry to the administrators of the Chapter's estates in Warmia. That is why the knights and representatives of the higher clergy became advocates of the monetary reform in Royal Prussia and of pegging the Prussian currency to the Polish one in order to simplify the system of conversion for everyday purposes. Doubtless, such a reform must have had supporters among the middle merchants in the big Prussian cities. On the other hand, the town councils, that is to say the representatives of the patricians of Gdansk, Elblag and Torun, although they did not reject the proposals for a monetary reform, yet strove to keep their minting rights and the attendant income. From the very first they discouraged the bolder projects for reforming the monetary system in Prussia.

The Estates of Royal Prussia had been concerning themselves with this matter ever since the beginning of the 16th century. The situation became more acute after 1511, when the Teutonic Order began to mint silver coins of a still lower value. The Royal Prussian Estates protested against such a procedure (1516). It was probably then that Copernicus took up the matter, either at the initiative of Bishop Luzjanski or the Chapter. In any case, in the middle of August 1517, during his stay at Olsztyn, he wrote the first outline of a monetary treatise, entitled Meditata. This outline contained most of the later ideas for reform which Copernicus elaborated in further studies.

In 1519, the Prussian Estates formally requested Copernicus to give his opinion in the matter of monetary reform. During that year, when still in Olsztyn, Copernicus translated (with minor amendments) his first study in Latin, into German which language was easier to understand for, at least, the burghers of the Third Estate. The treatise was to be discussed at the assembly in Torun at the close of 1519, but the outbreak of the war postponed the whole matter for more than two years.

It was only after the truce between Poland and the Teutonic Knights had been concluded that the question of monetary reform was put on the agenda of the assembly in Grudzadz, in the later half of March 1522. At the motion of Maciej Drzewicki, Bishop of Włocławek and envoy of King Sigismund I, the assembly was to discuss the introduction of a uniform Crown currency which would be legal tender also in Royal Prussia. Copernicus, as mentioned before, was present at the convention as the envoy of the Warmian Chapter. He was then asked to read his treatise on the monetary system.

In this treatise, entitled Modus cudendi monetam (On the Method of Minting Money), Copernicus, mathematician and astronomer, first analysed conditions in Prussia, and then proceeded to use the scientific method of observation of Nature in dealing with socio-economic phenomena. He treated money exclusively as an economic factor, and he saw the source of its value only in its silver or gold content; in this, he was a follower of the so-called metallistic or substantional theory. He also formulated an important economic law called the law of bad money, according to which good money is driven out of circulation by bad money and is taken away either for reminting or for commercial purposes (this law was later attributed to Sir Thomas Gresham and is now called Gresham's law). In order to remedy this evil, he proposed to withdraw inferior currency and introduce a uniform silver coin of high intrinsic value, struck in one mint only in Royal Prussia, with the stamp and in its name, and that the very minting of money should not bring any profit. These views were in harmony with progressive economic theories in the age of the Renaissance and represented a definite break with the opinions prevalent in both Prussias. They were in line with the interests of the rural population of the poorer town dwellers as well as of landowners. The then modern stipulation that the striking of the new money should be centralized and the large Prussian towns deprived of profit from minting rights was certain to arouse protests.

Copernicus, prompted by Bishop Drzewicki's demands that uniform royal money should be introduced on the entire territory of the Polish Kingdom, added in Grudziadz one more important and vital stipulation at the close of the treatise: he suggested that the value of the new Royal Prussian money should be the same as that of the money minted in Cracow by striking three Prussian shillings equal in value to one Polish grosz. In this way, without depriving Royal Prussia of the right to her own money, an important step would have been taken towards a more efficient circulation of the royal and Prussian currencies, which in turn would facilitate financial transactions and become a factor in the integration of the Polish Crown and Royal Prussia. This then was also a contribution on Copernicus' part to an even closer bringing together of the Prussian lands with the Polish Kingdom. After the secularization of the Prussia of the Teutonic Order (1525) and the emergence of the vassal Duchy of Prussia, ruled by Duke Albrecht, the money question in both parts of Prussia required regulating. The reform which King Sigismund I requested was based on the Treatise on Minting Money, drawn up and presented, in 1526, to the Estates of Royal Prussia by Justus Ludwik Decius, adviser and personal secretary to the King. The draft reform provided for the minting of a new coinage, of higher quality, which would, however, continue to be a source of income to the ruler. Decius did not provide for the withdrawal from circulation of the old coins of low value, for he supposed erroneously that it would be automatically driven out by the new currency. He proposed that the coinage in the Crown territories, in Prussia and Lithuania should be made uniform in respect of weight and metallic composition, with the provision that there should be one mint in Prussia, to be set up in Torun.

These assumptions, which differed considerably from Copernicus' projects and were not so far reaching, were discussed by the assembly of Prussian Estates in summer 1526, during King Sigismund I's visit to Gdansk. On July 17th, the King proclaimed a new ordinance (i.e. statute) for Royal Prussia, in which the monetary reform was announced (there were to be grosze, shillings and denarii), which would lead to the currency's being unified with that in the Polish Kingdom; the reform was also to be introduced in the Duchy of Prussia. The King's decision caused an animated discussion among the Estates and a number of reservations regarding Decius' treatise.

It is very probable that Copernicus was also invited to attend the debates in Gdansk, or he may have been there in the company of Bishop Maurycy Ferber. In any case, the letter (in Latin) from the Royal Prussian Estates to Decius, written in Gdansk, and dated July 18th, 1526, bears all the marks of his style and views. The letter contains a critique of Decius' project: once again, the effect of the "law of bad money" is recalled, which will drive out of circulation the new, better royal money. Copernicus, whom we may take to have been the author of the letter, did not agree to the minting of money being a source of income to the king. But he accepted the proposal of one monetary system for the Crown lands, Prussia and Lithuania. He considered that coins of the same alloy and value should circulate freely throughout the territory of the Commonwealth of Poland, although the shilling was to remain the basic monetary unit in Royal Prussia because of its long-standing tradition. Next, Copernicus suggested that the monetary unit of the Duchy of Prussia (i.e. grosz) should have the image of King Sigismund with his name and title in Latin on the rim, while the shillings of Royal Prussia should bear the crest of the Polish Kingdom and the royal title on the rim, the reverse having the crest of Prussia.

While criticizing some of the provisions of Decius' project, Copernicus called on him to take part in the discussions on carrying out the monetary reform in Prussia in connection with the opening of the Torun mint, as intended by the King.

Eventually, the proposal for a new uniform currency for Royal Prussia and the Duchy of Prussia was to be put on the agenda of the assembly of Prussian Estates and Duke Albrecht's envoys on May 8th, 1528, at Malbork. At the end of March, Bishop Ferber, who appreciated the importance of this matter, summoned Dr Nicolaus to Lidzbark in order to discuss with him the attitude which should be adopted towards the monetary question. There seems to be no doubt that Copernicus prepared a third version of his treatise on money precisely for this meeting, in which he made use of the results of the discussions and arguments against Decius' ideas. At the beginning of April, in Lidzbark, this version, entitled Monetae cudendae ratio (On Minting Money), was probably amended finally after the talks with Bishop Ferber. On April 7th, the Bishop summoned the Chapter and requested it to send Copernicus to the assembly at Malbork, where he would assist the Bishop with his experienced counsel. Canon Feliks Reich, who also attended the discussions on monetary questions and possibly expected to take part in the Malbork sessions, wanted to become acquainted with Copernicus' treatise. Not everything was clear to him in the new version of the reform. In his letter of April 19th, Copernicus elucidated some of its principles. He also emphasized the need of voting the reform and introducing it as soon as possible, which would also be of advantage to the "King, Our Lord", who would receive the planned tax from the Estates in a new and better money.

Monetae cudendae ratio, the most extensive and also the most mature version of Copernicus' monetary treatise, written again in Latin (spring 1528), contained all the fruit of the several years of discussions at the forum of the Prussian Estates and of the polemics with Decius. Dr Nicolaus reiterated in it most of his ideas including the thesis of good money being driven out by bad, and substantiated them with an extensive exposition of the history of Prussia from the end of the 14th century. The part about the dire effects of the debasement of money has a truly dramatic ring. Copernicus appealed warmly to the rulers of the Prussian lands who "look on with indifference and permit their sweetest Motherland, towards which their duties, after love of God, are the greatest, and for the sake of which they should sacrifice even their life, to decline painfully through their everyday lazy negligence". The rulers ought not to seek profits from minting money, and after new good money is introduced, the old debased money should be with-drawn. Though Copernicus agreed to the establishment of two Prussian mints, one for Royal Prussia, the other for the Duchy of Prussia, coins issuing from both mints were to bear the crest of the Polish king. Prussian money, which enjoyed royal protection, should be on equal footing with Crown money.

As envoy of the Warmian Chapter, Copernicus attended the debates of the General Diet of Royal Prussia, held in Malbork some time after May 9th, 1528, at which envoys of Albrecht, Duke of Prussia, were also present. On May 14th, he was elected member of the special working commission, made up of representatives of Royal Prussia and the Duchy of Prussia; among them were miniers from Gdansk and Elblag. The commission discussed, above all, the ways and means of withdrawing the old coins, and the form and size of the new Prussian grosz, to be introduced by order of the King. It is not known whether Dr Nicolaus acquinted the commission with the contents of the final version of his treatise on money. Perhaps the differences in opinion between the other members of the commission (especially the envoys of the large Prussian towns) held him back; perhaps also his reticence was due to the absence of Decius, his main opponent, whose ideas were beginning to win over a majority of the representatives of the Estates.

Anyway, his treatise was made available to the envoys of Duke Albrecht, whose chancellery received a copy, made by Canon Feliks Reich also for the benefit of the Warmian Chapter. He it was who represented Bishop Ferber at the General Diet of Royal Prussia in the second half of July 1528, in Torun, attended also by Decius. Reich took part in the deliberation of the Estates on the draft monetary reform in Prussia, tabled by him, and on July 22nd, at the request of the meeting, he summed up the proposals put forward so far; it is possible that he presented also some of the principles contained in the final version of the Copernican treatise.

The next day, the Estates voted into effect the principles of the monetary reform, i.e. the ordinance of the Torun mint which was to serve both Royal Prussia and Ducal Prussia. This then—initially—amounted to the fulfilment of one of Copernicus' main stipulations. The new Prussian money was to circulate freely throughout the territory of the Polish Crown and was to be standardized with its currency, which constituted another success for Copernicus' ideas.

But his other proposals were never realized. First of all, minting continued to be considered a source of profit for the king. Neither were all the types of old coins withdrawn from circulation, apart from those struck prior to 1521. Also the proposal to maintain the shilling as the basic monetary unit in Prussia was rejected, and the Polish grosz introduced instead, which turned out later to be no bad thing as it made for closer ties between the monetary systems of Prussia and the Crown. But as early as in 1530, King Sigismund permitted Gdansk, Elblag and Duke Albrecht to open their own mints (the latter in Königsberg). The coins were struck in accordance with the Polish standards but the names of the towns were marked on them.

The reform of the Prussian coinage, adopted in 1528, realized, if only in part, some of the ideas advanced by Copernicus. In a modified form, it introduced order into the financial relations in Prussia and bound it even closer to the Polish Crown.

The enforcement of the reform, to be sure, ran into difficulties. The Torun mint issued an insufficient amount of the new Prussian coins, so that the old inferior ones continued in circulation. This became the subject of the deliberations at the assembly held in Elblag during February 1529, and most probably attended by Copernicus and Bishop Ferber. The assembly adopted a resolution on the withdrawal of old Prussian denarii.

Copernicus also took part in the convention of Prussian Estates held between October 28th and 31st 1530, in Elblag, to which he was delegated by Bishop Ferber, who was already ill, as the most experienced representative of the Chapter. The Elblag convention, attended by Decius and Albrecht's envoys, was to discuss the vital question of the relation of the gold coins, then in circulation, to the new silver Prussian coins. During the session of October 30th, Dr Nicolaus took the floor in the controversial matter of the value of the gold coin. Copernicus said that it was impossible to establish the value of the gold coin for it was not known how many additives the alloy had. It would be better, therefore, to consider how many coins could be minted from one grzywna (an ancient monetary unit containing 3,688 grams of silver) of pure silver or gold. Thus the problem was put on the level of scientific analysis instead of improvized calculations, and the envoys of the large towns refused to take part in the discussion. Copernicus was also for maintaining the old value of the gold coins, a proposal which ran counter to the demands of Duke Albrecht's envoys. Eventually, the whole matter was shelved.

After 1530, Copernicus did not attend any more assemblies which concerned themselves with the detailed procedures to be adopted to secure full implementation of the Prussian monetary reform.

Copernicus turned once more to economic matters in 1531, when inspecting the estates of the Warmian Chapter in the region of Olsztyn; he drew up what was called the "Olsztyn Bread Tariff (Ratio panaria Allensteinensis) which was to be enforced in all the towns of Warmia. This time it was a matter concerning trade and prices. In the Tariff, Copernicus examined the ratio between the price of grain and that of bread, taking the view that the price of bread should be equal to that of the grain used for its baking; the costs of other ingredients in the bread and the baker's fee ought to be contained in the value of the by-products left over from milling (as bran). The price of bread should therefore be dependent on the material costs of its production. In this Copernicus followed the mediaeval principle of what was called a "just price," a principle fitting the condition of small scale commodity production. It protected the consumer against excessive exploitation on the part of bread producers. So in this case, too, Dr Nicolaus had in mind the good of society at large.

The achievements of Copernicus the economist are considerable. Through his exact and innovatory definition of the essence and function of money and his original proposal for monetary reform, he secured for himself a permanent place in the history of European, progressive economic thinking, showing in this domain, too, the unusually wide scope of his mind. His research methods led him not only to the description and cognition of the essence of the subject investigated but also to establishing the relationship between various phenomena and to a comprehensive examination of the problem in its purely economic aspects, irrespective of religious or legal motives.

De Revolutionibus

Astronomy was Copernicus' greatest passion. He conducted studies and research even during the 1520-1521 war and the destruction of his Frombork home. We know that when writing the Commentariolus he had already in mind a larger work in which he intended to present a new astronomical theory. At the time, he made use of data taken from other sources, and only in determining the length of the year did he refer to his own observations. The writing of another, more extensive work demanded the making of many new observations.

The number of astronomical observations now known to have been made by Copernicus is not very big. This is because, on the one hand, we know only about those observations which have been used and noted in the book; and on the other, because, it must be said that not many observations were really needed for a reform in astronomy. Those that we know about had a purposefully selected subject and served, in conjunction with analogous observations made in antiquity, to determine the fundamental parametres of the new theory, and their purposefulness was confirmed in the form of new and important (though not bearing on the very essence of Copernican astronomy) determinations.

Purposefulness and the systematic conduct of his observations distinguish Copernicus as an observer, while the observations themselves are neither particularly accurate nor new as concerns the methods with which they were carried out. The measuring instruments, made by the astronomer himself, were a replica of the classical instruments of ancient astronomers, described by Ptolemy in the Almagest. The only original instrument he used was the one he made during his first stay in Olsztyn, around 1517, preserved in part to this day on the wall of the arcaded gallery in Olsztyn castle. In this instrument, the beam of sunlight reflected from a horizontal mirror fell on a chart or table on the wall, the grid of which made it possible to calculate the time separating the moment of observation from the equinox.

It was no accident that the Olsztyn table, which was probably used more for demonstration purposes than accurate measurements, was constructed at a time when Copernicus was intent on investigations into the apparent movement of the Sun and the theory of precession. It was precisely in 1516 that Copernicus found himself among a group of experts who were invited by the Lateran Council, then taking place in Rome, to send their opinions on the ways and means of reforming the Julian calendar. The invitation was transmitted by Bernard Sculteti, Dean of the Warmian Chapter, who was in Rome at the time. This shows that Copernicus was already well-known as a competent astronomer, at least to a close circle of specialists, in spite of his living so far away from the European centres of learning.

Copernicus' opinion in the matter of the reform of the calendar has not been preserved; we know its substance only indirectly from a reference to it by the author in the introduction to De Revolutionibus. Copernicus said that amendments could be introduced into the calendar only after more accurate study of the movements of Sun and Moon. It is from this introduction or dedication to Pope Paul III that we learn that he had begun these more accurate studies, connected with the reform of the calendar, at the time of the Lateran Council. It was in the years 1515-1516 that he conducted his observations of the positions of the Sun. These observations he later used in De Revolutionibus, which he was soon to begin the long and arduous labour of writing.

Scientific contacts with Cracow were maintained throughout. In 1524, Bernard Wapowski, who had befriended Copernicus during his student days in Cracow, sent him a book by Johannes Werner, a mathematician and astronomer from Nuremberg who had lately died, which contained a treatise entitled De Motu Octavae Sphaerae (On the Movement of the Eighth Sphere). In it were discussed various questions connected with precession, which in geocentric astronomy was explained as the movement of the "eighth" sphere of fixed stars, moved by appropriate outer supra-stellar spheres. Werner needed three such outer spheres for his theory. Copernicus wrote to Wapowski on June 3rd, 1524, a letter containing an extensive negative review of Werner's book. He did not reveal in this letter his own theory of precession the details of which he was now working out for his De Revolutionibus, but simply criticized Werner's methods of investigation. He was particularly critical of his loose treatment of the observations of ancient astronomers and their negative assessment which ran counter to Copernicus' own opinion, for he considered their observations to be the basis for new studies.

In the twenties, and more precisely sometime around 1523, Copernicus' investigations led him to a new discovery. This resulted from the observation of planets in opposition, that is at the moment when they are at a point on the celestial sphere opposite to the Sun. Three observations of a planet in three oppositions allow for the determination of its orbit, among other things, for the determination of the direction taken in space by the line of apsides, i.e. the line joining a planet's aphelion and perihelion. The comparison of the data obtained from his own observations with those of the ancient astronomers, as expounded in Ptolemy's Almagest, led him to the assertion that the notion about the immobility of the position of planetary orbits in space, prevalent since antiquity, was wrong. For it appeared that the lines of apsides had changed their position when compared with the position given 1300 years before by Ptolemy. This discovery by Copernicus, which was later eclipsed by his great heliocentric theory, has nevertheless remained for science ever since, although the figures for the velocity of the motion of the lines of apsides required considerable corrections.

The discovery of the mobility of planetary apsides led Copernicus to the introduction of certain changes in the geometrical models of planetary orbits as compared with those in the Commentariolus. The difference lay in that the system of two circles was, for each planet, replaced by an eccentric circle. From the mathematical point of view, the new model was exactly equivalent to the old one, but it simplified the presentation of the motion of the lines of apsides.

De Revolutionibus was ready in manuscript from around 1530 (the latest observation entered in it is dated March 12th, 1529). But Copernicus did not intend to publish it, as he said himself, for he was afraid of the ridicule on the part of those "who are dull of wit and flit amidst the true scholars like drones among bees". When in 1535, Bernard Wapowski paid a visit to the astronomer at Frombork, he obtained only his consent to publish an astronomical almanac calculated with the use of tables drawn up in accordance with the new theory. This project, however, was not carried out because of Bernard Wapowski's death in the same year.

Copernicus' unwillingness to publicize the results of his inquiries did not prevent the information about them spreading slowly throughout Europe. In 1533, Copernicus' ideas on the motion of the Earth were discussed at the papal court; three years later, Cardinal Nicholas Schonberg wrote from Rome to Copernicus, encouraging him to make his discoveries known. But of really decisive influence was the visit in 1539 of a young mathematician, Georg Joachim von Lauchen, known as Rheticus, a professor at Wittenberg University. He undertook the journey to Poland especially in order to learn about the work of Copernicus, about which news had already reached the Wittenberg group of scholars headed by Philip Melanchthon. The latter was soon to reject the heliocentric theory as absurd. Rheticus, however, became an enthusiast for Copernican astronomy. The first result of this visit was that Copernicus resumed work on the manuscript of De Revolutionibus. He now had at his disposal books presented to him by Rheticus, including the original Greek text of the Almagest, free of the many errors and distortions of the Latin edition, and Regiomontanus' Trigonometry. This made possible the introduction of certain additions to the chapter dealing with spherical trigonometry. Also the layout of the whole book was altered. Rheticus' enthusiasm and the encouragement of those close to him, particularly by, as he described him in De Revolutionibus, "my great friend Tiedeman Giese, Bishop of Chelmno" converted the astronomer to the idea of having the book published.

The first exposition of the new theory in print came in 1540, during Rheticus' stay in Warmia. Having studied Copernicus' manuscript, Rheticus compiled an extensive summary, published in Gdansk as The First Narration about Nicolaus Copernicus' Book on Revolutions. This Narratio prima is valuable especially for the parts in which the author presents the facts and opinions known to him from his direct contacts with Copernicus. Particularly important is the list of motives which apparently led Copernicus to recognize the facts of the Earth's motion. In the first place he mentions precession. Only later come the premises concerning the place of the Sun in the planetary system and the preservation of the principle of the uniform circular motion. The closing arguments are certainly the outcome of a discovery already made earlier. They speak of the teleological value of the theory of the Earth's motion and about the harmony of the world revealed by them.

The First Narration was in the form of a letter to Johannes Schoner, a Nuremberg astronomer, and publisher of scientific books. Probably the plans for the publication of the new theory were discussed earlier in Nuremberg, during Rheticus' visit there.

On leaving Frombork in the autumn of 1541, Rheticus took with him the manuscript of De Revolutionibus. The work was to be printed in Nuremberg. But before that, as a permanent resident of Wittenberg, he published the trigonometry which was contained in the closing chapters of Book One. It is composed of plane and spherical trigonometry and a seven-figure table of the sinus function, compounded by Rheticus, which here took the place of the five-figure table of Copernicus.

Copernicus' trigonometry, like the slightly earlier works by Regiomontanus and Werner, was based on formulae used by ancient (Ptolemy) and Arab (Jabir ibn Aflah) scholars. The introduction of the secant function, new in European science, was Copernicus' own achievement. It is not mentioned in the printed Trigonometry, but he calculated the table for this function and noted it in one of the books in his library.

The printing of De Revolutionibus began in Nuremberg in the first half of 1542. The manuscript which the printer Johannes Petreius received from Rheticus was not entirely ready for print. More important in its effects, as it turned out, was the fact that the publication was entrusted to the publisher and theologian, Andreas Osiander. He had for some time been interested in the publication of De Revolutionibus and wrote to Copernicus and Rheticus suggesting to the author that in order to "quieten the peripatetics and theologians whose protests you fear" he should present his new theory as a hypothesis convenient for calculations, not as a description of the world corresponding to reality. Copernicus rejected those suggestions and explicitly presented his view in the dedicating letter written for De Revolutionibus in June 1542. This did not alter Osiander's attitude, who introduced changes in the book in accordance with the conventional view on the veracity of scientific theories. The anonymous preface, which he added, To the Reader About the Assumptions of this Work reduced the contents of the book to the level of hypothesis " … for it is clear that this science completely ignores and simply does not know the causes of the apparent inequalities of movements…. So let no one expect from astronomy anything certain in relation to hypotheses, for it cannot produce anything certain in this respect." Moreover, the title of the book was distorted. Instead of simply On Revolutions or Six Books on Revolutions the longer title was introduced, De Revolutionibus orbium coelestium (On the Revolutions of Heavenly Bodies). Finally, Copernicus' preface to Book One was removed, an eulogy of the astronomical sciences which "treat … of the causes of all the phenomena in the sky, and finally explain the whole system of the universe".

Nicolai Copernici Torunensi De Revolutionibus orbium coelestium, Libri VI appeared in March 1543, shortly before the death of its author. The Nuremberg edition opens with the anonymous preface by Osiander and the letter by Cardinal Schonberg of 1536. Then comes the Letter of Dedication to Pope Paul III. In this letter Copernicus returns to the reasons which prompted him to entertain the idea that the Earth moved:

"That is why I wish Your Holiness to know that, in turning my thoughts to another principle for calculating the motions of the spheres of the universe, I was prompted by nothing other than the observation that in their studies of them the mathematicians are not in agreement with one another. Above all, they have so many doubts as to the motion of the Sun and the Moon that they are unable even to determine and calculate the constant magnitude of the tropical year. Next, when determining the motions both of those two and of the other five planets they do not use the same assumptions and premises … They adopted … a great many assumptions which are obviously inconsistent with the fundamental principles of uniformity of motion. Neither did they discover or they failed to deduce the most important thing, namely, the system of the universe and the established order of its parts …"

Here we have the most important motives which made Copernicus undertake a reconstruction of astronomy: "determination of the tropical year" which required a correct theory of precession, mentioned already by Rheticus in the Narratio prima; inconsistency with the fundamental principles of the uniformity of motion, mentioned in the first place in the Commentariolus; lastly, the "system of the universe and the established order of its parts," an argument which probably resulted from the later rationalization of the process of discovery. Further on in the Letter Copernicus refers to the precursory statements by ancient writers: "I have taken the trouble to read anew all the works of the philosophers accessible to me in order to find out whether any of them did not by chance express an opinion on the motion of the spheres of the universe differing from the hypotheses accepted by the professors of mathematical sciences. And I did find, first in Cicero's, a remark that Niketas thought that the Earth moved. Then in Plutarch I found a few more names of people of the same opinion …: the Pythagorean Phylolaos thinks that (the Earth) revolves round the fire along an inclined circle as do the Sun and the Moon. Heracleides of Pontus and the Pythagorean Ekphantos though they believe that the Earth does move, think that it is a rotary, not translatory motion … My interest having thus been aroused, I too began to ponder about the movements of the Earth". Here also, it is easy to find the elements of the later reasoning. In the closing paragraph of the Letter, the author anticipates objections of theological nature concerning the inconsistency of the new theory with the teachings of Holy Scripture: "It is possible that there will be such who like to drivel and in spite of complete ignorance of mathematics arrogate to themselves the right to express their opinions about them referring to some place in the Holy Scripture, wrongly and fallaciously explained to suit their intentions, and who dare to denounce and persecute this theory of mine. However I care not for such people …".

The opening chapters of Book One discuss the foundations of astronomy according to the Ptolemaic model. While rejecting Ptolemy's arguments about the Earth's being stationary, Copernicus considers natural (in the Aristotelian sense) the revolution of the Earth together with its surrounding atmosphere, and not requiring any external cause. He also modifies the philosophical concept of gravity, identified with gravitation towards the centre of the world, by describing it as a natural tendency of parts to concentrate into the form of a sphere, a tendency "existing also in the Sun, Moon and other shining planets." This essential modification of the Aristotelean laws of physic shows that in Copernicus' research methods the prime role was played by purely astronomical speculations, and that it is on results of these that the interpretation of the philosophy of nature depended.

Later on in the general part the author declares that the position of the Sun in the centre of the universe "is taught to us by the law of the order in which these bodies (planets) follow one another and by the harmony of the whole universe". This law of order is one of the most important arguments against the Ptolemaic system in which each planet was studied separately from the rest of the system. This argument is developed in the famous tenth chapter containing a description of the solar system, in which an "admirable order of the world and an established harmonious connection between the motion and the magnitude of the spheres, which cannot be discovered in any other way" is found to exist. The descriptive part of the book closes with a short exposition of the triple motion of the Earth. The rest of Book One is taken up with an exposition of plane and spherical trigonometry, printed earlier in a separate edition of 1542.

In Book Two Copernicus explains spherical astronomy. It closes with a catalogue of over 1,000 stars, patterned after Ptolemy. The sphere of fixed stars constituted a system to which Copernicus relates the phenomena connected with the apparent motion of the Sun, which he describes in Book Three. The first part of this book is devoted to a detailed exposition of the new theory of precession.

The discovery of the true cause of precession phenomena in the movement of the Earth's axis is among the most important elements of the new astronomy. The theory of this "third motion of the Earth," carefully documented mathematically, is based on more than 1800 years of observations, which made it possible to establish with great accuracy the velocity of precession motion. The observations used by Copernicus led him, on the other hand, to erroneously consider as real a periodic insignificant disturbance in that motion.

Copernicus presented the Earth's orbit in the same way as he had done in the Commentariolus i.e. using an eccentric circle (the centre of the circle did not therefore correspond to the Sun). An additional construction was needed to present the discovered changes in the eccentricity of the Earth's orbit.

Book Four contains the theory of the Moon's motion and methods for calculating solar and lunar eclipses. In developing his arguments against the Ptolemaic theory of the Moon, Copernicus expounds his own theory which corresponds to that in Commentariolus, but here it is extensively documented with the use of both old and new (i.e. his own) observations.

The last two books are devoted to the planets. In Book Five Copernicus studies the motion of the planets in the plane of the ecliptic, excluding, like his predecessors, the analysis of the latitudinal motion of the planets, which follows from the various inclinations of the planetary orbits in relation to the plane of the ecliptic. This analysis takes up the sixth and last book.

His own solution to the theory of the motion of the planets the author has prefaced with a short survey of the Ptolemaic theory, in which he criticizes, as he did in discussing the Moon, the use of the equant. The next chapter deals with phenomena observed in the motion of the planets as a result of the motion of the Earth. Heliocentric astronomy explains the loops described on the celestial sphere by the planets without recourse to the epicycle, used by Ptolemy, but by attributing them to the changing position of the observer, carried by the Earth in its movement round the Sun. Still requiring explanation, however, were the deviations from the uniform motion, caused by what is in fact the uneven motion of a planet on an elliptical orbit. We have already mentioned that the earlier solution to this problem given in the Commentariolus, which consisted of a circle concentric with the centre of the universe and of two epicycles, was replaced by an eccentric circle with only one small epicycle. These two equivalent geometrical constructions replace the real orbit of the planet just as well as did the Ptolemaic model with the equant. The equivalence of these two solutions was confirmed by Copernicus himself when he chose the new model (eccentric circle with epicycle) because he wanted to determine the changing planetary eccentricities without having recourse to additional constructions. The particular planets are discussed in the order of their diminishing distance from the Sun, i.e. beginning with Saturn and ending with Mercury. Using ancient observations together with his own, Copernicus was able to determine the dimensions and position of orbits, noting at the same time the mobility of the lines of the apsides.

The explanation of the motion of the lower planets, Venus and Mercury, required certain modifications. The relic from geocentric astronomy, which was preserved in De Revolutionibus in the determination of planetary orbits not in relation to the Sun but to the centre of the Earth's orbit (which lay outside the Sun), introduced certain disturbances in the motion of those planets, dependent on the position of the Earth at a given moment and most noticeable in the motion of Venus, the planet nearest to the Earth.

Mercury's orbit required special treatment. Because of the considerable eccentricity of this orbit and the impossibility of observing the planet except during the short periods when its angular distance from the Sun was greatest, the schema used by Copernicus yielded satisfactory results only for the moments close to the greatest elongation of Mercury. Similarly imprecise was the theory of Mercury's motion in geocentric astronomy. Unlike in the case of the other planets Copernicus worked out his theory of Mercury without the use of any observations of his own, which he could not carry out, as he himself says, because of the "Vistula vapours" obscuring the view. He had to make do with those recorded by the Nuremberg astronomer Bernard Walther. The comparison of ancient with new observations made it possible for Copernicus to establish the motion of Mercury's perihelion which amounts to one degree in 63 years, "if that motion is uniform."

The theory of the latitudinal motion of the planets in width, which comprises Book Six, bears the visible traces of geocentric astronomy in the form of periodic oscillations of the planetary orbits in the rhythm of the Earth's annual motion. Here, the true innovation consisted in the introduction by Copernicus of the inclination to the plane of the ecliptic of entire planetary orbits instead of, as in Ptolemy, the changing inclination of the epicycles. Apart from that, the exposition of the problem is modelled strictly on the Almagest.

The exhaustive presentation of all the astronomical questions of the day, the documented process of transition from information supplied by observation to theory, led to the universal recognition of Copernicus, the author of De Revolutionibus, as an innovator in astronomy even before leading scholars at the turn of the 16th century realized the significance and implications of the fundamental discoveries made by the Frombork astronomer.

Authors' Note

Twenty-five years since the publication of our essay, research on the science of the Renaissance has enormously enriched our understanding of what happened on the way to the "scientific revolution" of the seventeenth-century. In particular, the in-depth studies of Copernicus's mathematical astronomy have evaluated the astronomer's mathematical tools and the problems that he had to cope with or that he tried to cope with. We also may add here an unknown case of Copernicus's error in his geometric argument against Johann Werner's astronomical work of 1524 (cf. ch. 7 in Copernicus: Scholar and Citizen, Interpress Publishers, 1972). Yet, the recent Copernican literature itself is not free from errors distorting the overall picture of the astronomer's work. To name but one glaring example, there is the unfounded critique of the "postulates" in Copernicus's Commentariolus (cf. ch. 4 in Copernicus: Scholar and Citizen), presenting them as an orderless, logically-unrelated sequence. This has missed the obvious historical context of Copernicus's presentation, addressed to his contemporaries. It is enough to read the new "postulates" side by side with the corresponding opening chapters of a standard textbook of Ptolemaic astronomy (such as the "Epitome" by Peurbach and Regiomontanus). In short, there is a large number of valuable books on Copernicus and on the history of astronomy in general, but these books should always be read with an open mind.