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1575 by Tycho Brahe. Copernicus clearly laid out the assumptions on which he had based his work:

8 See, for example, Babb (1977). The passage of this work from Copernicus to Tycho, via a number of other astronomers, has been traced by Dobrzycki and Szczucki (1989). The title appearing on existing manuscripts translates as Nicholas Copernicus, Sketch of his Hypotheses for the Heavenly Motions. The authenticity of this title has been doubted widely on the basis that Copernicus would not have

1. There is no one center of all the celestial circles or spheres.

2. The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere.

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

4. The ratio of the earth's distance from the sun to the height of the firmament is so much smaller than the ratio of the earth's radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament.

5. Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth's motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged.

6. What appear to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve about the sun like any other planet. The earth has, then, more than one motion.

7. The apparent retrograde and direct motion of the planets arises not from their motion but from the earth's. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens.

His programme was to represent the motions of the heavenly bodies using uniform circular motions. This he considered to be the true goal of astronomy, and he noted that all previous attempts had been unsatisfactory in some way. The concentric spheres of Eudoxus failed accurately to predict the phenomena and, while Ptolemy had produced an accurate theory, it violated the principle of uniform circular motion through the introduction of the equant. The system of eccentrics and epicycles that Copernicus created was designed to rectify these problems. Of course, as Kepler later came to realize, it was precisely because the equant mechanism violated the principle of uniform circular motion that it was a step in the right direction.

The first three assumptions, in which the heliocentric nature of the system is stated clearly, put Copernicus in immediate conflict with the universally held Aristotelian view that the Earth was the centre of rotation for all the heavenly bodies, and assumption 4 accounts for the fact that no annual parallax had been observed for the fixed stars. The 'circumjacent elements' referred to in assumption 5 are the atmosphere and the waters that lie on the surface of the Earth, and the final two assumptions describe how the complex motion of the presented his system as a mere hypothesis. However, a thorough investigation of Copernicus' use of the term 'hypothesis' throughout his astronomical writings led Rosen (1959) strongly to criticize this view. The work was first published in Warsaw in 1854 (Koyré (1973)) but it took some time before a proper understanding of its place in the development of Copernicus' ideas was reached. For example, in Dreyer's History of Astronomy (Dreyer 1953) written in 1906, the Commentariolus is treated as a summary of the heliocentric system written after On the Revolutions. Quotations from the Commentariolus are taken from the translation in Rosen (1959).

Sun and planets are just manifestations of the motion of the Earth. No detailed explanations were given in the Commentariolus, but it is clear from the text that when Copernicus wrote it he had already planned On the Revolutions. The Commentariolus is in many ways a rough outline of Copernicus' mathematical theory, and when it was written he may well have believed that it would be a simple matter to add the mathematical demonstrations to his sketched-out theory. As it turned out, however, On the Revolutions became a far more extensive undertaking than envisaged originally.

The Commentariolus had two major shortcomings. First, Copernicus did not attempt to provide proof for the fundamental assumptions on which the work was based, preferring simply to state them as axioms. He must soon have realized that this would not be sufficient for his audience and that he would have to provide supporting evidence. In the end, the evidence that he did come up with in On the Revolutions was hardly convincing, something of which he was all too painfully aware. Second, the numerical parameters on which the models in the Commentariolus were based were largely those of the Alfonsine Tables, and these were simply not accurate enough for Copernicus' purposes. Thus, he realized that new parameters would have to be derived from observations.

The actual models that Copernicus used in the Commentariolus, which were similar but not identical to those appearing later in On the Revolutions, will not be discussed here, but one aspect is worthy of note. The theories of the Moon and planets are pretty much identical to those of Ibn al-Shatir, though of course Ibn al-Shatir's planetary theories were set in the context of a geocentric universe and the numerical parameters are different. Is this a coincidence? From the number of similarities, it seems clear that Copernicus must have come across the work of the Maragha observatory somehow, and there is evidence that this Islamic astronomy was known in Italy in the late fifteenth and early sixteenth centuries. Also, as we shall see below, Copernicus made extensive use of geometrical devices equivalent to the Tusrcouple. Thus, it appears likely that Copernicus came across these geometrical theories while on his travels.10

10 According to Swerdlow and Neugebauer ((1984)) 'the question therefore is not whether, but when, where, and in what form he learned of the Maragha theory' (see also Abbud (1962)). The problem of how Copernicus acquired the techniques he used is discussed by di Bono (1995), who suggests some alternative sources. For example, Veselovsky (1973) thought it rather more likely that Copernicus generated his equivalent of the "Tusi couple from remarks made by Proclus in his Commentary on the First Book of Euclid. Rosinska (1974) discusses how Islamic geometrical models could have found their way to Cracow in the fifteenth century, and Kren (1971) suggests that the Tiisi couple was described by Oresme (albeit badly) in his Questiones de spera, a series of questions concerning Sacrobosco's On the Sphere written some time before 1362.

After describing the motions of the Earth, Moon, and planets, Copernicus concluded proudly:

Altogether, therefore, thirty-four circles suffice to explain the entire structure of the universe and the entire ballet of the planets.

Subsequently, however, the examination of more observational data led Copernicus to realize that the theory presented in the Commentariolus was insufficient to predict the positions of the heavenly bodies accurately over long periods, and he had to discard many of the geometrical constructions and replace them with more complicated devices.

On the Revolutions

Copernicus' move to Frombork in 1510 led to a substantial increase in his administrative duties as a canon of the Chapter of Warmia, and he was also a respected physician, medicine being a subject he had studied inItaly. It was against this background that he began to write his extensive exposition of heliocentric astronomy that was to become On the Revolutions. He needed considerably more observational data, which he proceeded to collect over the years between 1512 and 1529. For example, a series of observations of the Sun performed by Copernicus in 1515 and 1516 led him to the conclusion that the eccentricity of the Sun's orbit was not constant as he had previously assumed.

Much of On the Revolutions essentially was complete by 1530, but Copernicus delayed publication. Part of the reason was his inability to find any direct evidence for the Earth's motion, and he realized that without this he was going to find it very difficult to convince the sceptics. In the Letter of Dedication to Pope Paul III he wrote:

... the scorn which I had reason to fear on account of the novelty and unconventionality of my opinion, almost induced me to abandon completely the work which I had undertaken.

Despite Copernicus' reticence, news of his work spread and aroused a great deal of interest. In 1539, Georg Rheticus, a young German professor, travelled to Frombork to find out more. He brought with him a number of recently published books including the 1538 Greek edition of the Almagest which was much more

11 It is not easy to state precisely how many circular motions were required in Ptolemy's system or Copernicus' final theory. A summary of different opinions can be found in Cohen (1985), p. 119. Contrary to what is often alleged, the system that was described in On the Revolutions actually is marginally more complex than that in the Almagest.

accurate than the Latin version Copernicus had been using, andRegiomontanus'

On Triangles.

Rheticus became an enthusiastic supporter of Copernicus' theory and he wrote an extensive summary, published in 1540 in the form of a letter to Johannes Schoner - an astronomer and publisher from Nuremberg - and which now is known usually by the abbreviated title Narratio prima or First Report.12 The publication of this concise well-written summary of Copernicus' theory led to a surge in interest, and may well have been at least partly responsible for inducing Copernicus to publish his work. The First Report was a very useful introduction to Copernican astronomy. In it, Rheticus stressed that Copernicus was attempting to reproduce celestial motions in accordance with the Pythagorean principle of uniform circular motions, and that he had 'liberated' astronomy from the equant. The work, which also included biographical information about Copernicus, was nearly always included in published editions of On the Revolutions, and was later published with Kepler's Secret of the Universe to help the reader understand Copernican astronomy.

Rheticus left Frombork in 1541 with a manuscript of On the Revolutions and set about arranging for its publication. The fact that Copernicus - who was worried about being misunderstood and ridiculed for his views - handed over his manuscript to Rheticus shows that a very high degree of trust had developed between them. In October 1542, when he took up his professorship at Leipzig, Rheticus entrusted the responsibility for the printing of Copernicus' treatise to Andreas Osiander, a Lutheran theologian closely associated with the distinguished Nuremberg printer Johann Petreius. Osiander had previously in 1541 written to Copernicus suggesting that in order to 'mollify the peripatetics and theologians whose opposition you fear'13 some words be added to the effect that the heliocentric theory was merely a hypothesis which, even if wrong, accurately reproduced the phenomena. Copernicus, of course, did not agree, since it had always been his aim to demonstrate the true structure of the planetary system, and as a computational scheme Ptolemy's astronomy, with parameters updated to take account of more recent observations, was perfectly adequate. However, Osiander took it upon himself to add an unsigned preface entitled To the Reader Concerning the Hypothesis of this Work in which he remarked:

For these hypotheses need not be true nor even probable. On the contrary, if they provide a calculus consistent with the observations, that alone is enough For

Translated in Rosen (1959).

Quoted from Rosen's commentary on the front matter of On the Revolutions in Copernicus

this art, it is quite clear, is completely and absolutely ignorant of the causes of the apparent nonuniform motions. And if any causes are devised by the imagination, as indeed very many are, they are not put forward to convince anyone that they are true, but merely to provide a reliable basis for computation So far as hypotheses are concerned, let no one expect anything certain from astronomy, which cannot furnish it, lest he accept as the truth ideas conceived for another purpose, and depart from this study a greater fool than when he entered it.

It is not known whether Copernicus ever saw this unwanted addition to the text, but Rheticus was furious and tried to force the publication of a corrected edition.

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