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p. 233. Astronomy in the Middle Ageslocked

  • Michael Hoskin


‘Astronomy in the Middle Ages’ examines how the ideas of Ptolemy and antiquity were preserved and transmitted, initially by the scholars of Islam. They built a number of observatories and also developed the astrolabe. It was the introduction of the astrolabe into the West at the turn of the Millennium that revived an interest in astronomy in the West. At the same time the writings of antiquity were recovered and translated and with the introduction of the printing press their ideas were more widely disseminated. Ptolemy's ideas in the Almagest were finally surpassed when Nicolaus Copernicus wrote his De revolutionibus, arguing that the Earth orbited the Sun.

It was in ad 622 that the prophet Mohammad fled Mecca to Medina, and before long the new religion of Islam had spread across the whole of North Africa and into Spain. Islam made specific demands upon the skills of astronomers. The month began with the new moon – not when Sun, Moon, and Earth were geometrically aligned, but two or three days later, when the crescent was seen by human eyes. Could this be regularized, so that neighbouring villages would agree on the beginning of the new month, even when the sky was clouded? The hours of prayer were set by the altitude of the Sun as it traversed the sky, and the need to determine these hours correctly eventually led to the institution of the office of muwaqqit, or mosque timekeeper, so giving astronomers a secure and respected position in the community. And the determination of the local direction of Mecca, the qibla, which dictated the layout of mosques and graveyards and much else, posed a challenging problem that muwaqqits and other astronomers sought to solve.

Long before the arrival of Islam, the great centre of learning in Alexandria had fallen on troubled times. The Almagest itself was to find its way to Constantinople, and in the 9th century a copy was purchased by emissaries from Baghdad, where the youthful and vibrant Muslim culture had woken up to the intellectual treasures surviving in the Greek language. At p. 24Baghdad it was translated by a team working in the House of Wisdom, first from Greek into Syriac and then from Syriac into Arabic. Other copies in Constantinople would gather dust, unread, until in the 12th century the emperor presented one as a ceremonial gift to the King of Sicily, where it was translated into Latin.

Despite the censure in the Koran, astrology flourished in the Muslim world at every level of society; and those astrologers who were more than mere fortune tellers based their predictions on tables of planetary positions. The success of the models of the Almagest was undisputed, but these models incorporated parameters that could be determined with ever greater accuracy as the centuries passed – and Ptolemy himself had explained how to do this. At first the measuring instruments used by astronomers for this purpose were modest in size, but as the observers’ ambitions grew so did the size of their instruments, and they looked to patrons to pay for their construction and housing.

At times, however, this aroused the hostility of the religious authorities, and a patron's death – or even his loss of nerve – could bring astronomical observation to an end. In Cairo the construction of an observatory began in 1120 on the order of the vizier, but in 1125 his successor was killed by command of the caliph, his crimes included communication with Saturn, and the observatory was demolished. In Istanbul an observatory for the astronomer Taqi al-Din was completed by Sultan Murad III in 1577 – as it happened, just in time for observations of a bright comet. Taqi al-Din, doubtless with an eye to his own prosperity, interpreted the apparition as boding well for the sultan in his fight against the Persians. But events turned out otherwise, and in 1580 religious leaders convinced the sultan that it was inviting misfortune to pry into the secrets of nature. The sultan therefore ordered the observatory to be destroyed ‘from its apogee to its perigee’.

p. 25Only two Islamic observatories enjoyed more than a brief existence. At Maragha, the present-day Maragheh in northern Iran, construction of an observatory for the distinguished Persian astronomer Nasir al-Din al-Tusi (1201–74) was begun in 1259 by Hulagu, the Mongol ruler of Persia. Its instruments included a 14-foot-radius mural quadrant (an instrument for measuring altitudes, attached to a wall aligned in the north–south direction) and an armillary sphere (used for other measurements of position) with circles five feet in radius. With the help of these instruments, a team of astronomers completed in 1271 a zij, or collection of astronomical tables with instructions for their use, in the tradition of Ptolemy's own Handy Tables. But in 1274 al-Tusi left Maragha for Baghdad, and although observations at the observatory continued into the next century, its creative period was already over.

The other major observatory of Islam enjoyed the advantage that the prince himself was an enthusiastic member of staff. At Samarkand in central Asia, Ulugh Beg (1394–1449), a provincial governor who was to succeed to the throne in 1447, began construction of a three-storey building in 1420. Its chief instrument, built on the principle that ‘bigger is better’, was a form of sextant no less than 130 feet in radius. This was mounted out of doors between marble walls aligned north–south, and the range of the instrument was chosen so that it could be used to observe the transit of the Sun, Moon, and the other five planets. The great achievement of Samarkand Observatory was a set of astronomical tables that included a catalogue of over 1,000 stars. Much earlier, the Baghdad astronomer Abd al-Rahman al-Sufi (903–86) had prepared a revision of Ptolemy's star catalogue in which he gave improved magnitudes and Arabic versions of the identifications; but he had left the stars themselves and their often inaccurate relative positions unchanged, and so Ulugh Beg's was to be the single important star catalogue of the Middle Ages. Samarkand Observatory fell into disuse soon after the murder of Ulugh Beg in 1449.

p. 26Observatories were for an elite, but every astrologer needed to make observations, and this became possible through the development of the astrolabe, an ingenious portable computer and observing instrument that had its roots in antiquity. The typical astrolabe consisted of a brass disc that could be suspended by use of a ring at the top edge. One side of the astrolabe was for observations of the angular altitude above the horizontal of a star or planet; the observer suspended the instrument and looked at the heavenly body along a sighting bar, and then read the angle on a scale around the circumference. The other side of the disc represented the celestial sphere projected on to the plane of the equator from the south celestial pole.

10. A 14th-century astrolabe preserved at Merton College, Oxford

p. 27Each line from the pole intersected the celestial sphere in one further point, and it intersected the plane of the equator (in a single point); the latter point was the ‘projection’ of the former. Because the brass disc was of course of finite size, and because the heavens south of the Tropic of Capricorn were of no practical interest, the projected skies extended from the north celestial pole (represented by the centre of the disc) as far as this Tropic but not beyond.

Circles of equal altitude at the latitude of the observer projected into cirles that were engraved on the disc, along with much else. So far, so good; but the stars of the rotating heavens also needed representation. This was achieved by means of a brass sheet that bore indications of the locations of the principal stars but was otherwise cut away as much as possible to reveal the coordinate circles below. This sheet rotated about the central point of the disc underneath, just as the stars rotate about the north celestial pole. The sheet also contained a representation of the ecliptic path of the Sun, and the observer needed to know (and mark) the Sun's current position on it.

This done, a single observation – typically, of the altitude of a star at night or of the Sun by day – would allow the observer to rotate the sheet into its correct current position, by moving it until the star (or the Sun) lay over the appropriate coordinate circle. This done, the entire heavenly sphere was now in position, and many questions could be answered – for example, which stars were currently above the horizon and what was the altitude of each. Time could be determined by aligning the Sun with a scale on the perimeter of the disc and reading off the hour on the scale. This was possible irrespective of whether it was by observation of the Sun or of a star that the sheet had been positioned: the astrolabe was a clock that could be used to tell the time night and day throughout the 24 hours.

A wide range of other information could be obtained easily from the astrolabe. For example, to determine the hour at which a given star p. 28would rise, the astronomer would rotate the sheet until the star was above the circle of zero altitude, and then read off the time. The astrolabe was a simple, ingenious, and versatile device that encouraged quantitative observation of the heavens.

A zij had been composed as early as the first half of the 9th century, in the House of Wisdom at Baghdad, by al-Khwarizmi, a corruption of whose name gives us the word ‘algorithm’. It made use of the parameters and computational procedures contained in a Sanskrit astronomical work that had been brought there around 770. In a later version, the zij was to be translated into Latin in the 12th century, and so became a vehicle by which Indian astronomical methods reached the West. By making possible the prediction of future planetary positions, zijes supplied the needs of the practising astronomer/astrologer, and great numbers of these tables were produced, often using parameters that improved on those of Ptolemy.

Islam had no counterpart to the emerging universities of the Christian West, and we look in vain for an Islamic thinker of sufficient originality to challenge the foundations of Aristotelian/Ptolemaic cosmology. Nevertheless, discussions of shukuk, or doubts, concerning Ptolemy were appearing regularly by the 10th century. The most obvious target was the Ptolemaic equant, which violated the basic principle of uniform circular motion, but the epicycle and eccentre also came in for criticism because they involved motions that, while uniform, did not take place about the central Earth. A philosophical purist in this was the Andalusian Muhammad ibn Rushd (1126–98), known to the Latins as Averroes; in the West Aristotle was to become ‘The Philosopher’, and Averroes ‘The Commentator’. Averroes recognized that Ptolemaic models ‘saved the appearances’ – reproduced the observed motions of the planets – but this did not make them true. His contemporary and fellow Andalusian Abu Ishaq al-Bitruji (Alpetragius) attempted to devise alternative models that met Aristotelian requirements, but of course with very unsatisfactory results.

p. 29In Cairo Ibn al-Haytham (Alhazen, 965–c.1040) tried to adapt the Ptolemaic models so that they could take on physical reality. In his On the Configuration of the World the heavens were formed of concentric spherical shells, within whose thicknesses smaller shells and spheres were located. His work was translated into Latin in the 13th century, and was to become one of the influences on Georg Peurbach in the 15th century.

The equant had long aroused misgivings among even the most practical-minded astronomers, and at Maragha in the 13th century al-Tusi succeeded in devising a geometrical substitute involving two small epicycles; Copernicus was at one stage in his career to adopt a similar device, and for the same reason, though historians have not yet identified an unambiguous link between them. An attempt to devise planetary models that were purged of all objectionable elements was made by Ibn al-Shatir, muwaqqit of the Umayyad mosque at Damascus, in the middle of the 14th century. His lunar model avoided the huge variations in the apparent size of the Moon implied by the lunar model of the Almagest, his solar model was based on new observations, and all his models were free not only of equants but also of eccentres. Epicycles, however, he found unavoidable, for reasons that we can well understand. By the time of al-Shatir, however, the Latin West had developed its own astronomical tradition, and was no longer reliant upon translation from the Arabic.

This independence had been slow in coming. In the Roman world, Greek had continued to be the language of scholars, and none of the major astronomical works of antiquity was written in Latin. With the collapse of the Roman Empire, knowledge of Greek almost completely disappeared in the West, so that the classics of ancient astronomy – even if available – could no longer be read. Ancius Manilius Severinus Boethius (c.480–524/5), a high official in the Roman Gothic kingdom, set himself to translate into Latin as many treatises of Plato and Aristotle as possible, but he had already left it too late. However, before his execution for defiance of his king over p. 30an injustice, Boethius did manage to translate a number of Greek works, several of them on logic, and these he set alongside logical writings by Roman authors such as Cicero. In this way he bequeathed to later centuries a corpus of texts in what became the one secular area of study where the medieval student might ‘compare and contrast’ and so come to his own conclusions. As a result, logical consistency was to become an obsession in the medieval university, where debates over the validity of epicycles, or whether certainty could in principle be attained in a planetary model, were meat and drink to the young students in Arts.

Just one (incomplete) work of Plato made its way into Latin during this period: his cosmological myth, Timaeus, two-thirds of which was translated by Calcidius (in the 4th or 5th century), who supplied a lengthy commentary. Astronomical works written in Latin in the early Middle Ages make sad reading, although the basic fact of the sphericity of the Earth was never lost to sight. Ambrosius Theodosius Macrobius, an African who lived in the early 5th century, wrote a commentary on Cicero's Dream of Scipio, and in this he expounded a cosmology in which a spherical Earth lay at the centre of the sphere of stars, which rotated daily from east to west. As it did so, it dragged the planetary spheres with it, though each of these also had its individual motion in the opposite direction. Macrobius is vague about the order of the planets because his sources differed. Martianus Capella of Carthage (c.365–440) wrote The Nuptials of Philology and Mercury, an allegory of a heavenly marriage at which each of the seven bridesmaids presented a compendium of one of the Liberal Arts. This account of astronomy is notable for the explanation of why Venus and Mercury are always seen near the Sun in the sky: they are circling the Sun, and so they accompany the Sun as it circles the Earth.

Christianity, like Islam, presented challenges to astronomers, chief among them the calculation of the date of Easter. In simple terms, Easter Day is the Sunday that follows the full moon that follows the spring equinox, and so its date in any given year depends on the p. 31cycles of both Sun and Moon. It might have been possible for the Christians of Alexandria, as inheritors of the accurate values for month and year handed down from Babylon, to calculate the appropriate date of Easter for some years ahead; but the Church authorities took the more practical course of trying to identify a period consisting of a number of years that almost equalled an integral number of months, and establishing the dates of Easter within the approaching years of this period. Once established, such a sequence could be repeated for future periods, indefinitely.

The cycle eventually adopted was one discovered by Babylonian astronomers in the 5th century bc but credited to the Greek Meton, whereby 235 lunar months equal 19 years (with an error of only a couple of hours). The definitive treatise, On the Divisions of Time, was written in 725 by the Venerable Bede (672/673–735) of Jarrow in England. In the calendar laid down by Julius Caesar, a leap year occurred every fourth year (without exception); every four years, therefore, the day of the week on which a given date occurred advanced by five, and so in 7 × 4 = 28 years it would return to its original day. Bede combined this with the 19-year Metonic cycle to produce an overall cycle of 19 × 28 = 532 years that catered for the luni-solar pattern of Easter together with the requirement that it occur on a Sunday.

The revival of astronomy – and astrology – among the Latins was stimulated around the end of the first millennium when the astrolabe entered the West from Islamic Spain. Astrology in those days had a rational basis rooted in the Aristotelian analogy between the microcosm – the individual living body – and the macrocosm, the cosmos as a whole. Medical students were taught how to track the planets, so that they would know when the time was favourable for treating the corresponding organs in their patients.

In 1085 the great Muslim centre of Toledo fell into Christian hands, and the intellectual riches of Islam and, more especially, Greece became accessible. Translators descended on Spain, the most p. 32notable being Gerard of Cremona (c.1114–87), whose innumerable translations included the Almagest and the Toledan Tables of al-Zarqali (d. 1100). These tables were then adapted for other places and proved immensely successful, although the underlying planetary models remained a mystery for the time being.

If the 12th century was the era of translations, the 13th was that of the assimilation of the works translated. In the emerging universities, Latin was the lingua franca, and so there was no language barrier to prevent students and teachers going where they wished. Prospective lawyers might go to Bologna and medical students to Padua, but in most disciplines Paris was pre-eminent.

There, as elsewhere, the Faculty of Arts provided the basic education in literacy and numeracy, through the medium of the seven Liberal Arts, which included astronomy. The Arts students were mostly boys in their teens, and the invention of printing lay in the future, so the level of instruction was inevitably elementary. A minority of students would eventually stay on for theological, medical, or legal studies in one of the higher faculties; medicine and law enjoyed their traditional prestige, while the writings of Augustine and the other Fathers of the Church ensured that theology was a challenging intellectual discipline. There was therefore tension between the teachers in these higher faculties and those trapped in the humdrum routine of Arts.

The bulk of the new translations, however, belonged to Arts, and provided the Parisian Masters of Arts with a lever to use in their struggle for improved status. At the same time, the arrival of the Aristotelian corpus, which owed nothing to Christian Revelation and which seemed to challenge certain basic Christian doctrines, aroused misgivings among the theologians. There followed decades of turmoil at Paris, until a synthesis was achieved by the Dominican friar Thomas Aquinas (1225–74), who assimilated Aristotle into Christian teaching so successfully that the 17th century would find it hard to make a separation of the two.

p. 33Research was not then the function of a university, and in astronomy the immediate teaching need had been for an elementary textbook that the young students might use. An attempt at this was made in the mid-13th century by John of Holywood (Johannis de Sacrobosco), but his Sphere was hopelessly inadequate when faced with the challenge of explaining the motions of the Sun, Moon, and lesser planets. Nevertheless, after the invention of printing the work offered more competent astronomers an excuse to write elaborate commentaries, and in this form it would become one of the best-sellers of all time.

Later in the 13th century an anonymous author made good some of the defects of the Sphere with his Theory of the Planets. This gave a simple (if only partly satisfactory) account of the Ptolemaic models of the various planets, with clear definitions. Meanwhile, at the court of King Alfonso X of Castile, the old Toledan Tables were replaced by the Alfonsine Tables; modern computer analysis has shown that these tables, which would be standard for the next 300 years, were calculated on Ptolemaic models with only the occasional updating of parameters.

It was not until the 14th century that the Latin West had sufficiently mastered its heritage from the past to be able to break new ground. One development of significance for astronomy came in terrestrial physics, for it was by arguing from the motion of projectiles that Aristotle had most convincingly demonstrated the Earth to be at rest: an arrow fired vertically fell to the ground at the very place from which it had been fired, and this proved that the Earth had not moved while the arrow was in flight.

However, Aristotle was at his least convincing when discussing the physics of projectile motion. An earthly body such as an arrow, he argued, would naturally move downwards towards the centre of the Earth, and its upward (and therefore unnatural) motion must be imposed upon it by an outside force – and not only imposed, but maintained for as long as the arrow was climbing. Aristotle thought p. 34the air itself was the only agent available to maintain the upward motion of the arrow; but sceptics had pointed out that this was implausible, since it was possible to fire arrows upwards in the teeth of a gale.

The Parisian masters Jean Buridan (c.1295 – c.1358) and Nicole Oresme (c.1320–82) agreed with Aristotle that a force must be at work, but they rejected any role for the air in this. They argued that an ‘incorporeal motive force’ must be imposed by the archer on the arrow, a force they termed ‘impetus’. Buridan suggested that the heavenly spheres – which though frictionless needed a permanent motive force (angelic intelligences?) if they were to rotate for ever – would spin eternally if endowed with the motive force of impetus at the Creation.

Oresme saw a significant implication of the concept of impetus. If the Earth were indeed rotating, the archer as he stood on its surface would be moving with it. As a result, as he prepared to fire the arrow, he would unknowingly confer on the arrow a sideways impetus. Endowed with this impetus, the arrow in flight would travel horizontally as well as vertically, keeping pace with the Earth, and so would fall to ground at the very place from which it had been fired. The flight of arrows, he said, therefore contributed nothing to disputes as to whether the Earth was or was not at rest. Nor, for that matter, did the other arguments traditionally invoked, including those from Scripture. Oresme was of the opinion that the Earth was indeed at rest; but it was no more than an opinion.

The invention of printing in the 15th century had many consequences, none more significant than the stimulus it gave to the mathematical sciences. All scribes, being human, made occasional errors in preparing a copy of a manuscript. These errors would often be transmitted to copies of the copy. But if the works were literary and the later copyists attended to the meaning of the text, they might recognize and correct many of the errors introduced by their predecessors. Such control could rarely be p. 35exercised by copyists required to reproduce texts with significant numbers of mathematical symbols. As a result, a formidable challenge faced the medieval student of a mathematical or astronomical treatise, for it was available to him only in a manuscript copy that had inevitably become corrupt in transmission.

After the introduction of printing, all this changed. The author or translator could now check proofs and ensure that the version set in type was faithful to his intentions; and the printer could then multiply perfect copies, to be distributed throughout Europe and available for purchase at prices that were modest compared with the cost of a handwritten manuscript.

Within a few decades the achievements of the Greek astronomers had been mastered and indeed surpassed. The New Theories of the Planets of Georg Peurbach (1423–61), the Austrian court astrologer, which appeared in print in 1474, described the Ptolemaic models that underlay the Alfonsine Tables. It also described physically-real representations of these same models, and it may have been the shortcomings of these that led Copernicus to take up astronomy.

In 1460 Peurbach and his young collaborator, Johannes Müller (1436–76) of Königsberg (in Latin, Regiomontanus), met the distinguished Constantinople-born Cardinal Johannes Bessarion (c.1395–1472). Bessarion was anxious to see the contents of Almagest made more accessible, and he persuaded the two astronomers to undertake the task. Peurbach died the following year, but Regiomontanus completed the assignment. Their Epitome of the Almagest, half the length of the original, appeared in print in 1496. It remains one of the best introductions to Ptolemy's masterpiece. The Almagest itself was published in an obsolete Latin translation in 1515, in a new translation in 1528, and in the Greek original in 1538. In 1543 a book would appear that surpassed it.

Nicolaus Copernicus (1473–1543) was born in Torún, Poland, and p. 36studied at the University of Cracow, where the professors of astronomy had made no secret of their dissatisfaction with the concept of the equant. He then went to Italy, where he studied canon law and medicine, learned some Greek, and developed his interest in astronomy. He is said to have lectured on the subject in Rome around 1500, to a large audience. In 1503 he returned to Poland to take up an administrative canonry of Frombork where his uncle was bishop, and he remained in the diocese for the rest of his life.

Whereas voluminous works by Aristotle were available in Latin in the later Middle Ages, Plato had fared less well: only two minor dialogues had been added to the Timaeus that Calcidius had translated in part long ago. All this changed in the Renaissance, as close contacts were resumed with the Greek world, resulting in an influx of Greek scholars into the West prior to the sack of Constantinople in 1453. Plato's dialogues were recovered and admired for their literary qualities, and his mathematical outlook on the cosmos began to supplant that of Aristotle the naturalist. Astronomers began to look for harmony and commensurability in planetary theory, and they failed to find it in the models of Ptolemy, even though the Alfonsine Tables continued to meet the need for tables of reasonable accuracy. In particular, the equant was seen as ‘a relation that nature abhors’, in the words of Copernicus's disciple Georg Joachim Rheticus (1514–74).

It happened that by now Ptolemy's Planetary Hypotheses had been lost to sight, and with it his overall cosmology. The Almagest offered models for the individual planets, but Ptolemy's apparent failure to present an integrated picture of the cosmos meant, as Copernicus would put it, that past astronomers

have not been able to discover or to infer the chief point of all – the structure of the universe and the true symmetry of its parts. But they are just like someone taking from different places hands, feet, head, and the other limbs, no doubt depicted very well but not modelled p. 37from the same body and not matching one another – so that such parts would produce a monster rather than a man.

It was from aesthetic considerations such as these, as much as from specific problems like the absurd variations in the apparent size of the Moon on the Ptolemaic model, that pressure for reform developed – even though in themselves the Ptolemaic models (with improved parameters) did all that could reasonably be asked of them.

There were clues as to the direction a reform might take. Aristotle's custom of citing those whom he intended to refute meant that every student knew of ancient authors who had argued that the Earth was in motion – and Aristotle's rebuttal was no longer so convincing. Peurbach had remarked on how for some unknown reason an annual period cropped up in the model of every single planet. Whatever it was that set Copernicus thinking, not many years after his return from Italy a manuscript by him entitled Commentariolus, or Little Commentary, began to circulate. In it he outlined his dissatisfaction with existing planetary models, their equants coming in for special criticism. He proposed a Sun-centred alternative, in which the Earth became a planet orbiting the Sun with an annual period, while the Moon lost its planetary status and became a satellite of Earth.

He showed how this led at last to an unambiguous order for the planets (now six in number), in both period and distance. We saw how Ptolemy plausibly assumed that the slower-moving planets were the highest in the sky; but this did not settle the order of Sun, Mercury, and Venus, which accompany each other as they move against the background stars and therefore appear to have the same period of one year. Once this period was accepted as being in fact that of the Earth-based observer, the true periods of Mercury and Venus could be identified, quite different from each other and from that of the Earth; and so an unambiguous sequence of periods could be established.

p. 38Copernicus was also able to measure the radii of the planetary orbits as multiples of the Earth–Sun distance; for example, when Venus appears furthest from the Sun (at ‘maximum elongation’), the angle Earth–Venus–Sun is a right angle, and by measuring the angle Venus–Earth–Sun the observer can establish the shape of the triangle and therefore the ratios of its sides. The sequence of periods and the sequence of distances proved to be identical. He was later to say of this:

Therefore in this arrangement we find that the world has a wonderful commensurability, and that there is a sure linking together in harmony of the movement and magnitude of the orbital circles, such as cannot be found in any other way.

This was a powerful consideration in an age dominated by the Platonic search for harmony in the cosmos. Meanwhile, at the more detailed level, Copernicus made a start in Commentariolus on developing equant-free models for the planets and Moon.

Years passed, during which Copernicus developed his mathematical astronomy, remote from the intellectual centres of Europe. In 1539, Rheticus, then a teacher of mathematics in the University of Wittenberg, paid him a visit. He found himself enthralled with Copernicus's achievement in developing geometrical models of planetary motions that rivalled those of the Almagest, but which were incorporated into a coherent, Sun-centred cosmovision. He secured Copernicus's permission to publish a First Report on this work, which he did the following year. He also persuaded Copernicus to allow him to take the completed manuscript (known by its abbreviated Latin title of De revolutionibus) to Nuremberg for printing. The task of seeing the work through the press he delegated to a Lutheran clergyman, Andreas Osiander (1498–1552), who with the best of intentions inserted an unauthorized and unsigned preface to the effect that the motion of the Sun was proposed merely as a convenient calculating device; the result was that readers who p. 39got no further than this preface had no inkling of the author's true purpose.

The overwhelming bulk of Copernicus's book was concerned with (equant-free) geometrical models of the planetary orbits, and in their daunting complexity these matched the models of the Almagest. Proof that they could become the basis of accurate planetary tables – demonstration that the heliocentric approach could pass the practical test – was to come later, with the publication in 1551 of the Prutenic Tables of Erasmus Reinhold (1511–53), which were computed using Copernicus's models. It was in the brief Book I of De revolutionibus that Copernicus outlined the striking consequences that follow from the basic assumption that the Earth is an ordinary planet orbiting the Sun.

As we have seen, the list of planets ordered by period was identical with the list of planets ordered by distance. Equally striking, the mysterious ‘wanderings’ that had given the planets their name now became the obvious and expected consequence of observing one planet from another: Mars seems to go backwards when opposite to the Sun in the sky simply because it is then that the Earth overtakes it ‘on the inside’. There is no longer any mystery as to why two planets, Mercury and Venus, are always seen near the Sun, whereas the other three may be observed at midnight; the orbits of Mercury and Venus are inside that of the Earth, while the others are outside.

True, the Earth was anomalous in being the only planet to have a satellite. It was true, too, that the ‘fixed’ stars did not show the apparent annual motion that one would expect if they were being observed from an Earth in annual orbit (Copernicans retorted that the stars were far away, and their ‘annual parallax’ was therefore too small for observers to detect). But these were details. The heliocentric universe was a true cosmos:

In the centre of all resides the Sun. For in this most beautiful temple, who would place this lamp in another or better place than that from p. 40

11. The outline diagram of the solar system, from Book I of Copernicus's De revolutionibus, showing the planets with their approximate periods. Note that no. V, the Earth, is unique in having a satellite, the Moon. Galileo's later telescopic discovery that Jupiter also has satellites helped ease the embarrassment felt by Copernicans because of this anomaly.

which it can illuminate the whole at one and the same time? As a matter of fact, not inappropriately do some call it the lantern of the universe; others, its mind; and others still, its ruler. The Thrice-Great Hermes calls it a ‘visible god’; Sophocles's Electra, ‘that which gazes upon all things’. And thus the Sun, as if seated on a kingly throne, governs the family of planets that wheel around it.

p. 41De revolutionibus is the culmination of the Greek programme to ‘save the appearances’ of the mysterious planets by geometrical models using combinations of circles rotating with uniform motion. It is an Almagest purged of equants, though every bit as complex. It would be a generation before its revolutionary implications sank in.