The Danish astronomer Tycho Brahe (1546–1601) was, like Wilhelm IV of Hesse-Kassel a prominent aristocrat. In the sixteenth century Denmark was effectively ruled by an oligarchy of about twenty aristocratic families. Both of Tycho’s parents were members of the oligarchy. His father Otte Brahe was a privy councillor and his mother Beate Bille was a powerful figure at the Danish court. His uncle Jørgen Thygesen Brahe, who actually brought him up (it’s a complex story), was admiral of the Danish navy. Jørgen Brahe’s brother in law, Peder Oxe, was Steward of the Realm and as such the most powerful man in the kingdom. Put simply Tycho was born with every possible privilege. Naturally, it was expected that he would follow a career either in politics or the military or both. In 1559 he went to university to study law but he had already been bitten by the astronomy bug. He was immensely impressed by the fact that the solar eclipse on 21 August 1560 had been predicted, even if the prediction was off by a day. This was the beginning of his realisation that more accurate observational data was required.

Tycho Brahe Source: Wikimedia Commons

In 1562, as was normal for a young Danish aristocrat, he set off on a study tour of the German universities. As before nominally to study law but he maintained his strong interest in astronomy. In 1563 he observed a conjunction of Jupiter and Saturn, which was his aha moment as far as the available planetary tables were concerned; both the Ptolemaic and Copernican tables were inaccurate, so he resolved to undertake something to correct this and began recording all of his astronomical observations. Having studied at Leipzig and Rostock, not just law and astronomy but also medicine and medicinal alchemy he returned to Demark in 1567. His father still wanted him to go into law but with the support of his quasi-uncle Peder Oxe, who had studied extensively and was a humanist scholar, Tycho was allowed to follow his desire to become a scholar.

Peder Oxe Source: Wikimedia Commons

Following further tours of Germany, where he acquired astronomical instruments, and the death of his father, which made him financially independent, in 1571 he set up his first observatory and alchemical laboratory at Herravad Abbey, with the help of another uncle Steen Bille.

In 1574 he published his first set of observations and began lecturing on astronomy at the University of Copenhagen. In 1575 he undertook another tour of Europe, partially in service of the Danish king. Tycho travelled throughout Europe meeting and talking to people looking at astronomical instruments and carrying out commissions from Frederick II (1534–1588). On this journey he visited Kassel and spent a week together with Wilhelm IV discussing astronomy.

Wilhelm IV Source: Wikimedia Commons

Wilhelm had a collection of astronomical instruments of a wider range and better quality than anything Tycho had previously encountered. By this point Wilhelm had several years behind him, as a serious astronomical observer and could give Tycho much practical advice. He also discussed his plans for creating a new star catalogue, plans that had been postponed due to the death of his father and having to take responsibility for his land. Tycho inspired Wilhelm to go ahead with programme and Wilhelm inspired Tycho to settle down, build an observatory and carry out a similar programme. Due to a death in Wilhelm’s family, Tycho must break off his visit after a week; the two men never met again but they corresponded much over the years until Wilhelm’s death and several people travelled between Hven and Kassel over the years reporting on the latest developments and achievements.

Tycho returned to Copenhagen in 1575 now determined to devote his life to astronomical research, leaving Denmark if necessary to set up in Basel or some other suitable European metropolis. Frederick II was very impressed with the tasks that he had commissioned Tycho to fulfil in his name and decided it was time to bind the obviously talented young aristocrat to his court. He praised Tycho and offered him an attractive range of different stewardships and fiefs. All of those on offer would have required Tycho to engage political or militarily or both in Danish life and that is exactly what he didn’t want so he demurred, asking for time to consider.

Frederick II of Denmark Portrait by Hans Knieper or Melchior Lorck, 1581.

It came to Frederick’s ears that Tycho was planning on leaving Denmark for Basel, for example. In the meantime Wilhelm of Kassel, whose sister was married to Frederick’s uncle, had sent an emissary to Copenhagen recommending that his cousin fulfil Tycho’s desires and help him to found an observatory in Denmark. Whether on his own initiative, or prompted by Tycho’s uncle Steen Billie, Frederick now offered Tycho the island of Hven, which lies between Denmark and Sweden as his fief with a yearly stipend generous enough to build and operate what would become the greatest observatory in Europe.

Tycho is credited in the popular history of astronomy with three major achievements: he is given credit for destroying the Aristotelian cosmological claims that the heavens are perfectand unchanging, the planet orbit on crystalline spheres and that comets are sublunar meteorological phenomena through his observations of the 1572 supernova and the 1577 comet. His major contributions were, of course, his more that twenty year long systematic astronomical observations and records that laid the foundations for the astronomy of the seventeenth century. Lastly he is given credit for the geo-heliocentric system, that bears his name, an important intermediate stage on the way to the acceptance of a heliocentric system.

Whilst the observational catalogue can be attributed to Tycho and his numerous employees alone and he is justifiably acknowledged as the second most important figure in sixteenth century astronomy, after Copernicus, as far as the other two achievements are concerned their sole attribution to Tycho is not justified and in fact produce a distortion in the historical record.

The Great comet of 1577, seen over Prague on November 12. Engraving made by Jiri Daschitzky. Source: Wikimedia Commons

As I pointed out in Part I the Aristotelian theory of comets had already begun to be questioned by Toscanelli, Peuerbach and Regiomontanus in the fifteenth century. As I explained in Part V, in the 1530s comets had again become a major topic of investigation and discussion under Europe’s leading astronomers. By the 1570s all the astronomers in Europe eagerly observed the supernova from 1572 and the comet from 1577 and Tycho was only one of several important astronomers, who recognised that these were supralunar phenomena and reported them as such. Michael Mästlin and Thaddaeus Hagecius ab Hayek both established and respected astronomers certainly had more influence on the acceptance of these new discoveries than Tycho in the 1570s. Really crucial for this important step towards a new cosmology was the acceptance by Christoph Clavius, professor of mathematics at the Collegio Romano, and as such the most influential Ptolemaic astronomer in Europe.

Star map of the constellation Cassiopeia showing the position (labelled I) of the supernova of 1572; from Tycho Brahe’s De nova stella Source: Wikimedia Commons

This very brief sketch shows that the dismantling of these aspects of Aristotelian cosmology was the result of numerous astronomers observing, discussing and offering new theories of nearly two centuries and not the heroic act of a single astronomer.  The end of celestial perfection and the destruction of Aristotle’s crystalline spheres was an important stage in the emergence of modern astronomer but it is not one that should  be credited to Tycho alone.

Regular readers of this blog should by now be well aware of the fact that I belong to the Simon Marius Society a small group of scholars mostly from the area around Nürnberg, who dedicate some of their time and energy to re-establishing the reputation of the Franconian mathematicus Simon Marius (1573–1625), who infamously discovered the four largest moons of Jupiter literally one day later than Galileo Galilei and got accused of plagiarism for his troubles. Galileo may have discovered them first but Marius won, in the long term, the battle to name them.

Frontispiece of Mundus Iovialis Source:Wikimedia Commons

In 2014 the Simon Marius Society organised many activities to celebrate the four-hundredth anniversary of the publication of his opus magnum, Mundus Jovialis (The World of Jupiter). Amongst other things was an international conference held in Nürnberg, which covered all aspects of Marius’ life and work. The papers from this conference were published in German in 2016: Simon Marius und seine Forschung (Acta Historica Astronomiae), (AVA, Leipzig).

Now after much effort and some delays the expanded translation, now includes the full English text of Mundus Jovialis, has become available in English: Simon Marius and his Research, Springer, New York, 2019.

The ebook is already available and the hardback version will become available on 19 August. I apologize for the horrendous price but the problem of pricing by academic publishers is sadly well known. Having copyedited the entire volume, which means I have read the entire contents very carefully I can assure you that there is lots of good stuff to read not only about Simon Marius but also about astronomy, astrology, mathematics, court life in the seventeenth century and other topics of historical interest. If you can’t afford a copy yourself try to persuade you institutional library to buy one! If your university library buys a copy from Springer then students can order, through the library, a somewhat cheaper black and white copy of the book.

The Guardian is making a serious bid for the year’s worst piece of #histsci reporting or as Adam Shapiro (@tryingbiology) once put it so expressively, #histsigh! The article in question has the shock, horror, sensation headline: Groundbreaking astronomer Kepler ‘may have practised alchemy’. Ignoring the fact for the moment that he probably didn’t, given the period and the milieu in which Kepler lived and worked saying that he may have been an alchemist is about as sensational as saying he may have been a human being.

Johannes Kepler Source: Wikimedia Commons

The period in which Kepler lived was one in which the interest in alchemy was very widespread, very strong and very open. For eleven years he was Imperial Mathematicus at the court in Prague of the German Emperor Rudolph II, which was a major centre for all of the so-called occult sciences and in particular alchemy. In Prague Kepler’s original employer Tycho Brahe had been for years a practitioner of Paracelsian alchemical medicine (a very widespread form of medicine at the time), which to be fair the article sort of says. What they say is that Tycho was an alchemist, without pointing out that his alchemy was restricted to medical alchemy.

Tycho Brahe Source: Wikimedia Commons

One of his colleagues was the Swiss clockmaker Jost Bürgi, who had come to Prague from Hesse-Kassel,

Jost Bürge Source: Wikimedia Commons

where the Landgrave Moritz was a major supporter of alchemy, who appointed Johannes Hartmann (1568–1631) to the first ever chair for chemistry, actually Paracelsian medicine, at the university of Marburg. The real surprise is not that Kepler was an alchemist or practiced alchemy but rather that given the time and milieu in which he lived and worked that he wasn’t and didn’t.

Johannes Hartmann Source: Wikimedia Commons

How can I be so sure that Kepler didn’t dabble in alchemy? Simply because if he had, he would have written about it. Kepler is a delight, or a nightmare, for the historian, there is almost no figure that I know of in #histSTM, who was as communicative as Kepler. He wrote and published eighty three books and pamphlets in his lifetime covering a very wide range of topics and in all his written work he was always keen to explain in great detail to his readers just what he was doing and his thoughts on what he was doing. He wrote extensively and very openly on his mathematics, his astronomy, his astrology, his family, his private affairs, his financial problems and all of his hopes and fears. If Kepler had in anyway been engaged with alchemy, he would have written about it. If anybody should chime in now with, yes but alchemists kept they activities secret, I would point out in Kepler’s time the people practicing alchemy, particularly the Paracelsians, were anything but secretive. And it was with the Paracelsians that Kepler had the closest contact.

There are a few letters exchanged between Kepler and his Paracelsian physician friends, which show quite clearly that although Kepler displayed the natural curiosity of a scientific researcher in their alchemistic activities he did not accept the basic principles of alchemy. In his notorious exchange with Robert Fludd, he is very dismissive of Fludd’s alchemical activities. Kepler was not an alchemist.

From a historical point of view particularly bad is the contrast deliberately set up in the article between good science, astronomy and mathematics, and ‘dirty’ pseudo- science’, alchemy. This starts with the title:

Groundbreaking astronomer Kepler ‘may have practised alchemy’

Continues with the whole of the first paragraph:

The pioneering astronomer Johannes Kepler may have had his eyes on the heavens, but chemical analysis of his manuscripts suggests he was “willing to get his hands dirty” and may have dabbled in alchemy.

“Kepler, who died in 1630, drew on Copernicus’s work to find laws of planetary motion that paved the way for Isaac Newton’s theory of gravity” is contrasted with “The authors speculate that Kepler could have learned the “pseudo-chemical science.” 

A ‘pioneering astronomer’ with ‘his eyes on the heavens’, serious scientific activity, but ‘dabbled in alchemy’. Whoever wrote these lines obviously knows nothing about Kepler’s astronomical writing nor about early 17^thcentury alchemy.

The article through its choice of descriptive terms tries to set up a black/white dichotomy between the man who paved the way for modern astronomy, good, and the practitioners of alchemy in the early seventeenth century, bad. However if we actually look at the real history everything dissolves into shades of grey.

Kepler was not just an astronomer and mathematician but also a practicing astrologer. People might rush in here with lots of Kepler quotes condemning and ridiculing the nativity horoscope astrology of his age, all of them true. However, he famously said one shouldn’t throw the baby out with the bath water defending the basic idea of astrology and presenting his own unique system of astrology based entirely on aspects, that is the angular position of the planets relative to each other. The author of the piece has obviously never turned the pages of either Kepler’s Mysterium Cosmographicum or his Harmonice Mundi. As I commented on Twitter, during a discussion of this article, Kepler’s cosmological heuristic with which he generated all of his successful astronomy was, viewed from a modern rational standpoint, quite simply bat shit insane. Things are not looking good for our pioneering astronomer.

Kepler’s Platonic solid model of the solar system, from Mysterium Cosmographicum (1596) Kepler’s explanation as to why there are only five planets and their order around the sun! Source: Wikimedia Commons

On the other side, as I have noted on several occasions, alchemy included much that we now label applied and industrial chemistry.  For example, alchemists were responsible for the production of pigments for painters and gunpowder for fireworks and cannons, and were often glassmakers. Alchemists were historically responsible for developing the laboratory equipment and methodology for chemical analysis. In the period under discussion many alchemists, including Tycho, were Paracelsian physicians, who are credited with the founding of the modern pharmacological industry. Historians of alchemy tend to refer to the alchemy of the seventeenth century as chymistry because it represents the historical transition from alchemy to chemistry. Not so much a pseudo-science as a proto-science.

Let us now consider the so-called evidence for the articles principle claim. Throughout the article it is stated that the evidence was found on Kepler’s manuscripts, plural. But when the evidence is actually discussed it turns out to be a single manuscript about the moon. On this manuscript the researchers found:

“…very significant amounts of metals associated with the practice including gold, silver, mercury and lead on the pages of Kepler’s manuscript about the moon, catalogued as “Hipparchus” after the classical astronomer.”

Is alchemy the only possible/plausible explanation for the traces of metals found on this manuscript? Could one suggest another possibility? All of these metals could have been and would have been used by a clock and instrument maker such as Jost Bürgi, who was Kepler’s close colleague and friend throughout his eleven years in Prague. Bürgi also had a strong interest in astronomy and might well have borrowed an astronomical manuscript. Of course such a solution doesn’t make for a sensational article, although all the available evidence very strongly suggests that Kepler was not an alchemist.

One final point that very much worries me is the provenance of this document. It is four hundred years old, who has owned it in the meantime? Where has it been stored? Who has had access to it? Until all of these questions can be accurately answered attributing its contamination to Kepler is just unfounded speculation.

Before continuing with Tycho Brahe’s contributions to the development of modern astronomy it pays to take stock of the existing situation in the last quarter of the sixteenth century. The Middle Ages had cobbled together a model of the cosmos that consisted of three separate but interlocking blocks: Aristotelian cosmology, Ptolemaic astronomy and Aristotelian physics, whereby it should be noted that the medieval Aristotelian physics was, to paraphrase Edward Grant, not Aristotle’s physics. In order for a new astronomy to come into use, as we shall see, the whole model had to dissembled and each of the three blocks replaced with something new.

As we saw at the beginning, some aspects of Aristotelian cosmology–supralunar perfection and cometary theory–were already under scrutiny well before Copernicus published his De revolutionibus. They now fell following the European wide observations of the supernova in 1572 and the great comet of 1577; the Aristotelian crystalline spheres went with them, although Clavius, the leading Ptolemaic astronomer of the age, whilst prepared to sacrifice supralunar perfection and Aristotelian cometary theory, was not yet prepared to abandon the crystalline spheres. The model was beginning to crumble at the edges.

The acceptance of Copernicus’ heliocentric system had been very meagre but the interest in his mathematical models, his astronomical data and the planetary tables and ephemerides based on them had originally been very great. However, it quickly became clear that they were no more accurate or reliable than those delivered by the Ptolemaic system and the initial interest and enthusiasm gave way to disappointment and frustration. Out of this situation both Wilhelm IV in Kassel and Tycho Brahe in Denmark, following Regiomontanus’ initiative from a century earlier, decided that what was needed was to go back to basics and produce new star catalogues and planetary tables based on new accurate observations and set about doing just that. We have already looked to Wilhelm’s efforts; we now turn to Tycho’s.

Granted the island of Hven and the necessary financial support to carry out his project by Frederick II, the Danish king, Tycho set to work.

Frederick II of Denmark Portrait by Hans Knieper or Melchior Lorck, 1581.

Whereas it is theoretically possible to question the claim that Wilhelm IV had built an observatory, no such doubt exists in Tycho’s case. What he erected on his island was not so much an observatory, as a research institute the like of which had never existed before in Europe.

The centrepiece of Tycho’s establishment was his palace Uraniborg, a magnificent purpose built red brick residence and observatory. The structure included a large mural quadrant and outer towers on the balconies of which a large array of self designed and constructed instruments were situated.

Source: Wikimedia Commons

Engraving of the mural quadrant from Brahe’s book Astronomiae instauratae mechanica (1598) Source: WIkimedia Commons

As it turned out that the accuracy of the tower-mounted instrument was affected by vibration caused by the wind, Tycho constructed a second observatory, Stjerneborg. This observatory was effectively situated underground in a large pit to reduce wind vibration of the instruments.

Drawing of an above ground view of Stjerneborg Willem Blaeu – Johan Blaeu, Atlas Major, Amsterdam, 1662 Source: Wikimedia Commons

Schematic of Stjerneborg showing underground chambers: Woodcut from F.R. Friis “Tyge Brahe”, Copenhagen, 1871 Source: Wikimedia Commons

As well as his two state of the art observatories, Tycho also constructed alchemical laboratories in the cellars of Uraniborg, to carry out experiments in Paracelsian pharmacology. To publish the results of his researches Tycho constructed his own printing press and to ensure that he would have enough paper for those publications, he also constructed a water powered paper mill.

Whereas Wilhelm’s astronomical activities were a side project to his main occupation of ruling Hesse-Kassel and the work on his star catalogue was carried out by just two people, Rothmann and Bürgi, Tycho’s activities on Hven were totally dedicated to astronomy and he employed a small army of servants and assistants. Alongside the servants he needed to run his palace and its extensive gardens Tycho employed printers and papermakers and a large number of astronomical observers. Some of those who worked as astronomers on Hven and later in Prague, such as Longomontanus, who later became professor for astronomy in Copenhagen, did so for many years. Others came to work for him for shorter periods, six or nine months or a year. These shorter-term periods working for Tycho worked like a form of postgrad internship for those thus employed. Good examples of this are the Dutch cartographer and Globemaker Willem Janszoon Blaeu (1571–1638), who spent six months on Hven in 1595-96

Willem Janszoon Blaeu Source: Wikimedia Commons

and the Franconian mathematician and astronomer Simon Marius (1573–1625) who spent six months in Tycho’s observatory in Prague in 1601 shorty before Tycho’s death.

Tycho’s observation programme was massive and very much for the duration, starting in the mid 1570s and continuing up to his death in 1601[1]. His teams spent every night of the year, weather permitting, systematically observing the heavens. Two teams, one in Uraniborg and the other in Stjerneborg, made the same observations parallel to but completely independent of each other, allowing Tycho to compare the data for errors. They not only, over the years, compiled a star catalogue of over 700 stars[2] with an accuracy of several factors higher than anything produced earlier but also systematically tracked the orbits of the planets producing the data that would later prove so crucial for Johannes Kepler’s work.

When Tycho was satisfied with the determination of the position of a given star then it was engraved on a large celestial globe that he had had constructed in Germany on one of his journeys. When Willem Janszoon Blaeu was on Hven, Tycho allowed him to make a copy of this globe with the new more accurate stellar positions, which he took with him when he returned to The Netherlands. So from the very beginning Blaeu’s commercial celestial spheres, which dominated the market in the seventeenth century, were based on the best astronomical data available.

Tycho not only systematically observed using instruments and methods known up to his times but devoted much time, effort and experimentation to producing ever better observing instruments with improved scales for more accurate readings. He also studied and developed methods for recognising and correcting observational errors. It is not an exaggeration to say that Tycho dedicated his life to producing observational astronomical data on a level and of a quality never before known in European astronomy.

In 1588 Tycho’s patron and benefactor Frederick II died and after a period of regency his son, who was only eleven years old when he died, was crowned king as Christian IV in 1596.

Portrait Christian IV by Pieter Isaacsz 1612 Source: Wikimedia Commons

Due to a mixture of court intrigue and his own arrogance, Tycho fell into disfavour and Christian cut off his finances from the crown. Still a wealthy man, from his private inheritances, Tycho packed up his home and some of his instruments and left Denmark heading south through Germany in 1597, looking for a new patron. In 1599 he settled in Prague under the patronage of Rudolf II as Imperial Mathematicus,

Rudolf II Portrait by Martino Rota Source: Wikimedia Commons

erecting a new observatory in a castle in Benátky nad Jizerou about fifty kilometres from Prague.

Benátky Castle Source: Wikimedia Commons

Tycho’s biggest problem was that he had vast quantities of, for the time, highly accurate astronomical data that now needed to be processed and he was in desperate need of a mathematician who was capable of carrying out the work. Fate intervened in the form of the still relatively young Johannes Kepler ((1571–1630), who turned up in Prague in 1600 frantically looking for employment.

Johannes Kepler Source: Wikimedia Commons

This was a partnership made in hell rather than heaven but it did not last long as Tycho died under unclear circumstances[3] in October 1601, with Kepler inheriting his position as Imperial Mathematicus. I will deal with Kepler’s leading role in the story of modern astronomy in later episodes but we still need to look at Tycho’s last contribution, the so-called Tychonic system.

[1]In his Bibliographical Directory of Tycho Brahe’s Artisans, Assistants, Clients, Students, Coworkers and Other Famuli and Associates, pages 251–309 in his On Tycho’s Island: Tycho Brahe, Science, and Culture in the Sixteenth Century, John Robert Christianson list 96 names.

[2]When he left Hven Tycho increased his star catalogue to 1000, taking the missing stars from the Ptolemaic star catalogue

[3]Anybody who brings up, in the comments, the harebrained theory that Kepler murdered Tycho in order to obtain his astronomical data will not only get banned from the Renaissance Mathematicus in perpetuity but will be cursed by demons, who will visit them in their sleep every night for the rest of their pathetic lives.

One of the things attributed to Tycho Brahe is the geo-heliocentric model of the cosmos. In this system the Earth remains at the centre and the Moon and the Sun both orbit the Earth, whereas the other five planets orbit the Sun. This system combines most of the advantages of Copernicus’ heliocentric system without the problems caused by a moving Earth. As such, as we shall see, the Tychonic system became one of the two leading contenders later in the seventeenth century. The only problem is that although it is named after him, Tycho wasn’t the only person to suggest this model and he almost certainly wasn’t the first to think of it.

A 17th century illustration of the Hypothesis Tychonica from Hevelius’ Selenographia, 1647 page 163, whereby the Sun, Moon, and sphere of stars orbit the Earth, while the five known planets (Mercury, Venus, Mars, Jupiter, and Saturn) orbit the Sun. Source: Wikimedia Commons

The first to publish a version of the geo-heliocentric model was Nicolaus Reimers Baer (1551–1600), known as Ursus, in his Nicolai Raymari Ursi Dithmari Fundamentum astronomicum (Straßburg 1588). Ursus’ system differed from Tycho’s in that he included diurnal rotation.

Nicolaus Reimers Baer, Fundamentum Astronomicum 1588 geo-heliocentric planetary model Source: Wikimedia Commons

Ursus was a self-taught astronomer, who in his youth had worked as a pig-herd until Heinrich Rantzau (1526–1598), a humanist scholar and astrologer, recognised his talents and employed him as a mathematician.

Heinrich Rantzau Source: Wikimedia Commons

There followed a period as a private tutor and a year, 1586–87, in Kassel with Wilhelm. During his time in Kassel he translated De revolutionibus into German for Jost Bürgi, who couldn’t read Latin. In exchange Bürgi taught Ursus prosthaphaeresis, a method of using trigonometrical formulas to turn multiplications into sums to simplify calculations. From 1591 till his death, in 1600, Ursus was Imperial Mathematicus to Rudolf II in Prague.

Tycho was outraged that somebody published “his system” before he did and immediately accused Ursus of plagiarism, both of the geo-heliocentric system and of prosthaphaeresis, citing an earlier visit to Hven together with Rantzau, when Ursus was in his service. The two astronomers delivered a very unseemly public squabble through a series of publications; Tycho emphasising Ursus’ lowly birth and lack of formal qualifications and Ursus giving as good as he got in return. However, when Tycho left Hven and approached Prague, Ursus fled fearing the aristocrat’s wrath. When Kepler came to Prague to work with Tycho the first task that Tycho gave him was to write an account of the dispute, naturally expecting Kepler to find in his favour. Kepler wrote his report but didn’t ever publish it. Nicholas Jardine published a heavily annotated English translation in his The Birth of History and Philosophy of Science. Kepler’s ‘A Defence of Tycho against Ursus’ with Essays on its Provenance and Significance, CUP (2nd rev. ed. 1988)[1].

Tycho’s false accusation of theft of the trigonometrical method of prosthaphaeresis is, however, very revealing. Tycho was not the discoverer/inventor[2] of prosthaphaeresis. As far as can be ascertained, the method was originally discovered by Johannes Werner (1468–1522) but was actually taught to Tycho by the itinerant mathematician/astronomer from Breslau, Paul Wittich (c. 1546–1586). It turns out that that Wittich was probably the inspiration for both Tycho’s and Ursus’ decision to adopt a geo-heliocentric system. Wittich played around with the Capellan system, in which Mercury and Venus orbit the Sun in a geocentric system. He sketches of his thoughts are contained in his copy of De revolutionibus.

Paul Wittich’s 1578 Capellan geoheliocentric planetary model – as annotated in his copy of Copernicus’s De revolutionibus in February 1578 Source: Wikimedia Commons

Following Wittich’s, comparatively early, death Tycho went to a lot of trouble and expense to obtain both of Wittich’s copies of Copernicus’ book, suggesting he was desperately trying to cover up the origins of “his system.” Another indication of Wittich’s possible or even probable influence is the fact that David Origanus (1558–1629), who had been influenced by Wittich at the University of Frankfurt an der Oder, also “independently” invented a geo-heliocentric system but with diurnal rotation like Ursus’ system.

David Origanus Source: Wikimedia Commons

The route from a Capellan system to a full geo-heliocentric system was probably the route taken by both the physician and astrologer Helisaeus Roeslin (1545–1616) and the court mathematicus Simon Marius (1573–1625), who both claimed independent discovery of the system.

Simon Marius Source: Wikimedia Commons

I think it should be clear by now that a geo-heliocentric system, whether with or without diurnal rotation was seen as a logical development by several astronomers following the publication of De revolutionibus, for it combined most of the advantages of Copernicus’ system, whilst not requiring the Earth to orbit the Sun, solving as it did the problem of the missing, or better said undetectable, solar stellar parallax. Such a system also solved another perceived, empirical problem, which has been largely forgotten today, that of star size.

If the cosmos were heliocentric then the lack of detectable parallax would mean that the so-called fixed stars were absurdly distant and much worse, given the naked-eye false perception the size of the star discs, all the more absurdly immense. Tycho used this as a valid empirical argument alongside religious ones to categorically reject a heliocentric system. Because the geo-heliocentric system didn’t require stellar parallax then the distance to the fixed stars was considerably shorter and thus the star size also much smaller. The apparent star size argument would continue to play a significant role in the astronomical system debate until the end of the seventeenth century.

Tycho, naturally, hoped to use his vast quantity of freshly won, comparatively accurate celestial data to prove the empirical reality of his system. Unfortunately, he died before he could really set this project in motion. On his deathbed he extracted the promise from Johannes Kepler, his relatively new assistant, to use the data to prove the validity of his system. As is well known, Kepler did nothing of the sort but actually used Tycho’s hard won data to develop his own totally novel heliocentric system, of which more later.

However, a geo-heliocentric model of the cosmos, with or without diurnal rotation, remained, as we shall see later, one of the leading contenders amongst astronomers right up to about 1660-70. The definitive version based on Tycho’s own data was produced by Christen Sørensen, known as Longomontanus, (1562-1647),

Tycho’s longest serving and most loyal assistant, in his Astronomia Danica (1622).

Longomontanus’ system was published in direct opposition to Kepler’s heliocentric one. Unlike Tycho’s, Longomontanus’ system had diurnal rotation.

Today we tend to view the various geo-heliocentric systems, with hindsight, as more than somewhat bizarre, but they provided an important and probably necessary bridge between a pure geocentric model and a pure heliocentric one, delivering many of the perceived advantages of heliocentricity, without having to solve the problems created by an Earth flying at high speed around the Sun.

[1]A highly recommended read

[2]Chose your word according to your philosophy of mathematics

Vienna and its university played a very central role in introducing the study of mathematics, cartography and astronomy into Northern Europe in the fifteenth and sixteenth century. In early blog posts I have dealt with Georg von Peuerbach and Johannes Regiomontanus, Conrad Celtis and his Collegium poetarum et mathematicorum, Georg Tannstetter and the Apians, and Emperor Maximilian and his use of the Viennese mathematici. Today, I’m going to look at the beginnings of the University of Vienna and the establishment of the mathematical science as a key part of the university’s programme.

The University of Vienna was founded in 1365 by Rudolf IV, Duke of Austria (1339–1365) and his brothers Albrecht III, (c. 1349–1395) and Leopold III (1351–1386) both Dukes of Austria.

Rudolf IV, Duke of Austria Source: Wikimedia Commons

Like most young universities it’s early decades were not very successful or very stable. This began to change in 1384 when Heinrich von Langenstein (1325–1397) was appointed professor of theology.

Presumably Heinrich von Langenstein (1325-1397), Book miniature in Rationale divinorum officiorum of Wilhelmus Durandus, c. 1395

Heinrich von Langenstein studied from 1358 in Paris and in 1363 he was appointed professor for philosophy on the Sorbonne advancing to Vice Chancellor. He took the wrong side during the Western Schism (1378–1417) and was forced to leave the Sorbonne and Paris in 1382. Paris’ loss was Vienna’s gain. An excellent academic and experienced administrator he set the University of Vienna on the path to success. Most important from our point of view is the study of mathematics and astronomy at the university. We tend to think of the curriculum of medieval universities as something fixed: a lower liberal arts faculty teaching the trivium and quadrivium and three higher faculties teaching law, medicine and theology. However in their early phases new universities only had a very truncated curriculum that was gradually expanded over the early decades; Heinrich brought the study of mathematics and astronomy to the young university.

Heinrich was a committed and knowledgeable astronomer, who established a high level of tuition in mathematics and astronomy. When he died he left his collection of astronomical manuscripts and instruments to the university. Henry’s efforts to establish astronomy as a discipline in Vienna might well have come to nothing if a successor to teach astronomy had not been found. However one was found in the person of Johannes von Gmunden (c. 1380–1442).

Initial from British Library manuscript Add. 24071 Canones de practica et utilitatibus tabularum by Johannes von Gmunden written 1437/38 by his student Georg Prunner Possibly a portrait of Johannes Source: Johannes von Gmunden (ca. 1384–1442) Astronom und Mathematiker Hg. Rudolf Simek und Kathrin Chlench, Studia Medievalia Septentrionalia 12

Unfortunately, as is often the case with medieval and Renaissance astronomers and mathematicians, we know almost nothing personal about Johannes von Gmunden. There is indirect evidence that he comes from Gmunden in Upper Austria and not one of the other Gmunden’s or Gmund’s. His date of birth is an estimate based on the dates of his studies at the University of Vienna and everything else we know about him is based on the traces he left in the archives of the university during his life. He registered as a student at the university in 1400, graduating BA in 1402 and MA in 1406.

His MA was his licence to teach and he held his first lecture in 1406 on the Theoricae planetarum by Gerhard de Sabbioneta (who might well not have been the author) a standard medieval astronomy textbook, establishing Johannes’ preference for teaching astronomy and mathematics. In 1407, making the reasonable assumption that Johannes Kraft is Johannes von Gmunden, thereby establishing that his family name was Kraft, he lectured on Euclid. 1408 to 1409 sees him lecturing on non-mathematical, Aristotelian texts and 1410 teaching Aristotelian logic using the Tractatus of Petrus Hispanus. In the same year he also taught Euclid again. 1411 saw a return to Aristotle but in 1412 he taught Algorismus de minutiis i.e. sexagesimal fractions. The Babylonian sexagesimal number system was used in European astronomy down to and including Copernicus in the sixteenth century, Aristotelian logic again in 1413 but John Pecham’s Perspectiva in 1414.

Johannes von Gmunden Algorismus de minutiis printed by Georg Tannstetter 1515 Source: Johannes von Gmunden (ca. 1384–1442) Astronom und Mathematiker Hg. Rudolf Simek und Kathrin Chlench, Studia Medievalia Septentrionalia 12

Around this time Johannes took up the study of theology, although he never proceeded past BA, and 1415 and 16 see him lecturing on religious topics although he also taught Algorismus de minutiis again in 1416. From 1417 till 1434, with breaks, he lectured exclusively on mathematical and astronomical topics making him probably the first dedicated lecturer for the mathematical disciplines at a European university. Beyond his lectures he calculated and wrote astronomical tables, taught students how to use astronomical instruments (for which he also wrote instruction manuals), including the construction of cheap paper instruments.

Johannes von Gmunden instructions for constructing an astrolabe rete Wiener Codex ÖNB 5296 fol. 6r Source: Johannes von Gmunden (ca. 1384–1442) Astronom und Mathematiker Hg. Rudolf Simek und Kathrin Chlench, Studia Medievalia Septentrionalia 12

He collected and also wrote extensive astronomical texts. As well as his teaching duties, Johannes served several times a dean of the liberal arts faculty and even for a time as vice chancellor of the university. His influence in his own time was very extensive; there are more than four hundred surviving manuscripts of Johannes Gmunden’s work in European libraries and archives.

When he died Johannes willed his comparatively large collection of mathematical and astronomical texts and instruments to the university establishing a proper astronomy department that would be inherited with very positive results by Georg von Peuerbach and Johannes Regiomontanus. Perhaps the most fascinating items listed in his will are an Albion and an instruction manual for it.

Albion front side Source: Seb Falk’s Twitter feed

Albion rear Source: Seb Falk’s Twitter feed

The Albion is possibly the most fascinating of all medieval astronomical instruments. Invented by Richard of Wallingford (1292–1336), the Abbot of St Albans, mathematician, astronomer, horologist and instrument maker, most well known for the highly complex astronomical clock that he designed and had constructed for the abbey.

Richard of Wallingford Source: Wikimedia Commons

The Albion, ‘all by one’, was a highly complex and sophisticated, multi-functional astronomical instrument conceived to replace a whole spectrum of other instruments. Johannes’ lecture from 1431 was on the Albion.

Johannes von Gmunden did not stand alone in his efforts to develop the mathematical sciences in Vienna in the first half of fifteenth century; he was actively supported by Georg Müstinger (before 1400–1442), the Prior of the Augustinian priory of Klosterneuburg.

Klosterneuburg

Müstinger became prior of Klosterneuburg in 1418 and worked to turn the priory into an intellectual centre. In 1421 he sent a canon of the priory to Padua to purchase books for over five hundred florins, a very large sum of money. The priory became a centre for producing celestial globes and cartography. It produced a substantial corpus of maps including a mappa mundi, of which only the coordinate list of 703 location still exist. Scholar who worked in the priory and university fanned out into the Southern German area carrying the knowledge acquired in Vienna to other universities and monasteries.

Johannes’ status and influence are nicely expressed in a poem about him and Georg von Peuerbach written by Christoph Poppenheuser in 1551:

The great Johannes von Gmunden, noble in knowledge, distinguished in spirit, and dignified in piety                                                                                                                                         And you Peuerbach, favourite of the muses, whose praise nobody can sing well enough                                                                                                                                           And Johannes, named after his home town, known as far away as the stars for his erudition

The tradition established in Vienna by Heinrich von Langenstein, Johannes von Gmunden and Georg Müstinger was successfully continued by Georg von Peuerbach (1423–1461), who contrary to some older sources was not a direct student of Johannes von Gmunden arriving in Vienna only in 1443 the year after Johannes death. However Georg did find himself in a readymade nest for the mathematical disciplines, an opportunity that he grasped with both hands developing further Vienna’s excellent reputation in this area.

As I stated earlier in this series only a comparatively small number of astronomers accepted the whole of Copernicus’ theory, both cosmology and astronomy. More interestingly almost none of them had any lasting impact during the final decades of the sixteenth century on the gradual acceptance of heliocentrism. Although he appears to have abandoned Copernicus’ astronomy later in life, Rheticus did have a strong impact with his Narratio Prima(1540), which through its various editions was the first introduction to the heliocentric hypothesis for many readers. Two others, whose impact was principally in the seventeenth century, were Kepler and Galileo, who will be dealt with later. However, one astronomer who did play an important role in the sixteenth century was Michael Mästlin.

Michael Mästlin portrait 1619 artist unknown

Michael Mästlin (1550-1631) stood at the end of a long line of important Southern German astronomers and mathematicians. A graduate of the University of Tübingen he was a student of Philipp Apian (1531–1589),

Philipp Apian, artist unknown Source: Wikimedia Commons

who was a student of his more famous father Peter Apian (1495–1552) in Ingolstadt. Peter Apian had studied under Georg Tannstetter (1482–1535) in Vienna, who had studied under Andreas Stiborius (c. 1464–1515) and Johannes Stabius (1450–1522) first in Ingolstadt then in Vienna. In 1584 Mästlin succeeded his teacher Philipp Apian as professor for astronomy and mathematics at Tübingen. An active astronomer since the beginning of the 1570s Mästlin was regarded as a leading German astronomer and consulted by the Protestant princes on matters astronomical, astrological and mathematical.

Mästlin represents the transitional nature of the times probably better than any other astronomer. His Epitome Astronomiae (1582), a university textbook, which went through a total of seven editions, was a standard Ptolemaic geocentric text that he continued to teach from until his death in 1631.

However, at the same time he taught selected students the fundaments of Copernican heliocentric astronomy. Earlier accounts claimed that he did this in secret but all of the available evidence suggests that he did so quite openly. This quasi revolutionary act of teaching famously produced one significant result in that Mästlin introduced Copernican astronomy to the young Johannes Kepler, who would go on to become the most important propagator of heliocentric astronomy in the early seventeenth century.

One subject on, which the German Protestant princes consulted Mästlin was the proposed Gregorian calendar reform from 1582. Mästlin launched a vitriolic polemic against it largely on religious grounds with his Gründtlicher Bericht von der allgemeinen und nunmehr bei 1600 Jahren von dem ersten Kaiser Julio bis jetzt gebrauchten jarrechnung oder kalender (Rigorous report on the general and up till now for 1600 years used calculation of years or calendar from the first Caesar Julio) (1583). The Protestant princes accepted his advice and as a result didn’t adopt the new calendar until 1700.

On the other side of the religious divide the man charged by the Pope to promote and defend the new calendar was the Jesuit professor of astronomy and mathematics at the Collegio Romano, Christoph Clavius (1538–1612).

Christoph Clavius. Engraving Francesco Villamena, 1606 Source: Wikimedia Commons

Although Clavius was a convinced defender of the Ptolemaic system until his death, he did play a central role in the developments that led to the eventual acceptance of the heliocentric system. The Catholic universities in the last quarter of the sixteenth century still didn’t really pay the mathematical disciplines much attention and their teaching of astronomy had not really progressed beyond the High Middle Ages. Clavius introduced modern mathematics and astronomy into the Jesuit educational reform programme, following the fundamental principle of that programme, if you want to win the debate with your non-Catholic opponents you need to be better educated than them. Many Jesuit and Jesuit educated mathematicians and astronomers, who came out of the pedagogical programme established by Clavius, would, as we shall see, make significant and important contributions to the developments in astronomy in the seventeenth century.

Clavius was also the author of a number of excellent up to date textbooks on a full range of mathematical topics. His astronomy textbook In Sphaeram Ioannis de Sacro Bosco commentarius, the first edition appearing in 1570 and further updated editions appearing in 1581, 1585, 1593, 1607, 1611 and posthumously in 1618, was the most widely read astronomy textbook in the last decades of the sixteenth and early decades of the seventeenth centuries. It was strictly Ptolemaic but he presented, described and commented upon Copernicus’ heliocentric hypothesis. Although he showed great respect for Copernicus as a mathematical astronomer, he of course rejected the hypothesis. However, anybody who read Clavius’ book would be informed of Copernicus work and could if interested go looking for more information. One should never underestimate the effect of informed criticism, and Clavius’ criticism was well informed, for disseminating a scientific hypothesis. Many people certainly had their first taste of the heliocentric hypothesis through reading Clavius.

Another group who had a positive impact on the propagation of the heliocentric hypothesis in the last quarter of the sixteenth century was the so-called English School of Mathematics. Whilst Robert Recorde (1510–1558) and John Dee (1527–c. 1608) were not committed supporters of Copernicus, they did much to spread knowledge of the heliocentric hypothesis. As we have already seen John Feild (c. 1520–1587) was a declared supporter of Copernicus but as his Copernican ephemerides proved no more accurate than the Ptolemaic ones his influence diminished. Not so Dee’s foster son Thomas Digges (c. 1546–1595).

His 1576 edition of his father’s A Prognostication everlastingcontained an appendix A Perfit Description of the Caelestiall Orbes according to the most aunciente doctrine of the Pythagoreans, latelye revived by Copernicus and by Geometricall Demonstrations approved, which is an annotated translation of part of the cosmological first book of De revolutionibus into English, which continued to have an impact on English readers long after Digges’ demise.

Source: Linda Hall Library

Thomas Harriot (c. 1560–1621) was another, who was committed to the heliocentric hypothesis.

Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

His biggest problem was that he published none of his scientific or mathematical work but he was well networked and contributed extensively to the debate through correspondence. The influence of this group would, as we will see, have an impact on the early acceptance of Kepler’s work inEngland.

Another figure in the last quarter of the sixteenth century, who, although not an astronomer, made a very important contribution to the cosmological debate, was the physician William Gilbert (1544–1603).

William Gilbert (1544–1603) artist unknown. Source: Wellcome Library via Wikimedia Commons

Gilbert is well known in the history of science as the author of the first modern scientific investigation of magnetism in his De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth).

Gilbert carried out many of his experiments with spherical magnets, which he called terella, from which he deduced his belief that the Earth itself is a spherical magnet. Based on his erroneous belief that a suspended terella rotates freely about its axis he came to accept and propagate diurnal rotation. Book VI of De magnete, the final book, is devoted to an analysis of the Earth as a spherical magnet based on the results of Gilbert’s experiments with his terella.

In Chapter III of Book VI, On the Daily Magnetic Revolution of the Globes, as Against the Time-Honoured Opinion of a primum mobile: A Probable Hypothesis, Gilbert gives a detailed review of the history of a geocentric system with diurnal rotation starting with Heraclides of Pontus and going through to Copernicus. Gilbert rejects the whole concept of celestial spheres, dismissing them as a human construction with no real existence. He brings the standard physical arguments that it is more logical that the comparatively small Earth rotates once in twenty-four hours rather than the vastly larger sphere of the fixed stars. In the following chapter he then argues that magnetism is the origin of this rotation. In Chapter V he discusses the arguments for and against movement of the Earth. At the end of Chapter III Gilbert writes, “I pass by the earth’s other movements, for here we treat only of the diurnal rotation…” so what he effectively promotes is a geocentric system with diurnal rotation. Later in his De Mundo Nostro Sublunari Philosophia Nova (New Philosophy about our Sublunary World), Gilbert propagated a full heliocentric system but this book was first published posthumously in 1651 and had no real influence on the astronomical discussion.

Diagram of the cosmos De Mundo p. 202 Source: Wikimedia Commons

Gilbert’s De magnete was a widely read and highly influential book in the first half of the seventeenth century. Galileo praised it but criticised its lack of mathematics. As we shall see it had a massive influence on Kepler. Because of its status the book definitely had a major impact on the acceptance of geo-heliocentric systems with diurnal rotation rather than without later in the seventeenth century.

We will stop briefly and take stock in 1593, fifty years after the publication of De revolutionibus. We have seen that within Europe astronomers had already begun to question the inherited Ptolemaic system during the fifteenth century. In the sixteenth century a major debate developed about both the astronomical and cosmological models. The Aristotelian theories of comets, the celestial spheres and celestial immutability all came under attack and were eventually overturned. Alternative models–Aristotelian homocentricity, the Capellan system and geocentricity with diurnal rotation–were promoted.  With the publication of Copernicus’ De revolutionibus with its heliocentric hypothesis the debates went into overdrive. Only a comparatively small number of astronomers propagated the heliocentric system and an even smaller number of them actually went on to have a real impact on the discussion. A much larger number showed an initial strong interest in the mathematical models in De revolutionibus and the planetary tables and ephemerides based on them, in the hope they would generate better, more accurate data for applications such as astrology, cartography and navigation. This proved not to be the case as Copernicus’ work was based on the same inaccurate and corrupted ancient data, as Ptolemaic geocentric tables. Recognising this both Wilhelm IV in Kassel and Tycho Brahe on Hven began programmes of extensive new astronomical observations. However, this very necessary new data only became generally available well into the seventeenth century. Other astronomers partially convinced by Copernicus’ arguments turned to Capellan models with Mercury and Venus orbiting the Sun rather than the Earth and full geo-heliocentric models with the Moon and the Sun orbiting the Earth and all the other five planets orbiting the Sun. This was the situation at the beginning of the 1590s but a young Johannes Kepler (1571–1630), who would have a massive impact on the future astrological and cosmological models, was waiting in the wings.

During the Middle Ages it was common practice for those working in the crafts to keep the knowledge of their trades secret, masters passing on those secrets orally to new apprentices. This protection of trade secrets, perhaps, reached a peak during the Renaissance in the glassmaking centre of Venice, where anybody found guilty of revealing the secrets of the glassmaking was sentenced to death. Although there were in some crafts manuscripts, which made it into print, describing the work processes involved in the craft these were of very limited distribution. All of this began to change with the invention of moving type book printing. Over the sixteenth and seventeenth centuries printed books began to appear describing in detail the work processes of various crafts. I have already written a post about one such book, De re metallica by Georgius Agricola (1494–1555). However, Agricola’s book was not the first printed book on metallurgy that honour goes to the Pirotechnia of Vannoccio Biringuccio published posthumously in Italian in 1540. Agricola was well aware of Biringuccio’s book and even plagiarised sections of it in his own work.

Title page, De la pirotechnia, 1540, Source: Science History Museum via Wikipedia Commons

Whereas Agricola was himself not a miner or metal worker but rather a humanist physician, whose knowledge of the medieval metallurgical industry was based on observation and questioning of those involved, Biringuccio, as we will see, spent his whole life engaged in one way or another in that industry and his book was based on his own extensive experiences.

Born in Siena 20 October 1480 the son of Lucrezia and Paolo Biringuccio, an architect.

Siena 1568

As a young man Vannoccio travelled throughout Italy and Germany studying metallurgical operations. In Siena he was closely associated with the ruling Petrucci family and after having run an iron mine and forge for Pandolfo Petrucci, he was appointed to a public position at the arsenal and in 1513 director of the mint.

Petrucci coat of arms Source: Wikimedia Commons

He was exiled from Siena in 1516 after the Petruccis fell from power and undertook further travels throughout Italy and visited Sicily in 1517. In 1523 the Petruccis were reinstated and Vannoccio returned to Siena and to his position in the arsenal. In 1526 the Petruccis fell from power again and he was once again forced to leave his hometown. He worked in both the republics of Venice and Florence casting cannons and building fortifications. In 1531 in a period of political peace he returned once more to Sienna, where he was appointed a senator, and architect and director of building construction. Between 1531 and 1535 he cast cannons and constructed fortification in both Parma and Venice. In 1536 he was offered a job in Rome and after some hesitation accepted the post of head of the papal foundry and director of papal munitions. It is not known when or where he died but there is documentary evidence that he was already dead on 30 April 1539.

His Pirotechnia was first published posthumously in Venice in 1540, it was printed by Venturino Roffinello, published by Curtio Navo and dedicated to Bernardino di Moncelesi da Salo. Bernardino is mentioned both in the book’s preface as well as in the text. The Pirotechnia consists of ten books, each one dealing with a separate theme in the world of Renaissance metallurgy, transitioning from the wining of metal ores, over their smelting to the use of the thus produced materials in the manufacture of metal objects and dealing with a whole host of side topic on the way. Although by no means as lavishly illustrated as De re metallica, the book contains 84 line drawings** that are as important in imparting knowledge of the sixteenth century practices as the text.

Book I, is titled Every Kind of Mineral in General, after a general introduction on the location of ores it goes on the deal separately with the ores of gold, silver, copper, lead, tin and iron and closes with the practice of making steel and of making brass.

Book II continues the theme with what Biringuccio calls the semi-minerals an extensive conglomeration of all sorts of things that we wouldn’t necessarily call minerals. Starting with quicksilver he moves on to sulphur then antimony, marcasite (which includes all the sulphide minerals with a metallic luster), vitriol, rock alum, arsenic, orpiment and realgar.

This is followed by common salt obtained from mine or water and various other salts in general then calamine Zaffre and manganese. The book now takes a sharp turn as Biringuccio deals with the loadstone and its various effects and virtues. His knowledge in obviously not first hand as he repeats the standard myths about loadstones losing their power and virtue in the presence of diamonds, goat’s milk and garlic juice. He now move on to, ochre, bole, emery, borax, azure and green azure. Pointing out that many of the things he has dealt with are rocks rather than metals he now introduces rock crystal and all important gems in general before closing the book with glass.

Book III covers the assaying and smelting metal ores concentring on silver, gold and copper.

Book IV continues with a related theme, the various methods for separating gold from silver.

Having covered separation of gold and silver Book V covers the alloys of gold, silver, copper, lead and tin.

Following the extraction of metals, their assays, separation and alloys, Book VI turns to practical uses of metals: the art of casting in general and particular.

Book VII the various methods of melting metals.

Having dealt with the casting of bells and cannons in Book VII, Book VIII deals the small art of casting.

Book IX is a bit of a mixed bag titled, Concerning the Procedure of Various Operations of Fire. The book opens with a very short chapter on alchemy. Biringuccio has already dealt with alchemical transmutation fairy extensively in Book I when discussing the production of gold. He doesn’t believe in it: These men [alchemists] in order to arrive at such a port have equipped their vessels with sails and hard-working oarsmen and have sailed with guiding stars, trying every possible course, and, finally submerged in the impossible (according to my belief) not one of them to my knowledge has yet come to port. In Book XI he acknowledges that although transmutation doesn’t work, alchemists have developed many positive things: …it is surely a fine occupation, since in addition to being very useful to human need and convenience, it gives birth every day to new and splendid effects such as the extraction of medicinal substances, colours and perfumes, and an infinite number of compositions of things. It is known that many arts have issued solely from it; indeed, without it or its means it would have been impossible for them ever to have been discovered by man except through divine revelation.The next chapter deal briefly with sublimation and very extensively with distillation both of which he acknowledges are products of the alchemists.

He now takes a sharp turn left with a chapter on Discourse and Advice on How to Operate a Mint Honestly and with Profit. This is followed with chapters on goldsmith, coppersmith, ironsmith and pewterer work, leading on to chapters on wire drawing, preparing gold for spinning, removing gold from silver and other gilded objects, and the extraction of every particle of gold and silver from slags of ore.

The book closes with making mirrors from bell metal and three chapters on working with clay.

Book X closes out Biringuccio’s deliberations with essays on making saltpetre and gunpowder, then moving on to the uses of gunpowder in gunnery, military mining, and fireworks, the later in both military and civil circumstances.

Biringuccio’s efforts proved successful with Italian editions of the book appearing in 1540 (Sienna), 1550 (Venetia), 1558/9 (Venegia), 1559 (Venetia), 1678 (Bologna), and 1914 (Barese). French editions appeard in 1556 (Paris), 1572 (Paris), 1627 (Rouen), and 1856 (Paris). A German edition appeared in 1925 (Braunschweig). There were only partial translation into English in 1555 (London) and 1560 (London). The first full English translation was made by Martha Teach Gnudi & Cyril Stanley Smith with notes and an introduction in 1941 (New Haven), which was republished by Dover Books in New York in 1990. It is the Dover edition that forms the basis of this blog post.

Biringuccio’s Pirotechnia is an important publication in the histories of technology, metallurgy, inorganic chemistry and the crafts and trades in general and deserves to be much better known.

**I have only chosen a selection of the drawings. On some subjects such as the use of bellows Biringuccio brings wholes rows of illustrations to demonstrate the diverse methods used.

It is not an exaggeration to say that the invention of telescope was a very major turning point in the general history of science and in particular the history of astronomy. Basic science is fundamentally empirical; people investigating the world make observations with their senses–taste, sight, touch, smell, hearing–then try to develop theories to describe and explain what has been observed and recorded. The telescope was the first ever instrument that was capable of expanding or strengthening one of those senses that of sight. The telescope made it possible to see things that had never been seen before.

The world’s oldest known surviving telescope Source with full details

The road to the telescope was a long one and one of the questions is why it wasn’t invented earlier. There are various legends or myths about devices to enable people to see things at a distance throughout antiquity and various lens shaped objects also from the distant past that might or might not have been lenses. Lenses in scientific literature in antiquity and the early middle ages were burning lenses used to focus sunlight to ignite fires. The first definite use of lenses to improve eyesight were the so-called reading stones, which emerged around 1000 CE, approximately hemispherical lenses, placed on documents to help those suffering from presbyopia, weakening of the ability of the eye to focus due to aging.

Source: Zeiss

Reading glasses utilising plano-convex lenses first appeared around 1290.

The earliest pictorial evidence for the use of eyeglasses is Tommaso da Modena’s 1352 portrait of the cardinal Hugh de Provence reading in a scriptorium Source: Wikimedia Commons

The current accepted theory of the discovery of simple lenses is that in the Middle Ages monks cutting gems to decorate reliquary discovered the simple magnifying properties of the gemstones they were grinding and polishing.

Reliquary Cross, French, c. 1180 Source: Wikimedia Commons

By the middle of the fifteenth century eye glasses utilising both convex and concave lenses were being manufactured and traded, so why did it take until 1608 before somebody successfully combined a concave lens and convex lens to create a simple so-called Dutch telescope?

There are in fact earlier in the sixteenth century in the writings of Girolamo Fracastoro (ca. 1476–1553) and Giambattista della Porta (1532–1615) descriptions of the magnifying properties of such lens combinations but these are now thought to refer to special eyeglasses rather than telescopes.

The early lenses were spherical lenses, which were hand ground and polished and as a result were fairly inaccurate in their form tending to deviate from their ideal spherical form the further out one goes from the centre.  These deformations caused distortions in the images formed and combining lenses increased the level of distortion making such combinations next to useless. It is now thought that the breakthrough came through the use of a mask to stop down the diameter of the eyepiece lens cutting out the light rays from the periphery, restricting the image to the centre of the lens and thus massively reducing the distortion. So who made this discovery? Who first successfully developed a working telescope?

This question has been hotly discussed and various claims just as hotly disputed since at least the middle of the seventeenth century. However, there now exists a general consensus amongst historian of optics.

[To see the current stand on the subject read the bog post that I wrote at this time last year, which I don’t intend to repeat here]

Popular accounts of the early use of the telescope in astronomy almost always credit Galileo Galilei, at the time a relatively unknown professor for mathematics in Padua, with first recognising the potential of the telescope for astronomy; this is a myth.

As can be seen from the quote from the French newsletter AMBASSADES DV ROY DE SIAM ENVOYE’ A L’ECELence du Prince Maurice, arriué à la Haye le 10. Septemb.1608., recording the visit of the ambassador of the King of Siam (Thailand), who was also present at the first demonstration of the telescope the potential of this new instrument, as a tool for astronomy was recognised from the very beginning:

…even the stars which normally are not visible for us, because of the scanty proportion and feeble sight of our eyes, can be seen with this instrument.

In fact the English polymath Thomas Harriot (1560–1621) made the earliest known telescopic, astronomical observations but, as with everything else he did, he didn’t publish, so outside of a small group of friends and acquaintances his work remained largely unknown. Also definitely contemporaneous with, if not earlier than, Galileo the Franconian court mathematicus, Simon Marius (1573–1625), began making telescopic observations in late 1609. However, unlike Galileo, who as we will see published his observations and discoveries as soon as possible, Marius didn’t publish until 1614, which would eventually bring the accusation of having plagiarised Galileo.  At the Collegio Romano, the Jesuit University in Rome, Odo van Maelcote (1572–1615) and Giovanni Paolo Lembo (1570–1618) were also making telescopic observations within the same time frame. There were almost certainly others, who didn’t make their observations public.

Before we turn to the observations and discoveries that these early telescopic observers made, we need to look at a serious technical problem that tends to get ignored by popular accounts of those discovery, how does a telescope work? In 1608 when the telescope first saw the light of day there existed absolutely no scientific explanation of how it worked. The group of early inventors almost certainly discovered its magnifying effect by accident and the first people to improve it and turn it into a viable scientific instrument, again almost certainly, did so by trial and error. At this point the problem is not to find the optical theory needed to develop better telescopes systematically but to find the optical theory necessary to justify the result the telescope produced. Using any sort of instrument in science requires a scientific explanation of how those results are achieved and as already stated at the beginning no such theory existed. The man, who came to the rescue, was Johannes Kepler in the second of his major contributions to the story of heliocentric astronomy.

Already in 1604 in his Ad Vitellionem Paralipomena Astronomiae pars optica, Kepler had published the first explanation of how lenses focus light rays and how eyeglasses work to compensate for short and long sightedness so he already had a head start on explaining how the telescope functions.

Source

Francesco Maurolico (1494–1575) had covered much of the same ground in his Theoremata de lumine et umbra earlier than Kepler but this work was only published posthumously in 1611, so the priority goes to Kepler.

In 1611 Kepler published his very quickly written Dioptrice, in which he covered the path of light rays through single lenses and then through lens combinations. In this extraordinary work he covers the Dutch or Galilean telescope, convex objective–concave eyepiece, the astronomical or Keplerian telescope, convex objective–convex eyepiece, the terrestrial telescope, convex objective–convex eyepiece–convex–field–lens to invert image, and finally for good measure the telephoto lens! Galileo’s response to this masterpiece in the history of geometrical optics was that it was unreadable!

Source: Wikimedia Commons

In the next section we will turn to the discoveries that the various early telescopic astronomical observers made and the roles that those various discoveries played in the debates on, which was the correct astronomical model of the cosmos. A much more complicated affair than it is often presented.

Since its very beginnings in the Fertile Crescent, European astronomy has always involved a lot of complicated and tedious mathematical calculations. Those early astronomers described the orbits of planets, lunar eclipses and other astronomical phenomena using arithmetical or algebraic algorithms. In order to simplify the complex calculations needed for their algorithms the astronomers used pre-calculated tables of reciprocals, squares, cubes, square roots and cube roots.

Cuniform reciprocal table Source

The ancient Greeks, who inherited their astronomy from the Babylonians, based their astronomical models on geometry rather than algebra and so needed other calculation aids. They developed trigonometry for this work based on chords of a circle. The first chord tables are attributed to Hipparkhos (c. 190–c. 120 BCE) but they did not survive. The oldest surviving chord tables are in Ptolemaeus’ Mathēmatikē Syntaxis written in about 150 CE, which also contains a detailed explanation of how to calculate such a table in Chapter 10 of Book I.

Ptolemaeus’ Chord Table taken from Toomer’s Almagest translation. The 3rd and 6th columns are the interpolations necessary for angles between the given ones

Greek astronomy travelled to India, where the astronomers replaced Ptolemaeus’ chords with half chords, that is our sines. Islamic astronomers inherited their astronomy from the Indians with their sines and cosines and the Persian astronomer Abū al-Wafāʾ (940–998 CE) was using all six of the trigonometrical relations that we learnt at school (didn’t we!) in the tenth century.

Abū al-Wafāʾ Source: Wikimedia Commons

Astronomical trigonometry trickled slowly into medieval Europe and Regiomontanus (1536–1576)  (1436–1476) was the first European to produce a comprehensive work on trigonometry for astronomers, his De triangulis omnimodis, which was only edited by Johannes Schöner and published by Johannes Petreius in 1533.

Source

Whilst trigonometry was a great aid to astronomers calculating trigonometrical tables was time consuming, tedious and difficult work.

A new calculating aid for astronomers emerged during the sixteenth century, prosthaphaeresis, by which, multiplications could be converted into additions using a series of trigonometrical identities:

Prosthaphaeresis appears to have first been used by Johannes Werner (1468–1522), who used the first two formulas with both sides multiplied by two.

However Werner never published his discovery and it first became known through the work of the itinerant mathematician Paul Wittich (c. 1546–1586), who taught it to both Tycho Brahe (1546–1601) on his island of Hven and to Jost Bürgi (1552–1632) in Kassel, who both developed it further. It is not known if Wittich learnt the method from Werner’s papers on one of his visits to Nürnberg or rediscovered it for himself. Bürgi in turn taught it to Nicolaus Reimers Baer (1551–1600) in in exchange translated Copernicus’ De revolutionibus into German for Bürgi, who couldn’t read Latin. This was the first German translation of De revolutionibus. As can be seen the method of prosthaphaeresis spread throughout Europe in the latter half of the sixteenth century but was soon to be superceded by a superior method of simplifying astronomical calculations by turning multiplications into additions, logarithms.

As is often the case in the histories of science and mathematics logarithms were not discovered by one person but almost simultaneously, independently by two, Jost Bürgi and John Napier (1550–1617) and both of them seem to have developed the idea through their acquaintance with prosthaphaeresis. I have already blogged about Jost Bürgi, so I will devote the rest of this post to John Napier.

John Napier, artist unknown Source: Wikimedia Commons

John Napier was the 8^th Laird of Merchiston, an independently owned estate in the southwest of Edinburgh.

Merchiston Castle from an 1834 woodcut Source: Wikimedia Commons

His exact date of birth is not known and also very little is known about his childhood or education. It is assumed that he was home educated and he was enrolled at the University of St. Andrews at the age of thirteen. He appears not to have graduated at St. Andrews but is believed to have continued his education in Europe but where is not known. He returned to Scotland in 1571 fluent in Greek but where he had acquired it is not known. As a laird he was very active in the local politics. His intellectual reputation was established as a theologian rather than a mathematician.

It is not known how and when he became interested in mathematics but there is evidence that this interest was already established in the early 1570s, so he may have developed it during his foreign travels. It is thought that he learnt of prosthaphaeresis through John Craig (d. 1620) a Scottish mathematician and physician, who had studied and later taught at Frankfurt an der Oder, a pupil of Paul Wittich, who knew Tycho Brahe. Craig returned to Edinburgh in 1583 and is known to have had contact with Napier. The historian Anthony à Wood (1632–1695) wrote:

one Dr. Craig … coming out of Denmark into his own country called upon John Neper, baron of Murcheston, near Edinburgh, and told him, among other discourses, of a new invention in Denmark (by Longomontanus as ’tis said) to save the tedious multiplication and division in astronomical calculations. Neper being solicitous to know farther of him concerning this matter, he could give no other account of it than that it was by proportionable numbers. [Neper is the Latin version of his family name]

Napier is thought to have begum work on the invention of logarithms about 1590. Logarithms exploit the relation ship between arithmetical and geometrical series. In modern terminology, as we all learnt at school, didn’t we:

A^m + Aⁿ = A^m+n

A^m/Aⁿ = A^m-n

These relationships were discussed by various mathematicians in the sixteenth century, without the modern notation, in particularly by Michael Stefil (1487–1567) in his Arithmetica integra (1544).

Michael Stifel Source: Wikimedia Commons

Michael Stifel’s Arithmetica Integra (1544) Source: Wikimedia Commons

What the rules for exponents show is that if one had tables to convert all numbers into powers of a given base then one could turn all multiplications and divisions into simple additions and subtractions of the exponents then using the tables to covert the result back into a number. This is what Napier did calling the result logarithms. The methodology Napier used to calculate his tables is too complex to deal with here but the work took him over twenty years and were published in his Mirifici logarithmorum canonis descriptio… (1614).

Napier coined the term logarithm from the Greek logos (ratio) and arithmos (number), meaning ratio-number. As well as the logarithm tables, the book contains seven pages of explanation on the nature of logarithms and their use. A secondary feature of Napier’s work is that he uses full decimal notation including the decimal point. He was not the first to do so but his doing so played an important role in the acceptance of this form of arithmetical notation. The book also contains important developments in spherical trigonometry.

Edward Wright  (baptised 1561–1615) produced an English translation of Napier’s Descriptio, which was approved by Napier, A Description of the Admirable Table of Logarithmes, which was published posthumously in 1616 by his son Samuel.

Gresham College was quick to take up Napier’s new invention and this resulted in Henry Briggs (1561–1630), the Gresham professor of geometry, travelling to Edinburgh from London to meet with Napier. As a result of this meeting Briggs, with Napier’s active support, developed tables of base ten logarithms, Logarithmorum chilias prima, which were publish in London sometime before Napier’s death in 1617.

He published a second extended set of base ten tables, Arithmetica logarithmica, in 1624.

Napier’s own tables are often said to be Natural Logarithms, that is with Euler’s number ‘e’ as base but this is not true. The base of Napierian logarithms is given by:

NapLog(x) = –10⁷ln (x/10⁷)

Natural logarithms have many fathers all of whom developed them before ‘e’ itself was discovered and defined; these include the Jesuit mathematicians Gregoire de Saint-Vincent (1584–1667) and Alphonse Antonio de Sarasa (1618–1667) around 1649, and Nicholas Mercator (c. 1620–1687) in his Logarithmotechnia (1688) but John Speidell (fl. 1600–1634), had already produced a table of not quite natural logarithms in 1619.

Napier’s son, Robert, published a second work by his father on logarithms, Mirifici logarithmorum canonis constructio; et eorum ad naturales ipsorum numeros habitudines, posthumously in 1619.

This was actually written earlier than the Descriptio, and describes the principle behind the logarithms and how they were calculated.

The English mathematician Edmund Gunter (1581–1626) developed a scale or rule containing trigonometrical and logarithmic scales, which could be used with a pair of compasses to solve navigational problems.

Table of Trigonometry, from the 1728 Cyclopaedia, Volume 2 featuring a Gunter’s scale Source: Wikimedia Commons

Out of two Gunter scales laid next to each other William Oughtred (1574–1660) developed the slide rule, basically a set of portable logarithm tables for carry out calculations.

Napier developed other aids to calculation, which he published in his Rabdologiae, seu numerationis per virgulas libri duo in 1617; the most interesting of which was his so called Napier’s Bones.

These are a set of multiplication tables embedded in rods. They can be used for multiplication, division and square root extraction.

An 18th century set of Napier’s bones Source: Wikimedia Commons

Wilhelm Schickard’s calculating machine incorporated a set of cylindrical Napier’s Bones to facilitate multiplication.

The Swiss mathematician Jost Bürgi (1552–1632) produced a set of logarithm tables independently of Napier at almost the same time, which were however first published at Kepler’s urging as, Arithmetische und Geometrische Progress Tabulen…, in 1620. However, unlike Napier, Bürgi delivered no explanation of the how his table were calculated.

Tables of logarithms became the standard calculation aid for all those making mathematical calculations down to the twentieth century. These were some of the mathematical tables that Babbage wanted to produce and print mechanically with his Difference Engine. When I was at secondary school in the 1960s I still carried out all my calculations with my trusty set of log tables, pocket calculators just beginning to appear as I transitioned from school to university but still too expensive for most people.

Not my copy but this is the set of log tables that accompanied me through my school years

Later in the late 1980s at university in Germany I had, in a lecture on the history of calculating, to explain to the listening students what log tables were, as they had never seen, let alone used, them. However for more than 350 years Napier’s invention served all those, who needed to make mathematical calculations well.

A widespread myth in the popular history of astronomy is that Galileo Galilei (1564–1642) was the first or even the only astronomer to realise the potential of the newly invented telescope as an instrument for astronomy. This perception is very far from the truth. He was just one of a group of investigator, who realised the telescopes potential and all of the discoveries traditionally attributed to Galileo were actually made contemporaneously by several people, who full of curiosity pointed their primitive new instruments at the night skies. So why does Galileo usually get all of the credit? Quite simply, he was the first to publish.

Galileo’s “cannocchiali” telescopes at the Museo Galileo, Florence

Starting in the middle of 1609 various astronomers began pointing primitive Dutch telescopes at the night skies, Thomas Harriot (1560–1621) and his friend and student William Lower (1570–1615) in Britain, Simon Marius (1573–1625) in Ansbach, Johannes Fabricius (1587–1616) in Frisia, Odo van Maelcote (1572–1615) and Giovanni Paolo Lembo (1570–1618) in Rome, Christoph Scheiner (1573 or 1575–1650) in Ingolstadt and of course Galileo in Padua. As far as we can ascertain Thomas Harriot was the first and the order in which the others took up the chase is almost impossible to determine and also irrelevant, as it was who was first to publish that really matters and that was, as already stated, Galileo.

Harriot made a simple two-dimensional telescopic sketch of the moon in the middle of 1609.

Thomas Harriot’s initial telescopic sketch of the moon from 1609 Source: Wikimedia Commons

Both Galileo and Simon Marius started making telescopic astronomical observations sometime late in the same year. At the beginning Galileo wrote his observation logbook in his Tuscan dialect and then on 7 January 1610 he made the discovery that would make him famous, his first observation of three of the four so-called Galilean moons of Jupiter.

It was on this page that Galileo first noted an observation of the moons of Jupiter. This observation upset the notion that all celestial bodies must revolve around the Earth. Source: Wikimedia Commons

Galileo realised at once that he had hit the jackpot and immediately changed to writing his observations in Latin in preparation for a publication. Simon Marius, who made the same discovery just one day later, didn’t make any preparations for immediate publication. Galileo kept on making his observations and collecting material for his publication and then on 12 March 1610, just two months after he first saw the Jupiter moons, his Sidereus Nuncius (Starry Messenger of Starry Message, the original Latin is ambiguous) was published in Padua but dedicated to Cosimo II de Medici, Fourth Grand Duke of Tuscany. Galileo had already negotiated with the court in Florence about the naming of the moons; he named them the Medicean Stars thus taking his first step in turning his discovery into personal advancement.

Title page of Sidereus nuncius, 1610, by Galileo Galilei (1564-1642). *IC6.G1333.610s, Houghton Library, Harvard University Source: Wikimedia Commons

What exactly did Galileo discover with his telescope, who else made the same discoveries and what effect did they have on the ongoing astronomical/cosmological debate? We can start by stating quite categorically that the initial discoveries that Galileo published in his Sidereus Nuncius neither proved the heliocentric hypothesis nor did they refute the geocentric one,

The first discovery that the Sidereus Nuncius contains is that viewed through the telescope many more stars are visible than to the naked-eye. This was already known to those, who took part in Lipperhey’s first ever public demonstration of the telescope in Den Haag in September 1608 and to all, who subsequently pointed a telescope of any sort at the night sky. This played absolutely no role in the astronomical/cosmological debate but was worrying for the theologians. Christianity in general had accepted both astronomy and astrology, as long as the latter was not interpreted deterministically, because the Bible says  “And God said, Let there be lights in the firmament of the heaven to divide the day from night; and let them be for signs, and for seasons, and for days, and years:” (Gen 1:14). If the lights in the heavens are signs from God to be interpreted by humanity, what use are signs that can only be seen with a telescope?

Next up we have the fact that some of the nebulae, indistinct clouds of light in the heavens, when viewed with a telescope resolved into dense groups of stars. Nebulae had never played a major role in Western astronomy, so this discovery whilst interesting did not play a major role in the contemporary debate. Simon Marius made the first telescopic observations of the Andromeda nebula, which was unknown to Ptolemaeus, but which had already been described by the Persian astronomer, Abd al-Rahman al-Sufi (903–986), usually referred to simply as Al Sufi. It is historically interesting because the Andromeda nebula was the first galaxy to be recognised outside of the Milky Way.

Al Sufi’s drawing of the constellation Fish with the Andromeda nebula in fount of it mouth

Galileo’s next discovery was that the moon was not smooth and perfect, as required of all celestial bodies by Aristotelian cosmology, but had geological feature, mountains and valleys, just like the earth i.e. the surface was three-dimensional and not two-dimensional, as Harriot had sketched it. This perception of Galileo’s is attributed to the fact that he was a trained painter used to creating light and shadows in paintings and he thus recognised that what he was seeing on the moons surface was indeed shadows cast by mountains.

As soon as he read the Sidereus Nuncius, Harriot recognised that Galileo was correct and he went on to produce the first real telescopic map of the moon.

Thomas Harriot’s 1611 telescopic map of the moon Source: Wikimedia Commons

Galileo’s own washes of the moon, the most famous illustrations in the Sidereus Nuncius, are in fact studies to illustrate his arguments and not accurate illustrations of what he saw.

Galileo’s sketches of the Moon from Sidereus Nuncius. Source: Wikimedia Commons

That the moon was earth like and for some that the well-known markings on the moon, the man in the moon etc., are in fact a mountainous landscape was a view held by various in antiquity, such as Thales, Orpheus, Anaxagoras, Democritus, Pythagoras, Philolaus, Plutarch and Lucian. In particular Plutarch (c. 46–c. 120 CE) in his On the Face of the Moon in his Moralia, having dismissed other theories including Aristotle’s wrote:

Just as our earth contains gulfs that are deep and extensive, one here pouring in towards us through the Pillars of Herakles and outside the Caspian and the Red Sea with its gulfs, so those features are depths and hollows of the Moon. The largest of them is called “Hecate’s Recess,” where the souls suffer and extract penalties for whatever they have endured or committed after having already become spirits; and the two long ones are called “the Gates,” for through them pass the souls now to the side of the Moon that faces heaven and now back to the side that faces Earth. The side of the Moon towards heaven is named “Elysian plain,” the hither side, “House of counter-terrestrial Persephone.”

So Galileo’s discovery was not so sensational, as it is often presented. However, the earth-like, and not smooth and perfect, appearance of the moon was yet another hole torn in the fabric of Aristotelian cosmology.

Of course the major sensation in the Sidereus Nuncius was the discovery of the four largest moons of Jupiter.

Galileo’s drawings of Jupiter and its Medicean Stars from Sidereus Nuncius. Image courtesy of the History of Science Collections, University of Oklahoma Libraries. Source: Wikimedia Commons

This contradicted the major premise of Aristotelian cosmology that all of the celestial bodies revolved around a common centre, his homo-centricity.  It also added a small modicum of support to a heliocentric cosmology, which had suffered from the criticism, if all the celestial bodies revolve around the sun, why does the moon continue to revolve around the earth. Now Jupiter had not just one but four moons, or satellites as Johannes Kepler called them, so the earth was no longer alone in having a moon. As already stated above Simon Marius discovered the moons of Jupiter just one day later than Galileo but he didn’t publish his discovery until 1614. A delay that would later bring him a charge of plagiarism from Galileo and ruin his reputation, which was first restored at the end of the nineteenth century when an investigation of the respective observation data showed that Marius’ observations were independent of those of Galileo.

The publication of the Sidereus Nuncius was an absolute sensation and the book quickly sold out. Galileo went, almost literally overnight, from being a virtually unknown, middle aged, Northern Italian, professor of mathematics to the most celebrated astronomer in the whole of Europe. However, not everybody celebrated or accepted the truth of his discoveries and that not without reason. Firstly, any new scientific discovery needs to be confirmed independently by other. If Simon Marius had also published early in 1610 things might have been different but he, for whatever reasons, didn’t publish his Mundus Jovialis (The World of Jupiter) until 1614. Secondly there was no scientific explanation available that explained how a telescope functioned, so how did anyone know that what Galileo and others were observing was real? Thirdly, and this is a very important point that often gets ignored, the early telescopes were very, very poor quality suffering from all sorts of imperfections and distortions and it is almost a miracle that Galileo et al discovered anything with these extremely primitive instruments.

As I stated in the last episode, the second problem was solved by Johannes Kepler in 1611 with the publication of his Dioptrice.

A book that Galileo, always rather arrogant, dismissed as unreadable. This was his triumph and nobody else was going to muscle in on his glory. The third problem was one that only time and improvements in both glass making and the grinding and polishing of lenses would solve. In the intervening years there were numerous cases of new astronomical discoveries that turned out to be artefacts produced by poor quality instruments.

The first problem was the major hurdle that Galileo had to take if he wanted his discoveries to be taken seriously. Upon hearing of Galileo discoveries, Johannes Kepler in Prague immediately put pen to paper and fired off a pamphlet, Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) congratulating Galileo, welcoming his discoveries and stating his belief in their correctness, which he sent off to Italy. Galileo immediately printed and distributed a pirate copy of Kepler’s work, without even bothering to ask permission, it was after all a confirmation from the Imperial Mathematicus and Kepler’s reputation at this time was considerably bigger than Galileo’s.

A reprint of Kepler’s letter to Galileo, originally issued in Prague in 1610

However, Kepler’s confirmations were based on faith and not personal confirmatory observations, so they didn’t really solve Galileo’s central problem. Help came in the end from the Jesuit astronomers of the Collegio Romano.

Odo van Maelcote and Giovanni Paolo Lembo had already been making telescopic astronomical observations before the publication of Galileo’s Sidereus Nuncius. Galileo also enjoyed good relations with Christoph Clavius (1538–1612), the founder and head of the school of mathematics at the Collegio Romano, who had been instrumental in helping Galileo to obtain the professorship in Padua. Under the direction of Christoph Grienberger (1561–1636), soon to be Clavius’ successor as professor for mathematics at the Collegio, the Jesuit astronomers set about trying to confirm all of Galileo’s discoveries. This proved more than somewhat difficult, as they were unable, even with Galileo’s assistance via correspondence, to produce an instrument of sufficient quality to observe the moons of Jupiter. In the end Antonio Santini (1577–1662), a mathematician from Venice, succeeded in producing a telescope of sufficient quality for the task, confirmed for himself the existence of the Jupiter moons and then sent a telescope to the Collegio Romano, where the Jesuit astronomers were now also able to confirm all of Galileo’s discovery. Galileo could not have wished for a better confirmation of his efforts, nobody was going to doubt the word of the Jesuits.

In March 1611 Galileo travelled to Rome, where the Jesuits staged a banquet in his honour at which Odo van Maelcote held an oration to the Tuscan astronomer. Galileo’s strategy of dedicating the Sidereus Nuncius to Cosimo de Medici and naming the four moons the Medicean Stars paid off and he was appointed court mathematicus and philosophicus in Florence and professor of mathematics at the university without any teaching obligations; Galileo had arrived at the top of the greasy pole but what goes up must, as we will see, come down.

On Twitter this morning physicist and science writer Graham Farmelo inadvertently drew my attention to a reader’s letter in The Guardian from Sunday by a Collin Moffat. Upon reading this load of old cobblers, your friendly, mild mannered historian of Renaissance mathematics instantly turned into the howling-with-rage HISTSCI_HULK. What could possibly have provoked this outbreak? I present for your delectation the offending object.

I fear Thomas Eaton (Weekend Quiz, 12 October) is giving further credence to “fake news” from 1507, when a German cartographer was seeking the derivation of “America” and hit upon the name of Amerigo Vespucci, an obscure Florentine navigator. Derived from this single source, this made-up derivation has been copied ever after.

The fact is that Christopher Columbus visited Iceland in 1477-78, and learned of a western landmass named “Markland”. Seeking funds from King Ferdinand of Spain, he told the king that the western continent really did exist, it even had a name – and Columbus adapted “Markland” into the Spanish way of speaking, which requires an initial vowel “A-”, and dropped “-land” substituting “-ia”.

Thus “A-mark-ia”, ie “America”. In Icelandic, “Markland” may be translated as “the Outback” – perhaps a fair description.

See Graeme Davis, Vikings in America (Birlinn, 2009).

Astute readers will remember that we have been here before, with those that erroneously claim that America was named after a Welsh merchant by the name of Richard Ap Meric. The claim presented here is equally erroneous; let us examine it in detail.

…when a German cartographer was seeking the derivation of “America” and hit upon the name of Amerigo Vespucci, an obscure Florentine navigator.

It was actually two German cartographers Martin Waldseemüller and Matthias Ringmann and they were not looking for a derivation of America, they coined the name. What is more, they give a clear explanation as to why and how the coined the name and why exactly they chose to name the newly discovered continent after Amerigo Vespucci, who, by the way, wasn’t that obscure. You can read the details in my earlier post. It is of interest that the supporters of the Ap Meric theory use exactly the same tactic of lying about Waldseemüller and Ringmann and their coinage.

The fact is that Christopher Columbus visited Iceland in 1477-78, and learned of a western landmass named “Markland”.

Let us examine what is known about Columbus’ supposed visit to Iceland. You will note that I use the term supposed, as facts about this voyage are more than rather thin. In his biography of Columbus, Felipe Fernandez-Armesto, historian of Early Modern exploration, writes:

He claimed that February 1477–the date can be treated as unreliable in such a long –deferred recollection [from 1495]–he sailed ‘a hundred leagues beyond’ Iceland, on a trip from Bristol…

In “Christopher Columbus and the Age of Exploration: An Encyclopedia”[1] edited by the American historian, Silvio A. Bedini, we can read:

The possibility of Columbus having visited Iceland is based on a passage in his son Fernando Colón’s biography of his father. He cites a letter from Columbus stating that in February 1477 he sailed “a hundred leagues beyond the island of Til” (i.e. Thule, Iceland). But there is no evidence to his having stopped in Iceland or spoken with anyone, and in any case it is unlikely that anyone he spoke to would have known about the the Icelandic discovery of Vinland.

This makes rather a mockery of the letter’s final claim:

Seeking funds from King Ferdinand of Spain, he told the king that the western continent really did exist, it even had a name – and Columbus adapted “Markland” into the Spanish way of speaking, which requires an initial vowel “A-”, and dropped “-land” substituting “-ia”.

Given that it is a well established fact that Columbus was trying to sail westward to Asia and ran into America purely by accident, convinced by the way that he had actually reached Asia, the above is nothing more than a fairly tale with no historical substance whatsoever.

To close I want to address the question posed in the title to this brief post. Given that we have a clear and one hundred per cent reliable source for the name of America and the two men who coined it, why oh why do people keep coming up with totally unsubstantiated origins of the name based on ahistorical fantasies? And no I can’t be bothered to waste either my time or my money on Graeme Davis’ book, which is currently deleted and only available as a Kindle.

[1] On days like this it pays to have one book or another sitting around on your bookshelves.

Felipe Fernández-Armesto, Columbus, Duckworth, London, ppb 1996, p. 18. Christopher Columbus and the Age of Exploration: An Encyclopedia, ed. Silvio A. Bedini, Da Capo Press, New York, ppb 1992, p. 314

The publication of Galileo’s Sidereus Nuncius was by no means the end of the spectacular and game changing telescopic astronomical discoveries during that first hot phase, which spanned 1610 to 1613. There were to be three further major discoveries, one of which led to a bitter priority dispute that would in the end play a role in Galileo’s downfall and another of which would sink Ptolemaeus’ geocentric model of the cosmos for ever.

The first new discovery post Sidereus Nuncius was the rather strange fact that Saturn appeared to have ears or as Galileo put it, it was three bodies “accompanied by two attendants who never leave his side.”

Galileo’s drawings of Saturn

What Galileo had in fact observed were the rings of Saturn, which however because of the relative positions of Saturn and the Earth were not discernable as rings but as strange semi-circular projections on either side of the planet. What exactly the strange protrusions visible on Saturn were would remain a mystery until Christiaan Huygens solved the problem much later in the century. The astronomers of the Collegio Romano claimed priority on the Saturn discovery. Whether they or Galileo saw the phenomenon first cannot really be determined but it demonstrates once again that Galileo was by no means the only one making these new telescopic discoveries. Saturn’s two “attendants” didn’t really play a role in the ongoing astronomy/cosmology debate but the next discovery did in a very major way.

Probably stimulated by a letter from his one time student Benedetto Castelli (1578–1643) Galileo turned his attention to Venus and its potential phases.

Benedetto Castelli Source: Wikimedia Commons

If Venus was indeed lit by the sun then in both Ptolemaeus’ geocentric system and in a heliocentric system it would, like the moon, display phases but these phases would differ according to whether Venus orbited the Earth in a geocentric system or the sun in either a heliocentric or a geo-heliocentric one. Galileo’s observations clearly showed that the phases of Venus were consistent with a solar orbit and not a terrestrial one.

The Phases of Venus in both systems

The pure Ptolemaic geocentric system was irredeemably sunk but not, and that must be strongly emphasised, a number of geo-heliocentric systems. As already mentioned earlier, because they never strayed far from the sun’s vicinity and in a geocentric system even shared the sun orbital period, Mercury and Venus had since antiquity been assumed, by some, to orbit the sun whereas the sun orbited the earth in what is known as the Capellan system; a system that was very popular in the Middle Ages and had been praised as such by Copernicus in his De revolutionibus. Phases of Venus indicating a solar orbit were, of course, also consistent with a full Tychonic system in which the planets, apart from the moon, orbited the sun, which in turn together with the moon orbited the earth, as well as several variant semi-Tychonic systems. It was assumed that Mercury also orbited the sun, although its phases were first observed by  Pierre Gassendi (1592–1655) in 1631. The heliocentric phases of Venus were also discovered independently by Thomas Harriot, who, as always, didn’t publish, by Simon Marius, whose discovery was published by Kepler, and by the Collegio Romano astronomers, who also didn’t published but announced their discovery in their correspondence.

The other major telescopic discovery was the presence of blemishes or spots on the surfaces of the sun, again something that contradicted Aristotle’s assumption of the perfection of the celestial bodies. This discovery led to one of Galileo’s biggest priority disputes. This whole sorry episode began with a communication from the Augsburger banker and science fan, Marcus Welser(1558–1614), who was also a close friend of the Jesuits.

Marcus Welser Source: Wikimedia Commons

This communication contained three letters on sunspots written by the Ingolstädter Jesuit Christoph Scheiner (1573 or 75–1650) under the pseudonym, Appeles.

Christoph Scheiner (artist unknown)

Welser wanted to hear Galileo’s opinion on Scheiner’s discovery. Galileo was deeply offended, the heavens were his territory and only he was allowed to make discoveries there! The dispute was carried on two levels, the first was the question of priority and the second was the question of how to interpret what had been observed. Although, during the whole dispute Galileo kept changing the date when he first observed sunspots, in order to establish his priority and to claim the discovery as his, viewed with hindsight the priority dispute was a bit of a joke. We now know that Thomas Harriot  had recorded observations of sunspot before either Galileo or Scheiner but because he never published his observations, they were blissfully unaware of his priority. Even stranger, Johannes Fabricius (1587–1616), the son of Kepler’s intellectual sparing partner David Fabricius, had brought home a telescope from university in Leiden, where Rudolph Snell (1546–1613) was already holding lectures on the telescope in 1610, and together with his father had not only been observing sunspots but had already published a pamphlet on his observation in Wittenberg in 1611, where he was now studying.

The second part of the dispute was by far and away the more important. Scheiner had initially interpreted the sunspots as shadows cast upon the surface of the sun by small satellites orbiting it. It is was possible that through this interpretation he wished to preserve the Aristotelian perfection of this celestial body. Galileo opposed this interpretation and was convinced, correctly as it turned out, that the sunspots were actually some sort of blemishes on the surface of the sun.

Galileo answered Scheiner’s letters with three of his own, in the process stepping up his observation of the sunspots, as well as gathering observational reports from other astronomers. He was able to show through the quality of his observations and through mathematical analysis that the sunspots must be on the surface of the sun and that the sun must be revolving about its axis. With time Scheiner came to accept Galileo’s conclusions. Scheiner published three more sunspot letters under the title Accuratior Disquisitio in 1612.

The Accademia dei Lincei, which had elected Galileo a member when he came to Rome to celebrate the Jesuit’s confirmation of his telescopic discoveries, published Scheiner’s original three letters together with Galileo’s three answering letters in a book titled, Istoria e Dimontrazioni, in 1613.

Having in his opinion won the priority dispute and proved that the sunspots were on the surface of the sun, Galileo basically gave up on his solar observations; Scheiner did not. Having built what was effectively the first Keplerian or astronomical telescope with two convex lenses, instead of one convex and one concave, as in the Dutch or Galilean telescope, giving a much wider field of vision and a much clearer and stronger image, Scheiner set out on a programme of solar astronomy.

Scheiner Observing the Sun

The astronomical telescope provided an inverted image but this was irrelevant as Scheiner was projecting the image onto paper in order to simplify the drawing on the sunspots and also to protect his eyes. A method also used by Fabricius and Galileo. He mounted his telescope on a special holder that allowed him to follow the sun in its journey across the heavens.

Scheiner’s Helioscope

The end of this programme was his Rosa Ursina sive Sol, published in 1626-30, which remained the most important book on solar astronomy until the nineteenth century.

Scheiner’s Sunspot Observations

Galileo’s and Scheiner’s priority dispute entails a strong sense of historical irony. Not only did Harriot begin observing sunspots earlier than both of them and Johannes Fabricius publish on the subject before either of them but Chinese and Korean astronomers had been recording naked-eye observations of sunspots since the first millennium BCE. There are also scattered observations of sunspots beginning with the ancient Greeks and down through the Middle Ages in Europe.

A drawing of a sunspot in the Chronicles of John of Worcester 1129 Source: Wikimedia Commons

Famously Kepler recorded observations of a large sunspot that he made in 1607 mistakenly believing that he was observing a transit of Mercury.

1613 marks the end of the first phase of astronomical telescopic discoveries, partially because the observers continued to use Dutch or Galilean telescopes instead of changing to the vastly superior Keplerian or astronomical telescopes, largely influenced by Galileo’s authority, he publicly rubbished astronomical telescopes, basically because he hadn’t started using them first; the transition to the better instruments would take a couple of decades to be completed.

The first period of telescopic, astronomical discoveries came to an end in 1613, which was seventy years after the publication of Copernicus’ De revolutionibus. This makes it a good point to stop and take stock of the developments that had taken place since the appearance of that epoch defining magnum opus. First we need to remind ourselves of the situation that had existed before Copernicus heliocentric hypothesis entered the world and triggered a whole new cosmology and astronomy debate. The mainstream standpoint was an uneasy combination of Aristotelian cosmology and Ptolemaic astronomy. Uneasy because, as some saw it, the Ptolemaic deferent and epicycle model of planetary motion contradicted Aristotle’s homocentric principle, which led to a revival of homocentric astronomy. Others saw the principle of uniform circular motion contradicted by Ptolemaeus’ use of the equant point. In fact, we know that the removal of the equant point, for exactly this reason, was the starting point of Copernicus’ own reform efforts. Another minority view that was extensively discussed was a geocentric system with diurnal rotation, as originated in antiquity by Heraclides of Pontus, regarded by some as more rational or acceptable than that the sphere of the fixed stars rotated once in twenty-four hours. Also still up for debate was the Capellan system with Mercury and Venus orbiting the Sun in a geocentric system. Then came Copernicus and added a new radical alternative to the debate.

By 1613 most of the Aristotelian cosmology had been disposed of bit for bit. Aristotle’s sublunar meteorological comets had definitely become supralunar astronomical objects, although what exactly they were was still largely a mystery. As we shall see Galileo later embarrassed himself by maintaining a position on comets very close to that of Aristotle. The comets becoming supralunar had also disposed of Aristotle’s crystalline spheres, although Copernicus seems to have still believed in them. The telescopic discovery of the geographical features on the Moon and the spots on the Sun had put an end to Aristotle’s perfection of the celestial spheres. They together with the comets and the supernovas of 1573 and 1604, both of which had clearly been shown to be supralunar, also contradicted his immutability of the heavens. The discovery of the four largest moons of Jupiter ended the homocentric concept and the discovery of the phases of Venus, originating in a solar orbit, ruled a pure geocentric system but not a geo-heliocentric one. As a result of all these changes cosmology was up for grabs.

In astronomy the biggest single change was that nearly all astronomers, following Copernicus, now believed in the reality of their models and no longer viewed them as purely mathematical constructions designed to save the phenomena. This was a major shift as previously the discussion of the reality of the heavens was regarded as a discussion for philosophers and definitely not astronomers. So which models were up for discussion? Had in the intervening seventy years the debate simplified, reduced to a choice between two competing models, Ptolemaic geocentrism and Copernican heliocentrism, as Galileo would have us believe twenty years later? Actually no, if anything the situation had got considerably more confused with a whole raft full of astronomical models jostling for a place at the table. What were these competing models?

Given the telescopic observations of the phases of Venus and the assumption of similar phases for Mercury, a pure Ptolemaic geocentric model should have been abandoned but there was still a hard core that refused to simply give up this ancient model. Christoph Clavius (1538–1612) in the last edition of his Sphaera, the standard Jesuit textbook on astronomy, acknowledged problems with the geocentric model but urged his readers to find solutions to the problems within the model. As late as 1651 Giovanni Battista Riccioli (1598–1671), in the famous frontispiece to his Almagestum novum, shows Ptolemaeus lying defeated on the ground, whilst the heliocentric and geo-heliocentric systems are weighed against each other, but he is saying, I will rise again.

Frontispiece of Riccioli’s 1651 New Almagest. Source: Wikimedia Commons

Due to William Gilbert’s revival of the Heraclidian diurnal rotation, we now have two geocentric models, with and without diurnal rotation. The Copernican heliocentric system is, of course, still very much in the running but with much less support than one might expect after all the developments of the intervening seventy years.

Despite the phases of Venus all the various geo-heliocentric models are still in contention and because of the lack of empirical evidence for movement of the Earth these are actually more popular at this point in time than heliocentric ones. However, despite the lack of empirical evidence diurnal rotation enjoys a surprising level of popularity. We have a Capellan system, Venus and Mercury orbit the Sun, which orbits the Earth, both with and without diurnal rotation. Very much in consideration is the full Tychonic system; the five planets orbit the Sun, which together with the Moon orbits the Earth. Once again both with and without diurnal rotation. Riccioli favoured another variation with Venus, Mercury and Mars orbiting the Sun but with Jupiter and Saturn orbiting the Earth along with the Sun and Moon.

Perhaps the most interesting development was Kepler’s heliocentric system. Whilst Kepler regarded his system as Copernican, others regarded his elliptical system as a rival to not only to the geocentric and geo-heliocentric system but also to the Copernican heliocentric system with its deferent and epicycle orbital models. The most prominent example of this being Galileo, who promoted the Copernican system, whilst deliberately ignoring Kepler’s more advanced developments.

We can find solid evidence for this multiplicity of systems in various sources. The earliest in a card game devised by Johann Praetorius (1573–1616), professor for astronomy at the University of Altdorf near Nürnberg, which only exists in manuscript.

Source: Wikimedia Commons

Source: All playing card images Wikimedia Commons

Another much read source is the extraordinary Anatomy of Melancholy by the Oxford scholar Robert Burton (1577–1640). First published in 1621, it was republished five times over the next seventeen years, each edition being massively modified and expanded.

The Anatomy of Melancholy frontispiece 1638 ed. Source: Wikimedia Commons

In a section entitled Melancholy of the Air Burton discusses the various astronomical models, favouring the system of David Origanus (1558–1629), professor for Geek Greek and mathematics at the University of Frankfurt an der Oder, a Tychonic system with diurnal rotation.

Source: Wikimedia Commons

Burton, as well as being one of the most erudite scholars of the seventeenth century, was also a practicing astrologer, who is said to have hung himself in his Oxford chambers to fulfil his own prediction of his death.

Already mentioned above is Giovanni Battista Riccioli, whose Almagestum novum (1551) contains descriptions of a wide range of different systems.

Riccioli as portrayed in the 1742 Atlas Coelestis (plate 3) of Johann Gabriel Doppelmayer. Source: Wikimedia Commons

The book also contains a list of 126 arguments pro and contra heliocentricity, 49 for and 77 against, in which religios arguments play only a very minor role.

Another Jesuit was Athanasius Kircher (1602–1680), who sat at the centre of a world spanning astronomy correspondence network, receiving astronomical data from Jesuits all of the world, collating it and re-distributing it to astronomers throughout Europe.

Source: Wikimedia Commons

He described six different systems as late as 1656 in his Itinerarium extaticum, with a revised edition from 1671.

Diagrams of the different world systems, Ptolemaic, Platonic, Egyptian, Copernican, Tychonic and semi-Tychonic from Iter Exstaticum (1671 ed.) p. 37 Source:

Contrary to a widespread view the question of the correct astronomical system was still very much an open question throughout most of the seventeenth century, largely because there existed no conclusive empirical evidence available to settle the question.

I spend a lot of my time trying to unravel and understand the complex bundle that is Renaissance or Early Modern mathematics and the people who practiced it. Regular readers of this blog should by now be well aware that the Renaissance mathematici, or mathematical practitioners as they are generally known in English, did not work on mathematics as we would understand it today but on practical mathematics that we might be inclined, somewhat mistakenly, to label applied mathematics. One group of disciplines that we often find treated together by one and the same practitioner consists of astronomy, cartography, navigation and the design and construction of tables and instruments to aid the study of these. This being the case I was delighted to receive a review copy of Margaret E. Schotte’s Sailing School: Navigating Science and Skill, 1550–1800[1], which deals with exactly this group of practical mathematical skills as applied to the real world of deep-sea sailing.

Schotte’s book takes the reader on a journey both through time and around the major sea going nations of Europe, explaining, as she goes, how each of these nations dealt with the problem of educating, or maybe that should rather be training, seamen to become navigators for their navel and merchant fleets, as the Europeans began to span the world in their sailing ships both for exploration and trade.

Having set the course for the reader in a detailed introduction, Schotte sets sail from the Iberian peninsular in the sixteenth century. It was from there that the first Europeans set out on deep-sea voyages and it was here that it was first realised that navigators for such voyages could and probably should be trained. Next we travel up the coast of the Atlantic to Holland in the seventeenth century, where the Dutch set out to conquer the oceans and establish themselves as the world’s leading maritime nation with a wide range of training possibilities for deep-sea navigators, extending the foundations laid by the Spanish and Portuguese. Towards the end of the century we seek harbour in France to see how the French are training their navigators. Next port of call is England, a land that would famously go on, in their own estimation, to rule the seven seas. In the eighteenth century we cross the Channel back to Holland and the advances made over the last hundred years. The final chapter takes us to the end of the eighteenth century and the extraordinary story of the English seaman Lieutenant Riou, whose ship the HMS Guardian hit an iceberg in the Southern Atlantic. Lacking enough boats to evacuate all of his crew and passengers, Riou made temporary repairs to his vessel and motivating his men to continuously pump out the waters leaking into the rump of his ship, he then by a process of masterful navigation, on a level with his contemporaries Cook and Bligh, brought the badly damaged frigate to safety in South Africa.

In each of our ports of call Schotte outlines and explains the training conceived by the authorities for training navigators and examines how it was or was not put into practice. Methods of determining latitude and longitude, sailing speeds and distances covered are described and explained. The differences in approach to this training developed in each of the sea going European nations are carefully presented and contrasted. Of special interest is the breach in understanding of what is necessary for a trainee navigator between the mathematical practitioners, who were appointed to teach those trainees, and the seamen, who were being trained, a large yawning gap between theory and practice. When discussing the Dutch approach to training Schotte clearly describes why experienced coastal navigators do not, without retraining, make good deep-sea navigators. The methodologies of these two areas of the art of navigation are substantially different.

The reader gets introduced to the methodologies used by deep-sea navigators, the mathematics developed, the tables considered necessary and the instruments and charts that were put to use. Of particular interest are the rules of thumb utilised to make course corrections before accurate methods of determining longitude were developed. There are also detailed discussions about how one or other aspect of the art of navigation was emphasised in the training in one country but considered less important in another. One conclusion the Schotte draws is that there is not really a discernable gradient of progress in the methods taught and the methods of teaching them over the two hundred and fifty years covered by the book.

As well as everything you wanted to know about navigating sailing ships but were too afraid to ask, Schotte also delivers interesting knowledge of other areas. Theories of education come to the fore but an aspect that I found particularly fascinating were her comments on the book trade. Throughout the period covered, the teachers of navigation wrote and marketed books on the art of navigation. These books were fairly diverse and written for differing readers. Some were conceived as textbooks for the apprentice navigators whilst others were obviously written for interested, educated laymen, who would never navigate a ship. Later, as written exams began to play a greater role in the education of the aspirant navigators, authors and publishers began to market books of specimen exam questions as preparation for the exams. These books also went through an interesting evolution. Schotte deals with this topic in quite a lot of detail discussing the authors, publishers and booksellers, who were engaged in this market of navigational literature. This is detailed enough to be of interest to book historians, who might not really be interested in the history of navigation per se.

Schotte is excellent writer and the book is truly a pleasure to read. On a physical level the book is beautifully presented with lots of fascinating and highly informative illustrations. The apparatus starts with a very useful glossary of technical terms. There is a very extensive bibliography and an equally extensive and useful index. My only complaint concerns the notes, which are endnotes and not footnotes. These are in fact very extensive and highly informative containing lots of additional information not contained in the main text. I found myself continually leafing back and forth between main text and endnotes, making continuous reading almost impossible. In the end I developed a method of reading so many pages of main text followed by reading the endnotes for that section of the main text, mentally noting the number of particular endnotes that I wished to especially consult. Not ideal by any means.

This book is an essential read for anybody directly or indirectly interested in the history of navigation and also the history of practical mathematics. If however you are generally interested in good, well researched, well written history then you will almost certainly get a great deal of pleasure from reading this book.

[1] Margaret E. Schotte, Sailing School: Navigating Science and Skill, 1550–1800, Johns Hopkins University Press, Baltimore, 2019.

When contemplating the advent of the heliocentric hypothesis in the Early Modern Period, one of the first things that occurs to many people is the conflict between the emerging new astronomy and Christianity, in particular the Holy Roman Catholic Church. What took place in those early years was actually very different to what most people think occurred and to a large extent has over the years been blown up out of all proportions.

To a certain extent some sort of conflict was pre-programmed, as the Bible, which the majority in this period believed to be basically true , clearly presented a geocentric world, even to a small extent a flat earth given the Old Testament’s fundamentally Babylonian origins and the new astronomy was attempting to establish a heliocentric one. This situation called for a lot of diplomatic skill on the part of those proposing the new heliocentric cosmological system, a skill that some of those proponents, most notably Galileo Galilei failed to display.

Between the publication of Copernicus’ De revolutionibus, which was actively supported by several leading figures within the Catholic Church, and the sensational telescopic discoveries of 1610-1613 there was surprising little backlash against heliocentrism from any of the European Christian communities. I have dealt with this in detail in an earlier post and don’t intend to repeat myself here. The real problems first began in around 1615 and were provoked by Galileo Galilei and the Carmelite theologian Paolo Antonio Foscarini (c. 1565–1616).

Source: Wikimedia Commons

Again I have already dealt with this in great detail in two earlier posts, here and here, so I will only outline the real bone of contention now, which surprisingly has little to do with the science and a lot to do with who gets to interpret the Holy Word of God e.g. The Bible.

From its foundation the Catholic Church had claimed the exclusive right to interpret the Bible for its followers, i.e. all true Christians. With time that interpretation was anchored in the writings of the early church fathers, what they had written was holy gospel and to openly contradict it was considered to be heresy. The Church was not only a powerful religious institution but also a powerful political one and over the centuries the adage that power corrupts and absolute power corrupts absolutely certainly proved true within the Catholic Church. This led to several attempts to reform the Church and bring it back to the ‘true path’ as outlined in the gospels.

Before what we now know as The Reformation, notable attempts on varying levels were made by, amongst other, John Wycliffe (c. 1320s–1384) in England, Jan Hus (c. 1372–1415) in Bohemia and Desiderus Erasmus (1466–1536), although Erasmus’ reform efforts were very moderate when compared to the other two and those that came after. In the sixteenth century that which we call the Protestant Reformation broke out in several parts of Europe instigated by Martin Luther (1483–1546), Philipp Melanchthon (1497–1560), Thomas Müntzer (1489–1525), Huldrych Zwingli (1484–1531), Jean Calvin (1509–1564) and a host of other minor figure, such as Andreas Osiander (1496 or 1498–1552), who wrote the infamous Ad lectorum in De revolutionibus. The major characteristic of the Reformation was that those calling for reform demanded the right for each individual to be allowed to interpret The Bible for themselves, thus removing the Church’s monopoly on biblical interpretations. This was of course unacceptable for the Catholic Church, which in turn launched its Counter Reformation, with the Council of Trent (1545–1563), to try and stem the tide of dissent. This was the situation in 1615 just three years before the outbreak of the Thirty Years War, one of the bloodiest conflicts in the history of Europe triggered by just this religious dispute, when Galileo made the move that turned the Catholic Church against heliocentrism and began Galileo’s own downfall.

Before we examen what Galileo actually did to so annoy the Catholic Church, it pays to look at the historical context in which this all took place. Too often people try to judge what happened from a presentist point of view, thereby distorting the historical facts. As usual when I write on this subject I am not trying to apologise for the Catholic Church’s actions or to excuse them, merely to present them within the practices and beliefs at the beginning of the seventeenth century. Firstly, this was a historical period in which all social, cultural and political institutions were hierarchical and fairly rigidly structured. It was an age of absolutism in which most rulers, including or above all the Pope, had and exercised absolute power. Secondly, there was no such thing as freedom of speech or freedom of thought in either religious or secular society. Those at the top largely prescribed what could or could not be said or thought out loud. Anybody who pushed against those prescriptions could expect to be punished for having done so.

Galileo Portrait by Ottavio Leoni Source: Wikimedia Commons

In 1615 both Foscarini and Galileo tried to tell the Church how to reinterpret those passages in the Bible that presupposed a geocentric cosmos in order to make a heliocentric cosmos theologically acceptable. This was simply not on. In my comments I will restrict myself to the case of Galileo. Modern commentators think that what Galileo said in his Letter to Castelli and in the extended version, his Letter to Christina, is eminently sensible and applaud him for his theological analysis but in doing so they miss several important points. In the Renaissance intellectual hierarchy theologians were at the top and mathematici, and Galileo was a mere mathematicus, were very much at the bottom. In fact the social status of the mathematicus was so low that Galileo telling the theologians how to do their job was roughly equivalent to the weekly cleaning lady telling the owner of a luxury villa how to run his household. This was definitely a massive failure on Galileo’s part, one that he should have been well aware of. The very low social and intellectual status of mathematici was the reason why he insisted on being appointed court philosophicus and not just mathematicus to the Medicean court. Philosophers ranked just below theologians in the hierarchy. Also given the fact that the Reformation/Counter Reformation conflict was rapidly approaching its high point in the Thirty Years War, this was not the time to tell the Catholic Church how to interpret the Bible.

As formal complaints began to be made about his Letter to Castelli, Galileo realised that he had gone too far and claimed that the copies in circulation had been changed by his enemies to make him look bad and presented the Church with a modified version to show what “he had actually written.” I fact we now know that the unmodified version was his original letter.

The writings of Foscarini and Galileo on the subject now led the Church to formally examine the relationship between Catholic doctrine and the heliocentric hypothesis, for the first time, and the result was not good for Galileo and the heliocentric hypothesis. A commission of eleven theologians, known as Qualifiers, undertook this examination and came to the conclusion that the idea that the Sun is stationary is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture…”; while the Earth’s movement “receives the same judgement in philosophy and … in regard to theological truth it is at least erroneous in faith.” The first part is obvious the Bible states clearly that it is the Sun that moves and not the Earth and as the heliocentric hypothesis directly contradicts Holy Scripture it is formally heretical. The second part is more interesting because it that the hypothesis is philosophically, read scientifically, absurd and foolish. Although the language used here in the judgement is rather extreme it was a fact in 1615 that there existed no empirical proof for the heliocentric hypothesis, actually most of the then available empirical evidence supported a geocentric cosmos. If there had been empirical support for heliocentrism then the Church’s judgement might well have been different, as Roberto Bellarmino (1542–1621) wrote in his infamous letter to Foscarini:

Third, I say that, if there were a real proof that the Sun is in the centre of the universe, that the Earth is in the third sphere, and that the Sun does not go round the Earth but the Earth round the Sun, then we should have to proceed with great circumspection in explaining passages of Scripture which appear to teach the contrary, and we should rather have to say that we did not understand them than declare an opinion to be false which is proved to be true.

Roberto Bellarmino Source: Wikimedia Commons

In other words, if you provide proof of your hypothesis, then we will be prepared to reinterpret the Bible.

This was the point where Galileo, realising that he was potentially in serious trouble, first rushed to Rome to peddle his theory of the tides, which he appeared to believe delivered the necessary empirical proof for the heliocentric hypothesis.

Source: Wikimedia Commons

This theory had been developed together with Paolo Sarpi (1552–1623) in the 1590’s and basically claimed that the tides were caused by the movements of the Earth, in the same way that water sloshes around in a moving bowl. The theory has however a fatal empirical flaw; it only allows for one high tide in twenty-four hours whereas there are actually two. Galileo tried to deal with this discrepancy with a lot of hand waving but couldn’t really provide a suitable explanation. This was, however, irrelevant in 1615, as Galileo having through his actions poked the proverbial bear with a sharp stick, nobody was prepared to listen to his latest offerings and his efforts fell on deaf ears.

The inevitable happened, the Church formally banned heliocentricity in 1616, although it was never actually declared heretical, something that only the Pope could do and no Pope ever did, and books explicating the heliocentric hypothesis were placed on the Index of forbidden books. Interestingly Copernicus’ De revolutionibus was only placed on the Index until corrected and rather surprisingly this was carried out fairly quickly, the corrected version becoming available to Catholic scholars already by 1621. The Church had realised that this was an important book that should not be banned completely. The corrections consisted or removing or correcting the surprisingly few places in the text where the heliocentric hypothesis was stated as being scientifically true. This meant that Catholics were permitted to write about and discuss heliocentricity as a hypothesis but not to claim that it was empirically true.

Galileo who together with Foscarini had provoked this whole mess got off relatively lightly. At the Pope’s request he was personally informed by Cardinal Roberto Bellarmino that he could no longer hold or teach the heliocentric theory and given a document confirming this in writing. He was not punished in anyway and continued to be popular amongst leading figures in the Church including Maffeo Barberini, the future Pope Urban VIII.

Many modern commentators say why couldn’t the Church accept the eminently sensible suggestion made by Galileo and Foscarini and thus avoid the whole sorry mess. The answer is quite simple. If they had done so they would have surrendered their absolute right to interpret Holy Scripture, which, as pointed out above, lay at the centre of the Reformation/Counter Reformation conflict; a right that the Catholic Church has not surrendered up to the present day.

People with only a minimal knowledge of the history of medicine might be forgiven for automatically thinking of doctors when talk turns to medical consultation, diagnosis and treatment in earlier ages. However in the High Middle Ages and down into the Renaissance physicians, barber surgeons, apothecaries, midwifes, herbalist all competed with each other for patients, in particular the university educated physicians and apothecaries were rivals. In the Early Modern Period the physicians set a campaign in motion to create a medical hierarchy with themselves at the top able to dictate to the other practitioners. Historian of medicine Hannah Murphy has written an excellent volume describing this process of social change in the world of medicine in Reformation Nuremberg, A New Order of Medicine: The Rise of Physicians in Reformation Nuremberg[1]

The introduction to Murphy’s is titled Inventing Medical Reform and starts with Joachim Camerarius’ Short and Ordered Considerations for the Formation of a Well-Ordered Medicine (1571) outlining his proposed reform of medicine in the city of Nuremberg in which physicians would be authorised to oversee the work of apothecaries and only physicians would be permitted to undertake diagnosis. As a brief side note this is the physician Joachim Camerarius the younger, the son of the much more famous Joachim Camerarius the elder, classicist, colleague and biographer of Philipp Melanchthon.

Joachim Camerarius the younger Source: Wikimedia Commons

The programme set out by Camerarius in his Short and Ordered Considerations was not immediately accepted and put into practice by the Nuremberg city council but over the next few decades something similar was gradually put into place in Nuremburg; a process that involved a major political, cultural and social war between the physicians and the apothecaries. This gradual development is the subject of Murphy’s book. The rest of the introduction is devoted to a general road map of her work.

The book is divided into six chapters or perhaps, better said sections, each one of which deals with an aspect of the life and work of Early Modern physicians and how they relate to the changes in the role and status of the physicians that were taking place. These topics are initially handled for a given individual, and then developed for the city of Nuremberg in general with parallels being drawn for other cities and regions within the Holy Roman Empire. So what initially appears to be a very narrow and specialised study widens to cover a substantially area of Europe.

The opening chapter looks at a new, contemporary pharmacopeia, the Dispensatorium of Valerius Cordus, i.e. a catalogue of recipes for medical remedies. This area would become central in the dispute between the apothecaries and the physicians who could prescribe the remedies and which remedies should or could be prescribed.

The second chapter takes a detailed look at the position, role, and status of the city physician and how it differed from that of other sections of society in particular from that of the apothecaries. Moving on Murphy deals with the subject of anatomy, another area where the role of the physician would undergo a major change especially following the work of the century’s greatest anatomist, Andreas Vesalius. Turning away from the practical Murphy next addresses the role that books played in the life and work of the physician. We remain, for the next section, in the realm of the written word. In the absence of journals, which today play a major role in transmitting medical and related information, the early modern physicians had their correspondence. I personally am constantly amazed at just how many letters early modern scholars exchanged in their lifetimes with their colleagues throughout Europe. Thankfully, for the historian, some of these collections of correspondence have survived down the centuries and provide us with as valuable a source of information, as they once provided their authors and recipients. The final chapter returns to the starting point and a closer detailed look at Camerarius’ New Order of Medicine. Moving on Murphy now shows how the status and function of the physicians and apothecaries did change over time and the moves and disputes that accompanied those changes.

The book closes with a brief conclusion summarising what had been achieved by the Nuremberger physicians, I quote:

In their legal and civic battle with apothecaries, in their claim to profession primacy over surgeons and midwifes, in their bid to establish themselves as the arbiters of legitimate medicine, early modern physicians were decisively victorious.

They had succeeded in establishing a new order, one that basically still exists today. This leads to a, for historians, very interesting epilogue in which Murphy outlines how these not insignificant changes in the medical landscape of Europe became forgotten and at the same time mythologised down the succeeding centuries.

The book is pleasantly illustrated with the, in the mean time standard for academic publications, grey in grey prints. It has extensive endnotes, which largely consist of bibliographical references to the even more extensive bibliography of primary and secondary literature. The academic apparatus is rounded off by a good index.

Despite extensive historical research resulting in a highly detailed and dense text with intensive historical analysis, Murphy’s book is well written and a comparatively light read. Murphy has written an excellent book that delivers up a masterful demonstration of how a narrowly focused piece of historical research can be worked and presented so that it shines a light on a wide ranging historical development. The book should be of interest to anybody involved in the history of European medicine over the last five hundred years but will also make an interesting read for any early modern historian interested in going beyond the boundaries of their own discipline.

[1] Hannah Murphy, A New Order of Medicine: The Rise of Physicians in Reformation Nuremberg, University of Pittsburgh Press, Pittsburgh, 2019

One single occurrence in the year 1618 played a significant role in the history of astronomy, the appearance of a great comet. In fact there were three comets in 1618 but only one of them, a so-called great comet, made history. Great comets are those that are not just visible to astronomers but those that put on a spectacular display for the general public, the most well known being Comet Halley. The great comet of 1618 is important for the emergence of modern astronomy for three different reasons.

An image of the great comet of 1618 as seen above the Southern German city of Augsburg

The first is that the Swiss, Jesuit Johann Baptist Cysat (c. 1587–1657), a student of Christoph Scheiner (1573–1650), who had assisted Scheiner with his sunspot observations,

Johann Baptist Cysat, holding a Jacob’s staff Source: Wikimedia Commons

became the first astronomer to observe a comet with a telescope giving the first ever description of a comet’s nucleus in his Mathemata astronomica de loco, motu, magnitudine et causis cometae qui sub finem anni 1618 et initium anni 1619 in coelo fulsit. Ingolstadt Ex Typographeo Ederiano 1619 (Ingolstadt, 1619). He followed Tycho Brahe in believing that comets orbited the sun. He also demonstrated the orbit was parabolic not circular.

Source ETH Library Zurich

Johannes Kepler visited Cysat in Ingolstadt and the two astronomers corresponded, however only one of their letters is extant. Kepler, naturally, also observed the great comet of 1618 and wrote and published one of his, often overlooked but actually important books, on it and comets in general in 1619, his De cometis libelli tres I. astronomicus, theoremata continens de motu cometarum … II. physicus, continens physiologiam cometarum novam … III. astrologicus, de significationibus cometarum annorum 1607 et 1618 / autore Iohanne Keplero …

Source: ETH Library Zurich

This is one of the most important publications on comets in the seventeenth century and became a standard reference work in the 1680s, when a very major and very important debate was launched by the appearance of several bright comets. Unlike Cysat, Kepler thought that the trajectory of comets was rectilinear and only appeared curved because of the movement of the earth, he of course being a supporter of heliocentricity whereas Cysat supported geo-heliocentricity.

Kepler’s view on the trajectory of comets is interesting because already in 1610, having read Astronomia Nova, Sir William Lower (1570-1615), English landowner, member of parliament, and student and friend of Thomas Harriot, who together with Harriot had made careful observations of Comet Halley in 1607, suggested that comets also follow an elliptical orbit. However, his very perceptive views on the topic remained largely unknown at the time.

Cartoon of Sir William Lower with telescope John Prydderch his neighbour and observing companion with a Jacob staff Artist: The initials “JMS” appear in the corner of the cartoon. The front cover of the Journal of the Astronomical Society of Wales in the late 1890’s, also hand drawn, bore this insginia and stood for J. M. Staniforth, the artist-in-chief of the Western Mail newspaper

Another astronomer who made careful observations of all three of the 1618 comets was the Jesuit Orazio Grassi (1583–1654).

Orazio Grassi

Grassi published his views, which he had expounded as a lecture at the Collegio Romano, the Jesuit university, as De Tribus Cometis Anni MDCXVIII also in 1619.

Source: Wikimedia Commons

Like Cysat and Kepler he concluded that the comets were definitely supralunar and like Cysat, following Tycho, he concluded that they orbited the sun, like Tycho seeing this as a confirmation of the geo-heliocentric hypothesis. Grassi’s publication is notorious in the history of astronomy because it unintentionally launched one of the most infamous disputes in the history of astronomy, infamous because his opponent was none other than Galileo Galilei.

Galileo had not actually observed the comets of 1618 being confined to his bed by illness but was asked for his opinion on them by one of his fellow members of the Accademia dei Lincei, Virginio Cesarini (1595–1624).

Virginio Cesarini, by Van Dyck Source: Wikimedia Commons

Galileo published his views, as a pernicious attack on Grassi’s De Tribus Cometis under the title Discorso delle Comete also in 1619 with a student of his, Mario Guiducci (1583–1646), as the named author, although it was an open secret that Galileo was the main author. Although Galileo always maintained that Guiducci and not he was the author, the manuscript that is still extant is largely in Galileo’s own hand and those paragraphs written by Guiducci have been corrected by Galileo.

Source: Wikimedia Commons

Surprisingly in Discorso delle Comete Galileo turns against the, in the meantime, general consensus amongst astronomers formed over the best part of one hundred years of comet observations that comets are supralunar celestial phenomena and argues instead, with Aristotle, that they are sublunar meteorological phenomena. He argued that the failure to determine parallax was not because comets were distant objects but because they were simply optical phenomena that like rainbows display no parallax. This theory, of course, directly contradicts the telescopic observations of the comet made by Cysat. Galileo might not of known of Cysat’s observations or he might simply have ignored them. It should be remembered that in all his writings on heliocentricity, Galileo totally ignored the writings of Kepler, although he was well aware of them. What Galileo is actually arguing against is the correct view expressed by both Cysat and Grassi that comets orbit the sun, as they use this to bolster a Tychonic geo-heliocentric model of the cosmos, which is unacceptable to Galileo. Galileo also took the opportunity in the Discorso to take another swing at Scheiner on the subject of sunspots.

Under the pseudonym Lotario Sarsi Sigensanso, an anagram of his Latin name (his original lecture had been published anonymously, as was usual for Jesuits), Grassi published an answer to the Galileo/Guiducci Discorso delle Comete, his Libra astronomica ac philosophica also in 1619.

Source: Wikimedia Commons

Here he presented scientific arguments and experimental tests to show that comets were definitely not optical phenomena. This of course further angered Galileo, who responded with one of his most famous publications Il Saggiatore, put out by the Accademia dei Lincei in 1623. Here we see a famous historical play on words. Grassi’s title Libra astronomica translates as The Astronomical Balance, i.e. weighing up the arguments, and Galileo’s answer Il Saggiatore translates as The Assayer.

Source: Wikimedia Commons

One general point that has to be made in this dispute is that although Grassi fought his corner energetically, even going so far as to suggest that some of Galileo’s arguments were theologically suspect, his tone was always correct and courteous. Opposed to this, Galileo was constantly aggressive, abusive and insulting not only towards Grassi but also towards all the others such as Tycho and Scheiner, who appeared in his polemical crosshairs. This continued, in fact was even amplified, in Il Saggiatore, where he took on all those he considered to be his intellectual adversaries. As well as viciously attacking Grassi he openly accused both Simon Marius and Christoph Scheiner of plagiarism, false accusations in both cases.

Il Saggiatore is famous for its ‘Two Books’ passage and Galileo’s statement that ‘the book of nature is written in the language of mathematics’. One should point out that Galileo actually wrote geometry not mathematics, as it is usually translated. The two books topos was not new with Galileo but goes back to the Middle Ages. People get all excited by the language of mathematics quote but by the time Galileo wrote it in 1623 it was a commonplace. Copernicus’ De revolutionibus has the statement, “Let no one untrained in geometry enter here.” Copernicus very definitely wanted to take the explanation of the cosmos away from the philosophers and give it to the mathematicians. This sentiment was certainly shared amongst others by Gerolamo Cardano (1501–1576), Niccolò Fontana Tartaglia (1499–157), Giambattista Benedetti (1530–1590), who anticipated much of Galileo’s work on the laws of fall, Tycho Brahe (1546–1601), Christen Longomontanus (1562–1647), John Dee (1527–1608), Thomas Digges (c. 1546–1595), Thomas Harriot (c. 1560–1621), Johannes Kepler (1571–1630), Simon Stevin (1548­–1620) as well as Christoph Clavius (1538–1612) and all the excellent Jesuit mathematical scholars who came out of his programme of mathematical education at the Collegio Romano. When Galileo coined his phrase in 1623 he was rather stating the obvious and not something spectacularly new. The so-called scientific revolution has been explicitly referred to as the mathematization of science, a process that was well underway before Galileo dropped his platitude into the debate. This was even acknowledged by some of the prominent opponents to this development such as the occultists Giordano Bruno (1548–1600) and Robert Fludd (1574–1637), who both explicitly rejected it.

The other point to note, which gets over looked by most people, is that Galileo’s statement was made in the specific dispute that I have just sketched above. In this dispute it was Grassi, who argued scientifically and mathematically, whereas Galileo didn’t.

One thing that Galileo could do better than any of his rivals was write and Il Saggiatore is a masterpiece of invective and polemic, leading people to oversee or ignore the fact that Galileo was actually in the wrong. The text was immensely popular, which led to two developments. Firstly, because of his attacks on Grassi and Scheiner he alienated the Jesuits the most mathematically competent scholars, not only in the Catholic Church but also in the whole of Europe. It should be remembered that it was the Jesuits at the Collegio Romano, who had provided the very necessary confirmation of all of Galileo’s telescopic discoveries and also celebrated him for them. He would no longer be able to rely on their support in the future. Secondly it found favour with Maffeo Barberini (1568–1644), who in 1623 was elected Pope Urban VIII. Barberini was an old friend and supporter of Galileo’s and a close associate of the Accademia dei Lincei, who celebrated his election and amongst other things presented him with a copy of Il Saggiatore, which he enjoyed immensely. He granted Galileo a couple of private audiences, an unusual honour for a mere mathematicus, and Galileo became a Papal favourite, something that would prove to be a two edged sword.

In popular presentations of the so-called scientific or astronomical revolutions Galileo Galilei is almost always presented as the great champion of heliocentricity in the first third of the seventeenth century. In fact, as we shall see, his contribution was considerably smaller than is usually claimed and mostly had a negative rather than a positive influence. The real champion of heliocentricity in this period was Johannes Kepler, who in the decade between 1617 and 1627 published four major works that laid the foundations for the eventual triumph of heliocentricity over its rivals. I have already dealt with one of these in the previous post in this series, the De cometis libelli tres I. astronomicus, theoremata continens de motu cometarum … II. physicus, continens physiologiam cometarum novam … III. astrologicus, de significationibus cometarum annorum 1607 et 1618 / autore Iohanne Keplero …, which was published in 1619 and as I’ve already said became the most important reference text on comets in the 1680’s during a period of high comet activity that we will deal with in a later post.

Source: ETH Library Zurich

Chronologically the first of Kepler’s influential books from this decade was Volume I (books I–III) of his Epitome Astronomiae Copernicanae published in 1617, Volume II (book IV) followed in 1620 and Volume III (books V–VII) in 1621. This was a text book on heliocentric astronomy written in question and answer dialogue form between a teacher and a student spelling out the whole of heliocentric astronomy and cosmology in comparatively straight forward and simple terms, the first such textbook. There was a second edition containing all three volumes in 1635.

Second edition 1635 Source

This book was highly influential in the decades following its publication and although it claims to be a digest of Copernican astronomy, it in fact presents Kepler’s own elliptical astronomy. For the first time his, now legendary, three laws of planetary motion are presented as such together. As we saw earlier the first two laws–I. The orbit of a planet is an ellipse and the Sun is at one of the focal points of that ellipse II: A line connecting the Sun and the planet sweeps out equal areas in equal times–were published in his Astronomia Nova in 1609. The third law was new first appearing in, what he considered to be his opus magnum, Ioannis Keppleri Harmonices mundi libri V (The Five Books of Johannes Kepler’s The Harmony of the World) published in 1619 and to which we now turn our attention.

Source: Wikimedia Commons

Kepler’s first book was his Mysterium Cosmographicum published in 1597 with its, to our way of thinking, somewhat bizarre hypothesis that there are only six planets because the spaces between their orbits are defined by the five regular Platonic solids.

Kepler’s Platonic solid model of the Solar System from Mysterium Cosmographicum Source: Wikimedia Commons

Although his calculation in 1597 showed a fairly good geometrical fit for his theory, it was to Kepler’s mind not good enough and this was his motivation for acquiring Tycho Brahe’s newly won more accurate data for the planetary orbits. He believed he could quite literally fine tune his model using the Pythagorean theory of the harmony of the spheres, that is that the ratio of the planetary orbits build a musical scale that is only discernable to the enlightened Pythagorean astronomer. The Harmonices Mundi was that fine tuning.

The first two books of the Harmonices Mundi layout Kepler’s geometrical theory of music, which geometrical constructions produced harmonious musical intervals and which disharmonious ones, based on which are constructible with straight edge and compass, harmonious, and which are not, disharmonious. The third book is Kepler’s contribution to the contemporary debate on the correct division of the intervals of the musical scale, in which Vincenzo Galilei (1520–1591), Galileo’s father, had played a leading role. The fourth book is the application of the whole to astrology and the fifth its application to astronomy and it is here that we find the third law.

In the fifth Kepler compare all possible ratios of planetary speeds and distances constructing musical scales for planets and musical intervals for the relationship between planets. It is here that he, one could say, stumbles upon his third law, which is known as the harmony law. Kepler was very much aware of the importance of his discovery as he tells us in his own words:

“After I had discovered true intervals of the orbits by ceaseless labour over a very long time and with the help of Brahe’s observations, finally the true proportion of the orbits showed itself to me. On the 8^th of March of this year 1618, if exact information about the time is desired, it appeared in my head. But I was unlucky when I inserted it into the calculation, and rejected it as false. Finally, on May 15, it came again and with a new onset conquered the darkness of my mind, whereat there followed such an excellent agreement between my seventeen years of work at the Tychonic observations and my present deliberation that I at first believed that I had dreamed and assumed the sought for in the supporting proofs. But it is entirely certain and exact that the proportion between the periodic times of any two planets is precisely one and a half times the proportion of the mean distances.”

Translated into modern notation the third law is P₁²/P₂²=R₁³/R₂³, where P is the period of a planet and R is the mean radius of its orbit. It can be argues that this was Kepler’s greatest contribution to the history of the emergence of heliocentricity but rather strangely nobody really noticed its true significance until Newton came along at the end of the seventeenth century.

However they should have done because the third law gives us is a direct mathematical relationship between the size of the orbits of the planets and their duration, which only works in a heliocentric system. There is nothing comparable for either a full geocentric system or for a geo-heliocentric Tychonic or semi-Tychonic system. It should have hit the early seventeenth-century astronomical community like a bomb but it didn’t, which raises the question why it didn’t. The answer is because it is buried in an enormous pile of irrelevance in the Harmonices Mundi and when Kepler repeated it in the Epitome he gave it no real emphasis, so it remained relatively ignored.

On a side note, it is often thought that Kepler had abandoned his comparatively baroque Platonic solids concepts from the Mysterium Cosmographicum but now that he had, in his opinion, ratified it in the Harmonices Mundi he published a second edition of the book in 1621.

Second Edition 1621 Source

Ironically the book of Kepler’s that really carried the day for heliocentricity against the geocentric and geo-heliocentric systems was his book of planetary tables based on Tycho Brahe’s data the Tabulae Rudolphinae (Rudolphine Tables) published in 1627, twenty-eight years after he first began working on them. Kepler had in fact been appointed directly by Rudolph II in Prague to produce these tables at the suggestion of Tycho in 1601. Turning Tycho’s vast collection of data into accurately calculated tables was a horrendous and tedious task and over the years Kepler complained often and bitterly about this burden.

Tabulae Rudolphinae The frontispiece presents in graphic form a potted history of Western astronomy Source

However, he persevered and towards the end of the 1620s he was so far. Because he was the Imperial Mathematicus and had prepared the tables under the orders of the Emperor he tried to get the funds to cover the printing costs from the imperial treasury. This proved to be very difficult and after major struggles he managed to acquire 2000 florins of the more than 6000 that the Emperor owed him, enough to pay for the paper. He began printing in Linz but in the turmoil of the Thirty Years War the printing workshop got burnt down and he lost the already printed pages. Kepler decamped to Ulm, where with more difficulties he succeeded in finishing the first edition of 1000 copies. Although these were theoretically the property of the Emperor, Kepler took them to the Frankfurt book fair where he sold the entire edition to recoup his costs.

The Tabulae Rudolphinae were pretty much an instant hit. The principle function of astronomy since its beginnings in Babylon had always been to produce accurate tables and ephemerides for use initially by astrologers and then with time also cartographers, navigators etc. Astronomical systems and the astronomers, who created them, were judged on the quality and accuracy of their tables. Kepler’s Tabulae Rudolphinae based on Tycho’s data were of a level of accuracy previous unknown and thus immediately won many supporters. Those who used the tables assumed that their accuracies was due to Kepler’s elliptical planetary models leading to a gradually increasing acceptance of heliocentricity but this was Kepler’s system and not Copernicus’. Supported by the Epitome with the three laws of planetary motion Kepler’s version of heliocentricity became the dominant astronomical/cosmological system over the next decades but it would be another thirty to forty years, long after Kepler’s death, before it became the fully accepted system amongst astronomers.

Without a doubt the most well-known, in fact notorious, episode in the transition from a geocentric to a heliocentric cosmology/astronomy in the seventeenth century was the publication of Galileo Galilei’s Dialogo sopra i due massimi sistemi del mondo (Dialogue Concerning the Two Chief World Systems) in 1632 and his subsequent trial and conviction by the Supreme Sacred Congregation of the Roman and Universal Inquisition or simply Roman Inquisition; an episode that has been blown up out of all proportions over the centuries. It would require a whole book of its own to really do this subject justice but I shall deal with it here in two sketches. The first to outline how and why the publication of this book led to Galileo’s trial and the second to assess the impact of the book on the seventeenth century astronomical/cosmological debate, which was much less than is often claimed.

Frontispiece and title page of the Dialogo, 1632 Source: Wikimedia Commons

The first salient point is Galileo’s social status in the early seventeenth century. Nowadays we place ‘great scientists’ on a pedestal and accord them a very high social status but this was not always the case. In the Renaissance, within society in general, natural philosophers and mathematicians had a comparatively low status and within the ruling political and religious hierarchies Galileo was effectively a nobody. Yes, he was famous for his telescopic discoveries but this did not change the fact that he was a mere mathematicus. As court mathematicus and philosophicus to the Medici in Florence he was little more than a high-level court jester, he should reflect positively on his masters. His role was to entertain the grand duke and his guests at banquets and other social occasions with his sparkling wit, either in the form of a discourse or if a suitable opponent was at hand, in a staged dispute. Points were awarded not for truth content but for verbal brilliance. Galileo was a master at such games. However, his real status as a courtier was very low and should he bring negative attention to the court, they would drop him without a thought, as they did when the Inquisition moved against him.

Galileo Portrait by Ottavio Leoni Source: Wikimedia Commons

As a cardinal, Maffeo Barberini (1568–1644) had befriended Galileo when his first came to prominence in 1611 and he was also an admirer of the Accademia dei Lincei. When he was elected Pope in 1623 the Accademia celebrated his election and amongst other things presented him with a copy of Galileo’s Il Saggiatore, which he read and apparently very much enjoyed. As a result he granted Galileo several private audiences, a great honour. Through his actions Barberini had raised Galileo to the status of papal favourite, a situation not without its dangers.

C. 1598 painting of Maffeo Barberini at age 30 by Caravaggio Source: Wikimedia Commons

Mario Biagioli presents the, I think correct, hypothesis that having raised Galileo up as a court favourite Barberini then destroyed him. Such behaviour was quite common under absolutist rulers, as a power demonstration to intimidate potential rebels. Galileo was a perfect victim for such a demonstration highly prominent and popular but with no real political or religious significance. Would Barberini have staged such a demonstration at the time? There is evidence that he was growing more and more paranoid during this period. Barberini, who believed deeply in astrology, heard rumours that an astrologer had foreseen his death in the stars. His death was to coincide with a solar eclipse in 1630. Barberini with the help of his court astrologer, Tommaso Campanella (1568–1639) took extreme evasive action and survived the cosmic threat but he had Orazio Morandi (c. 1570–1630), a close friend and supporter of Galileo’s, arrested and thrown in the papal dungeons, where he died, for having cast the offending horoscope.

Turning to the Dialogo, the official bone of contention, Galileo succeeded in his egotism in alienating Barberini with its publication. Apparently during the phase when he was very much in Barberini’s good books, Galileo had told the Pope that the Protestants were laughing at the Catholics because they didn’t understand the heliocentric hypothesis. Of course, during the Thirty Years War any such mockery was totally unacceptable. Barberini gave Galileo permission to write a book presenting and contrasting the heliocentric and geocentric systems but with certain conditions. Both systems were to be presented as equals with no attempts to prove the superiority or truth of either and Galileo was to include the philosophical and theological opinion of the Pope that whatever the empirical evidence might suggest, God in his infinite wisdom could create the cosmos in what ever way he chose.

The book that Galileo wrote in no way fulfilled the condition stated by Barberini. Presented as a discussion over four days between on the one side a Copernican, Salviati named after Filippo Salviati (1682–1614) a close friend of Galileo’s and Sagredo, supposedly neutral but leaning strongly to heliocentricity, named after Giovanni Francesco Sagredo (1571–1620) another close friend of Galileo’s. Opposing these learned gentlemen is Simplicio, an Aristotelian, named after Simplicius of Cilicia a sixth-century commentator on Aristotle. This name is with relative certainty a play on the Italian word “semplice”, which means simple as in simple minded. Galileo stacked the deck from the beginning.

The first three days of discussion are a rehash of the previous decades of discoveries and developments in astronomy and cosmology with the arguments for heliocentricity, or rather against geocentricity in its Ptolemaic/Aristotelian form, presented in their best light and the counter arguments presented decidedly less well. Galileo was leaving nothing to chance, he knew who was going to win this discussion. The whole thing is crowned with Galileo’s theory of the tides on day four, which he falsely believed, despite its very obvious flaws, to be a solid empirical proof of the Earth’s movements in a heliocentric model. This was in no way an unbiased presentation of two equal systems but an obvious propaganda text for heliocentricity. Worse than this, he placed the Pope’s words on the subject in the mouth of Simplicio, the simpleton, not a smart move. When it was published the shit hit the fan.

However, before considering the events leading up to the trial and the trial itself there are a couple of other factors that prejudiced the case against Galileo. In order to get published at all, the book, as with every other book, had to be given publication permission by the censor. To repeat something that people tend to forget, censorship was practiced by all secular and all religious authorities throughout the whole of Europe and was not peculiar to the Catholic Church. Freedom of speech and freedom of thought were alien concepts in the world of seventeenth century religion and politics. Galileo wanted initially to title the book, Dialogue on the Ebb and Flow of the Seas, referring of course to his theory of the tides, and include a preface to this effect. He was told to remove both by the censor, as they, of course, implied a proof of heliocentricity. Because of an outbreak of the plague, Galileo retired to Florence to write his book and preceded to play the censor in Florence and the censor in Rome off against each other, which meant that the book was published without being properly controlled by a censor. This, of course, all came out after publication and did not help Galileo’s case at all; he had been far too clever for his own good.

Another major problem had specifically nothing to do with Galileo in the first instance but rebounded on him at the worst time.  On 8 March 1632 Cardinal Borgia castigated the Pope for not supporting King Philipp IV of Spain against the German Protestants. The situation almost degenerated into a punch up with the Swiss Guard being called in to separate the adversaries. As a result Barberini decided to purge the Vatican of pro-Spanish elements. One of the most prominent men to be banished was Giovanni Ciampoli (1589–1643) Barberini’s chamberlain. Ciampoli was an old friend and supporter of Galileo and a member of the Accademia dei Lincei. He was highly active in helping Galileo trick the censors and had read the manuscript of the Dialogo, telling Barberini that it fulfilled his conditions. His banishment was a major disaster for Galileo.

Giovanni Ciampoli Source: Wikimedia Commons

One should of course also not forget that Galileo had effectively destroyed any hope of support from the Jesuits, the leading astronomers and mathematicians of the age, who had very actively supported him in 1611, with his unwarranted and libellous attacks on Grazi and Scheiner in his Il Saggiatore. He repeated the attacks on Scheiner in the Dialogo, whilst at the same time plagiarising him, claiming some of Scheiner’s sunspot discoveries as his own. There is even some evidence that the Jesuits worked behind the scenes urging the Pope to put Galileo on trial.

When the Dialogo was published it immediately caused a major stir. Barberini appointed officials to read and assess it. Their judgement was conclusive, the Dialogo obviously breached the judgement of 1616 forbidding the teaching of heliocentricity as a factual theory. Anybody reading the Dialogo today would confirm that judgement. The consequence was that Galileo was summoned to Rome to answer to the Inquisition. Galileo stalled claiming bad health but was informed either he comes or he would be fetched. The Medici’s refused to support him; they did no consider him worth going into confrontation with the Pope for.

Ferdinando II de’ Medici Grand Duke of Tuscany in Coronation Robes (school of Justus Sustermans). Source: Wikimedia Commons

We don’t need to go into details of the trial. Like all authoritarian courts the Inquisition didn’t wish to try their accused but preferred them to confess, this was the case with Galileo. During his interviews with the Inquisition Galileo was treated with care and consideration because of his age and bad health. He was provided with an apartment in the Inquisition building with servants to care for him. At first he denied the charges but when he realised that this wouldn’t work he said that he had got carried away whilst writing and he offered to rewrite the book. This also didn’t work, the book was already on the market and was a comparative best seller, there was no going back. Galileo thought he possessed a get out of jail free card. In 1616, after he had been interviewed by Bellarmino, rumours circulated that he had been formally censured by the Inquisition. Galileo wrote to Bellarmino complaining and the Cardinal provided him with a letter stating categorically that this was not the case. Galileo now produced this letter thinking it would absolve him of the charges. The Inquisition now produced the written version of the statement that had been read to Galileo by an official of the Inquisition immediately following his interview with Bellarmino expressly forbidding the teaching of the heliocentric theory as fact. This document still exists and there have been discussions as to its genuineness but the general consensus is that it is genuine and not a forgery. Galileo was finished, guilty as charged. Some opponents of the Church make a lot of noise about Galileo being shown the instruments of torture but this was a mere formality in a heresy trial and at no point was Galileo threatened with torture.

The rest is history. Galileo confessed and formally adjured to the charge of grave suspicion of heresy, compared to heresy a comparatively minor charge. He was sentenced to prison, which was immediately commuted to house arrest. He spent the first months of his house arrest as the guest of Ascanio II Piccolomini (1590–1671), Archbishop of Siena,

Ascanio II Piccolomini Source: Wikimedia Commons

until Barberini intervened and sent him home to his villa in Arcetri. Here he lived out his last decade in comparative comfort, cared for by loyal servants, receiving visitor and writing his most important book, Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences).

Galileo’s real crime was hubris, trying to play an absolutist ruler, the Pope, for a fool. Others were executed for less in the seventeenth century and not just by the Catholic Church. Galileo got off comparatively lightly.

What role did the Dialogo actually play in the ongoing cosmological/astronomical debate in the seventeenth century? The real answer is, given its reputation, surprisingly little. In reality Galileo was totally out of step with the actual debate that was taking place around 1630. Driven by his egotistical desire to be the man, who proved the truth of heliocentricity, he deliberately turned a blind eye to the most important developments and so side lined himself.

We saw earlier that around 1613 there were more that a half a dozen systems vying for a place in the debate, however by 1630 nearly all of the systems had been eliminated leaving just two in serious consideration. Galileo called his book Dialogue Concerning the Two Chief World Systems, but the two systems that he chose to discuss, the Ptolemaic/Aristotelian geocentric system and the Copernican heliocentric system, were ones that had already been rejected by almost all participants in the debate by 1630 . The choice of the pure geocentric system of Ptolemaeus was particularly disingenuous, as Galileo had helped to show that it was no longer viable twenty years earlier. The first system actually under discussion when Galileo published his book was a Tychonic geo-heliocentric system with diurnal rotation, Christen Longomontanus (1562–1647), Tycho’s chief assistant, had published an updated version based on Tycho’s data in his Astronomia Danica in 1622. This was the system that had been formally adopted by the Jesuits.

The second was the elliptical heliocentric system of Johannes Kepler, of which I dealt with the relevant publications in the last post.

Galileo completely ignores Tycho, whose system could explain all of the available evidence for heliocentricity, because he didn’t want to admit that this was the case, arguing instead that the evidence must imply a heliocentric system. He also, against all the available empirical evidence, maintained his belief that comets were sublunar meteorological phenomena, because the supporters of a Tychonic system used their perceived solar orbit as an argument for their system.  He is even intensely disrespectful to Tycho in the Dialogo, for which Kepler severely castigated him. He also completely ignores Kepler, which is even more crass, as the best available arguments for heliocentricity were to be found clearly in Kepler published works. Galileo could not adopt Kepler’s system because it would mean that Kepler and not he would be the man, who proved the truth of the heliocentric system.

Although the first three days of the Dialogo provide a good polemic presentation for all of the evidence up till that point for a refutation of the Ptolemaic/Aristotelian system, with the very notable exception of the comets, Galileo’s book was out dated when it was written and had very little impact on the subsequent astronomical/cosmological debate in the seventeenth century. I will indulge in a little bit of hypothetical historical speculation here. If Galileo had actually written a balanced and neutral account of the positive and negative points of the Tychonic geo-heliocentric system with diurnal rotation and Kepler’s elliptical heliocentric system, it might have had the following consequences. Firstly, given his preeminent skills as a science communicator, his book would have been a valuable contribution to the ongoing debate and secondly he probably wouldn’t have been persecuted by the Catholic Church. However, one can’t turn back the clock and undo what has already been done.

I will close this overlong post with a few brief comments on the impact of the Church’s ban on the heliocentric theory, the heliocentric hypothesis was still permitted, and the trial and sentencing of Galileo, after all he was the most famous astronomer in Europe. Basically the impact was much more minimal than is usually implied in all the popular presentations of the subject. Outside of Italy these actions of the Church had almost no impact whatsoever, even in other Catholic countries. In fact a Latin edition of the Dialogo was published openly in Lyon in 1641, by the bookseller Jean-Antoine Huguetan (1567–1650), and dedicated to the French diplomat Balthasar de Monconys (1611–1665), who was educated by the Jesuits.

Within Italy well-behaved Catholics censored their copies of Copernicus’ De revolutionibus according to the Church’s instructions but continued to read and use them. Censored copies of the book are virtually unknown outside of Italy. Also within Italy, astronomers would begin their discussions of heliocentricity by stating in the preface that the Holy Mother Church in its wisdom had declared this system to be false, but it is an interesting mathematical hypothesis and then go on in their books to discuss it fully. On the whole the Inquisition left them in peace.

***A brief footnote to the above: this is a historical sketch of what took place around 1630 in Northern Italy written from the viewpoint of the politics, laws and customs that ruled there at that time. It is not a moral judgement on the behaviour of either the Catholic Church or Galileo Galilei and I would be grateful if any commentators on this post would confine themselves to the contextual historical facts and not go off on wild moral polemics based on hindsight. Comments on and criticism of the historical context and/or content are, as always, welcome.