Category Archives: History of Astrology

The emergence of modern astronomy – a complex mosaic: Part IX

In 1542 the manuscript of De revolutionibusarrived at Petreius’ printing office in Nürnberg followed by Rheticus who intended to see it through the press. I argued in Part VII that Johannes Petreius had in fact commissioned Rheticus to see if Copernicus had written anything substantial on his astronomical theories and if so to persuade him to allow Petreius to publish it. Petreius’ printing office was certainly the right address for the publication of a major new work on astronomy, as he was certainly the leading scientific publisher–astrology, astronomy, mathematics–in the Holy Roman Empire of German States and probably the whole of Europe but who was Johannes Petreius?


The Petreius printing office in Nürnberg Photo by the author

He was born Hans Peter, whereby Peter is the family name, into a family of wealthy farmers in the Lower Franconia village of Langendorf near Hammelburg in 1496 or 1497. He matriculated at the university of Basel in 1512, graduating BA in 1515 and MA in 1517. He next appears as a witness in a court case in Basel in 1519, where he is described, as working as a proofreader for the Basler printer publisher Adam Petri. This explains why he had chosen to study in Basel, as Adam Petri was his uncle. Petri is the Swizz German version of the name Peter. Presumably, having learnt the black art, as printing was known, from his uncle he moved to Nürnberg in 1523 and set up his own printing office. The was almost certainly an attempt by the Peter family to cash in on the gradual collapse of the Koberger printing office following the death of Aton Koberger in 1513. The Petri-Froben-Amerbach printing cooperative had been Koberger’s licensees in Basel, printing his titles on commission.


Source: Wikimedia Commons

Hans Peter now sporting the Latinised name, Johannes Petreius, succeeded in establishing himself against the local competition and by 1535 was the leading printer publisher in Nürnberg. Like most other printer publishers Petreius’ main stock in trade was printing religious volumes but in the 1530s he began to specialise in printing scientific texts. Exactly why he chose to follow this business path is not known but it was probably the ready availability of the large number of mathematical, astrological and astronomical manuscripts brought to Nürnberg by Regiomontanus when he set up his own printing office in 1471. This hypothesis is supported by the fact that several of Petreius’ earliest scientific publications were all of manuscripts from this collection, all of which were edited for publication by Johannes Schöner, who would later be the addressee of Rheticus’ Narratio  Prima.

This series of publications started with Schöner’s edition of Regiomontanus’ own De Triangulis in 1533, a very important work in the history of trigonometry. This was also one of the volumes that Rheticus took with him to Frombork, as a present for Copernicus.

Schöner followed this with Regiomontanus’ Tabulae astronomicaein 1536. Petreius’ activities in the area were not however restricted to Schöner’s output. Earlier he published the first Greek edition of Ptolemaeus’ Tetrabiblos, under the title Astrologica, edited by Joachim Camerarius (1500–1574), which included Camerarius’ translation into Latin of Books I & II and partial translations of Books III & IV together with his notes on Books I & II and the Greek text of the Centiloquium, a collection of one hundred astrological aphorism falsely attributed to Ptolemaeus, with a Latin translation by Giovanni Pontano (1426–1503).


Opening chapter of the first printed edition of Ptolemy’s Tetrabiblos, transcribed into Greek and Latin by Joachim Camerarius (Nuremberg, 1535). Source: Wikimedia Commons

A year earlier Petreius had published Johann Carion’s Practica new – auffs 1532 mit einer auslegung des gesehen cometen. Through these publications it is clear that the principle interest is in astrology and it is here that money was to be made. Over the next twenty plus years Petreius published more texts from Regiomontanus edited by Schöner, some of Schöner’s own works on astronomy and cartography, reckoning and algebra books from Christoph Rudolff  (c. 1500–before 1543) and Michael Stifel (1487–1567). Various scientific texts edited by Peter Apian including his and Georg Tannstetter’s edition of Witelo’s Perspectiva (1535), another of the volumes that Rheticus took with him to Frombork for Copernicus. Various Arabic astrological texts, the Tractatus astrologicae (1540) of Lucas Gauricus (1575–1558), who along with Schöner and Cardano was one of the most important astrologers of the first half of the sixteenth century. Petreius became the publisher of Gerolamo Cardano (1501–1576) north of the Alps, publishing his works on mathematics, astronomy, medicine, astrology and philosophy, all of which were highly successful.


Source: Wikimedia Commons

He also published alchemical works from Abū Muḥammad Jābir ibn Aflaḥ better known in the West as Geber. As well as all this, Petreius commissioned and published the first German translation of Vitruvius’ De architectura, a bible for Renaissance artist-engineers.

Petreius’ scientific catalogue was very wide but also had depth, including as it did various classics by Regiomontanus, Schöner, Stifel, Cardano and Witelo. If anybody could adequately present Copernicus’ masterpiece to the world then it was Johannes Petreius.

Rheticus had originally intended seeing Copernicus’ manuscript through the press but Philipp Melanchthon had other plans for his errant protégée. In the meantime Rheticus had, at the request of Joachim Camerarius, who was now rector of the University of Leipzig and had obviously been impressed by Rheticus during their meeting in Tübingen, been offered a chair in mathematics at Leipzig.


Joachim Camerarius, 18th-century engraving by Johann Jacob Haid. Source: Wikimedia Commons

In the autumn of 1542 Rheticus, under pressure from Melanchthon, left Nürnberg and preceded to Leipzig, where he was appointed professor of higher mathematics i.e. astronomy and music and his direct involvement in De revolutionibus came to an end. Petreius still needed an editor to see Copernicus’ weighty tome through the press and this duty was taken over, with serious consequences by Nürnberg’s Lutheran Protestant preacher, Andreas Osiander (1496 or 1498–1552).


Andreas Osiander portrait by Georg Pencz Source: Wikimedia Commons

Osiander was born in the small town of Gunzenhausen to the south of Nürnberg, the son of Endres Osiander a smith and Anna Herzog. His father was also a local councillor who later became mayor. He matriculated at the University of Ingolstadt in 1515 where he, amongst other things, studied Hebrew under the great humanist scholar and great uncle of Melanchthon, Johannes Reuchlin. In 1520 he was ordained a priest and called to Nürnberg to teach Hebrew at the Augustinian Cloister, a hot bed of reformatory debate, where he also became a reformer. In 1522 he as appointed preacher at the St Lorenz church and became a leading voice for religious reform. Osiander achieved much influence and power in Nürnberg when the city-state became the very first Lutheran Protestant state.

Osiander first became involved with Petreius when the latter started publishing his religious polemics. Petreius also published numerous religious works by both Luther and Melanchthon. Where or how Osiander developed his interest and facility in the mathematical sciences is simply not know but they are attested to by Cardano in the preface to one of his books published by Petreius. In fact it was Osiander, who was responsible for the correspondence between Cardano and the Petreius printing office and he edited Cardano’s books there. When or how Osiander became an editor for Petreius is also not known. In his capacity as editor of De revolutionibus Osiander committed what many have as one of the greatest intellectual crimes in the history of science, he added the infamous ad lectorum, an address to the reader with which the book opens.


Latin Wikisource

The ad lectorum is an essay that it pays to read in full but here we will just consider the salient points, Osiander writes:

There have already been widespread reports about the new novel hypothesis of this work, which declares that the earth moves whereas the sun is at rest in the centre of the universe.

Here Osiander lets us know that knowledge of Copernicus’ heliocentric hypothesis was already widespread–spread by the Commentariolus, the Narratio Prima and by rumour–indicating that there was going to be a high level of expectancy to learn the mathematical details of the system. He goes on:

Hence certain scholars, I have no doubt, are deeply offended and believe that the liberal arts, which were established long ago on a sound basis, should not be thrown in confusion.

Anticipating criticism from conservative circles Osiander goes into defensive mode:

But if these men are willing to examine the matter closely, they will find that the author has done nothing that is blameworthy. For it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study. Then he must conceive and devise the causes of these motions or hypotheses about them. Since he cannot in any way attain to the true causes, he will adopt whatever suppositions enable the motions to be computed correctly from the principles of geometry for the future as well as the past.

Here we have the crux of Osiander’s defence. Astronomers are here to produce geometrical models in order to provide accurate predictions of celestial motions and not to determine the unobtainable true causes of those motions. This argument has been dubbed instrumentalist and some hail Osiander as the first instrumentalist philosopher of science. Instrumentalism is a metaphysical attitude to scientific theories that enjoyed a lot of popularity in modern physics in the twentieth century; it doesn’t matter if the models we use describe reality, all that matters in that they predict the correct numerical results. Osiander expands on this viewpoint:

For these hypotheses need not be true or even probable. On the contrary, if they provide a calculus consistent with the observations, that alone is enough.

Here we have the core of why the ad lectorum caused so much outrage over the centuries. Osiander is stating very clearly that the mathematical models of astronomers are useful for predictive purposes but not for describing reality. A view that was fairly commonplace over the centuries amongst those concerned with the subject. Copernicus, however, very clearly deviates from the norm in De revolutionibus in that he presents his heliocentric system as a real model of the cosmos. Osiander’s ad lectorum stands in clear contradiction to Copernicus’ intentions. Osiander then goes into more detail illustrating his standpoint before closing his argument as follows:

…the astronomer will take as his first choice that hypothesis which is easiest to grasp. The philosopher will perhaps rather seek the semblance of the truth. But neither of them will understand or state anything certain, unless it has been divinely revealed to him.

Here we have Osiander restating the standard scholastic division of responsibilities, astronomers provide mathematical models to deliver accurate predictions of celestial motions for use by others, philosophers attempt to provide explanatory models of those motions but truth can only be delivered by divine revelation. The modern astronomy, whose gradual emergence we are tracing had to break down this division of responsibilities in order to become accepted as we shall see in later episodes. Osiander closes with a friendly appeal to the reader to permit the new hypotheses but not to take them too seriously, and thereby make a fool of himself.

Therefore alongside the ancient hypotheses, which are no more probable, let us permit these new hypotheses also the become known, especially since they are admirable as well as simple and bring with them a huge treasure of very skilful observations. So far as hypotheses are concerned, let no one expect anything certain from astronomy, which cannot furnish it, lest he accept as the truth ideas conceived for another purpose, and depart from this study a greater fool than he entered it. Farewell.

There is a widespread belief that Osiander somehow smuggled his ad lectorum into De revolutionibus without the knowledge of either Copernicus or Petreius but the historical evidence speaks against this. There are surviving fragments of a correspondence between Osiander and Copernicus that make it clear that Osiander discussed the stratagem of presenting De revolutionibus as a hypothesis rather that fact with him; although we don’t know how or even if Copernicus reacted to this suggestion. More telling is the situation between Petreius and Osiander.

There is absolutely no way that Osiander could have added the ad lectorum without Petreius’ knowledge. This is supported by subsequent events. When the book appeared Tiedemann Giese was outraged by the presence of the ad lectorum and wrote a letter to the city council of Nürnberg demanding that it be removed and the book reissued without this blemish. The council consulted Petreius on the subject and he let them know in no uncertain terms that it was his book and what he put in it was his business and nobody else’s.

Petreius’ reaction illustrates an important point that modern commentators often overlook. Our concept of copyright didn’t exist in the sixteenth century, the rights to a publish work in general lay with the publisher and not the author. This is clearly demonstrated by the fact that when a publication provoked the ire of the authorities, civil or clerical, it was the printer publisher, who first landed before the court and then in goal rather than the author.

The ad lectorum was anonym but any reader, who was paying attention should have realised through the phrasing that Copernicus was not the author. The Nürnberger astronomer and instrument maker Johannes Pratorius (1537–1615), another Wittenberg graduate, wrote in his copy of De revolutionibus that Rheticus, when Pratorius visited him in 1569, had revealed to him that Osiander was the author of the ad lectorum.


Source: Wikimedia Commons

Michael Maestlin’s copy contains the same information also from Rheticus via Peter Apian. Kepler’s second hand copy had this information added by its original owner Hieronymus Schreiber (birth date unknown–1547), yet another Wittenberg graduate, who had received a gift copy signed by Petreius, because he had substituted for Rheticus in Wittenberg during the latter’s time in Frombork. All of this indicates that Osiander’s authorship of the ad lectorem was circulating on the astronomers’ grapevine by 1570 at the latest. It was first put into print, and thus made general public, by Kepler in his Astronomia Nova in 1609.

As with most books in the Early Modern Period there was no publication date for De revolutionibus but it seems to have been finished by 20thApril 1543, as Rheticus signed a finished copy on this date. According to a legend, put in the world by Tiedemann Giese, Copernicus received his copy, which was placed into his hands, on his dying day the 24thMay 1543. Owen Gingerich, who is the expert on the subject, estimates that the 1stedition probably had a print run of about 400 copies, which carried the mathematical details of Copernicus’ hypothesis out into the wide world.






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Filed under Early Scientific Publishing, History of Astrology, History of Astronomy, Renaissance Science

The emergence of modern astronomy – a complex mosaic: Part VIII

We left Georg Joachim Rheticus[1](1514–1574) just setting out on his journey from Feldkirch to Frombork for what would turn out to be one of the most fateful meetings in the history of science. Our wealthy professor of mathematics travelled in style accompanied by a famulus Heinrich Zell (?–1564), a Wittenberg student, who would later have a career as cartographer, astronomer and librarian. What is rarely mentioned in detail is that Rheticus travelled from Feldkirch to Wittenberg, which is where he collected Zell, and then having acquired permission to extend his sabbatical, continued on his way to Frombork. In total this is a journey of more than 1500 kilometres, hard enough even today but a major expedition in the middle of the sixteenth century.

We have no direct account of the initial meeting between the twenty-five year old mathematics professor and the sixty-six year old cathedral canon.


Portrait of Copernicus holding a lily of the valley, published in Nicolaus Reusner’s Icones (1587), based on a sketch by Tobias Stimmer (c. 1570), allegedly based on a self-portrait by Copernicus. Source: Wikimedia Commons

They obviously got on well, as Rheticus ended staying in the area for two and a half years. Shortly after his arrival Rheticus fell ill and Copernicus took him to Löbau, the home of his friend Tiedemann Giese (1480–1550) Bishop of Kulm, to convalesce.


Portrait of Tiedemann Giese by Hans Schenck, Source: Wikimedia Commons

This episode illustrates an important aspect of Rheticus’ visit. Here was a Lutheran Protestant professor of mathematics from the home of Lutheran Protestantism, Wittenberg University visiting a Catholic cathedral canon in the middle of a deeply Catholic area. Despite the fact that this visit took place in the middle of the Reformation and the beginnings of the Counter Reformation Rheticus was always treated as an honoured guest by all those, who received him whether Protestant, Albrecht, Duke of Prussia,


Albrecht, Duke of Prussia portrait by Lucas Cranach the elder Source: Wikimedia Commons

or Catholic, Copernicus, Giese and above all the Prince-Bishop of Frombork, Johannes Danticus (1485–1548), who although strongly anti-Reformation was also an admirer of Philipp Melanchthon (1497–1560), whom he had met personally.


Johannes Dantiscus Source: Wikimedia Commons

This courtesy across the religious divide amongst scholars during this period of European religious turmoil was actually very common and contradicts a popular image of hate, rejection and bigotry on all fronts and at all levels.

We know of Rheticus’ convalescence in Löbau, because he mentions it on the first page of his Narratio Prima (The First Account) the booklet he wrote shortly after his arrival in Frombork and the first published account of Copernicus’ heliocentric system. He explains that because of his illness he has had barely ten weeks to familiarise himself with the manuscript of Copernicus’ magnum opus in order to describe and explain it in the Narratio Prima, which is an open letter to Johannes Schöner, his Nürnberger astrology teacher and one of Johannes Petreius’ expert editors.


Johannes Schöner Source: Wikimedia Commons

The introduction also makes clear that he had promised Schöner, and probably through him Petreius, this report before leaving Nürnberg. Johannes Petreius’ dedicatory letter to Rheticus in his edition of the fourteenth-century physician Antonius de Motulmo’s De iudiciis nativitatumwas a direct response to the Narratio Prima. He goes on to give a very brief outline of the work, making no mention of the fact that Copernicus’ system is heliocentric. He says that he has mastered the first three books, of six, grasped a general idea of the forth and begun to conceive the hypotheses of the rest. He says he is going to skip the first two books for which he has a special plan; he originally intended to write a Narratio Secunda, which never materialised. He then plunges into his description.

The first four sections are technical astronomical accounts of: The Motion of the Fixed Stars, General Considerations of the Tropical Year, The Change in the Obliquity of the Ecliptic, and The Eccentricity of the Sun and the Motion of the Solar Apogee. In the fifth section, The Kingdom of the World Change with the Motion of the Eccentric, Rheticus changes tack completely and presents us with an astrological theory of cyclical historical change. I shall quote the beginning of this extraordinary section:

I shall add a prediction. We see that all kingdoms have had their beginnings when the centre of the eccentric was at a special point on the small circle. Thus, when the eccentricity of the sun was at its maximum, the Roman government became a monarchy; as the eccentricity decreased, Rome too declined, as aging, and then fell. When the eccentricity reached the boundary and quadrant of mean value, the Mohammedan faith was established; another great empire came into being and increased very rapidly, like the change in the eccentricity. A hundred years hence, when the eccentricity will be at its minimum, this empire too will complete its period.

This calculation does not differ much from the saying of Elijah, who prophesied under divine inspiration that the world would endure only 6,000 years, during which time nearly two revolutions are completed[2].

There is nothing about this to be found in Copernicus’ De revolutionibus but Copernicus certainly read the Narratio Prima before it was published and didn’t object to it or ask Rheticus to remove it. Such astrological cyclical theories of history were en vogue during the Early Modern Period. The most well known one was written by Johannes Carion (1499–1537), who together with Philipp Melanchthon was a student of Johannes Stöffler (1442–1531). Carion had also received language tuition from the slightly older Melanchthon.  Carion was court astrologer to the Elector Joachim I of Brandenburg (1484–1535).


Johann Carion, portrait by Lucas Cranach the Elder Source: Wikimedia Commons

Carion wrote a chronicle based on Biblical prophecies, which divided world history into three 2000-year periods. The chronicle was published shortly after Carion’s death. Following Carion’s death this chronicle passed into Melanchthon’s hands, who reworked it and published it again. Rheticus a student of Melanchthon obviously joined the Carion tradition in his astrological excurse in the Narratio Prima, which goes into long technical detail on the following pages.

In the next section Rheticus returns to Copernicus’ astronomy, Special Consideration of the Length of the Tropical Year. Up till now we have no indication at all from Rheticus that the system he is describing is a heliocentric one. We are now about one third of the way through and Rheticus’ next section is General Considerations Regarding the Motions of the Moon,Together with the New Lunar Hypothesis. At the end of this section we can read:

These phenomena, besides being ascribed to the planets, can be explained, as my teacher shows, by a regular motion of the spherical earth; that is, by having the sun occupy the centre of the universe, while the earth revolves instead of the sun on the eccentric, which it has pleased him to name the great circle. Indeed, there is something divine in the circumstance that a sure understanding of celestial phenomena must depend on the regular and uniform motions of the terrestrial globe alone.

He casual drops the information that we are indeed in a heliocentric world system in passing, as if were the most natural thing in the world. Having in the previous sections demonstrated Copernicus’ abilities as a theoretical astronomer he finally lets the cat out of the bag. There now follow eight sections in which he explains how the new hypothesis functions with the whole of astronomy.

The book closes with a non-astronomical section, In Praise of Prussia. This is a general polemic about how wonderful Prussia and the Prussian are and how well Rheticus has been received and treated by his Prussian hosts. It does, however, contain a section describing Giese’s attempts to persuade Copernicus to publish De revolutionibus and that Copernicus’ response to these enticements is to suggest that he will publish his tables of astronomical data without revealing the methods used to obtain them.

The Narratio Prima is dated 23 September 1539 by Rheticus, who took the manuscript to Danzig where it was printed and published by Franz Rhode in 1540 with the help of a donation towards the printing costs from Johann von Werden (c. 1495–1554) the mayor of Danzig. The title page is interesting as it begins with an honourable address to Johannes Schöner followed by The Books of Revolutions then an equally honourable naming of Copernicus but Rheticus, the author, is simply described as a young student of mathematics[3].


Title page of the 1st edition of the Narratio Prima Source: Wikimedia Commons

The Narratio Prima was fairly obviously conceived as a test balloon for Copernicus’ heliocentric hypothesis. It seems to have been well received and one recipient took his enthusiasm for the text much further. Rheticus had sent a copy to his mentor Achilles Pirmin Gasser (1505-1577),


Achilles Permin Gasser Source: Wikimedia Commons

who published a second edition of the book with a new dedicatory letter and Rheticus named on the title page in Basel in 1541.


First page of a later edition of the Narratio Prima with Rheticus named as author

The positive reception of the Narratio Prima and the lack of negative reactions seem to have finally convinced Copernicus to allow De revolutionibus to be published.

The Narratio Prima is rather long winded, strong on rhetoric and polemic but rather weak on its scientific content. There are no diagrams and Rheticus tends to rely on philosophical arguments rather than mathematical ones. He does, however, display a high degree or erudition, his text is full of classical quotes and allusions, which doesn’t actually make it easier for those who don’t have a classical eduction to plow through his, at times, rather turgid prose.

A third edition of the Narratio Prima was included in the second edition of De revolutionibus published by Heinric Petri in Basel in 1566. The forth and a fifth editions were included in the first and second editions of Johannes Kepler’s Mysterium Cosmographicum in 1597 and 1621. As such, more people probably learnt of Copernicus’ heliocentric system from the Narratio Prima than any other source.

Rheticus stayed in Frombork helping Copernicus to prepare his manuscript for publication by Petreius in Nürnberg. In October 1541 Rheticus left for Wittenberg, where he published an edited and improved version of the trigonometrical section of Derevolutionibusunder Copernicus’s name, De lateribus et angulis triangulorum (On the Sides and Angles of Triangles), which appeared in 1542.


This very useful publication also helped to increase Copernicus’ reputation in astronomical and mathematical circles. Rheticus would dedicate much of his future life to the publication of improved trigonometrical table.

In 1542 the manuscript of De revolutionibus arrived at Petreius’ printing office in Nürnberg followed by Rheticus who intended to see it through the press.

[1]There are no known portraits of Rheticus

[2]The Elijah prophecy is from the Talmud not the Bible.

[3]AD CLARISSMUM VIRUM D. IOANNEM SCHONERUM, DE LIBRIS REVOLUTIONUM eruditissimi viri & Mathematici excellentissimi, Reverendi D. Doctoris Nicolai Copernici Torunnaei, Canonici Varmiensis, per quendam Iuvenem, Mathematicae studiosum NARRATIO PRIMA (To that Famous Man Johann Schöner Concerning the Books of Revolutions of That Most Learned Man and Excellent Mathematician, the Venerable Doctor Nicolaus Copernicus of Toruń, Canon of Warmia, by a certain young student of mathematics)




Filed under Early Scientific Publishing, History of Astrology, History of Astronomy, Renaissance Science

The emergence of modern astronomy – a complex mosaic: Part VII

In his Commentariolus from around 1510 Copernicus tells us that his is planning to write a larger more technical work on his heliocentric hypothesis:

However I have thought it well, for the sake of brevity, to omit from this sketch mathematical demonstration, reserving these for my larger work

We don’t actually know when he started writing this work or when he finished it. As a canon of the cathedral of Frombork he was administrator in the prince-bishopric of Varmia, a position that he took seriously throughout his life, meaning that astronomy remained a part time occupation. It would be reasonable to assume that he started on the larger work, which would eventually become De revolutionibus, not long after completing the Commentariolus. Various experts have estimated that he finished the bulk of the book around 1530. However, he was very reluctant to publish, what would become his magnum opus. There is a standard myth that he feared religious censure and thus didn’t want to publish. There is, however, a well-founded theory that he was reluctant to publish because he couldn’t actually deliver what he had promised. In the Commentariolus he assured his readers that his heliocentric system would be simpler that the Ptolemaic geocentric one. In the end the system that he presented in De revolutionibus was more complex than the geocentric one in Peuerbach’s Theoricarum novarum planetarum, published by Regiomontanus in Nürnberg in 1473 from which Copernicus had learnt his astronomy. Also, although Copernicus’ system offered some advantages and simplifications over the geocentric system Copernicus could offer no real proof for his radical suggestion and the empirical physical evidence against a moving earth was still overwhelming. All of this raises the questions would Copernicus have ever submitted his manuscript for publication left to his own devices and what finally pushed him over the edge, so that he did publish? The answer is not what but who. Copernicus was convinced to publish by the young Wittenberger professor of mathematics, Georg Joachim Rheticus (1514–1574). (Note: there are no known portraits of Rheticus)

Rheticus was born Georg Joachim Iserin the son of Georg Iserin, a town physician, and Thomasina de Porris, a minor Italian aristocrat, in Feldkirch in what is now Austria. In 1528 Georg Iserin was found guilty of stealing from his patients, executed and the family name banned in perpetuity. Georg Joachim Rheticus became Georg Joachim de Porris. The family tragedy was alleviated somewhat for the young Georg Joachim, when Achilles Pirmin Gasser (1505–1577), another town physician, historian and astrologer, took over his upbringing and education.


Achilles Permin Gasser Source: Wikimedia Commons

In 1528 Gasser sent him to the Fraumünster collegiate church in Zurich, where he got to know and became friends with Conrad Gesner (1516–1565), who would go on to become an important sixteenth century polymath.


Conrad Gesner Source: Wikimedia Commons

In 1532 Gasser sent him to his own alma mater, the Lutheran University of Wittenberg. Here Rheticus, with an obvious aptitude for the mathematical sciences, attracted the attention of Philipp Melanchthon (1497–1560), the rector of the university and founder of the Lutheran Protestant education system.


Philipp Melanchthon portrait by Lucas Cranach the elder Source: Wikimedia Commons

Melanchthon, who had studied under Johannes Stöffler (1452–1531) and become an enthusiastic fan of astrology, was on the look out for talented mathematicians with whom to equip the new Protestant schools and university to further the growth of a new generation of astronomer/astrologers. It was in Wittenberg that Georg Joachim adopted the toponym Rheticus based in the Roman name for his home district Rhaetia In 1536 Rheticus graduated MA and Melanchthon appointed him professor for the lower mathematics, that is arithmetic and geometry, in Wittenberg.

In 1538 Rheticus took leave of absence from the university to go on an extended study tour of Southern Germany. Such tours were common practice on the mediaeval university and he went with the support of and a letter of introduction from Melanchthon. This letter was addressed to Johannes Schöner in Nürnberg, Philipp Apian in Ingolstadt and Philipp Imser in Tübingen.

The first station on his journey was Nürnberg where he studied astrology with Johannes Schöner (1477–1547) the professor of mathematics at the local gymnasium and a good friend of Melanchthon.


Johannes Schöner Source: Wikimedia Commons

Here he got to know Nürnberg’s comparatively large mathematical community. He became friends with Georg Hartmann (1489–1564) a leading Renaissance instrument maker


Georg Hartmann Source: Astronomie in Nürnberg

and with mathematician later theologian Thomas Venatorius (1488­–1551). Rheticus also became acquainted with Johannes Petreius (1497–1550) the leading European printer/publisher of mathematical/astronomical/astrological texts.


Johannes Petreius Source: Wikimedia Commons

It was almost certainly in Nürnberg that Rheticus became aware of Copernicus, an astronomer in the distant north, who had an interesting new astronomical hypothesis.

I think Rheticus left Nürnberg with a commission from Petreius to go and visit Copernicus and ascertain if he had a book about his heliocentric hypothesis and if so to persuade him to allow Petreius to publish it. There is no known letter of commission and it is probable that none ever existed but there is strong circumstantial evidence to support this theory. When Rheticus left Nürnberg he carried with him six especially bound printed volumes, including three of Petreius’ best mathematical volumes, as a present for Copernicus.  Of course Rheticus’ Narratio Prima, the first ever printed account of Copernicus’ hypothesis, was in the form of an open letter addressed to Schöner in Nürnberg, who had close connections with Petreius. Rheticus received an answer to his Narratio Prima in the form of a letter from Andreas Osiander  (1498–1552), Nürnberg’s Lutheran preacher, who worked as an editor for Petreius and who would go on to edit De revolutionibus.


Andreas Osiander portrait by Georg Pencz Source: Wikimedia Commons

But if Rheticus was fulfilling a commission for Petreius, what did he get out of the deal. Consideration of the legal dispute over his mother’s will indicate that Rheticus was independently wealthy, so some sort of financial payment was probably not involved. However, in 1538 Rheticus was a young, unknown academic at the very beginning of his career and Petreius, as a leading European printer/publisher, was in a position to offer him career-advancing inducements. In 1542 Petreius published an edition of two speeches that Rheticus had held in Wittenberg, Orationes duae prima de astronomia & geographia altera de physica, habitae Vuittebergae / à Ioachimo Rhetico. Neither of these speeches is particularly significant and well below the level of academic text that Petreius usually published, certainly a step up for a novice academic. On 1 August 1540 Petreius went a step further dedicating to Rheticus his edition of the fourteenth-century physician Antonius de Motulmo’s De iudiciis nativitatum, one of the manuscripts brought to Nürnberg by Regiomontanus and edited by Schöner. In the sixteenth century book dedications were important and valuable instruments of credit, most often used to win the favour of important and wealthy patrons, to dedicate such a book to a mere mathematicus, and a novice at that, was a great honour indeed. The dedication is in the form of a fairly long letter, which praises Rheticus highly and urges him to bring Copernicus’ book to Petreius in Nürnberg for publication. Lastly in 1541 Petreius began to publish the annual prognostica of Achilles Gasser, Rheticus’ mentor. Rich rewards for Rheticus’ services.

There, of course, remains the question, would Petreius issue such a commission? The answer is a resounding yes. Having come across Girolamo Cardano’s Practica arithmetice et mensurandi singularis at the Frankfurt Book Fair he instructed Osiander to write to Cardano offering to become his Northern European publisher. Cardano quickly accepted the offer and the Cardano-Petreius partnership proved very profitable for both of them with Petreius publishing Cardano’s best selling volumes on mathematics, astrology, medicine and philosophy. Petreius also commissioned Walter Hermann Ryff (c. 1500–after 1551), a man perhaps best described as a sixteenth-century scientific hack, to produce the first German translation of Vitruvius’ De architectura, Vitruvius Teutsch: Nemlichen des aller namhafftigisten vn[d] hocherfarnesten, Römischen Architecti, und Kunstreichen Werck oder Bawmeisters, Marci Vitruuij Pollionis, Zehen Bücher von der Architectur vnd künstlichem BawendEin Schlüssel vnd einleytung aller Mathematische[n]. Lastly Petreius negotiated with Erasmus Reinhold (1511–1553), Rheticus’ fellow professor of mathematics in Wittenberg, to publish an edition of his extensive horoscope collection. Petreius had earlier published Cardano’s collection with great success. However this project together with Petreius’ planned publication of Reinhold’s Tabulae prutenticae collapsed with Petreius’ death in 1551.

It is often argued that Copernicus could not have know about the Archimedean manuscript The Sand Reckoner with its references to Aristarchus’ heliocentric hypothesis, as this was first published in Basel in 1544. However, Rheticus could have brought that knowledge with him from Nürnberg, as Venatorius was the editor of that Latin/Greek edition of the works of Archimedes published in Basel, based on a Greek manuscript brought to Nürnberg from Rome by Willibald Pirckheimer (1470-1530) and the Latin translation of Jacobus Cremonensis from the manuscript collection of Regiomontanus.

Leaving Nürnberg in 1539, Rheticus did not immediately head north to Frombork. There is no corroborative evidence that he visited Philipp Apian (1531–1589) the professor for mathematics in Ingolstadt but he did go to Tübingen. Melanchthon’s letter of introduction was addressed to Philipp Imser (1550–1570), Stöffler’s successor as professor of mathematics in Tübingen, however just at this time Imser was, following religious differences, suspended from his chair and Rheticus, instead, met up with Joachim Camerarius (1500-1574), humanist scholar, close friend of Melanchthon and his later biographer. Camerarius was another member of the Nürnberger group, who had been rector of the local gymnasium, appointed by Melanchthon, and had worked extensively as an editor for Petreius. Since 1535 he had been rector of the University of Tübingen and would later have a major influence on Rheticus’ career. From Tübingen Rheticus travelled home to Feldkirch, where he visited Achilles Gasser and whence he set out on his journey to Varmia and his fateful meeting with Copernicus.


Filed under History of Astrology, History of Astronomy, Renaissance Science

The emergence of modern astronomy – a complex mosaic: Part IV

Part I  Part II Part III

There is general agreement amongst historians of science that a major factor in the emergence of modern science in general and modern astronomy in particular was the (re)invention of moveable type printing and the arrival of the printed book in the middle of the fifteenth century. I say reinvention because moveable type printing emerged twice before in China in the eleventh century CE and in Korea in the fourteenth century, as I explained in an earlier post. For a long time it was a commonplace in the historical narrative that the printed book, like gunpowder and the compass, was a Chinese invention but extensive long-term research has failed to produce any evidence of a technology transfer and it is now thought that Johannes Gutenberg’s was an independent invention. Even within Europe Gutenberg was not the first to experiment with moveable type and his real invention was the printing press, inclusive printing ink.


Book Printers from Jost Amman  Professionals and Craftsmen

Less than twenty years after Gutenberg published his Bible, Regiomontanus printed and published the first printed astronomy book Peuerbach’s Theoricae Novae Planetarum (Nürnberg, 1473) followed by a handful of other astronomy/astrology books. Unfortunately he died before he could publish their Epytoma in almagesti Ptolemei, which was first published by Ratdolt in Venice in 1496. Both titles became standard astronomy textbooks throughout Europe for more than one hundred years. Famously also being the texts from which Copernicus learnt his astronomy and cosmology.


Theoricae Novae Planetarum Source: Wikimedia Commons

This marked the start of a wave of printed astronomy/astrology books throughout the sixteenth and seventeenth centuries including the works of Apian, Copernicus, Tycho, Kepler, Galileo and many other less well-known figures. Printing made reliable, consistent text available to a wide circle of readers. Whereas a copy of a manuscript in Copenhagen might well have serious deviations compared with a manuscript of the same work in Venice, printed copies of a book were in theory the same wherever their owners lived and worked.


The Astronomer from Jost Amman’s Professionals and Craftsmen Source: Wikimedia Commons

As I pointed out in a reply to an earlier comment in this series the printed great works of astronomy, such as Copernicus’ De revolutionibusor Apian’s Astronomicum Caesareum, would have been way beyond the pocket of the average university student of the period but the professional astronomers, their patron and the institutions could and did acquire copies thus making them, at least potentially, accessible to those students. Interestingly Kepler bought a second hand copy of Copernicus’ De revolutionibus when he was still a student.

However, printing advanced the general dissemination and progress of astronomy and its related fields through purpose written textbooks. The most obvious example of this is Peter Apian’s Cosmographia, originally published by the author in Landshut in 1524. This was a basic introduction to astronomy, astrology, surveying, cartography etc. In total, over the sixteenth century, the book went through thirty-two expanded and improved editions all of which were, somewhat strangely, edited and published by Gemma Frisius and not Apian. Similar textbooks were produced by Oronce Fine, Michael Mästlin and many other sixteenth century mathematical authors.


Title page of Apian’s Cosmpgraphia

It was not just major monographs that profited from the invention of movable type printing. Such astronomical/astrological tools as ephemerides benefited from a certain level of consistency given by print as opposed to hand written manuscripts with their copying errors. In fact a large part of Regiomontanus’ posthumous reputation was based on his printed ephemeris, one of the few books he was able to publish before his untimely demise.

Regiomontanus also led the way in producing printed astronomical/astrological calendars, volumes much in demand from all those working in the wider field of astronomy. In fact astronomical/astrological ephemera of all types–calendars, prognostica, single-sheet wall calendars, almanacs–became a mainstay of the early printing industry providing a much need flow of ready cash.


Regiomontanus Calendar Source: University of Glasgow

To give an idea of the scope of this activity, one of the calendars of Simon Marius (1573–1625), which had to be withdrawn because of political complaints by the local authorities, was said by the printer publisher to have had an edition of 12,000. Marius was only a small local astrologer; the editions of the calendars and prognostica of an Apian or a Kepler would have been much larger. An astronomical monograph, such as De revolutionibus, would have had high production costs and an edition of maybe 500. It would take several years before it turned a profit for the printer publisher if at all. The author got nothing for his troubles. A calendar (wall or pocket), prognostica or almanac had comparatively low production costs, a large edition and if the author was established sold very rapidly. The profits were usually shared fifty-fifty between the printer and the author, a reliable stream of income for both parties. Gutenberg raised some of the finance for his Bible by printing and issuing an astro-medical single-sheet wall calendar.

In an important work, Astrology and the Popular Press: English Almanacs 1500–1800historian Bernard Capp showed that astrological ephemera made up by far and away the largest sector of publishing in the early centuries of printing and more importantly that the editorial sections of the cheap almanacs were one of the major sources for disseminating the latest developments in astronomy, in particular, in the seventeenth century, heliocentricity.


Almanack by John Tulley, 1692. Book exhibited in the Cambridge Public Library, Cambridge, Massachusetts Source: Wikimedia Commons

Along with the development of moving type printing came an increased use of illustrations leading to a rapid development in the techniques used to produce them–woodblock printing, copperplate engraving and etching.


Woodblock cutter Jost Amman’s Professionals and Craftsmen Source: Wikimedia Commons

These techniques were then extended to other field related to astronomy, cartography and globe making. Printed copies of Ptolemaeus’ Geographia with maps were already being printed in the last quarter of the fifteenth century. There also quickly developed a market for large scale printed wall maps, the most famous early example being Waldseemüller’s world map that gave the very recently discovered fourth part of the world the name America after Amerigo Vespucci (1454–1512). Waldseemüller also seems to have printed the first terrestrial globe, a small globe containing the same map of the world. Unfortunately we only have a small number of printed globe gores and no surviving finished globes.


Waldseemüller World Map 1507 (Wikipedia Commons)

Johannes Schöner (1477–1547) was the first to start producing serial printed globes, his first terrestrial globe in 1515 and the matching celestial globe in 1517, establishing a tradition for matching pairs of printed globes that continued until the end of the nineteenth century. Judging by comments from his correspondence his globe printing enterprise was both very successful and very lucrative. Gemma Frisius (1508–1555) took up the baton producing printed globes to be sold with reprints of Schöner’s cosmographia, the descriptive book sold with each globe to explain how to use it. Gemma’s assistant was Gerhard Mercator, who would go on to become the most successful printed globe maker of the second half of the sixteenth century. Mercator’s globes inspired both the great Dutch cartographical houses of Hondius and Blaeu, who would dominate the European globe making and cartography industry in the seventeenth century. England’s first commercial globe printer, Joseph Moxon (1627–1691) learnt his handwork from Willem Janszoon Blaeu (c. 1570–1630). Printed globe making was big business in the sixteenth and seventeenth centuries and the globes were used to teach both astronomy and astrology.


Pair of globes by Gerard Mercator (Globe Museum, Austrian National Library).

Of course all of the above applies equally well to printed maps. Along with the demand for large wall maps, a market developed for collections of printed maps, what we now call atlases. Bound collection of manuscript maps existed before the invention of printing but being the product of hundreds of hours of manual labour these tended to be art treasures for rich patrons rather than practical books for everyday usage. The man, who did most to change this was Abraham Ortelius (1527–1598), whose Theatrum Orbis Terrarum, a bound, standardised, collection of maps, produced especially for traders first published in 1570 was a runaway success. Initial less successful was the more academic Atlas of his good friend and rival Gerhard Mercator. However, both publications laid the foundations for the commercial success of the cartographical publications of Blaeu and Hondius.


Theatrum Orbis Terrarum Title Page Source: Wikimedia Commons

A somewhat different approach was taken by Sebastian Münster (1488–1552), with his Cosmographia, first published in 1544, which was not just a collection of maps but also a full geographical and historical description of the world. In its numerous editions it was almost certainly the biggest selling book in the sixteenth century.


Title page of the first edition of Münster’s Cosmographia Source: Wikimedia Commons

Like nearly-all-the-other globe makers and cartographers described here Münster was an astrologer and astronomer. Other astrologer/astronomers in the sixteenth century, who were also commercially successful as cartographers were Peter and Philipp Apian, Oronce Fine and Michael Mästlin.

It should be clear from the above that the advent of movable type printing had a very large impact on the dissemination of astronomy and its related fields at the same time raising its status in the Early Modern Period in Europe and bringing it to a much wider audience.


Filed under Early Scientific Publishing, History of Astrology, History of Astronomy, History of Cartography, Renaissance Science, Uncategorized

The emergence of modern astronomy – a complex mosaic: Part III

You can read Part I here and Part II here

Although I dealt with the special case of Vienna and the 1st Viennese School of Mathematics in the first post of this series, it is now time to turn to the general history of the fifteenth-century university and the teaching of astronomy. Although the first, liberal arts, degree at the medieval university theoretically encompassed the teaching of the quadrivium, i.e. arithmetic, geometry, music and astronomy, in reality the level of teaching was very low and often neglected all together. Geometry was a best the first six books of Euclid and at worst just book one and astronomy was the Sphaeraof Sacrobosco, a short non-technical introduction.

This all began to change in the fifteenth century. The humanist universities of Northern Italy and of Poland introduced dedicated chairs for mathematics, whose principle purpose was the teaching of astrology to medical students. However, to fully understand astrology and to be able to cast horoscopes from scratch students first had to learn astronomy, which in turn entailed first having to learn arithmetic and geometry, as well as the use of mathematical and astronomical instruments. The level of mathematical tuition on the university increased considerable. The chairs for mathematics that Galileo would occupy at the end of the sixteenth century in Pisa and Padua were two such astrology chairs.

As the first European university, Krakow introduced two such chairs for mathematics and astronomy relatively early in the fifteenth century.


The founding of the University of Krakow in 1364, painted by Jan Matejko (1838–1893) Source: Wikimedia Commons

It was here at the end of the century  (1491–1495) that Copernicus first learnt his astronomy most probably in the lectures of Albert Brudzewski (c. 1445–c.1497) using Peuerbach’s Theoricae Novae Planetarum and Regiomontanus’ Astronomical Tables. Brudzewski also wrote an important commentary on Peuerbach’s Theoricae Novae Planetarum,Commentum planetarium in theoricas Georgii Purbachii (1482).Krakow was well endowed with Regiomontanus’ writings thanks to the Polish astrologer Marcin Bylica (c.1433–1493), who had worked closely with Regiomontanus on the court ofMatthias Corvinus (1443–1490) in Budapest and who when he died bequeathed his books and instruments to the University of Krakow, including the works of Regiomontanus and Peuerbach.

From Krakow Copernicus went on to Northern Italy and its humanist universities. Between 1496 and 1501 he studied canon law in Bologna, Europe’s oldest university.


The entry of some students in the Natio Germanica Bononiae, the nation of German students at Bologna; miniature of 1497. Source: Wikimedia Commons

Here he also met and studied under/worked with the professor for astronomer Domenico Maria Novara da Ferrara (1454–1504), who claimed to be a student of Regiomontanus and it is known that he studied under Luca Pacioli (c. 1447–1517), who was also Leonardo’s mathematics teacher. Although none of Novara da Ferrara writings have survived he is said to have taken a critical attitude to Ptolemaic astronomy and he might be the trigger that started Copernicus on his way. In late 1501 Copernicus moved to the University of Padua, where he studied medicine until 1503, a course that would also have included instruction in astrology and astronomy. In 1503 he took a doctorate in canon law at the University of Ferrara. Sometime in the early sixteenth century, probably around 1510 he wrote an account of his first thoughts on heliocentricity, now known as the Commentariolus, which was never published but seems to have circulated fairly widely in manuscript. We will return to this later.

The first German university to install a dedicated chair for mathematics/astronomy was Ingolstadt in the 1470s.


The Hohe Schule (High School), The main building of the University of Ingolstadt 1571 Source: Wikimedia Commons

As with the North Italian universities this was principally to teach astrology to medical student. This chair would prove to be an important institution for spreading the study of the mathematical sciences. In 1491/1492 the humanist scholar and poet, Conrad Celtis (1459–1508) was appointed professor of poetics and rhetoric in Ingolstadt. Celtis had a strong interest in cartography as a part of history and travelled to Krakow in 1489 in order to study the mathematical sciences. In Ingolstadt Celtis was able to turn the attention of Andreas Stiborius (1464–1515) and Johannes Stabius (1468–1522) somewhat away from astrology and more towards cartography. In 1497 Celtis received a call from the University of Vienna and taking Stiborius and Stiborius’ star student Georg Tannstetter (1482–1535) with him he decamped to Vienna, where he set up his Collegium poetarum et mathematicorum, with Stiborius as professor for mathematics. In 1502 he also fetched Johannes Stabius. From 1502 Tannstetter also began to lecture on mathematics and astronomy in Vienna. Stiborius, Stabius and Tannstetter form the foundations of what is known as the 2ndViennese School of Mathematics. Tannstetter taught several important students, most notably Peter Apian, who returned to Ingolstadt as professor for mathematics in the 1520, a position in which he was succeeded by his son Philipp. Both of them made major contributions to the developments of astronomy and cartography.

Stabius’ friend and colleague Johannes Werner also studied in Ingolstadt before moving to and settling in Nürnberg. One of the few astronomical writing of Copernicus, apart from De revolutionibus, that exist is the so-called Letter against Werner in which Copernicus harshly criticised Werner’s Motion of the Eighth Sphere an essay on the theory of precession of the equinox.

Another graduate of Ingolstadt was Johannes Stöffler (1452–1531), who having had a successful career as an astronomer, astrologer and globe and instrument maker was appointed the first professor of mathematics at the University of Tübingen.


The Old Auditorium University of Tübingen Source: Wikimedia Commons

Amongst his student were Sebastian Münster (1488–1552) the most important cosmographer of the sixteenth century and Philipp Melanchthon (1497–1560), who as a enthusiastic fan of astrology established chairs for mathematics and astronomy at all of the protestant schools and universities that he established starting in Wittenberg, where the first professor for lower mathematic was Jakob Milich (1501–1559) another graduate of the University of Vienna. Milich’s fellow professor for astronomy in Wittenberg Johannes Volmar (?–1536), who started his studies in Krakow. The successors to Milich and Volmar were Georg Joachim Rheticus (1514–1574) and Erasmus Reinhold (1511–1553).

Another Melanchthon appointment was the first professor for mathematics on the Egidien Obere Schule in Nürnberg, (Germany’s first gymnasium), the globe maker Johannes Schöner (1477–1547), who would play a central role in the heliocentricity story. Schöner had learnt his mathematics at the university of Erfurt, one of the few German universities with a reputation for mathematics in the fifteenth century. When Regiomontanus moved from Budapest to Nürnberg he explained his reasons for doing so in a letter to the Rector of Erfurt University, the mathematician Christian Roder, asking him for his active support in his reform programme.

The Catholic universities would have to wait for Christoph Clavius (1538–1612) at the end of the sixteenth century before they received dedicated chairs for astronomy to match the Lutheran Protestant institutions. However, there were exceptions. In Leuven, where he was actually professor for medicine, Gemma Frisius (1508–1555) taught astronomy, astrology, cartography and mathematics. Amongst his long list of influential pupils we find Johannes Stadius (1527–1579), Gerhard Mercator (1512–1594) and John Dee (1527–1609). In France, François I appointed Oronce Fine (1494–1555) Royal lecturer for mathematics at the University of Paris. He was not a very impressive mathematician or astronomer but a highly influential teacher and textbook author. In Portugal, Pedro Nunes (1502–1578) was appointed the first professor of mathematics at the university of Coimbra as well as to the position of Royal Cosmographer.


The University of Coimbra Palace Gate. Source: Wikimedia Commons

Over the fifteenth and sixteenth centuries the mathematical sciences, driven mainly by astrology and cartography, established themselves in the European universities, where the professors and lecturers, as we shall see, played a central role in the reform and renewal of astronomy.








Filed under History of Astrology, History of Astronomy, History of Cartography, History of medicine, Renaissance Science

The emergence of modern astronomy – a complex mosaic: Part I

I have recently been involved in more that one exchange on the subject as to what tipped the scales in favour of heliocentricity against geocentricity in the Early Modern Period. People have a tendency to want to pin it down to one crucial discovery, observation or publication but in reality it was a very gradual process that took place over a period of at least three hundred and fifty years and involved a very large number of people. In what follows I intend to sketch that process listing some, but probably not all, of the people involved. My list might appear to include people, who at first might not appear to have contributed to the emergence of modern astronomy if one just considers heliocentricity. However, all of those who raised the profile of astronomy and emphasised its utility in the Early Modern Period raised the demand for better and more accurate astronomical data and improved models to produce it. The inclusion of all these factors doesn’t produce some sort of linear progress but more a complex mosaic of many elements some small, some simple, some large and some spectacular but it is not just the spectacular elements that tells the story but a sum of all the elements. So I have cast my nets very wide.

The first question that occurs is where to start. One could go back all the way to Aristarchus of Samos (c.310–c.230 BCE) but although he and his heliocentric theories were revived in the Early Modern Period, it was largely with hindsight and he played no real role in the emergence of heliocentricity in that time. However, we should definitely give a nod to Martianus Capella (fl.c. 410–420), whose cosmos model with Mercury and Venus orbiting the Sun in an otherwise geocentric model was very widespread and very popular in the Middle Ages and who was quoted positively by Copernicus.


The Capellan system Source: Manuscript Florenz, Biblioteca Medicea Laurenziana, San Marco 190, fol. 102r (11th century) via Wikimedia Commons

Another nod goes to Jean Buridan (c.1300–c.1358/61), Nicole Oresme (c.1320-1325–1382), Pierre d’Ailly (1351–1420) and Nicholas of Cusa (1401–1464) all of whom were well-known medieval scholars, who discussed the model of geocentrism with diurnal rotation, a model that was an important step towards the acceptance of heliocentricity.

I start with a figure, who most would probably not have on the radar in this context, Jacopo d’Angelo (c.1360–1411). He produced the first Latin translation of Ptolemaeus’ Geōgraphikḕ Hyphḗgēsis(Geographiaor Cosmographia) in Florence in 1406.


Manuscript: d’Angelo’s translation of Ptolemy’s Geography Source: Scan from Nancy Library (Hosted at Wikicommons, early 15th century).

This introduced a new concept of cartography into Europe based on a longitude and latitude grid, the determination of which requires accurate astronomical data. Mathematical, astronomy based cartography was one of the major forces driving the reform or renewal of astronomy in the Early Modern Period. Another major force was astrology, in particular astro-medicine or as it was known iatromathematics, which was in this period the mainstream school medicine in Europe. Several of the astronomy reformers, most notably Regiomontanus and Tycho, explicitly stated that a reform of astronomy was necessary in order to improve astrological prognostications. A third major driving force was navigation. The Early Modern Period includes the so call great age of discovery, which like mathematical cartography was astronomy based. Slightly more nebulous and indirect were new forms of warfare, another driving force for better cartography as well as the collapse of the feudal system leading to new forms of land owner ship, which required better surveying methods, also mathematical, astronomy based. As I pointed out in an earlier post the people working in these diverse fields were very often one and the same person the Renaissance mathematicus, who was an astrologer, astronomer, cartographer, surveyor or even physician.

Our next significant figure is Paolo dal Pozzo Toscanelli (1397–1482), like Jacopo d’Angelo from Florence, a physician, astrologer, astronomer, mathematician and cosmographer.


Paolo dal Pozzo Toscanelli. Detail taken from the 19th century honorary monument to Columbus, Vespucci and Toscanelli dal Pozzo in the Basilica di Santa Croce in Florence (Italy). Source: Wikimedia Commons

Most famous for his so-called Columbus world map, which confirmed Columbus’ erroneous theory of the size of the globe. In our context Toscanelli is more important for his observation of comets. He was the first astronomer in the Early Modern Period to treat comets as astronomical, supralunar objects and try to record and measure their trajectories. This was contrary to the ruling opinion of the time inherited from Aristotle that comets were sublunar, meteorological phenomena. Toscanelli did not publish his observations but he was an active member of a circle of mathematically inclined scholars that included Nicholas of Cusa, Giovanni Bianchini (1410 – c.1469), Leone Battista Alberti (1404 – 1472),Fillipo Brunelleschi (1377 – 1446) and most importantly a young Georg Peuerbach (1423–1461) with whom he probably discussed his ideas.

Here it is perhaps important to note that the mathematical practitioners in the Early Modern Period did not live and work in isolation but were extensively networked, often far beyond regional or national boundaries. They communicated extensively with each other, sometimes in person, but most often by letter. They read each other’s works, both published and unpublished, quoted and plagiarised each other. The spread of mathematical knowledge in this period was widespread and often surprisingly rapid.

We now turn from Northern Italy to Vienna and its university. Founded in 1365, in 1384 it came under the influence of Heinrich von Langenstein (1325–1397), a leading scholar expelled from the Sorbonne in Paris, who introduced the study of astronomy to the university, not necessarily normal at the time.


Probably Heinrich von Langenstein (1325-1397), Book illumination im Rationale divinorum officiorum des Wilhelmus Durandus, circa 1395 Source: Archiv der Universität Wien, Bildarchiv Signatur: 106.I.1840 1395

Heinrich was followed by Johannes von Gmunden (c.1380–1442) who firmly established the study of astronomy and is regarded as the founder of the 1stViennese School of Mathematics.


Johannes von Gmunden Calendar Nürnberg 1496 Source: Wikimedia Commons

Georg Peuerbach the next member of the school continued the tradition of astronomical studies established by Heinrich and Gmunden together with his most famous student Johannes Regiomontanus.


Johannes Regiomontanus Source: Wikimedia Commons

It can’t be a coincidence that Peuerbach and Regiomontanus extended Toscanneli’s work on comets, with Regiomontanus even writing a pamphlet on the determination of parallax of a moving comet, which was only publish posthumously in the sixteenth century. The two Viennese astronomers also designed and constructed improved astronomical instruments, modernised the trigonometry necessary for astronomical calculations and most importantly with Peuerbach’s Theoricarum novarum planetarum(New Planetary Theory),


Georg von Peuerbach, Theoricae novae planetarum, Edition Paris 1515 Source: Wikimedia Commons

first published by Regiomontanus in Nürnberg in 1472, and their joint Epytoma in almagesti Ptolemei, a modernised, shortened improved edition of Ptolemaeus’ Syntaxis Mathematiké


Epytoma in almagesti Ptolemei: Source

first published by Ratdolt in Venice in 1496, produced the standard astronomy textbooks for the period right up into the seventeenth century.

The work on the Viennese School very much laid the foundations for the evolution of the modern astronomy and was one of the processes anchoring the ‘modern’ study of astronomy an the European universities, How the journey continues will be told in Part II of this series.











Filed under Early Scientific Publishing, History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, Renaissance Science, University History

The Seven Learned Sisters

I have suffered from a (un)healthy[1]portion of imposter syndrome all of my life. This is the personal feeling in an academic context that one is just bluffing and doesn’t actually know anything and then any minute now somebody is going to unmask me and denounce me as an ignorant fraud. I always thought that this was a personal thing, part of my general collection of mental and emotional insecurities but in more recent years I have learned that many academics, including successful and renowned ones, suffer from this particular form of insecurity. On related problem that I have is the belief that anything I do actually know is trivial, generally known to everyone and therefore not worth mentioning[2]. I experienced an example of this recently on Twitter when I came across the following medieval illustration and its accompanying tweet.


Geometria Source: Wikimedia Commons

Woman teaching geometry to monks. In the Middle Ages, it is unusual to see women represented as teachers, in particular when the students appear to be monks. Euclid’s Elementa, in the translation attributed to Adelard of Bath, 1312.

I would simply have assumed that everybody knew what this picture represents and not commented. It is not a “women teaching geometry to monks” as the tweeter thinks but a typical medieval personification of Geometria, one of the so-called Seven Learned Sisters. The Seven Learned Sisters are the personifications of the seven liberal arts, the trivium (grammar, rhetoric and dialectic)

and the quadrivium (arithmetic, geometry, music and astronomy),

which formed the curriculum in the lower or liberal arts faculty at the medieval university. The seven liberal arts, however, have a history that well predates the founding of the first universities. In what follows I shall only be dealing with the history of the quadrivium.

As a concept this four-fold division of the mathematical sciences can be traced back to the Pythagoreans. The mathematical commentator Proclus (412–485 CE) tells us, in the introduction to his commentary on the first book of Euclid’s Elements:

The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving.

The earliest know written account of this division can be found at the beginning of the late Pythagorean Archytas’ book on harmonics, where he identifies a set of four sciences: astronomy, geometry, logistic (arithmetic) and music. Archytas’ dates of birth and death are not known but he was, roughly speaking, a contemporary of Plato. He was the teacher of Eudoxus (c.390–c.337 BCE) Harmonics, by the way, is the discipline that later became known as music in the quadrivium.

Without mentioning Archytas, Plato (428/427 or 424/423 – 348/347 BCE), who was highly influenced by the Pythagoreans,takes up the theme in his Republic (c.380 BCE). In a dialogue with Glaucon, Plato explains the merits of learning the “five” mathematical sciences; he divides geometry into plane geometry (two dimensional) and solid geometry (three dimensional). He also refers to harmonics and not music.

In the CE period the first important figure is the Neo-Pythagorean, Nicomachus of Gerasa (c.60–c.120 CE), who wrote an Introduction to Arithmeticand a Manual of Harmonics, which are still extant and a lost Introduction to Geometry. The four-fold division of the mathematical sciences only acquired the name quadrivium in the works of Boethius (c.477–524 CE), from whose work the concept of the seven liberal arts was extracted as the basic curriculum for the medieval university. Boethius, who saw it as his duty to rescue the learning of the Greeks, heavily based his mathematical texts on the work of Nicomachus.

Probably the most influential work on the seven liberal arts is the strange De nuptiis Philologiae et Mercurii (“On the Marriage of Philology and Mercury“) of Martianus Capella (fl.c. 410-420). The American historian H. O. Taylor (1856–1941) claimed that On the Marriage of Philology and Mercurywas “perhaps the most widely used schoolbook in the Middle Ages,” quoted from Martianus Capella and the Seven Liberal Artsby William Harris Stahl.[3]Stahl goes on to say, “It would be hard to name a more popular textbook for Latin reads of later ages.”

Martianus introduces each of the members of the trivium and quadrivium as bridesmaids of the bride Philology.

“Geometry enters carrying a radius in her right hand and a globe in her left. The globe is a replica of the universe, wrought by Archimedes’ hand. The peplos she wears is emblazoned with figures depicting celestial orbits and spheres; the earth’s shadow reaches into the sky, giving a purplish hue to the golden globes of the sun and moon; there are gnomons of sundials and figures showing intervals weights, and measures. Her hair is beautifully groomed, but her feet are covered with grime and her shoes are worn to shreds with treading across the entire surface of the earth.”[4]


A 16th century Geometria in a printed copy of the Margarita Philosophica

“As she enters the celestial hall, Arithmetic is even more striking in appearance than was Geometry with her dazzling peplos and celestial globe. Arithmetic too wears a robe, hers concealing an “intricate undergarment that holds clues to the operations of universal nature.” Arithmetic’s stately bearing reflects the pristine origin, antedating the birth of the Thunder God himself. Her head is an awesome sight. A scarcely perceptible whitish ray emanates from her brow; then another ray, the projection of a line, as it were, coming from the first. A third ray and a fourth spring out, and so on, up to a ninth and a tenth ray–all radiating from her brow in double and triple combinations. These proliferate in countless numbers and in a moment are miraculously retracted into the one.”[5]An allusion to the Pythagorean decade.


Gregor Reisch Margarita Philosophica: Arthimetica presiding over a computing competition between Hindu-Arabic numerals and a reckoning board

“Astronomy like her sister Geometry, is a peregrinator of the universe. She has traversed all the heavens and can reveal the constellations lying beneath the celestial arctic circle. […] Astronomy tells us that she is also familiar with the occult lore of Egyptian priest, knowledge hoarded in their sanctums; she kept herself in seclusion in Egypt for nearly forty thousand years, not wishing to divulge those secrets. She is also familiar with antediluvian Athens.”[6]


“Harmony herself is ineffably dazzling and Martianus is stricken in his efforts to describe her. A lofty figure, her head aglitter with gold ornaments, she walks along between Apollo and Athena. Her garment is tiff with incised and laminated gold; it tinkles softly and soothingly with every measured step She carries in her right hand what appears to be a shield, circular in form. It contains many concentric circles, and the whole is embroidered with striking figure. The circular chords encompass one another and from them pours forth a concord of all tones: Small models of theatrical instruments, wrought of gold, hang suspended from Harmony’s left hand. No know instrument produces sounds to compare with those coming from the strange rounded form.”[7]



I have included Stahl’s passages of Martianus’ descriptions of the quadrivium to make clear then when I talk of the disciplines being personified as women I don’t just mean that they get a female name but are fully formed female characters. This of course raises the question, at least for me, why the mathematical disciplines that were taught almost exclusively to men in ancient Greece, the Romano-Hellenistic culture and in the Middle Ages should be represented by women. Quite honestly I don’t know the answer to my own question. I assume that it relates to the nine ancient Greek Muses, who were also women and supposedly the daughters of Zeus and Mnemosyne (memory personified). This however just pushes the same question back another level. Why are the Muses female?


Having come this far it should be noted that although the quadrivium was officially part of the curriculum on medieval universities it was on the whole rather neglected. When taught the subjects were only taught at a very elementary level, arithmetic based on the primer of Boethius, itself an adaption of Nicomachus, geometry from Euclid but often only Book One and even that only partially, music again based on Boethius and astronomy on the very elementary Sphere of Sacrobosco. Often the mathematics courses were not taught during the normal classes but only on holidays, when there were no normal lectures. At most universities the quadrivium disciplines were not part of the final exams and often a student who had missed a course could get the qualification simple by paying the course fees. Mathematics only became a real part of the of the university curriculum in the sixteenth century through the efforts of Philip Melanchthon for the protestant universities and somewhat later Christoph Clavius for the Catholic ones. England had to wait until the seventeenth century before there were chairs for mathematics at Oxford and Cambridge.

[1]On the one hand imposter syndrome can act as a spur to learn more and increase ones knowledge of a given subject. On the other it can lead one to think that one needs to know much more before one closes a given research/learn/study project and thus never finish it.

[2]To paraphrase some old Greek geezer, the older I get and the more I learn, the more I become aware that what I know is merely a miniscule fraction of that which I could/should know and in reality I actually know fuck all.

[3]William Harris Stahl, Martianus Capella and the Seven Liberal Arts: Volume I The Quadrivium of Martianus Capella. Latin Traditions in the Mathematical Science, With a Study of the Allegory and the Verbal Disciplines by Richard Johnson with E. L. Burge, Columbia University Press, New York & London, 1971, p. 22

[4]Stahl pp. 125–126

[5]Stahl pp. 149–150

[6]Stahl p. 172

[7]Stahl p. 203


Filed under History of Astrology, History of Astronomy, History of Mathematics, Mediaeval Science, Renaissance Science, Uncategorized