Category Archives: Renaissance Science

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

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.







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

Vienna and Astronomy the beginnings.

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.



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.







Filed under History of Astronomy, History of Cartography, History of science, Renaissance Science

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

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

Geoheliocentric cosmology, 16th century

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


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

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

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.


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

Kepler was wot, you don’t say?


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 17thcentury 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.










Filed under History of Alchemy, History of Astrology, History of Astronomy, History of science, Myths of Science, Renaissance Science

Everything you wanted to know about Simon Marius and were too afraid to ask – now in English

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.


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

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

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.






Filed under History of Astronomy, Renaissance Science