Category Archives: History of science

Christoph and the Calendar

The first substantive history of science post that I wrote on this blog was about the Jesuit mathematician and astronomer Christoph Clavius. I wrote this because at the time I was preparing a lecture on the life and work of Clavius to be held in his hometown Bamberg. Clavius is one of my local history of science celebrities and over the years I have become the local default Clavius expert and because of his involvement in the Gregorian calendar reform of 1572 I have also become the local default expert on that topic too.

Christoph Clavius

Christoph Clavius

All of this means that I have become very sensitive to incorrect statements about either Clavius or the Gregorian calendar reform and particularly sensitive to false statements about Clavius’ involvement in the latter. Some time back the Atlas Obscura website had a ‘time week’ featuring a series of blog post on the subject of time one of which, When The Pope Made 10 Days Disappear, was about the Gregorian calendar reform and contained the following claim:

The new lead astronomer on the project, Jesuit prodigy Christopher Clavius, considered this and other proposals for five years.

The brief statement contains three major inaccuracies, the most important of which, is that Clavius as not the lead astronomer, or lead anything else for that matter, on the project. This is a very widespread misconception and one to which I devote a far amount of time when I lecture on the subject, so I thought I would clear up the matter in a post. Before doing so I would point out that I have never come across any other reference to Clavius as a prodigy and there is absolutely nothing in his biography to suggest that he was one. That was the second major inaccuracy for those who are counting.

Before telling the correct story we need to look at the wider context as presented in the article before the quote I brought above we have the following:

A hundred years later, Pope Gregory XIII rolled up his sleeves and went for it in earnest. After a call for suggestions, he was brought a gigantic manuscript. This was the life’s work of physician Luigi Lilio, who argued for a “slow 10-day correction” to bring things back into alignment, and a new leap year system to keep them that way. This would have meant that years divisible by 100 but not by 400 (e.g. 1800, 1900, and 2100) didn’t get the extra day, thereby shrinking the difference between the solar calendar and the Earthly calendar down to a mere .00031 days, or 26 seconds.

Luigi LIlio Source: Wikimedia Commons

Luigi LIlio
Source: Wikimedia Commons

This is correct as far as it goes, although there were two Europe wide appeals for suggestions and we don’t actually know how many different suggestions were made as the relevant documents are missing from the Vatican archives. It should also be pointed out the Lilio was a physician/astronomer/astrologer and not just simply a physician. Whether or not his manuscript was gigantic is not known because it no longer exists. Having decided to consider Lilio’s proposal this was not simply passed on to Christoph Clavius, who was a largely unknown mathematicus at the time, which should be obvious to anybody who gives more than five minutes thought to the subject.

The problem with the calendar, as far as the Church was concerned, was that they were celebrating Easter the most important doctrinal festival in the Church calendar on the wrong date. This was not a problem that could be decided by a mere mathematicus, at a time when the social status of a mathematicus was about the level of a bricklayer, it was far too important for that. This problem required a high-ranking Church commission and one was duly set up. This commission did not consider the proposal for five years but for at least ten and possibly more, again we are not sure due to missing documents. It is more than likely that the membership of the commission changed over the period of its existence but because we don’t have the minutes of its meetings we can only speculate. What we do have is the signatures of the nine members of the commission who signed the final proposal that was presented to the Pope at the end of their deliberations. It is to these names that we will now turn our attention.

The names fall into three distinct groups of three of which the first consists of the high-ranking clerics who actually lead this very important enquiry into a fundamental change in Church doctrinal practice. The chairman of the committee was of course a cardinal,Guglielmo Sirleto (1514–1584) a distinguished linguist and from 1570 Vatican librarian.

Cardinal Guglielmo Sirleto Source: Wikimedia Commons

Cardinal Guglielmo Sirleto
Source: Wikimedia Commons

The vice chairman was Bishop Vincenzo Lauro (1523–1592) a Papal diplomat who was created cardinal in 1583. Next up was Ignatius Nemet Aloho Patriarch of Antioch and head of the Syriac Orthodox Church till his forced resignation in 1576. Ignatius was like his two Catholic colleagues highly knowledgeable of astronomy and was brought into the commission because of his knowledge of Arabic astronomy and also to try to make the reform acceptable to the Orthodox Churches. The last did not function as the Orthodox Churches initially rejected the reform only adopting it one after the other over the centuries with the exception of the Russian Eastern Orthodox Churches, whose church calendar is still the Julian one, which is why they celebrate Christmas on 6 7 January.

Our second triplet is a mixed bag. First up we have Leonardo Abela from Malta who functioned as Ignatius’ translator, he couldn’t speak Latin, and witnessed his signature on the commissions final report. He is followed by Seraphinus Olivarius an expert lawyer, whose role was to check that the reform did not conflict with any aspects of cannon law. The third member of this group was Pedro Chacón a Spanish mathematician and historian, whose role was to check that the reform was in line with the doctrines of the Church Fathers.

Our final triplet consists of what might be termed the scientific advisors. Heading this group is Antonio Lilio the brother of Luigi and like his brother a physician and astronomer. He was here to elucidate Luigi’s plan, as Luigi was already dead. The lead astronomer, to use the Atlas Obscura phase, was the Dominican monk Ignazio Danti (1536–1582) mathematician, astronomer, cosmographer, architect and instrument maker.

Ignazio Danti Source: Wikimedia Commons

Ignazio Danti
Source: Wikimedia Commons

In a distinguished career Danti was cosmographer to Cosimo I, Duke of Tuscany whilst professor of mathematics at the university of Pissa, professor of mathematics at the University of Bologna and finally pontifical mathematicus in Rome. For the Pope Danti painted the Gallery of Maps in the Cortile del Belvedere in the Vatican Palace and deigned and constructed the instruments in the Sundial Rome of the Gregorian Tower of Tower of Winds above the Gallery of Maps.

Map of Italy, Corsica and Sardinia - Gallery of Maps - Vatican Museums. Source: Wikimedia Commons

Map of Italy, Corsica and Sardinia – Gallery of Maps – Vatican Museums.
Source: Wikimedia Commons

After the calendar reform the Pope appointed him Bishop of Altari. Danti was one of the leading mathematical practitioners of the age, who was more than capable of supplying all the scientific expertise necessary for the reform, so what was the role of Christoph Clavius the last signer of the commission’s recommendation.

The simple answer to this question is that we don’t know; all we can do is speculate. When Clavius (1538–1612) first joined the commission he was, in comparison to Danti, a relative nobody so his appointment to this high level commission with its all-star cast is somewhat puzzling. Apart from his acknowledged mathematical skills it seems that his membership of the Jesuit Order and his status as a Rome insider are the most obvious reasons. Although relative young the Jesuit Order was already a powerful group within the Church and would have wanted one of theirs in such a an important commission. The same thought concerns Clavius’ status as a Rome insider. The Church was highly fractional and all of the other members of the commission came from power bases outside of Rome, whereas Clavius, although a German, as professor at the Collegio Romano counted as part of the Roman establishment, thus representing that establishment in the commission. It was probably a bit of all three reasons that led to Clavius’ appointment.

Having established that Clavius only had a fairly lowly status within the commission how did the very widespread myth come into being that he was somehow the calendar reform man? Quite simply after the event he did in fact become just that.

When Pope Gregory accepted the recommendations of the commission and issued the papal bull Inter gravissimas on 24 February 1582, ordering the introduction of the new calendar on 4 October of the same year,


he granted Antonio Lilio an exclusive licence to write a book describing the details of the calendar reform and the modifications made to the process of calculating the date of Easter. The sales of the book, which were expected to be high, would then be the Lilio family’s reward for Luigi Lilio having created the mathematical basis of the reform. Unfortunately Antonio Lilio failed to deliver and after a few years the public demand for a written explanation of the reform had become such that the Pope commissioned Clavius, who had by now become a leading European astronomer and mathematician, to write the book instead. Clavius complied with the Pope’s wishes and wrote and published his Novi calendarii romani apologia, Rome 1588, which would become the first of a series of texts explaining and defending the calendar reform. The later was necessary because the reform was not only attacked on religious grounds by numerous Protestants, but also on mathematical and astronomical grounds by such leading mathematicians as François Viète and Michael Maestlin. Over the years Clavius wrote and published several thousand pages defending and explicating the Gregorian calendar reform and it is this work that has linked him inseparably with the calendar reform and not his activities in the commission.


Filed under History of Astronomy, History of Mathematics, History of science, Local Heroes, Renaissance Science

The orbital mechanics of Johann Georg Locher a seventeenth-century Tychonic anti-Copernican

Our favourite guest blogger Chris Graney is back with a question. Busy translating the Disquisitiones mathematicae de controversis et novitatibus astronomicis (1614) of Johann Georg Locher, a student of Christoph Scheiner at the University of Ingolstadt, he came across a fascinating theory of orbital mechanics, which he outlines in this post. Chris’s question is how does this theory fit in with seventeenth-century force dependent orbital theories? Read the post and enlighten Chris with your history of astronomy wisdom!

Did Johann Georg Locher write something very interesting in 1614 about how the Earth could orbit the Sun under the influence of gravity? I am hoping that the RM and his many readers might be able to weigh in on this.

Who is Locher? He is the author of the 1614 Disquisitiones Mathematicae (Mathematical Disquisitions), an anti-Copernican book known primarily because Galileo made sport of it within his Dialogue Concerning the Two Chief World Systems: Ptolemaic and Copernican. It is the “booklet of theses, which is full of novelties” that Galileo has the anti-Copernican Simplicio drag out in order to defend one or another wrong-headed idea. Galileo describes the booklet’s author as producing arguments full of “falsehoods and fallacies and contradictions,” as “thinking up, one by one, things that would be required to serve his purposes, instead of adjusting his purposes step by step to things as they are,” and as being excessively bold and self-confident, “setting himself up to refute another’s doctrine while remaining ignorant of the basic foundations upon which the greatest and most important parts of the whole structure are supported.” As far as I can tell, little is known about Locher himself other than what he says in his book: he was from Munich; he studied at Ingolstadt under the Jesuit astronomer Christopher Scheiner. This is the same Scheiner who Galileo debated regarding sunspots. Some writers treat the Disquisitions as Scheiner’s work.

I became better acquainted with the Disquisitions through Dennis Danielson’s work on Milton, in which it plays a part. This prompted me to look at Locher’s work directly. Then I discovered that Locher wields Tycho Brahe’s star size argument against Copernicus, that he illustrates the Disquisitions lavishly, and that the Disquisitions is short. So I decided to read and translate it cover-to-cover.

The Disquisitions turns out to be fascinating. It is nothing like what one might expect from reading the Dialogue. And among the gems within it is this thing that Locher thinks up:

Imagine an L-shaped rod, buried in the Earth, with a heavy iron ball attached to it, as shown in the left-hand figure below. The heaviness or gravity of the ball (that is, its action of trying to reach its natural place at the center of the universe—in 1614 Newtonian physics was many decades in the future; Aristotelian physics was the rule) presses down on the rod, but the rigidity of the rod keeps the ball from falling.

Now imagine the rod being hinged at the Earth’s surface (at point A in the right-hand figure below). The heaviness of the ball will now cause the rod to pivot about the hinge. The ball will fall along an arc of a circle whose center is A, striking the Earth at B.


Now imagine the Earth is made smaller relative to the rod. The same thing will still occur—the rod pivots; the iron ball falls in a circular arc (below left). If the Earth is imagined to be smaller still, the rod will be what hits the ground, not the ball (below right), so the ball stops at C, but the ball still falls in a circular arc whose center is A.


If you imagine the Earth to be smaller and smaller, the ball still falls, driven by its gravity, in a circular arc (below). You can see where Locher is going! He is thinking his way toward a limiting case.


At last Locher says to imagine the rod to be pivoting on the center of the universe itself—the Earth vanishing to a point. Surely, he says, in this situation, a complete and perpetual revolution will take place around that same pivot point A (fiet reuolutio integra & perpetua circa idem A).


Now, he says, we have demonstrated that perpetual circular motion of a heavy body is possible. And if we imagine the Earth in the place of the iron ball, suspended over the center of the universe, now we have a thought experiment (cogitatione percipi possit—it may be able to be perceived by thought) that shows how the Earth might be made to revolve about that center (and about the sun, which would be at the center in the Copernican system). But this sort of thing does not exist, he says, and if it did exist, it would not help the Copernicans any, because no phenomena are saved—that is, no observations are explained—by means of it.

Below is Locher’s sketch of this. Curves MN, OP, and QR are the surface of the Earth, being imagined smaller and smaller. S is the iron ball. A is the center of the universe. Circle CHIC is the path of the orbiting ball.


So it seems that in 1614 an anti-Copernican—a student of one of Galileo’s adversaries—proposed a mechanism to explain the orbit of the Earth, and that mechanism involved a fall under a central force. This is not the Newtonian explanation of Earth’s orbit, but it does have significant elements in common with Newton. And, Locher was definitely an anti-Copernican. Indeed, while he illustrates telescopic discoveries such as the phases of Venus, and states that the telescope shows that the world is structured according to the Tychonic system (sun, moon, and stars circle Earth, planets circle sun), he clearly rejects Copernicus—on the grounds of the star size problem (and the Copernican tendency to invoke the Creator’s majesty to get around that problem) and on the grounds that a moving Earth grossly complicates the motions of bodies moving over its surface.


The history of orbital mechanics is not my bailiwick, so I ask RM readers whether they think Locher is a “first”? Is this really as interesting as it seems to me? Or do RM readers know of others who proposed the “an orbit is a fall under a central force” idea prior to Locher? Whether I search in English or in Latin I can find neither primary nor secondary sources that discuss the Disquisitions’ treatment of orbits, nor can I find primary or secondary sources that discuss orbits and central forces in general prior to the late-seventeenth century. In fact, I can find little written on the Disquisitions itself (outside of its role in the Dialogue), and what I have found typically conflicts with what is actually in the Disquisitions (for example, one author describes the Disquisitions as a book “in which the proponents of Earth’s motion were violently attacked,” but actually Locher’s worst words are for Simon Marius, a fellow supporter of the Tychonic system, while his most favorable words are for Galileo). But many of you are much more well-read than I am.

My searches did turn up one interesting item, however. Locher uses the term forced suspension to describe what is going on in an orbit (motus huius continui caussa est violenta suspensio—the cause of this continuing motion is forced suspension) and I have found that term in what appears to be another seventeenth-century Jesuit’s commentary on the work of Thomas Aquinas.

With luck the translation of Disquisitions will be published in a year or so.


Filed under History of Astronomy, History of science

Christmas Trilogy 2015 Part 1: The famous witty Mrs Barton


Younger readers might be excused if they thought that the IT Girl phenomenon, as illustrated by the likes of Paris Hilton and Kim Kardashian, was a product of the computer social media age but those of us who are somewhat more mature can remember such as Jacqueline Lee “Jackie” Kennedy Onassis (née Bouvier) and Bianca Jagger (born Bianca Pérez-Mora Macias), who were IT Girls of their respective generations. In fact I assume there have been IT Girls as long as there has been human society. That is young attractive women, who became famous or even infamous purely on the strength of their appearances and social behaviour.

In the Augustan age of London at the beginning of the eighteenth century one such IT Girl was Catherine Barton who’s beauty was celebrated at the Kit-Kat Club, drinking den of the Whig Party grandees, in the following verse[1]:

At Barton’s feet the God of Love

His Arrows and his Quiver lays,

Forgets he has a Throne above,

And with this lovely Creature stays.

Not Venus’ Beauties are more bright,

But each appear so like the other,

That Cupid has mistook the Right,

And takes the Nymph to be his Mother.

Apparently the only image of the young Catherine Barton Source: Wikimedia Commons

Apparently the only image of the young Catherine Barton
Source: Wikimedia Commons

Now those not already in the know are probably wondering why I’m wittering on about an eighteenth-century It Girl instead of the history of science, especially in the first part of my traditional Christmas Trilogy, which is normally dedicated to Isaac Newton who was born 25 December 1642 (os). The answer is very simple, because the charming Catherine Barton was Newton’s niece, the daughter of his half sister Hannah Baton née Smith, and his housekeeper for part of the thirty years that he lived in London.

It is not know for certain when Newton brought his niece, who was born in 1679, from her native Lincolnshire to look after his house in London but not before 1696 when he first moved there himself and probably not later than 1700, however she stayed with her uncle until she married John Conduitt in 1717.

As well as being the toast of London’s high society Catherine Barton played an important part in Newton’s London life. For example she was closely acquainted with the satirist Jonathan Swift and it was through his friendship with Barton that the Tory Swift approached the Whig Newton in 1713 to try to persuade him to relinquish the Mastership of the Mint, an important political sinecure that the Tories wished to bestow on one of their own, in exchange for a state pension of £2,000 per annum, a very large sum of money. An offer than Newton simply refused remaining Master of the Mint until his death.

Catherine’s fame or maybe notoriety extended beyond London to the continent. Rémond de Monmort, a member of the French Regency Council, who met her in 1716 whilst visiting Newton later wrote of her, “I have retained the most magnificent idea in the world of her wit and her beauty”. More famously Voltaire wrote of her:

I thought in my youth that Newton made his fortune by his merit. I supposed that the Court and the city of London named him Master of the Mint by acclamation. No such thing. Isaac Newton had a very charming niece, Madame Conduitt, who made a conquest of the minister Halifax. Fluxions and gravitation would have been of no use without a pretty niece.

Voltaire was wrong. It was indeed Charles Montagu, Lord Halifax, who appointed Newton initially to the Wardenship of the Mint in 1696, the two had been friends when Montagu was a student at Cambridge in the 1680s, but this was before Newton had brought Catherine to London so Montagu could not have known her then. However Voltaire’s quip was almost certainly based on knowledge of a real scandal involving Lord Halifax and Catherine Barton.

Charles Montagu, 1st Earl of Halifax by Sir Godfrey Kneller (NPG) Source: Wikimedia Commons

Charles Montagu, 1st Earl of Halifax by Sir Godfrey Kneller (NPG)
Source: Wikimedia Commons

Halifax had become acquainted with Catherine by 1703 at the latest when he engraved a toasting glass at the Kit-Kat Club with her name and composed the following verse to her:

Stampt with her reigning Charms, this Standard Glass

Shall current through the Realms of Bacchus pass;

Full fraught with beauty shall new Flames impart,

And mint her shining Image on the Heart.


Montagu may have been a successful politician and a great economics expert but he was no poet. Toasting a beauty at the Kit-Kat Club does not constitute a scandal but Halifax’s will, originally drafted in 1706, did. In a codicil he bequeathed Catherine £3,000 and all his jewels, “as a small Token of the great Love and Affection I have long had for her”. Faced with this anything but small token, and there was worse to come, Newton’s nineteenth-century biographers were left snapping for air in their attempts to find a not scandalous explanation for this act. Later in the year he even purchased a £200 per annum annuity for her. Was she his lover, his mistress? This explanation seems to offer itself. In 1710 Mrs Mary de la Rivière Manly a Tory satirist published a satire on the Whig’s, which featured a mistress called Bartica for the Halifax figure.

As I said above, the situation got worse in 1713 when Halifax revoked the first codicil and drew up a new one bequeathing £5,000 to Mrs Barton with the grant during her life of the rangership and lodge of Bushey Park and all its furnishings, to enable her to maintain the house and garden, the manor of Apscourt in Surrey. “These Gifts and Legacies, I leave to her as a Token of the sincere Love, Affection, and Esteem I have long had for her Person, and as a small Recompence for the Pleasure and Happiness I have had in her Conversation”.

Flamsteed, always eager to to get in a jibe against Newton, writing to Abraham Sharp on hearing of the bequest after Halifax’s death said sarcastically that it was given to Mrs Barton “for her excellent conversation”. In his desperate attempt to avoid the obvious implications for the morality of the Newton household, Augustus De Morgan, in his Newton biography, constructed a secrete marriage between Catherine and Halifax to explain the level of the bequest, which now, including the worth of the house, stood at about £25,000, a very large sum indeed. However when Catherine married John Conduitt, a retired soldier, following a whirlwind romance in 1717, she gave her status as spinster and not widow. Newton appeared to have no problems with the bequest, ever a shrewd businessman rather than a moralist, as he assisted Catherine with negotiations with Halifax’s heirs to settle the bequest.

Catherine is also one of two sources for the infamous apple story, the other being William Stukeley, Newton’s personal physician in his later life. Her version of the story appears in her husbands never finished or published memoir of Newton’s life and more importantly, it was she who told the story to Voltaire, who published it and thus started the legend.

Newton spent his last days living with the Conduitts and it fell to Catherine’s husband John to divide up the spoils amongst the various half brothers and sisters and their offspring. These eager to screw as much as possible out of Uncle Isaac’s estate forced Conduitt to sell off Newton’s extensive library of almost 2,000 volumes and wanted him to also sell off Newton’s papers convinced that anything connected with the great man would fetch a good price. Conduitt persuaded them to let the papers be sorted and evaluated for publication and in the end only Newton’s Chronology, an original draft of Principia and his Observations upon the Prophecies were printed and published the rest of his papers becoming the property of Catherine and her husband. After their deaths the papers passed to their daughter Catherine, who married the Hon. John Wallop, Viscount Lymington. Their son became the second Earl of Portsmouth and thus Newton’s papers were passed down through the years by the Portsmouth family who eventually disposed of them in the 1930s, but what became of them then is another story.

Female beauty and glamour are not things that one would normally think of if somebody mentions the name of Isaac Newton, but through the famous witty Mrs Barton these things did indeed play a role in Newton’s later life.








[1] This and all other quotes, as indeed the meat of the story, are all taken from Richard Westfall’s excellent Newton biography Never at Rest


Filed under History of science, Newton, Uncategorized

The greatest villain in the history of science?

In the popular version of the so-called astronomical revolution Andreas Osiander, who was born on the 19th December 1496 or 1498, is very often presented as the greatest villain in the history of science because he dared to suggest in the ad lectorum (to the reader) that he added to the front of Copernicus’ De revolutionibus that one could regard the heliocentric hypothesis as a mere mathematical model and not necessarily a true representation of the cosmos. Is the judgement of history just and who was Andreas Osiander anyway?

Andreas Osiander portrait by Georg Pencz Source: Wikimedia Commons

Andreas Osiander portrait by Georg Pencz
Source: Wikimedia Commons

Andreas Osiander was born in Gunzenhausen, a small town to the south of Nürnberg, the son of Endres Osannder a smith and Anna Herzog. His father was also a local councillor, who later became mayor. He entered the University of Ingolstadt in 1515 where he, amongst other things, studied Hebrew under Johannes Reuchlin one of the greatest humanist scholars in Germany at that time, the great uncle from Philipp Melanchthon and the leading Hebrew scholar of the age. In 1520 Osiander was ordained a priest and called to Nürnberg to teach Hebrew at the Augustinian Cloister. This had been a major centre for reformatory debate for a number of years and it is here that Osiander became a religious reformer. In 1522 he was appointed preacher at the Saint Lorenz church in Nürnberg and became the leading voice for religious reform in the city. In 1525 Nürnberg, a city-state, became the first state to officially adopt the Lutheran Protestant religion, and Osiander became a highly influential and powerful figure. He was largely responsible for converting Albrecht of Prussia to Protestantism and also had a major influence on Thomas Cranmer, later Archbishop of Canterbury and author of the Common Book of Prayer. A trivial pursuits fact is that Cranmer married one of Osiander’s nieces.

Osiander’s first links with the printer/publisher Johannes Petreius was as the author of polemical religious tracts, which Petreius published. How he became an editor for Petreius is not know. It is also not known when and where Osiander developed his interest in and knowledge of the mathematical sciences. What is certain is that it was Osiander who, after Petreius had discovered Cardano’s books at the book fair in Frankfurt, who wrote to the Italian mathematician/physician/philosopher on Petreius’ behalf offering to publish his books in Germany; an offer that Cardano was more than willing to accept. Osiander then became the editor of those books of Cardano’s that Petreius published over the years; a service for which Cardano thanks him very warmly in the preface to one of his books, praising him highly for his abilities as an editor.

When Rheticus published his account of Copernicus’ heliocentric astronomy in his Narratio Prima, in the form of an open letter addressed to Johannes Schöner, another of Petreius’ editors, it was Osiander who wrote to Rheticus on behalf of the publishing house showing great interest in the cyclical astrological theory of history outlined by Rheticus in his little book.

After Rheticus had brought the manuscript of De revolutionibus to Nürnberg, Philipp Melanchthon pressured him to take up the professorship for mathematics in Leipzig and Osiander took over the task of seeing the text through the press. It is here that Osiander added the ad lectorum to the finished book, which has, over the centuries, pulled down so much odium on his head. Is this harsh judgement of his actions justified or have we, as I believe, been blaming the wrong man for the last four and a half centuries.

In the early days of printing there was no such thing as authors rights. The rights to a book lay with the printer/publisher, who was also the first port of call should the authorities decide that a book or pamphlet was seditious, blasphemous or in any other way unacceptable. And please remember our concepts of freedom of speech simply did not exist in sixteenth-century Europe. The ad lectorum was added to De revolutionibus certainly with Petreius’ knowledge and almost certainly at his instigation. This is confirmed by his reaction as Copernicus’ friend Bishop Tiedemann Giese complained to the city council of Nürnberg about the inclusion of the ad lectorum in his dead friend’s magnum opus. Consulted by the council on the subject Petreius basically flew off the handle and told them to get stuffed, it was his book and he’d put what the hell he liked in it.

Osiander continued to edit the books of Cardano for Petreius but in 1548 the city of Nürnberg accepted the Augsburg Interim an edict issued by Charles V, Holy Roman Emperor, who had just won a decisive victory against the Protestant forces, forcing the Protestant states within the Empire to revert to Catholicism. In a moonlight flit Osiander fled the city of Nürnberg and made his way north to Königsberg, where Albrecht appointed him professor of theology at the newly established university. This caused much bad blood, as Osiander was not a qualified theologian. In this position Osiander became embroiled in a major theological dispute with the supporters of Melanchthon in Wittenberg over the doctrine of justification. This dispute is known in German church history as the Osiander Dispute and led to a schism between the two parties, with Osiander basically forming his own branch of Protestantism.

Osiander died in 1552 a controversial figure both in the history of religion and the history of science. However as I have sketched above I think his bad reputation in the history of science is not really justified and the real villain of the piece, if there is one, is Johannes Petreius. I say if there is one, because many historians are of the opinion that the ad lectorum saved the De revolutionibus from being condemned straight away, when it was published, and allowed the heliocentric hypothesis it contained to spread relatively unhindered and become established.



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

Mensis or menstruation?

I recently stumbled upon this rather charming rant by Anglo-Danish comedian, writer, broadcaster and feminist Sandi Toksvig.

Women's Calendar


Now I’m a very big fan of Ms Toksvig and was very sad when she retired as presenter of BBC Radio 4’s excellent News Quiz, so I don’t want to give the impression that I’m trying to put her down, but if she had know a little bit more about the early history of the calendar then she might not have jumped to the conclusion that this supposed bone calendar must have been made by a woman.

Before I start to explain why Ms Toksvig might be mistaken in her assumption that this purported primitive calendar came from the hands of a woman I would like to waste a few words on all such artefacts. There are a number of bone and stone objects of great antiquity bearing some number of scratches, incisions, notches, indentations or other forms of apparent marking and someone almost always comes along and declares them to be purposely created mathematical artefacts with one or other function. I must say that being highly sceptical by nature I treat all such claims with more than a modicum of wariness. Even assuming that the markings were made by a human hand might they not have been made in an idle moment by a Neolithic teenager trying out his newly acquired flint knife or in the case of our incised bone by an early musician making himself scraper to accompany the evening camp fire sing-a-long? What I’m am saying is that there are often multiple possible explanations for the existence of such marked artefacts and regarding them as signs of some sort of mathematical activity is only one of those possibilities.

However, back to Ms Toksvig and her revelation. She is of course assuming that the twenty-eight incisions are the result of a women counting off the days between her periods, the menstrual cycle being roughly twenty-eight days for most women. Now if Ms Toksvig had taken her thoughts a little further she might have realised that the word menstruation derives from the Latin word for month, which is mensis: a month being originally a lunar month which, depending on how you measure it, has approximately twenty-eight days. In fact much human thought has been expended over the centuries over the fact that a lunar month and the menstrual circle have the same length.

What we have here with this incised bone could well be not a menstrual record, as Ms Toksvig seems to assume, but a mensis record or part of a lunar calendar. This supposition is lent credence by the fact that, with the very notable exception of the ancient Egyptian calendar, all early cultures and civilisations had lunar and not solar calendars including the ancient Romans before Gaius Julius Caesar borrowed the Egyptian solar calendar, the forerunner of our own Gregorian one.

Assuming that the archaeologist or anthropologist who decided that said bone was a primitive calendar was right and it is not the idle whittling of some bored stone-age teenager, we of course still have no idea whether it was the work of a man or a woman.


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

Hans Holbein and the Nürnberg–Ingolstadt–Vienna Renaissance mathematical nexus.

There is a strong tendency, particularly in the popular history of science, to write about or present scientists as individuals. This leads to a serious distortion of the way that science develops and in particular propagates the lone genius myth. In reality science has always been a collective endeavour with its practitioners interacting in many different ways and on many different levels. In the Renaissance, when travelling from one end of Europe to the other would take weeks and letters often even longer, one might be excused for thinking that such cooperation was very low level but in fact the opposite was the truth, with scholars in the mathematical sciences exchanging information and ideas throughout Europe. A particularly strong mathematical nexus existed in the Southern German speaking area between the cities of Nürnberg, Ingolstadt and Vienna in the century between 1450 and 1550. Interestingly two of the paintings of the Northern Renaissance artist Hans Holbein the Younger open a door into this nexus.

Holbein (c. 1497–1543) was born in Augsburg the son of the painter and draughtsman Hans Holbein the Elder. As a young artist he lived and worked for a time in Basel where he became acquainted with Erasmus and worked for the printer publisher Johann Froben amongst others. Between 1526 and 1528 he spent some time in England in the household of Thomas More and it is here that he painted the second portrait I shall be discussing. The next four years find him living in Basel again before he returned to England in 1532 where he became associated with the court of Henry VIII, More having fallen out of favour. It was at the court that he painted, what is probably his most well know portrait, The Ambassadors in 1533.

Hans Holbein The Ambassadors Source: Wikimedia Commons

Hans Holbein The Ambassadors
Source: Wikimedia Commons

The painting shows two courtiers, usually identified as the French Ambassador Jean de Dinteville and Georges de Selve, Bishop of Lavaur standing on either side of a set of shelves laden with various books and instruments. There is much discussion was to what the instruments are supposed to represent but it is certain that, whatever else they stand for, they represent the quadrivium, arithmetic, geometry music and astronomy, the four mathematical sciences taught at European medieval universities. There are two globes, on the lower shelf a terrestrial and on the upper a celestial one. The celestial globe has been positively identified, as a Schöner globe and the terrestrial globe also displays characteristics of Schöner’s handwork.

Terrestrial Globe The Ambassadors Source Wikimedia Commons

Terrestrial Globe The Ambassadors
Source Wikimedia Commons

Celestial Globe The Ambassadors Source Wikimedia Commons

Celestial Globe The Ambassadors
Source Wikimedia Commons

Johannes Schöner (1477–1547) was professor for mathematics at the Egidienöberschule in Nürnberg, the addressee of Rheticus’ Narratio Prima, the founder of the tradition of printed globe pairs, an editor of mathematical texts for publication (especially for Johannes Petreius the sixteenth centuries most important scientific publisher) and one of the most influential astrologers in Europe. Schöner is a central and highly influential figure in Renaissance mathematics.

On the left hand side of the lower shelf is a copy of Peter Apian’s Ein newe und wolgegründete underweisung aller Kauffmanns Rechnung in dreyen Büchern, mit schönen Regeln und fragstücken begriffen (published in Ingolstadt in 1527) held open by a ruler. This is a popular book of commercial arithmetic, written in German, typical of the period. Peter Apian (1495–1552) professor of mathematics at the University of Ingolstadt, cartographer, printer-publisher and astronomer was a third generation representative of the so-called Second Viennese School of Mathematics. A pupil of Georg Tannstetter (1482–1535) a graduate of the University of Ingolstadt who had followed his teachers Johannes Stabius and Andreas Stiborious to teach at Conrad Celtis’ Collegium poetarum et mathematicorum, of which more later. Together Apian and Tannstetter produced the first printed edition of the Optic of Witelo, one of the most important medieval optic texts, which was printed by Petreius in Nürnberg in 1535. The Tannstetter/Apian/Petreius Witelo was one of the books that Rheticus took with him as a present for Copernicus when he visited him in 1539. Already, a brief description of the activities of Schöner and Apian is beginning to illustrate the connection between our three cities.

Apian's Arithmetic Book The Ambassadors Source: Wikimedia Commons

Apian’s Arithmetic Book The Ambassadors
Source: Wikimedia Commons

When Sebastian Münster (1488–1552), the cosmographer, sent out a circular requesting the cartographers of Germany to supply him with data and maps for his Cosmographia, he specifically addressed both Schöner and Apian by name as the leading cartographers of the age. Münster’s Cosmographia, which became the biggest selling book of the sixteenth century, was first published by Heinrich Petri in Basel in 1544. Münster was Petri’s stepfather and Petri was the cousin of Johannes Petreius, who learnt his trade as printer publisher in Heinrich’s printing shop in Basel. The Petri publishing house was also part of a consortium with Johann Amerbach and Johann Froben who had employed Hans Holbein in his time in Basel. Wheels within wheels.

The, mostly astronomical, instruments on the upper shelf are almost certainly the property of the German mathematician Nicolaus Kratzer (1487–1550), who is the subject of the second Holbein portrait who will be looking at.

Nicolas Kratzer by Hans Holbein Source: Wikimedia Commona

Nicolas Kratzer by Hans Holbein
Source: Wikimedia Commona

Born in Munich and educated at the universities of Cologne and Wittenberg Kratzer, originally came to England, like Holbein, to become part of the Thomas More household, where he was employed as a tutor for More’s children. Also like Holbein, Kratzer moved over to Henry VIII’s court as court horologist or clock maker, although the clocks he was responsible for making were more probably sundials than mechanical ones. During his time as a courtier Kratzer also lectured at Oxford and is said to have erected a monumental stone sundial in the grounds of Corpus Christi College. One polyhedral sundial attributed to Kratzer is in the Oxford Museum for the History of Science.

Polyhedral Sundial attributed to Nicolas Kratzer Source: MHS Oxford

Polyhedral Sundial attributed to Nicolas Kratzer
Source: MHS Oxford

In 1520 Kratzer travelled to Antwerp to visit Erasmus and here he met up with Nürnberg’s most famous painter Albrecht Dürer, who regular readers of this blog will know was also the author of a book on mathematics. Dürer’s book contains the first printed instructions, in German, on how to design, construct and install sundials, so the two men will have had a common topic of interest to liven there conversations. Kratzer witnessed Dürer, who was in Antwerp to negotiate with the German Emperor, painting Erasmus’ portrait and Dürer is said to have also drawn a portrait of Kratzer that is now missing. After Kratzer returned to England and Dürer to Nürnberg the two of them exchanged, at least once, letters and it is Kratzer’s letter that reveals some new connections in out nexus.

Albrecht Dürer selfportrait Source: Wikimedia Commons

Albrecht Dürer selfportrait
Source: Wikimedia Commons

In his letter, from 1524, Kratzer makes inquires about Willibald Pirckheimer and also asks if Dürer knows what has happened to the mathematical papers of Johannes Werner and Johannes Stabius who had both died two years earlier.

Willibald Pirckheimer (1470–1530) a close friend and patron of Dürer’s was a rich merchant, a politician, a soldier and a humanist scholar. In the last capacity he was the hub of a group of largely mathematical humanist scholars now known as the Pirckheimer circle. Although not a mathematician himself Pirckheimer was a fervent supporter of the mathematical sciences and produced a Latin translation from the Greek of Ptolemaeus’ Geōgraphikḕ or Geographia, Pirckheimer’s translation provided the basis for Sebastian Münster’s edition, which was regarded as the definitive text in the sixteenth century. Stabius and Werner were both prominent members of the Pirckheimer circle.

Willibald Pirckheimer by Albrecht Dürer Source: Wikimedia Commons

Willibald Pirckheimer by Albrecht Dürer
Source: Wikimedia Commons

The two Johanneses, Stabius (1450–1522) and Werner (1468–1522), had become friends at the University of Ingolstadt where the both studied mathematics. Ingolstadt was the first German university to have a dedicated chair for mathematics. Werner returned to his hometown of Nürnberg where he became a priest but the Austrian Stabius remained in Ingolstadt, where he became professor of mathematics. The two of them continued to correspond and work together and Werner is said to have instigated the highly complex sundial on the wall of the Saint Lorenz Church in Nürnberg, which was designed by Stabius and constructed in 1502.

St Lorenz Church Nürnberg Sundial 1502 Source: Astronomie in Nürnberg

St Lorenz Church Nürnberg Sundial 1502
Source: Astronomie in Nürnberg

It was also Werner who first published Stabius’ heart shaped or cordiform map projection leading to it being labelled the Werner-Stabius Projection. This projection was used for world maps by Peter Apian as well as Oronce Fine, France’s leading mathematicus of the sixteenth century and Gerard Mercator, of whom more, later. The network expands.

Mercator cordiform world map 1538 Source: American Geographical Society Library

Mercator cordiform world map 1538
Source: American Geographical Society Library

In his own right Werner produced a partial Latin translation from the Greek of Ptolemaeus’ Geographia, was the first to write about prosthaphaeresis (a trigonometrical method of simplifying calculation prior to the invention of logarithms), was the first to suggest the lunar distance method of determining longitude and was in all probability Albrecht Dürer’s maths teacher. He also was the subject of an astronomical dispute with Copernicus.

Johannes Werner Source: Wikimedia Commons

Johannes Werner
Source: Wikimedia Commons

Regular readers of this blog will know that Stabius co-operated with Albrecht Dürer on a series of projects, including his famous star maps, which you can read about in an earlier post here.

Johannes Statius Portrait by Albrecht Dürer Source: Wikimedia Commons

Johannes Statius Portrait by Albrecht Dürer
Source: Wikimedia Commons

An important non-Nürnberger member of the Pirckheimer Circle was Conrad Celtis (1459–1508), who is known in Germany as the arch-humanist. Like his friend Pirckheimer, Celtis was not a mathematician but believed in the importance of the mathematical sciences. Although already graduated he spent time in 1489 on the University of Kraków in order to get the education in mathematics and astronomy that he couldn’t get at a German university. Celtis had spent time at the humanist universities of Northern Italy and his mission in life was to demonstrate that Germany was just as civilised and educated as Italy and not a land of barbarians as the Italians claimed. His contributions to the Nuremberg Chronicle can be viewed as part of this demonstration. He believed he could achieve his aim by writing a comprehensive history of Germany including, as was common at the time its geography. In 1491/92 he received a teaching post in Ingolstadt, where he seduced the professors of mathematics Johannes Stabius and Andreas Stiborius (1464–1515) into turning their attention from astrology for medicine student, their official assignment, to mathematical cartography in order to help him with his historical geography.

Conrad Celtis Source: Wikimedia Commons

Conrad Celtis
Source: Wikimedia Commons

Unable to achieve his ends in Ingolstadt Celtis decamped to Vienna, taking Stabius and Stiborius with him, to found his Collegium poetarum et mathematicorum as mentioned above and with it the so-called Second Viennese School of Mathematics; the first had been Peuerbach and Regiomontanus in the middle of the fifteenth century. Regiomontanus spent the last five years of his life living in Nürnberg, where he set up the world’s first scientific publishing house. Stiborius’ pupil Georg Tannstetter proved to be a gifted teacher and Peter Apian was by no means his only famous pupil.

The influence of the Nürnberg–Ingolstadt–Vienna mathematicians reached far beyond their own relatively small Southern German corridor. As already stated Münster in Basel stood in contact with both Apian and Schöner and Stabius’ cordiform projection found favour with cartographers throughout Northern Europe. Both Apian and Schöner exercised a major influence on Gemma Frisius in Louvain and through him on his pupils Gerard Mercator and John Dee. As outlined in my blog post on Frisius, he took over editing the second and all subsequent editions of Apian’s Cosmographia, one of the most important textbooks for all things astronomical, cartographical and to do with surveying in the sixteenth century. Frisius also learnt his globe making, a skill he passed on to Mercator, through the works of Schöner. Dee and Mercator also had connections to Pedro Nunes (1502–1578) the most important mathematicus on the Iberian peninsular. Frisius had several other important pupils who spread the skills in cosmography, and globe and instrument making that he had acquired from Apian and Schöner all over Europe.

Famously Rheticus came to Nürnberg to study astrology at the feet of Johannes Schöner, who maintained close contacts to Philipp Melanchthon Rheticus patron. Schöner was the first professor of mathematics at a school designed by Melanchthon. Melanchthon had learnt his mathematics and astrology at the University of Tübingen from Johannes Stöffler (1452–1531) another mathematical graduate from Ingolstadt.

Kupferstich aus der Werkstatt Theodor de Brys, erschienen 1598 im 2. Bd. der Bibliotheca chalcographica Source: Wikimedia Commons

Kupferstich aus der Werkstatt Theodor de Brys, erschienen 1598 im 2. Bd. der Bibliotheca chalcographica
Source: Wikimedia Commons

Another of Stöffler’s pupils was Sebastian Münster. During his time in Nürnberg Rheticus became acquainted with the other Nürnberger mathematicians and above all with the printer-publisher Johannes Petreius and it was famously Rheticus who brought the manuscript of Copernicus’ De revolutionibus to Nürnberg for Petreius to publish. Rheticus says that he first learnt of Copernicus’s existence during his travels on his sabbatical and historians think that it was probably in Nürnberg that he acquired this knowledge. One of the few pieces of astronomical writing from Copernicus that we have is the so-called Letter to Werner. In this manuscript Copernicus criticises Werner’s theory of trepidation. Trepidation was a mistaken belief based on faulty data that the rate of the precession of the equinoxes is not constant but varies with time. Because of this highly technical dispute amongst astronomers Copernicus would have been known in Nürnberg and thus the assumption that Rheticus first heard of him there. Interestingly Copernicus includes observations of Mercury made by Bernhard Walther (1430–1504), Regiomontanus partner, in Nürnberg; falsely attributing some of them to Schöner, so a connection between Copernicus and Nürnberg seems to have existed.

In this brief outline we have covered a lot of ground but I hope I have made clear just how interconnected the mathematical practitioners of Germany and indeed Europe were in the second half of the fifteenth century and the first half of the sixteenth. Science is very much a collective endeavour and historians of science should not just concentrate on individuals but look at the networks within which those individual operate bringing to light the influences and exchanges that take place within those networks.


Filed under History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, History of science, Renaissance Science

The Renaissance Mathematicus “Live & Uming”

Those of you with nothing better to do can listen to a podcast of the Renaissance Mathematicus (that’s me folks!) searching for words, desperately trying to remember names, uming & ahing, thinking on his feet (I was actually sitting down the whole time) and generally stumbling his way through an eighty minute spontaneous, unrehearsed, live interview with Scott Gosnell of Bottle Rocket Science on such scintillated topics, as why the Pope got his knickers in a twist over Galileo or that notorious seventeenth century religious fanatic Isaac Newton. In fact the same boring load of old codswallop that you can read at you leisure here on this blog. As I say if you have nothing more exciting to do, such as watching paint dry or listening to the grass grow, then go listen.

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