Category Archives: History of Cartography

The House of Blaeu vs.The House of Hondius – The Battle of the Globes and Atlases

There is a South to North trajectory in the evolution of the modern mathematical cartography in Europe over the two hundred years between fourteen hundred and sixteen hundred. Ptolemaic mathematical cartography re-entered Europe in Northern Italy with the first translation into Latin of his Geographia by Jacobus Angulus in 1406. Following this the first modern first modern cartographers, including Paolo dal Pozzo Toscanelli, were also situated in Northern Italy. By the middle of the fifteenth century the main centre of cartographical activity had moved north to Vienna and was centred around Kloster-Neuburg and the University with its First Viennese School of Mathematics, Georg von Peuerbach and Johannes Regiomontanus. Towards the end of the century printed editions of Ptolemaeus’ work began to appear both north and south of the Alps. The beginning of the sixteenth century saw the main centres of cartographic development in the Southern German sphere. Two principle schools are identifiable, the Nürnberg-Vienna school, whose main figures are Johannes Stabius, Peter Apian and Johannes Schöner, and the South-Western school with Waldseemüller and Ringmann in Saint-Dié-des-Vosges and Sebastian Münster in Basel. Again by the middle of the century the centre had once again moved northwards to Leuven and the Flemish school founded by Gemma Frisius and including the two great atlas makers Abraham Ortelius and Gerard Mercator. At the start of the seventeenth century the final step northwards had been taken and the new state of The United Provinces (The Netherlands) had taken the lead in modern cartography. This final step is the subject of this post.

Willem Janszoon Blaeu was born into a prosperous herring trading family in Alkmaar or Uitgeest in 1471. As would have been expected he was sent at an early age to Amsterdam to learn the family trade but it did not appeal to him and he worked instead as a carpenter and clerk in the office of his cousin. In late 1595 his life took a radical turn when he travelled to Hven to study astronomy under Tycho Brahe. It is not known what level of foreknowledge Blaeu took to Hven with him but he spent six months there studiously learning astronomy, instrument making, geodesy and cartography with Tycho and his staff. When he started his observing marathon Tycho had had a large brass globe constructed on which he, over the years, engraved the positions of all the stars that he had measured. Blaeu was given permission to transfer this data to a globe of his own. In 1596 he returned to Alkmaar and his wife Maertgen Cornilisdochter who bore his eldest son Joan on 21 September. On 21 February 1598 Blaeu in Alkmaar and Tycho in Hamburg both observed a lunar eclipse to determine the relative longitude of the two cities.

Portrait of Willem Janszoon Blaeu Artist unknown

Sometime in 1598/9 Blaeu took his family to Amsterdam and set up shop as a printer, instrument maker, globe maker and cartographer; making his first celestial globe, 34 cm diameter, for Adriaan Anthoniszoon, using Tycho’s data; this was the first publication of that data. However Blaeu’s new career was not going to be simple as he had an established competitor, Jocodus Hondius.

Jocodus Hondius was born Joost de Hondt in Wakken and grew up in Ghent, both now in Belgium, on 14 October 1563. He received an education in mathematics and learnt engraving, drawing and calligraphy. He had already established himself as a successful engraver when he was forced by the Spanish, as a Calvinist, to flee to London in 1584. In London he worked for and with Richard Hakluyt and Edward Wright and expanded his knowledge of geography and cartography through contact with the English explorers Francis Drake, Thomas Cavendish and Walter Raleigh. Around 1589 he published a wall map in London showing Drake’s voyage around the world. In 1593 he moved back to The Netherlands, establishing himself in Amsterdam.

Self-portrait of Jodocus Hondas taken from one of his maps

Portrait of Francis Drake by Jodocus Hondas from his Drake world map

He formed an alliance with the Plantin printing house in Leiden for who he made several globes. In 1602 he matriculated at the University of Leiden to study mathematics. In 1604 he made the most important decision of his career in that he bought the copper printing plates of the of both Mercator’s edition of Ptolemaeus’ Geographia and Mercator’s Atlas from his heirs.He published a new edition of Mercator’s Ptolemaeus, Claudïï Ptolemaeï Alexandrini geographicae libri octo graecog latini, in the same year. He set up his own publishing house in Amsterdam in December 1604. In the sixteenth century Mercator’s Atlas had failed to establish itself in a market dominated by Ortelius’ Theatum Orbis Terrarum, however Hondius republished it in 1606 with 36 new maps and it became a best seller.

Atlas sive Cosmographiae Meditationes de Fabrica Mundi et Frabicati Figura
Mercator (left) and Hondius (right) shown working together on tittle page of 1630 Atlas
Slightly ironical as they never met and both were dead by then.

Meanwhile Blaeu had established himself as a globe maker and astronomer. Following the tradition established by Johannes Schöner and continued by Mercator Blaeu issued a pair of 23.5 cm globes, terrestrial and celestial, in 1602. His rival Hondius introduced the southern constellation on a celestial globe produced in cooperation with the astronomer-cartographer Petrus Plancius in 1598. Blaeu followed suite in 1603. Hondius produced a pair of 53.5 cm globes in 1613; Blaeu countered with a pair of 68 cm globes in 1616, which remained the largest globes in production for over 70 years.

Hondas celestial globe 1600
Source: Linda Hall Library

A matching pair of Blaeu globes

As an astronomer Blaeu discovered the star P Cygni, only the third variable star to be discovered. In 1617 Willebrord Snellius published his Eratosthenes Batavus (The Dutch Eratosthenes) in which he described his measurement of a meridian arc between Alkmaar and Bergen op Zoom. This was done in consultation with Blaeu, who had learnt the art of triangulation from Tycho, using a quadrant, with a radius of more than 2 metres, constructed by Blaeu. Blaeu specialised in publishing books on navigation beginning in 1605 with his Nieuw graetbouck and established himself as the leading Dutch publisher of such literature.

Source: Wikimedia Commons

Title page
Source: Wikimedia Commons

Quadrant constructed by Blaeu for Snellius now in Museum Boerhaave in Leiden
Source: Wikimedia Commons

Jodocus Hondius died in 1612 and his sons Jodocus II and Henricus took over the publish house later going into partnership with Jan Janszoon their brother in law. They continued to publish new improved version of the Mercator-Hondius Atlas. Blaeu had already established himself as the successful publisher of wall maps when he began planning a major atlas to rival that of the house of Hondius. That rivalry is also reflected in a name change that Blaeu undertook in 1617. Up till then he had signed his work either Guilielmus Janssonius or Willem Janszoon, now he started add the name Blaeu to his signature probably to avoid confusion with Jan Janszoon (Janssonius), his rival.

Jan Janszoon Original copperplate from his Atlas Novus 1647

In 1630 the strangest episode in the battle of the globes and atlases took place when Jodocus II’s widow sold 37 of the copper plates of the Mercator-Hondius Atlas to Willem Blaeu. He published them together with maps of his own in his Atlantic Appendix in 1631. In 1636 Blaeu published the first two volumes of his own planned world atlas as Atlas Novus or Theatrum Orbis Terrarum, thus reviving the old Ortelius name.

In 1633 the States General (the government of the United Provinces) appointed Blaeu mapmaker of the Republic. In the same year he was appointed cartographer and hydrographer of the Vereenighde Oostindische Compagnie (VOC) – The Dutch East India Company. His son Joan inherited the VOC position, as did his grandson Joan II; The Blaeu family held this prestigious position from 1633 till 1712.

Willem Blaeu had great plans to publish several more volumes of his world atlas but he didn’t live to see them realised, dying 21 October 1638. The publishing house passed to his two sons Joan (1596-1673) and Cornelis (c.1610-1644). The last two volumes prepared by Willem appeared in 1640 and 1645. Joan completed his father’s atlas with a sixth volume in 1655.

Along with all his other achievements Willem Janszoon Blaeu made a substantial improvement to the mechanical printing press by adding a counter weight to the pressure bar in order to make the platen rise automatically. This ‘Blaeu’ or ‘Dutch’ press became standard throughout the low countries and was also introduced into England. The first printing press introduced into America in 1639 was a Blaeu press.

Although he held a doctorate in law, Joan devoted his life to the family cartographic publishing business. In 1662 he set the high point of the atlas battle with the House of Hondius with the publication of the Atlas Maior; containing 600 double page maps and 3,000 pages of text it was the most spectacular atlas of all time. Along with its lavish maps the Atlas Maior contained a map of Hven and pictures of the house and stellar observatory on the island where Willem Janszoon Blaeu first learnt his trade. Whereas Willem was careful not to take sides in the dispute between the different systems for the cosmos – geocentric, heliocentric, geo-heliocentric – in the Atlas Maior, Joan committed to heliocentricity.

Joan Blaeu. By J.van Rossum
Source: Wikimedia Commons

Blaeu Atlas Maior 1662-5, Volume 1
Nova Et Accvratissima Totius Terrarvm Orbis Tabvla
Source: National Library of Scotland

The rivalry between the Houses of Hondius and Blaeu, pushing each other to new heights of quality and accuracy in their maps and globes led to them totally dominating the European market in the first half of the sixteenth century, particularly in the production of globes where they almost had a monopoly. Globes in the period, which weren’t from one of the Amsterdam producers, were almost always pirated copies of their products.

As an interesting footnote, as with all things mathematical England lagged behind the continent in cartography and globe making. Although there had been earlier single globes made in on the island, England’s first commercial producer of terrestrial and celestial globes, Joseph Moxon, learnt his trade from Willem Janszoon Blaeu in Amsterdam. In 1634 Blaeu had published a manual on how to use globes, Tweevoudigh onderwijs van de Hemelsche en Aerdsche globen (Twofold instruction in the use of the celestial and terrestrial globes). In the 1660s, Moxon published his highly successful A Tutor to Astronomie and Geographie. Or an Easie and speedy way to know the Use of both the Globes, Cœlestial and Terrestrial : in six Books, which went through many editions, however the first edition was just an English translation of Blaeu’s earlier manual.

The Dutch painter Jan Vermeer often featured globes and maps in his paintings and it has been shown that these are all reproductions of products from the Blaeu publishing house.

Vermeer’s Art of Painting or The Allegory of Painting (c. 1666–68)
With Blaeu Wall Map
Google Art Project Source: Wikimedia Commons

Jan Vermeer The Astronomer with Blaeu celestial globe and right on the wall a Blaeu wall map
Source: Wikimedia Commons

Jan Vermeer The Geographer with Blaeu terrestrial globe and again right a Blaeu wall map
Source: Wikimedia Commons

The Blaeu wall map used in Vermeers’ The Astronomer and The Geographer

We tend to emphasise politicians, artists and big name scientists, as the people who shape culture in any given age but the cartographic publishing houses of Hondius and Blaeu made significant contributions to shaping the culture of The United Provinces in the so-called Dutch Golden Age and deserve to be much better known than they are.

 

 

 

 

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

All at sea

As I’ve said more than once in the past, mathematics as a discipline as we know it today didn’t exist in the Early Modern Period. Mathematics, astronomy, astrology, geography, cartography, navigation, hydrography, surveying, instrument design and construction, and horology were all facets or sub-disciplines of a sort of mega-discipline that was the stomping ground of the working mathematicus, whether inside or outside the university. The making of sea charts – or to give it its technical name, hydrography – combines mathematics, geography, cartography, astronomy, surveying, and the use of instruments so I am always happy to add a new volume on the history of sea charts to my collection of books on cartography and hydrography.

I recently acquired the “revised and updated” reissue of Peter Whitfield’s Charting the Oceans, a British Library publication.

The original edition from 1996 carried the subtitle Ten Centuries of Maritime Maps (missing from the new edition) and this is what Whitfield delivers in his superb tome. The book has four sections: Navigation before Charts, The Sea-Chart and the Age of Exploration, Sea-Charts in Europe’s Maritime Age and War, Empire and Technology: The Last 200 years. As can be seen from these section titles Whitfield not only deals with the details of the hydrography and the charts produced but defines the driving forces behind the cartographic developments: explorations, trade, war and colonisation. This makes the book to a valuable all round introduction of the subject highly recommended to anybody looking for a general overview of the topic.

However, what really makes this book very special is the illustrations.

The Nile Delta, c. 1540, from Piri Re’is Kitab-i Bahriye
Charting the Oceans page 90

A large format volume, more than fifty per cent of the pages are adorned with amazing reproductions of the historical charts that Whitfield describes in his text.

Willem van de Velde II, Dutch Ships in a Calm, c. 1665
Charting the Oceans page 132

Beautifully photographed and expertly printed the illustrations make this a book to treasure. Although not an academic text, in the strict sense, there is a short bibliography for those, whose appetites wetted, wish to delve deeper into the subject and an excellent index. Given the quality of the presentation the official British Library shop price of £14.99 is ridiculously low and a real bargain. If you love maps all I can say is buy this book.

Title page to the English edition of Lucas Janszoon Waghenaer’s Spiegheel der Zeevaert, 1588
Charting the Oceans page 109

The A Very Short Introduction series of books published by the Oxford University Press is a really excellent undertaking. Very small format 11×17 and a bit cm, they are somewhere between 100 and 150 pages long and provide a concise introduction to a single topic. One thing that distinguishes them is the quality of the authors that OUP commissions to write them; they really are experts in their field. The Galileo volume, for example, is authored by Stillman Drake, one of the great Galileo experts, and The Periodic Table: A Very Short Introduction was written by Mr Periodic Table himself, Eric Scerri. So when Navigation: A Very Short Introduction appeared recently I couldn’t resist. Especially, as it is authored by Jim Bennett a man who probably knows more about the topic then almost anybody else on the surface of the planet.

Mr Bennett does not disappoint, in a scant 135-small-format-pages he delivers a very comprehensive introduction to the history of navigation. He carefully explains all of the principal developments down the centuries and does not shy away from explaining the intricate mathematical and astronomical details of various forms of navigation.

Navigation: A Very Short Introduction page 50

The book contains a very useful seven page Glossary of Terms, a short but very useful annotated bibliography, which includes the first edition of Whitfield’s excellent tome, and a comprehensive index. One aspect of the annotated bibliography that particularly appealed to me was his comments on Dava Sobel’s Longitude; he writes:

“[It] …has the disadvantage of being very one-sided despite the more scrupulous work found in in earlier books such as Rupert T. Gould, The Marine Chronometer: Its History and Development (London, Holland Press, 1960); and Humphrey Quill, John Harrison: The Man Who Found Longitude (London, John Baker, 1966)”

I have read both of these books earlier and can warmly recommend them. He then recommends Derek Howse, Greenwich Time and the Discovery of Longitude (Oxford, Oxford University Press, 1980), which sits on my bookshelf, and Derek Howse, Nevil Maskelyne: The Seaman’s Astronomer, (Cambridge, Cambridge University Press, 1989), which I haven’t read. However it was his closing comment that I found most interesting:

“A welcome recent corrective is Richard Dunn and Rebekah Higgitt, Ships, Clocks, and Stars: The Quest for Longitude (Collins: Glasgow, 2014)”. A judgement with which, regular readers of this blog will already know, I heartily concur.

The flyleaf of the Navigation volume contains the following quote:

‘a thoroughly good idea. Snappy, small-format…stylish design…perfect to pop into your pocket for spare moments’ – Lisa Jardine, The Times

Another judgement with which I heartily concur. Although square centimetre for square centimetre considerably more expensive than Whitfield’s book the Bennett navigation volume is still cheap enough (official OUP price £7.99) not to break the household budget. For those wishing to learn more about the history of navigation and the closely related mapping of the seas I can only recommend that they acquire both of these excellent publications.

 

 

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Filed under History of Cartography, History of Mathematics, History of Navigation

One line to rule them all

A standard concept in the modern politico-military terminology is that of mission creep. This describes the, in the last sixty or seventy years often observed, phenomenon of a military intervention by a dominant power that starts with a so-called police action with a couple of hundred combatants and then within a couple of years grows to a full scale military operation involving thousands of troops and the expenditure of sums of money with an eye watering large number of zeros at the end. Famous examples of mission creep were the Americans in Viet Nam and the Russians in Afghanistan. In fact since the Second World War the American have become world champions in mission creep.

As a historian I, and I strongly suspect virtually all of my historian colleagues, experience a form of mission creep in every field of study to which I turn my attention. In fact the progress of my entire career as a historian of science has been one massive example of mission creep. It all started, at the age of sixteen, when I first learned that Isaac Newton was the (co)discoverer/inventor[1] of the calculus that I so loved at school. (Yes, I know that makes me sound a little bit strange but there’s no accounting for taste). This of course set me off on the trail of the whole history of mathematics, but that is not what I want to talk about here; let us stick with Newton. At some point I started to wonder why Newton, whom I saw as very much the theoretical mathematician and physicist, should have invented a telescope. This set me on the trail of the entire history of the telescope and because the telescope is an optical instrument, with time, the history of optics, not just in the early modern period but backwards through time into the European Middle Ages, the Islamic Empire and Antiquity. Of course Newton is most well known as physicist and astronomer and at some point I started investigating the pre-history of his work in astronomy. This eventually led me back to the Renaissance astronomers, not just Copernicus but all those whose work provided the foundations for Copernicus’s own work.

At some point it became very clear to me that to talk of Renaissance astronomers was in some sense a misnomer because those who pursued the study of astronomy in this time did so within a discipline that encompassed not just astronomy but also astrology, cartography (with a large chunk of geography and history in the mix), navigation, surveying, geodesy as well as the mathematical knowledge necessary to do all of these things. These were not separate disciplines as we see them now but different facets of one discipline. Over the years my studies have expanded to cover all of these facets and one into which I have delved very deeply is the history of cartography with the associated history of surveying. All of this is a rather longwinded explanation of why I have been reading Charles Withers’ new book Zero Degrees[2]

 

This book describes the history of how the Greenwich Meridian became the Prime Meridian.

A brief explanation for those who are not really clear what a meridian is; a meridian (or line of longitude) is any ‘straight’ line on the globe of the of the earth connecting the North Pole with the South Pole, where here straight means taking the shortest path between the two poles, as a meridian is by nature curved because it lies on the surface of the globe. Meridians are by their very nature arbitrary, abstract and non-real. We can chose to put a meridian wherever we like, they are an artificial construct and not naturally given. The Prime Meridian is a singular, unique, universally accepted meridian from which all other meridians (lines of longitude) are measured. The recognition of the necessity for a Prime Meridian is a fairly recent one in human history and Withers’ book deals with the history of the period between that recognition in the Early Modern Period to the realisation of a Prime Meridian at the beginning of the twentieth century.

The first thing that Withers made me aware of is that a meridian is not a singular object but one that has at least four separate functions and at least two different realisations. Meridians are used for navigation, for time determination, for cartography and for astronomy. The latter is because astronomers project our latitude and longitude coordinate system out into space in order to map the heavens. Nothing says that one has to use the same meridians for each of these activities and for much of the period of history covered by Withers people didn’t.

On the realisation of meridians Withers distinguishes two geographical and observed. The majority of meridians in use before the late seventeenth century were geographical. What does this mean? It meant that somebody simply said that they make their measurements or calculations from an imaginary line, the meridian, through some given geographical point on the surface of the earth. Ptolemaeus to whom we own our longitude and latitude coordinate system, although he had predecessors in antiquity, used the Azores as his zero meridian although he didn’t know with any real accuracy where exactly the Azores lay. Also the Azores is a scattered island group and he doesn’t specify exactly where within this island group his zero meridian ran. We have a lovely example of the confusion caused by this inaccuracy. On 4 May 1493 Pope Alexander VI issued the papal bull Inter caetera, which granted the Crowns of Castile and Aragon all the lands to the west and south of a meridian 100 leagues and south of the Azores or the Cape Verde islands.

This led to a whole series of treaties and papal bulls carving up the globe between Spain (Castile and Aragon) and Portugal. The 1494 Treaty of Tordesillas moved the line to a meridian 370 leagues west of the Portuguese Cape Verde islands now explicitly giving Portugal all new discoveries east of this meridian. I’m not going to go into all the gory details but this led to all sorts of problems because nobody actually knew where exactly this meridian or its anti-meridian on the other side of the globe lay. Ownership disputes in the Pacific between Spain and Portugal were pre-programmed. These are classical examples of geographical meridians.

The Cantino planisphere of 1502 shows the line of the Treaty of Tordesillas.
Source: Wikimedia Commons

The first observed meridian in the Early Modern Period was the Paris Meridian surveyed by Jean-Félix Picard in the 1660s. Such meridians are called observed because their exact position on the globe is determined astronomically using a transit telescope.

In the Early Modern Period there was no consensus as to which meridian should be used for which purpose and on the whole each country used its own zero meridian. I fact it was not unusual for several different zero meridians to be used for different purposes or even the same purpose, with one country. For geographers, cartographers and navigators crossing borders chaos ruled. The awareness that a single Prime Meridian would be beneficial for all already existed in the seventeenth century but it wasn’t until the nineteenth century that serious moves were made to solve the problem.

The discussion were long and very complicated and involved scientific, political and pragmatic considerations, which often clashed with each other. On the political level nationalism, of course, raised its ugly head. Surprisingly, at least for me, there was also a very heated discussion as to whether the Prime Meridian should be a geographical or an observed meridian. I personally can discern no reasons in favour of a geographical Prime Meridian but various participants in the discussions could. Another problem was one or more Prime Meridians? Separate ones for cartography, navigation, astronomy and time determination.

Withers deals with all of these topics in great detail and very lucidly in his excellent summery of all of the discussions leading up to the International Meridian Conference in Washington in 1884, which forms the climax of his book.

The delegates to the International Meridian Conference in Washington in 1884
Source: Wikimedia Commons

This is a truly fascinating piece of the history of science and in Withers it has found a more than worthy narrator and I recommend his book whole-heartedly for anybody who might be interested in the topic. Very important is his penultimate chapter Washington’s Afterlife. Every year in October people in the Internet announce that on this day in 1884 (I can’t be bothered to look up the exact date) the Greenwich Meridian became the world’s Prime Meridian and every year my #histsci soul sisterTM Rebekah ‘Becky’ Higgitt (who played a significant role in the genesis of Withers’ book, as can be read in the acknowledgements) announces no it didn’t, the resolutions reached in Washington were non-binding. In fact the acceptance of Greenwich as the Prime Meridian took quite some time after the Washington Conference, some even accepting it initial only for some but not all the four functions sketched above. France, whose Paris Meridian was the main contender against Greenwich, only finally accepted Greenwich as the Prime Meridian in 1912.

I do have a couple of minor quibbles about Withers’ book. In the preface he outlines the structure of the book saying what takes place in each section. He repeats this in greater detail in the introduction. Then he starts each chapter with a synopsis of the chapter’s contents, often repeating what he has already said in the introduction, and closes the chapter with a summary of its contents. It was for this reader a little bit too much repetition. My second quibble concerns the illustrations and tables of which there are a fairly large number in the book. These are all basically black and white but are in fact printed black on a sort of pastel grey. I assume that the book designer thinks this makes them somehow artistically more attractive but I personally found that it makes it more difficult to determine the details, particularly on the many maps that are reproduced. Whatever I wouldn’t let these rather personal minor points interfere with my genuine whole-hearted recommendation.

[1] Chose the word that best fits your personal philosophy of mathematics

[2] Charles W. J. Withers, Zero Degrees: Geographies of the Prime Meridian, Harvard University Press, Cambridge Massachusetts, London England, 2017

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Filed under History of Cartography, History of Navigation, History of science

Why Mathematicus?

“The Renaissance Mathematiwot?”

“Mathematicus, it’s the Latin root of the word mathematician.”

“Then why can’t you just write The Renaissance Mathematician instead of showing off and confusing people?”

“Because a mathematicus is not the same as a mathematician.”

“But you just said…”

“Words evolve over time and change their meanings, what we now understand as the occupational profile of a mathematician has some things in common with the occupational profile of a Renaissance mathematicus but an awful lot more that isn’t. I will attempt to explain.”

The word mathematician actually has its origins in the Greek word mathema, which literally meant ‘that which is learnt’, and came to mean knowledge in general or more specifically scientific knowledge or mathematical knowledge. In the Hellenistic period, when Latin became the lingua franca, so to speak, the knowledge most associated with the word mathematica was astrological knowledge. In fact the terms for the professors[1] of such knowledge, mathematicus and astrologus, were synonymous. This led to the famous historical error that St. Augustine rejected mathematics, whereas his notorious attack on the mathematici[2] was launched not against mathematicians, as we understand the term, but against astrologers.

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome Source: Wikimedia Commons

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome
Source: Wikimedia Commons

However St. Augustine lived in North Africa in the fourth century CE and we are concerned with the European Renaissance, which, for the purposes of this post we will define as being from roughly 1400 to 1650 CE.

The Renaissance was a period of strong revival for Greek astrology and the two hundred and fifty years that I have bracketed have been called the golden age of astrology and the principle occupation of our mathematicus is still very much the casting and interpretation of horoscopes. Mathematics had played a very minor role at the medieval universities but the Renaissance humanist universities of Northern Italy and Krakow in Poland introduced dedicated chairs for mathematics in the early fifteenth century, which were in fact chairs for astrology, whose occupants were expected to teach astrology to the medical students for their astro-medicine or as it was known iatro-mathematics. All Renaissance professors of mathematics down to and including Galileo were expected to and did teach astrology.

A Renaissance Horoscope Kepler's Horoskop für Wallenstein Source: Wikimedia Commons

A Renaissance Horoscope
Kepler’s Horoskop für Wallenstein
Source: Wikimedia Commons

Of course, to teach astrology they also had to practice and teach astronomy, which in turn required the basics of mathematics – arithmetic, geometry and trigonometry – which is what our mathematicus has in common with the modern mathematician. Throughout this period the terms Astrologus, astronomus and mathematicus – astrologer, astronomer and mathematician ­– were synonymous.

A Renaissance mathematicus was not just required to be an astronomer but to quantify and describe the entire cosmos making him a cosmographer i.e. a geographer and cartographer as well as astronomer. A Renaissance geographer/cartographer also covered much that we would now consider to be history, rather than geography.

The Renaissance mathematicus was also in general expected to produce the tools of his trade meaning conceiving, designing and manufacturing or having manufactured the mathematical instruments needed for astronomer, surveying and cartography. Many were not just cartographers but also globe makers.

Many Renaissance mathematici earned their living outside of the universities. Most of these worked at courts both secular and clerical. Here once again their primary function was usually court astrologer but they were expected to fulfil any functions considered to fall within the scope of the mathematical science much of which we would see as assignments for architects and/or engineers rather than mathematicians. Like their university colleagues they were also instrument makers a principle function being horologist, i.e. clock maker, which mostly meant the design and construction of sundials.

If we pull all of this together our Renaissance mathematicus is an astrologer, astronomer, mathematician, geographer, cartographer, surveyor, architect, engineer, instrument designer and maker, and globe maker. This long list of functions with its strong emphasis on practical applications of knowledge means that it is common historical practice to refer to Renaissance mathematici as mathematical practitioners rather than mathematicians.

This very wide range of functions fulfilled by a Renaissance mathematicus leads to a common historiographical problem in the history of Renaissance mathematics, which I will explain with reference to one of my favourite Renaissance mathematici, Johannes Schöner.

Joan Schonerus Mathematicus Source: Wikimedia Commons

Joan Schonerus Mathematicus
Source: Wikimedia Commons

Schöner who was a school professor of mathematics for twenty years was an astrologer, astronomer, geographer, cartographer, instrument maker, globe maker, textbook author, and mathematical editor and like many other mathematici such as Peter Apian, Gemma Frisius, Oronce Fine and Gerard Mercator, he regarded all of his activities as different aspects or facets of one single discipline, mathematica. From the modern standpoint almost all of activities represent a separate discipline each of which has its own discipline historians, this means that our historical picture of Schöner is a very fragmented one.

Because he produced no original mathematics historians of mathematics tend to ignore him and although they should really be looking at how the discipline evolved in this period, many just spring over it. Historians of astronomy treat him as a minor figure, whilst ignoring his astrology although it was this that played the major role in his relationship to Rheticus and thus to the publication of Copernicus’ De revolutionibus. For historians of astrology, Schöner is a major figure in Renaissance astrology although a major study of his role and influence in the discipline still has to be written. Historians of geography tend to leave him to the historians of cartography, these whilst using the maps on his globes for their studies ignore his role in the history of globe making whilst doing so. For the historians of globe making, and yes it really is a separate discipline, Schöner is a central and highly significant figure as the founder of the long tradition of printed globe pairs but they don’t tend to look outside of their own discipline to see how his globe making fits together with his other activities. I’m still looking for a serious study of his activities as an instrument maker. There is also, as far as I know no real comprehensive study of his role as textbook author and editor, areas that tend to be the neglected stepchildren of the histories of science and technology. What is glaringly missing is a historiographical approach that treats the work of Schöner or of the Renaissance mathematici as an integrated coherent whole.

Western hemisphere of the Schöner globe from 1520. Source: Wikimedia Commons

Western hemisphere of the Schöner globe from 1520.
Source: Wikimedia Commons

The world of this blog is at its core the world of the Renaissance mathematici and thus we are the Renaissance Mathematicus and not the Renaissance Mathematician.

[1] That is professor in its original meaning donated somebody who claims to possessing a particular area of knowledge.

[2] Augustinus De Genesi ad Litteram,

Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant. II, xvii, 37

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

Repeat after me! – They knew it was round, damn it!

Last week saw various reports about a rare stolen copy of a Columbus letter that had turned up in the Library of Congress and has now been restored to its Italian owners; a comparatively happy end to one of a series of recent stories about the theft of precious books and documents from archives and libraries. Unfortunately the report on the website of NPR (that’s National Public Radio a non-commercial public American educational radio network) opened with the following paragraph:

The heist of a major historical document apparently went undiscovered for more than 20 years. Now, a stolen letter from Christopher Columbus spreading the news that the world isn’t flat has been returned from the U.S. to Italy.

As some readers might already have guessed the second sentence, specifically the phrase spreading the news that the world isn’t flat, had me screaming and banging my head against the wall to relieve the pain. This is just horrendously wrong in several different ways.

Posthumous portrait of Christopher Columbus by Sebastiano del Piombo, 1519. There are no known authentic portraits of Columbus. Source: Wikimedia Commons

Posthumous portrait of Christopher Columbus by Sebastiano del Piombo, 1519. There are no known authentic portraits of Columbus.
Source: Wikimedia Commons

On his first voyage Columbus set sail from Spain in September 1492 and after approximately a month of sailing westward he landed on a set of previous unknown islands, unknown to the Europeans that is. This voyage proves or disproves absolutely nothing about the shape of the earth. To even contemplate a voyage proving the earth to be spherical and not flat we would have to fast forward thirty years to the return to Spain of the one ship and eighteen men from Ferdinand Magellan’s disastrous circumnavigation in 1522; just for the record Magellan was not one of the eighteen survivors, so to call him the first man to circumnavigate the world, as many people do, is simply false. Some flat-earthers could, and probably do/did, argue that Magellan’s fleet just sailed round in a circle on a flat disc and not around a spherical earth so even that is not a totally convincing proof (even if the objection is somewhat iffy).

Let us return to the good Cristoforo. One could argue that he set sail westward to reach the Spice Islands, instead of heading to the east, as was normal because he believed the earth to be a sphere and also believed that that sphere was small enough that the route west to the Spice Islands was shorter and thus quicker than the route east (A belief, as it turns out, that was based on faulty calculation, of which more later). Having reached what he erroneously believed to be the Spice Islands, leading to the equally erroneous name, the West Indies, he believed that he had proved the world to be spherical. There is however a fundamental flaw in this argument. Columbus did not sail westward because he believed the earth to be a sphere; he did so because he, like almost every other educated European, knew that it was a sphere, knowledge that had been part of the European cultural heritage for the best part of two thousand years.

This should in the meantime be well known, but for those, like the NPR reporter(s), who have been sitting at the back and not paying attention let us pass review over those two thousand years.

We have no direct records but latter authors tell us that the Pythagoreans in the sixth century BCE already accepted that the earth was spherical. Their reasons for doing so are unknown but it was possible in analogy to the celestial sphere of the so-called fixed stars. If you look up into the heavens on a clear dark night the sky appears to take the form of an inverted bowl or hemisphere. By the latest in the fourth century BCE, Aristotle, who would go on to have a massive influence on European intellectual history, knew that the earth was spherical and he offers up a series of empirical proofs for this claim. For example he wrote, “there are stars seen in Egypt and […] Cyprus which are not seen in the northerly regions.” Since this could only happen on a curved surface, he too believed Earth was a sphere “of no great size, for otherwise the effect of so slight a change of place would not be quickly apparent.” (De caelo, 298a2–10). He also pointed out that the shadow of the earth on the moon during a lunar eclipse is circular. Following Aristotle all Greek schools of philosophy accepted that the earth was spherical and following them the Romans. There was no doubt in the classical world that the earth was a sphere. Ptolemaeus, the most influential Greek astronomer, brought a series of arguments and proofs for the spherical form of the earth in his Syntaxis Mathematiké (Almagest) in the second century CE. Most notably that as ships approach over the horizon one sees the top of the mast before one sees the hull.

A lot of this specific knowledge got temporarily lost within Europe in the Early Middle Ages but still almost nobody who was educated doubted that the earth was a sphere. With the rise of the Islamic empire the astronomers writing in Arabic adopted the views of Aristotle and Ptolemaeus including the spherical form of the earth.

Back in the third century BCE the astronomer mathematician Eratosthenes from Alexandria determined the size of the sphere using the angle of the sun’s shadow and a bit of basic trigonometry. He achieved a fairly accurate result, its accuracy depends on which Stadia (an ancient measure of length) you think he used; we don’t know for certain. Other geographers and astronomers also determined the size of the earth’s sphere; all arriving at reasonable ball park figures. Ptolemaeus, in his Geōgraphikḕ (Geography) also determined that the known land area the oikoumenè, Europe, Africa and Asia, stretched over 180° of the earth’s surface from east to west.

In the High Middle Ages, Europe regained this knowledge, largely via the Islamic Empire through Spain and Sicily. The standard European university astronomy text Johannes de Sacrobosco’s De sphaera mundi, written in the twelfth century CE, contained all the standard Greek arguments for a spherical earth including the lunar eclipse shadow, ship breasting the horizon and the change in visible asterism travelling from south to north. There existed no doubt amongst the educated in the Middle Ages that the earth was a sphere.

Picture from a 1550 edition of De sphaera, showing the earth to be a sphere. Source: Wikimedia Commons

Picture from a 1550 edition of De sphaera, showing the earth to be a sphere.
Source: Wikimedia Commons

When Columbus started making his plans at the end of the fifteenth century he knew that the world was a sphere, as did all of the people he tried to get to back his scheme. The only disputed point was how big the earth’s sphere was, how long the central landmass, Europe, Africa and Asia, was and thus how far the Spice Islands were if one sailed west from Europe. It was here that Columbus made some fundamental calculating errors. The Arabic astronomer al-Farghānī gave 5623 Arabic miles (being 111.8 km) as the length of one degree of longitude, whereas Ptolemaeus gave 6023 Roman miles (being 89.7 km). Columbus took al-Farghānī’s figure but multiplied it with the length of a Italian mile (much shorter than the Arabic one) to determine the circumference of the earth thus arriving at a figure that was far too small: approx. 25,255 km instead of al-Farghānī’s very accurate figure of 40,248 km. Ptolemaeus’ estimate of the spread of the main landmass was 180°, whereas it is in fact only about 130°. Columbus however took the even more inaccurate estimate of Marius from Tyre of 225°. The sum of these error meant that Columbus thought he only had about 3,700 km from the Canary Islands to Japan instead of the real 19,600 km! Having convinced his sponsors of the correctness of his calculations he set sail. If America had not been in the way Columbus and his entire crew would have stared starved to death on the open ocean.

So where does the myth of the flat earth come from? There were a few European scholars in antiquity and the early Middle Ages who, against the evidence, still argued that the earth was flat. However none of them enjoyed much support. One of the ironies of history is that Copernicus probably drew attention to the most famous of them, the third century cleric Lucius Caecilius Firmianus Lactantius, by mentioning him in his De revolutionibus. The real myth of the medieval flat earth begins first in the eighteenth and nineteenth centuries and has two principal sources. Probably the most influential of these was the American author Washington Irving who in his fictional biography of Columbus claimed that Columbus had to fight against the Church’s belief that the world was flat in order to get permission and backing for his voyage, a complete fabrication. This falsehood was supported by the nineteenth centuries false interpretation of the medieval T and O Mappa Mundi.

The Hereford Mappa Mundi, about 1300, Hereford Cathedral, England. Source: Wikimedia Commons

The Hereford Mappa Mundi, about 1300, Hereford Cathedral, England.
Source: Wikimedia Commons

These medieval world maps were in the form of a circle, the O, with the three known continents, Europe, Africa and Asia, displayed in the form of a T with east at the top. These maps were interpreted in the nineteenth century as indicating that the medieval cartographers believed the earth to be a flat disc. This is not without irony as they were circular in order to indicate that the world in a sphere. The myth of the flat medieval world was taken up by two figures well known to readers of this blog John William Draper (1811–1882) and Andrew Dickson White (1832–1918) in their widespread myth of the eternal war between religion and science. Science believing in a spherical earth whereas the reactionary Church believed in a flat one.

That Europe in the Middle Ages believed in a flat earth is a total myth that just doesn’t seem to want to die. The next time somebody tells you that the medieval Church thought the world was flat, or that Columbus was a revolutionary for believing in a spherical earth or any other version of this nonsense, do me a favour, take a large, heavy, flat, round, metal object, such as a frying pan, and beat them around the head with it.

 

 

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

The Arch-Humanist

The name Conrad Celtis is not one that you’ll find in most standard books on the history of mathematics, which is not surprising as he was a Renaissance humanist scholar best known in his lifetime as a poet. However, Celtis played an important role in the history of mathematics and is a good example of the fact that if you really wish to study the evolution of the mathematical sciences it is necessary to leave the narrow confines of the mathematics books.

Conrad Celtis: Gedächtnisbild von Hans Burgkmair dem Älteren, 1507 Source: Wikimedia Commons

Conrad Celtis: Gedächtnisbild von Hans Burgkmair dem Älteren, 1507
Source: Wikimedia Commons

Born Konrad Bickel or Pyckell, (Conrad Celtis was his humanist pseudonym) the son of a winemaker, in Franconian Wipfield am Main near Schweinfurt on 1 February 1459, he obtained his BA at the University of Cologne in 1497. Unsatisfied with the quality of tuition in Cologne he undertook the first of many study journeys, which typified his life, to Buda in 1482, where he came into contact with the humanist circle on the court of Matthias Corvinus, the earlier patron of Regiomontanus. 1484 he continued his studies at the University of Heidelberg specialising in poetics and rhetoric, learning Greek and Hebrew and humanism as a student of Rudolf Agricola, a leading Dutch early humanist scholar. Celtis obtained his MA in 1485. 1486 found him underway in Italy, where he continued his humanist studies at the leading Italian universities and in conversation with many leading humanist scholars. Returning to Germany he taught poetics at the universities of Erfurt, Rostock and Leipzig and on 18 April 1487 he was crowned Poet Laureate by Emperor Friedrich III in Nürnberg during the Reichstag. In Nürnberg he became part of the circle of humanists that produced the Nürnberger Chronicle to which he contributed the section on the history and geography of Nürnberg. It is here that we see the central occupation of Celtis’ life that brought him into contact with the Renaissance mathematical sciences.

During his time in Italy he suffered under the jibes of his Italian colleges who said that whilst Italy had perfect humanist credentials being the inheritors of the ancient Roman culture, Germany was historically a land of uncultured barbarians. This spurred Celtis on to prove them wrong. He set himself the task of researching and writing a history of Germany to show that its culture was the equal of Italy’s. Celtis’ concept of history, like that of his Renaissance contemporaries, was more a mixture of our history and geography the two disciplines being regarded as two sides of the same coin. Geography being based on Ptolemaeus’ Geographia (Geographike Hyphegesis), which of course meant cartography, a branch of the mathematical sciences.

Continuing his travels in 1489 Celtis matriculated at the University of Kraków specifically to study the mathematical sciences for which Kraków had an excellent reputation. A couple of years later Nicolaus Copernicus would learn the fundamentals of mathematics and astronomy there. Wandering back to Germany via Prague and Nürnberg Celtis was appointed professor of poetics and rhetoric at the University of Ingolstadt in 1491/92. Ingolstadt was the first German university to have a dedicated chair for mathematics, established around 1470 to teach medical students astrology and the necessary mathematics and astronomy to cast a horoscope. When Celtis came to Ingolstadt there were the professor of mathematics was Andreas Stiborius (born Stöberl 1464–1515) who was followed by his best student Johannes Stabius (born Stöberer before 1468­–1522) both of whom Celtis convinced to support him in his cartographic endeavours.

In 1497 Celtis received a call to the University of Vienna where he established a Collegium poetarum et mathematicorum, that is a college for poetry and mathematics, with Stiborius, whom he had brought with him from Ingolstadt, as the professor for mathematics. In 1502 he also brought Stabius, who had succeeded Stiborius as professor in Ingolstadt, and his star student Georg Tanstetter to Vienna. Stiborius, Stabius and Tanstetter became what is known, to historians of mathematics, as the Second Viennese School of Mathematics, the First Viennese School being Johannes von Gmunden, Peuerbach and Regiomontanus, in the middle of the fifteenth century. Under these three Vienna became a major European centre for the mathematical sciences producing many important mathematicians the most notable being Peter Apian.

Although not a mathematician himself Conrad Celtis, the humanist poet, was the driving force behind one of the most important German language centres for Renaissance mathematics and as such earns a place in the history of mathematics. A dedicated humanist, wherever he went on his travels Celtis would establish humanist societies to propagate humanist studies and it was this activity that earned him the German title of Der Erzhumanist, in English the Arch Humanist. Celtis died in 1508 but his Collegium poetarum et mathematicorum survived him by twenty-two years, closing first in 1530

 

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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.

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