Category Archives: History of Cartography

Scotland’s premier topographer

For those of us, who grew up in the UK with real maps printed on paper, rather than the online digital version offered up by Google Maps, the Ordnance Survey has been delivering up ever more accurate and detailed maps of the entire British Isles since their original Principal Triangulation of Great Britain carried out between 1791 and 1853.

Principal Triangulation of Great Britain Source: Wikimedia Commons

Supplied with this cartographical richness it is easy to forget that England and Scotland once had separate mapping histories, before James VI & I[1] became monarch of both countries in 1603, and later the Act of Union in 1707, joined them together as one nation. 

Rather bizarrely, the Ptolemaic world map rediscovered in Europe in the fifteenth century but originating in the second century CE gives an at least recognisable version of England but with Scotland turned through ninety degrees, pointing to the east rather than the north. 

1482 version of the Ptolemaic map of the British Isles Source: National Library of Wales via Wikimedia Commons

The same image can be found on a world map from the eleventh century in the manuscript collection of Sir Robert Cotton (1570/1–1631). 

Detail of the 11th-century map of the world showing Britain and Ireland: Cotton MS Tiberius B V/1, f. 56v Source: British Library Medieval Manuscripts blog

The most developed of the maps of Britain drawn by the monk Matthew Paris (c. 1200–1259), also in the Cotton manuscript collection, has Scotland north of England but very strangely divided into two parts north of the Antonine Wall joined by a bridge at Stirling.

Detail of a map of Britain by Matthew Paris showing Scotland: Cotton MS Claudius D VI/1, f. 12v Source: British Library Medieval Manuscripts blog

Whereas on Matthew Paris’ map, the northern part of Scotland is only attached by the bridge at Stirling, on the Hereford Mappa mundi from c. 1300, Britain looks like a shapeless slug squashed down into the northwest corner of the map with Scotland, a separate island, floating to the north. 

Britain on the Hereford Mappa Mundi (Scotland separated left). Source

On the medieval Gough Map, the date of which is uncertain, with estimates varying between 1300 and 1430, Scotland, whilst hardly recognisable, had at least achieved its true north pointing orientation, although the map itself has east at the top. 

Gough Map Source: Wikimedia Commons

The version of Britain on the Ptolemaic, the eleventh century Cotton, and the Hereford world maps show almost no details. Matthew Paris’ map is part of a pilgrimage itinerary and shows the towns on route and very prominently the rivers but otherwise very little detail. The Gough map, like the Paris map emphasises towns rivers and route. Also compared to the Ptolemaic map, its depictions of the coastlines of England and Wales are much improved. However, its depiction of the independent kingdom of Scotland is extremely poor.

All the maps presented so far show Scotland in a much wider geographical context, part of the world or part of Britain. The oldest known existing single map of Scotland was created by John Hardyng (1378–1465) an English soldier turned chronicler, who set out to prove that the English kings had a right to rule over Scotland. As part of the fist version of his Chronicle of the history of Britain, which he presented to King Henry VI of England, in a failed attempt to instigate an invasion of Scotland, he included a strangely rectangular map of Scotland with west at the top and north to the right. 

John Hardyng’s map of Scotland: Lansdowne MS 204, ff. 226v–227r Source: British Library Medieval Manuscripts blog

As can be seen, this map contains much more detail of the Scottish towns, displaying castles and walls, as well as in two cases churches instead. 

Detail of John Hardyng’s map of Scotland, showing Glasgow, Edinburgh, Dunfermline and St Andrews: Lansdowne MS 204, f. 226v Source: British Library Medieval Manuscripts blog

The next map of Scotland was produced by the English antiquarian, cartographer, and early scholar of Anglo-Saxon and literature, Laurence Nowell (1530–c. 1570) in the mid 1560s. Around the same time he produced a pocket-sized map of Britain entitled A general description of England and Ireland with the costes adioyning for his patron Sir William Cecil, 1st Baron Burghley (1520–1598) Elizabeth I chief adviser.

William Cecil, 1st Baron Burghley portrait attributed to Marcus Gheeraerts the Younger Source: National Portrait Gallery via Wikimedia Commons

His map of Scotland, with west at the top, is much more detailed than any previous maps and bears all the visual hallmarks of comparatively modern mapmaking.  

Map of Scotland by Laurence Nowell: Cotton MS Domitian A XVIII, ff. 98v–99r Source: British Library Medieval Manuscripts blog

With Nowell we have entered the Early Modern Period and the birth of modern mapmaking in the hands of Gemma Frisius (1508–1555), who published the first account of triangulation in 1533, Abraham Ortelius (1527–1598) creator of the first modern atlas[2] in 1570, and Gerard Mercator (1512–1594) the greatest globe and mapmaker of the century. As I have already detailed in an earlier post, England lagged behind the continental developments, as in all of the mathematical disciplines. 

Burghley motivated and arranged sponsorship for other English mapmakers, which led to the publication of the first English atlas, created by Christopher Saxton (c. 1540–c. 1610), in 1579, following a survey, which took place from 1574 to 1578. Scotland was at this time still an independent country, so Saxton’s atlas only covers the counties of England and Wales.

Saxton England and Wales proof map Source: British Library

Various projects were undertaken to improve the quality of Saxton’s atlas of which, the most successful was by the John Speed (1551/2–1629), who published his The Theatre of the Empire of Great Britaine, which was dated 1611, in 1612. By now James had been sitting on the throne on both countries for nine years, however, Speed’s Theatre only contains a general map of Scotland and not detailed maps of the Scottish counties. 

John Speed’s map of Scotland

Why was this? The annotations to the facsimile edition of Speed’s Theatre give two reasons for this. Firstly, the book was originally conceived in 1590, when the two kingdoms were still independent of each other, and it was production delays that led to the later publication date, when modification to include the Scottish counties would have led to further delays. However, in our context, the mapping of Scotland, it is the second reason that is more interesting:

Secondly, Speed knew of the Scotsman Timothy Pont’s work in surveying Scotland. The have extended the Theatre to include maps for Scotland similar to those for England, Wales and Ireland would have been to duplicate Pont’s efforts, even if cartographical aspects were differently emphasised by the two men.[3]

We have now reached the title topographer of this blog post, Timothy Pont (c. 1560–c. 1614), who was he and why is there no Pont’s Atlas of Scotland?

Timothy Pont was the first person to make an almost complete topographical survey of Scotland. Unfortunately, as with many people from the Early Modern Period, we only have a sketchy outline of his life and no known portrait, in fact we know far more about his father, Robert Pont (1529–1606), a minister, judge, and reformer, an influential legal, political, and religious man, who rose to be Moderator of the General Assembly of the Church of Scotland, in 1575. Timothy was his eldest child by his first wife Catherine daughter of Masterton of Grange, with whom he had two sons and two daughters[4]. By his second wife Sarah Denholme he had one daughter and by his third wife Margaret Smith he had three sons.

In 1574 Timothy received an annual grant of church funds from his father, he matriculated at the University of St Andrews in 1508 and graduated M.A. in 1583. It was possibly at St Andrews that he learnt the art of cartography, but it is not known for certain. It is not known when he carried out his survey of Scotland. Only his map of Clydesdale contains a date, (Sept. et Octob: 1596 Descripta) and it appears he ended his travels around this time and that he began them after graduating from St Andrews.

Pont’s Map of Lanark from 1596 Source

Somewhat earlier in 1592, he had received a commission to undertake a mineral reconnaissance of Orkney and Shetland, so his activities were obviously known. In 1593 his father again supported him financially, assigning him an annuity from Edinburg Town Council.

His wanderings and topographical activities apparently terminated, in 1600 Timothy was appointed minister of the parish of Dunnet in Caithness. He is recorded as having visited Edinburg in 1605. In 1609, he applied unsuccessfully for a grant of land in the north of Ireland. There is evidence that he was still Parson of Dunnet in 1610 but in 1614 another held the post, and in 1615, Isabel Pont is recorded as his widow both facts indicating that he had died sometime between 1611 and 1614. Unfortunately, as is often the case with mapmakers in the Early Modern Period, we have no real information as to how Pont carried out his surveys or which methods he used. 

We now turn to Pont’s activities as a topographer and mapmaker. Pont never finished his original project of producing an atlas of Scotland. Only one of Pont’s maps, Lothian and Linlithgow,

Pont’s map, Lothian and Linlithgow,

was engraved during his lifetime, by Jodocus Hondius the elder in Amsterdam,

Lothian and Linlithgow engraved by Jodocus Hondius the elder in Amsterdam
Same map in Joan Blaeu’s Atlas of Scotland Source: Wikimedia commons

sometime between 1603 and 1612. However, the map, dedicated to James VI &I, was first published in the Hondius-Mercator Atlas in 1630. In a letter from 1629, Charles I wrote in a letter that his father had intended to financially support Pont’s project and granted the antiquarian Sir James Balfour of Denmilne (1600-1657), the Lord Lyon King-of-Arms, who had acquired the maps from Pont’s heirs, money to plan the publication of the maps. 

Sir James Balfour artist unknown Source: (c) National Galleries of Scotland; Supplied by The Public Catalogue Foundation via Wikimedia Commons

At this point Sir John Scot, Lord Scotstarvit (1585-1670) entered the story. Already a correspondent of Willem (1571–1638) and Joan Blaeu (1596–1679), of the Amsterdam cartographical publishing House of Blaeu, he informed them of Balfour’s acquisition of Pont’s topographical survey of Scotland, Willem Blaeu having already asked Scot about maps of Scotland in 1626. Through Scot’s offices Pont’s maps made their way to Amsterdam. What then followed is briefly described by Joan Blaeu in his Atlas Novus in 1654.

Scot collected them and other maps and sent them over to me but much torn and defaced. I brought them into order and sometimes divided a single map. into several parts. After this Robert and James Gordon gave this work the finishing touches. and added thereto, besides the corrections in Timothy Pont’s maps, a few maps of their own.

Robert Gordon of Straloch (1580–1661) and his son James Gordon of Rothiemay (c. 1615–1686) were Scottish mapmakers, who obviously played a central role in preparing Pont’s maps for publication.

Source: National Portrait Gallery

Robert was called upon to undertake this work by Charles I in a letter from 1641; Charles entreated him “to reveis the saidis cairtiss”. Acts of parliament exempted him from military service, whilst he undertook this task and the General Assembly of the Church of Scotland published a request to the clergy, to afford him assistance. 

The exact nature of the role undertaken by Robert and James Gordon in the revision of the maps is disputed amongst historians and I won’t go into that discussion here. However, following his father’s death in 1661, James preserved all of Pont’s surviving maps, along with his and his father’s own cartographical work and passed them on to the Geographer Royal to Charles II, Sir Robert Sibbald (1641–1722), in the 1680s. Sibbald’s own papers along with the Pont maps were placed in the Advocates Library following his death in 1772. The Advocates Library became the National Library of Scotland, where Pont’s maps still reside[5].

Robert Sibbald artist unknown Source: Wikimedia Commons

As already indicated above Pont’s maps formed the nucleus of Joan Blaeu’s Atlas of Scotland, the fifth volume of his Theatrum Orbis Terrarum sive Atlas Novus published in Amsterdam in Latin, French, and German in 1654.

Joan Blaeu Atlas of Scotland German title page
Caithness Blaeu’s Atlas of Scotland The parish of Dunnet where Pont was minister is in the bottom corner od the rectangular bay Source: Wikimedia Commons
Pont’s map of the area around Dunnet

This was the first atlas of Scotland, and it wasn’t really improved on in any way until the military survey of Scotland carried out by William Roy (1726–1790) between 1747 and 1755. Roy would go on to be appointed surveyor-general and his work and lobbying led to the establishment of the Ordnance Survey, whose Principal Triangulation of Great Britain, mentioned at the beginning of this post, began in 1791, one year after his death. 

My attention was first drawn to Pont’s orthographical survey of Scotland by advertising for a new permanent exhibition “Treasures of the National Library of Scotland”, which prominently features Pont’s maps, so I went looking for the story of this elusive mapmaker. 


[1] For any readers confused by James VI & I, he was James VI of Scotland and James I of England

[2] This and other uses of the term atlas here are anachronistic as Mercator first used the term in the title of his Atlas, sive cosmographicae meditationes de fabrica mundi published in 1585

[3] The Counties of BRITAIN: A Tudor Atlas by John Speed, Introduction by Nigel Nicolson, County Commentaries by Alasdair Hawkyard, Published in association with The British Library, Pavilion, London 1998, p. 265

[4] I can’t resit noting that Timothy’s youngest sister, Helen, married an Adam Blackadder!

[5] The National Library of Scotland has an extensive website devoted to Pont and his maps from which much of the information for this blog post was culled

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Filed under Early Scientific Publishing, History of Cartography, Renaissance Science

A terrible fortnight for the HISTSCI_HULK

It’s been a tough two weeks for my old buddy the HISTSCI_HULK, who has now packed his bags and departed for pastures unknown screaming, “you can all kiss my posterior!” That not what he actually said but you get the message. 

So, what has upset the #histSTM pedant this time and what was the straw that finally broke the poor monsters back? It all started with Nicolaus Copernicus’ birthday on 19 February. As per usual this year, numerous people, including myself, posted on social media to mark the occasion. Our attention was drawn to the post on Twitter by the Smithsonian National Air and Space Museum, so we followed the link to their website and were less than happy about what we found there:

A rigid code of respect for ancient cultures and thought governed the early Renaissance, a period during which resistance to traditional concepts was met with hostility. Therefore, the Polish astronomer, Nicolaus Copernicus, whose ideas changed the course of astronomy forever, did not release his manuscript for publication until he was on his deathbed.

De revolutionibus Source: Wikimedia Commons

PIFFLE! snorted the HISTSCI_HULK, TOTAL PIFFLE! 

The early Renaissance was a period of lively scientific debate characterised by clashes of contrasting, conflicting, and even contradictory theories, and ideas. The debate in astronomy, to which Copernicus contributed, had been rumbling on since at least the middle of the fifteenth century. Also, it is not true that he “didn’t release his manuscript for publication until he was on his deathbed”. Rheticus published his Narratio Prima, as a trial balloon, in 1540. Following its relatively positive reception, Copernicus gave the manuscript of De revolutionibus to Rheticus to take to Petreius in Nürnberg to be published. At the time, as far as we known, he was still healthy. Printing and publishing a book takes time and by the time the book was finished, Copernicus had suffered a stroke and lay on his deathbed. Finally, the reason why Copernicus held De revolutionibus back for so long was because he couldn’t deliver. In the Commentariolus, Copernicus stated he would prove his hypothesis that the cosmos was heliocentric, but he had failed in this endeavour and so was reluctant to publish, a reluctance that was dissolved by the positive reception of the Narratio Prima.

Looking further on the Smithsonian National Air and Space Museum website, under Ancient Times and the Greeks, we find the following: 

Plato wondered why the starlike planets moved relative to the stars. Trying to answer the question was to occupy the attention of astronomers for many centuries.

Plato was more interested in the how rather than the why. Astronomers sought a mathematical explanation for the celestial movements. 

Under Ptolemy’s Planetary System we find the following

In the theory of Ptolemy, the planets moved in small orbits while revolving in large orbits about the Earth. This theory, although incorrect, could explain the apparent motions of the planets and also account for changes in their brightness.

This is an attempt to explain the deferent–epicycle model of planetary motion that Ptolemaeus presented. If one didn’t already know how Ptolemaeus’ system functioned, one certainly would have no idea after reading this. 

This is what is being described: The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and an equant (•). Source: Wikimedia Commons

The HISTSCI_HULK, COME ON SMITHSONIAN YOU CAN DO BETTER THAN THIS!

Already more than somewhat miffed the HISTSCI_HULK had the misfortune fourteen days later to view the article posted by the magazine History Today to acknowledge the birthday of Gerard Mercator on 5 March, he flipped out completely, thundering:

WHAT IS THIS HEAP OF ROTTING GARBAGE? WHY DOESN’T SOMEBODY FLUSH IT DOWN THE TOILET WITH ALL THE OTHER EXCREMENT?

Let us examine the offending object, the opening paragraph truly is a stinker:

The age of discovery that began with Christopher Columbus, along with Ferdinand Magellan’s conclusive demonstration that the Earth is round, created a demand for new maps and confronted cartographers with the problem of how to depict the spherical Earth on a flat surface. Of the various solutions, or ‘projections’, the one accepted as the best was that of Gerardus Mercator, which is still in use today. It was also Mercator who first used the term ‘atlas’ for a collection of maps.

In my opinion the age of discovery is an unfortunate misnomer, as I pointed out in a fairly recent blog post on the subject, preferring the term, Contact Period. It didn’t start with Columbus but was well underway by the time he found backing for his first voyage. 

… along with Ferdinand Magellan’s conclusive demonstration that the Earth is round …!!

Where to start? 1) Nobody of significance in Europe need a demonstration that the Earth was round in 1521, it had been an accepted fact for around a thousand years by then. 2) Ferdinand Magellan didn’t demonstrate anything, he died on route on the island of Mactan, waging imperialist war against the indigenous inhabitants. 3) Any nineteenth century flat earther would counter the claim that he “conclusive demonstration that the Earth is round” by stating that he merely sailed in a circle around the flat Earth disc.

… created a demand for new maps and confronted cartographers with the problem of how to depict the spherical Earth on a flat surface.

This statement would have historians of mapmaking and map projection tearing their hair out, that’s if they have any to tear out. The problem of how to project a spherical earth onto a flat surface had been extensively discussed by Ptolemaeus in his Geographia in the second century CE, a book that re-entered Europe at the beginning of fifteenth century more than one hundred years before Magellan undertook his fateful voyage. 

Of the various solutions, or ‘projections’, the one accepted as the best was that of Gerardus Mercator, which is still in use today.

Ignoring for a moment that “accepted as the best” is total rubbish, which of Mercator’s projections? He used at least two different ones and his son a third. Our author is, of course, referring to the so-called Mercator Projection. First off there is no such thing as “the best projection.” All projections have their strengths and weaknesses and, which projection one uses is dependent, or should be, on the task in hand. The Mercator projection allows a mariner to plot a course of constant compass bearing as a straight line on a sea chart. 

Yes, it was Mercator who first used the term atlas for a collection of maps. Our author at least got that right.

The next paragraph is a potted biography, which is OK but is littered with small inaccuracies:

He was born Gerhard Kremer at Rupelmonde in Flanders (now in Belgium), the seventh and last child of an impoverished German family which had recently moved there. His father was a cobbler, but the surname meant ‘merchant’ and Gerhard turned it into Latin as Mercator after his father and mother died when he was in his teens. A great-uncle who was a priest made sure that he got a good education and after graduating from the University of Louvain in 1532 he studied mathematics, geography and astronomy under Gemma Frisius, the Low Countries’ leading figure in these fields. He learned the craft of engraving from a local expert called Gaspar Van der Heyden and the three men worked together in the making of maps, globes and astronomical instruments for wealthy patrons, including the Holy Roman Emperor Charles V.

When Mercator was born his parents were only visiting his uncle or great-uncle, it is not known for certain whether he was the brother or uncle of Mercator’s father, in Rupelmonde. Following his birth, they returned to Gangelt in the Duchy of Jülich. Whether the family was German, or Flemish is not known for certain. They first moved permanently to Rupelmonde when Mercator was six years old. He adopted the Latin name of Mercator, meaning merchant as does Kremer, not when his parents died but when his uncle/great-uncle sent him to a Latin school. In the school he became Gerardus Mercator Rupelmundanus. After graduating MA on the liberal arts faculty of the University of Louvain in 1532, he left the university and only returned two years later, in 1534, to study geography, mathematics, and astronomy under the guidance of Gemma Frisius. He learnt the art of globe making when he assisted Frisius and Gaspar Van der Heyden to construct a terrestrial globe in 1535. This is followed by another paragraph of biography:

In 1538 Mercator produced a map of the world on a projection shaped like a pair of hearts. His inability to accept the Bible’s account of the universe’s creation got him into trouble with the Inquisition in 1544 and he spent some months in prison on suspicion of heresy before being released. John Dee, the English mathematician, astrologer and sage, spent time in Louvain from 1548 and he and Mercator became close friends.

The sentences about the cordiform projection (heart shaped, devised by Johannes Stabius before Magellan “sailed around the world” by the way) world maps and about John Dee are OK.  Why he refers to Dee as an astrologer but not Frisius or Mercator, who were both practicing astrologers, puzzles me. I’m also not sure why he calls Dee a sage, or what it’s supposed to mean. However, his account of Mercator’s arrest on suspicion of heresy is simply bizarre. He was arrested in 1543 on suspicion of being a Lutheran. Whilst in prison he was accused of suspicious correspondence with the Franciscan friars of Mechelen. No evidence was found to support either accusation, and he was released after four months without being charged. Nothing to do with, “His inability to accept the Bible’s account of the universe’s creation.”

We are now on the home straight with the final paragraph. Mostly harmless biography but it contains a real humdinger!

In 1552 Mercator moved to Duisburg in the Duchy of Cleves in Germany, where he enjoyed the favour of the duke. He set up a cartographic workshop there with his staff of engravers and perfected the Mercator projection, which he used in the map of the world he created in 1569. It employed straight lines spaced in a way that provided an accurate ratio of latitude and longitude at any point and proved a boon to sailors, though he never spent a day at sea himself [my emphasis]. In the 1580s he began publishing his atlas, named after the giant holding the world on his shoulders in Greek mythology, who was now identified with a mythical astronomer-king of ancient times. Strokes in the early 1590s partly paralysed Mercator and left him almost blind. A final one carried him off in 1594 at the age of 82 and he was buried in the Salvatorkirche in Duisburg.

I studied mathematics at university and have been studying/teaching myself the history of map projections for maybe the last thirty years and I have absolutely no idea what the phrase, straight lines spaced in a way that provided an accurate ratio of latitude and longitude at any point, is supposed to mean. I’m certain the author, when he wrote it, didn’t have the faintest clue what he was saying and tried to bluff. I also pity any reader who tries to make any sense out of it. It’s balderdash, hogwash, gobbledygook, poppycock, mumbo-jumbo, gibberish, baloney, claptrap, prattle, or just plain total-fucking-nonsense! What it definitively isn’t, in anyway whatsoever, is a description of the Mercator projection.

This wonderful piece of bullshit caused the HISTSCI_HULK to flip out completely. Imitating Charles Atlas, he tore his facsimile edition of the Mercator-Hondius Atlas in half with his bare hands and threw it out of the window. It’s a hard back by the way.

The term Atlas, as used by Mercator had nothing to do with the mythological Greek Titan Atlas, who by the way, holds the cosmos on his shoulders and not the Earth, but rather bizarrely the equally mythical King Atlas of Mauritania, who according to legend was a wise philosopher, mathematician, and astronomer, who is credited with having produced the first celestial globe. As Mercator explains: “I have set this man Atlas, so notable for his erudition, humaneness, and wisdom as a model for my imitation.”

Bizarrely, the article is illustrated, not by Mercator’s 1569 world map based on his projection, but the double planisphere world map from 1587 created by his son Rumold Mercator (1541–1599), which was based on it, and which first appeared in Isaac Casaubon’s edition of Strabo’s Geographia, published in Geneva. It was incorporated into later editions of the Atlas. 

Source: Wikimedia Commons

History Today is a popular English monthly history magazine, which according to Wikipedia, and I quote, “presents serious and authoritative history to as wide a public as possible.” Judging by this article, you could have fooled me. History Today has more than 300,000 followers on Twitter, that’s more than 300,000 potential readers for this garbage. The article was written by Richard Cavendish (1930–2016), an Oxford graduate, who specialised in medieval studies. Most well known as a historian of the occult his work, quoting Wikipedia once more, “is highly regarded for its depth of research and agnostic stance towards its sometimes controversial subject matter,” and, “He also wrote regularly for the British journal History Today.” The article was written in 2012, but the editor, Paul Lay, who considered it “serious and authoritative history” then, is the same editor, who thought it suitable to trot out again in 2022. 

Having within a fortnight been confronted by two horrible examples of how not to write popular #histSTM, the HISTSCI_HULK was more than somewhat mentally fragile when he stumbled on the offending object that finally caused him to snap, pack his bag, and depart, vowing never to read another word ever again. The offending object? A page from the book of the four-year-old daughter of a historian, who I know on Twitter:

THAT’S BLEEDIN’ INDOCTRINATION, THAT IS, SCREECHED THE HISTSCI_HULK AS HE SLAMMED THE DOOR SHUT ON HIS WAY OUT

“He made an amazing discovery.” As we obviously have to do with Galileo’s telescopic discoveries, there were more than one, we will restrict ourselves to those. All of Galileo’s telescopic discoveries were made independently, in the same time period, by other astronomers and they were also confirmed by the Jesuit astronomers of the Collegio Romano, so in fact anybody, who had anything to say on the topic, not only believed him but also congratulated him for having made them. 

“Galileo changed how people think about the Sun and Earth.” If any single person is going to be given credit for that then surely it should be Copernicus. In fact, it is, in my opinion, wrong to credit any single person with this. The shift in perception from a geocentric cosmos to a heliocentric one was a gradual accumulative process to which a fairly number of people contributed.

“He built a new telescope to study space.” I have difficulties with the new in this sentence. Galileo, like quite a large number of people built a so-called Dutch telescope with which to make astronomical observations. He was by no means unique in doing this and not even the first to do so. What should be expressed here is that Galileo was one of a number of people, who constructed telescopes, after it was invented in 1608, in order to make astronomical observations.

“He proved that Earth travels around the Sun.” Apart from the fact that the sentence isn’t even grammatically correct, it should read “the Earth”, it’s simple false. The problem that faced all the early supporters of a heliocentric model of the cosmos was that they simply couldn’t prove the hypothesis.

“People thought it was the other way around.” Of course, they did because that’s what our senses tell us. We all have to learn that it’s not true!

I have a very simple question. Why do people present young, impressionable children with garbage like this?

In case anybody is concerned, I’m sure the HISTSCI_HULK will return when he’s calmed down.  

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

Renaissance science – XXVII

Early on in this series I mentioned that a lot of the scientific developments that took place during the Renaissance were the result of practical developments entering the excessively theoretical world of the university disciplines. This was very much the case in the mathematical sciences, where the standard English expression for the Renaissance mathematicus is mathematical practitioner. In this practical world, areas that we would now regard as separate disciples were intertwined is a complex that the mathematical practitioners viewed as one discipline with various aspects, this involved astronomy, cartography, navigation, trigonometry, as well as instrument and globe making. I have already dealt with trigonometry, cartography and astronomy and will here turn my attention to navigation, which very much involved the other areas in that list.

The so-called Age of Discovery or Age of Exploration, that is when Europeans started crossing the oceans and discovering other lands and other cultures, coincides roughly with the Renaissance and this was, of course the main driving force behind the developments in navigation during this period. Before we look at those developments, I want to devote a couple of lines to the terms Age of Discovery and Age of Exploration. Both of them imply some sort of European superiority, “you didn’t exist until we discovered you” or “your lands were unknown until we explored them.” The populations of non-European countries and continents were not sitting around waiting for their lands and cultures to be discovered by the Europeans. In fact, that discovery very often turned out to be highly negative for the discovered. The explorers and discoverers were not the fearless, visionary heroes that we tend to get presented with in our schools, but ruthless, often brutal chancers, who were out to make a profit at whatever cost.  This being the case the more modern Contact Period, whilst blandly neutral, is preferred to describe this period of world history.

As far as can be determined, with the notable exception of the Vikings, sailing in the Atlantic was restricted to coastal sailing before the Late Middle Ages. Coastal sailing included things such as crossing the English Channel, which, archaeological evidence suggests, was done on a regular basis since at least the Neolithic if not even earlier. I’m not going to even try to deal with the discussions about how the Vikings possibly navigated. Of course, in other areas of the world, crossing large stretches of open water had become common place, whilst the European seamen still clung to their coast lines. Most notable are the island peoples of the Pacific, who were undertaking long journeys across the ocean already in the first millennium BCE. Arab and Chinese seamen were also sailing direct routes across the Indian Ocean, rather than hugging the coastline, during the medieval period. It should be noted that European exploited the navigation skills developed by these other cultures as they began to take up contact with the other part of the world. Vasco da Gamma (c. 1460–1524) used unidentified local navigators to guide his ships the first time he crossed the Indian Ocean from Africa to India. On his first voyage of exploration of the Pacific Ocean from 1768 to 1771, James Cook (1728–1779) used the services of the of the Polynesian navigator, Tupaia (c. 1725–1770), who even drew a chart, in cooperation with Cook, Joseph Banks, and several of Cooks officer, of his knowledge of the Pacific Ocean. 

Tupaia’s map, c. 1769 Source: Wikimedia Commons

There were two major developments in European navigation during the High Middle Ages, the use of the magnetic compass and the advent of the Portolan chart. The Chinese began to use the magnetic properties of loadstone, the mineral magnetite, for divination sometime in the second century BCE. Out of this they developed the compass needle over several centuries. It should be noted that for the Chinese, the compass points South and not North. The earliest Chinese mention of the use of a compass for navigation on land by the military is before 1044 CE and in maritime navigation in 1117 CE.

Diagram of a Ming Dynasty (1368–1644) mariner’s compass Source: Wikimedia Commons

Alexander Neckam (1157–1219) reported the use of the compass for maritime navigation in the English Channel in his manuscripts De untensilibus and De naturis rerum, written between 1187 and 1202.

The sailors, moreover, as they sail over the sea, when in cloudy whether they can no longer profit by the light of the sun, or when the world is wrapped up in the darkness of the shades of night, and they are ignorant to what point of the compass their ship’s course is directed, they touch the magnet with a needle, which (the needle) is whirled round in a circle until, when its motion ceases, its point looks direct to the north.

This and other references to the compass suggest that it use was well known in Europe by this time.

A drawing of a compass in a mid 14th-century copy of Epistola de magnete of Peter Peregrinus. Source: Wikimedia Commons

The earliest reference to maritime navigation with a compass in the Muslim world in in the Persian text Jawāmi ul-Hikāyāt wa Lawāmi’ ul-Riwāyāt (Collections of Stories and Illustrations of Histories) written by Sadīd ud-Dīn Muhammad Ibn Muhammad ‘Aufī Bukhārī (1171-1242) in 1232. There is still no certainty as to whether there was a knowledge transfer from China to Europe, either direct or via the Islamic Empire, or independent multiple discovery. Magnetism and the magnetic compass went through a four-hundred-year period of investigation and discovery until William Gilbert (1544–1603) published his De magnete in 1600. 

De Magnete, title page of 1628 edition Source: Wikimedia Commons

The earliest compasses used for navigation were in the form of a magnetic needle floating in a bowl of water. These were later replaced with dry mounted magnetic needles. The first discovery was the fact that the compass needle doesn’t actually point at the North Pole, the difference is called magnetic variation or magnetic declination. The Chinese knew of magnetic declination in the seventh century. In Europe the discovery is attributed to Georg Hartmann (1489–1564), who describes it in an unpublished letter to Duke Albrecht of Prussia. However, Georg von Peuerbach (1423–1461) had already built a portable sundial on which the declination for Vienna is marked on the compass.

NIMA Magnetic Variation Map 2000 Source: Wikimedia Commons

There followed the discovery that magnetic declination varies from place to place. Later in the seventeenth century it was also discovered that declination also varies over time. We now know that the Earth’s magnetic pole wanders, but it was first Gilbert, who suggested that the Earth is a large magnet with poles. The next discovery was magnetic dip or magnetic inclination. This describes the fact that a compass needle does not sit parallel to the ground but points up or down following the lines of magnetic field. The discovery of magnetic inclination is also attributed to Georg Hartmann. The sixteenth century English, seaman Robert Norman rediscovered it and described how to measure it in his The Newe Attractive (1581) His work heavily influenced Gilbert. 

Illustration of magnetic dip from Norman’s book, The Newe Attractive Source: Wikimedia Commons

The Portolan chart, the earliest known sea chart, emerged in the Mediterranean in the late thirteenth century, not long after the compass, with which it is closely associated, appeared in Europe. The oldest surviving Portolan, the Carta Pisana is a map of the Mediterranean, the Black Sea and part of the Atlantic coast.

Source: Wikimedia Commons

The origins of the Portolan chart remain something of a mystery, as they are very sophisticated artifacts that appear to display no historical evolution. A Portolan has a very accurate presentation of the coastlines with the locations of the major harbours and town on the coast. Otherwise, they have no details further inland, indicating that they were designed for use in coastal sailing. A distinctive feature of Portolans is their wind roses or compass roses located at various points on the charts. These are points with lines radiating outwards in the sixteen headings, on later charts thirty-two, of the mariner’s compass.

Central wind rose on the Carta Pisana

Portolan charts have no latitude or longitude lines and are on the so-called plane chart projection, which treats the area being mapped as flat, ignoring the curvature of the Earth. This is alright for comparatively small areas, such as the Mediterranean, but leads to serious distortion, when applied to larger areas.

During the Contact Period, Portolan charts were extended to include the west coast of Africa, as the Portuguese explorers worked their way down it. Later, the first charts of the Americas were also drawn in the same way. Portolan style charts remained popular down to the eighteenth century.

Portolan chart of Central America c. 1585-1595 Source:

A central problem with Portolan charts over larger areas is that on a globe constant compass bearings are not straight lines. The solution to the problem was found by the Portuguese cosmographer Pedro Nunes (1502–1578) and published in his Tratado em defensam da carta de marear (Treatise Defending the Sea Chart), (1537).

Image of Portuguese mathematician Pedro Nunes in Panorama magazine (1843); Lisbon, Portugal. Source: Wikimedia Commons

The line is a spiral known as a loxodrome or rhumb lines. Nunes problem was that he didn’t know how to reproduce his loxodromes on a flat map.

Image of a loxodrome, or rhumb line, spiraling towards the North Pole Source: Wikimedia Commons

The solution to the problem was provided by the map maker Gerard Mercator (1512–1594), when he developed the so-called Mercator projection, which he published as a world map, Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata (New and more complete representation of the terrestrial globe properly adapted for use in navigation) in 1569.

Source: Wikimedia Commons
The 1569 Mercator world map Source: Wikimedia Commons.

On the Mercator projection lines of constant compass bearing, loxodromes, are straight lines. This however comes at a price. In order to achieve the required navigational advantage, the lines of latitude on the map get further apart as one moves away from the centre of projection. This leads to an area distortion that increases the further north or south on goes from the equator. This means that Greenland, slightly more than two million square kilometres, appear lager than Africa, over thirty million square kilometres.

Mercator did not publish an explanation of the mathematics used to produce his projection, so initially others could reproduce it. In the late sixteenth century three English mathematicians John Dee (1527–c. 1608), Thomas Harriot (c. 1560–1621), and Edward Wright (1561–1615) all individually worked out the mathematics of the Mercator projection. Although Dee and Harriot both used this knowledge and taught it to others in their respective functions as mathematical advisors to the Muscovy Trading Company and Sir Walter Raleigh, only Wright published the solution in his Certaine Errors in Navigation, arising either of the Ordinarie Erroneous Making or Vsing of the Sea Chart, Compasse, Crosse Staffe, and Tables of Declination of the Sunne, and Fixed Starres Detected and Corrected. (The Voyage of the Right Ho. George Earle of Cumberl. to the Azores, &c.) published in London in 1599. A second edition with a different, even longer, title was published in the same year. Further editions were published in 1610 and 1657. 

Source: Wikimedia Commons
Wright explained the Mercator projection with the analogy of a sphere being inflated like a bladder inside a hollow cylinder. The sphere is expanded uniformly, so that the meridians lengthen in the same proportion as the parallels, until each point of the expanding spherical surface comes into contact with the inside of the cylinder. This process preserves the local shape and angles of features on the surface of the original globe, at the expense of parts of the globe with different latitudes becoming expanded by different amounts. The cylinder is then opened out into a two-dimensional rectangle. The projection is a boon to navigators as rhumb lines are depicted as straight lines. Source: Wikimedia Commons

His mathematical solution for the Mercator projection had been published previously with his permission and acknowledgement by Thomas Blundeville (c. 1522–c. 1606) in his Exercises (1594) and by William Barlow (died 1625) in his The Navigator’s Supply (1597). However, Jodocus Hondius (1563–1612) published maps using Wright’s work without acknowledgement in Amsterdam in 1597, which provoked Wright to publish his Certaine Errors. Despite its availability, the uptake on the Mercator projection was actually very slow and it didn’t really come into widespread use until the eighteenth century.

Wright’s “Chart of the World on Mercator’s Projection” (c. 1599), otherwise known as the Wright–Molyneux map because it was based on the globe of Emery Molyneux (died 1598) Source: Wikimedia Commons

Following the cartographical trail, we have over sprung a lot of developments in navigation to which we will return in the next episode. 

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Renaissance science – XXVI

I wrote a whole fifty-two-part blog post series on The Emergence of Modern Astronomy, much of which covered the same period as this series, so I’m not going to repeat it here. However, an interesting question is, did the developments in astronomy during the Humanist Renaissance go hand in hand with humanism and to what extent, or did the two movements run parallel in time to each other without significant interaction? 

The simple answer to my own questions is yes, humanism and the emergence of modern astronomy were very closely interlinked in the period between 1400 and the early seventeenth century. This runs contrary to a popular conception that the Humanist Renaissance was purely literary and in no way scientific. In what follows I will briefly sketch some of that interlinking. 

To start, two of the driving forces behind the desire to renew and improve astronomy, the rediscovery of Ptolemaic mathematics-based cartography and the rise in importance of astrology were very much part of the Humanist Renaissance, as I have already documented in earlier episodes of this series. It is not a coincidence that many of the leading figures in the development of modern astronomy were also involved, either directly or indirectly, in the new cartography. Also, nearly all of them were active astrologers. 

Turning to the individual astronomers, the man, who kicked off the debate on the astronomical status of comets, a debate that, I have shown, played a central role in the evolution of modern astronomy, Paolo dal Pozzo Toscanelli (1397–1482) a member of the Florentine circle of prominent humanist scholars that included Filippo Brunelleschi, Marsilio Ficino, Leon Battista Alberti and Cardinal Nicolaus Cusanus, all of whom have featured in earlier episodes of this series.

Paolo dal Pozzo Toscanelli Source: Wikimedia Commons

Toscanelli, who is best known as the cosmographer, who supplied Columbus with a misleading world map, was one of those who met the Neoplatonic philosopher Georgius Gemistus Pletho (c. 1355–c. 1452) at the Council of Florence. Pletho introduced Toscanelli to the work of the Greek geographer Strabo (c. 64 BCE–c. 24 CE), which was previously unknown in Italy. 

Turning to the University of Vienna and the so-called First Viennese School of Mathematics, already during the time of Johannes von Gmunden (c. 1380–1442) and Georg Müstinger (before 1400–1442), Vienna had become a major centre for the new cartography as well as astronomy. However, it is with the next generation that we find humanist scholars at work. Toscanelli’s unpublished work on comets might have remained unknown if it hadn’t been for Georg von Peuerbach (1423–1461). As a young man Peuerbach had travelled extensively in Italy and become acquainted with the circle of humanists to which Toscanelli belonged. He shared an apartment in Rome with Cusanus and personally met and exchanged ideas with Toscanelli. Returning to Vienna he lectured on poetics and took a leading role in reviving classical Greek and Latin literature, a central humanist concern. Today he is, of course, better known for his work as an astronomer and as the teacher of Johannes Müller, better known Regiomontanus.

First page of Peuerbach’s Theoricae novae planetarum in the Manuscript Krakau, Biblioteca Jagiellońska, Ms. 599, fol. 1r (15th century) Source: Wikimedia Commons

Regiomontanus (1436–1476) became a member of the familia (household) of the leading Greek humanist scholar Basilios Bessarion (1403–1472), a pupil of Pletho. He travelled with Bessarion through Italy, working as his librarian finding and copying Latin and Greek manuscripts on astronomy, astrology and mathematics for Bessarion’s library. Bessarion had taught him Greek for this purpose. Leaving Bessarion’s service Regiomontanus served as librarian for the humanist scholars, János Vitéz Archbishop of Esztergom (c. 1408–1472) a friend of Peuerbach’s and then Matthias Corvinus (1443–1490) King of Hungary. 

Regiomontanus woodcut from the 1493 Nuremberg Chronicle Source: Wikimedia Commons

When Regiomontanus left Hungary for Nürnberg he took a vast collection of Geek and Latin manuscripts with him, with the intention of printing them and publishing them. At the same time applying humanist methods of philology to free them of their errors accumulated through centuries of copying and recopying. A standard humanist project as was the Epitome of Ptolemaeus that he and Peuerbach produced under the stewardship of Bessarion.

The so-called Second Viennese School of mathematics was literally founded by a humanist, when Conrad Celtis (1459–1508) took the professors of mathematics Andreas Stiborius (1464–1515) and Johann Stabius (before 1468–1522), along with the student Georg Tanstetter (1482–1535) from Ingolstadt to Vienna, where he founded his Collegium poetarum et mathematicorum, that is a college for poetry and mathematics, in 1497. Ingolstadt had established the first ever German chair for mathematics to teach astrology to medical students, also basically a humanist driven development.

Conrad Celtis: In memoriam by Hans Burgkmair the Elder, 1507
Source: Wikimedia Commons

The wind of humanism was strong in Vienna, where Peter Apian (1495–1552) was Tanstetter’s star pupil becoming like his teacher a cosmographer, returning to Ingolstadt, where his star pupil was his own son Philipp (1531–1589), like his father a cosmographer. Philipp became professor in Tübingen, where he was Michael Mästlin’s teacher, instilling him with the Viennese humanism. As should be well known Mästlin was Kepler’s teacher.

Source: Wikimedia Commons

Back-tracking, we must consider the central figure of the emergence of modern astronomy, Nicolaus Copernicus (1473–1543). There are no doubts about Copernicus’ humanist credentials.

Copernicus holding lily-of-the-valley: portrait in Nicolaus Reusner’s Icones (1587) Source: Wikimedia Commons

He initially studied at the University of Krakow, the oldest humanist university in Europe north of the Italian border. He continued his education at various North Italian humanist universities, where he continued to learn his astronomy from the works of Peuerbach and Regiomontanus (as he had already done in Krakow) under the supervision of Domenico Maria da Novara (1454–1504) a Neoplatonist, who regarded himself as a student of Regiomontanus.

Domenico Maria da Novara Source Museo Galileo

In Northern Italy Copernicus received a full humanist education even learning Greek and some Hebrew. Establishing his humanist credentials, Copernicus published a Latin translation from the Greek of a set of 85 brief poems by the seventh century Byzantine historian Theophylact Somicatta, as Theophilacti scolastici Simocati epistolae morales, rurales et amatoriae interpretatione Latina in 1509. He also wrote some Greek poetry himself.

Source

Copernicus is often hailed as the first modern astronomer but as many historians have pointed out, his initial intention, following the lead of Regiomontanus, was to restore the purity of Greek astronomy, a very humanist orientated undertaking. He wanted to remove the Ptolemaic equant point, which he saw as violating the Platonic ideal of uniform circular motion. De revolutionibus was modelled on Ptolemaeus’ Mathēmatikē Syntaxis, or more accurately on the Epytoma in almagesti Ptolemei of Peuerbach and Regiomontanus.

Tycho Brahe (1546–1601) was also heavily imbued with the humanist spirit. His elaborate, purpose-built home, laboratory, and observatory on the island of Hven, Uraniborg, was built in the style of the Venetian architect Andrea Palladio (1508–1580),

Portrait of Palladio by Alessandro Maganza Source: Wikimedia Commons

the most influential of the humanist architects, and was one of the earliest buildings constructed in the Renaissance style in Norther Europe.

Source:

All of the Early Modern astronomers from Toscanelli down to at least Tycho, and very much including Copernicus, were dedicated to the humanist ideal of restoring what they saw as the glory of classical astronomy from antiquity. Only incidentally did they pave a road that led away from antiquity to modern astronomy. 

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OHMS or everything you wanted to know about the history of trigonometry and didn’t know who to ask

When I was a kid, letters from government departments came in buff, manila envelopes with OHMS printed on the front is large, black, capital letters. This acronym stood for, On Her Majesty’s Service and earlier during Liz’s father’s reign (and no I’m not that old, although I was just born in his reign), On His Majesty’s Service, implying that civil servants worked directly for the monarch.  This was, of course, the origin of the title of Ian Fleming’s eleventh James Bond novel, On Her Majesty’s Secret Service

When I started learning trigonometry at school this acronym took on a whole new meaning as a mnemonic for the sine relation in right angle triangles, Opposite over Hypotenuse Means Sine. Recently it occurred to me that we had no mnemonic for the other trigonometric relations. Now in those days or even later when the trigonometry I was taught got more complex, I wasn’t aware of the fact that this mathematical discipline had a history. Now, a long year historian of mathematics, I am very much aware of the fact that trigonometry has a very complex, more than two-thousand-year history, winding its way from ancient Greece over India, the Islamic Empire and Early Modern Europe down to the present day. 

The Canadian historian of mathematics, Glen van Brummelen has dedicated a large part of his life to researching, writing up and publishing that history of trigonometry. The results of his labours have appeared in three volumes, over the years, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton University Press, Princeton and Oxford, 2009, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, Princeton and Oxford, 2013 and most recently The Doctrine of TrianglesA History of Modern Trigonometry, Princeton University Press, Princeton and Oxford, 2021. He describes himself as the “best trigonometry historian, and the worst trigonometry historian”, as he is the only one[1]

A review of these three volumes could be written in one sentence, if you are interested in the history of trigonometry, then these three masterful volumes are essential. One really doesn’t need to say more, but in what follows I will give a brief sketch of each of the books. 

The Mathematics of the Heavens and the Earth: The Early History of Trigonometry delivers exactly what it says on the cover. The book opens with a brief but detailed introduction to the basics of spherical astronomy, because for a large part of the period covered, what we have is not the history of plane trigonometry, that’s the stuff we all learnt at school, but spherical trigonometry, that is the geometry of triangles on the surface of a sphere, which was developed precisely to do spherical astronomy. 

A friendly warning for potential readers this is not popular history but real, hardcore history of mathematics with lots of real mathematical examples worked through in detail. However, given the way Van Brummelen structures his narrative, it is possible to skip the worked examples and still get a strong impression of the historical evolution of the discipline. This is possible because Van Brummelen gives a threefold description of every topic that he elucidates. First comes a narrative, fairly non-technical, description of the topic he is discussing. This is followed by an English translation of a worked example from the historical text under discussion, followed in turn by a technical explication of the text in question in modern terminology. Van Brummelen’s narrative style is clear and straightforward meaning that the non-expert reader can get good understanding of the points being made, without necessarily wading through the intricacies of the piece of mathematics under discussion. 

The book precedes chronologically. The first chapter, Precursors, starts by defining what trigonometry is and also what it isn’t. Having dealt with the definitions, Van Brummelen moves onto the history proper dealing with things that preceded the invention of trigonometry, which are closely related but are not trigonometry. 

Moving on to Alexandrian Greece, Van Brummelen takes the reader through the beginnings of trigonometry starting with Hipparchus, who produced the first chord table linking angles to chords and arcs of circles, Moving on through Theodosius of Bithynia and Menelaus of Alexandria and the emergence of spherical trigonometry. He then arrives at Ptolemy his astronomy and geography. Ptolemy gets the longest section of the book, which given that everything that follows in some way flows from his work in logical. Here we also get two defining features of the book. The problem of calculating trigonometrical tables and what each astronomer or mathematician contributed to this problem and the trigonometrical formulas that each of them developed to facilitate calculations. 

From Greece we move to India and the halving of Hipparchus’ and Ptolemy’s chords to produce the sine function and later the cosine that we still use today. Van Brummelen takes his reader step for step and mathematician for mathematician through the developments of trigonometry in India. 

The Islamic astronomers took over the baton from the Indians and continued the developments both in astronomy and geography. It was Islamic mathematicians, who developed the plane trigonometry that we know today rather than the spherical trigonometry. As with much other mathematics and science, trigonometry came into medieval Europe through the translation movement out of Arabic into Latin. Van Brummelen traces the development in medieval Europe down to the first Viennese School of mathematics, John of Gmunden, Peuerbach, and Regiomontanus. This volume closes with Johannes Werner and Copernicus, with a promise of a second volume. 

In the book itself, the brief sketch above is filled out in incredible detail covering all aspects of the evolution of the discipline, the problems, the advances, the stumbling stones and the mathematicians and astronomers, who discovered each problem, solved, or failed to solve them. To call Van Brummelen comprehensive would almost be an understatement. Having finished this first volume, I eagerly awaited the promised second volume, but something else came along instead.

Having made clear in his first book that the emphasis is very much on spherical trigonometry rather than plane trigonometry, in his second book Van Brummelen sets out to explain to the modern reader what exactly spherical trigonometry is, as it ceased to be part of the curriculum sometime in the modern period. What we have in Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry is a spherical trigonometry textbook written from a historical perspective. The whole volume is written in a much lighter and more accessible tone than The Mathematics of the Heavens and the Earth. After a preface elucidating the purpose of the book there follow two chapters, Heavenly Mathematics and Exploring the Sphere, which lay out and explain the basics in clear and easy to follow steps.

Next up, we have the historical part of the book with one chapter each on The Ancient Approach and The Medieval Approach. These chapters could be used as an aid to help understand the relevant sections of the authors first book. But fear not the reader must not don his medieval personality to find their way around the complexities of spherical trigonometry because following this historical guide we are led into the modern textbook.

The bulk of the book consists of five chapters, each of which deals in a modern style with an aspect of spherical trigonometry: Right Angle Triangles, Oblique Triangles, Areas, Angles and Polyhedra, Stereographic Projection, and finally Navigation by the Stars. The chapter on stereographic projection is particularly interesting for those involved with astrolabes and/or cartography. 

The book closes with three useful appendices. The first is on Ptolemy’s determination of the position of sun. The second is a bibliography of textbooks on or including spherical trigonometry with the very helpful indication, which of them are available on Google Books. The final appendix is a chapter by chapter annotated list of further reading on each topic. 

If you wish to up your Renaissance astrology game and use the method of directions to determine your date of death, which require spherical trigonometry to convert from one celestial coordinate system to another, then this is definitely the book for you. It is of course also a brilliant introduction for anybody, who wishes to learn the ins and outs of spherical trigonometry. 

I bought Van Brummelen’s first book when it was published, in 2009, and read it with great enthusiasm, but experienced a sort of coitus interruptus, when in stopped in the middle of the Renaissance, the period that interested me most. I was consoled by the author’s declaration that a second volume would follow, which I looked forward to with great expectations. Over the years those expectations dimmed, and I began to fear that the promised second volume would never appear, so I was overjoyed when the publication of The Doctrine of Triangles was announced this year and immediately placed an advanced order. I was not disappointed. 

The modern history of trigonometry continues where the early history left off, tracing the developments of trigonometry in Europe from Regiomontanus down to Clavius and Gunter in the early seventeenth century. There then follows a major change of tack, as Van Brummelen delves into the origins of logarithms.

Today in the age of the computer and the pocket calculator, logarithmic tables are virtually unknown, a forgotten relic of times past. I, however, grew up using my trusty four figure log tables to facilitate calculations in maths, physics, and chemistry. Now, school kids only know logarithms as functions in analysis. One thing that many, who had the pleasure of using log tables, don’t know is that Napier’s first tables were of the logarithms of trigonometrical factions in order to turn the difficult multiplications and divisions of sines, cosines et al in spherical trigonometry into much simpler additions and subtractions and therefore Van Brummelen’s detailed presentation of the topic.

Moving on, in his third chapter, Van Brummelen now turns to the transition of trigonometry as a calculation aid in spherical and plane triangles to trigonometrical functions in calculus. There where they exist in school mathematics today. Starting in the period before Leibniz and Newton, he takes us all the way through to Leonard Euler in the middle of the eighteenth century. 

The book now undergoes a truly major change of tack, as Van Brummelen introduces a comparative study of the history of trigonometry in Chinese mathematics. In this section he deals with the Indian and Islamic introduction of trigonometry into China and its impact. How the Chinese dealt with triangles before they came into contact with trigonometry and then the Jesuit introductions of both trigonometry and logarithms into China and to what extent this influenced Chinese geometry of the triangle. A fascinating study and an enrichment of his already excellent book.

The final section of the book deals with a potpourri of developments in trigonometry in Europe post Euler. To quote Van Brummelen, “A collection of short stories is thus more appropriate here than a continuous narrative.” The second volume of Van Brummelen’s history is just as detailed and comprehensive as the first. 

All three of the books display the same high level of academic rigour and excellence. The two history volumes have copious footnotes, very extensive bibliographies, and equally extensive indexes. The books are all richly illustrated with many first-class explanatory diagrams and greyscale prints of historical title pages and other elements of the books that Van Brummelen describes. All in all, in his three volumes Van Brummelen delivers a pinnacle in the history of mathematics that sets standards for all other historians of the discipline. He really does live up to his claim to be “the best historian of trigonometry” and not just because he’s the only one.

Coda: If the potential reader feels intimidated by the prospect of the eight hundred and sixty plus pages of the three volumes described here, they could find a gentle entry to the topic in Trigonometry: A Very Short Introduction (OUP, 2020), which is also authored by Van Brummelen, a sort of Van Brummelen light or Van Brummelen’s greatest hits.

In this he covers a wide range of trigonometrical topics putting them into their historical context. But beware, reading the Very Short Introduction could well lead to further consumption of Van Brummelen’s excellent work. 


[1] This is not strictly true as Van Brummelen has at least two predecessors both of who he quotes in his works. The German historian Anton von Braunmühl, who wrote several articles and a two volume Vorlesung über Geschichte der Trigonometrie (Leipzig, 1900/1903) and the American Sister Mary Claudia Zeller, The Development of Trigonometry from Regiomontanus to Pitiscus (Ann Arbor 1944)

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Renaissance Science – XXII

Perhaps surprisingly, land surveying as we know it today, a mathematical discipline utilising complex technological measuring instruments is very much a product of the practical mathematics of the Renaissance. Why surprisingly? Surveying is an ancient discipline that has its origins in humanity becoming settled many thousands of years ago. Ancient monuments such as the pyramids or Stonehenge definitely required some level of surveying in their construction and there are surviving documents from all literate ancient societies that refer to methods or the practice of surveying. 

All surveying uses some aspects of geometry and as Herodotus famously claimed geometry (Greek: geōmetría from geōmétrēs), which literally means measurement of earth or land, had its origins in Egyptian surveying for tax purposes. According to his account, King Sesostris divided all the lands in Egypt amongst its inhabitants in return for an annual rent. However, every year the Nile floods washing away the parts of the plots:

The country is converted into a sea, and nothing appears but the cities, which looked like islands in the Aegean. 

Those whose land had been lost objected to paying the rent, so Sesostris summoned those affected to appear before him.

Upon which, the king sent persons to examine, and determine by measurement the exact extent of the loss: and thenceforth only such a rent was demanded of him as was proportionate to the reduced size of his land. From this practice, I think, geometry first came to be known in Egypt, whence it passed into Greece.

According to legend, both Thales and Pythagoras, are reputed to have learnt their geometry in Egypt.

In all early cultures surveying was fairly primitive with measurements being made with ropes and measuring rods. In Egypt, surveyors were known as rope stretchers (harpedonaptai), the ropes used for measuring being stretched to avoid sagging.

A rope being used to measure fields. Taken from the Tomb of Menna, TT69. (c. 1500–1200 BCE) Source: Wikimedia Commons

Longer distances were either measured by estimation or by pacing. In ancient Egypt and Greece Bematistae (step measurer) where trained to walk with equal length paces and the historical records of Alexander the Great’s campaigns suggest that they were indeed highly accurate. This measuring of distances by pacing in reflected in our word mile, which is the Latin word for a thousand, mille, meaning a thousand paces.

The Latin for surveyor was agrimensores, meaning field measurers. They were also called gromatici after the groma a surveyor’s pole, an early instrument for determining lines at right angles to each other. 

The groma or gruma was a Roman surveying instrument. It comprised a vertical staff with horizontal cross-pieces mounted at right angles on a bracket. Each cross piece had a plumb line hanging vertically at each end. It was used to survey straight lines and right angles, thence squares or rectangles. They were stabilized on the high ground and pointed in the direction it was going to be used. The helper would step back 100 steps and place a pole. The surveyor would tell him where to move the pole and the helper would set it down.

(Lewis, M. J. T., Surveying instruments of Greece and Rome, McGraw Hill Professional, 2001, p. 120)
Staking out a right angle using a groma

Another instrument used for the same purpose was the dioptra. The dioptra was a sighting tube or, alternatively an alidade, that is a rod with a sight at each end, attached to a stand. If fitted with protractors, it could be used to measure angles. Hero from Alexandria wrote a whole book on this instrument and its use but there are doubts that the dioptra in the complex form described by Hero was actually used in field surveying.

Dioptra as described by Hero of Alexandria Source: Wikimedia Commons

The methods used by the Romans in field surveying were described in the works of technical authors such as Sextus Julius Frontinus (c. 40–103 CE) and Gaius Julius Hyginus (c. 64 BCE–17 CE).

All of the surveying described in antiquity was fairly small scale–measuring fields, determining boundaries, laying out military camps, etc–and geometrically centred on squares and rectangles. Cartography was done using astronomical determinations of latitude and longitude, whereby the latter was difficult, and distances estimated or paced. Nothing really changed in Europe during the medieval period. The surveying that was done was carried out using the same methods that the Romans had used. However, during the fifteenth century things began to change substantially and the first question is why?

The rediscovery of Ptolemaeus’ Geographia at the beginning of the fifteenth century, as described here, and the subsequent substantial increase in cartographical activity, as described here, played a major role, but as already stated above Ptolemaic cartography relied almost exclusively on astronomical methods and did not utilise field surveying. However, there was an increased demand for internal accuracy in maps that astronomical methods could not supply. Secondly, changes in land ownership led to an increased demand for accurate field surveying of estates that required more sophisticated methods than those of the agrimensores. Lastly, we have a good example of the knowledge crossover, typical for the Renaissance, as described in Episode V of this series. The surveyors of antiquity were artisans producing practical knowledge for everyday usage. In the Renaissance, university educated scholars began to interest themselves for this practical knowledge and make contributions to its development and it is these developments that we will now look at. 

The biggest change in surveying was the introduction of the simple geometrical figure the triangle into surveying, as Sebastian Münster, one of the most influential cosmographers (today we would say geographer) of the period, wrote in a German edition of his Cosmographia. Beschreibung aller Lender durch Sebastianum Münsterum in 1550:

Every thing you measure must be measured in triangles.

Actually, the theory of similar triangles, as explained in Euclid’s Elements, had been used in surveying in antiquity, in particular to determine the height of things or for example the width of a river. A method that I learnt as a teenager in the Boy Scouts.

What was new as we will see was the way that triangles were being used in surveying and that now it was the angles of the triangles that were measured and not the length of the sides, as in the similar triangles’ usage. We are heading towards the invention and usage of triangulation in surveying and cartography, a long-drawn-out process.

In his Ludi rerum mathematicarum (c. 1445), the architect Leon Battista Alberti describes a method of surveying by taking angular bearings of prominent points in the area he is surveying using a self-made circular protractor to create a network of triangles. He concludes by explaining that one only needs to the length of one side of one triangle to determine all the others. What we have here is an early description of a plane table surveying (see below) and step towards triangulation that, however, only existed in manuscript 

Alberti Ludi rerum mathematicarum 

Münster learnt his geometry from Johannes Stöffler (1452–1531), professor for mathematics in Tübingen, who published the earliest description of practical geometry for surveyors. In his De geometricis mensurationibus rerum (1513),

Johannes Stöffler Engraving from the workshop of Theodor de Brys, Source: Wikimedia Commons

Stöffler explained how inaccessible distances could be measured by measuring one side of a triangle using a measuring rod (pertica) and then observing the angles from either end of the measured stretch. However, most of the examples in his book are still based on the Euclidian concept of similar triangles rather than triangulation. In 1522, the printer publisher Joseph Köbel, who had published the Latin original, published a German version of Stöffler’s geometry book. 

Joseph Köbel Source: Wikimedia Commons

Both Peter Apian in his Cosmographia (1524) and Oronce Fine in his De geometria practica (1530) give examples of using triangles to measure distances in the same way as Stöffler.

Source

Fine indicating that he knew of Stöffler’s book. Apian explicitly uses trigonometry to resolve his triangles rather than Euclidian geometry. Trigonometry had already been known in Europe in the Middle Ages but hadn’t been used before the sixteenth century in surveying. Fine, however, still predominantly used Euclidian methods in his work, although he also, to some extent, used trigonometry.

A very major development was the publication in 1533 of Libellus de locorum describendum ratione (Booklet concerning a way of describing places) by Gemma Frisius as an appendix to the third edition of Apian’s Cosmographia, which he edited, as he would all edition except the first. Here we have a full technical description of triangulation published for the first time. It would be included in all further editions in Latin, Spanish, French, Flemish, in what was the most popular and biggest selling manual on mapmaking and instrument making in the sixteenth and seventeenth centuries.

Source: Wikimedia Commons

1533 also saw the publication in Nürnberg by Johannes Petreius (c. 1497–1550) of Regiomontanus’s De triangulis omnimodis (On triangles of every kind) edited by the mapmaker and globe maker, Johannes Schöner (1477–1547).

Source:

This volume was originally written in 1464 but Regiomontanus died before he could print and publish it himself, although he had every intention of doing so. This was the first comprehensive work on trigonometry in Europe in the Early Modern Period, although it doesn’t cover the tangent, which Regiomontanus handled in his Tabula directionum (written 1467, published 1490), an immensely popular and oft republished work on astrology. 

Regiomontanus built on previous medieval works on trigonometry and the publication of his book introduces what Ivor Grattan Guinness has termed The Age of Trigonometry. In the sixteenth century it was followed by Rheticus’ separate publication of the trigonometrical section of Copernicus’s De revolutionibus, as De lateribus et angulis triangulorium in 1542. Rheticus (1514–1574) followed this in 1551 with his own Canon doctrinae triangulorum. This was the first work to cover all six trigonometric functions and the first to relate the function directly to triangles rather than circular arcs.

Source: Wikimedia Commons

Rheticus spent the rest of his life working on his monumental Opus Palatinum de Triangulis, which was, however, first published posthumously by his student Lucius Valentin Otho in 1596. Rheticus and Otho were pipped at the post by Bartholomaeus Pitiscus (1561–1613), whose Trigonometriasive de solutione triangulorum tractatus brevis et perspicuous was published in 1595 and gave the discipline its name.

Source: Wikimedia Commons

Pitiscus’ work went through several edition and he also edited and published improved and corrected editions of Rheticus’ trigonometry volumes. 

Through Gemma Frisius’ detailed description of triangulation and sixteenth century works on trigonometry, Renaissance surveyors and mapmakers now had the mathematical tools for a new approach to surveying. What they now needed were the mathematical instruments to measure distances and angles in the field and they were not slow in coming.

The measure a straight line of a given distance as a base line in triangulation surveyors still relied on the tools already used in antiquity the rope and the measuring rod. Ropes were less accurate because of elasticity and sagging if used for longer stretches. In the late sixteenth century, they began to be replaced by the surveyor’s chain, made of metal links but this also suffered from the problem of sagging due to its weight, so for accuracy wooden rods were preferred. 

A Gunter chain photographed at Campus Martius Museum. Source: Wikimedia Commons

In English the surveyor’s chain is usually referred to as Gunter’s chain after the English practical mathematician Edmund Gunter (1581–1626) and he is also often referred to erroneously as the inventor of the surveyor’s chain but there are references to the use of the surveyor’s chain in 1579, when Gunter was still a child. 

He did, however, produce what became a standardised English chain of 100 links, 66 feet or four poles, perches, or rods long, as John Ogilby (1600–1676) wrote in his Britannia Atlas in 1675:

…a Word or two of Dimensurators or Measuring Instruments, whereof the mosts usual has been the Chain, and the common length for English Measures 4 Poles, as answering indifferently to the Englishs Mile and Acre, 10 such Chains in length making a Furlong, and 10 single square Chains an Acre, so that a square Mile contains 640 square Acres…’

An English mile of 5280 feet was thus 80 chains in length and there are 10 chains to a furlong. An acre was 10 square chains. I actually learnt this antiquated system of measurement whilst still at primary school. The name perch is a corruption of the Roman name for the surveyor’s rod the pertica. 

To measure angles mapmakers and surveyors initially adopted the instruments developed and used by astronomers, the Jacob staff, the quadrant, and the astrolabe. An instrument rarely still used in astronomy but popular in surveying was the triquetum of Dreistab. The surveyors triquetum consists of three arms pivoted at two points with circular protractors added at the joints to measure angles and with a magnetic compass on the side to determine bearings. 

Surveyors then began to develop variants of the dioptra. The most notable of these, that is still in use today albeit highly modernised, was the theodolite, an instrument with sights capable of measuring angles both vertically and horizontally. The name first occurs in the surveying manual A geometric practice named Pantometria by Leonard Digges (c. 1515–c. 1559) published posthumously by his son Thomas (c. 1546–1595) in 1571.

Leonard Digges  A geometric practice named Pantometria Source

However, Digges’ instrument of this name could only measure horizontal angles. He described another instrument that could measure both vertical and horizontal angles that he called a topographicall instrument. Josua Habermehl, about whom nothing is known, but who was probably a relative of famous instrument maker Erasmus Habermehl (c. 1538–1606), produced the earliest known instrument similar to the modern theodolite, including a compass and tripod, in 1576. In 1725, Jonathan Sisson (1690–1747) constructed the first theodolite with a sighting telescope.

Theodolite 1590 Source:

A simpler alternative to the theodolite for measuring horizontal angles was the circumferentor. This was a large compass mounted on a plate with sights, with which angles were measured by taking their compass bearings.

18th century circumferentor

Instruments like the triquetum and the circumferentor were most often used in conjunction of another new invention, the plane table. Gemma Frisius had already warned in his Libellus de locorum describendum rationeof the difficulties of determining the lengths of the sides of the triangles in triangulation using trigonometry and had described a system very similar to the plane table in which the necessity for these calculation is eliminated. 

Surveying with plane table and surveyor’s chain

The plane table is a drawing board mounted on a tripod, with an alidade. Using a plumb bob, the table is centred on one end of a baseline, levelled by eye or after its invention (before 1661) with a spirit level, and orientated with a compass. The alidade is placed on the corresponding end of the scaled down baseline on the paper on the table and bearings are taken of various prominent features in the area, the sight lines being drawn directly on the paper. This procedure is repeated at the other end of the baseline creating triangles locating the prominent figures on the paper without having to calculate.

Philippe Danfrie (c.1532–1606) Surveying with a plane table

As with the theodolite there is no certain knowledge who invented the plane table. Some sources attribute the invention of the plane table to Johannes Praetorius (1537–1616), professor for mathematics at the University of Altdorf, as claimed by his student Daniel Schwentner (1585–1636). However, there was already a description of the plane table in “Usage et description de l’holomètre”, by Abel Foullon (c. 1514–1563) published in Paris in 1551. It is obvious from his description that Foullon hadn’t invented the plane table himself. 

The plane table is used for small surveys rather than mapmaking on a large scale and is not triangulation as described by Gemma Frisius. Although the Renaissance provided the wherewithal for full triangulation, it didn’t actually get used much for mapping before the eighteenth century. At the end of the sixteenth century Tycho Brahe carried out a triangulation of his island of Hven, but the results were never published. The most notable early use was by Willebrord Snel (1580–1626) to measure one degree of latitude in order to determine the size of the earth in 1615. He published the result in his Eratosthenes batavus in Leiden in 1617. He then extended his triangulation to cover much of the Netherlands.

Snel’s Triangulation of the Dutch Republic from 1615 Source: Wikimedia Commons

In the late seventeenth century Jean Picard (1620–1682) made a much longer meridian measurement in France using triangulation. 

Picard’s triangulation and his instruments

In fourteen hundred European surveyors were still using the same methods of surveying as the Romans a thousand years earlier but by the end of the seventeenth century when Jean-Dominique Cassini (1625–1712) began the mapping of France that would occupy four generations of the Cassini family for most of the eighteenth century, they did so with the fully developed trigonometry-based triangulation that had been developed over the intervening three hundred years. 

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

Renaissance Science – XVII

As we saw in the last episode, Ptolemaeus’ Geographia enjoyed a strong popularity following its rediscovery and translation into Latin from Greek at the beginning of fifteenth century, going through at least five printed editions before the end of the century. The following century saw several important new translation and revised editions both in Latin and in the vernacular. This initial popularity can at least be partially explained by the fact that Ptolemaeus’ Mathēmatikē Syntaxis and his Tetrabiblos, whilst not without rivals, were the dominant books in medieval astronomy and astrology respectively. But the Geographia, although, as explained in the previous episode, in some senses related to the other two books, was a book about mapmaking. So how did affect European mapmaking in the centuries after its re-emergence? To answer this question, we first need to look at medieval European, terrestrial mapmaking.

Mapmaking was relatively low level during the medieval period before the fifteenth century and although there were certainly more, only a very small number of maps have survived. These can be divided into three largely distinct categories, regional and local maps, Mappa Mundi, and portolan charts. There are very few surviving regional or local maps from the medieval period and of those the majority are from 1350 or later, mapmaking was obviously not very widespread in the early part of the Middle Ages. There are almost no maps of entire countries, the exceptions being maps of Palestine,

Map of Palestine according to Burchard of Mount Sion Manuscript c. 1300 entitled: “De more vivendi diversarum gentium, secundum Hieronymum in libro II contra Iovinianum, quae illis cibariis vesci solent, quibus abundant” Source: Wikimedia Commons

the Matthew Paris and Gough maps of Britain,

The most developed of Matthew Paris’s four maps of Britain 13th century (Cotton MS Claudius D VI, fol. 12v). The work is organised around a central north-south itinerary from Dover to Newcastle. The crenellations of both the Antonine Wall and Hadrian’s Wall can be seen in the upper half of the drawing. British Library, London. via Wikimedia Commons

and Nicolas of Cusa’s maps of Germany and central Europe. 

Nicolas of Cusa map of central Europe printed edition 1491 Germanisches Nationalmuseum Nürnberg via Wikimedia Commons

The Mappa Mundi are the medieval maps of the known world. These range from very simple schematic diagrams to the full-blown presentations of the oikoumenikos, the entire world as known to European antiquity, consisting of the three continents of Asia, Europe, and Africa. The sketch maps are mostly of two different types, the zonal maps, and the T-O maps. 

The zonal maps show just the eastern hemisphere divided by lines into the five climata or climate zones, as defined by Aristotle. These are the northern frigid zone, the northern temperate zone, the equatorial tropical zone, the southern temperate zone, and the southern frigid zone, of which the Greek believed only the two temperate zones were habitable. In the medieval period, zonal maps are mostly found in copies of Macrobius’ Commentarii in Somnium Scipionis (Commentary on Cicero’s Dream of Scipio).

Macrobius zonal world map c. 1050 Source: British Library

T-O sketch maps show a diagrammatic presentation of the three know continents, Asia, Europe, and Africa enclosed within a double circle representing the ocean surrounding oikoumenikos. The oikoumenikos is orientated, that is with east at the top and is divided into three parts by a T consisting of the Mediterranean, the Nile, and the Danube, with the top half consisting of Asia and the bottom half with Europe on the left and Africa on the right. T-O maps have their origin in the works of Isidore, his De Natura Rerum and Etymologiae. He writes in De Natura Rerum

So the earth may be divided into three sides (trifarie), of which one part is Europe, another Asia, and the third is called Africa. Europe is divided from Africa by a sea from the end of the ocean and the Pillars of Hercules. And Asia is divided from Libya with Egypt by the Nile… Moreover, Asia – as the most blessed Augustine said – runs from the southeast to the north … Thus we see the earth is divided into two to comprise, on the one hand, Europe and Africa, and on the other only Asia

This T and O map, from the first printed version of Isidore’s Etymologiae, identifies the three known continents as populated by descendants of Sem, Iafeth and Cham. Source: Wikimedia Commons

For most people the term Mappa Mundi evokes the large circular, highly coloured maps of the oikoumenikos, packed with symbols and text such as the Hereford and Ebstorf maps, rather that the small schematic ones.

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

These are basically T-O maps but appear to be geographically very inaccurate. This is because although they give an approximate map of the oikoumenikos, they are not intended to be geographical maps, as we understand them today. So, what are they? The clue can be found in the comparatively large number of regional maps of Palestine, the High Middle Ages is a period where the Catholic Church and Christianity dominated Europe and the Mappa Mundi are philosophical maps depicting the world of Christianity. 

Recreation of the Ebstorf Map of about 1235; the original was destroyed by wartime bombing Source: Wikimedia Commons

These maps are literally orientated, that is East at the top and have Jerusalem, the hub of the Christian world, at their centre. The Hereford map has the Garden of Eden at the top in the east, whereas the Ebstrof map, has Christ’s head at the top in the east, his hands on the sides north and south and his feet at the bottom in the south, so that he is literally holding the world. The much smaller Psalter map has Christ above the map in the east blessing the world.

Psalter world map, ca. 1260 British Library via Wikimedia Commons

These are not maps of the world but maps of the Christian world. The illustrations and cartouches scattered all over the maps elucidate a motley collection of history, legends and myths that were common in medieval Europe. These Mappa Mundi are repositories of an extensive collection of information, but not the type of geographical knowledge we expect when we hear the word map.

The third area of medieval mapping is the portolan charts, which pose some problems. These are nautical charts that first appeared in the late thirteenth century in the Mediterranean and then over the centuries were extended to other sea areas. They display a detailed and surprising accurate stretch of coastline and are covered with networks of rhumb lines showing compass bearings.

The oldest original cartographic artifact in the Library of Congress: a portolan nautical chart of the Mediterranean. Second quarter of the 14th century. Source: Wikimedia Commons

Portolan charts have no coordinates. The major problem with portolan charts is their origin. They display an accuracy, at the time, unknown in other forms of mapping but the oldest known charts are fully developed. There is no known development leading to this type of mapping i.e., there are no known antecedent charts. The second problem is the question, are they based on a projection? There is some discussion on this topic, but the generally accepted view is that they are plate carrée or plane chart projection, which means that the mapmakers assumes that the area to be map is flat. This false assumption is OK if the area being mapped is comparatively small but leads to serios problems of distortion, when applied to larger areas.

Maps, mapping, and map making began to change radically during the Renaissance and one of the principle driving factors of that change was the rediscovery of Ptolemaeus’ Geographia. It is important to note that the Geographia was only one factor and there were several others, also this process of change was gradual and drawn out. 

What did the Geographia bring to medieval mapmaking that was new? It reintroduced the concept of coordinates, longitude and latitude, as well as map projection. As Ptolemaeus points out the Earth is a sphere, and it is mathematically impossible to flatten out the surface of a sphere onto a flat sheet without producing some sort of distortion. Map projections are literally what they say they are, they are ways of projecting the surface of the sphere onto a flat surface. There are thousands of different projections, and the mapmaker has to choose, which one is best suited to the map that he is drawing. As Ptolemaeus points out for a map of the world, it is actually better not the draw it on a flat sheet but instead to draw it on a globe. 

The Geographia contains instructions for drawing a map of the Earth i.e., the oikoumenikos, and for regional maps. For his regional maps Ptolemaeus uses the plate carrée or plane chart projection, the invention of which he attributes to his contemporary Marinus of Tyre. In this projection, the lines of longitude (meridians) and latitude (parallels) are parallel sets of equally spaced lines. For maps of the world, he describes three other projections. The first of these was a simple conic projection in which the surface of the globe is projected onto a cone, tangent to the Earth at the 36th parallel. Here the meridians are straight lines that tend to close towards the poles, while the parallels are concentric arcs. The second was a modified cone projection where the parallels are concentric arcs and the meridians curve inward towards the poles.

Ptolemaeus’ projection I above and II below Source: Marjo T Nurminen, “The Mapmakers’ World”, Pool of London Press, 2014

His third projection, a perspective projection, needn’t interest us here as it was hardly used, however the art historian Samuel Y Edgerton, who died this year, argued that the rediscovery of Ptolemaeus’ third projection at the beginning of the fifteenth century was the impulse that led to Brunelleschi’s invention of linear perspective.

A mid-15th century Florentine Ptolemaic map of the world Ptolemy’s 1st projection.
A printed Ptolemaic world map using his 2nd projection Johannes Schnitzer (1482). Source: Wikimedia Commons

From very early on Renaissance cosmographers began to devise and introduce new map projections, at the beginning based on Ptolemaeus’ projections. For example, in his In Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei, from 1514, Johannes Werner (1468–1522) introduced the heart shaped or cordiform projection devised by his friend and colleague Johannes Stabius (1540–1522), now know as the Werner-Stabius projection. This was used by several mapmakers in the sixteenth century, perhaps most famously by Oronce Fine (1494–1555) in 1536.

Oronce Fine World Map 1536 Source: Wikimedia Commons

Francesco Rosselli (1455–died before 1513) introduced an oval projection with his world map of 1508

World Map oval by Francesco Rosselli, copper plate engraving on vellum 1508, National Maritime Museum via Wikimedia Commons

It should be noted that prior to the rediscovery of the Geographia, map projection was not unknown in medieval Europe, as the celestial sphere engraved on the tympans or climata of astrolabes are created using a stereographic projection.

Animation showing how celestial and geographic coordinates are mapped on an astrolabe’s tympan through a stereographic projection. Hypothetical tympan (40° north latitude) of a 16th-century European planispheric astrolabe. Source: Wikimedia Commons

The first wave of Renaissance mapmaking concerned the Geographia itself. As already noted, in the previous episode, the first printed edition with maps appeared in Bologna in 1477. This was closely followed by one produced with copper plate engravings, which appeared in Rome in 1478. An edition with maps printed with woodblocks in Ulm in 1482. Another edition, using the same plates as the 1478 edition appeared in Rome in 1490. Whereas the other fifteenth century edition only contained the twenty-seven maps described by Ptolemaeus in his text, the Ulm edition started a trend, that would continue in later editions, of adding new contemporary maps to the Geographia. These editions of the Geographia represent the advent of the modern atlas, to use an anachronistic term, an, at least nominally, uniform collection of maps with text bound together in book. It would be approximately a century before the first real modern atlas, that of Abraham Ortelius, would be published, but as Elizabeth Eisenstein observed, the European mapmakers first had to catch up with Ptolemaeus. 

These printed edition of the Geographia also illustrate another driving force behind the radical increase in mapmaking during the Renaissance, the invention of the printing press. The invention of the printing press and the development of cooper plate engraving, as well as woodblock printing meant that the multiple reproduction of maps and plans became much easier and also much cheaper. 

Another factor behind the increase in mapmaking was the so-called age of discovery. The Portuguese had been working their way down the coast of Africa throughout the fifteenth century and Bartolomeu Dias (c. 1450–1500) rounded the southern tip of Africa, for the first time in 1488, paving the way for the first trip by a European by an ocean route to India by Vasco da Gama (c. 1460s–1524) in 1497–99. Of course, as every school kid knows “In fourteen hundred and ninety-two, Columbus sailed the ocean blue” or put for formally the Genoese seaman Christopher Columbus (1451–1506) undertook his first voyage to Asia in service of the Spanish Crown in 1492 and accidentally discovered the so-called forth continent, which Martin Waldseemüller (c. 1475–1520) and Matthias Ringmann (c. 1482–1511) incorrectly christened America in 1507, in honour of Amerigo Vespucci (1451–1512), whom they falsely believed to be the discoverer of the new, to Europeans, continent. 

The initial maps produced by the European discovery expedition carried the portolan chart tradition out from the Mediterranean into the Atlantic Ocean, down the coast of Africa and eventually across the Atlantic to the coasts of the newly discovered Americas.

Kunstmann II or Four Finger Map. Dating from the period circa 1502‒6 Source: World Digital Library

Although not really suitable for maps of large areas the tradition of the portolan charts survived well into the seventeenth century. In 1500, Juan de la Cosa (c. 1450–1510) produced a world portolan chart. This is the earliest known map to include a representation of the New World.

Juan de la Cosa world map 1500

The 1508 edition of the Geographia published in Rome was the first edition to include the European voyages of exploration to the New World. The world map drawn by the Flemish mapmaker Johan Ruysch (c. 1460–1533), who had himself sailed to America, includes the north coast of South America and some of the West Indian islands. On the other side it also includes eastern Asia with China indicated by a city marked as Cathaya, however, Japan (Zinpangu) is not included.

Ruysch’s 1507 map of the world. Source: Wikimedia Commons

Ruysch’s map bears a strong resemblance to the Cantarini-Rosselli world map published in Venice or Florence in 1506. Drawn by Giovanni Matteo Conarini (died 1507) and engraved by Francesco Rosselli (1455–died before 1513), which was the earliest known printed map containing the New World. The Ruysch map and the Cantarini-Rosselli probably shared a common source. 

The most famous map showing the newly discovered fourth continent is, of course, the Waldseemüller world map of 1507, which gave America its name.

Universalis Cosmographia, the Waldseemüller wall map dated 1507, depicts America, Africa, Europe, Asia, and the Oceanus Orientalis Indicus separating Asia from the Americas. Source: Wikimedia Commons

Of interest here is the fact that Waldseemüller apparently also published a small, printed globe of his wall map, which is the earliest known printed globe.

Waldseemüller globe gores of 1507 Source: Wikimedia Commons

The age of the modern terrestrial globe was ushered in by the earliest known, surviving manuscript globe produced by Martin Behaim (1549-1507) in 1493. Because he had supposedly taken part on Portuguese expedition along the African coast, he was commissioned, by the city council of Nürnberg, during a visit to the city of his birth,  to produce a globe and a large wall map of the world for the council chamber. The map no longer exists. Behaim’s main source for his maps was Ptolemaeus’ Geographia.

Behaim Globe Germanisches Nationalmuseum Nürnberg

Waldseemüller’s globe had apparently little impact and only four sets of globe gores still exist but none of the finished globes. The person who really set the production of printed globes in motion was the Nürnberger mathematicus Johannes Schöner (1477–1547), who produced his first printed terrestrial globe in 1515, which did much to cement the name America given to the fourth continent by Waldseemüller and Ringmann. Schöner was the owner of the only surviving copy of the Waldseemüller map.

Schöner Terrestrial Globe 1515, Historisches Museum Frankfurt

Like Behaim and Waldseemüller, Schöner’s main source of information was Ptolemaeus’ Geographia, of which he owned a heavily annotated copy, and which like them he supplemented with information from various other sources. In 1517, he also produced a matching, printed celestial globe, establishing the tradition of matching globe pairs that persisted down to the nineteenth century.

Schöner was not the only Nürnberger mathematicus, who produced globes. We know that Georg Hartmann (1489–1564), who acted as Schöner’s globe salesman in Nürnberg, when Schöner was still living in Kirchehrenbach, also manufactured globes, but none of his have survived. Although they weren’t cheap, it seems that Schöner’s globes sold very well, well enough to motivate others to copy them. Both Waldseemüller, with his map, and Schöner, with his globes, published an accompanying cosmographia, a booklet, consisting of instructions for use as well as further geographical and historical information. An innovative printer/publisher in Louvain reprinted Schöner’s cosmographia, Lucullentissima quaedam terrae totius descriptio, and commissioned Gemma Frisius (1508–1555) to make a copy of Schöner’s globe to accompany it. Frisius became a globe maker, as did his one-time student and assistant Gerard Mercator (1512-1594), who went on to become the most successful globe maker in Europe.

Gemma Frisius globe 1536

Both Willem Janszoon Blaeu (1571–1638) and Jodocus Hondius (1563–1612) emulated Mercator’s work establishing the Netherlands as the major European map and globe making centre in the seventeenth century.

Another factor that contributed to the spread of map making in the sixteenth century was the Renaissance development of realism in painting. This was a combination of the invention of linear perspective during the fifteenth century on the one hand and on the other, the development of Naturalism beginning in the late fourteenth century in the Netherlands. During the sixteenth century many notable artists were also map makers and several map makers were also artists. 

Dürer-Stabius world map a rare example of Ptolemaeus’ 3rd projection

It became fashionable during the Renaissance for those in power to sponsor and employ those working in the sciences. This patronage also included map makers. On the one hand this meant employing map makes to make maps as status symbols for potentates to display their magnificence. A good example is the map galleries that Egnatio Danti (1536–1586) was commissioned to create in the Palazzo Vecchio in Florence for Cosimo I de’ Medici and in the Vatican for Pope Gregory XIII.

Source: Fiorani The Marvel of Maps p. 110 Note that the map is up side down!

Similarly, Peter Apian ((1495–1552) was commissioned to produce maps for the Holy Roman Emperor, Charles V

Peter Apian cordiform world map 1530 Source: British Library

His son Philipp (1531–1589) did the same for Duke Albrecht V of Bavaria.

Overview of the 24 woodblock prints of Apian’s map of Bavaria

Another example is Oronce Fine (1494–1555), who made maps for Francis I. The first English atlas created by Christopher Saxton (c. 1540–c. 1610) was commissioned by Thomas Seckford, Master of Ordinary on the instructions of William Cecil, 1stBaron Burghley (1520–1598), Queen Elizabeth’s chief advisor.

Saxton England and Wales proof map Source: British Library

These maps came more and more to serve as aids to administration. The latter usage also led to European rulers commissioning maps of their new overseas possessions. 

Another area that required map making was the changes in this period in the pursuit of warfare. Larger armies, the increased use of artillery, and a quasi-professionalisation of the infantry led to demand for maps for manoeuvres during military campaigns. 

Starting around 1500 mapping took off in Renaissance Europe driven by the various factors that I’ve sketched above, a full account would be much more complex and require a book rather than a blog post. The amount of mapmaking increased steadily over the decades and with it the skill of the mapmakers reaching a first high point towards the end of the century in the atlases of Ortelius, De Jode, and Mercator. The seventeenth century saw the establishment of a major European commercial map and globe making industry dominated by the Dutch map makers, particularly the Houses of Blaeu and Hondius.

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Renaissance Science – XVI

In terms of the books rediscovered from antiquity during the Renaissance one of those that had the biggest impact was Ptolemaeus’ Geōgraphikḕ Hyphḗgēsis, which became known in Latin as either the Geographia or Cosmographia. Claudius Ptolemaeus or (Klaúdios Ptolemaîos in Greek) is a scholar, who had a major impart on the development of the mathematical sciences in the second century CE and then again when his writings were rediscovered in the High Middle Ages during the twelfth century translation movement. He wrote important texts on astronomy, astrology, cosmology, harmony (music), and optics, amongst others. However, we know next to nothing about the man himself, neither his date of birth nor his date of death, nor very much else. He lived and worked in the city of Alexandria and people in the Middle Ages made the mistake of thinking he was a member of the Ptolemaic dynasty that ruled Egypt from 323–30 BCE. There is a possibility that he acquired the name because he came from the town of Ptolemaîos Hermaiou in Upper Egypt.

Three of his books the Mathēmatikē Syntaxis (better known in English as the Almagest) on astronomy, the Tetrabiblos or Apotelesmatiká on astrology and the Geōgraphikḕ Hyphḗgēsis on geography form a sort of trilogy. He says in the introduction of the Tetrabiblos that the study of the science of the stars is divided into two parts. The first, his Mathēmatikē Syntaxis, describes where to find the celestial objects and the second, his Tetrabiblos, explains their influence. The Geōgraphikḕ Hyphḗgēsis is in different ways directly related to both books. It is related to the Mathēmatikē Syntaxis in that both works use a latitude/longitude coordinate system to map their respective realms, the sphere of the earth and the sphere of the heavens. This interconnectedness in reflected in the fact that in Early Modern Europe a cosmographer was somebody, who mapped both the celestial and terrestrial spheres. The Geōgraphikḕ Hyphḗgēsis is in three parts, a theoretical introduction on mapping, a gazetteer of the coordinates of a long list of places and, geographical features, and a collection of maps. Like the Mathēmatikē Syntaxis, the Geōgraphikḕ Hyphḗgēsis built on earlier works in the disciple, most notably that of Marinus of Tyre (c. 70–130 CE). To cast a horoscope in Greek astrology, one needs the coordinates of the place for which the horoscope in being cast, the Geōgraphikḕ Hyphḗgēsisdelivered those coordinates. In antiquity the last known reference to the Geōgraphikḕ Hyphḗgēsis was in the work of Cassiodorus (c. 485–c. 585). 

All three of these books by Ptolemaeus were translated into Arabic by the ninth century. Both the Mathēmatikē Syntaxisand the Tetrabiblos had a major impact in Islamic culture, although both were criticised, changed, improved on in wide ranging commentaries by Islamic scholars. It was here that the Mathēmatikē Syntaxis acquired the name Almagestmeaning the greatest to distinguish it from a shorter, less important astronomical text from Ptolemaeus. Geōgraphikḕ Hyphḗgēsis, however had very little impact on Islamic map making being used almost exclusively in an astrological context.

The Mathēmatikē Syntaxis was translated into Latin three times in the twelfth century. Twice from Arabic once by Abd al-Masīḥ of Winchester and once by Gerard of Cremona (1114–1187) and once directly from Greek in Sicily by an unknown translator. These translations establish Ptolemaic astronomy as the de facto medieval European astronomy. In the twelfth century the Tetrabiblos was also translated from Arabic into Latin by Plato of Trivoli in 1138 and directly from Greek into Latin by William of Moerbeke (c. 1220–c. 1286). Integrated into Christian theology by Albertus Magnus and Thomas Aquinas it dominated European astrology right up to the end of the seventeenth century. 

Unlike the Mathēmatikē Syntaxis and the Tetrabiblos the Geōgraphikḕ Hyphḗgēsis was apparently not translated either from Arabic or Greek during the twelfth century. Giacomo or Jacopo d’Angelo of Scarperia better known in Latin as Jacobus Angelus obtained a Greek manuscript, found in Constantinople that he translated, into Latin in about 1406.

Jacobus Angelus’ Latin translation of Ptolemaeus’ Geographia Early 15th century Source via Wikimedia Commons

Here it obtained the title of Geographia or Cosmographia. There is some discussion or even doubt about how genuine the book is, as the oldest known Greek manuscript only dates back to the thirteenth century.

A Byzantine Greek world map according to Ptolemy’s first (conic) projection. From Codex Vaticanus Urbinas Graecus 82, Constantinople c. 1300. Source: Wikimedia Commons

Despite criticism of the quality of Jacobus Angelus’ translation it proved very popular, and the first printed edition appeared in Venice in 1475. However, it contained no maps. A second edition was printed in Rome in 1478, which contained maps printed from copper engravings. The engravings were begun by Konrad Sweynheym (who together with Arnold Pannartz set up the first printing press in Italy) and were completed by Arnold Buckinck after Sweynheym’s death in 1476. The first edition of Geographia with maps printed using woodcuts was published in Ulm in 1482. Three major printed editions in les than a decade indicate the popularity of the book. 

First page of the 1482 Ulm edition go Gepgraphis Source: Wikimedia Commons

The quality, or rather supposed lack of it, of Jacobus Angelus’ translation led to a series of new translations from the Greek. The Nürnberger mathematicus Johannes Werner (1468–1522)

Artist unknown Source: Wikimedia Commons

published a new translation of the theoretical first section, his In Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei, in Nürnberg in 1514.

Source:

This in turn was heavily criticised by Willibald Pirckheimer (1470–1530) Nürnberger politician, soldier, humanist scholar and friend and patron of Albrecht Dürer.

Willibald Pirckheimer portrait by Dürer Souce: Wikimedia Commons

Pirckheimer, an excellent classist, published his own translation of the entire text in Nürnberg in 1525.

Claudius Ptolemaeus (Greek, Alexandria (?) A.D. 100?–?170 Alexandria (?)) In Claudii Ptolemaei Geographiacae Enarrationis Libri octo., March 30, 1525 German, Willibald Pirckheimer The Metropolitan Museum of Art, New York, Rogers Fund, 1920 (20.83-) Source
Claudius Ptolemaeus (Greek, Alexandria (?) A.D. 100?–?170 Alexandria (?)) In Claudii Ptolemaei Geographiacae Enarrationis Libri octo., March 30, 1525 German, Willibald Pirckheimer The Metropolitan Museum of Art, New York, Rogers Fund, 1920 (20.83-) Source

Earlier in the fifteenth century another Nürnberger, Regiomontanus (1436–1476), had heavily criticised the Angelus translation. In the catalogue that he published when he set up his scientific printing press in Nürnberg. he announced that he intended to produce and print a new edition of the text, but he died too early to fulfil his intention. Pirckheimer included Regiomonatanus’ criticisms in the introduction to his own new translation of the text.

Pirckheimer’s edition formed the basis for the revised and edited edition published by the cosmographer, Sebastian Münster (1488–1552), in 1540 in Basel. Münster published an updated edition with extra illustrations in 1550. Münster’s Geographia was generally regarded as the standard Latin reference text of the work.

Geographiae Claudii Ptolemaei Alexandrini, Philosophi ac Mathematici praestantissimi, Libri VIII, partim à Bilbaldo Pirckheymero . MÜNSTER, Sebastian (1488-1552), ed. Edité par Basel: Heinrich Petri, March 1552 [colophon], 1552
Geographiae Claudii Ptolemaei Alexandrini, Philosophi ac Mathematici praestantissimi, Libri VIII, partim à Bilbaldo Pirckheymero . MÜNSTER, Sebastian (1488-1552), ed. Edité par Basel: Heinrich Petri, March 1552 [colophon], 1552

The Portuguese mathematicus Pedro Nunes (1502–1578), noted for his contributions to the history of navigation, who was appointed Royal Cosmographer in 1529 and Chief Royal Cosmographer in 1547 by King Joāo III o Piedoso,

Image of Portuguese mathematician Pedro Nunes in Panorama magazine (1843); Lisbon, Portugal. Source: Wikimedia Commons

published his Tratado da sphera com a Theorica do Sol e da Lua in Lisbon in 1537. This was a based on a collection of texts and included the first, theoretical, section of Ptolemaeus’ Geographia. To make it more accessible Nunes published it in Latin, Spanish and Portuguese.

There were, naturally, also other vernacular translations of the work published in the sixteenth century, as for example this description of an Italian translation (borrowed from amateur astronomer and book collector, David Kolb, on Facebook):

Here is another one of the gems from my collection. I proudly present Claudius Ptolemy’s “La Geografia di Claudio Tolomeo Alessandrino” that was published in 1574. This volume is an expanded edition of his treatise on geography. Claudius Ptolemy lived in Alexandria during the 2nd century and is better known by astronomers for his astronomical treatise “The Almagest”. This is the third edition of the Italian translation by Girolamo Ruscelli, which was first printed by Vincenzo Valgrisi in Venice, in 1561. This edition is revised and corrected by Giovanni Malombra. The engraved maps, which are enlarged copies of Giacomo Gastaldi’s maps in his Italian edition of Venice, 1548, are generally the same in the Venice 1561, 1562 (Latin), and 1564 editions printed in Venice. Sixty-three of the maps are printed from the same plates as the 1561 edition. The exceptions are the Ptolemaic world map, “Tavola prima universale antica, di tutta la terra conosciura fin’ a’ tempi di Tolomeo,” which is on a revised conical projection, and the additional map “Territorio di Roma duodecima tavola nuova d’Europa” which is new to this edition. The atlas contains 27 Ptolemaic maps and 38 new maps.

The cosmographer Gerard Mercator (1512–1594), famous for introducing the name atlas for a collection of maps, initially intended to publish a large multi-volume work, which he never completed before he died.

Mercator the Frans Hogenberg portrait of 1574 Source: Wikimedia Commons

The first volume was intended to be his Geographia. In 1578 he published his Tabulae geographicae Cl. Ptolemaei ad mentem auctoris restitutis ac emendatis. (Geographic maps according to Claudius Ptolemy, drawn in the spirit of the author and expanded by Gerard Mercator). This was followed by a second edition in 1584 his Geographiae Libri Octo: recogniti iam et diligenter emendati, containing his revised version of Ptolemaeus’ text.

Geographiae Libri Octo :recogniti iam et diligenter emendati cum tabulis geographicis ad mentem auctoris restitutis ac emendatis ; Cum gratia & Priuilegio Sac Caes. Maiestat. Source:

 I hope I have made clear just how important the rediscovery of the Geōgraphikḕ Hyphḗgēsis was in the fifteenth and sixteenth centuries given the number of editions, of which I have only named a few, and the status of the authors, who produced those editions. In the next episode we will examine its impact on the map making in Europe during this period. 

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An eighteenth-century cartographical community in Nürnberg

If you walk up Burgstraße in the city of Nürnberg in the direction of the castle, you will see in front of you the impressive Baroque Fembohaus, which from 1730 to 1852 was the seat of the cartographical publishing house Homännische Erben, that is “Homann’s Heirs” in English. But who was Homann and why was the business named after his heirs?

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Fembohaus Source: Wikimedia Commons

Johann Baptist Homann (1664–1724) was born in Öberkammlach in the south of Bavaria. He was initial educated at a Jesuit school and at some point, entered the Dominican Cloister in Würzburg, where he undertook, according to his own account, his “studia humaniora et philosophica.”

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Johann Baptists Homann (1664–1725) Portrait by Johann Wilhelm Windter (c. 1696– 1765) Source: Wikimedia Commons

In 1687 he left the cloister moved to Nürnberg and converted to Protestantism. Over the next ten years he vacillated between Catholicism and Protestantism, leaving Nürnberg during the Catholic phases, and returning during the Protestant phases. In 1691 in Nürnberg, he was registered for the first time as a notary public. Around the same time, he started his career as a map engraver. It is not known how or where he learnt this trade, although there are claims that he was entirely self-taught. A map of the district surrounding Nürnberg, produced in 1691/92, shows Homann already as a master in cartographic engraving. From 1693 to 1695 he was in Vienna, then he returned for a time to Nürnberg, leaving again for Erlangen in 1696. Around 1696 to 1697, he was engraving maps in Leipzig.

He appears to have final settled on life as a protestant and permanent residency in Nürnberg in 1698. In 1702 he established a dealership and publishing house for cartography in the city, producing and selling maps, globes, and atlases. His dealership also produced and sold scientific instruments. The field that Homann had chosen to enter was by the beginning of the eighteenth century well established and thriving, with a lot of very powerful competition, in particular from France and Holland. Homann entered the market from a mercantile standpoint rather than a scientific one. He set out to capture the market with high quality products sold more cheaply than the competition, marketing copies of maps rather than originals. In a relatively short time, he had established himself as the dominant cartographical publisher in Germany and also a European market leader.

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Planiglobii Terrestris Cum Utroq[ue] Hemisphærio Cælesti Generalis Exhibitio, Nürnberg 1707 Source: Wikimedia Commons

His dealership offered single sheet maps for sale, but he became the first German cartographer to sell atlases on a large scale and is considered the second most important German cartographer after Mercator. His first atlas with forty maps appeared in 1707. This was expanded to the Großen Atlas über die ganze Welt (The Big Atlas of the Entire World), with one hundred and twenty-six maps in 1716.

1716_Homann_Map_of_Burgundy,_France_-_Geographicus_-_Burgundiae-homan-1716-2

A fine example of Homann’s 1716 map of Burgundy, one of France’s most important wine regions. Extends to include Lake Geneva in the southwest, Lorraine in the north, Champaigne (Champagne) and Angers to the northwest and Bourgogne to the west. Depicts mountains, forests, castles, and fortifications and features an elaborate title cartouche decorated with cherub winemakers in the bottom right. A fine example of this rare map. Produced by J. H. Homann for inclusion in the Grosser Atlas published in Nuremberg, 1716. Source: Wikimedia Commons

By 1729 it had around one hundred and fifty maps. Johann Baptist’s success was richly acknowledged in his own lifetime. In 1715 he was appointed a member of the Preußischen Akademie der Wissenschaften (The Prussian Academy of Science) and in 1716 he was appointed Imperial Geographer by the Holy Roman Emperor, Karl VI.

1730_Homann_Map_of_Scandinavia,_Norway,_Sweden,_Denmark,_Finland_and_the_Baltics_-_Geographicus_-_Scandinavia-homann-1730

A detailed c. 1730 J. B. Homann map of Scandinavia. Depicts both Denmark, Norway, Sweden, Finland and the Baltic states of Livonia, Latvia and Curlandia. The map notes fortified cities, villages, roads, bridges, forests, castles and topography. The elaborate title cartouche in the upper left quadrant features angels supporting a title curtain and a medallion supporting an alternative title in French, Les Trois Covronnes du Nord . Printed in Nuremburg. This map must have been engraved before 1715 when Homann was appointed Geographer to the King. The map does not have the cum privilegio (with privilege; i.e. copyright authority given by the Emperor) as part of the title, however it was included in the c. 1750 Homann Heirs Maior Atlas Scholasticus ex Triginta Sex Generalibus et Specialibus…. as well as in Homann’s Grosser Atlas . Source: Wikimedia Commons

The publishing house continued to grow and prosper until Johann Baptist’s death in 1724, when it was inherited by his son Johann Christian Homann (1703–1730).

Johann Christian studied medicine and philosophy in Halle. He graduated doctor of medicine in 1725, following which he went on a study trip, first returning to Nürnberg in 1729. During his absence the publishing house was managed by Johann Georg Ebersberger (1695–1760) and later together with Johann Christian’s friend from university Johann Michael Franz (1700­–1761).

homann-north-africa-morocco-1728

Hand coloured copper engraving by J. Chr. Homann, showing noth west Africa with the Canary Islands and two large cityviews. Source: Wikimedia Commons

When Johann Christian died in 1730, he willed the business to Ebersberger and Franz, who would continue to run the business under the name Homännische Erben. The publishing house passed down through several generations until Georg Christoph Fembo (1781­–1848) bought both halves of the business in 1804 and 1813. Fembo’s son closed the business in 1852 and in 1876 the entire collection of books, maps, engravings, and drawing were auctioned off, thus destroying a valuable source for the history of German cartography.

Today there is a big market for fictional maps based on fantasy literature such as Lord of the Rings. This is nothing new and Early Modern fiction also featured such fictional maps, for example Thomas More’s Utopia (1516). One very popular medieval myth concerns the Land of Cockaigne, a fictional paradise of pleasure and plenty also known as The Land of Milk and Honey. The German version is Schlaraffenland (literally the Land of the Lazy Apes). The most well-known version of the myth in the seventeenth century was written by Johann Andreas Schneblins (d. 1702) and based on Schneblins’ account of his travels in the utopia of Schlaraffenland Homann produced a map his very popular Accurata Utopiae Tabula.

2880px-1694_-_Johann_Baptist_Homann_Schlarraffenlandes_(Accurata_Utopiæ_Tabula)

“Accurata Utopiæ Tabula” (also named “Schlarraffenlandes”) designed by Johann Baptist Homann and printed in 1694 Source: Wikimedia Commons

From the very beginning one distinctive feature of the publishing house was Homann’s active cooperation with other scholars and craftsmen. From the beginning Johann Baptist worked closely with the engraver, art dealer, and publisher Christoph Weigel the Older (1665–1725).

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Christoph Weigel, engraved by Bernhard Vogel of a portrait by Johann Kupetzky Source:Wikimedia Commons

Weigel’s most significant publication was his Ständebuch (1698) (difficult to translate but Book of the Trades and Guilds).

Der Pulvermacher Kupferstich Regensburger Ständebuch 1698 Christoph Weigel der Ältere 1654 172

Gunpowder makers, engraving Regensburger Ständebuch, 1698, Christoph Weigel der Ältere (1654, 1725)

Weigel was very successful in his own right but he cooperated very closely with Homann on his map production.

Homann also cooperated closely with the scholar, author, schoolteacher, and textbook writer Johann Hübner (1668–1731).

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Johann Hübner, engraving by Johann Kenckel Source: Wikimedia Commons

Together the two men produced school atlases according to Hübner’s pedagogical principles. In 1710 the Kleiner Atlas scholasticus von 18 Charten (Small School Atlas with 18 Maps) was published.

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Kleiner Atlas scholasticus von 18 Charten

This was followed in 1719 by the Johann Baptist Homann / Johann Hübner: Atlas methodicus / explorandis juvenum profectibus in studio geographico ad methodum Hubnerianam accommodatus, a Johanne Baptista Homanno, Sacrae Caesareae Majestatis Geographo. Noribergae. Anno MDCCXIX. Methodischer Atlas / das ist, Art und Weise, wie die Jugend in Erlernung der Geographie füglich examiniret werden kann / nach Hübnerischer Lehr-Art eingerichtet von Johann Baptist Homann, Nürnberg, 1719. The title, given here in both Latin and German translates as Methodical Atlas in the manner in which the youth can be reasonably examined in the study of geography according to the pedagogic principles of Hübner, presented by Johann Baptist Homann.

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Charte von Europa. Charte von Asia. Charte von Africa. Charte von America. Johanne Baptista Homanno, Norimbergae, 1719 Atlas methodicus / explorandis juvenum profectibus in studio geographico ad methodum Hubnerianam accommodatus

Johann Gottfried Gregorii (1685–1770) was a central figure in the intellectual life of eighteenth-century Germany. A geographer, cartographer, historian, genealogist, and political journalist, he put out a vast number of publications, mostly under the pseudonym Melissantes.

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Johann Gottfried Gregorii Source: Wikimedia Commons

In his geographical, cartographical, and historical work he cooperated closely with both Johann Baptist Homann and Christoph Weigel.

 One of the Homann publishing house’s most important cooperation’s was with the Nürnberg astronomer Johann Gabriel Doppelmayr (1677–1750).

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Johann Gabriel Doppelmayr Source: Wikimedia Commons

Doppelmayr was professor for mathematics at the Aegidianum, Germany’s first modern high school, and is best known for two publication his Historische Nachricht Von den Nürnbergischen Mathematicis und Künstlern (1730), an invaluable source for historian of science and his celestial atlas, Atlas Novus Coelestis (1742). Doppelmayr had been supplying celestial charts for the Homann atlases but his Atlas Novus Coelestis, which was published by Homännische Erben, contained thirty spectacular colour plates and was a leading celestial atlas in the eighteenth century.

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PHÆNOMENA circa quantitatem dierum artificialium et solarium perpetuo mutabilem, ex Hypothesi copernicana deducta, cum aliis tam Veterum quam recentiorum Philosophorum, Systematibus mundi notabilioribus, exhibita – Engraved between 1735 and 1742.

Doppelmayr’s successor as professor of mathematics at the Aegidianum was Georg Moritz Lowitz (1722–1774), who went on to become professor for practical mathematics at the University of Göttingen.

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Georg Moriz Lowiz Source: Wikimedia Commons

He worked together with Johann Michael Franz and produced several astronomical publications for the Homännische Erben. Franz as well as being co-manager of the publishing house was also an active geographer, who became professor in Göttingen in 1755. He also published a series of his own books on geographical themes. He sold his share of the publishing house on his younger brother Jacob Heinrich Franz (1713–1769) in 1759.

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Johann Michael Franz: Belgium, Luxemburg; Johann Michael Franz – Circulus Burgundicus – 1758

Without any doubt Homann’s most important or significant employee, at least with hindsight, was the cartographer and astronomer Tobias Mayer (1723–1762), who is these days is best known for having calculated the Moon’s orbit accurately enough to make the lunar distance method of determining longitude viable. A self-taught mathematicus he had already published a town plan of Esslingen, two books on mathematics and one on fortifications, when he was appointed to the Homännische Erben in 1746.

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Tobias Mayer Source: Wikimedia Commons

It was during his time in Nürnberg that he did his work on lunar astronomy. Like Lowitz, and Franz, Mayer also became a professor in Göttingen, in his case for economics and mathematics.

The three Göttingen professors–Lowitz, Franz, and Mayer–whilst still working for Homann in Nürnberg founded the Cosmographische Gesellschaft (Cosmographical Society), with the aim of improving the standards of cartography and astronomy. Due to lack of funding they never really got their plans of their grounds. Their only products being some propaganda publications for the society written by Franz and one publication from Mayer on his lunar research.

Abb.-58-Tobias-Mayer-Bericht-von-den-Mondskugeln-1750

Each of the scholars, briefly sketched here was a leading figure in the intellectual landscape of eighteenth-century Germany and they were all to some extent rivals on the open knowledge market. However, they cooperated rather than competed with each other and in doing so increased the quality of their output.

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The alchemist, who became a cosmographer

As an Englishman brought up on tales, myths and legends of Francis Drake, Walter Raleigh, Admiral Lord Nelson, the invincible Royal Navy and Britannia rules the waves, I tend not to think about the fact that Britain was not always a great seafaring nation. As an island there were, of course, always fisher boats going about their business in the coastal waters and archaeology has shown us that people have been crossing the strip of water between Britain and the continent, as long as the island has been populated. However, British sailors only really began to set out onto the oceans for distant lands in competition to their Iberian brethren during the Early Modern Period. Before the start of these maritime endeavours there was a political movement in England to get those in power to take up the challenge and compete with the Spanish and the Portuguese in acquiring foreign colonies, gold, silver and exotic spices. One, today virtually unknown, man, whose writings played a not insignificant role in this political movement was the alchemist Ricard Eden[1] (c. 1520–1576).

Richard Eden[2] was born into an East Anglian family of cloth merchants and clerics, the son of George Eden a cloth merchant. He studied at Christ’s College Cambridge (1534–1537) and then Queen’s College, where he graduated BA in 1538 and MA in 1544. He studied under Sir Thomas Smith (1533–1577) a leading classicist of the period, who was also politically active and a major supporter of colonialism, which possibly influenced Eden’s own later involvement in the topic.

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A c. 19th-century line engraving of Sir Thomas Smith. Source: Wikimedia Commons

Through Smith, Eden was introduced to John Cheke (1514–1557), Roger Ascham (c. 1515–1568) and William Cecil (1520–1598), all of whom were excellent classicists and statesmen. Cecil would go on under Elizabeth I to become the most powerful man in England. From the beginning Eden moved in the highest intellectual and political circles.

After leaving Cambridge Eden was appointed first to a position in the Treasury and then distiller of waters to the royal household, already indicating an interest in and a level of skill in alchemy. Eden probably acquired his interest in alchemy from his influential Cambridge friends, who were all eager advocates of the art. However, he lost the post, probably given to someone else by Somerset following Henry VIII’s death in 1547 and so was searching for a new employer or patron.

Through a chance meeting he became acquainted with the rich landowner Richard Whalley, who shared his interest in alchemy. Whalley provided him with a house for his family and an income, so that he could devote himself to both medicinal and transmutational alchemy. His activities as an alchemist are not of interest here but one aspect of his work for Whalley is relevant, as it marked the beginning of his career as a translator.

Whalley was obviously also interested in mining for metal ores, because he commissioned Eden to translate the whole of Biringuccio’s Pirotechnia into English. Although he denied processing any knowledge of metal ores, Eden accepted the commission and by 1552 he had completed twenty-two chapters, that is to the end of Book 2. Unfortunately, he lent the manuscript to somebody, who failed to return it and so the project was never finished. In fact, there was no English translation of the Pirotechnia before the twentieth century. Later he produced a new faithful translation of the first three chapters dealing with gold, silver and copper ores, only omitting Biringuccio’s attacks on alchemy, for inclusion, as we shall see, in one of his later works.

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

In 1552, Eden fell out with Whalley and became a secretary to William Cecil. It is probable the Cecil employed him, as part of his scheme to launch a British challenge to the Iberian dominance in global trade. In his new position Eden now produced a translation of part of Book 5 of Sebastian Münster’s Cosmographia under the title A Treatyse of the New India in 1553. As I explained in an earlier blog post Münster’s Cosmographia was highly influential and one of the biggest selling books of the sixteenth century.

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This first cosmographical publication was followed in 1555 by his The Decades of the newe worlde or west India, containing the nauigations and conquests of the Spanyardes… This was a compendium of various translations including those three chapters of Biringuccio, probably figuring that most explorers of the Americas were there to find precious metals. The main parts of this compendium were taken from Pietro Martire d’Anghiera’s De orbe novo decades and Gonzalo Fernández de Oviedo y Valdés’ Natural hystoria de las Indias.

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Source: The British Library

Pietro Martire d’Anghiera (1457–1526) was an Italian historian in the service of Spain, who wrote the first accounts of the explorations of Central and South America in a series of letters and reports, which were published together in Latin. His De orbe novo (1530) describes the first contacts between Europeans and Native Americans.

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Source: Wikimedia Commons

Gonzalo Fernández de Oviedo y Valdés (1478–1557) was a Spanish colonist, who arrived in the West Indies a few years after Columbus. His Natural hystoria de las Indias (1526) was the first text to introduce Europeans to the hammock, the pineapple and tobacco.

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MS page from Oviedo’s La Natural hystoria de las Indias. Written before 1535, this MS page is the earliest known representation of a pineapple Source: Wikimedia Commons

Important as these writings were as propaganda to further an English involvement in the new exploration movement in competition to the Iberian explorers, it was probably Eden’s next translation that was the most important.

As Margaret Schotte has excellently documented in her Sailing School (Johns Hopkins University Press, 2019) this new age of deep-sea exploration and discovery led the authorities in Spain and Portugal to the realisation that an active education and training of navigators was necessary. In 1552 the Spanish Casa de la Contratación established a formal school of navigation with a cátedra de cosmografia (chair of cosmography). This move to a formal instruction in navigation, of course, needed textbooks, which had not existed before. Martín Cortés de Albacar (1510–1582), who had been teaching navigation in Cádiz since 1530, published his Breve compendio de la sphere y de la arte de navegar in Seville in 1551.

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Retrato de Martín Cortés, ilustración del Breve compendio de la sphera y de la arte de navegar, Sevilla, 1556. Biblioteca Nacional de España via Wikimedia Commons

In 1558, an English sea captain from Dover, Stephen Borough (1525–1584), who was an early Artic explorer, visited Seville and was admitted to the Casa de la Contratación as an honoured guest, where he learnt all about the latest instruments and the instruction for on going navigators. On his return to England, he took with him a copy of Cortés’ Breve compendio, which he had translated into English by Richard Eden, as The Arte of Navigation in 1561. This was the first English manual of navigation and was immensely popular going through at least six editions in the sixteenth century.

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In 1562, Eden became a companion to Jean de Ferrières, Vidame of Chartres, a Huguenot aristocrat, who raised a Protestant army in England to fight in the French religious wars. Eden, who was acknowledged as an excellent linguist, stayed with de Ferrières until 1573 travelling extensively throughout France and Germany. Following the St. Batholomew’s Day massacre, which began in the night of 23–24 August 1572, Eden together with de Ferrières party fled from France arriving in England on 7 September 1573. At de Ferrières request, Elizabeth I admitted Eden to the Poor Knights of Windsor, a charitable organisation for retired soldiers, where he remained until his death in 1576.

After his return to England Eden translated the Dutch musician and astrologer, Jean Taisnier’s Opusculum perpetua memoria dignissimum, de natura magnetis et ejus effectibus, Item de motu continuio, which was a plagiarism of Petrus Peregrinus de Maricourt’s (fl. 1269) Epistola de magnete and a treatise on the fall of bodies by Giambattista Benedetti (1530–1590) into English.

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This was published posthumously together with his Arte of Navigation in 1579. His final translation was of Ludovico de Varthema’s (c. 1470–1517) Intinerario a semi-fictional account of his travels in the east. This was published by Richard Willes in The History of Travayle an enlarged version of his Decades of the newe worlde in 1577.

Eden’s translations and publications played a significant role in the intellectual life of England in the sixteenth century and were republished by Richard Hakluyt (1553–1616) in his The Principal Navigations, Voiages, Traffiques and Discoueries of the English Nation (1589, 1598, 1600), another publication intended as propaganda to promote English colonies in America.

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Unlike Sebastian Münster or Richard Hakluyt, Eden has been largely forgotten but he made important and significant contributions to the history of cosmography and deserves to be better known.

[1] I want to thank Jenny Rampling, whose book The Experimental Fire, which I reviewed here, made me aware of Richard Eden, although, I have to admit, he turns up, managing to slip by unnoticed in other books that I own and have read.

[2] The biographical details on Eden are mostly taken from the ODNB article. I would like to thank the three wonderful people, who provided me with a pdf of this article literally within seconds of me asking on Twitter

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