Category Archives: History of Cartography

Why North?

Recently on Twitter, Vintage Maps posted a fifteenth century map of England, Scotland, and  Wales that was somewhat unusual in that South was at the top, so Scotland was at the bottom.

Numerous people found it bizarre or irritating and it was obvious that many people are somehow convinced that North must be at the top of a map. I can understand why, but there is no law, scientific necessity, or any compelling reason whatsoever as to why maps should be so orientated that North is at the top and in fact at other times and in other cultures maps did in fact have other orientations. To quote Jerry Brotton on the topic:

Ortelius describes the position from which a viewer looks at a world map, which is closely related to orientation – the location from which we take our bearings. Strictly speaking, orientation usually refers to relative position or direction; in modern times it has become established as fixing location relative to the points on a magnetic compass. But long before the invention of the compass in China in the second century AD, world maps were oriented according to one of the four cardinal directions: north, south, east and west. The decision to orientate maps according to one prime direction varies from one culture to another (as will be seen from the twelve maps discussed in this book), but there is no purely geographical reason why one direction is better than any other, or why modern Western maps have naturalized the assumption that north should be at the top of all world maps.

            Why north ultimately triumphed as the prime direction in the Western geographical tradition, especially considering its initially negative connotations for Christianity (discussed in Chapter 2), has never been fully explained. Later Greek maps and early medieval charts, or portolans, were drawn using magnetic compasses, which probably established the navigational superiority of the north-south axis over an east-west one; but even so there is little reason why south could not have been adopted as the simplest point of cardinal orientation instead, and indeed Muslim mapmakers continued to draw maps with south at the top long after the adoption of the compass. Whatever the reasons for the ultimate establishment of the north as the prime direction on world maps, it is quite clear that, as subsequent chapters will show, there are no compelling grounds for choosing one direction over another.[1]

It’s not just maps, all earlier cultures that had reached a certain level of development had buildings and other structures aligned to the four cardinal directions long before the invention of the compass, so how? Before I answer, I should explain that all that follows applies to the northern hemisphere, as all the maps discussed were all created in the northern hemisphere. 

Brotton:

Etymologically, ‘orientation’ stems from the original root oriens, which refers to the east, or the direction of the rising sun. Virtually all ancient cultures record their ability to orient themselves according to an east-west axis based on observations of the rising (eastern) and setting (western) sun, and a north-south axis measured according to the position of the North Star or the midday sun.[2]

However, these observations are not accurate enough to orientate a building, so how do you do that without a compass?

To lay out a basic east-west, north-south cross on the ground you just need a stick, or to give it its fancy name a gnomon, and a piece of string. You place the stick upright in the ground and draw a circle around it using the piece of string. You follow the shadow of the stick, which varies in length during the day and when it just touches the circle you mark that point. When it just touches the circle for the second time you mark that point. If you now join up those point the connecting line runs east-west. A north-south line is a right angle to this through the middle of the circle.

Source:

The oldest world map, the Babylonian Imago Mundi (sometime between the 9th and 7th centuries BCE) is centred on the Euphrates, which runs north-south, so it has north at the top.

Imago Mundi Babylonian map, the oldest known world map, 6th century BCE Babylonia. Now in the British Museum. Source: Wikimedia Commons

Greek mapmakers also orientated their maps with north at the top, which I suspect is strongly influenced by the fact that the Mediterranean, which is at the centre of all Greek cartography, runs east-west, combined with the importance of the pole star in Greek astronomy.

The oldest surviving Ptolemaic world map, redrawn according to his 1st projection by monks at Constantinople under Maximus Planudes around 1300 Source: Wikimedia Commons

Chinese maps were mostly orientated with north at the top, although the Han dynasty maps (202 BCE–202 CE) have south at the top. Brotton argues that in China the sun comes from the south, so the emperor looks to the south towards the sun and the people look to the north when looking up to the emperor, hence the north orientation. 

The Composite Map of the Ming Empire (Da Ming Hunyi Tu) reflects the political situation in AD 1389 but was likely painted much later. Original Chinese labels were later covered with Manchu on paper slips. Source: Wikimedia Commons

Turning once again to Brotton: 

Such orientation [east-west, north-south] was as much symbolic and sacred as directional. In polytheistic sun- worshipping cultures, the east (oriens) was revered as the direction of renewal and life, closely followed by south, while the west was understandably associated with decline and death, and north with darkness and evil. The Judeo-Christian tradition developed these associations by orienteering places of worship as well as maps towards the east, which was ultimately regarded as the location of the Earthly Paradise. In contrast the west was associated with mortality, and the direction faced by Christ on the cross. The north became a sign of evil and satanic influence and was often the direction in which the heads of excommunicants and the unbaptised faced when they were buried.[3]

The European medieval mappae mundi (mappa mundi literally means cloth of the world) were not topological or geographical maps as we known them, but rather philosophical maps, which were intended to illustrate the Christian world view. In the middle, they had the Holy City, Jerusalem, which according to medieval Christian thought lay at the centre of the world. East was at the top with the Garden of Eden, as it stands in the Bible, “And the Lord God planted a garden eastward in Eden” (Genesis 2:8).

The Hereford Mappa Mundi, about 1300, Hereford Cathedral, England. Jerusalem is the small ornate circle in the middle of the map, the Garden of Eden or Paradise is the small circle at the top centre, and God sits on his throne above the Garden of Eden Source: Wikimedia Commons

Continuing with Brotton:

Islam and mapmakers like al-Idrīsī inherited a similar reverence for the east, although it developed an even stronger interest in the cardinal directions with the Qur’ānic injunction to its believers to pray in the sacred direction of Mecca, regardless of their location on the globe; finding the direction (known as qibla, or ‘sacred direction’) and direction to Mecca and the Kā’aba inspired some of the most complicated and elaborate maps and diagrammatic calculations of the medieval period. Most of the communities who converted to Islam in its early phase of rapid international expansion in the seventh and eight centuries lived directly north of Mecca, leading them to regard qibla as due south. As a result, most Muslim world maps, including al-Idrīsī were orientated with south at the top. This also neatly established continuity with the tradition of the recently conquered Zoroastrian communities in Persia, which regarded south as sacred.[4]

Source: Lost Maps of the Caliphs: Drawing the World in Eleventh-Century Cairo, Yossef Rapport and Emilie Savage-Smith, University of Chicago Press, Chicago and London, 2018, Plate 1

Abu Abdullah Muhammad al-Idrisi al-Qurtubi al-Hasani as-Sabti (1100–1165) to give him his full Arabic name, was a Muslim geographer and cartographer, who lived for many years in Palermo, at the court of the Norman king of Sicily Roger II (1095–1154).

Source: Lost Maps of the Caliphs: Drawing the World in Eleventh-Century Cairo, Yossef Rapport and Emilie Savage-Smith, University of Chicago Press, Chicago and London, 2018, Plate 4

Roger commissioned him to create a map of the world and the result after many years work was the Tabula Rogeriana published in 1154. It is considered to the most accurate map of the world in pre-modern times. It, of course, has south at the top, as did all medieval Islamic maps.

Tabula Rogeriana 19th century reconstruction with labels in Latin Source: Wikimedia Commons

I think it was possibly the influence of medieval Islamic maps that led to south orientated maps in Europe in the late medieval early Renaissance period, such as the map that inspired this whole post. Another well-known example of a south orientated European Renaissance map is the 1500 Romweg map of the Nürnberger cartographer and instrument maker Erhard Etzlaub (c. 1460–c. 1531).

1500 Romweg map of the Nürnberger cartographer and instrument maker Erhard Etzlaub (c. 1460–c. 1531). Source: Wikimedia Commons

This is a printed roadmap for pilgrims travelling to Rome for the Holy Year in 1500. It is considered to be the first modern European map with a scale to determine distances. All of Etzlaub’s maps have south at the top. 

Interestingly the Gough Map of Britain, which is difficult to date, but which was probably produced in the late fourteenth century has east at the top like the mappae mundi.

The Gough Map. North lies to the left of the map. Source: Wikimedia Commons

Earlier than Etzlaub, the first medieval, European “mathematical” maps, which emerged as the mappae mundi were still being produced were the portolan charts, which began to appear in the Mediterranean as navigation aids in the fourteenth century. These are mostly orientated with north at the top but there are examples with other orientations. 

The 1559 chart from Joan Oliva of the Mediterranean has west at the top but the small inserted circular chart of the Atlantic is interesting. If viewed along the axis of the main chart it also has west at the top but if viewed alone for itself, it has north at the top.

Peter Whitfield, Charting the Oceans,The British Library, London, 2017, p. 87

Pierre Desceliers’ 1550 world map, probably intended to be laid out on a table has two orientations. If viewed from the southern hemisphere it has north at the top but if viewed. from the northern hemisphere it has south at the top. The two orientations are indicated by the written labels.

Map of the World Pierre Desceliers 1550 Source: British Library via Wikimedia Commons

We find the same double orientation on the earlier Mediterranean chart of Albino de Canepa from 1498, indicated by the pavilions.

Mediterranean chart of Albino de Canepa 1498 Source: Wikimedia Commons

Jorge Aguiar’s Mediterranean map of 1492 is south orientated

Jorge Aguiar’s Mediterranean map of 1492 Source: Wikimedia Commons

As is the world map of Nicolas Desliens of 1566.*

Nicolas Desliens World Map 1566

I think that the re-emergence of the Ptolemaic world map at the beginning of the fifteenth century and the development of modern cartography that it triggered which eventually led to the dominance of north orientation in mapmaking, perhaps combined with the increased use of the magnetic compass. 

Of course, town plans, estate maps and plans of large building complexes are also maps and these are often not north orientated but according to what is the most rational way to view them as in this town plan. 

There is strong evidence that the current universal north orientation of maps leads to the way that the viewer perceives the world. Other orientation change our perception. We start with a map of Europe viewed from the USSR perspective

Various cartographers have created modern south orientated maps to provoke people into reconsidering their perceptions of the world. A good example is this world map.

“McArthur’s Universal Corrective Map of the World” (1979) is not only south orientated but is also centred on the west pacific rather than the Atlantic. Stuart McArthur, sought to confront “the perpetual onslaught of ‘downunder’ jokes—implications from Northern nations that the height of a country’s prestige is determined by its equivalent spatial location on a conventional map of the world”[5]
Source: Wikimedia Commons

Interesting in this context, whilst editing this blog post on Sunday 27 August 2022, I stumbled across a conference presenting and discussing the Te Moana Meridian concept on that day. This is a political movement attempting to move the prime meridian 180° from Greenwich to the middle of Te-moana-nui-o-Kiwa (the Pacific Ocean in Te Reo Māori (‘the language of Māori’)). If world maps were thus centred, instead of one the middle of the Atlantic, it would radically change peoples perceptions of the world.

Te Moana Meridian explores how the arbitrary location of the prime meridian reinforces British and Western imperial and colonial hegemony, historically, and into the present. Through a polyphony of tactics the exhibition proposes a practical means for redressing this skewing of global diplomacy. In centering Te Moana-Nui-ā-Kiwa, the exhibition proposes a more equitable and multilateral system for negotiating time and space.

Finally, I close with this west orientated map of the Mediterranean by Sabine Réthoré and I can’t improve on the description by Amro Ali in this article

The “Mediterranean Without Borders” map was produced, in the political euphoria of 2011, by Paris-based artist Sabine Réthoré. Its profound simple 90-degree rotation not only underwrites an artistic streak, but can also largely impact one’s perspective. The end result is that the question is no longer about north-south as much as it is about parity and closeness. In the context of Mediterranean geopolitics, refugees crossing and drowning, fortress Europe, colonial history, skewed markets, condescending north to south (top to bottom) attitudes, post-colonial stagnation and so forth, means the simple rotation of the map is a big political statement with humanizing tendencies that make transnational ties look more intimate. That is an artistic statement in itself. This does not mean it will work for all maps, but it does so with the Mediterranean basin given the weight of its contemporary politics and long rich history.

The next time you look at a map, maybe you should turn it upside down or even sideways and try to see what it depicts from a new perspective. There really is no reason why north should be at the top.  

*A special thanks goes to Matthew Edney , when inadvertently drew my attention to the Nicolas Desliens World Map on Twitter as I was composing this blog post


[1] Jerry Brotton, A History of the World in Twelve Maps, Allen Lane, 2012, pp. 10-11

[2] Brotton p. 57

[3] Brotton p. 57

[4] Brotton pp. 57-58

[5] Wood, D., Kaiser, W. L., Abramms, B., Seeing through MapsMany Ways to See the World, ODT Inc., 2006, pp. 50-51

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History of science is global history

The simple statement that the history of science is global history is for me and, I assume, for every reasonably well-informed historian of science a rather trivial truism. So, I feel that James Poskett and the publishers Viking are presenting something of a strawman with the sensational claims for Poskett’s new book, HorizonsA Global History of Science[1]; claims that are made prominently by a series of pop science celebrities on the cover of the book. 

“Hugely Important,” Jim al-Khalili, really? 

“Revolutionary and revelatory,” Alice Roberts what’s so revolutionary about it?  

“This treasure trove of a book puts the case persuasively and compellingly that modern science did not develop solely in Europe,” Jim al-Khalili, I don’t know any sane historian of science, who would claim it did.

“Horizons is a remarkable book that challenges almost everything we know about science in the West. [Poskett brings to light an extraordinary array of material to change our thinking on virtually every great scientific breakthrough in the last 500 years… An explosive book that truly broadens our global scientific horizons, past and present.”] Jerry Brotton (The bit in square brackets is on the publisher’s website not on the book cover) I find this particularly fascinating as Brotton’s own The RenaissanceA Very Short Introduction (OUP, 2006) very much emphasises what is purportedly the main thesis of Horizons that science, in Brotton’s case the Renaissance, is not a purely Western or European phenomenon.

On June 22, Canadian historian Ted McCormick tweeted the following:

It’s not unusual for popular history to present as radical what has been scholarly consensus for a generation. If this bridges the gap between scholarship and public perception, then it is understandable. But what happens when the authors who do this are scholars who know better?

This is exactly what we have with Poskett’s book, he attempts to present in a popular format the actually stand amongst historian of science on the development of science over the last approximately five hundred years. I know Viking are only trying to drum up sales for the book, but I personally find it wrong that they use misleading hyperbole to do so. 

Having complained about the publisher’s pitch, let’s take a look at what Poskett is actually trying to sell to his readers and how he goes about doing so. Central to his message is that claims that science is a European invention/discovery[2] are false and that it is actually a global phenomenon. To back up his stand that such claims exist he reproduces a series of rather dated quotes making that claim. I would contend that very, very few historians of science actually believe that claim nowadays. He also proposes, what he sees as a new approach to the history of science of the last five hundred years, in that he divides the period into four epochs or eras, in which he sees science external factors during each era as the defining or driving force behind the scientific development in that era. Each is split into two central themes: Part One: Scientific Revolution, c. 1450–1700 1. New Worlds 2. Heaven and Earth, Part Two: Empire and Enlightenment, c. 1650–1800 3. Newton’s Slaves 4. Economy of Nature, Part Three:  Capitalism and Conflict, c. 1790–­1914 5. Struggle for Existence 6. Industrial Experiments, Part Four: Ideology and Aftermath, c. 1914–200 7. Faster Than Light 8. Genetic States.

I must sadly report that Part One, the area in which I claim a modicum of knowledge, is as appears recently oft to be the case strewn with factual errors and misleading statements and would have benefited from some basic fact checking.

New Worlds starts with a description of the palace of Emperor Moctezuma II and presents right away the first misleading claim. Poskett write:

Each morning he would take a walk around the royal botanical garden. Roses and vanilla flowers lined the paths, whilst hundreds of Aztec gardeners tended to rows of medicinal plants. Built in 1467, this Aztec botanical garden predated European examples by almost a century.[3]

Here Poskett is taking the university botanical gardens as his measure, the first of which was establish in Pisa in 1544, that is 77 years after Moctezuma’s Garden. However, there were herbal gardens, on which the university botanical gardens were modelled, in the European monasteries dating back to at least the ninth century. Matthaeus Silvaticus (c.1280–c. 1342) created a botanical garden at Salerno in 1334. Pope Nicholas V established a botanical garden in the Vatican in 1544. 

This is not as trivial as it might a first appear, as Poskett uses the discovery of South America to make a much bigger claim. First, he sets up a cardboard cut out image of the medieval university in the fifteenth century, he writes:

Surprisingly as it may sound today, the idea of making observations or preforming experiments was largely unknown to medieval thinkers. Instead, students at medieval universities in Europe spent their time reading, reciting, and discussing the works of Greek and Roman authors. This was a tradition known as scholasticism. Commonly read texts included Aristotle’s Physics, written in the fourth century BCE, and Pliny the Elder’s Natural History, written in the first century CE. The same approach was common to medicine. Studying medicine at medieval university in Europe involved almost no contact with actual human bodies. There was certainly no dissections or experiments on the working of particular organs. Instead, medieval medical students read and recited the works of the ancient Greek physician Galen. Why, then, sometime between 1500 and 1700, did European scholars turn away from investigating the natural world for themselves?[4]

His answer:

The answer has a lot to do with colonization of the New World alongside the accompanying appropriation of Aztec and Aztec and Inca knowledge, something that traditional histories of science fail to account for.[5]

Addressing European, medieval, medical education first, the practical turn to dissection began in the fourteenth century and by 1400 public dissections were part of the curriculum of nearly all European universities. The introduction of a practical materia medica education on a practical basis began towards the end of the fifteenth century. Both of these practical changes to an empirical approach to teaching medicine at the medieval university well before any possible influence from the New World. In general, the turn to empiricism in the European Renaissance took place before any such influence, which is not to say that that process was not accelerated by the discovery of a whole New World not covered by the authors of antiquity. However, it was not triggered by it, as Poskett would have us believe. 

Poskett’s next example to bolster his thesis is quite frankly bizarre. He tells the story of José de Acosta (c. 1539–1600), the Jesuit missionary who travelled and worked in South America and published his account of what he experienced, Natural and Moral History of the Indies in 1590. Poskett tells us: 

The young priest was anxious about the journey, not least because of what ancient authorities said about the equator. According to Aristotle, the world was divided into three climatic zones. The north and south poles were characterized by extreme cold and known as the ‘frigid zone’. Around the equator was the ‘torrid zone’, a region of burning dry heat. Finally, between the two extremes, at around the same latitudes as Europe, was the ‘temperate zone’. Crucially, Aristotle argued that life, particularly human life, could only be sustained in the ‘temperate zone’. Everywhere else was either too hot nor too cold.

Poskett pp. 17-18

Poskett goes on to quote Acosta:

I must confess I laughed and jeered at Aristotle’s meteorological theories and his philosophy, seeing that in the very place where, according to his rules, everything must be burning and on fire, I and all my companions were cold.

Poskett p. 18

Instead of commenting on Acosta’s ignorance or naivety, Aristotle’s myth of the ‘torrid zone’ had been busted decades earlier, at the very latest when Bartolomeu Dias (c. 1450–1500) had rounded the southern tip of Africa fifty-two years before Acosta was born and eight-two year before he travelled to Peru, Poskett sees this as some sort of great anti-Aristotelian revelation. He writes:

This was certainly a blow to classical authority. If Aristotle had been mistaken about the climate zones, what else might he have been wrong about?

Poskett p.18

This is all part of Poskett’s fake narrative that the breakdown of the scholastic system was first provoked by the contact with the new world. We have Poskett making this claim directly:

It was this commercial attitude towards the New World that really transformed the study of natural history. Merchants and doctors tended to place much greater emphasis on collecting and experimentation over classical authority.[6]

This transformation had begun in Europe well before any scholar set foot in the New World and was well established before any reports on the natural history of the New World had become known in Europe. The discovery of the New World accelerated the process but it in no way initiated it as Poskett would have his readers believe. Poskett once again paints a totally misleading picture a few pages on:

This new approach to natural history was also reflected in the increasing use of images. Whereas ancient texts on natural history tended not to be illustrated, the new natural histories of the sixteenth and seventeenth centuries were full of drawings and engravings, many of which were hand-coloured. This was partly a reaction to the novelty of what had been discovered. How else would those in Europe know what a vanilla plant or a hummingbird looked like?

Poskett pp.29-30

Firstly, both ancient and medieval natural history texts were illustrated, I refer Mr Proskett, for example, to the lavishly illustrated Vienna Dioscorides from 512 CE. Secondly, the introduction of heavily illustrated, printed herbals began in the sixteenth century before any illustrated natural history books or manuscripts from the New World had arrived in Europe. For example, Otto Brunfels’ Herbarium vivae eicones three volumes 1530-1536 or the second edition of Hieronymus Bock’s Neu Kreütterbuch in 1546 and finally the truly lavishly illustrated De Historia Stirpium Commentarii by Leonhard Fuchs published in 1542. The later inclusion of illustrations plants and animals from the New World in such books was the continuation of an already established tradition. 

Poskett moves on from natural history to cartography and produced what I can only call a train wreck. He tells us:

The basic problem, which was now more pressing [following the discovery of the New World], stemmed from the fact that the world is round, but a map is flat. What then was the best way to represent a three-dimensional space on a two-dimensional plane? Ptolemy had used what is known as a ‘conic’ projection, in which the world is divided into arcs radiating out from the north pole, rather like a fan. This worked well for depicting one hemisphere, but not both. It also made it difficult for navigators to follow compass bearings, as the lines spread outwards the further one got from the north pole. In the sixteenth century, European cartographers started experimenting with new projections. In 1569, the Flemish cartographer Gerardus Mercator produced an influential map he titled ‘New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation’. Mercator effectively stretched the earth at the poles and shrunk it in the middle. This allowed him to produce a map of the world in which the lines of latitude are always at right angles to one another. This was particularly useful for sailors, as it allowed them to follow compass bearings as straight lines.

Poskett p. 39

Where to begin? First off, the discovery of the New World is almost contemporaneous with the development of the printed terrestrial globe, Waldseemüller 1507 and more significantly Johannes Schöner 1515. So, it became fairly common in the sixteenth century to represent the three-dimensional world three-dimensionally as a globe. In fact, Mercator, the only Early Modern cartographer mentioned here, was in his time the premium globe maker in Europe. Secondly, in the fifteenth and sixteenth centuries mariners did not even attempt to use a Ptolemaic projection on the marine charts, instead they used portulan charts–which first emerged in the Mediterranean in the fourteenth century–to navigate in the Atlantic, and which used an equiangular or plane chart projection that ignores the curvature of the earth. Thirdly between the re-emergence of Ptolemy’s Geographia in 1406 and Mercator’s world map of 1569, Johannes Werner published Johannes Stabius’ cordiform projection in 1514, which can be used to depict two hemispheres and in fact Mercator used a pair of cordiform maps to do just that in his world map from 1538. In 1508, Francesco Rosselli published his oval projection, which can be used to display two hemispheres and was used by Abraham Ortelius for his world map from 1564. Fourthly, stereographic projection, known at least since the second century CE and used in astrolabes, can be used in pairs to depict two hemispheres, as was demonstrated by Mercator’s son Rumold in his version of his father’s world map in 1587. Fifthly, the Mercator projection if based on the equator, as it normally is, does not shrink the earth in the middle. Lastly, far from being influential, Mercator’s ‘New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation’, even in the improved version of Edward Wright from 1599 had very little influence on practical navigation in the first century after it first was published. 

After this abuse of the history of cartography Poskett introduces something, which is actually very interesting. He describes how the Spanish crown went about creating a map of their newly won territories in the New World. The authorities sent out questionnaires to each province asking the local governors or mayors to describe their province. Poskett notes quite correctly that a lot of the information gathered by this method came from the indigenous population. However, he once again displays his ignorance of the history of European cartography. He writes:

A questionnaire might seem like an obvious way to collect geographical information, but in the sixteenth century this idea was entirely novel. It represented a new way of doing geography, one that – like science more generally in this period – relied less and less on ancient Greek and Roman authority.

Poskett p. 41

It would appear that Poskett has never heard of Sebastian Münster and his Cosmographia, published in 1544, probably the biggest selling book of the sixteenth century. An atlas of the entire world it was compiled by Münster from the contributions from over one hundred scholars from all over Europe, who provided maps and texts on various topics for inclusion in what was effectively an encyclopaedia. Münster, who was not a political authority did not send out a questionnaire but appealed for contributions both in publications and with personal letters. Whilst not exactly the same, the methodology is very similar to that used later in 1577 by the Spanish authorities. 

In his conclusion to the section on the New World Poskett repeats his misleading summation of the development of science in the sixteenth century:

Prior to the sixteenth century, European scholars relied almost exclusively on ancient Greek and Roman authorities. For natural history they read Pliny for geography they read Ptolemy. However, following the colonization of the Americas, a new generation of thinkers started to place a greater emphasis on experience as the main source of scientific knowledge. They conducted experiments, collected specimens, and organised geographical surveys. This might seem an obvious way to do science to us today, but at the time it was a revelation. This new emphasis on experience was in part a response to the fact that the Americas were completely unknown to the ancients.

Poskett p. 44

Poskett’s claim simply ignores the fact that the turn to empirical science had already begun in the latter part of the fifteenth century and by the time Europeans began to investigate the Americas was well established, those investigators carrying the new methods with them rather than developing them in situ. 

Following on from the New World, Poskett takes us into the age of Renaissance astronomy serving up a well worn and well know story of non-European contributions to the Early Modern history of the discipline which has been well represented in basic texts for decades. Nothing ‘revolutionary and revelatory’ here, to quote Alice Roberts. However, despite the fact that everything he in presenting in this section is well documented he still manages to include some errors. To start with he attributes all of the mechanics of Ptolemy’s geocentric astronomy–deferent, eccentric, epicycle, equant–to Ptolemy, whereas in fact they were largely developed by other astronomers–Hipparchus, Apollonius–and merely taken over by Ptolemy.  

Next up we get the so-called twelfth century “scientific Renaissance” dealt with in one paragraph. Poskett tells us the Gerard of Cremona translated Ptolemy from Arabic into Latin in 1175, completely ignoring the fact that it was translated from Greek into Latin in Sicily at around the same time. This is a lead into the Humanist Renaissance, which Poskett presents with the totally outdated thesis that it was the result of the fall of Constantinople, which he rather confusingly calls Istanbul, in 1453, evoking images of Christians fleeing across the Adriatic with armfuls of books; the Humanist Renaissance had been in full swing for about a century by that point. 

Following the introduction of Georg of Trebizond and his translation of the Almagest from Greek, not the first as already noted above as Poskett seems to imply, up next is a very mangled account of the connections between Bessarion, Regiomontanus, and Peuerbach and Bessarion’s request that Peuerbach produce a new translation of the Almagest from the Greek because of the deficiencies in Trebizond’s translation. Poskett completely misses the fact that Peuerbach couldn’t read Greek and the Epitome, the Peuerbach-Regiomontanus Almagest, started as a compendium of his extensive knowledge of the existing Latin translations. Poskett then sends Regiomontanus off the Italy for ten years collecting manuscripts to improve his translation. In fact, Regiomontanus only spent four years in Italy in the service of Bessarion collecting manuscripts for Bessarion’s library, whilst also making copies for himself, and learning Greek to finish the Epitome.

Poskett correctly points out that the Epitome was an improved, modernised version of the Almagest drawing on Greek, Latin and Arabic sources. Poskett now claims that Regiomontanus introduced an innovation borrowed from the Islamic astronomer, Ali Qushji, that deferent and epicycles could be replaced by the eccentric. Poskett supports this argument by the fact that Regiomontanus uses Ali Qushji diagram to illustrate this possibility. The argument is not original to Poskett but is taken from the work of historian of astronomy, F. Jamil Ragip. Like Ragip, Poskett now argues thus:

In short, Ali Qushji argued that the motion of all the planets could be modelled simply by imagining that the centre of their orbits was at a point other than the Earth. Neither he nor Regiomontanus went as far as to suggest this point might in fact be the Sun. By dispensing with Ptolemy’s notion of the epicycle, Ali Qushji opened the door for a much more radical version of the structure of the cosmos.[7]

This is Ragip theory of what motivated Copernicus to adopt a heliocentric model of the cosmos. The question of Copernicus’s motivation remains open and there are numerous theories. This theory, as presented, however, has several problems. That the planetary models can be presented either with the deferent-epicycle model or the eccentric model goes back to Apollonius and is actually included in the Almagest by Ptolemy as Apollonius’ theorem (Almagest, Book XII, first two paragraphs), so this is neither an innovation from Ali Qushji nor from Regiomontanus. In Copernicus’ work the Sun is not actually at the centre of the planetary orbits but slightly offset, as has been pointed out his system is not actually heliocentric but more accurately heliostatic. Lastly, Copernicus in his heliostatic system continues to use the deferent-epicycle model to describe planetary orbits.

Poskett is presenting Ragip’s disputed theory to bolster his presentation of Copernicus’ dependency on Arabic sources, somewhat unnecessary as no historian of astronomy would dispute that dependency. Poskett continues along this line, when introducing Copernicus and De revolutionibus. After a highly inaccurate half paragraph biography of Copernicus–for example he has the good Nicolaus appointed canon of Frombork Cathedral after he had finished his studies in Italy, whereas he was actually appointed before he began his studies, he introduces us to De revolutionibus. He emphasis the wide range of international sources on which the book is based, and then presents Ragip’s high speculative hypothesis, for which there is very little supporting evidence, as fact:

Copernicus suggested that all these problems could be solved if we imagined the Sun was at the centre of the universe. In making this move he was directly inspired by the Epitome of the Almagest. Regiomontanus, drawing on Ali Qushji, had shown it was possible to imagine that the centre of all the orbits of the planets was somewhere other than the Earth. Copernicus took the final step, arguing that that this point was in fact the Sun.[8]

We simply do not know what inspired Copernicus to adopt a heliocentric model and to present a speculative hypothesis, one of a number, as the factual answer to this problem in a popular book is in my opinion irresponsible and not something a historian should be doing. 

Poskett now follows on with the next misleading statement. Having, a couple of pages earlier, introduced the Persian astronomer Nasir al-Din al-Tusi and the so-called Tusi couple, a mathematical device that allows linear motion to be reproduced geometrically with circles, Poskett now turns to Copernicus’ use of the Tusi couple. He writes:

The diagram in On the Revolution of the Heavenly Spheres shows the Tusi couple in action. Copernicus used this idea to solve exactly the same problem as al-Tusi. He wanted a way to generate an oscillating circular movement without sacrificing a commitment to uniform circular motion. He used the Tusi couple to model planetary motion around the Sun rather than the Earth. This mathematical tool, invented in thirteenth-century Persia, found its way into the most important work in the history of European astronomy. Without it, Copernicus would not have been able to place the Sun at the centre of the universe.[9] [my emphasis]

As my alter-ego the HISTSCI_HULK would say the emphasised sentence is pure and utter bullshit!

The bizarre claims continue, Poskett writes:

The publication of On the Revolution of the Heavenly Spheres in 1543 has long been considered the starting point for the scientific revolution. However, what is less often recognised is that Nicolaus Copernicus was in fact building on a much longer Islamic tradition.[10]

When I first read the second sentence here, I had a truly WTF! moment. There was a time in the past when it was claimed that the Islamic astronomers merely conserved ancient Greek astronomy, adding nothing new to it before passing it on to the Europeans in the High Middle Ages. However, this myth was exploded long ago. All the general histories of astronomy, the histories of Early Modern and Renaissance astronomy, and the histories of Copernicus, his De revolutionibus and its reception that I have on my bookshelf emphasise quite clearly and in detail the influence that Islamic astronomy had on the development of astronomy in Europe in the Middle Ages, the Renaissance, and the Early Modern period. Either Poskett is ignorant of the true facts, which I don’t believe, or he is presenting a false picture to support his own incorrect thesis.

Having botched European Renaissance astronomy, Poskett turns his attention to the Ottoman Empire and the Istanbul observatory of Taqi al-Din with a couple of pages that are OK, but he does indulge in a bit of hype when talking about al-Din’s use of a clock in an observatory, whilst quietly ignoring Jost Bürgi’s far more advanced clocks used in the observatories of Wilhelm IV of Hessen-Kassel and Tycho Brahe contemporaneously. 

This is followed by a brief section on astronomy in North Africa in the same period, which is basically an extension of Islamic astronomy with a bit of local colouration. Travelling around the globe we land in China and, of course, the Jesuits. Nothing really to complain about here but Poskett does allow himself another clangour on the subject of calendar reform. Having correctly discussed the Chinese obsession with calendar reform and the Jesuit missionaries’ involvement in it in the seventeenth century Poskett add an aside about the Gregorian Calendar reform in Europe. He writes:

The problem was not unique to China. In 1582, Pope Gregory XIII had asked the Jesuits to help reform the Christian Calendar back in Europe. As both leading astronomers and Catholic servants, the Jesuits proved an ideal group to undertake such a task. Christoph Clavius, Ricci’s tutor at the Roman College [Ricci had featured prominently in the section on the Jesuits in China], led the reforms. He integrated the latest mathematical methods alongside data taken from Copernicus’s astronomical tables. The result was the Gregorian calendar, still in use today throughout many parts of the world.[11]

I have no idea what source Poskett used for this brief account, but he has managed to get almost everything wrong that one can get wrong. The process of calendar reform didn’t start in 1582, that’s the year in which the finished calendar reform was announced in the papal bull Inter gravissimas. The whole process had begun many years before when the Vatican issued two appeals for suggestion on how to reform the Julian calendar which was now ten days out of sync with the solar year. Eventually, the suggestion of the physician Luigi Lilio was adopted for consideration and a committee was set up to do just that. We don’t actually know how long the committee deliberated but it was at least ten years. We also don’t know, who sat in that committee over those years; we only know the nine members who signed the final report. Clavius was not the leader of the reform, in fact he was the least important member of the committee, the leader being naturally a cardinal. You can read all of the details in this earlier blog post. At the time there were not a lot of Jesuit astronomers, that development came later and data from Copernicus’ astronomical tables were not used for the reform. Just for those who don’t want to read my blog post, Clavius only became associated with the reform after the fact, when he was commissioned by the pope to defend it against its numerous detractors.  I do feel that a bit of fact checking might prevent Poskett and Viking from filling the world with false information about what is after all a major historical event. 

The section Heaven and Earth closes with an account of Jai Singh’s observatories in India in the eighteenth century, the spectacular instruments of the Jantar Mantar observatory in Jaipur still stand today. 

Readers of this review need not worry that I’m going to go on at such length about the other three quarters of Poskett’s book. I’m not for two reasons. Firstly, he appears to be on territory where he knows his way around better than in the Early Modern period, which was dealt with in the first quarter Secondly, my knowledge of the periods and sciences he now deals with are severely limited so I might not necessarily have seen any errors. 

There are however a couple more train wrecks before we reach the end and the biggest one of all comes at the beginning of the second quarter in the section titled Newton’s Slaves. I’ll start with a series of partial quote, then analyse them:

(a) Where did Newton get this idea [theory of gravity] from? Contrary to popular belief, Newton did not make his great discovery after an apple fell on his head. Instead in a key passage in the Principia, Newton cited the experiments of a French astronomer named Jean Richer. In 1672, Richer had travelled to the French colony of Cayenne in South America. The voyage was sponsored by King Louis XIV through the Royal Academy of Science in Paris.

[…]

(b) Once in Cayenne, Richer made a series of astronomical observations, focusing on the movements of the planets and cataloguing stars close to the equator.

[…]

(c) Whilst in Cayenne, Richer also undertook a number of experiments with a pendulum clock.

[…]

(d) In particular, a pendulum with a length of just one metre makes a complete swing, left to right, every second. This became known as a ‘seconds pendulum’…

[…]

(e) In Cayenne, Richer noticed that his carefully calibrated pendulum was running slow, taking longer than a second to complete each swing.

[…]

(f) [On a second voyage] Richer found that, on both Gorée and Guadeloupe, he needed to shorten the pendulum by about four millimetres to keep it running on time.

[…]

(g) What could explain this variation?

[…]

(h) Newton, however, quickly realised the implications the implications of what Richer had observed. Writing in the Principia, Newton argued that the force of gravity varied across the surface of the planet. 

[…]

(i) This was a radical suggestion, one which seemed to go against common sense. But Newton did the calculations and showed how his equations for the gravitational force matched exactly Richer’s results from Cayenne and Gorée. Gravity really was weaker nearer the equator.

[…]

(j) All this implied a second, even more controversial, conclusion. If gravity was variable, then the Earth could not be a perfect sphere. Instead, Newton argued, the Earth must be a ‘spheroid’, flattened at the poles rather like a pumpkin. 

[…]

(k) Today, it is easy to see the Principia as a scientific masterpiece, the validity of which nobody could deny. But at the time, Newton’s ideas were incredibly controversial.

[…]

(l) Many preferred the mechanical philosophy of the French mathematician René Descartes. Writing in his Principles of Philosophy (1644), Descartes denied the possibility of any kind of invisible force like gravity, instead arguing that force was only transferred through direct contact. Descartes also suggested that, according to his own theory of matter, the Earth should be stretched the other way, elongated like an egg rather than squashed like a pumpkin.

[…]

(m) These differences were not simply a case of national rivalry or scientific ignorance. When Newton published the Principia in 1687, his theories were in fact incomplete. Two major problems remained to be solved. First, there were the aforementioned conflicting reports of the shape of the Earth. And if Newton was wrong about the shape of the Earth, then he was wrong about gravity.[12]

To begin at the beginning: (a) The suggestion or implication that Newton got the idea of the theory of gravity from Richer’s second pendulum experiments is quite simply grotesque. The concept of a force holding the solar system together and propelling the planets in their orbits evolved throughout the seventeenth century beginning with Kepler. The inverse square law of gravity was first hypothesised by Ismaël Boulliau, although he didn’t believe it existed. Newton made his first attempt to show that the force causing an object to fall to the Earth, an apple for example, and the force that held the Moon in its orbit and prevented it shooting off at a tangent as the law of inertia required, before Richer even went to Cayenne.

(c)–(g) It is probable that Richer didn’t make the discovery of the difference in length between a second pendulum in Northern Europe and the equatorial region, this had already ben observed earlier. What he did was to carry out systematic experiments to determine the size of the difference.

(l) Descartes did not suggest, according to his own theory of matter, that the Earth was an elongated spheroid. In fact, using Descartes theories Huygens arrived at the same shape for the Earth as Newton. This suggestion was first made by Jean-Dominique Cassini and his son Jacques long after Descartes death. Their reasoning was based on the difference in the length of one degree of latitude as measured by Willebrord Snel in The Netherlands in 1615 and by Jean Picard in France in 1670. 

This is all a prelude for the main train wreck, which I will now elucidate. In the middle of the eighteenth century, to solve the dispute on the shape of the Earth, Huygens & Newton vs the Cassinis, the French Academy of Science organised two expeditions, one to Lapland and one to Peru in order to determine as accurately as possible the length of one degree of latitude at each location. Re-enter Poskett, who almost completely ignoring the Lapland expedition, now gives his account of the French expedition to Peru. He tells us:

The basic technique for conducting a survey [triangulation] of this kind had been pioneered in France in the seventeenth century. To begin the team needed to construct what was known as a ‘baseline’. This was a perfectly straight trench, only a few inches deep, but at least a couple of miles long.[13]

Triangulation was not first pioneered in France in the seventeenth century. First described in print in the sixteenth century by Gemma Frisius, it was pioneered in the sixteenth century by Mercator when he surveyed the Duchy of Lorraine, and also used by Tycho Brahe to map his island of Hven. To determine the length of one degree of latitude it was pioneered, as already stated, by Willebrord Snell. However, although wrong this is not what most disturbed me about this quote. One of my major interests is the history of triangulation and its use in surveying the Earth and determining its shape and I have never come across any reference to digging a trench to lay out a baseline. Clearing the undergrowth and levelling the surface, yes, but a trench? Uncertain, I consulted the book that Poskett references for this section of his book, Larrie D Ferreiro’s Measure of the EarthThe Enlightenment Expedition that Reshaped the World (Basic Books, 2011), which I have on my bookshelf. Mr Ferreiro make no mention of a baseline trench. Still uncertain and not wishing to do Poskett wrong I consulter Professor Matthew Edney, a leading expert on the history of surveying by triangulation, his answer:

This is the first I’ve heard of digging a trench for a baseline. It makes little sense. The key is to have a flat surface (flat within the tolerance dictated by the quality of the instruments being used, which wasn’t great before 1770). Natural forces (erosion) and human forces (road building) can construct a sufficiently level surface; digging a trench would only increase irregularities.[14]

The problems don’t end here, Poskett writes:

La Condamine did not build the baseline himself. The backbreaking work of digging a seven-mile trench was left to the local Peruvian Indians.[15]

This is contradicted by Ferreiro who write:

Just as the three men completed the alignment for the baseline, the rest of the expedition arrived on the scene, in time for the most difficult phase of the operation. In order to create a baseline, an absolutely straight path, seven miles long and just eighteen inches wide, had to be dug into, ripped up from, and scraped out of the landscape. For the scientists, who had been accustomed to a largely sedentary life back in Europe, this would involve eight days of back breaking labour and struggling for breath in the rarefied air. “We worked at felling trees,” Bouguer explained in his letter to Bignon, “breaking through walls and filling in ravines to align [a baseline] of more than two leagues.” They employed several Indians to help transport equipment, though Bouguer felt it necessary that someone “keep an eye on them.”[16]

Poskett includes this whole story of the Peruvian Indians not digging a non-existent baseline trench because he wants to draw a parallel between the baseline and the Nazca Lines, a group of geoglyphs made in the soil of the Nazca desert in southern Peru that were created between 500 BCE and 500 CE. He writes:

The Peruvian Indians who built the baseline must have believed that La Condamine wanted to construct his own ritual line much like the earlier Inca rulers.[17]

Also:

Intriguingly some are simply long straight lines. They carry on for miles, dead straight, crossing hills and valleys. Whilst their exact function is still unclear, many historians now believe they were used to align astronomical observations, exactly as La Condamine intended with his baseline.[18]

The Nazca lines are of course pre-Inca. The ‘many historians’ is a bit of a giveaway, which historians? Who? Even if the straight Nazca lines are astronomically aligned, they by no means serve the same function as La Condamine’s triangulation baseline, which is terrestrial not celestial.  

To be fair to Poskett, without turning the baseline into a trench and without having the Indians dig it, Ferreiro draws the same parallel but without the astronomical component: 

For their part, the Indians were also observing the scientists, but to them “all was confusion” regarding the scientists’ motives for this arduous work. The long straight baseline the had scratched out of the ground certainly resembled the sacred linear pathways that Peruvian cultures since long before the Incas, had been constructing.[19]

Poskett’s conclusion to this section, in my opinion, contains a piece of pure bullshit.

By January 1742, the results were in. La Condamine calculated that the distance between Quito and Cuenca was exactly 344,856 metres. From observations made of the stars at both ends of the survey, La Condamine also found that the difference in latitude between Quit and Cuenca was a little over three degrees. Dividing the two, La Condamine concluded that the length of a degree of latitude at the equator was 110,613 metres. This was over 1,000 metres less than the result found by the Lapland expedition, which had recently returned to Paris. The French, unwittingly relying on Indigenous Andean science [my emphasis] had discovered the true shape of the Earth. It was an ‘oblate spheroid’, squashed at the poles and bulging at the equator. Newton was right.[20]

Sorry, but just because Poskett thinks that a triangulation survey baseline looks like an ancient, straight line, Peruvian geoglyph doesn’t in anyway make the French triangulation survey in anyway dependent on Indigenous Andean science. As I said, pure bullshit. 

The next section deals with the reliance of European navigators of interaction with indigenous navigators throughout the eighteenth century and is OK. This is followed by the history of eighteenth-century natural history outside of Europe and is also OK. 

At the beginning of the third quarter, we again run into a significant problem. The chapter Struggle for Existence open with the story of Étienne Geoffroy Saint-Hilaire, a natural historian, who having taken part in Napoleon’s Egypt expedition, compared mummified ancient Egyptian ibises with contemporary ones in order to detect traces of evolutions but because the time span was too short, he found nothing. His work was published in France 1818, but Poskett argues that his earliest work was published in Egyptian at the start of the century and so, “In order to understand the history of evolution, we therefore need to begin with Geoffroy and the French army in North Africa.” I’m not a historian of evolution but really? Ignoring all the claims for evolutionary thought in earlier history, Poskett completely blends out the evolutionary theories of Pierre Louis Maupertuis (1751), James Burnett, Lord Monboddo, (between 1767 and 1792) and above all Darwin’s grandfather Erasmus, who published his theory of evolution in his Zoonomia (1794–1796). So why do we need to begin with Étienne Geoffroy Saint-Hilaire?

Having dealt briefly with Charles Darwin, Poskett takes us on a tour of the contributions to evolutionary theory made in Russia, Japan, and China in the nineteenth century, whilst ignoring the European contributions. 

Up next in Industrial Experiments Poskett takes us on a tour of the contributions to the physical sciences outside of Europe in the nineteenth century. Here we have one brief WTF statement. Poskett writes:

Since the early nineteenth century, scientists had known that the magnetic field of the Earth varies across the planet. This means that the direction of the north pole (‘true north’) and the direction that the compass needle points (‘magnetic north’) are not necessarily identical, depending on where you are.[21]

Magnetic declination, to give the technical name, had been known and documented since before the seventeenth century, having been first measured accurately for Rome by Georg Hartmann in 1510, it was even known that it varies over time for a given location. Edmund Halley even mapped the magnetic declination of the Atlantic Ocean at the end of the seventeenth century in the hope that it would provide a solution to the longitude problem. 

In the final quarter we move into the twentieth century. The first half deals with modern physics up till WWII, and the second with genetic research following WWII, in each case documenting the contribution from outside of Europe. Faster than Light, the modern physics section, move through Revolutionary Russia, China, Japan, and India; here Poskett connects the individual contributions to the various revolutionary political movements in these countries. Genetic States moves from the US, setting the background, through Mexico, India, China, and Israel.  I have two minor quibbles about what is presented in these two sections.

Firstly, in both sections, instead of a chronological narrative of the science under discussion we have a series of biographical essays of the figures in the different countries who made the contribution, which, of course, also outlines their individual contributions. I have no objections to this, but something became obvious to me reading through this collection of biographies. They all have the same muster. X was born in Y, became interested in topic Z, began their studies at some comparatively local institute of higher education, and then went off to Heidelberg/Berlin/Paris/London/Cambridge/Edinburg… to study with some famous European authority, and acquire a PhD. Then off to a different European or US university to research, or teach or both, before to returning home to a professorship in their mother country. This does seem to suggest that opposed to Poskett’s central thesis of the global development of science, a central and dominant role for Europe.  

My second quibble concerns only the genetics section. One of Poskett’s central theses is that science in a given epoch is driven by an external to the science cultural, social, or political factor. For this section he claims that the external driving force was the Cold War. Reading through this section my impression was that every time he evoked the Cold War he could just have easily written ‘post Second World War’ or even ‘second half of the twentieth century’ and it would have made absolutely no difference to his narrative. In my opinion he fails to actually connect the Cold War to the scientific developments he is describing.

The book closes with a look into the future and what Poskett thinks will be the force driving science there. Not surprisingly he chooses AI and being a sceptic what all such attempts at crystal ball gazing are concerned I won’t comment here.

The book has very extensive end notes, which are largely references to a vast array of primary and mostly secondary literature, which confirms what I said at the beginning that Poskett in merely presenting in semi-popular form the current stand in the history of science of the last half millennium. There is no separate bibliography, which is a pain if you didn’t look to see something the first time it was end noted, as in subsequent notes it just becomes Smith, 2003, sending you off on an oft hopeless search for that all important first mention in the notes. There are occasional grey scale illustrations and two blocks, one of thirteen and one of sixteen, colour plates. There is also an extensive index.

So, after all the negative comments, what do I really think about James Poskett, highly praised volume. I find the concept excellent, and the intention is to be applauded. A general popular overview of the development of the sciences since the Renaissance is an important contribution to the history of science book market. Poskett’s book has much to recommend it, and I personally learnt a lot reading it. However, as a notorious history of science pedant, I cannot ignore or excuse the errors than I have outlined in my review, some of which are in my opinion far from minor. The various sections of the book should have been fact checked by other historians, expert in the topic of the section, and this has very obviously not been done. It is to be hoped that this will take place before a second edition is published. 

Would I recommend it? Perhaps surprisingly, yes. James Poskett is a good writer and there is much to be gained from reading this book but, of course, with the caveat that it also contains things that are simply wrong. 


[1] James Poskett, Horizons: A Global History of Science, Viking, 2022 

[2] Take your pick according to your personal philosophy of science.

[3] Poskett p. 11

[4] Poskett p. 16

[5] Poskett 16

[6] Poskett p. 23

[7] Poskett p. 59

[8] Poskett p. 61

[9] Poskett p. 62

[10] Poskett p. 62

[11] Poskett p. 84

[12] Poskett pp. 101-104

[13] Poskett p. 107

[14] Edney private correspondence 27.07.2022

[15] Poskett p. 108

[16] Ferreiro p. 107

[17] Poskett p. 111

[18] Poskett p. 110

[19] Ferreiro p. 107

[20] Poskett pp. 111-112

[21] Poskett p. 251

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Filed under Book Reviews, Early Scientific Publishing, History of Astronomy, History of botany, History of Cartography, History of Geodesy, History of Islamic Science, History of Navigation, Natural history, Renaissance Science

The Wizard Earl’s mathematici 

In my recent post on the Oxford mathematician and astrologer Thomas Allen, I mentioned his association with Henry Percy, 9th Earl of Northumberland, who because of his strong interest in the sciences was known as the Wizard Earl.

HENRY PERCY, 9TH EARL OF NORTHUMBERLAND (1564-1632) by Sir Anthony Van Dyck (1599-1641). The ‘Wizard Earl’ was painted posthumously as a philosopher, hung in Square Room at Petworth. This is NT owned. via Wikimedia Commons

As already explained there Percy actively supported four mathematici, or to use the English term mathematical practitioners, Thomas Harriot (c. 1560–1621), Robert Hues (1553–1632), Walter Warner (1563–1643), and Nathaniel Torporley (1564–1632). Today, I’m going to take a closer look at them.

Thomas Harriot is, of course, the most well-known of the four; I have already written a post about him in the past, so I will only brief account of the salient point here.

Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

He graduatied from Oxford in 1580 and entered the service of Sir Walter Raleigh (1552–1618) in 1583. At Raleigh’s instigation he set up a school to teach Raleigh’s marine captains the newest methods of navigation and cartography, writing a manual on mathematical navigation, which contained the correct mathematical method for the construction of the Mercator projection. This manual was never published but we can assume he used it in his teaching. He was also directly involved in Raleigh’s voyages to establish the colony of Roanoke Island.

Sir Walter Ralegh in 1588 artist unknown. Source: Wikimedia Commons

In 1590, he left Raleigh’s service and became a pensioner of Henry Percy, with a very generous pension, the title to some land in the North of England, and a house on Percy’s estate, Syon House, in Middlesex.[1] Here, Harriot lived out his years as a research scientist with no obligations.

Syon House Attributed to Robert Griffier

After Harriot, the most significant of the Wizard Earl’s mathematici was Robert Hues. Like Harriot, Hues attended St Mary’s Hall in Oxford, graduating a couple of years ahead of him in 1578. Being interested in geography and mathematics, he was one of those who studied navigation under Harriot in the school set up by Raleigh, having been introduced to Raleigh by Richard Hakluyt (1553–1616), another student of Thomas Allen and a big promoter of English colonisation of North America.  

Hakluyt depicted in stained glass in the west window of the south transept of Bristol Cathedral – Charles Eamer Kempe, c. 1905. Source: Wikimedia Commons

Hues went on to become an experienced mariner. During a trip to Newfoundland, he came to doubt the published values for magnetic declination, the difference between magnetic north and true north, which varies from place to place.

In 1586, he joined with Thomas Cavendish (1560–1592), a privateer and another graduate of the Harriot school of navigation, who set out to raid Spanish shipping and undertake a circumnavigation of the globe, leaving Plymouth with three ships on 21 July. After the usual collection of adventures, they returned to Plymouth with just one ship on 9 September 1588, as the third ever ship to complete the circumnavigation after Magellan and Drake. Like Drake, Cavendish was knighted by Queen Elizabeth for his endeavours.

Thomas Cavendish An engraving from Henry Holland’s Herōologia Anglica (1620). Animum fortuna sequatur is Latin for “May fortune follow courage.” Source: Wikimedia Commons

Hues undertook astronomical observations throughout the journey and determined the latitudes of the places they visited. In 1589, he served with the mathematicus Edward Wright (1561–1615), who like Harriot worked out the correct mathematical method for the construction of the Mercator projection, but unlike Harriot published it in his Certaine Errors in Navigation in 1599.

Source: Wikimedia Commons

In August 1591, he set out once again with Cavendish on another attempted circumnavigation, also accompanied by the navigator John Davis (c. 1550–1605), another associate of Raleigh’s, known for his attempts to discover the North-West passage and his discovery of the Falkland Islands.

Miniature engraved portrait of navigator John Davis (c. 1550-1605), detail from the title page of Samuel Purchas’s Hakluytus Posthumus or Purchas his Pilgrimes (1624). Source: Wikimedia Commons

Cavendish died on route in 1592 and Hues returned to England with Davis in 1683. On this voyage Hues continued his astronomical observations in the South Atlantic and made determinations of compass declinations at various latitudes and the equator. 

Back in England, Hues published the results of his astronomical and navigational research in his Tractatus de globis et eorum usu (Treatise on Globes and Their Use, 1594), which was dedicated to Raleigh.

The book was a guide to the use of the terrestrial and celestial globes that Emery Molyneux (died 1598) had published in 1592 or 1593.

Molyneux CEltial Globe Middle Temple Library
A terrestrial globe by Emery Molyneux (d.1598-1599) is dated 1592 and is the earliest such English globe in existence. It is weighted with sand and made from layers of paper with a surface coat of plaster engraved with elaborate cartouches, fanciful sea-monsters and other nautical decoration by the Fleming Jodocus Hondius (1563-1611). There is a wooden horizon circle and brass meridian rings.

Molyneux belong to the same circle of mariners and mathematici, counting Hues, Wright, Cavendish, Davis, Raleigh, and Francis Drake (c. 1540–1596) amongst his acquaintances. In fact, he took part in Drake’s circumnavigation 1577–1580. These were the first globes made in England apparently at the suggestion of John Davis to his patron the wealthy London merchant William Sanderson (?1548–1638), who financed the construction of Molyneux’s globes to the tune of £1,000. Sanderson had sponsored Davis’ voyages and for a time was Raleigh’s financial manager. He named his first three sons Raleigh, Cavendish, and Drake.

Molyneux’s terrestrial globe was his own work incorporating information from his mariner friends and with the assistance of Edward Wright in plotting the coast lines. The circumnavigations of Drake and Cavendish were marked on the globe in red and blue line respectively. His celestial globe was a copy of the 1571 globe of Gerard Mercator (1512–1594), which itself was based on the 1537 globe of Gemma Frisius (1508–1555), on which Mercator had served his apprenticeship as globe maker. Molyneux’s globes were engraved by Jodocus Hondius (1563–1612), who lived in London between 1584 and 1593, and who would upon his return to the Netherlands would found one of the two biggest cartographical publishing houses of the seventeenth century.

Hues’ Tractatus de globis et eorum usu was one of four publications on the use of the globes. Molyneux wrote one himself, The Globes Celestial and Terrestrial Set Forth in Plano, published by Sanderson in 1592, of which none have survived. The London public lecturer on mathematics Thomas Hood published his The Vse of Both the Globes, Celestiall and Terrestriall in 1592, and finally Thomas Blundeville (c. 1522–c. 1606) in his Exercises containing six treatises including Cosmography, Astronomy, Geography and Navigation in 1594.

Hues’ Tractatus de globis has five sections the first of which deals with a basic description of and use of Molyneux’s globes. The second is concerned with matters celestial, plants, stars, and constellations. The third describes the lands, and seas displayed on the terrestrial globe, the circumference of the earth and degrees of a great circle. Part four contains the meat of the book and explains how mariners can use the globes to determine the sun’s position, latitude, course and distance, amplitudes and azimuths, and time and declination. The final section is a treatise, inspired by Harriot’s work on rhumb lines, on the use of the nautical triangle for dead reckoning. Difference of latitude and departure (or longitude) are two legs of a right triangle, the distance travelled is the hypotenuse, and the angle between difference of latitude and distance is the course. If any two elements are known, the other two can be determined by plotting or calculation using trigonometry.

The book was a success going through numerous editions in various languages. The original in Latin in 1593, Dutch in 1597, an enlarged and corrected Latin edition in 1611, Dutch again in 1613, enlarged once again in Latin in 1617, French in 1618, another Dutch edition in 1622, Latin again in 1627, English in 1638, Latin in 1659, another English edition also in 1659, and finally the third enlarged Latin edition reprinted in 1663. There were others.

The title page of Robert Hues (1634) Tractatvs de Globis Coelesti et Terrestri eorvmqve vsv in the collection of the Biblioteca Nacional de Portugal via Wikimedia Commons

Hues continued his acquaintance with Raleigh in the 1590s and was one of the executors of Raleigh’s will. He became a servant of Thomas Grey, 15th Baron Gray de Wilton (died 1614) and when Grey was imprisoned in the Tower of London for his involvement in a Catholic plot against James I & VI in 1604, Hues was granted permission to visit and even to stay with him in the Tower. From 1605 to 1621, Northumberland was also incarcerated in the Tower because of his family’s involvement in the Gunpowder Plot. Following Grey’s death Hues transferred his Tower visits to Northumberland, who paid him a yearly pension of £40 until his death in 1632.

He withdrew to Oxford University and tutored Henry Percy’s oldest son Algernon, the future 10th Earl of Northumberland, in mathematics when he matriculated at Christ’s Church in 1617.

Algernon Percy, 10th Earl of Northumberland, as Lord High Admiral of England, by Anthony van Dyck. Source: Wikimedia Commons

In 1622-23 he would also tutor the younger son Henry.

Oil painting on canvas, Henry Percy, Baron Percy of Alnwick (1605-1659) by Anthony Van Dyck Source: Wikimedia Commons

During this period, he probably visited both Petworth and Syon, Northumberland’s southern estates. He in known to have had discussion with Walter Warner on reflection. He remained in Oxford discussing mathematics with like minded fellows until his death.

Compared to the nautical adventures of Harriot and Hues, both Warner and Torporley led quiet lives. Walter Warner was born in Leicestershire and educated at Merton College Oxford graduating BA in 1579, the year between Hues and Harriot. According to John Aubrey in his Brief Lives, Warner was born with only one hand. It is almost certain that Hues, Warner, and Harriot met each other attending the mathematics lectures of Thomas Allen at Oxford. Originally a protégé of Robert Dudley, 1st Earl of Leicester, (1532–1588), he entered Northumberland’s household as a gentleman servitor in 1590 and became a pensioner in 1617. Although a servant, Warner dined with the family and was treated as a companion by the Earl. In Syon house, he was responsible for purchasing the Earl’s books, Northumberland had one of the largest libraries in England, and scientific instruments. He accompanied the Earl on his military mission to the Netherlands in 1600-01, acting as his confidential courier.       

Like Harriot, Warner was a true polymath, researching and writing on a very wide range of topics–logic, psychology, animal locomotion, atomism, time and space, the nature of heat and light, bullion and exchange, hydrostatics, chemistry, and the circulation of the blood, which he claimed to have discovered before William Harvey. However, like Harriot he published almost nothing, although, like Harriot, he was well-known in scholarly circles. Some of his work on optics was published posthumously by Marin Mersenne (1588–1648) in his Universæ geometriæ (1646).

Source: Google Books

It seems that following Harriot’s death Warner left Syon house, living in Charing Cross and at Cranbourne Lodge in Windsor the home of Sir Thomas Aylesbury, 1st Baronet (!576–1657), who had also been a student of Thomas Allen, and who had served both as Surveyor of the Navy and Master of the Mint. Aylesbury became Warner’s patron.

This painting by William Dobson probably represents Sir Thomas Aylesbury, 1st Baronet. 
Source: Wikimedia Commons

Aylesbury had inherited Harriot’s papers and encouraged Warner in the work of editing them for publication (of which more later), together with the young mathematician John Pell (1611–1685), asking Northumberland for financial assistance in the endeavour.

Northumberland died in 1632 and Algernon Percy the 10th Earl discontinued Warner’s pension. In 1635, Warner tried to win the patronage of Sir Charles Cavendish and his brother William Cavendish, enthusiastic supporters of the new scientific developments, in particular Keplerian astronomy. Charles Cavendish’s wife was the notorious female philosopher, Margaret Cavendish. Warner sent Cavendish a tract on the construction of telescopes and lenses for which he was rewarded with £20. However, Thomas Hobbes, another member of the Cavendish circle, managed to get Warner expelled from Cavendish’s patronage. Despite Aylesbury’s support Warner died in poverty. 

Nathaniel Torporley was born in Shropshire of unknow parentage and educated at Shrewsbury Grammar Scholl before matriculating at Christ Church Oxford in 1581. He graduated BA in 1584 and then travelled to France where he served as amanuensis to the French mathematician François Viète (1540–1603).

François Viète Source: Wikimedia Commons

He is thought to have supplied Harriot with a copy of Viète’s Isagoge, making Harriot the first English mathematician to have read it.

Source

Torporley returned to Oxford in 1587 or 1588 and graduated MA from Brasenose College in 1591. 

He entered holy orders and was appointed rector of Salwarpe in Worcestershire, a living he retained until 1622. From 1611 he was also rector of Liddington in Wiltshire. His interest in mathematics, astronomy and astrology attracted the attention of Northumberland and he probably received a pension from him but there is only evidence of one payment in 1627. He was investigated in 1605, shortly before the Gunpowder Plot for having cast a nativity of the king. At some point he published a pamphlet, under the name Poulterey, attacking Viète. In 1632, he died at Sion College, on London Wall and in a will written in the year of his death he left all of his books, papers, and scientific instrument to the Sion College library.

Although his papers in the Sion College library contain several unpublished mathematical texts, still extant today, he only published one book his Diclides Coelometricae; seu Valuae Astronomicae universales, omnia artis totius munera Psephophoretica in sat modicis Finibus Duarum Tabularum methodo Nova, generali et facillima continentes, (containing a preface, Directionis accuratae consummata Doctrina, Astrologis hactenus plurimum desiderata and the Tabula praemissilis ad Declinationes et coeli meditations) in London in 1602.

Source

This is a book on how to calculate astrological directions, a method for determining the time of major incidents in the life of a subject including their point of death, which was a very popular astrological method in the Renaissance. This requires spherical trigonometry, and the book is interesting for containing new simplified methods of solving right spherical triangles of any sort, methods that are normally attributed to John Napier (1550–1617) in a later publication. The book is, however, extremely cryptic and obscure, and almost unreadable. Despite this the surviving copies would suggest that it was widely distributed in Europe.

Our three mathematici came together as executors of Harriot’s will. Hues was charged with pricing Harriot’s books and other items for sale to the Bodleian Library. Hues and Torporley were charged with assisting Warner with the publication of Harriot’s mathematical manuscripts, a task that the three of them managed to bungle. In the end they only managed to publish one single book, Harriot’s algebra Artis Analyticae Praxis in 1631 and this text they castrated.

Source

Harriot’s manuscript was the most advanced text on the topic written at the time and included full solutions of algebraic equations including negative and complex solutions. Either Warner et al did not understand Harriot’s work or they got cold feet in the face of his revolutionary new methods, whichever, they removed all of the innovative parts of the book making it basically irrelevant and depriving Harriot of the glory that was due to him.

For myself the main lesson to be learned from taking a closer look at the lives of this group of mathematici is that it shows that those interested in mathematics, astronomy, cartography, and navigation in England the late sixteenth and early seventeenth centuries were intricately linked in a complex network of relationships, which contains hubs one of which was initially Harriot and Raleigh and then later Harriot and Northumberland. 


[1] For those who don’t know, Middlesex was a small English county bordering London, in the South-West corner of Essex, squeezed between Hertfordshire to the north and Surry in the South, which now no longer exists having been largely absorbed into Greater London. 

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

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

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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Filed under History of Astronomy, History of Cartography, History of Islamic Science, History of Mathematics, History of Navigation

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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