Regular readers of my series of posts on English mathematical practitioners in the late sixteenth and early seventeenth centuries might have noticed the name John Davis popping up from time to time. Unlike most of the other mathematical practitioners featured here in the early modern history of cartography, navigation, and scientific instrument design, who were basically mathematicians who never or seldom went to sea, John Davis (c. 1550–1605) was a mariner and explorer, who was also a mathematician, who wrote an important and widely read book on the principles of navigation, which included the description of an important new instrument that he had designed.
John Davis was born and grew up in Sandridge Barton, the manor farm on the Sandrige Estate of Stoke Gabriel in Devon, a small village on the river Dart about six kilometres up-river from Dartmouth, which was an important port in the early modern period, so it seems that Davis was destined to go to sea. Amongst his neighbours, on the Sandrige Estate, were the five sons of the Gilbert-Raleigh family, Humphrey, John and Adrian Gilbert and their half brothers Carew and Walter Raleigh. Both Humphrey Gilbert (c. 1539–1583) and Walter Raleigh (c. 1552–1618) were important Elizabethan explorers and Carew Raleigh (c. 1550–c. 1625) was a naval commander. Adrian Gilbert (c. 1541–1628), who became an MP was an intimate friend of the young John Davis as was Walter Raleigh. Little is known of his childhood and youth, but we do know that he early became a friend and pupil of the leading Elizabethan mathematical practitioner, John Dee (1527–c. 1608). Davis’ friendship with the Gilbert-Raleigh brothers and John Dee would prove helpful in his first major exploration endeavour, the search for the Northwest Passage.
Throughout the Middle Ages, Europe had imported good, in particular spices, from Asia via a complex, largely overland route that ended in Northern Italy, from whence the city of Nürnberg distributed them all over Europe. As the European began to venture out onto the high seas in the fifteenth century, the question arose, whether it was possible to reach Asia directly by sea? The Portuguese began to edge their way down the West African coast and in 1487/88 Bartolomeu Dias (c. 1450–1500) succeeded in rounding the southern end of Africa.
Between 1479 and 1499 Vasco da Gama (c. 1460–1524) succeeded, with the help of an Arabic pilot, in crossing the Indian Ocean and bringing back a cargo of spices from India to Portugal. This established an initial Portuguese dominance over the oceanic route sailing eastwards to Asia, which with time they extended to the so-called Spice Islands.
As every school kid knows, Christopher Columbus (1451–1506) believed that there was open water between the west coast of Europe and east coast of China, and that he could reach Asia faster and easier sailing west across the ocean rather the east around Africa. In 1492, he put his theory to the test and, having vastly underestimated the distance involved, just as he was running out of food, his small fleet fortuitously ran into the Americas, although they weren’t called that yet. In 1519, the Spanish seaman Ferdinand Magellan (1480–1521) proved it was possible to get past the southern tip of America and into the Pacific Ocean. The last remnants of his very battered fleet returning to Spain, without Magellan, who was killed on the way, in 1522, becoming the first people to circumnavigate the globe.
In 1577, Francis Drake (c. 1540–1596) set out to attack the Spanish on the west coast of the America, decided to return via the Pacific Ocean arriving back in England in 1580, becoming the second to circumnavigate the globe, and the first commander to survive the journey. Between 1586 and 1588, Thomas Cavendish (1560-1592), a protégé of Walter Raileigh, became the third man to circumnavigate the globe, on what was the first planned voyage to do so.
The successful circumnavigations via the southern tip of the Americas led to speculation whether it was possible to reach the Pacific Ocean by rounding the northern end of the Americas. These speculations led to the search for the so-called Northwest Passage, an endeavour in which English mariners would dominate.
Already in 1497, Henry VII sent the Italian mariner, John Cabot (C. 1450–c. 1500) to attempt to find the Northwest Passage. He is thought to have landed once somewhere on the coast of what is now Canada before returning to Bristol. In 1508, Cabot’s son Sebastian (c. 1474–1557) followed his father in trying to find the Northwest Passage. He is thought to have sailed as far north as Hudson Bay. In 1524, the Portuguese mariner, Estêvão Gomes (c. 1483–1538), who had mutinied on the Magellan circumnavigation, bringing his ship back to Spain in 1521, was commissioned by the Spanish Crown to seek a northern route through the Americas, reaching Nova Scotia before returning to Spain.
In 1551, the Muscovy Trading Company was founded in London with the specific intention of finding a Northeast Passage to China by sailing around the northern coast of Russia. A project for which they were granted exclusive rights by the English Crown. The Muscovy Company employed John Dee to teach cartography and navigation to its ships’ officers. They failed in their endeavour to find the Northeast Passage but did establish successful trading deals with Russia.
In the 1560s Humphrey Gilbert wrote a detailed treatise supporting the idea of a government supported endeavour to search for the Northwest Passage. In 1574, the privateer Martin Frobisher (c. 1535–1594) petitioned the Privy Council for permission and financial support for an expedition to find the Northwest Passage. They referred him to the Muscovy Company, who eventually agreed to licence his voyage. Altogether Frobisher undertook three attempts, in 1596 with three ships, in 1597 with a much larger fleet and finally in 1578 with a total of fifteen ships. Although he explored much of the coast and islands of Northern Canada the undertaking was basically an expensive flop. On the second expedition Frobisher’s master was Christopher Hall. Frobisher and Hall were coached by Dr John Dee in geometry and cosmography in order to improve their use of the instruments for navigation in their voyage.
In 1583, Humphrey Gilbert launched an attempt, based on letters patent, that he had acquired from the crown in 1578, to establish an English colony in North America. His half-brother Walter Raleigh sailed with him but had to turn back due to lack of food on his ship. Having taken possession of Newfoundland by force, he then left again without establishing a colony due to lack of supplies. The return journey was a disaster with the loss of the biggest vessel with most of there stores and Gilbert died of blood poisoning, having stepped on a nail.
The only halfway positive outcome was that Walter Raleigh received a royal charter based on Gilbert’s letters patent and would in turn go on to found, with Thomas Harriot (c. 1560–1621), as his cartography and navigation advisor, the first English colony in North America on Roanoke Island in 1584. Only halfway positive because the Roanoke colony was also a failure.
It was against this background of one hundred years of failure, from John Cabot to Martin Frobisher, to find a northwest passage that John Davis became involved in the launching of yet another expedition to find one, initiated by his childhood friend Adrian Gilbert and John Dee. Gilbert and Dee, appealed to Sir Francis Walsingham (1573–1590) Secretary of State for funding in 1583. Whilst Walsingham favoured the idea politically, no money from the state was forthcoming. Instead, the planned expedition was financed privately by the London merchant, William Sanderson (c.1548–1638).
Sanderson was trained by Thomas Allen, an assistant to the Muscovy Company, who supplied the Queen’s Navy with hemp, rope, flax, and tallow, which he imported from the Baltic countries. As a young man, Sanderson travelled with Allen throughout the Baltic, France, Germany, and the Netherlands. According to his son, he became wealthy when he inherited the family estates following the death of his elder brother. In either 1584 or 1585 he married Margaret Snedall, daughter of Hugh Snedall, Commander of the Queen’s Navy Royal, and Mary Raleigh sister to Walter Raleigh. Sanderson would go on to become Walter Raleigh’s financial manager.
Here we have once again a merchant financing exploration in the early stumbling phase of the British Empire, a concept that was first floated by John Dee and was propagated by the various members of the Gilbert-Raleigh clan. As we saw in an earlier post, it was the merchants Thomas Smith and John Wolstenholme, who later founded the East India Trading Company, who financed the mathematical lectures of Thomas Hood (1556–1620). Above, we saw that the Muscovy Trading Company financed Frobisher’s efforts to find the Northwest Passage. The founding of the British Empire was driven by trade, and it remained a trading empire throughout its existence. Trade in spices, gold, opium, tea, slaves and other commodities drove and financed the existence of the Empire.
Davis led three expeditions in search of the Northwest Passage in 1585, 1586, and 1587. He failed to find the passage but carried out explorations and surveys of much territory between Greenland and Northern Canada liberally spraying the map with the names of Sanderson, Raleigh, and Gilbert. On these voyages Davis proved his skill as a navigator and marine commander, his logbooks being a model for future mariners and although the expeditions failed in their main aim, they can certainly be counted as successful.
In 1591, he was part of Thomas Cavendish’s voyage to attempt to find the Northwest Passage from the western end in the Pacific. The voyage was a disaster, Cavendish losing most of his crew in a battle with the Portuguese and setting sail for home. Davis carried on to the Straits of Magellan but was driven back by bad weather, also turning for home. He too lost most of his crew on the return journey but is purported in 1592 to be the first English man to discover the Falkland Islands, a claim that is disputed.
Davis sailed as master with Walter Raleigh on his voyages to Cádiz and the Azores in 1596 and 1597. He sailed as pilot with a Dutch expedition to the East Indies between 1598 and 1600. From 1601 to 1603 he was pilot-major on the first English East India Company voyage led by Sir James Lancaster (c. 1554–1618), a privateer and trader.
Although a success, the voyage led to a dispute between Davis and Lancaster, the later accusing the pilot of having supplied false information on details of trading. Annoyed, Davis sailed in 1604 once again to the East Indies as pilot to Sir Edward Michelbourne (c. 1562–1609) an interloper who had been granted a charter by James I & VI despite the East India Company’s crown monopoly on trade with the East. On this voyage he was killed off Singapore by a Japanese pirate whose ship he had seized. Thus, ending the eventful life of one of Elizabethan England’s greatest navigators.
All the above is merely an introduction to the real content of this post, Davis’ book on navigation and his contribution to the development of navigation instruments. However, this introduction should serve to show two things. Firstly, that when Davis wrote about navigation and hydrography, he did so as a highly experienced mariner and secondly just how incestuous the exploration and navigation activities in late sixteenth century England were.
In 1594, Davis published his guide to navigation for seamen, which could with some justification be called Navigation for Dummies. It was the first book on navigation actually written by a professional navigator. To give it its correct title:
THE SEAMAN’S SECRETS; Deuided into 2, partes, wherein is taught the three kindes of Sayling, Horizontall, Peradoxal, and sayling vpon a great Circle: also an Horizontall Tyde Table for the easie finding of the ebbing and flowing of the Tydes, with a Regiment newly calculated for the finding of the Declination of the Sunne, and many other necessary rules and Instruments, not heretofore set foorth by any.
Newly published by Iohn Dauis of Sandrudge, neere Dartmouth, in the County of Deuon. Gent.
Imprinted at London by Thomas Dawson, dwelling at the three Cranes in the Vinetree, and are these to be solde. 1595
David Waters write, “his work gives in the briefest compass the clearest picture of the art of navigation at this time.”
Davis defines his three kinds of sailing thus:
Horizontal [plane] Navigation manifesteth all the varieties [changes] of the ship’s motion within the Horizontal plain superfices [on a plane chart], where every line [meridian] is supposed parallel.
This was the traditional and most common form of navigation at the time Davis wrote his book and he devotes the whole of the first part of the book to it.
Paradoxal Navigation demonstrateth [on circumpolar charts] the true motion of the ship upon any corse assigned … neither circular nor strait, but concurred or winding … therefore called paradoxal, because it is beyond opinion that such lines should be described by plain horizontal motion.
What Davis is defining here is rhumb line or Mercator sailing.
Great circle navigation he considered as the ‘chiefest of all the three kinds of sayling’, and defined it as one ‘in whom all the others are contained … continuing a corse by the shortest distance between places not limited to any one corse.’
He lists the instruments necessary for a skilful seaman:
A sea compass, a cross staff, a quadrant, an Astrolaby, a chart, an instrument magnetical for finding the variations of the compass, an Horizontal plain sphere, a globe and a Paradoxal compass.
He then qualifies the list:
But the sea Compass, Chart and Cross Staff are instruments sufficient for the Seaman’s use … for the Cross Staffe, Compass and the chart are so necessarily joined together as that the one say not well be without the other … for as the Chart sheweth the courses, so doth the compasse direct the same, and the cross-staffe by every particular observed latitude doth informe the truth of such course, and also give the certaine distance that the ship hath sayled upon the same.
Davis describes the technique of plane (horizontal) sailing as–’the god observation of latitude, careful reckoning of the mean course steered (corrected for variation), and careful estimation of the distance run’. Of these ‘the pilot has only his height [latitude] in certain.’
Davis gives clear definition of special terms such as course and traverses and delivers an example of how he wrote up his ship’s journal. His was the first book published to give such things.
He gave much space to how to calculate the tides, including the use of ‘An Horizontal Tyde-Table,’ an instrument for calculating tide times.
Davis goes into a lot of details on how to calibrate the cross-staff, he paid particular attention to the problem of parallax produced by placing the end of the cross-staff in the wrong position on the face. This is interesting given his development of the back-staff.
In order to determine one’s latitude, it was necessary to determine the altitude of the sun at noon. This was usually done using a cross-staff, also known as a Jacob’s staff, but could also be done with a quadrant or a mariner’s astrolabe.
The cross-staff suffered from a couple of problems. As well as the eye parallax problem, already discussed, the user had to hold the staff so that the lower tip of the traverse rested on the horizon, whilst the upper tip was on the sun, then the angle of altitude could be read off on the calibrated scale on the staff. There were different sized traverses for different latitudes and there were scales on the staff for each traverse, a topic that Davis delt with in great detail. It was difficult for the user to view both tips at the same time. Added to this the user was basically staring directly into the sun.
To get round these problems Davis invented the backstaff. At the end of the staff was a horizon vane through which the user viewed the horizon with his back to the sun. An arc, ewith a shadow vane, was attached to the staff which could slide back and forth until its shadow fell on the horizon vane the angle of altitude could be read off on the calibrated staff. This staff did not suffer from the eye parallax problem, the user only had to observe the horizon and not the sun at the same time, and the user did not have to look directly into the sun.
Davis’ original back staff could only measure a maximum angle of altitude of 45°, which was OK as long as he was sailing in the north but was too small when he started sailing further south, so he developed a more advanced model that could measure angles up to 90°.
This evolved over time into the so-called Davis quadrant.
Better than the cross-staff for measuring the sun’s altitude, the back-staff became the instrument of choice, particularly for English mariners for more than a century, but it was not perfect. Unlike the cross-staff, it could not be used at night to determine latitude by measuring stellar altitudes, also its use was limited by overcast weather when the sun was not strong enough to cast a shadow. To help with the latter problem, John Flamsteed replaced the shadow vane with a lens that focused the sunlight on the horizon vane instead of a shadow. The weak sunlight focused by the lens could be better seen that the faint shadow. The backstaff with lens evolved into the Hadley quadrant, which in turn evolved into the sextant still in use today.
Davis also gives an extensive description of how to navigate using a terrestrial globe. This was very innovative because mass produced printed globes were a fairly recent invention, Johannes Schöner (1477–1547) produced the first serial printed terrestrial globe in 1515, and were not easy to come by. It was Davis, who persuaded his own patron, William Sanderson, to finance Emery Molyneux’s creation of the first printed terrestrial and celestial globes in England in 1592.
Davis emphasised that the terrestrial globe was particularly good for instruction in navigation because all three forms of sailing–plane, rhumb line, great circle–could be demonstrated on it.
In his original list of instruments for the seaman, Davis included the Paradoxal compass but he doesn’t actually explain anywhere what this instrument is. John Dee, who remember was John Davis’ teacher, also mentions the Paradoxal compass in his writings without explanation. There is talk of how he created a Paradoxal chart for Humphrey Gilbert for his fatal 1583 expedition. It turns out that the Paradoxal compass and Paradoxal chart are one and the same and that it is an azimuthal equidistant circumpolar chart, with the north pole at its centre and the lines of latitude at 10° interval as concentric circles. The azimuthal equidistant projection goes back at least to al-Bīrūnī (973–after 1050) in the eleventh century.
In his book on plane sailing, Davis discusses the drawbacks of the plane chart or equirectangular projection, which assumes that the world is flat and on which both lines of longitude and latitude are straight equidistant parallel line which cross at right angles, which according to Ptolemaeus was invented by Marinus of Tyre (c. 70–130 CE) in about 100 CE. A plane chart is OK for comparatively small areas, the Mediterranean for example, and Davis praises its usefulness for coastal regions. However, it distorts badly the further you move away from its standard parallel.
As a result, it is useless for exploration in the far north and hence the use of the Paradoxal compass. The use of such circumpolar maps became standard for polar exploration in the following centuries.
Straight forward, clear and direct The Seaman’s Secret was very popular and went through several new editions in the decades following Davis’ death. A year after it was published Davis published a second book, his The World’s Hydrographical Description or to give it its full title:
Wherein is proved not only by Aucthoritie of Writers, but also by late experience of Travellers and Reasons of Substantial Probabilitie, that the Worlde in all his Zones, Clymats, and places, is habitable and inhabited, and the Seas likewise universally navigable without any naturall anoyance to hinder the same,
Whereby appears that from England there is a short and
speedie passage into the South Seas, to China,
Molucca, Philippina, and India, by Northerly
To the Renowne, Honour, and Benifit of Her Majesties State and
Published by J. DAVIS OF SANDRUG BY DARTMOUTH
In the Countie of Devon, Gentleman. ANNO 1595, May 27.
Imprinted at London
BY THOMAS DAWSON Dwelling at the Three Cranes in the Vinetree, and there to be sold.
The ‘by Northerly Navigation’ reveals that it is in fact a long plea for a return to exploration to find the Northwest Passage.
With his The Seaman’s Secrets based on his own extensive experience as an active navigator and his invention of the backstaff, John Davis made a substantial contribution to the development of mathematical navigation in the Early Modern Period.
 David Waters, The Art of Navigation in England in Elizabethan and Early Stuart Times, Yale University Press, New Heaven, 1958, p.201
 All the above is distilled from Water’s page 202.
This is the fourthin a series of discussion of selected parts of Paul Strathern’s The Other Renaissance: From Copernicus to Shakespeare, (Atlantic Books, 2023). For more general details on both the author and his book see the first post in this series.
Strathern introduces us to today’s subjects thus:
We now come to two figures who used ingenious mathematical techniques to unravel their own versions of the truth. These were Gerardus Mercator and François Viète, both of whom lived exciting lives (though not always pleasantly so), and whose works would play a part in transforming the world in which we live.
Although Mercator’s biography is well documented Strathern still manages to screw up his facts. He tells us that his father was from Gangelt and was therefore German. Gangelt was at this time in the Duchy of Jülich and the inhabitants spoke a dialect of what would become Dutch. I do wish people would look more deeply at nationality, ethnicity etc in history, just because somewhere is German or whatever today doesn’t mean it was in the sixteenth century. Then he tells us:
During Mercator’s youth, two historic events took place which would change Europe forever. Mercator was just five when Luther instigated what would become the Reformation, and he was ten years old when the survivors of Magellan’s three-year expedition to circumnavigate the globe arrived back in Seville. By this time young Mercator’s father had died, and his uncle had taken on the role of his guardian.
Mercator was actually fifteen when his father died, and his uncle placed him in the school of the Brethren of the Common Life in ‘s-Hertogenbosch. Here Strathern drops a paragraph that brought tears to my eyes the first time I read it, not really believing what I had just read. The second time through I started weeping and the third time I just wanted to burn the whole thing down.
Even so, the main curriculum was still based on the traditional scholastic trivium of grammar, logic and rhetoric, all of which were of course taught in Latin. However, in a gesture towards the renaissance of classical knowledge, the curriculum had been extended to include Ptolemy and his Geography. The Ancient Greek polymath had written this work in Alexandria around AD 150. The fact that it was written in Ancient Greek meant that it had remained unknown to Europe during the medieval era, as scholars only knew Latin. It was not translated until 1406, when its appearance created a great stir. Meanwhile Ptolemy’s geocentric cosmology, which Aristotle had passed on, would not be refuted by Copernicus until 1543, when Mercator was in his thirties. But much of Ptolemy’s Geography, especially his map of the world – consisting of a chart which stretched from the Atlantic coast in the west to Sinae (China) in the east – had come as a revelation to the young Mercator.
Ptolemy’s Mathēmatikē Syntaxis (Almagest) and his Tetrabiblos were available and widely read in Latin in the medieval period, both of them having been translated directly from the original Greek in the twelfth century, but apparently his Geōgraphikḕ Hyphḗgēsis (Geographia) was not as, “written in Ancient Greek meant that it had remained unknown to Europe during the medieval era, as scholars only knew Latin.” This is of course total bullshit. There was no Latin translation of the Geographia in Europe in the Middle Ages because there was neither a Greek nor an Arabic manuscript of the work known before a Greek manuscript was discovered in Constantinople in the early fifteenth century and translated by Jacobus Angelus in 1406.
Meanwhile Ptolemy’s geocentric cosmology, which Aristotle had passed on [my emphasis], would not be refuted by Copernicus until 1543, when Mercator was in his thirties.
Please savour this gem of a sentence, you will probably search high and low to find its equivalent in stupidity in a supposedly serious, ‘academic’ publication. Strathern claims to be an academic author. Aristotle (384–322 BCE) passed on the geocentric cosmology of Ptolemy, written c. 150 CE!
Having imbibed Ptolemaic geography at school, Mercator now goes off to university:
In 1530, at the age of eighteen, Mercator travelled to the similarly prestigious University of Leuven. Here he passed the entry matriculation, where his name appears in the Latin form he had adopted at school followed by the classification pauperes ex castro (poor students of the castle). This indicated that he was given lodgings in one of the communal dormitories set aside for unprivileged students in the castle by the fish market. Rich students lived separately in their own rooms in a more salubrious quarter of the city.
Pauperes does in fact mean that he was a poor student but ex castro refers to the college he was in Castle College (Dutch: De Burcht or Het Kasteel, Latin: Paedagogium Castri) the oldest of the Leuven colleges, founded in 1431. All the students, rich or poor, lived in the same college building, although the quality of their rooms varied.
Strathern now slips in a reference to Vesalius:
Despite such domestic segregation, all students mingled freely, attending the same lectures, and it was here that Mercator formed a friendship with one of his more privileged contemporaries, named Andreas Vesalius, of whom we will hear more later. Suffice to say that Vesalius would become one of the great luminaries of the northern Renaissance, on a par with Mercator himself, with whom he retained a lifelong friendship.
Although they almost certainly knew each other, I know of no special friendship between Mercator and Vesalius. However, there was one between Vesalius and Gemma Frisius, about whom more soon, they even, infamously, stole part of a corpse on a gibbet together.
Having graduated MA in 1532, Mercator took himself off to Antwerp for two years, rather than progressing on to one of the higher faculties to study, theology, law, or medicine. During these two years, he took up contact with Franciscus Monachus, (c. 1490 – 1565), a Minorite friar at the monastery in Mechelen, who had earlier taught geography at the University of Leuven. Strathern introduces Monachus thus:
As we have seen, in 1494 Pope Alexander VI had brokered the Treaty of Tordesillas, which aimed to avert a dangerous clash between the two Catholic countries most involved in exploration – namely, Portugal and Spain. The pope had drawn a line north–south through the middle of the Atlantic Ocean: all land discovered to the west of this line (i.e. the New World) would belong to Spain, while all land discovered to the east of it (Africa and Asia) would belong to Portugal. Illustrating this ruling, as well as making allowances for consequent discoveries, Monachus drew two circular maps. One depicted the western hemisphere of the Americas, and the other outlined the eastern hemisphere: Africa, India and the lands to the east, which he named Alta India (in effect ‘Beyond India’). In the light of Magellan’s circumnavigation, the next obvious step was to create a model of the world in the form of a globe.
His globe, which did not survive, came first, and was constructed with the engraver Gaspard van der Heyden(c. 1496 – c. 1549). The two hemispherical maps are in an open letter describing the globe to his patron, Jean II Carondelet (1469–1545), Archbishop of Palermo, entitled De Orbis Situ ac descriptione ad Reverendiss. D. archiepiscopum Panormitanum, Francisci, Monachi ordinis Franciscani, epistola sane qua luculenta. (A very exquisite letter from Francis, a monk of the Franciscan order, to the most reverend Archbishop of Palermo, touching the site and description of the globe) in 1524.
Strathern now launches into a brief history of terrestrial globe-making, of which I will only give extracts that mostly need correcting:
Monachus was not the first to do this. Indeed, in line with the rebirth of classical knowledge, it was known that the Ancient Greek philosopher Crates of Mallus (now south-east Turkey) had produced a globe as early as the second century BC.
Nothing to criticise here but Strathern then goes into a discussion in which he states:
This illustrated Crates’s belief that the world consisted of five distinct climactic zones.
The climate zones or climata are, of course, standard Greek cosmography and predate Crates. First hypothesised by Parmenides and then modified by Aristotle. We move on:
A rather more accurate representation appeared during the Arab Golden Age, when in 1267 the Persian astronomer Jamal al-Din travelled to Beijing and created a terrestrial globe for Kublai Khan.
Jamal al-Din didn’t create a terrestrial globe for Kublai Khan in Beijing. When he travelled to Beijing, to become head of the Islamic Astronomical Bureau he took seven astronomical instruments of Islamic type with him, namely an armillary sphere, a parallactic ruler, an instrument for determining the time of the equinoxes, a mural quadrant, a celestial and a terrestrial globe, and an astrolabe with him.
Just prior to the geographical revolution which had taken place during Mercator’s childhood, the German navigator, merchant and map-maker Martin Behaim constructed the Erdapfel (earth apple), the earliest-known surviving globe, which followed the prevailing ideas held by Columbus, omitting any large land mass between western Europe and China.
Martin Behaim was not a navigator.
This appeared in 1492, and over the coming years it inspired a number of more accurate globes. One, constructed out of two glued-together lower halves of an ostrich egg, was among the first to include the New World. Another, cast in copper, imitated medieval maps which illustrated undiscovered regions with dragons, monsters or mythical beasts. It also labelled the unknown region to the south of China Hic sunt dracones (Here be dragons), which would become a popular appellation covering unknown regions in later maps.
Both the provenance of the Ostrich Egg Globe and its supposed date (1604) are, to say the least, disputed and I would not include it in any serious account of the history of globes.
The copper globe, that it is very similar to, is the Lenox Globe (1610) and its undiscovered regions are not illustrated with dragons, monsters, or mythical beasts. It is in fact only one of two maps known to bear the legend HC SVNT DRACONES (Latin: hic sunt dracones means here are dragons), the other is the Ostrich Egg Globe.
The handful of globes that Strathern has mentioned in his brief survey are all so-called manuscript globes i.e., they are handmade unique examples. Strathern makes no mention whatsoever of the most important development in globe history, a very significant one for Mercator, the advent of the printed globe. The earliest known printed globe, of which only sets of gores exist, was the small globe printed of the Waldseemüller world map that gave America its name.
This globe was relatively insignificant is the history of the globe, the major breakthrough came with the work of the Nürnberger mathematicus, Johannes Schöner (1477–1547). Schöner went into serial production of a terrestrial globe in 1515 and a matching celestial globe in 1517.
In the 1530s he produced a new updated pair of globes. We will return to Schöner and the influence of his globes on Mercator.
But first back to Strathern:
However, the most significant feature of these globes for Mercator was that, unlike with previous medieval maps, their geographical features were drawn or painted upon solid round surfaces. A map on a globe represented the actual size and shape of its geographical features, whereas a continuous map on a flat rectangular chart was bound to distort shapes, stretching them the further they were from the Equator [my emphasis]. The understanding of this fundamental distinction would be the making of Mercator.
That all flat maps distort was well-known to Ptolemy, who in his Geographia explicitly states that a globe is the best representation of the world. To transfer the map from the globe to a flat map one needs a projection, Ptolemy describes three different ones, and each projection, of which there are numerous, distorts differently. Strathern seems to imply here that there is only one map projection and the distortion that he describes here is that of the Mercator projection!
But first of all he [Mercator] would have to understand the complexities of maps and globes.
These he learned from a curious character by the name of Gemma Frisius…
Although only four years older than Mercator, at this stage he may well have taught Mercator mathematics.
Why is Gemma Frisius (1508–1555) a curious character? Strathern gives no explanation for this statement. There is also no ‘may well’ about it, when Mercator returned to Leuven in 1534 after his two-year time-out, he spent two years studying geography, mathematics, and astronomy under Gemma Frisius’ guidance. He also in this period learnt the basics of instrument and globe making from Frisius. Strathern now delivers up a very garbled and historically highly inaccurate account of how Frisius and Mercator became globe makers.
Around 1530, when Frisius was in his early twenties, a local goldsmith called Gaspar van der Heyden produced ‘an ingenious all-in-one terrestrial/celestial globe’. This incorporated a geographical map of the world, on which were also inscribed the main stars of the heavens. Such was the complexity of this muddled enterprise that it required a three-part booklet to explain how to understand it. The task of writing this was assigned to Frisius, and its title gives an indication of the difficulties involved: On the Principles of Astronomy and Cosmography, with Instruction for the Use of Globes and Information on the World and on Islands and Other Places Recently Discovered.
What actually happened is somewhat more complex. Schöner had become a highly successful globe maker and his globes were being sold over all in Europe. However, there was a greater demand than he could supply.
Jean II Carondelet, the Archbishop of Palermo, who as we saw above was Franciscus Monachus’ patron and dedicatee of his De Orbis Situ, commissioned the Antwerp printer/publisher Roeland Bollaert, who had printed the De Orbis Situ, to reprint Schöner’s Appendices in opusculum Globi Astriferi, in 1527, and the engraver Gaspard van der Heyden was commissioned to engrave the celestial globe to accompany it. In 1529, Gemma Frisius edited an improved second edition of Peter Apian’s Cosmographia, which was printed and published by Roeland Bollaert. Gemma Frisius, who had earlier studied under Monarchus, began to work together with Gaspar van der Heyden, and it was Gemma Frisius who created the ‘ingenious all-in-one terrestrial/celestial globe’, which van der Heyden engraved. Gemma wrote the accompanying booklet Gemma Phrysiusde Principiis Astronomiae & Cosmographiae deque usu globi ab eodem editi (1530), which was published by the Antwerp publisher Johannes Graheus. It is probably that Roeland Bollaert had died in the meantime. In this book Gemma Frisius acknowledges his debt to Johannes Schöner. Monarchus had also acknowledged his debt to both Schöner and Peter Apian in his De Orbis Situ. Gemma Frisius and van der Heyden later produced a new pair of globes, 1536, terrestrial and 1537, celestial, and this time Mercator was employed to add the cartouches in italic script to the globes, his introduction to globe making.
Strathern now tells us about Gemma Frisius’ book and its influence on Mercator:
Within this cornucopia of often extraneous knowledge were to be found the sound principles which Frisius would later pass on to Mercator. Most importantly, these involved such vital cartographic elements as the principles of longitude and latitude, which form a network covering the surface of the globe. The lines of longitude are drawn down the surface of the globe at regular intervals from the North Pole to the South Pole.* As long as a ‘meridian’ or middle point (line zero) is established, it is possible to record how far one’s position lies east or west of this line from pole to pole. By this time, navigators were beginning to carry shipboard clocks. As a rough-and-ready method for discovering how far east (or west) they had travelled from their home port, they could measure the time discrepancy between noon on the shipboard clock (i.e. noon at their home port) and noon at their current location (the sun’s zenith).
* Both of these were of course theoretical concepts at the time, conjectured from the fact that a globe must have a top (northernmost point) and a bottom (southernmost point.) It would be some five centuries before the existence of the actual poles was confirmed by discovery.
The lines of latitude are drawn around the globe, beginning at its widest girth (the Equator), and then ascending in regular diminishing circles towards the North Pole, and also descending at regular intervals to the South Pole. In order to establish their longitude, navigators had learned to measure the precise location above the horizon of stars in the sky. This also could be compared to their location when at the home port. Such measurements were taken with an astrolabe (literally ‘star taker’), the forerunner of the sextant.
Reading these atrocious paragraphs, I asked myself why do I bother? Why don’t I just throw the whole thing in the next trash can and walk quietly away? However, being a glutton for punishment, I persevere. But where to begin? I will start with the origins of the longitude and latitude system, at the same time dealing with the mind bogglingly stupid starred footnote.
Most people don’t realise but the longitude and latitude system of cartographical location was first developed in astronomy to map the skies. In the northern hemisphere, if you look up into the night sky, the heavens appear to form a sphere around the Earth and there are stars that every night circle the same point in the heavens, that point is the astronomical north pole. In fact, as we now know it’s the Earth that turns not those circumpolar stars, but for our mapping purpose that is irrelevant. The astronomical or celestial north pole is of course directly above the terrestrial north pole, on a straight line perpendicular to the plane of the equator. You can observe the same phenomenon in the southern hemisphere, defining the south celestial and terrestrial poles, but as the European astronomers could not see the heavens further south than the Tropic of Capricorn, that doesn’t need to concern us at the moment. Note the north and south poles are not theoretical concepts but real points on both the celestial and terrestrial spheres. The lines of longitude are the theoretical great circles around the celestial sphere passing through the north and south poles. The annual path of the Sun defines the Equator and the Tropics of Cancer and Capricorn, the principal lines of latitude. The Poles, the Equator, and the two Tropics are the principal features on the armillary sphere, the earliest three-dimensional model of the celestial sphere created by astronomers, sometime around the third century BCE.
At some point somebody had the clever idea of shrinking this handy mapping network down from the celestial sphere on to the terrestrial sphere, the Earth. The first cartographer to use longitude and latitude for terrestrial maps was probably Eratosthenes (C. 276–c. 195 BCE). His prime meridian (line of longitude) passed throughAlexandria and Rhodes, while his parallels (lines of latitude) were not regularly spaced, but passed through known locations, often at the expense of being straight lines. (Duane W. Roller, Eratosthenes Geography, Princeton University Press, 2010 pp. 25–26). Hipparchus (c. 190–c. 120 BCE) was already using the same system that we use today. Ptolemy, of course, used the longitude and latitude system in his Geographia, in fact a large part of the book consists of tables of longitude and latitude from hundreds of places from which it is possible to reconstruct maps. If as Strathern claims, Mercator studied the Geographia at school then he didn’t need Gemma Frisius to explain longitude and latitude to him.
Strathern’s “By this time, navigators were beginning to carry shipboard clocks. As a rough-and-ready method for discovering how far east (or west) they had travelled from their home port, they could measure the time discrepancy between noon on the shipboard clock (i.e. noon at their home port) and noon at their current location (the sun’s zenith) can only be described as a historical cluster fuck! Dave Sobel’s Longitude (Walker & Company, 1995), for all its errors, and it has many, which tells the story of how John Harrison (1693–1776) produced the first marine chronometer, that is a clock accurate and reliable enough under testing condition to enable the determination of longitude, his H4 in 1761, was almost certainly the biggest popular history of science best-seller ever! Apparently, Strathern has never heard of it!
The whole is much, much worse when you know that the first person to hypothesise the determination of longitude using an accurate mechanical clock was Gemma Frisius and he did so in Chapter nine of his On the Principles of Astronomy and Cosmography, the only one of his publications that Strathern mentions:
… it is with the help of these clocks and the following methods that longitude is found. … observe exactly the time at the place from which we are making our journey. … When we have completed a journey … wait until the hand of our clock exactly touches the point of an hour and, at the same moment by means of an astrolabe… find out the time of the place we now find ourselves. … In this way I would be able to find the longitude of places, even if I was dragged off unawares across a thousand miles.
Gemma Frisius was, however, of the difficulties that the construction of such a clock would involve:
… it must be a very finely made clock which does not vary with change of air.
More than a hundred years later the French astronomer Jean-Baptiste Morin (1583–1656), who propagated the lunars method of determining longitude wrote:
I do not know if the Devil will succeed in making a longitude timekeeper but it is folly for man to try
Strathern is not much better on latitude, The lines of latitude are drawn around the globe, beginning at its widest girth (the Equator), and then ascending in regular diminishing circles towards the North Pole, and also descending at regular intervals to the South Pole. In order to establish their longitude [sic, I assume that should read latitude!] navigators had learned to measure the precise location above the horizon of stars in the sky. This also could be compared to their location when at the home port. Such measurements were taken with an astrolabe (literally ‘star taker’), the forerunner of the sextant. Latitude is determined by measuring either the height of the Sun, during the day, or the Pole Star, at night. That’s why in marine slang the daytime measurement is called “shooting” the sun. As David King is fond of repeating, the astrolabe was never used for navigation. It is possible that fifteenth century navigators used a mariner’s astrolabe, but more likely that they used a quadrant or a Jacob’s staff. Frisius’ lifetime is too early for the backstaff, which was first described by John Davis (c.1550–1605) in his The Seaman’s Secrets in 1594. It is the backstaff that was the forerunner of the sextant not the astrolabe.
The errors continue:
In order to prepare the maps for incorporation on the globe, they first had to be copied to a uniform scale so that they could be aligned with other maps. All this required a sophisticated understanding of the maps involved, and required the use of geometry, trigonometry and especially triangulation.
This last method enabled the map-makers to calculate the precise location of a distant geographical feature – such as a mountain, town or river mouth – using the known location of two other features. The modern version of this method was invented by Frisius in 1533, and worked as follows. First a line of known length was drawn between two features (Brussels and Antwerp in Frisius’s early experiment). Then the surveyor would draw a line from each end of the known line directly towards the unlocated feature (Middelberg, in Frisius’s case) and measure the angles between these lines and the ends of the known line. This gave him a triangle with a base of known length, and two base angles. From these it was a simple matter of geometry to ‘triangulate’ the distances to and position of the unlocated feature.
Gemma Frisius was indeed the first to describe triangulation in the third edition of Apian’s Cosmographia in 1533 but Strathern’s account of how it works is arse backwards. Triangulation is a trigonometrical method of surveying, which is then used to draw maps. First you have to accurately measure your baseline on the ground, in Gemma Frisius’ example between Brussels and Antwerp. Then from the two endpoints the angles of observation of a third point, Middelburg in Gemma’s example, are measured enabling the completion of the triangle on the drawing board and thus the determination of the distances between the endpoints of the baseline and the third point using trigonometry. Gemma Frisius’ example is purely theoretical as you can’t actually see Middelburg from either Brussels or Antwerp.
Strathern devotes some time to Mercator’s biography, his setting up as an independent cartographer and instrument maker and his marriage, then delivers the next piece of history of cartography ignorance:
A year later, in 1538, he produced his first etched map of the world, Orbis Imago. This map is highly ingenious in its representation of the globe on a flat surface. The map is in two parts, which join at a tangent. The first part views the world from above the North Pole, the second from above the South Pole. But instead of showing two semicircles, each view is a rounded heart-shape with an indentation curving in towards the pole. This tearing-apart of the semicircle enabled Mercator to represent the land masses without the distorted exaggeration which would have occurred if the maps had stretched to contain two semicircles. A cut-out of these two-dimensional shapes can be twisted and folded into a semblance of a three-dimensional globe, and there is no doubt that Mercator had something similar in mind. When presented in this form, a flat map of the world did not distort the land masses; however, it also did not provide an accurate picture of the distances between various geographical features so was of little use to mariners.
Mercator’s Orbis Imago is a double cordiform (heart shaped) polar projection and Strathern seems to think that Mercator invented it, he didn’t. The cordiform projection is also known as the Stab-Werner projection named after Johannes Stabius (1540–1522), who invented it and Johannes Werner (1468–1522), who first published/publicised it, in his partial translation of Ptolemy’s Geographia (1514). The two mathematici were friends, who knew each other from their mutual time at the University of Ingolstadt. Both Peter Apian in 1530 and the French mathematicus Oronce Fine (1494–1555) in 1531 produced single cordiform projection world maps, of which Mercator was almost certainly aware as the sixteenth century, European, cartography scene was strongly networked.
More importantly in 1532 Oronce Fine also produced a double cordiform polar projection world map and Mercator’s Orbis Imago is fairly obviously merely an improved version of Fine’s map.
The Stab-Werner projection is Equal-area i.e., area measure is conserved everywhere and Equidistant i.e., all distances from one (or two) points are correct. It was never intended for use by mariners.
Apart from its geometric ingenuity, Mercator’s Orbis Imago has two other features of note. The view over the South Pole includes a large-scale representation of Antarctica, which he named Terra Australis Incognita (Unknown Southern Land). According to historical records, neither Australia nor Antarctica had yet been discovered by Europeans; however, the existence of such a land mass had long been a theoretical supposition – considered a necessary counterbalance to the land masses of the northern hemisphere.
The Terra Australis Incognita first appeared in the sixteenth century on the globes of Johannes Schöner and it has been shown that Oronce Fine took the details for his maps from Schöner’s work and that Mercator took his from Fine.
Mercator’s map also included the word ‘America’ as a name for the large land mass to the west of Europe.
The German map-maker Martin Waldseemüller had been the first to use the name ‘America’ on a map, in 1507. This labelled a large island, straddling the Equator, which he had named after Amerigo Vespucci, the Florentine explorer whose voyages had provided extensive mapping of the south-east coast of this territory which Vespucci first named the New World.
However, in later maps new evidence had led Waldseemüller to take a more tentative view of Vespucci’s claims, and he replaced ‘America’ with the inscription ‘Terra Incognita’, suggesting that the Terra de Cuba discovered by Columbus was in fact an eastern part of Asia. Mercator’s labelling of America, as well as his clear outlining of the northern and southern parts of this landmass, confirmed once and for all this name.
There now follows a long biographical section that I won’t comment on; I’m only here for the history of cartography. We now arrive at the ominous 1569 world map, and what is probably the worst account of the Mercator projection that I have ever read.
From now on Mercator buried himself in his work. His ambition was no less than to produce a complete map of the world which could be used by navigators.
Throughout history, large-scale maps had usually been centred upon a known location. For instance, Ptolemy’s map was centred on the Mediterranean. Later maps, such as the large round medieval Mappa Mundi,* had Jerusalem as their centre, with the known world radiating outwards from this central holy point. Mercator decided that his map would have no centre. Instead it would be projected onto a grid of longitude and latitude lines – which would become known as Mercator’s projection. On a globe these lines are curved, but on Mercator’s flat surface they were rectilinear straight lines. This inevitably stretched the scale of the map the further it moved from the Equator. For instance, on Mercator’s map the Scandinavian peninsula appeared to be three times the size of the Indian subcontinent, whereas in fact India is one and a half times larger than Scandinavia. But this would in no way hamper navigation, which relied upon location established by lines of latitude and longitude. A ship could sail across an ocean following a constant compass bearing. This may have appeared curved on Mercator’s flat map, but owing to the bulge of the globe it did in fact represent the most direct route.
Ptolemy’s world map in not centred on the Mediterranean; the Mediterranean lies in the top half of the map on the lefthand side.
The starred footnote to “the large round medieval Mappa Mundi,” “*This remains on public display at Hereford Cathedral in England,” seems very strongly to imply that Strathern thinks there was only ever one large round medieval Mappa Mundi, which is of course total rubbish.
Mercator’s infamous 1596 map is centred on the Atlantic Ocean setting a standard for European world maps that would lead to the cartographers being accused of politically portraying the world from a Eurocentric standpoint.
Projecting a map on to a grid of longitude and latitude lines is not the Mercator projection. The printed Ptolemaic world maps of the late fifteenth century are projected on to a grid of longitude and latitude lines (see above), as are the world maps of John Ruysch (1507), Martin Waldseemüller (1507), Francesco Rosseli (1508), Dürer-Stabius (1515), Peter Apian (1530) and Oronce Fine (1536) all on various map projections.
On a globe these lines are curved, but on Mercator’s flat surface they were rectilinear straight lines. This inevitably stretched the scale of the map the further it moved from the Equator.
This is rubbish! In order to have a map on which a loxodrome or rhomb line is a straight-line Mercator systematically widened the distance between the lines of latitude towards the north and south poles, according to a set mathematical formular, which he didn’t reveal. Strathern makes no mention of Pedro Nunes (1520–1578), who first determined the rhumb line as the course of constant bearing on a globe was a spiral, the basis of Mercator’s work. Mercator had drawn rhumb line spirals on his globe from 1541.
A ship could sail across an ocean following a constant compass bearing. This may have appeared curved on Mercator’s flat map, but owing to the bulge of the globe it did in fact represent the most direct route.
Once again Strathern is spouting rubbish. As already stated above on the Mercator projection a course of constant compass bearing, the rhumb line, is a straight-line, the whole point of the projection, and it does not represent the most direct route. The most direct route is the arc of the great circle of the globe that passes through the point of departure and the destination. However, to sail such a course means having to constantly change the compass bearing, so although longer the course of constant compass bearing is easier to navigate.
Yet what happened when a ship travelled beyond the edge of the map? If a ship set sail from China, heading east across the Pacific Ocean, it would soon reach the limit. But if the navigator rolled the map into a cylinder, with the eastern edge of the map attached to the western edge, the solution to this problem was obvious. The navigator could simply continue from the eastern border of the map across the Pacific to the west coast of America. In this he would also be aided by corresponding map references on lines of longitude and latitude.
This is simply cringe worthy. If someone was sailing from China across the Pacific to the west coast of America, they would use a chart of the Pacific for the voyage.
From now on navigators would adopt Mercator’s projection, both for continental and for local charts. The entire world had become ‘orientated’. Originally this word meant ‘aligned to the east’; on Mercator’s projection the world was aligned north, south, east and west, by means of longitude and latitude. And any point on this flattened globe could be pinpointed, as if on a graph, by reading off its precise position in numbers along the lines of longitude and latitude. Dangerous shoals, rocks, river mouths, cities and towns, mountains, borders and even entire countries could be mapped and ‘orientated’. Mercator completed his task in 1569, and to this day Mercator’s projection is how we envisage the world when it is mapped onto a flat surface.
Nobody adopted the Mercator projection in 1569 because Mercator did not explain how to construct it. It first came into use at the end of the century when Edward Wright (1581–1626) revealed the mathematics of the Mercator projection in his Certaine Errors in Navigation (1599).Even then the take up of the Mercator projection for marine charts was a slow process only really becoming general in the early eighteenth century. Strathern still seems to be under the illusion that the cartographical longitude and latitude grid somehow originated with Mercator, whereas by the time Mercator created his 1569 world map it had been in use for about eighteen centuries. The Mercator projection is only one of numerous ways thatwe envisage the world when it is mapped onto a flat surface and there is in fact a major debate which projection should be used. The use of alongitude and latitude grid does not necessarily imply that a map has to have north at the top.
But Mercator’s task was not complete. For the next twenty-six years he painstakingly created more than a hundred maps, all scaled according to his projection. During the final years of his life he started binding these together with the intention of making them into a book. For the front cover he planned to have an engraving of the Ancient Greek Titan named Atlas, kneeling, with the world balanced on his shoulders. Hence the name which would come to be attached to such compilations of maps.
Mercator did not start binding his maps together with the intention of making them into a book during the final years of his life. His Atlas was part of a major complex publishing project, beginning in 1564, when he began compiling his Chronologia, which was first published in 1569:
The first element was the Chronologia, a list of all significant events since the beginning of the world compiled from his literal reading of the Bible and no less than 123 other authors of genealogies and histories of every empire that had ever existed. (Wikipedia)
The Chronologia developed into an even wider project, the Cosmographia, a description of the whole Universe. Mercator’s outline was (1) the creation of the world; (2) the description of the heavens (astronomy and astrology); (3) the description of the earth comprising modern geography, the geography of Ptolemy and the geography of the ancients; (4) genealogy and history of the states; and (5) chronology. Of these the chronology had already been accomplished, the account of the creation and the modern maps would appear in the atlas of 1595, his edition of Ptolemy appeared in 1578 but the ancient geography and the description of the heavens never appeared. (Wikipedia)
The maps, that would eventually appear posthumously in his Atlas, were not drawn using the Mercator projection, which is totally unsuitable for normal regional maps. The Atlas was not named after the Titan, who carried the world on his shoulders, but after a mythical king of Mauretania credited with creating the first globe, who Mercator described in the preface to his 1589 map collection, “Italiae, Sclavoniae, Grecia”, thus “I have set this man Atlas, so notable for his erudition, humaneness, and wisdom as a model for my imitation.” The name Atlas was first used on the 1595 posthumous map collection Atlas Sive Cosmographicae Meditationes de Fabrica Mundi et Fabricati Figura, published by his son Rumold Mercator (1541–199). King Atlas was first replaced on the cover by the Titan Atlas in later edition in the seventeenth century.
Having royally screwed up the life and work of Mercator, Strathern now turns to the French jurist and mathematician François Viète (1540–1603).
Having started Viète’s biography Strathern delivers this gem:
In 1564, Viète’s mathematical skills led to him entering the service of the Parthenay family, so that he could act as tutor to the twelve-year-old mathematical prodigy Catherine de Parthenay. Together they wrote a number of treatises on astronomy and trigonometry. In these, Viète used decimal notation several decades before this was introduced to the northern Renaissance by the Dutch mathematician Simon Stevin.
Decimal notation had been in use for a couple of centuries before Viète came along, what he tried to introduce without success was the use of decimal fractions.
After lots more biographical detail covering Viète’s political involvements, we get the following.
Viète had become involved in a dispute over the new calendar with the Jesuit monk Christopher Clavius, who had been charged with overseeing its compilation. Such was the subtlety of Viète’s mathematical argument that it was not until more than twenty years later (after his death) that a flaw was discovered in Viète’s calculations.
The Jesuits are an apostolic and not a monastic order, so Christoph Clavius is not a monk. Clavius was not charged with compiling the Gregorian Calendar, but with explicating and defending it after it had been introduced. Viète attacked both the new calendar and Clavius in a series of pamphlets in 1600, in particular the calculation of the lunar cycle. He gave a new timetable, which Clavius refuted, after Viète’s death, in his Explicatio in 1603. I don’t know but in my world from 1600 to 1603 is not twenty years.
What is more surprising is that, during the course of his hectic royal employment, he managed to produce a body of transformative mathematics. In this, Viète attempted to give algebra a foundation as rigid as that of the geometry of Euclid, whose theorems were built upon a number of self-evident axioms.
Viète did try to give algebra a new foundation but the analogy with Euclid’s Elements is badly chosen. The Elements, with its axiomatic approach, is the epitome of the synthetic proof methodology in mathematics. What Viète started was on the way to setting up algebra as the epitome of the analytical proof methodology; in fact, it was Viète, who replaced the term algebra with the term analysis.
At the same time he advocated the viewing of geometry in a more algebraic fashion. Instead of the necessarily inexact measurement with a ruler of lines, curves and figures drawn on paper, these were to be reduced to algebraic formulas, thus enabling them to be calculated in algebraic fashion, giving precise numerical answers.
This is a misrepresentation of what Viète actually did. He revived the geometric algebra that can be found in Euclid’s Elements. Here problems and theorems that we would present algebraically are handled as geometrical constructions. This is the reason why in our terminology x2 is referred to as x squared and an equation with x2 is a quadratic equation. For Euclid x is literally the side of a square or quadrate and x2 is its area. Similarly, x3 is the volume of a cube of side length x, hence the terms x cubed and cubic equation. Viète took this route because he wanted to demonstrate that the variables in an algebraic expression could represent geometrical objects, such as a line segment, and not just numbers. He didn’t develop these thoughts very far.
As we have seen, in the previous century Regiomontanus had attempted a similar standardization of algebra – but this had not become widely accepted.
Now Viète would attempt his own fundamental transformation of algebra. This branch of mathematics still largely consisted of a number of algorithms: rules of thumb to be followed in order to find the answer to a calculation. These had been set down in prose form – as indeed had all algebraic formulas. For instance: ‘In order to obtain the cubic power, multiply the unknown by its quadratic power.’ In modern notation, this can be simply put:
y x y2 = y3
Unfortunately Viète was hampered by the lack of an agreed symbol for ‘equals’ (=), as well as agreed symbols for ‘multiplication’ (x) and ‘division’ (÷) – which had also hampered acceptance of Regiomontanus’s notation. However, although Viète’s attempt to rationalize algebraic notation failed to gain widespread acceptance, it made many realize that such reform was long overdue.
The transformation of algebra from rhetorical algebra, in which everything is expressed purely in words, to symbolic algebra, in which symbols are used to express almost everything, had been taking place step for step for a couple of centuries, in the form of syncopated algebra which uses a mixture of words, abbreviations, and symbols in its expressions, before Viète made his contribution As is mostly the case in the evolution of science this was not a smooth linear progress but often a case of two steps forward and one step back. With his In artem analyticem isagoge (Introduction to the art of analysis) in 1591, Viète made a significant and important contribution to that progress. His major contribution was the introduction of letters, vowels, such as A, for variables and consonants, such as Z, for parameters in algebraic expressions. Strathern is correct is saying that Viète lacked symbols for some operators. Interestingly our equals sign, =, had been in use in Northern Italy for some time and had famously been introduced into Northern Europe by Robert Recorde (c. 1512–1558) in his Whetstone of Witte in 1557.
Viète actually managed a ‘one step back’ in his Isagoge. In an earlier step in syncopated algebra quadrate had been abbreviated to q and cube to c, so A2 was written Aq and A3 as Ac. A later development was to drop the abbreviation and write A2 as AA and A3 as AAA, an important step towards our use of superscripts to indicate the multiplicity of a variable. Viète reverted to using the abbreviations q and c. His Isagoge found quite a high level of acceptance; Regiomontanus’ notation, however, found no acceptance because it never existed!
More ambitiously, Viète pressed ahead with his attempt to unite algebra and geometry, though here too any general answer eluded him. But Viète’s efforts were not to be in vain. The very fact that he had attempted such innovations would reinforce the movement of maths in the direction of its modern incarnation, where solutions to both these problems would be found.
It would be the following century when Descartes managed to solve such problems, with the introduction of Cartesian coordinates: two lines at right angles, one representing the x-axis and the other the y-axis. Here the answers to an algebraic formula could be transformed into a line on a graph; likewise geometric lines could be seen as algebraic formulas.
Here we are talking about the creation of analytical geometry, which was developed independently, but contemporaneously, by both Pierre Fermat (1607–1665) and René Descartes (1596–1650). Fermat, who was according to his own account influenced by Viète, circulated his Methodus ad disquirendam maximam et minimam et de tangentibus linearum curvarum, based on work from 1629, in manuscript from 1636, although it was first published, posthumously in 1679. It was less influential in analytical geometry, Descartes having garnered the laurels, but had an important influence on the development of calculus, as acknowledged by Newton.
Descartes, for whom no influence by Viète has been determined, famously published his La Géométrie, as an appendix to his Discours de la méthode in 1637.
The real impact of the work coming with the publication of the second, expanded, Latin edition by Frans van Schooten Jr (1615–1660) in 1649. You can search La Géométrie, as much as you want but you won’t find any trace of an orthogonal, Cartesian coordinate system, as used today. This was first introduced by Frans van Schooten in the Latin edition.
The resemblance between these coordinates and the lines of latitude and longitude which Mercator drew on his maps is indicative. It was in this way that Mercator, and to a certain extent Viète, enabled the northern Renaissance to lay the foundations for our present world view. It was they who sought to devise a coordinated representation of our modern physical world in geography, and pointed the way to our modern theoretical world of multidimensional mathematics.
Well at least Strathern recognises that a longitude and latitude grid as used by Mercator is an orthogonal, coordinate system but as is fairly clear from this final paragraph he definitely suffers from the illusion that Mercator invented the orthogonal longitude and latitude grid, which is simply historical hogwash.
If someone was intending to write an essay about Gerard Mercator, one might think that they would first acquaint themselves with an extensive knowledge of cartography and its history, in which Mercator played a highly significant role. Paul Strathern apparently didn’t feel this was necessary and obviously didn’t bother, the result is a steaming heap of bovine manure masquerading as history.
Today I’m continuing my occasional series on the English mathematical practitioners of the Early Modern Period. In the post in this series about Edmund Gunter (1581–1626) I quoted the historian of navigation David Waters as follows:
Gunter’s De Sectore & Radio must rank with Eden’s translation of Cortes’s Arte de Navegar and Wright’s Certain Errors as one of the three most important English books ever published for the improvement of navigation.
As is fairly obvious from the David Waters quote, Edward Wright is one of the most important figures in the history of, not just English but European, navigation during the Early Modern Period. However, as is, unfortunately, all to often the case with mathematical practitioners from this period, we have very little biographical detail about his life and can only fill the gaps with speculation.
The younger son of Henry and Margaret Wright, he was baptised in the village of Garveston in Norfolk on 8 October 1561. His father, a man of “mediocrisfortunae” (modest means), was already deceased, when his elder brother Thomas entered Gonville and Caius College, Cambridge as a pensioner in 1574. Edward was probably educated by John Hayward at Hardingham school, like his elder brother, and also entered Gonville and Caius College, as a sizar, a student who earns part of his fees by working as a servant for other students, in December 1576. Unfortunately, Thomas died early in 1579. Edward graduated BA in the academic year 1580-81 and MA in 1584. He became a fellow of Gonville and Caius in 1587 and resigned his fellowship in 1596, having married Ursula Warren (died 1625) 8 August 1595. Oxbridge fellows were not permitted to marry. They had a son Thomas Wright (1596–1616), who was admitted sizar at Gonville and Caius in 1612.
Wright’s career in Cambridge parallels that of another significant mathematical practitioner born in the same year, Henry Briggs (1561–1630). Briggs went up to St John’s College in 1577, graduated BA in 1581 or 1582 and MA in 1585. He was awarded a fellowship in 1588. The two became friends and interacted over the years up till Wright’s death.
Another acquaintance of Wright’s, who he possibly got to know at Cambridge, was the aristocrat Robert Devereux (1565–1601), who graduated MA at Trinity College Cambridge in 1581, and who had succeeded to the title of Earl of Essex in in 1576 at the death of his father. Devereux, a soldier, was incredibly well connected in Elizabethan society becoming a favourite at Elizabeth’s Court and so would initially have been a good contact for the commoner Wright. However, he was still a close friend of Wright’s when he rebelled against Elizabeth at the end of the century, which could have proved dangerous for the mathematical practitioner, but apparently didn’t.
Another soldier and a good friend of Devereux’s, who also became a friend of Wright’s at Cambridge, was the astronomer and astrologer, Sir Christopher Heydon (1561–1623), who graduated BA in 1589 at Peterhouse Cambridge.
What we don’t know is who taught Edward Wright mathematics at Cambridge and how, why, and when he became deeply interested in navigation and cartography, which he very obviously did, whilst still at the university. The interest in sea voyages and all things navigational associated with them was very strong in England in the latter part of the sixteenth century, with England beginning to flex its deep-sea muscles and challenge the Spanish Portuguese duopoly on marine exploration and discovery, particularly following the defeat of the Spanish Armada in 1588. This could well have been Wright’s motivation as a mathematical practitioner to follow the lead of other practitioners such as John Dee (1527–1608/9) and Thomas Harriot (c. 1560–1621) and specialise in navigation.
That Wright had taken up the study of navigation and already acquired a substantial reputation is indicated by the Royal Mandate, issued by Elizabeth in 1589, instructing Gonville and Caius College to grant Wright leave of absence to carry out navigational studies on a raiding expedition to the Azores under the command of Sir George Clifford, 3rd Earl of Cumberland (1588–1605).
Cumberland was sailing as what is known as a privateer, which means piracy licensed by the Crown in exchange for a share of the profits. Sailing to the Azores, on the way Cumberland seized French Catholic league and Flemish vessels. In the Azores he attacked both the islands and various Portuguese and Spanish vessels making rich killings. Up till now, the expedition was a success, but the return journey was pretty much a disaster. Hit by storms many of the crew died of hunger and thirst on the return journey and the English ship the Margaret was shipwrecked off the coast of Cornwall. All the while Wright was carrying out his navigational studies. On the voyage he was accompanied by Richard Hues (1553–1632) a cartographical and navigational pupil of Thomas Harriot and one of the Wizard Earl’s mathematici. He also became acquainted with the navigator and explorer John Davis (c. 1550–1605).
Wright recorded his experiences of the Azores’ voyage in his most important publication: 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.), London: Printed … by Valentine Sims.
Another version of the work published in the same year was entitled: Wright, Edward (1599), Errors in nauigation 1 Error of two, or three whole points of the compas, and more somtimes, by reason of making the sea-chart after the accustomed maner … 2 Error of one whole point, and more many times, by neglecting the variation of the compasse. 3 Error of a degree and more sometimes, in the vse of the crosse staffe … 4 Error of 11. or 12. minures in the declination of the sunne, as it is set foorth in the regiments most commonly vsed among mariners: and consequently error of halfe a degree in the place of the sunne. 5 Error of halfe a degree, yea an whole degree and more many times in the declinations of the principall fixed starres, set forth to be obserued by mariners at sea. Detected and corrected by often and diligent obseruation. Whereto is adioyned, the right H. the Earle of Cumberland his voyage to the Azores in the yeere 1589. wherin were taken 19. Spanish and Leaguers ships, together with the towne and platforme of Fayal, London: Printed … [by Valentine Simmes and W. White] for Ed. Agas.
Before we turn to the navigational errors that Wright illuminated in his book, it also contains another piece of interesting information. Wright states that he sailed with Cumberland under the name Edward Carelesse. When he introduces himself in the book, he also states that he sailed with Sir Francis Drake, as Captain of the Hope, on his West Indian voyage of 1585-86, which evacuated Sir Walter Raleigh’s Virginia colony and brought the survivors back to England. Wright would have had the opportunity to make the acquaintance of Thomas Harriot, who was one of the rescued colonists. Capt. Walter Bigges and Lt. Crofts’ book A Summarie and True Discourse of Sir Frances Drakes West Indian Voyage (1589) confirms that Edward Carelesse was commander of the Hope. This voyage would fit into the gap between Wright’s MA, 1585 and the start of his fellowship in 1587.
The principal navigational error that Wright’s book addresses, and the reason why it is so important, is the problem of sailing the shortest route between two places on a sea voyage. In the early phase of European deep-sea exploration, mariners adopted the process of latitude sailing. Mariners could not determine longitude but could determine latitude fairly easily. Knowing the latitude of their destination they would sail either north or south until they reached that latitude and then sail directly east or west until they reached their desired destination. This was by no means the most direct route but prevented getting lost in the middle of the ocean.
The actual shortest route is a great circle, that is a circumference of the globe passing through both the point of departure and the destinations. However, it is very difficult to sail a great circle using a compass as you have to keep adjusting your compass bearing. Although not as short, far more practical for mariners would be a course that is a constant compass bearing, such a course is known as a rhumb line, rhumb, or loxodrome:
In navigation, a rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path of constant bearing as measured relative to true north. (Wikipedia)
The first to analyse the mathematics of rhumb lines, which takes the form of a spiral on the surface of a sphere, was the Portuguese mathematical practitioner Pedro Nunes (1502–1578) in his Tratado em defensam da carta de marear (Treatise Defending the Sea Chart), (1537).
Nunes determined that a course of constant bearing would be a rhumb, but he did not solve the problem of how to construct a marine chart on which a rhumb line would be a straight-line enabling navigators to simply read off the required compass bearing from the chart. This problem was first solved by the Flemish globe maker and cartographer, Gerard Mercator (1512–1594), who was friends with Nunes, with the publication of his world map of 1569, which introduced for the first time what is now known as the Mercator projection on which a course of constant compass bearing is a straight line.
Mercator explained in simple terms how he had achieved this, “We have progressively increased the degrees of latitude towards each pole in proportion to the lengthenings of the parallels with reference to the equator” but gave no exact mathematical prescription how to produce such a chart.
Both John Dee (1527–1609?), who personally knew Pedro Nunes and studied cartography under Mercator’s teacher Gemma Frisius (1508–155) and Thomas Harriot (c. 1560–1621) solved the problem of how to mathematically construct the Mercator projection. However, although both of them taught cartography and navigation, Dee to the captains of the Muscovy Trading Company and Harriot to Walter Raleigh’s captains, neither of them made their solution public. Enter Edward Wright.
Wright took up the problem of the marine chart and rhumb lines where Pedro Nunes had stopped, openly acknowledging his debt to Nunes in the preface to his Certaine Errors in Navigation:
Yet it may be, I shall be blamed by some, as being to busie a fault-finder myself. For when they shall, see their Charts and other instruments controlled which so long time have gone for current, some of them perhappes will scarcely with pacience endure it. But they may be pacified, if not by reason of the good that ensueth hereupon, yet towards me at the least because the errors I poynt at in the chart, have beene heretofore poynted out by others, especially by Petrus Nonius, out of whom most part of the first Chapter of the Treatise following is almost worde for worde translated;
He goes on to solve the problem of constructing the Mercator projection:
By help of this planisphaere with the meridians, rumbes, and parallels thus described therein, the rumbs may much more easily & truly be drawn in the globe then by these mechanical wayes which Petrus Nonius [Pedro Nunes] teacheth cap. 26 lib. 2 de obser. Reg. et Instr. Geom..
The problem that Wright solved is that as one proceeds north or south from the equator the circles of latitude get progressively smaller but when one unwraps the globe on the surface of a cylinder in the Mercator projection all the lines of latitude need to be the same length so that they cross all lines of latitude at right angles.
Wright’s principle was very simple: to increase the distance apart of the parallels of latitude to match the exaggeration arising from the assumption that they were equally long. Since the lengths of the parallels varied according to a factor cos λ, the correction factor was sec λ at any point. In order to plot the parallels on the new charts, Wright had effectively to perform the integration’ sec λdλ. This was done numerically—in his own words, “by perpetual addition of the Secantes answerable to the latitudes of each point or parallel into the summe compounded of all the former secantes. . . .,” (P. J. Wallace, Dictionary of Scientific Biography)
To save others having to repeat the protracted and tedious numerical iterations that he had carried out, Wright published a table of the necessary correcting factors for the distance between the lines of latitude. In the first edition of the book this table was only six pages long and contained the correction factors for every 10 minutes of latitude. In the second edition of the book, Certaine Errors in Navigation, Detected and Corrected with Many Additions that were not in the Former Edition…, published in London in 1610, the table had grown to 23 pages with factors for every minute of latitude.
The emergence of both Wright’s book and his method of constructing the Mercator projection into the public sphere is rather complex. He obviously wrote the major part of the manuscript of the book when he returned to Cambridge in 1598 but there are sections of the book based on observation made in London between 1594 and 1597. Wright’s development of the Mercator projection was first published, with his consent, in Thomas Blundevile’s His Exercises containing six Treatises in 1594, the first publication in English on plane trigonometry, he wrote:
[the new (Mercator) arrangement, which had been constructed] “by what rule I knowe not, unless it be by such a table, as my friende M.Wright of Caius College in Cambridge at my request sent me (I thanke him) not long since for that purpopse which table with his consent. I have here plainlie set down together with the use of thereof as followeth”. The table of meridiional parts was given at degree intervals.
Although he wrote a letter of apology to Wright, Wright condemned him for it in the preface to Certaine Errors:
“But the way how this [Mercator projection] should be done, I learned neither of Mercator, nor of any man els. And in that point I wish I had beene as wise as he in keeping it more charily to myself”
Hondius was by no means the only one to publish Wright’s method before he himself did so. William Barlow (1544–1625) included in his The Navigator’s Supply (1597) a demonstration of Wright’s projection “obtained of a friend of mone of like professioin unto myself”.
In 1598–1600 Richard Hakluyt published his Principle Navigations which contains two world charts on the new projection, that of 1600 a revision of the first. Although not attributed to Wright it is clear that they are his work.
Earlier, the navigator Abraham Kendall had borrowed a draft of Wright’s manuscript and unknown to Wright made a copy of it. He took part in Drake’s expedition to the West Indies in 1595 and died at sea in 1596. The copy was found in his possessions and believing it to be his work it was brought to London to be published. Cumberland showed the manuscript to Wright, who, of course recognised it as his own work.
Wright first publicly staked his claim to his work when he finally published the first edition of Certaine Errors in 1599. A claim that he reinforced with the publication of the second, expanded edition in 1610. However, it should not be assumed that mariners all immediately began to use Mercator projection sea charts for navigating. The acceptance of the Mercator marine chart was a slow process taking several decades. As well the method of producing the Mercator projection, Certaine Errors also includes other useful information on the practice of navigation such as a correction of errors arising from the eccentricity of the eye when making observations using the cross-staff, tables of declinations, and stellar and solar observations that he had made together with Christopher Haydon. The work also includes a translation of Compendio de la Arte de Navegar (Compendium of the Art of Navigation, 1581, 2nd ed., 1588) by the Spanish cosmographer Rodrigo Zamorano (1542–1620).
It is not clear how Wright lived after he had resigned from his fellowship. There are suggestions that he took up the position of Mathematicall Lecturer to the Citie of London when Thomas Hood resigned from the post after only four years in 1592. However, there is no evidence to support this plausible suggestion. Wright’s friend, Henry Briggs, was appointed the first Gresham professor of geometry in 1596, a position to hold public lectures also in London, which may have made the earlier lectureship superfluous. However, Wright was definitely employed by Thomas Smith and John Wolstenholme, who had sponsored Hood’s lectureship, as a lecturer in navigation for the East India Company at £50 per annum, probably from 1612 but definitely from 1614. Before his employment by the East India Company, he had been mathematical tutor to Prince Henry (1594–1612), the eldest son of King James I/IV, from about 1608, to whom he dedicated the second edition of Certaine Errors.
In the 1590s Wright was one of the investigators whose work contributed to William Gilbert’s De Magnete(1600) for which he wrote the opening address on the author and according to one source contributed Chapter XII of Book IV, Of Finding the Amount of Variation…
In this context he also wrote, Description and Use of the Two Instruments for Seamen to find out the Latitude … First Invented by Dr. Gilbert, published in Blundeville, Thomas; Briggs, Henry; Wright, Edward (1602),The Theoriques of the Seuen Planets… a work on the dip circle.
He also authored The Description and Vse of the Sphære. Deuided into Three Principal Partes: whereof the First Intreateth especially of the Circles of the Vppermost Moueable Sphære, and of the Manifould Vses of euery one of them Seuerally: the Second Sheweth the Plentifull Vse of the Vppermost Sphære, and of the Circles therof Ioyntly: the Third Conteyneth the Description of the Orbes whereof the Sphæres of the Sunne and Moone haue beene supposed to be Made, with their Motions and Vses. By Edward Wright. The Contents of each Part are more particularly Set Downe in the Table first published in London in 1613 with a second edition in 1627. This could be viewed as a general introduction to the armillary sphere, but was actually written was a textbook for Prince Henry. A year later he published A Short Treatise of Dialling Shewing, the Making of All Sorts of Sun-dials, Horizontal, Erect, Direct, Declining, Inclining, Reclining; vpon any Flat or Plaine Superficies, howsoeuer Placed, with Ruler and Compasse onely, without any Arithmeticall Calculationprobably also written for the Prince.
As well as the translation of Zamorano’s Compendio de la Arte de Navegar included in his Certaine Errors, he translated Simon Stevin’s The Hauen-finding Art, or The VVay to Find any Hauen or Place at Sea, by the Latitude and Variation. Lately Published in the Dutch, French, and Latine Tongues, by Commandement of the Right Honourable Count Mauritz of Nassau, Lord High Admiral of the Vnited Prouinces of the Low Countries, Enioyning all Seamen that Take Charge of Ships vnder his Iurisdiction, to Make Diligent Obseruation, in all their Voyages, according to the Directions Prescribed herein: and now Translated into English, for the Common Benefite of the Seamen of England, a text on determining longitude using magnetic variation.
In 1605, he also edited Robert Norman’s translation out of Dutch of The Safegarde of Saylers, or Great Rutter. Contayning the Courses, Dystances, Deapths, Soundings, Flouds and Ebbes, with the Marks for the Entring of Sundry Harboroughs both of England, Fraunce, Spaine, Ireland. Flaunders, and the Soundes of Denmarke, with other Necessarie Rules of Common Nauigation.
His most important work of translation was certainly that of John Napier’s Mirifici Logarithmorum Canonis Descriptio (Description of the Wonderful Canon of Logarithms, 1614) from the original Latin into English: A Description of the Admirable Table of Logarithmes: With a Declaration of the … Use thereof. Invented and Published in Latin by … L. John Nepair … and Translated into English by … Edward Wright. With an Addition of an Instrumentall Table to Finde the Part Proportionall, Invented by the Translator, and Described in the Ende of the Booke by Henry Brigs, etc approved by Napier and first published posthumously by Henry Briggs in 1616 and then again in 1618.
The development of mathematical navigation, cartography, and surveying in the Early Modern Period, in which Wright along with others played a central role, was by nature predominantly trigonometrical. Napier’s invention of logarithms made the complex trigonometrical calculations much easier to manage. This was something that Napier himself was acutely aware of and the majority of tables in his work were, in fact, logarithms of trigonometrical functions. By translating Napier’s work into English, Wright made it accessible to those mariners confronted with trigonometrical navigational problems, who couldn’t read Latin. The introduction contains the following poem:
The toylesome rules of due proportion
Done here by addition and subtraction,
By tripartition and tripartition,
The square and cubicke roots extraction:
And so, all questions geometricall,
But with most ease triangles-sphericall.
The use in great in all true measuring
of lands, plots, buildings, and fortification,
So in astronomy and dialling,
Geography and Navigation.
In these and like, yong students soon may gaine
The skilfull too, may save cost, time, & paine.
Wright was also acknowledged as a skilled designer of scientific instruments, but like his friend Edmund Gunter (1561–1626), he didn’t make them himself. He is known to have designed instruments for the astronomer/astrologer Sir Christopher Haydon and to have made astronomical observations with him in London in the early 1590s. We don’t know Wright’s attitude to astrology, but that of his two Cambridge friends was diametrically opposed. Haydon was the author of the strongest defence of astrology written in English in the early seventeenth century, his A Defence of Judiciall Astrologie (1603), whereas Henry Briggs was one of the few mathematical practitioners of the period, who completely rejected it, unlike John Napier who as an ardent supporter.
Wright’s work in navigation was highly influential on both sides of the North Sea.
Wright gets positively acknowledge, both in The Navigator (1642) by Charles Saltonstall (1607–1665) and in the Navigation by the Mariners Plain Scale New Plain’d (1659) by John Collins (1625–1683).
In England Wright’s work was also taken up by Richard Norwood (1590? –1675), the surveyor of Bermuda, who using Wright’s methods determined one degree of a meridian to be 367,196 feet (111,921 metres), surprisingly accurate, publishing the result in his The Seaman’s Practice, 1637. However, in his Norwood’s Epitomy, being the Application of the Doctrine of Triangles, 1645, he gives a clear sign that the Mercator chart still hasn’t been totally accepted 46 years after Wright first published the solution of how to construct it.
Although the ground of the Projection of the ordinary Sea-Chart being false, (as supposing the Earth and Sea to be plain Superficies [sufaces]) and so the conclusions thence derived must also for the most part erroneous; yet because it is most easy, and much used, and the errors in small distances not so evident, we will not wholly neglect it.
He actually devotes as much space, in this work, which continued to be published throughout the century in various editions, to plain sailing as he does to Mercator sailing. Interestingly in the section on Mercator sailing, he doesn’t, following Wright, just give a table of meridional parts but explains how to use trigonometry to calculate them.
Now that which he [Edward Wright] hath shewed to performe by the Chart it selfe [the table of meridional parts], we will shew to work by the Doctrine of plaine Triangles, using the helpe of the Table of Logarithme Tangents…
Although its impact was drawn out over several decades it is impossible to over emphasise Wright’s contribution to the histories of cartography and navigation by his publication of the mathematical means of constructing a Mercator chart.
 David Walters, The Art of Navigationin England in Elizabethan and Early Stuart Times, Yale University Press, 1958 p. 359
The so-called European Age of Discovery is usually considered to have begun as adventurers from the Iberian Peninsular began to venture out into the Atlantic Ocean in the fifteenth century, reaching a high point when Bartolomeu Dias (c. 1450–1500) first rounded the southern tip of Africa in 1488 and Christopher Columbus (1441–1506) accidentally ran into the Americas trying to reach the Indies by sailing west. Those who made successful voyages, basically meaning returned alive, passed on any useful information they had garnered to future adventurers. It would be first at the end of the sixteenth century that the governments of the sea faring nations first began to establish central, national schools of navigation that accumulated such navigational and cartographical knowledge, processed it, and then taught it to new generations of navigators. Through out the sixteenth century individual experts were hired to teach these skills to individual groups setting out on new voyages of discovery.
In England this function was filled by Thomas Harriot (c. 1560–1621), who not alone taught navigation and cartography to Walter Raleigh’s sailors but also sailed with them to North America, making him that continent’s first scientist. John Dee (1527–c. 1608) supplied the same service to the seamen of the Muscovy Trading Company, although, unlike Harriot, he did not sail with them. Richard Hakluyt (1553–1616), a promotor of voyages of discovery, collected, collated, and published much information on all the foreign voyages but only passed this information on in manuscript to Raleigh.
In the 1580s Dee disappeared off to the continent, Harriot after returning from the Americas disappeared into the private service of Henry Percy, 9th Earl of Northumberland (1564–1632) and Hakluyt, a clergyman, after returning from government service in Paris, investigating the voyages of the continental nations, went into private service. In Paris, in 1584, Hakluyt noted that there was a lectureship for mathematics at the Collège Royal and wrote a letter to Sir Francis Walsingham (c. 1532–1590), the Queen’s principal secretary, the most powerful politician in England and a major supporter of voyages of discovery. In his letter, Hakluyt, urged Walsingham to establish a lectureship for mathematics at Oxford University for scholars to study the theory of navigation and the application of mathematics to its problem, and a public lectureship of navigation in London to educate seamen.
Walsingham undertook nothing and the demand grew loud for some form of public lectureship in mathematics to supply the necessary mathematics-based information in navigation and cartography to English seamen. In 1588, a private initiative was launched by Sir Thomas Smith (c. 1558–1625), Sir John Wolstenholme (1562–1639), and John Lumley, 1st Baron Lumley and Thomas Hood (1556–1620) was appointed Mathematicall Lecturer to the Citie of London.
Thomas Hood, baptised 23 June 1556, was the son of Thomas Hood a merchant tailor of London. He entered Merchant Taylors’ School in 1567 and matriculated at Trinity College Cambridge in 1573. He graduated BA c. 1578, was elected a fellow of Trinity and graduated MA in 1581. He was granted a licence to practice medicine by Cambridge University in 1585 and, as already mentioned, lecturer for mathematics in London in 1588. This appointment and his subsequent publications indicate that he was a competent mathematical practitioner but from whom he learnt his mathematics is not known.
Before turning to Hood’s lectureship and the associated publications, it is interesting to look at those who sponsored the lectureship. Thomas Smith was the son and grandson of haberdashers and like Hood attended Merchant Taylors School, entering in 1571.
He entered the Worshipful Company of Haberdashers and the Worshipful Company of Skinners in 1580 and went on to have an impressive political career in the City of London, occupying a series of influential posts over the years. His father had founded the Levant Trading Company and Thomas was the first governor of the East India Company, when it was founded in 1600, but only held the post for four months having fallen into suspicion of being involved in the Essex Rebellion. He was reappointed governor in 1603 and with one break in 1606-7 remained in the post until 1621. Later, he was a subscriber to the Virginia Company, as was Hood, and obtained its royal charter in 1609 and became the new colony’s treasurer making him de facto non-resident governor until his resignation in 1620. His grandfather had founded the Muscovy Company and Smith also became involved in that. It’s easy to see why Smith was motivated to promote a lectureship in practical mathematics.
John Wolstenholme was cut from a very similar cloth to Smythe, son of another John Wolstenholme a customs’ official in London, he became a rich successful merchant at an early age.
Like Smythe a founding member of both the East India and Virginia Companies, he was also a strong supporter of the attempts to find the North-West Passage. He fitted out several of the expeditions, Henry Hudson (c. 1556–disappeared 1611) named Cape Wolstenholme, the extreme northern most point of the province of Quebec after him. William Baffin (c. 1584–1622) named Wolstenholme Island in Baffin Bay after him.
John Lumley was slightly different to the two powerful merchants, a member of the landed gentry, he was an art collector and bibliophile.
In the same year 1582, that the three founded Hood’s mathematical lectureship, Lumley founded with Richard Caldwell (1505?–1584), a physician, the Lumleian Lectures. Initially intended to be a weekly lecture course on anatomy and surgery they had been reduced to three lectures a year by 1616. They still exist as a yearly lecture on general medicine organised by the Royal College of Physicians.
The mathematical lectures finally came into being in 1588, following the threat of the Spanish Armada in that year. The original intended audience consisted of the captains of the city’s train bands or armed militia but also open to the ship’s captains, who rapidly became the main audience. The lectures were on geometry, astronomy, geography, hydrography, and the art of navigation. The lectures were originally held in the Staplers’ Chapel in Leadenhall Street but later moved to Smith’s private residence in Gracechurch Street, where he had held the inaugural lecture. In total Hood lectured for four years and later he attempted to obtain license to practice medicine in London from the Royal College of Physicians. This was denied him due to his inadequate knowledge of Galen. He was finally granted a conditional licence in 1597 and sometime after that he moved to Worcester, where he practiced medicine until his death in 1620.
His first publication was his inaugural lecture under the title, A COPIE OF THE SPEACHE:MADE by the Mathematicall Lecturer, unto the Worshipful Companye present. At the house of the Worshipfull M. Thomas Smith, dwelling in Gracious Street: the 4. of November, 1588. T. Hood. Imprinted at London by Edward Allde.
In this lecture he set out the reasons for the establishment of the lectureship and emphasised the importance of mathematics to people in all walks of life. He also sketched a history of mathematics from Adam down to his own times. The lectures were obviously successful, and he was urged to publish them, which he did to some extent.
His next major publication was The VSE OF THE CELESTIAL GLOBE IN PLANO; SET FOORTH IN TWO HEMISPHERES: WHEREIN ARE PLACED ALL THE MOST NOTa[ble] Starres of the heauen according to their longitude, latitude, magnitude, and constellation: Whereunto are annexed their names, both Latin Greeke, and Arabian or Chaldee; … (1590) They don’t write title like that anymore.
There is also an advert explaining that one can buy the hemispheres from the author at his address. He explains that he has presented the celestial spheres in plano in order to make it easier for seamen to read off the longitude and latitude of stars than it would be from a small globe. His beautifully coloured planispheres are the first printed planispheres in England. A seaman who bought Hood’s planispheres no longer needed to buy a celestial globe or planispheric astrolabe.
Before he published The Use of the Celestial Globe, he published a pamphlet on the use of a novel cross-staff that he had devised. Hood’s cross staff was a significant step towards the back staff, which eliminated the necessity of looking directly into the sun to take readings. This was so successful that he was urged to produce a similar pamphlet for the Jacobs Staff, and he obliged publishing two pamphlets in 1590,The vse of the two Mathematicall instrumentes, the crosse Staffe … and the Iacobes Staffe in two parts with separate titles. The pamphlets attracted the attention of the Lord Admiral, Lord Howard (1536–1624), who became his patron. Hood dedicated a second edition of the double pamphlet to Howard in 1596.
Hood’s finally publication of 1590 was a translation of The Geometry of Petrus Ramus, THE ELEMENTES OF GEOMETRIE: Written in Latin by that excellent Scholler, P. Ramus, Professor of the Mathematical Sciences in the Vuniverstie of Paris: And faithfully translated by Tho. Hood, Mathematicall Lecturer in the Citie of London. Knowledge hath no enemie but the ignorant.
Like many others in this period, Hood’s books were written in the form of dialogues between a master and a student, and he continued in this form with his next book on the use of globes in 1592. Serial production printed celestial and terrestrial globes had been in existence on the continent since Johannes Schöner (1477–1547) had produced the first pair in the second decade of the sixteenth century but none had been produced in England. Probably at the suggestion of John Davis (c. 1550–1605), a leading Elizabethan navigator, the London merchant William Sanderson (c. 1548–1638) commissioned and sponsored the instrument maker Emery Molyneux (died 1598) to produce the first English printed pair of globes, in the early 1590s. The globe gores were printed by the Flemish engraver Jodocus Hondius (1563–1612), at the time living in exile in London, who would go on to found one of the two largest publishing houses for maps and globes in Europe in the seventeenth century.
Sanderson request Hood to write a guide to the use of such globes and Hood complied publishing his THE VSE of both the Globes, Celestiall,and Terrestriall, most plainely deliuered in forme of a Dialogue. Containing most pleasant, and profitableconclusions forthe Mariner, and generally for all those, that are addicted to these kinde of mathematicall instrumentes in 1592.
In the same year Hood edited a new edition of the popular navigation manual A Regiment for the Sea by William Bourne (c. 1535–1582) which was originally published in 1574. Hood edition would be printed in two further editions.
In 1598 Hood published his The Making and Use of the Geometricall Instrument called a sector, the first printed account of this versatile instrument, which almost certainly informed the much more extensive account of the sector by Edmund Gunter (1581–1626) published in 1624.
Hood’s most peculiar publication was an English translation of the Elementa arithmeticae, logicis legibus deducta in usum Academiae Basiliensis. Opera et studio Christiani Urstisii originally published in 1579. Christiani Urstisii was the relatively obscure Swiss mathematician, theologian, and historian Christian Wurstisen (1544–1588).
Why Hood stopped his lectures after four years in nor clear, he seems to have been both popular and successful and later Smith and Wolstenholme would later employ Edward Wright (1561–1615), who we will meet again in the next post in this series, through the East India Company in the same role. However, after he ceased lecturing Hood continued to sell instruments and his hemisphere charts. Hood’s lectureship was an important step towards the professional teaching of navigation to mariners in England at the end of the sixteenth century.
Way back at the beginning of November I wrote what was intended to be the first of a series of posts about English mathematical practitioners, who were active at the end of the sixteenth and the beginning of the seventeenth centuries. I did not think it would be two months before I could continue that series with a second post, but first illness and then my annual Christmas trilogy got in the way and so it is only now that I am doing so. The subject of this post is a man for whom a whole series of mathematical instruments are named, Edmund Gunter (1581–1626).
Unfortunately, as is all to often the case with Renaissance mathematici, we know almost nothing about Gunter’s origins. His father was apparently a Welshmen from Gunterstown, Brecknockshire in South Wales but he was born somewhere in Hertfordshire sometime in 1581. Obviously from an established family he was educated at Westminster School as a Queen’s Scholar i.e., a foundation scholar (elected on the basis of good academic performance and usually qualifying for reduced fees). He matriculated at Christ Church Oxford 25 January 1599 (os). He graduated BA 12 December 1603 and MA 2 July 1606. He took religious orders and proceeded B.D. 23 November 1615. He was appointed Rector of St. George’s, Southwark and of St Mary Magdalen, Oxford in 1615, he retained both appointments until his death.
Whilst still a student in 1603, he wrote a New Projection of the Sphere in Latin, which remained in manuscript until it was finally published in 1623. This came to the attention of Henry Briggs (1561–1630), who had been appointed professor of geometry at the newly founded Gresham College in 1596, and as such was very much a leading figure in the English mathematical community. Briggs was impressed by the young mathematician befriending him and becoming his mentor. The two men spent much time together at Gresham College discussing topics of practical mathematics. In 1606, Gunter developed a sector, about which later, and wrote a manuscript describing it in Latin, without a known title. This circulated in manuscript for many years and was much in demand. Gunter gave into that demand and finally published it also in 1623.
When the first Gresham professor of astronomy, Edward Brerewood (c. 1556–1613) died 4 November 1613, Briggs recommended Gunter as his successor. However, Thomas Williams another Christ Church graduate, of whom little is known, was appointed just seven days later 11 November 1613. When Williams resigned from the post 4 March 1619, for reasons unknown, Briggs once again supported his friend for the position, this time with success. Gunter was appointed just two days later, 6 March 1619. Like his two rectorships, he retained the Gresham professorship until his death.
Apparently, he was already spending so much time at Gresham College before being appointed that when the mathematician William Oughtred (1574–1660) visited Henry Briggs there in 1618, he thought that Gunter was already professor there.
In the Spring 1618 I being at London went to see my honoured friend Master Henry Briggs at Gresham College: who then brought me acquainted with Master Gunter lately chosen Astronomical lecturer there, and was at that time in Doctor Brooks his chamber. With whom falling into speech about his quadrant, I showed him my Horizontal Instrument. He viewed it very heedfully: and questioned about the projecture and use thereof, often saying these words, it is a very good one. And not long after he delivered to Master Briggs to be sent to me mine own Instrument printed off from one cut in brass: which afterwards I understood he presented to the right Honourable the Earl of Bridgewater, and in his book of the sector printed six years after, among other projections he setteth down this.
Gunter and Oughtred would go on to become firm friends.
We now have the known details of the whole of Gunter’s life and can turn our attention to his mathematical output but before we do so there is an anecdote from Seth Ward (1617–1689), another mathematician and astronomer, concerning a position that Gunter did not get. In 1619, Henry Savile (1549–1622) established England’s first university chairs for mathematics the Savilian chairs for geometry and astronomy at Oxford. Savile’s first choice for the chair of geometry was Edmund Gunter and he invited him to an interview, according to John Aubrey (1626–1697) relating a report from Seth Ward:
[Gunter] brought with him his sector and quadrant, and fell to resolving triangles and doing a great many fine things. Said the grave knight [Savile], “Do you call this reading of geometry? This is showing of tricks, man!”, and so dismissed him with scorn, and sent for Henry Briggs.
Henry Briggs travelled all the way to Edinburgh to meet the inventor of this new calculating tool. After discussion with Napier, he received his blessing to produce a set of base ten logarithms. His Logarithmorum chilias prima, which were publish in London sometime before Napier’s death in 1617.
Many people don’t realise that Napier’s logarithmic tables were not straight logarithms but logarithms of trigonometrical functions. These are of particular use for astronomers and navigators. It is almost certainly through Brigg’s influence that Gunter’s first publication was a set of base ten, seven figure logarithmic tables of sines and tangents. His Canon Triangulorum sive Tabulae Sinuum et Tangentium Artificialum was published in Latin in 1620. An English translation was published in the same year. The terms sine and tangent were already in use, but it was Gunter, who introduced the terms cosine and cotangent in this publication. Later, on his scale or rule he introduced the short forms sin and tan.
In 1623, Gunter finally published his New Projection of the Sphere written in his last year as an undergraduate. He also published his most important book, Description and Use of the Sector, the Crosse-staffe and other Instruments. This was one of the most important guides to the use of navigational instruments for seamen and became something of a seventeenth century best seller in various forms. David Waters in his The Art of Navigation say this, ” Gunter’s De Sectore & Radio must rank with Eden’s translation of Cortes’s Arte de Navegar and Wright’s Certain Errors as one of the three most important English books ever published for the improvement of navigation.” 
His various publications were collected into The Works of Edmund Gunter, which went through six editions by 1680. Each edition having extra content by other authors. Isaac Newton (1642-1727) bought a copy of the second edition. The title page of the fifth edition is impressive:
The Works of Edmund Gunter: Containing the description and Use of the Sector, Cross-staff, Bow, Quadrant, And other Instruments. With a Canon of Artificial Sines and Tangents to a Radius of 10.00000 parts, and the Logarithms from Unite to 100000: The Uses whereof are illustrated in the Practice of Arithmetick, geometry, Astronomy, Navigation, Dialling and Fortification. And some Questions in Navigation added by Mr. Henry Bond, Teacher of mathematicks in Ratcliff, near London. To which is added, The Description and Use of another Sector and Quadrant, both of them invented by Mr. Sam. Foster, Late Professor of Astronomy in Gresham Colledge, London, furnished with more Lines, and differing from those of Me. Gunter′s both in form and manner of Working. The Fifth Edition, Diligentyl Corrected, and divers necessary Things and Matters (pertinent thereunto) added, throughout the whole work, not before Printed. By William Leybourne, Philomath. London Printed by A.C. for Francis Eglesfield at the Marigold in St. Pauls Church-yard. MDCLXXIII.
The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportion, multiplication, and division, geometry, and trigonometry, and for computing various mathematical functions, such as square and cube roots. Its several scales permitted easy and direct solutions of problems in gunnery, surveying and navigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. (Wikipedia)
The sector has many alleged inventors. The earliest was Fabrizio Mordente (1532–c. 1608). The invention is often credited to Galileo (1564–1642), who marketed a very successful variant in the early seventeenth century, including selling lessons and an instruction manual in its use. However, Galileo’s instrument was a development of one created by Guidobaldo dal Monte (1545–1607). It is not known if dal Monte developed the device independently or knew of Mordent’s. Thomas Hood (1556–1620) appear to have reinvented the instrument, a description of which he published in his Making and Use of the Sector, 1596.
Gunter developed Hood’s instruments adding addition scales, including a scale for use with Mercator’s new projection of the sphere.
The French Jewish scholar, Levi ben Geshon (1288–1344), published the first description of the cross staff or Jacob’s staff, used in astronomy, surveying, and navigation, in his Book of the Wars of the Lord (originally in Hebrew but also translated into Latin).
Gunter’s book also describes the Gunter Quadrant, basically a horary quadrant for telling the time by taking the altitude of the sun but with some additional functions.
There is also a description of the crossbow an alternative to the backstaff that never became popular.
Gunter’s most popular instrument was his scale. The Gunter scale or rule was a rule containing trigonometrical and logarithmic scales, which could be used with a pair of dividers to carry out calculations in astronomy and in particular navigations. The Gunter scale is basically a sector folded into a straight line without the hinge.Sailors simply referred to the rule as a Gunter. William Oughtred would go on to place two Gunter rules next to each other thus creating the slide rule and eliminating the need for dividers to carry out the calculations.
In 1622, Gunter engraved a new sundial at Whitehall, which carried many different dial plates supplying much astronomical data. At the behest of Prince Charles, he wrote and published an explanation of the dials, The Description and Use of His Majesties Dialsin Whitehall, 1624. The sundial was demolished in 1697.
Gunter’s most well-known instrument was his surveyor’s chain, which became the standard English Imperial chain. 100 links and 22 yards (66 feet) long, there are 10 chains in a furlong and 80 chains to a mile.
Although Gunter invented, designed, and described the use of several instruments, he didn’t actually make any of them. All of his instruments were produced by the London based, instrument maker Elias Allen (c. 1588–1652). Allen was born in Kent of unknown parentage and was apprenticed in 1602 to London instrument maker Charles Whitwell (c. 1568–1611) in the Grocer’s Company, serving his master for nine years. Following Whitwell’s death in 1611, Allen set up his own business. He rapidly became the foremost instrument maker in London, working mostly in brass, but occasionally in silver. He became very successful and made instruments for various aristocratic patrons and both James I and Charles I. Allen also produced the engravings in Gunter’s books, using them also as advertising in his shop.
He worked closely with various mathematicians including both Oughtred and Gunter. His workshop became a meeting place for discussion amongst mathematical practitioners. He was the first London instrument maker, who could make a living from just making instruments without working on the side as a map engraver or surveyor. His master Whitwell subsidised his income as a map engraver. He rose in status in the Grocers’ Company, becoming its treasurer in 1636 and its master for eighteen months in 1637-38. Over the years many of his apprentices became successful instrument maker masters in the own right, most notably Ralph Greatorex (1625–1675), who was associated with Oughtred, Samuel Pepys, John Evelyn, Samuel Hartlib, Christopher Wren, Robert Boyle, and Jonas Moore, the English scientific elite of the time.
Allen had the distinction of being one of the few seventeenth-century artisans to have his portrait painted. The Dutch artist Hendrik van der Borcht the Younger (1614–1676) produced the portrait, now lost, in about 1640. It still exists as an engraving done by the Bohemian engraver, Wenceslaus Hollar (1607–1677).
Edmund Gunter was not a mathematician as we understand the term today, but a mathematical practitioner, who exercised a large influence on the practical side of astronomy, navigation, and surveying in the seventeenth century through the instruments that he designed and the texts he wrote explaining how to use them.
 David Walters, The Art of Navigationin England in Elizabethan and Early Stuart Times, Yale University Press, 1958 p. 359
Using the simplest and widest definition as to what constitutes a scientific instrument, it is literally impossible to say who first created, devised, used a scientific instrument or when and where they did it. My conjecture would be that the first scientific instrument was some sort of measuring device, a rod, or a cord to standardise a unit of measurement, almost certainly taken from the human body: a forearm, the length of a stride or pace, maybe a foot, a unit that we still use today. It is obviously that all the early great civilisation, Indus valley, Yellow River, Yangtze River, Fertile Crescent and so on, definitely used measuring devices, possibly observational devices, instruments to measure or lay out angles, simple compasses to construct circles, all of them probably as much to do with architecture and surveying, as with anything we might now label science.
Did the early astronomers in China, India, Babylon use some sorts of instruments to help them make their observations? We know that later people used sighting tubes, like a telescope without the lenses, to improve the quality of their observations, did those first astronomers already use something similar. Simple answer, we don’t really know, we can only speculate. We do know that Indian astronomers used a quadrant in their observation of solar eclipses around 1000 BCE.
Turning to the Ancient Greeks we initially have a similar lack of knowledge. The first truly major Greek astronomer Hipparkhos (c. 190–c. 120 BCE) (Latin Hipparchus) definitely used astronomical instruments but we have no direct account of his having done so. Our minimal information of his instruments comes from later astronomers, such as Ptolemaios (c. 100–c. 170 CE). Ptolemaios tells us in his Mathēmatikē Syntaxis aka Almagest that Hipparkhos made observations with an equatorial ring.
At another point in the book Ptolemaios talks of making observations with an armillary sphere and compares his observations with those of Hipparkhos, leading some to think that Hipparkhos also used an armillary sphere. Toomer in his translation of the Almagest say there is no foundation for this speculation and that Hipparkhos probably used a dioptra. 
Ptolemaios mentions four astronomical instruments in his book, all of which are for measuring angles:
1) A double ring device and
2) a quadrant both used to determine the inclination of the ecliptic.
3) The armillary sphere, which he confusingly calls an astrolabe, used to determine sun-moon configurations.
4) His parallactic rulers, used to determine the moon’s parallax, which was called a triquetrum in the Middle Ages.
Ptolemaios almost certainly also used a dioptra a simple predecessor to the theodolite used for measuring angles both in astronomy and in surveying. As I outlined in the post on surveying, ancient cultures were also using instruments to carry out land measuring.
Around the same time as the armillary sphere began to emerge in ancient Greece it also began to emerge in China, with the earliest single ring device probably being used in the first century BCE. By the second century CE the complete armillary sphere had evolved ring by ring. When the armillary sphere first evolved in India is not known, but it was in full used by the time of Āryabhata in the fifth century CE.
A parallel development to the armillary sphere was the celestial globe, a globe of the heavens marked with the constellations. In Greece celestial globes predate Ptolemaios but none of the early ones have survived. In his Almagest, Ptolemaios gives instruction on how to produce celestial globes. Chinese celestial globes also developed around the time of their armillary spheres but, once again, none of the early ones have survived. As with everything else astronomical, the earliest surveying evidence for celestial globes in India is much later than Greece or China.
In late antiquity the astrolabe emerged, its origins are still not really clear. Ptolemaios published a text on the planisphere, the stereographic projection used to create the climata in an astrolabe and still used by astronomers for star charts today. The earliest references to the astrolabe itself are from Theon of Alexandria (c. 335–c. 414 CE). All earlier claims to existence or usage of astrolabes are speculative. No astrolabes from antiquity are known to have survived. The earliest surviving astrolabe is an Islamic instrument dated AH 315 (927-28 CE).
Late Antiquity and the Early Middle Ages saw a steady decline in the mathematical sciences and with it a decline in the production and use of most scientific instruments in Europe until the disappeared almost completely.
When the rapidly expanding Arabic Empire began filing their thirst for knowledge across a wide range of subjects by absorbing it from Greek, Indian and Chinese sources, as well as the mathematical disciplines they also took on board the scientific instruments. They developed and perfected the astrolabe, producing hundreds of both beautiful and practical multifunctional instruments.
As well large-scale astronomical quadrants they produced four different types of handheld instruments. In the ninth century, the sine or sinical quadrant for measuring celestial angles and for doing trigonometrical calculations was developed by Muḥammad ibn Mūsā al-Khwārizmī. In the fourteenth century, the universal (shakkāzīya) quadrant used for solving astronomical problems for any latitude. Like astrolabes, quadrants are latitude dependent and unlike astrolabes do not have exchangeable climata. Origin unknown, but the oldest known example is from 1300, is the horary quadrant, which enables the uses to determine the time using the sun. An equal hours horary quadrant is latitude dependent, but an unequal hours one can be used anywhere, but its use entails calculations. Again, origin unknown, is the astrolabe quadrant, basically a reduced astrolabe in quadrant form. There are extant examples from twelfth century Egypt and fourteenth century Syria.
Islamicate astronomers began making celestial globes in the tenth century and it is thought that al-Sufi’s Book of the Constellations was a major source for this development. However, the oldest surviving Islamic celestial globe made by Ibrahim Ibn Saîd al-Sahlì in Valencia in the eleventh century show no awareness of the forty-eight Greek constellations of al-Sufi’s book.
Islamicate mathematical scholars developed and used many scientific instruments and when the developments in the mathematical sciences that they had made began to filter into Europe during the twelfth century scientific renaissance those instruments also began to become known in Europe. For example, the earliest astrolabes to appear in Europe were on the Iberian Peninsula, whilst it was still under Islamic occupation.
The medieval period in Europe saw a gradual increase in the use of scientific instruments, both imported and locally manufactured, but the use was still comparatively low level. There was some innovation, for example the French Jewish scholar, Levi ben Geshon (1288–1344), published the first description of the cross staff or Jacob’s staff, used in astronomy, surveying, and navigation, in his Book of the Wars of the Lord (originally in Hebrew but also translated into Latin).
…of a staff of 4.5 feet (1.4 m) long and about one inch (2.5 cm) wide, with six or seven perforated tablets which could slide along the staff, each tablet being an integral fraction of the staff length to facilitate calculation, used to measure the distance between stars or planets, and the altitudes and diameters of the Sun, Moon and stars
Also, the magnetic compass came into use in Europe in the twelfth century, first mentioned by Alexander Neckam (1157–1217) in his De naturis rerum at the end of the century.
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.
Petrus Pereginus (fl. 1269) gave detailed descriptions of both the floating compass and the dry compass in his Epistola de magnete.
However, it was first in the Renaissance that a widespread and thriving culture of scientific instrument design, manufacture, and usage really developed. The steep increase in scientific instrument culture was driving by the substantial parallel developments in astronomy, navigation, surveying, and cartography that began around fourteen hundred that I have already outlined in previous episodes of this series. Renaissance scientific instrument culture is too large a topic to cover in detail in one blog post, so I’ll only do a sketch of some major points and themes with several links to other earlier related posts.
Already, the first Viennese School of Mathematics, which was heavily involved in the development of both astronomy and cartography was also a source of scientific instrument design and manufacture.Johannes von Gmunden (c. 1380–1442) had a notable collection of instruments including an Albion, a multipurpose instrument conceived by Richard of Wallingford (1292–1336).
Georg von Peuerbach (1423–1461) produced several instruments most notably the earliest portable sundial marked for magnetic declination.
His pupil Regiomontanus (1436–1476) wrote a tract on the construction and use of the astrolabe and there is an extant instrument from 1462 dedicated to Cardinal Bessarion and signed IOHANNES, which is assumed to have been made by him. At least eleven other Regiomontanus style astrolabes from the fifteenth century are known.
Stöffler also made celestial globes and an astronomical clock.
Mechanical astronomical clocks began to emerge in Europe in the fourteenth century, but it would not be until the end of the sixteenth century that mechanical clocks became accurate enough to be used as scientific instruments. The earliest clockmaker, who reached this level of accuracy being the Swiss instrument maker, Jost Bürgi (1552–1632).
Bürgi made numerous highly elaborate and very decorative mechanical clocks, mechanised globes and mechanised armillary spheres that were more collectors items for rich patrons rather than practical instruments.
This illustrates another driving force behind the Renaissance scientific instrument culture. The Renaissance mathematicus rated fairly low in the academical hierarchy, actually viewed as a craftsman rather than an academic. This made finding paid work difficult and they were dependent of rich patrons amongst the European aristocracy. It became a standard method of winning the favour of a patron to design a new instrument, usually a modification of an existing one, making an elaborate example of it and presenting it to the potential patron. The birth of the curiosity cabinets, which often also included collections of high-end instruments was also a driving force behind the trend. Many leading instrument makers produced elaborate, high-class instruments for such collections. Imperial courts in Vienna, Prague, and Budapest employed court instrument makers. For example, Erasmus Habermel (c. 1538–1606) was an incredibly prolific instrument maker, who became instrument maker to Rudolf II. A probable relative Josua Habermel (fl. 1570) worked as an instrument maker in southern Germany, eventually moving to Prague, where he probably worked in the workshop of Erasmus.
Whereas from Theon onwards, astrolabes were unique, individual, instruments, very often beautiful ornaments as well as functioning instruments, Georg Hartmann was the first instrument maker go into serial production of astrolabes. Also, Hartmann, although he didn’t invent them, was a major producer of printed paper instruments. These could be cut out and mounted on wood to produce cheap, functional instruments for those who couldn’t afford the expensive metal ones.
Gemma Frisius set up a workshop producing a range of scientific instruments together with his nephew (?) Gualterus Arsenius (c. 1530–c. 1580).
In France, Oronce Fine (1494–1555), a rough contemporary, who was appointed professor at the Collège Royal, was also influenced by Schöner in his cartography and like the Nürnberger was a major instrument maker. In Italy, Egnatio Danti (1536–1586) the leading cosmographer was also the leading instrument maker.
Their lead was followed by others, the first Vatican observatory was established in the Gregorian Tower in 1580.
In the early seventeenth century, Leiden University in Holland established the first European university observatory and Christian Longomontanus (1562–1647), who had been Tycho’s chief assistant, established a university observatory in Copenhagen
As in all things mathematical England lagged behind the continent but partial filled the deficit by importing instrument makers from the continent, the German Nicolas Kratzer (c. 1487–1550) and the Netherlander Thomas Gemini (c. 1510–1562). The first home grown instrument maker was Humfrey Cole (c. 1530–1591). By the end of the sixteenth century, led by John Dee (1527–c. 1608), who studied in Louven with Frisius and Mercator, and Leonard Digges (c. 1515–c. 1559), a new generation of English instrument makers began to dominate the home market. These include Leonard’s son Thomas Digges (c. 1546–1595), William Bourne (c. 1535–1582), John Blagrave (d. 1611), Thomas Blundeville (c. 1522–c. 1606), Edward Wright (1561–1615), Emery Molyneux (d. 1598), Thomas Hood (1556–1620), Edmund Gunter (1581–1626) Benjamin Cole (1695–1766), William Oughtred (1574–1660), and others.
The Renaissance also saw a large amount of innovation in scientific instruments. The Greek and Chinese armillary spheres were large observational instruments, but the Renaissance armillary sphere was a table top instrument conceived to teach the basic of astronomy.
In navigation the Renaissance saw the invention various variations of the backstaff, to determine solar altitudes.
Also new for the same purpose was the mariner’s astrolabe.
Edmund Gunter (1581–1626) invented the Gunter scale or rule a multiple scale (logarithmic, trigonometrical) used to solve navigation calculation just using dividers.
Due to the impact of Isaac Newton and the mathematicians grouped around him, people often have a false impression of the role that England played in the history of the mathematical sciences during the Early Modern Period. As I have noted in the past, during the late medieval period and on down into the seventeenth century, England in fact lagged seriously behind continental Europe in the development of the mathematical sciences both on an institutional level, principally universities, and in terms of individual mathematical practitioners outside of the universities. Leading mathematical practitioners, working in England in the early sixteenth century, such as Thomas Gemini (1510–1562) and Nicolas Kratzer (1486/7–1550) were in fact immigrants, from the Netherlands and Germany respectively.
In the second half of the century the demand for mathematical practitioners in the fields of astrology, astronomy, navigation, cartography, surveying, and matters military was continually growing and England began to produce some home grown talent and take the mathematical disciplines more seriously, although the two universities, Oxford and Cambridge still remained aloof relying on enthusiastic informal teachers, such as Thomas Allen (1542–1632) rather than instituting proper chairs for the study and teaching of mathematics.
Outside of the universities ardent fans of the mathematical disciplines began to establish the so-called English school of mathematics, writing books in English, giving tuition, creating instruments, and carrying out mathematical tasks. Leading this group were the Welsh man, Robert Recorde (c. 1512–1558), who I shall return to in a later post, John Dee (1527–c. 1608), who I have dealt with in several post in the past, one of which outlines the English School, other important early members being, Dee’s friend Leonard Digges, and his son Thomas Digges (c. 1446–1595), who both deserve posts of their own, and Thomas Hood (1556–1620) the first officially appointed lecturer for mathematics in England. I shall return to give all these worthy gentlemen, and others, the attention they deserve but today I shall outline the life and mathematical career of John Blagrave (d. 1611) a member of the landed gentry, who gained a strong reputation as a mathematical practitioner and in particular as a designer of mathematical instruments, the antiquary Anthony à Wood (1632–1695), author of Athenae Oxonienses. An Exact History of All the Writers and Bishops, who Have Had Their Education in the … University of Oxford from the Year 1500 to the End of the Year 1690, described him as “the flower of mathematicians of his age.”
John Blagrave was the second son of another John Blagrave of Bullmarsh, a district of Reading, and his wife Anne, the daughter of Sir Anthony Hungerford of Down-Ampney, an English soldier, sheriff, and courtier during the reign of Henry VIII, John junior was born into wealth in the town of Reading in Berkshire probably sometime in the 1560s. He was educated at Reading School, an old established grammar school, before going up to St John’s College Oxford, where he apparently acquired his love of mathematics. This raises the question as to whether he was another student, who benefitted from the tutoring skills of Thomas Allen (1542–1632). He left the university without graduating, not unusually for the sons of aristocrats and the gentry. He settled down in Southcot Lodge in Reading, an estate that he had inherited from his father and devoted himself to his mathematical studies and the design of mathematical instruments. He also worked as a surveyor and was amongst the first to draw estate maps to scale.
There are five known surviving works by Blagrave and one map, as opposed to a survey, of which the earliest his, The mathematical ievvel, from1585, which lends its name to the title of this post, is the most famous. The full title of this work is really quite extraordinary:
THE MATHEMATICAL IEVVEL
Shewing the making, and most excellent vse of a singuler Instrument So called: in that it performeth with wonderfull dexteritie, whatsoever is to be done, either by Quadrant, Ship, Circle, Cylinder, Ring, Dyall, Horoscope, Astrolabe, Sphere, Globe, or any such like heretofore deuised: yea or by most Tables commonly extant: and that generally to all places from Pole to Pole.
The vse of which Ievvel, is so aboundant and ample, that it leadeth any man practising thereon, the direct pathway (from the first steppe to the last) through the whole Artes of Astronomy, Cosmography, Geography, Topography, Nauigation, Longitudes of Regions, Dyalling, Sphericall triangles, Setting figures, and briefely of whatsoeuer concerneth the Globe or Sphere: with great and incredible speede, plainenesse, facillitie, and pleasure:
The most part newly founde out by the Author, Compiled and published for the furtherance, aswell of Gentlemen and others desirous or Speculariue knowledge, and priuate practise: as also for the furnishing of such worthy mindes, Nauigators,and traueylers,that pretend long voyages or new discoueries: By John Blagave of Reading Gentleman and well willer to the Mathematickes; Who hath cut all the prints or pictures of the whole worke with his owne hands. 1585•
Dig the spelling!
Blagrave’s Mathematical Jewel is in fact a universal astrolabe, and by no means the first but probably the most extensively described. The astrolabe is indeed a multifunctional instrument, al-Sufi (903–983) describes over a thousand different uses for it, and Chaucer (c. 1340s–1400) in what is considered to be the first English language description of the astrolabe and its function, a pamphlet written for a child, describes at least forty different functions. However, the normal astrolabe has one drawback, the flat plates, called tympans of climata, that sit in the mater and are engraved with the stereographic projection of a portion of the celestial sphere are limited in their use to a fairly narrow band of latitude, meaning that if one wishes to use it at a different latitude you need a different climata. Most astrolabes have a set of plates each engraved on both side for a different band of latitude. This problem led to the invention of the universal astrolabe.
The earliest known universal astrolabes are attributed to Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Zarqālī al-Tujibi (1029-1100), known simply as al-Zarqālī and in Latin as Arzachel, an Arabic astronomer, astrologer, and instrument maker from Al-Andalus, and another contemporary Arabic astronomer, instrument maker from Al-Andalus, Alī ibn Khalaf: Abū al‐Ḥasan ibn Aḥmar al‐Ṣaydalānī or simply Alī ibn Khalaf, about whom very little is known. In the Biographical Encyclopedia of Astronomers (Springer Reference, 2007, pp. 34-35) Roser Puig has this to say about the two Andalusian instrument makers:
ʿAlī ibn Khalaf is the author of a treatise on the use of the lámina universal (universal plate) preserved only in a Spanish translation included in the Libros del Saber de Astronomía (III, 11–132), compiled by the Spanish King Alfonso X. To our knowledge, the Arabic original is lost. ʿAlī ibn Khalaf is also credited with the construction of a universal instrument called al‐asṭurlāb al‐maʾmūnī in the year 1071, dedicated to al‐Maʾmūn, ruler of Toledo.
The universal plate and the ṣafīḥa (the plate) of Zarqalī (devised in 1048) are the first “universal instruments” (i.e., for all latitudes) developed in Andalus. Both are based on the stereographic meridian projection of each hemisphere, superimposing the projection of a half of the celestial sphere from the vernal point (and turning it) on to the projection of the other half from the autumnal point. However, their specific characteristics make them different instruments.
Al-Zarqālī’s universal astrolabe was known as the Azafea in Arabic and as the Saphaea in Europe.
Much closer to Blagrave’s time, Gemma Frisius (1508–1555) wrote about a universal astrolabe, published as the Medici ac Mathematici de astrolabio catholico liber quo latissime patientis instrumenti multiplex usus explicatur, in 1556. Better known than Frisius’ universal instrument was that of his one-time Spanish, student Juan de Rojas y Samiento (fl. 1540-1550) published in his Commentariorum in Astrolabium libri sex in 1551.
Although he never really left his home town of Reading and his work was in English, Blagrave, like the other members of the English School of Mathematics, was well aware of the developments in continental Europe and he quotes the work of leading European mathematical practitioners in his Mathematical Jewel, such as the Tübingen professor of mathematics, Johannes Stöffler (1452–1531), who wrote a highly influential volume on the construction of astrolabes, his Elucidatio fabricae ususque astrolabii originally published in 1513, which went through 16 editions up to 1620
or the works of Gemma Frisius, who was possibly the most influential mathematical practitioner of the sixteenth century. Blagrave’s Mathematical Jewel was based on Gemma Frisius astrolabio catholico.
The catholique planisphaer which Mr. Blagrave calleth the mathematical jewel briefly and plainly discribed in five books : the first shewing the making of the instrument, the rest shewing the manifold vse of it, 1. for representing several projections of the sphere, 2. for resolving all problemes of the sphere, astronomical, astrological, and geographical, 4. for making all sorts of dials both without doors and within upon any walls, cielings, or floores, be they never so irregular, where-so-ever the direct or reflected beams of the sun may come : all which are to be done by this instrument with wonderous ease and delight : a treatise very usefull for marriners and for all ingenious men who love the arts mathematical / by John Palmer … ; hereunto is added a brief description of the cros-staf and a catalogue of eclipses observed by the same I.P.
John Palmer (1612-1679), who was apparently rector of Ecton and archdeacon of Northampton, is variously described as the author or the editor of the volume, which was first published in 1658 and went through sixteen editions up to 1973.
Following The Mathematical Jewel, Blagrave published four further books on scientific instruments that we know of:
Baculum Familliare, Catholicon sive Generale. A Booke of the making and use of a Staffe, newly invented by the Author, called the Familiar Staffe (London, 1590)
Astrolabium uranicum generale, a necessary and pleasaunt solace and recreation for navigators … compyled by John Blagrave (London, 1596)
An apollogie confirmation explanation and addition to the Vranicall astrolabe (London, 1597)
None of these survive in large numbers.
Blagrave also manufactured sundials and his fourth instrument book is about this:
The art of dyalling in two parts (London, 1609)
Here there are considerably more surviving copies and even a modern reprint by Theatrum Orbis Terrarum Ltd., Da Capo Press, Amsterdam, New York, 1968.
People who don’t think about it tend to regard books on dialling, that is the mathematics of the construction and installation of sundials, as somehow odd. However, in this day and age, when almost everybody walks around with a mobile phone in their pocket with a highly accurate digital clock, we tend to forget that, for most of human history, time was not so instantly accessible. In the Early Modern period, mechanical clocks were few and far between and mostly unreliable. For time, people relied on sundials, which were common and widespread. From the invention of printing with movable type around 1450 up to about 1700, books on dialling constituted the largest genre of mathematical books printed and published. Designing and constructing sundials was a central part of the profession of mathematical practitioners.
As well as the books there is one extant map:
Noua orbis terrarum descriptio opti[c]e proiecta secundu[m]q[ue] peritissimos Anglie geographos multis ni [sic] locis castigatissima et preceteris ipsiq[ue] globo nauigationi faciliter applcanda [sic] per Ioannem Blagrauum gen[er]osum Readingensem mathesibus beneuolentem Beniamin Wright Anglus Londinensis cµlator anno Domini 1596
This is described as:
Two engraved maps, the first terrestrial, the second celestial (“Astrolabium uranicum generale …”). Evidently intended to illustrate Blagrave’s book “Astrolabium uranicum generale” but are not found in any copy of the latter. The original is in the Bodleian Library.
When he died in 1611, Blagrave was buried in the St Laurence Church in Reading with a suitably mathematical monument.
Blagrave was a minor, but not insignificant, participant in the mathematical community in England in the late sixteenth century. His work displays the typical Renaissance active interest in the practical mathematical disciplines, astronomy, navigation, surveying, and dialling. He seems to have enjoyed a good reputation and his Mathematical Jewel appears to have found a wide readership.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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).
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.
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).
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.
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.
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.
We find the same double orientation on the earlier Mediterranean chart of Albino de Canepa from 1498, indicated by the pavilions.
Jorge Aguiar’s Mediterranean map of 1492 is south orientated
As is the world map of Nicolas Desliens of 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.
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.
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, Horizons: A Global History of Science; 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 Renaissance: A 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 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.
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 NaturalHistory, 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?
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.
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?
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.
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?
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’ Herbariumvivae 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.
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.
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. [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.
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.
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.
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.
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 Earth: The 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.
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.
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.”
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.
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.
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.
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.
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.
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.
 James Poskett, Horizons: A Global History of Science, Viking, 2022
 Take your pick according to your personal philosophy of science.
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.
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. Here, Harriot lived out his years as a research scientist with no obligations.
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.
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.
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.
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 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.
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.
In 1622-23 he would also tutor the younger son Henry.
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).
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.
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).
He is thought to have supplied Harriot with a copy of Viète’s Isagoge, making Harriot the first English mathematician to have read it.
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.
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.
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.
 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.
If your philosophy of [scientific] history claims that the sequence should have been A→B→C, and it is C→A→B, then your philosophy of history is wrong. You have to take the data of history seriously.
John S. Wilkins 30th August 2009
Culture is part of the unholy trinity—culture, chaos, and cock-up—which roam through our versions of history, substituting for traditional theories of causation. – Filipe Fernández–Armesto “Pathfinders: A Global History of Exploration”