Category Archives: History of Cartography

An inventor of instruments

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. 

Gresham College, engraving by George Vertue, 1740 Source: Wikimedia Commons

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.

William Oughtred engraving by Wenceslaus Hollar Source: Wikimedia Commons There are apparently no portraits of Briggs or Gunter

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.

So, Henry Briggs became England’s first university professor of geometry and not Edmund Gunter. One should point out that Ward can only have heard the story second hand as he was only two years old in 1619.

In 1614, John Napier (1550–1617) published his Mirifici Logarithmorum Canonis Descriptio (Description of the Wonderful Canon of Logarithms, 1614), a new method of simplifying calculations. Edward Wright (1561–1615) produced an English translation, which was published posthumously in 1616. Napier’s logarithms were base:

NapLog(x) = –107ln (x/107)

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.” [1]

Waters opposite page 360

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 Workers of Edmund Gunter 5th ed. Title page with diagrams of the sector on the fly leaf

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.
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.

Waters opposite page 345

Gunter developed Hood’s instruments adding addition scales, including a scale for use with Mercator’s new projection of the sphere. 


Water opposite page 361
Waters page 361

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 image of a cross staff

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.

Boxwood Gunter-type sector, made by Isaac Carver and owned by George Lason; 1706 Whipple Museum
Illustration of a quadrant from Edmund Gunter’s Works (1653). Image © the Whipple Library.
Modern reproduction of the Gunter Quadrant Source

There is also a description of the crossbow an alternative to the backstaff that never became popular. 

; Navigation: an Astrolabe, a Cross-Staff, and a Back-Staff or Davis’s Sextant; Wellcome Collection;
; Navigation: a Cross-Staff or Cross-Bow, and a Sailor Using the Device; Wellcome Collection;

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.

Gunter scale front side
Gunter scale back side

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 Dials in 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. 

[1] David Walters, The Art of Navigation in England in Elizabethan and Early Stuart Times, Yale University Press, 1958 p. 359

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Filed under History of Astronomy, History of Cartography, History of Navigation, Renaissance Science, Uncategorized

Renaissance Science – XLVIII

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.

This is the Royal cubit rod of Amenemope – a 3320-year-old measuring rod which revealed that Egyptians used units of measurement taken from the human body. The basic unit was the cubit – the length from the elbow to the tip of the middle finger, about 45cm. Source: British Museum

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.

The easiest way to understand the use of an equatorial ring is to imagine a ring placed vertically in the east-west plane at the Earth’s equator. At the time of the equinoxes, the Sun will rise precisely in the east, move across the zenith, and set precisely in the west. Throughout the day, the bottom half of the ring will be in the shadow cast by the top half of the ring. On other days of the year, the Sun passes to the north or south of the ring, and will illuminate the bottom half. For latitudes away from the equator, the ring merely needs to be placed at the correct angle in the equatorial plane. At the Earth’s poles, the ring would be horizontal. Source: Wikipedia

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. [1]

Ptolemaios mentions four astronomical instruments in his book, all of which are for measuring angles: 

1) A double ring device and

Toomer p. 61

2) a quadrant both used to determine the inclination of the ecliptic.

Toomer p. 62

3) The armillary sphere, which he confusingly calls an astrolabe, used to determine sun-moon configurations. 

Toomer p. 218

4) His parallactic rulers, used to determine the moon’s parallax, which was called a triquetrum in the Middle Ages. 

Toomer p. 245

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.

Graphic reconstruction of the dioptra, by Venturi, in 1814. (An incorrect interpretation of Heron’s description) Source: Wikimedia Commons

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.

Armillary sphere at Beijing Ancient Observatory, replica of an original from the Ming Dynasty

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.

The Farnese Atlas holding a celestial globe is the oldest known surviving celestial globe dating from the second century CE Source: Wikimedia Commons

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).

North African, 10th century AD, Planispheric Astrolabe Khalili Collection via Wikimedia Commons

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.

Horary quadrant for a latitude of about 51.5° as depicted in an instructional text of 1744: To find the Hour of the Day: Lay the thread just upon the Day of the Month, then hold it till you slip the small Bead or Pin-head [along the thread] to rest on one of the 12 o’Clock Lines; then let the Sun shine from the Sight G to the other at D, the Plummet hanging at liberty, the Bead will rest on the Hour of the Day. Source: Wikimedia Commons
Astrolabic quadrant, made of brass; made for latitude 33 degrees 30 minutes (i.e. Damascus); inscription on the front saying that the quadrant was made for the ‘muwaqqit’ (literally: the timekeeper) of the Great Umayyad Mosque of Damascus. AH 734 (1333-1334 CE) British Museum

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.  

Canterbury Astrolabe Quadrant 1388 Source Wikimedia Commons
Astrolabe of Jean Fusoris, made in Paris, 1400 Source: Wikimedia Commons

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

A Jacob’s staff, from John Sellers’ Practical Navigation (1672) Source: Wikimedia Commons

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).

Albion front side Source: Seb Falk’s Twitter feed
Albion rear Source: Seb Falk’s Twitter feed

Georg von Peuerbach (1423–1461) produced several instruments most notably the earliest portable sundial marked for magnetic declination.

Folding sundial by Georg von Peuerbach

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.

Regiomontanus style astrolabe Source: Wikimedia Commons

Elements of his design were adopted by both Johannes Stöffler (1452–1531), the first professor of astronomy at the University of Tübingen, and by the Nürnberger mathematicus Georg Hartmann (1489–1564).

Stöffler also made celestial globes and an astronomical clock.

Celestial Globe, Johannes Stöffler, 1493; Landesmuseum Württemberg Source: Wikimedia Commons

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.

Bürgi Quartz Clock 1622-27
Source: Swiss Physical Society

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.

 1594 armillary sphere by Erasmus Habermel of Prague.

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. 

Hartmann astrolabe front
Hartmann astrolabe rear
Paper and Wood Astrolabe Hartmann Source: HSM Oxford

Hartmann lived and worked in Nürnberg, which as I have sketched in an earlier post, was for more than a century the scientific instrument capital of Europe with a massive produce of instruments of all sorts.

One of the most beautiful sets on instruments manufactured in Nürnberg late 16th century. Designed by Johannes Pretorius (1537–1616), professor for astronomy at the Nürnberger University of Altdorf and manufactured by the goldsmith Hans Epischofer (c. 1530–1585) Germanische National Museum

As well as astrolabes and his paper instruments Hartmann also produced printed globes, none of which have survived. Another Nürnberger mathematicus, Johannes Schöner (1477–1547) launched the printed pairs of terrestrial and celestial globes onto the market.

Celestial Globe by Johannes Schöner c. 1534 Source

His innovation was copied by Gemma Frisius (1508–1555), whose student Gerard Mercator (1512–1594) took up globe making on a large scale, launching the seventeenth century Dutch globe making industry. 

Gemma Frisius set up a workshop producing a range of scientific instruments together with his nephew (?) Gualterus Arsenius (c. 1530–c. 1580).  

Astronomical ring dial Gualterus Arsenius Source

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. 

Egnation Danti, Astrolabe, ca. 1568, brass and wood. Florence, Museo di Storia della Scienza Source: Fiorani The Marvel of Maps p. 49

A major change during the Renaissance was the emergence, for the first time in Early Modern Europe, of large-scale astronomical observatories, Wilhelm IV (1532–1592) in Hessen-Kassel beginning in about 1560 and Tycho Brahe (1546–1601) on the Island of Hven beginning in 1575. Both men commissioned new instruments, many of which were substantially improved in comparison with their predecessors from antiquity.

Sternwarte im Astronomisch-Physikalischen Kabinett, Foto: MHK, Arno Hensmanns Reconstruction of Wilhelm’s observatory
Tycho Brahe, Armillary Sphere, 1581 Source
Tycho Brahe quadrant

Their lead was followed by others, the first Vatican observatory was established in the Gregorian Tower in 1580.

View on the Tower of Winds (Gregorian tower) in Vatican City (with the dome of Saint Peter’s Basilica in the background). Source: Wikimedia Commons

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 

Drawing of Leiden Observatory in 1670, seen on top of the university building. Source: Wikimedia Commons
Copenhagen University Observatory Source: Wikimedia Commons

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.

Armillary Sphere by Carlo Plato, Rome, 1588 Museum of the History of Science

In navigation the Renaissance saw the invention various variations of the backstaff, to determine solar altitudes.

Davis quadrant (backstaff), made in 1765 by Johannes Van Keulen. On display at the Musée national de la Marine in Paris. Source: Wikimedia Commons

Also new for the same purpose was the mariner’s astrolabe.

Mariner’s Astrolabe c. 1600 Source: Wikimedia Commons

Edmund Gunter (1581–1626) invented the Gunter scale or rule a multiple scale (logarithmic, trigonometrical) used to solve navigation calculation just using dividers.

Gunter scale front
Gunter scale back Source

William Oughtred (1574–1660) combined two Gunter scales to produce the slide rule.

New in surveying were the surveyor’s chain,

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

the plane table,

Surveying with plane table and surveyor’s chain

the theodolite

Theodolite 1590 Source:

and the circumferentor.

18th century circumferentor

All of which were of course also used in cartography. Another Renaissance innovation was sets of drawing instruments for the cartographical, navigational etc draughtsmen.

Drawing instruments Bartholomew Newsum, London c. 1570 Source

The biggest innovation in instruments in the Renaissance, and within its context one of the biggest instrument innovation in history, were of course the telescope and the microscope, the first scientific instruments that not only aided observations but increased human perception enabling researchers to perceive things that were previously hidden from sight. Here is a blog post over the complex story of the origins of the telescope and one over the unclear origins of the microscope.

The Renaissance can be viewed as the period when instrumental science began to come of age. 

[1] The information on Ptolemaios’ instruments and the diagrams are taken from Ptolemy’s Almagest, translated and annotated by G. J. Toomer, Princeton Paperbacks, 1998


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


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.

Harpsden a small parish near Henley-on-Thames Survey by John Blagrave 1589 Source

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:


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!
Title Page Source Note the title page illustration is an  armillary sphere and not the Mathematical Jewel

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.

Full-page figure of the rete of Blagrave’s Jewel (Peterborough A.8.13) For more illustration from The Mathematical Jewel go here

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.

A copy of al-Zarqālī’s astrolabe Source: Wikimedia Commons

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.

Blagrave’s Mathematical Jewel was obviously popular because Joseph Moxon (1627–1691), England first specialist mathematical publisher, cartographer, instrument, and globe maker republished it under the title:

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.

Engraved frontispiece to John Palmer (ed.), ‘The Catholique Planispaer, which Mr Blagrave calleth the Mathematical Jewel’ (London, Joseph Moxon, 1658); woman, wearing necklace, bracelet, jewels in her hair, and a veil, and seated at a table, on which are a design of a mathematical sphere, a compass, and an open book; top left, portrait of John Blagrave, wearing a ruff; top right, portrait of John Palmer; top centre, an angel with trumpets.
Engraving David Loggan Source: British Museum

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 is depicted surrounded by allegorical mathematical figures, with five women each holding the five platonic solids and Blagrave (in the center) depicted holding a globe and a quadrant.
The monument was the work of the sculptor Gerard Christmas (1576–1634), who later in life was appointed carver to the navy. It is not known who produced the drawing of the monument. 
Modern reconstruction of the armillary sphere from the cover of The Mathematical Jewel created by David Harber a descendent of John Blagrave

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.  


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

Why North?

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

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

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

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

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


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

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

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


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

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

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

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

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

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

Turning once again to Brotton: 

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

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

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

Continuing with Brotton:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Mediterranean chart of Albino de Canepa 1498 Source: Wikimedia Commons

Jorge Aguiar’s Mediterranean map of 1492 is south orientated

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

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

Nicolas Desliens World Map 1566

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

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

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

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

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

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

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

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

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

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

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

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

[2] Brotton p. 57

[3] Brotton p. 57

[4] Brotton pp. 57-58

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


Filed under History of Cartography

History of science is global history

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

His answer:

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

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

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

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

Poskett pp. 17-18

Poskett goes on to quote Acosta:

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

Poskett p. 18

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

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

Poskett p.18

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

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

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

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

Poskett pp.29-30

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

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

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

Poskett p. 39

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

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

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

Poskett p. 41

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

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

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

Poskett p. 44

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

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

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

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

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

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

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

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

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

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

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

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

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

The bizarre claims continue, Poskett writes:

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

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

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

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

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

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

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

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

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

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


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


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


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


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


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


(g) What could explain this variation?


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


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


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


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


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


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

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

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

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

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

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

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

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

The problems don’t end here, Poskett writes:

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

This is contradicted by Ferreiro who write:

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[3] Poskett p. 11

[4] Poskett p. 16

[5] Poskett 16

[6] Poskett p. 23

[7] Poskett p. 59

[8] Poskett p. 61

[9] Poskett p. 62

[10] Poskett p. 62

[11] Poskett p. 84

[12] Poskett pp. 101-104

[13] Poskett p. 107

[14] Edney private correspondence 27.07.2022

[15] Poskett p. 108

[16] Ferreiro p. 107

[17] Poskett p. 111

[18] Poskett p. 110

[19] Ferreiro p. 107

[20] Poskett pp. 111-112

[21] Poskett p. 251


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

The Wizard Earl’s mathematici 

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

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

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

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

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

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

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

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

Syon House Attributed to Robert Griffier

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

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

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

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

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

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

Source: Wikimedia Commons

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Source: Google Books

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

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

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

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

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

François Viète Source: Wikimedia Commons

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


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. 

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


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

Scotland’s premier topographer

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

Principal Triangulation of Great Britain Source: Wikimedia Commons

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

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

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

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

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

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

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

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

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

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

Gough Map Source: Wikimedia Commons

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

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

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

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

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

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

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

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

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

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

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

Saxton England and Wales proof map Source: British Library

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

John Speed’s map of Scotland

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

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

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

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

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

Pont’s Map of Lanark from 1596 Source

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

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

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

Pont’s map, Lothian and Linlithgow,

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

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

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

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

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

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

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

Source: National Portrait Gallery

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

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

Robert Sibbald artist unknown Source: Wikimedia Commons

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

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

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

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

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

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

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

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

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


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

A terrible fortnight for the HISTSCI_HULK

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

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

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

De revolutionibus Source: Wikimedia Commons


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

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

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

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

Under Ptolemy’s Planetary System we find the following

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

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

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


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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Source: Wikimedia Commons

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

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


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

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

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

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

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

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

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


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

Renaissance science – XXVII

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

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

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

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

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

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

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

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

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

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

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

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

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

NIMA Magnetic Variation Map 2000 Source: Wikimedia Commons

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

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

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

Source: Wikimedia Commons

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

Central wind rose on the Carta Pisana

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

Renaissance science – XXVI

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

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

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

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

Paolo dal Pozzo Toscanelli Source: Wikimedia Commons

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

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

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

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

Regiomontanus woodcut from the 1493 Nuremberg Chronicle Source: Wikimedia Commons

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

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

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

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

Source: Wikimedia Commons

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

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

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

Domenico Maria da Novara Source Museo Galileo

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


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

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

Portrait of Palladio by Alessandro Maganza Source: Wikimedia Commons

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


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


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