Category Archives: History of Cartography

Saxton and Speed two early Elizabethan cartographers and the Flemish influence

It is possible to date the start of the gradual emergence of modern cartography to the first decade of the fifteenth century when Jacopo d’Angelo produced the first Latin translation of Ptolemaeus’ Geographia(Geōgraphikḕ Hyphḗgēsis); this important Greek work had not been translated in the great wave of scientific translations in the High Middle Ages. This new knowledge of Ptolemaeus’ cartography with its projections and its longitude and latitude grids first took hold in Northern Italy, where its most famous early exponent was physician and mathematicus Paolo dal Pozzo Toscanelli (1379–1482) author of the so-called Columbus map.


Paolo dal Pozzo Toscanelli Source: Wikimedia Commons

From Northern Italy the new cartographer spread fairly rapidly to Austria and by 1450 Vienna was a major centre for cartography. Not long after the invention of movable metal type printing editions of the Geographia began to appear, initially without maps but very soon with, and by 1500 various editions were making their way around Europe. From Vienna the knowledge of the new cartographer moved north into Germany, with two schools of cartography developing. The so-called historical school was centred on the St. Dié mapmakers in Lorraine and includes Sebastian Münster in Basel. Whereas the so-called mathematical school, also known as the Vienna-Nürnberg school, has Johannes Schöner and Peter Apian as its two most significant exponents. Both schools include both aspects of the Ptolemaic cartography, the historical and the mathematical, in their maps and the difference is rather more one of emphasis.

From Southern Germany the new cartography spread throughout Europe. Notable cartographers, for example, are Pedro Nunes in Portugal and Oronce Fine in France. However the major centre for the new cartography became the so-called Flemish school centred on Gemma Frisius at the University of Louvain. Its two most notable associates are Gerhard Mercator and Abraham Ortelius, the two most influential cartographers in the second half of the sixteenth century.

But what of England? As with the mathematical sciences in general, England lagged well behind the continent in terms of cartography. The first Britain to become acquainted with the new developments in cartography was probably John Dee, who following his graduation at Cambridge university travelled extensively on the continent and spent two years in Louvain studying and working together with both Gemma Frisius and Gerard Mercator.


John Dee artist unknown Source: Wikimedia Commons

During his travels he also formed close friendships with both Abraham Ortelius and Pedro Nunes. When he returned to Britain Dee brought the latest developments in the Ptolemaic cartography, Frisius’ new methods of surveying through triangulation and the latest astronomical, cartographical and surveying instruments with him from Louvain. The Flemish/Dutch influence is clearly visible in the early English atlases.

It is probably no coincidence that the two ministers at Elizabeth’s court in London who pushed hard for the introduction of the new cartography into England were Sir Francis Walsingham, principle secretary to Elizabeth, and William Cecil, 1stBaron Burghley, Elizabeth’s chief advisor, both of whom were Dee’s, somewhat unreliable, patrons at court.


Engraving of Queen Elizabeth I, William Cecil and Sir Francis Walsingham, by William Faithorne, 1655 Source: Wikimedia Commons

Their motivations for supporting the development of cartography were political and derived from military and commercial considerations and not academic or scientific ones. The same applies, of course to the general developments in cartography in the Early Modern Period throughout Europe. Burghley, the main driving force behind a new English cartography, possessed a self made atlas of manuscript maps from various sources that he is said to have always carried with him. Burghley’s atlas has survived and is now in the British Library.


William Cecil, 1st Baron Burghley from NPG artist unkown Source: Wikimedia Commons

Burghley saw the necessity, on political grounds, of organising and financing a new, modern map of the British Isles. The first cartographer, who appears to have received a commission to map Britain from Burghley, was John Rudd (c. 1498–1597). In 1561 Rudd, a graduate of Clare College and a fellow of St. John’s Cambridge, was granted a two-year paid leave of absence from his various positions in the Church of England in order to travel the country with the objective of mapping England. It is not know if Rudd fulfilled his objective, as no map of England can with certainty be assigned to him. However, it has been speculated that his work was a source for the new map of Britain published by Mercator in his atlas. Several of the maps in Burghley’s handmade atlas are attributed to Rudd.


This is a manuscript map of County Durham. It forms part of an atlas that belonged to William Cecil Lord Burghley, Elizabeth I’s Secretary of State. Burghley used this atlas to illustrate domestic matters. The map dates from 1569 and is by John Rudd, the man to whom Christopher Saxton was an apprentice to in 1570. Source: British Library

In his work Rudd employed Christopher Saxon (c. 1540–c.1610) as an assistant and taught him the art of surveying. Born in the West Riding of Yorkshire in 1542 or 1544 very little is known about Saxton’s childhood, although his employment by Rudd is confirmed by documents. On Burghley’s instructions Thomas Seckford, Master in Ordinary of the Court of Request at Elizabeth’s Court,


Thomas Seckford Source: East Anglian Times

commissioned Christopher Saxton in 1573 to survey all the English counties and produce an atlas of the realm. It is not certain what motivated Burghley to act at this time but it might have been the publication of Ortelius’ Theatrum orbis terrarumin 1570, which was much admired in England, and/or Philipp Apian’s Bairischen Landtafeln from 1566

The survey of England began in 1574 and of Wales in 1577; it was completed in 1578. The individual maps were engraved as soon as finished and the proofs sent to Burghley.

Saxton1 map England Royal MS 18 D lll no 5

Saxton England and Wales proof map Source: British Library

In 1579 the maps were bound together and publish as a book for which Saxton received ten-year exclusive publication rights from the crown.


Frontispiece Saxton The Counties of England and Wales Source: My facsimile copy

Although we now refer to Saxton’s book as an atlas at the time Mercator’s coining of the term still lay sixteen years in the future. It is not known how Saxton did his surveying work but the speed with which he completed the task and the general level of accuracy of his maps would suggest two things. Firstly that he had access to previous data, possibly from Rudd’s work amongst others, and secondly that he used triangulation in some form. The nationwide chain of beacons set up by the government to warn of a Spanish invasion from the Netherlands in 1567 would have provided him with a useful set of predetermined triangulation points. The pass issued by the Privey Council on 10 July 1576 for his survey of Wales also strongly suggests triangulation as his survey method.

An open Lettre to all Justices of peace mayours & others etc within the severall Shieres of Wales. That where the bearer hereof Christofer Saxton is appointed by her Maiestie vnder her signe and signet to set forth and describe Coates [Cartes] in particulerlie all the shieres in Wales. That the said Justices shalbe aiding and assisting vnto him to see him conducted vnto any towre Castle highe place or hill to view that country, and that he maybe accompanied with ij or iij honest men such as do best know the cuntrey for the best accomplishment of that service, and that at his departure from any towne or place that he hath taken the view of said towne do set forth a horseman that speak both welshe and englishe to safe conduct to the next market Towne, etc

“…any towre Castle highe place or hill to view that country…” strongly suggests triangulation.

There are 35 maps, each bearing the arms of the Queen and Thomas Seckford. Drawn by Saxton the maps were engraved by Augustine Ryther (5 maps) the only engraver who clearly identifies as English, Remigius Hogenberg (9 maps),Leonard Terwoort of Antwerp (5 maps), Cornelius Hogius (1 map), Johannes Rutlinger (1 map) all four of whom were Flemish, Francis Scatter (2 maps), Nicholas Reynold (1 maps) are both of uncertain origin. Of the remaining unsigned maps five are definitely engraved in the Flemish style. In general there are clearly Flemish elements in the style of all the maps.

It is not known for certain when John Dee and Christopher Saxton became acquainted and whether Dee had an influence on Saxton, but when Dee, as Warden of Christ’s College, Manchester (1595–1605), became involved in a boundary dispute he employed Saxton as his surveyor to settle the argument.

Although it sold well, Saxton’s atlas was not without its critics. Although some counties are presented on separate maps others are grouped together on one map. For example the 13 Welsh counties are presented on 7 maps or Kent, Sussex, Surry, Middlesex and London are all on one map. Because of the pages are uniform in size the map scales vary considerably. Also although the maps initially appear homogeneous the symbols used vary considerably from map to map, even between maps engraved by the same engraver.  None of Saxton’s maps have roads. All of these imperfections led to various attempts to improve on Saxton’s work.

The first of these was John Norden (c. 1547–1625), who started a series of county histories, each accompanied by a map, entitled Speculum Britanniae.


John Norden Source

The first volume Speculum Britanniae: the First Parte: an Historicall, & Chorographicall Discription of Middlesexwas published in 1593. The manuscript is in the British Library with corrections in Burghley’s handwriting, which points to Burghley being Norden’s sponsor. 1595 he wrote a manuscript “Chorographical Description” of Middlesex, Essex,Surry,Sussex,Hampshire, Wight, Guernsey andJersey, dedicated to Queen Elizabeth. In 1596 he published his Preparative to the Speculum Britanniae, dedicated to Burghley. The only other volume published by Norden was Speculi Britaniae Pars: the Description of Hartfordshirein 1598. He completed accounts of five other counties in manuscript of which three were published posthumously in 1720, 1728 and 1840. It was probably Burghley’s death in 1598 that put an end to Norden’s project.


John Norden’s map of Essex 1595 Source: British Library

The next attempt was undertaken by a friend and colleague of Norden’s, William Smith (c.1550–1618), antiquarian and Rouge Dragon at the College of Heralds. Unlike Norden, who had never left England, Smith spent five years living in Nürnberg, a major cartographical centre. In 1588 Smith completed The Particuler Description of England With The Portratures of Certaine the Chieffest Citties and Townes. Between 1602 and 1603 Smith anonymously published maps of Chester, Essex, Hertfordshire, Lancashire, Leicester, Norfolk Northamptonshire, Staffordshire, Suffolk, Surry, Warwickshire and Worcester probably engraved in Amsterdam and intended as sheets for a new atlas. Smith’s maps contain the roads missing from Saxton’s maps. It is thought that Smith abandoned his atlas project because of competition from John Speed (1551 or 52–1629)


William Smith map of Lancashire 1598 Source: British Library

Speed born in Farndon, Cheshire followed his father into the tailoring business. Moving to London he became a Freeman of the Merchant Taylor’s Guild, who devoted his free time to cartography.


John Speed Source: My facsimile copy

This activity attracted the attention of Sir Fulke Greville, 1stBaron Brooke (1554–1628) a leading Elizabethan statesman, who secured him a position at the Customs and with the support of the Queen, subsidized his map making.


Fulke Greville, 1st Baron Brooke Portrait by Edmund Lodge Source: Wikimedia Commons

A member of the society of Antiquities he became friends with such people as the historian William Camden (1551–1623) and the cartographer William Smith, who assisted him with his research. Speed published his atlas, The Theatre of the Empire of Great Britaine, which was dated 1611 in 1612. He regarded it as a supplement to his Historie of Great Britainepublished in 1611. The use of the word theatre in the title reflects the influence of Ortelius, whose own The Theatre of the World was published in English in 1606. The Empire of Great Britain is a term introduced by John Dee.


Speed title page Source: My facsimile copy

Whereas Christopher Saxton was a trained surveyor, who went out surveyed and drew his own maps, John Speed was a compiler who took his maps from various sources, including Saxton, and merely redrew them to a homogenous standard. Apart from Saxton (5 maps), Speed credits maps from John Norden (5), William Smith (2) and individual maps from Philip Symonson, John Harrington, William White, Thomas Durham and James Burrell. His maps of Wales are obviously based on Saxton’s although he doesn’t credit him. His of Ireland, which Saxton did not include in his atlas, are based on the work of Robert Lythe and Robert Jobson. However although not by him he doesn’t credit the majority of his maps. All of Speed’s maps were engraved by the Dutch engraver, Jodocus Hondius (1563–1612), who was himself one of the leading European cartographers and globe makers.

Obviously inspired by Saxton’s work Speed’s Theatre differs in that he includes Ireland and Scotland, both missing by Saxton. He gives each county a separate map and although he cannot reproduce them all to the same scale, due to page size, Like Saxton he includes a scale bar on each map. However, it is not known what length for the mile Speed used. His symbols are uniform through the entire book and on the back of each map sheet he includes topographical, administrative and historical comments. The margins of the maps often include the arms of the leading families or other informative historical drawings and following William Smith he includes plans and maps of the principle towns and cities. Speed’s Theatre is altogether a much more attractive and informative work than Saxton’s atlas even though it very clearly owes it existence to the earlier pioneering work, so it is fair to speak of a Saxon/Speed presentation of the counties of Britain.



The Eastern half of Saxton’s map of Essex (above) Speed’s version of the same (below ) to illustrate the similarities and the differences. The place where I spent the first fifteen years of my life, Thorp (now Thorpe-le-Soken) is roughly in the middle of the Tendering Hundred in the North-East corner of the county. Going south from there Little Clacton and Great Clacton are both marked but my birthplace on the coast, Clacton-on-Sea, obviously didn’t exist yet when the maps were drawn. Speed’s map contains a plan of the town of Colchester, “Britain’s oldest town”, where I went to school.

Unlike the Netherlands, where the fierce competition between the houses of Blaeu and Hondius led to ever better, ever more spectacular atlases and globes throughout the seventeenth century, following the publication of Speed’s Theatre, cartography on that scale ceased almost entirely in Britain. This meant that Speed’s Theatreremained the standard cartographical work in Britain for more than one hundred years. The burst of cartographical activity between Rudd and Speed remained a bubble rather than the start of tradition, as Gemma Frisius’, Abraham Ortelius’ and Gerard Mercator’s work had become in the Netherlands.












1 Comment

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

A sixteenth century bestseller by an amateur cosmographer

Sebastian Münster, who with his Cosmographia wrote and published what was probably the biggestselling book in the sixteenth century, was actually a professor for Hebrew by profession and only a passionate cosmographer in his free time. Born in Ingelheim am Rhein 20 January 1488 as the son of Endres Münster a churchwarden and master of the church hospital.


Sebastian Münster portrait by Christoph Amberger c. 1550 Source: Wikimedia Commons


Münster’s birthplace Ingelheim from the Cosmographia Source: Wikimedia Commons

He studied at a Franciscan school and entered the Order in 1505. In 1507 he was sent to Löwen and then Freiburg im Breisgau, where he studied under Gregor Reisch (c. 1467–1525), author of the well known encyclopaedic student textbook the Margarita Philosophica, in particular geography and Hebrew.


Ptolemeus and Astronomia from Gregor Reisch’s Margarita Philosophica Source: Wikimedia Commons

In 1509 he became a pupil of the humanist scholar Konrad Pelikan (1478–1556), who over the next five years taught him Hebrew, Greek, mathematics, and cosmography. In 1512 he was anointed a priest. Pelikan and Münster expanded their studies to include other Semitic languages, in particular Aramaic and Ethiopian.


Konrad Pelikan Source: Wikimedia Commons

From 1514 to 1518 he taught at the Franciscan high school in Tübingen. Parallel to his teaching he studied astrology, mathematics and cosmography under Johannes Stöffler. From 1518 he taught at the Franciscan high school in Basel and from 1521 to 1529 at the University of Heidelberg. In 1529 he left the Franciscan Order and became professor for Hebrew at the University of Basel as Pelikan’s successor, converting to Protestantism. In 1530 he married Anna Selber the widow of the printer/publisher Adam Petri, the cousin and printing teacher of Johannes Petreius. As a Hebraist he published extensively on language, theology and the Bible but it is his work as a cosmographer that interest us here. All of his books were published by his stepson Heinrich Petri.

In 1528 he published a pamphlet entitled Erklärung des neuen Instruments der Sunnen(Explanation of a new instrument of the Sun) in which he issued the following request, Let everyone lend a hand to complete a work in which shall be reflected…the entire land of Germany with all its territories, cities, towns, villages, distinguished castles and monasteries, its mountains, forests, rivers, lakes, and its products, as well as the characteristics and customs of its people, the noteworthy events that have happened and the antiquities which are still found in many places. He gave his readers instructions on how to record an area cartographically from a given point. This is the earliest indication of Münster’s intension to create a full geographical description of the German Empire. This first appeal proved in vain; it would be another sixteen years before he realised this high ambition. Münster satisfied himself with the publication of a small pamphlet Germaniae descriptioin 1530 based on a revised edition of a map of Middle Europe from Nicolaus Cusanus.

Turning his attention to ancient Greek geography Münster published Latin editions of Solinus’ Polyhistorand Pomponius Mela’s De situ orbis. In 1532 Münster drew a world map for Simon Grynaeus’ and Johann Huttich’s popular travel book Novus Orbis Regionum(“New World Regions”, which described the journeys of famous explorers. The map in not particular innovative and does not go much further in its information than the 1507 Waldseemüller world map. However it does contain a border of fascinating illustrations thought to have been created by Hans Holbein, who in his youth had worked for the Petri publishing house.


Münster’s 1532 World Map

In 1540 Münster issued his edition of Ptolemaeus’ Geographia, which was based on the Latin translation by Willibald Pirckheimer. His edition entitled, Geographia universalis, vetus et nova(“Universal Geography, Old and New”) was the first work to contain separate maps for each of the then four continents. In total the work contain forty-six maps drawn by Münster. The world map in this work differs substantially from the one from 1532.


Münster’s map of America Source: Wikimedia Commons

Münster’s  magnum opus his Cosmographiaor to give it its full title:

Cosmographia. Beschreibung aller Lender durch Sebastianum Münsterum: in welcher begriffen aller Voelker, Herrschaften, Stetten, und namhafftiger Flecken, herkommen: Sitten, Gebreüch, Ordnung, Glauben, Secten und Hantierung durch die gantze Welt und fürnemlich Teütscher Nation (Getruckt zu Basel: durch Henrichum Petri 1544)


Cosmographia title page

finally appeared in 1544 with 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. Over the next eighty years the work was published in thirty-seven editions, in German (21), Latin (5), French (6), Italian (3), Czech (1) and English (1) (although the English edition is an incomplete translation). The work was continually revised and expanded, the 1544 original had 600 pages and the final edition from 1628 1800. The work was published in six volumes, which in the 1598 edition were as follows:

Book I: Astronomy, Mathematics, Physical Geography, Cartography

Book II: England, Scotland, Ireland, Spain, France, Belgium, The Netherlands, Luxembourg, Savoy, Trier, Italy

Book III: Germany, Alsace, Switzerland, Austria, Carniola, Istria, Bohemia, Moravia, Silesia, Pomerania, Prussia, Livland

Book IV: Denmark, Norway, Sweden, Finland, Iceland, Hungary, Poland, Lithuania, Russia, Walachia, Bosnia, Bulgaria, Serbia, Greece, Turkey

Book V: Asia Minor, Cyprus, Armenia, Palestine, Arabia, Persia, Central Asia, Afghanistan, Scythia, Tartary India, Ceylon, Burma, China, East Indies, Madagascar, Zanzibar, America

Book VI: Mauritania, Tunisia, Libya, Egypt, Senegal, Gambia, Mali, South Africa, East Africa


Town plan of Bordeaux from the Cosmographia Source: Wikimedia Commons

As indicated in his original call for cooperation, Münster’s Cosmographia was much more than a simple atlas mapping the world but was an integrated description combining geography, cartography, history and ethnography to create an encyclopaedic depiction of the known world.


Chartre under attack from the Cosmographia Source: Wikimedia Commons

In total at least 50,000 German copies and 10,000 Latin ones left the Petri printing house in Basel over the eight-four years the book was in print, making it probably the biggest selling book, with the exception of the Bible, in the sixteenth century. The Cosmographiaset new standards in ‘modern’ geography and cartography and paved the way for the Civitates Orbis Terrarumof Georg Braun and Frans Hogenberg in 1572, the TheatrumOrbis Terrarum from Abraham Ortelius from 1570 and Mercator’s Atlas from 1595. Despite the competition from the superior atlases of Ortelius and Mercator, the Cosmographiasold well up to the final edition of 1628.

Münster’s Cosmographiais without a doubt a milestone in the evolution of modern cartography and geography and he deserves to be better known than he is. Bizarrely, although they mostly aren’t aware of it, Germans of a certain age are well aware of what Münster looks like, as his portrait was used for the 100 DM banknote from 1961 to 1995, when he was replaced by Clara Schumann.


Source: Wikimedia Commons



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

The Bees of Ingolstadt

The tittle of this blog post is a play on the names of a father and son duo of influential sixteenth century Renaissance mathematici. The father was Peter Bienewitz born 16 April 1495 in Leisnig in Saxony just south of Leipzig. His father was a well off shoemaker and Peter was educated at the Latin school in Rochlitz and then from 1516 to 1519 at the University of Liepzig. It was here that he acquired the humanist name Apianus from Apis the Latin for a bee, a direct translation of the German Biene. From now on he became Petrus Apianus or simply Peter Apian.


Apianus on a 16th-century engraving by Theodor de Bry Source: Wikimedia Commons

In 1519 he went south to the University of Vienna to study under Georg Tannstetter a leading cosmographer of the period.


Georg Tannstetter Portrait ca. 1515, by Bernhard Strigel (1460 – 1528) Source: Wikimedia Commons

Tannstetter was a physician, mathematician astronomer and cartographer, who studied mathematics at the University of Ingolstadt under Andreas Stiborius and followed Conrad Celtis and Stiborius to Vienna in 1503 to teach at Celtis’ Collegium poetarum et mathematicorum. The relationship between teacher and student was a very close one. Tannstetter edited a map of Hungary that was later printed by Apian and the two of them produced the first printed edition of Witelo’s Perspectiva, which was printed and published by Petreius in Nürnberg in 1535. This was one of the books that Rheticus took with him to Frombork as a gift for Copernicus.

In 1520 Apian published a smaller updated version of the Waldseemüller/ Ringmann world map, which like the original from 1507 named the newly discovered fourth continent, America. Waldseemüller and Ringmann had realised their original error and on their 1513 Carte Marina dropped the name America, However, the use by Apian and by Johannes Schöner on his 1515 terrestrial globe meant that the name became established.


Apian’s copy of the Waldseemüller world map, naming the new fourth continent America Source: Wikimedia Commons

Apian graduated BA in 1521 and moved first to Regensburg then Landshut. In 1524 he printed and published his Cosmographicus liber, a book covering the full spectrum of cosmography – astronomy, cartography, navigation, surveying etc. The book became a sixteenth century best seller going through 30 expanded editions in 14 languages but after the first edition all subsequent editions were written by Gemma Frisius.


Title page of Apian’s Cosmpgraphia

In 1527 Apian was called to the University of Ingolstadt to set up a university printing shop and to become Lektor for mathematics. He maintained both positions until his death in 1552.

In 1528 he printed Tannstetter’s Tabula Hungariaethe earliest surviving printed map of Hungary. In the same year Apian dedicated his edition of Georg von Peuerbach’s New Planetary Theory to his “famous teacher and professor for mathematics” Tannstetter.


Tabula Hungarie ad quatuor latera Source: Wikimedia Commons

One year earlier he published a book on commercial arithmetic, Ein newe und wolgegründete underweisung aller Kauffmanns Rechnung in dreyen Büchern, mit schönen Regeln und fragstücken begriffen(A new and well-founded instruction in all Merchants Reckoning in three books, understood with fine rules and exercises). It was the first European book to include (on the cover), what is know as Pascal’s triangle, which was known earlier to both Chinese and Muslim mathematicians.


This is one of the volumes lying on the shelf in Holbein’s painting The Ambassadors. Like his Cosmographicusit was a bestseller.

In the 1530s Apian was one of a group of European astronomers, which included Schöner, Copernicus, Fracastoro and Pena, who closely observed the comets of that decade and began to question the Aristotelian theory that comets are sublunar meteorological phenomena. He was the first European to observe and publish that the comet’s tail always points away from the sun, a fact already known to Chinese astronomers. Fracastoro made the same observation, which led him and Pena to hypothesise that the comet’s tail was an optical phenomenon, sunlight focused through the lens like translucent body of the comet. These observations in the 1530s led to an increased interest in cometary observation and the determination in the 1570s by Mästlin, Tycho and others that comets are in fact supralunar objects.


Diagram by Peter Apian from his book Astronomicum Caesareum (1540) demonstrating that a comet’s tail points away from the Sun. The comet he depicted was that of 1531, which we now know as Halley’s Comet. Image courtesy Royal Astronomical Society.

Through the Cosmographicus he became a favourite of Karl V, the Holy Roman Emperor, and Apian became the Emperor’s astronomy tutor. Karl granted him the right to display a coat of arms in 1535 and knighted him in 1541. In 1544 Karl even appointed him Hofpfalzgraf (Imperial Count Palatine), a high ranking court official.

Apian’s association with Karl led to his most spectacular printing project, one of the most complicated and most beautiful books published in the sixteenth century, his Astronomicum Caesareum (1540). This extraordinary book is a presentation of the then Standard Ptolemaic astronomy in the form of a series of highly complex and beautifully designed volvelles. A vovelle or wheel chart is a form of paper analogue computer. A series of rotating paper discs mounted on a central axis or pin that can be used to calculate various mathematical functions such as the orbital positions of planets.


Astronomicum Caesareum title page

The Astronomicum Caesareumcontains two volvelles for each planet, one to calculate its longitude for a given time and one to calculate its latitude.


Astronomicum Caesareum volvelle for longitude for Saturn


Astronomicum Caesareum volvelle for the latitude for Saturn

There is also a calendar disc to determine the days of the week for a given year.


Astronomicum Caesareum calendar volvelle

Finally there are vovelles to determine the lunar phases  as well as lunar and solar eclipse.


Astronomicum Caesareum : Disc illustrating a total eclipse of the moon 6 Octobre 1530


Astronomicum Caesareum solar eclisse volvelle

Johannes Kepler was very rude about the Astronomicum Caesareum, calling it a thing of string and paper. Some have interpreted this as meaning that it had little impact. However, I think the reverse is true. Kepler was trying to diminish the status of a serious rival to his endeavours to promote the heliocentric system. Owen Gingerich carried out a census of 111 of the approximately 130 surviving copies of the book and thinks that these represent almost the whole print run. This book is so spectacular and so expensive that the copies rarely got seriously damaged of thrown away.

Like other contemporary mathematici Apian designed sundials and astronomical instruments as well as marketing diverse volvelles for calculation purposes. Apian died in 1552 and was succeeded on his chair for mathematics by his son Philipp, the second of the bees from Ingolstadt.

Philipp Apian was born 14 September 1531, as the fourth of fourteen children (nine sons and five daughters) to Peter Apian and his wife Katharina Mesner.


Philipp Apian painting by Hans Ulrich Alt Source: Wikimedia Commons

He started receiving tuition at the age of seven together with Prince Albrecht the future Duke of Bavaria, who would become his most important patron.


Duke Albrecht V of Bavaria Hans Muelich Source: Wikimedia Commons

He entered the University of Ingolstadt at the age of fourteen and studied under his father until he was eighteen. He completed his studies in Burgundy, Paris and Bourges. In 1552 aged just 21 he inherited his fathers printing business and his chair for mathematics on the University of Ingolstadt. As well as teaching mathematics at the university, which he had started before his father died, Philipp studied medicine. He graduated in medicine several years later during a journey to Italy, where he visited the universities of Padua, Ferrara and Bolgna.

In 1554 his former childhood friend Albrecht, now Duke of Bavaria, commissioned him to produce a new map of Bavaria. During the summers of the next seven years he surveyed the land and spent the following two years drawing the map. The 5 metres by 6 metres map at the scale of 1:45,000, hand coloured by Bartel Refinger was hung in the library of the Bavarian palace.


Philipp Apian’s map of Bavaria

In 1566 Jost Amman produced 24 woodblocks at the smaller scale of 1:144,000, which Apian printed in his own print shop. Editions of this smaller version of the map continued to be issued up to the nineteenth century.


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

In 1576 he also produced a terrestrial globe for Albrecht. Map, woodblocks, woodblock prints and globe are all still extant.


Apian’s terrestrial globe

In 1568 Phillip converted to Protestantism and in the following year was forced by the Jesuit, who controlled the University of Ingolstadt to resign his post. In the same year, he was appointed professor for mathematics at the Protestant University of Tübingen. In Tübingen his most famous pupil was Michael Mästlin, who succeeded him as professor for mathematics at the university and would become Johannes Kepler’s teacher. An irony of history is that Philipp was forced to resign in Tübingen in 1583 for refusing to sign the Formal of Concord, a commitment to Lutheran Protestantism against Calvinism. He continued to work as a cartographer until his death in 1589.

There is a genealogy of significant Southern German Renaissance mathematici: Andreas Stiborius (1464–1515) taught Georg Tannstetter (1482–1535), who taught Peter Apian (1495–1552), who taught Philipp Apian (1531–1589), who taught Michael Mästlin (1550–1631), who taught Johannes Kepler (1571–1630)













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

Spicing up the evolution of the mathematical sciences

When we talk about the history of mathematics one thing that often gets forgotten is that from its beginnings right up to the latter part of the Early Modern Period almost all mathematics was developed to serve a particular practical function. For example, according to Greek legend geometry was first developed by the ancient Egyptians to measure (…metry) plots of land (geo…) following the annual Nile floods. Trade has always played a very central role in the development of mathematics, the weights and measures used to quantify the goods traded, the conversion rates of different currencies used by long distance traders, the calculation of final prices, taxes, surcharges etc. etc. A good historical example of this is the Islamic adoption of the Hindu place value decimal number system together with the associated arithmetic and algebra for use in trade, mirrored by the same adoption some time later by the Europeans through the trader Leonardo Pisano. In what follows I want to sketch the indirect impact that the spice trade had on the evolution of the mathematical sciences in Europe during the Renaissance.

The spice trade does not begin in the Renaissance and in fact had a long prehistory going back into antiquity. Both the ancient Egyptians and the Romans had extensive trade in spices from India and the Spice Islands, as indeed the ancient Chinese also did coming from the other direction.


The spice trade from India attracted the attention of the Ptolemaic dynasty, and subsequently the Roman empire. Source: Wikimedia Commons

Throughout history spice meant a much wider range of edible, medicinal, ritual and cosmetic products than our current usage and this trade was high volume and financially very rewarding. The Romans brought spices from India across the Indian Ocean themselves but by the Middle Ages that trade was dominated by the Arabs who brought the spices to the east coast of Africa and to the lands at the eastern end of the Mediterranean, known as the Levant; a second trade route existed overland from China to the Levant, the much fabled Silk Road. The Republic of Venice dominated the transfer of spices from the Levant into Europe, shipping them along the Mediterranean.


The economically important Silk Road (red) and spice trade routes (blue) blocked by the Ottoman Empire c. 1453 with the fall of the Byzantine Empire, spurring exploration motivated initially by the finding of a sea route around Africa and triggering the Age of Discovery. Source: Wikimedia Commons

Here I go local because it was Nürnberg, almost literally at the centre of Europe, whose traders collected the spices in Venice and distributed them throughout Europe. As Europe’s premier spice traders the Nürnberger Patrizier (from the Latin patrician), as they called themselves, grew very rich and looking for other investment possibilities bought up the metal ore mines in central Europe. In a short period of time they went from selling metal ore, to smelting the ore themselves and selling the metal, to working the metal and selling the finished products; each step producing more profit. They quite literally produced anything that could be made of metal from sewing needles to suits of armour. Scientific and mathematical instruments are also largely made of metal and so Nürnberg became Europe’s main centre for the manufacture of mathematical instruments in the Renaissance. The line from spice to mathematical instruments in Nürnberg is a straight one.


Torquetum designed by Johannes Praetorius and made in Nürnberg

By the middle of the fifteenth century the Levant had become a part of the Ottoman Empire, which now effectively controlled the flow of spices into Europe and put the screws on the prices. The Europeans needed to find an alternative way to acquire the much-desired products of India and the Spice Islands, cutting out the middlemen. This need led to the so-called age of discovery, which might more appropriately be called the age of international sea trade. The most desirable and profitable trade goods being those spices.

The Portuguese set out navigating their way down the west coast of Africa and in 1488 Bartolomeu Dias succeeded in rounding the southern most tip of Africa and entering the Indian Ocean.


Statue of Bartolomeu Dias at the High Commission of South Africa in London. Source: Wikimedia Commons

This showed that contrary to the Ptolemaic world maps the Indian Ocean was not an inland sea but that it could be entered from the south opening up a direct sea route to India and the Spice Islands.


A printed map from the 15th century depicting Ptolemy’s description of the Ecumene, (1482, Johannes Schnitzer, engraver). Showing the Indian Ocean bordered by land from the south Source: Wikimedia Commons

In 1497 Vasco da Gama took that advantage of this new knowledge and sailed around the Cape, up the east coast of Africa and then crossing the Indian Ocean to Goa; the final part of the journey only being made possible with the assistance of an Arab navigator.


The route followed in Vasco da Gama’s first voyage (1497–1499) Source: Wikimedia Commons

Famously, Christopher Columbus mistakenly believed that it would be simpler to sail west across, what he thought was, an open ocean to Japan and from there to the Spice Islands. So, as we all learn in school, he set out to do just that in 1492.

In fourteen hundred and ninety two

Columbus sailed the ocean blue.

The distance was of course much greater than he had calculated and when, what is now called, America had not been in the way he and his crews would almost certainly have all died of hunger somewhere out on the open seas.


Columbus’ voyage. Modern place names in black, Columbus’s place names in blue Source: Wikimedia Commons

The Portuguese would go on over the next two decades to conquer the Spice Islands setting up a period of extreme wealth for themselves. Meanwhile, the Spanish after the initial disappointment of realising that they had after all not reached Asia and the source of the spices began to exploit the gold and silver of South America, as well as the new, previously unknown spices, most famously chilli, that they found there. In the following centuries, eager also to cash in on the spice wealth, the English and French pushed out the Portuguese in India and the Dutch did the same in the Spice Islands themselves. The efforts to establish sea borne trading routes to Asia did not stop there. Much time, effort and money was expended by the Europeans in attempts to find the North West and North East Passages around the north of Canada and the north of Russia respectively; these efforts often failed spectacularly.

So, you might by now be asking, what does all this have to do with the evolution of the mathematical science as announced in the title? When those first Portuguese and Spanish expedition set out their knowledge of navigation and cartography was to say the least very rudimentary. These various attempts to reach Asia and the subsequent exploration of the Americas led to an increased effort to improve just those two areas of knowledge both of which are heavily based on mathematics. This had the knock on effect of attempts to improve astronomy on which both navigation and cartography depend. It is not chance or coincidence that the so-called age of discovery is also the period in which modern astronomy, navigation and cartography came of age. Long distance sea trading drove the developments in those mathematically based disciplines.

This is not something that happened overnight but there is a steady curve of improvement in this disciplines that can be observed over the two plus centuries that followed Dias’ first rounding of the Cape. New instruments to help determine latitude and later longitude such as mariners’ astrolabe (which is not really an astrolabe, around 1500) the backstaff (John Davis, 1594) and the Hadley quadrant (later sextant, 1731) were developed. The Gunter Scale or Gunter Rule, a straight edge with various logarithmic and trigonometrical scales, which together with a pair of compasses was used for cartographical calculations (Edmund Gunter, early seventeenth century). William Oughtred would go on to lay two Gunter Scales on each other and invent the slide rule, also used by navigators and cartographers to make calculations.

New surveying instruments such as the surveyor’s chain (also Edmund Gunter), the theodolite (Gregorius Reisch and Martin Waldseemüller independently of each other but both in 1512) and the plane table (various possible inventors, middle of the sixteenth century). Perhaps the most important development in both surveying and cartography being triangulation, first described in print by Gemma Frisius in 1533.

Cartography developed steadily throughout the sixteenth century with cartographers adding the new discoveries and new knowledge to their world maps (for example the legendary Waldseemüller world map naming America) and searching for new ways to project the three-dimensional earth globe onto two-dimensional maps. An early example being the Stabius-Werner cordiform projection used by Peter Apian, Oronce Fine and Mercator.


Cordiform projection in a map of the world by Apianus 1524 which is one of the earliest maps that shows America Source: Wikimedia Commons

This development eventually leading to the Mercator-Wright projection, a projection specifically designed for marine navigators based on Pedro Nunes discovery that a path of constant bearing is not a great circle but a spiral, known as a loxodrome or rhumb line. Nunes is just one example of a mathematical practitioner, who was appointed to an official position to develop and teach new methods of navigation and cartography to mariners, others were John Dee and Thomas Harriot.


Pedro Nunes was professor of mathematics at the University of Coimbra and Royal Cosmographer to the Portuguese Crown. Source: Wikimedia Commons

To outline all of the developments in astronomy, navigation and cartography that were driven by the demands the so-called age of discovery, itself triggered by the European demand for Asian spices would turn this blog post into a book but I will just mention one last thing. In his one volume history of mathematics, Ivor Grattan-Guinness calls this period the age of trigonometry. The period saw a strong development in the use of trigonometry because this is the mathematical discipline most necessary for astronomy, navigation and cartography. One could say a demand for spices led to a demand for geometrical angles.



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

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

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

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

Portrait of Willem Janszoon Blaeu Artist unknown

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

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

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

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

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

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

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

Hondas celestial globe 1600
Source: Linda Hall Library

A matching pair of Blaeu globes

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

Source: Wikimedia Commons

Title page
Source: Wikimedia Commons

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

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

Jan Janszoon Original copperplate from his Atlas Novus 1647

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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






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

All at sea

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

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

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

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

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

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

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

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

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

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

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

Navigation: A Very Short Introduction page 50

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

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

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

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

The flyleaf of the Navigation volume contains the following quote:

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

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




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

One line to rule them all

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1 Comment

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