Category Archives: Early Scientific Publishing

Renaissance Science – XXI

One of the products of the Republic of Letters during the Humanist Renaissance was the beginning or the foundation of the modern European library. Naturally they didn’t invent libraries; the concept of the library goes back quite a long way into antiquity. To a great extent, libraries are a natural consequence of the invention of writing. When you have writing, then you have written documents. If you preserve those written documents then at some point you have a collection of written documents and when that collection becomes big enough, then you start to think about storage, sorting, classification, listing, cataloguing and you have created an archive or a library. I’m not going try and sort out the difference between an archive and a library and will from now on only use the term library, meaning a collection of books, without answering the question, what constitutes a book?

The oldest know libraries are the collections of clay tablets found in the temples of Sumer, some of which date back to the middle of the third millennium BCE. There were probably parallel developments in ancient Egypt but as papyrus doesn’t survive as well as clay tablets there is less surviving evidence for early Egyptian libraries. There is evidence of a library in the Sumerian city of Nippur around two thousand BCE and a library with a classification system in the Assyrian city of Nineveh around seven hundred BCE. The Library of Ashurbanipal in Nineveh contained more than thirty thousand clay tablets containing literary, religious, administrative, and scientific works. Other ancient cultures such as China and India also developed early libraries.

Library of Ashurbanipal Mesopotamia 1500-539 BC Gallery, British Museum, Source: Wikimedia Commons

The most well-known ancient library is the legendary Library of Alexandria, which is clouded in layers of myth. The library was part of the of the Mouseion, a large research institute, which was probably conceived by Ptolemy I Soter (c. 367–282 BCE) but first realised by his son Ptolemy II Philadelphus (309–246 BCE). Contrary to popular myth it was neither destroyed by Christian zealots nor by Muslim ones but suffered a steady decline over a number of centuries. For the full story read Tim O’Neill’s excellent blog post on the subject, which also deals with a number of the other myths. As Tim points out, Alexandria was by no means the only large library during this period, its biggest rival being the Library of Pergamum founded around the third century BCE. The Persian Empire is known to have had large libraries as did the Roman Empire.

Artistic rendering of the Library of Alexandria, based on some archaeological evidence Source: Wikimedia Commons

With the gradual decline of the Western Roman Empire, libraries disappeared out of Europe but continued to thrive in the Eastern Empire, the future Byzantium. The Islamic Empire became the major inheritor of the early written records of ancient Greece, Egypt, Persia, and Rome creating in turn their own libraries throughout their territories. These libraries became to source of the twelfth century translation movement, also known as the scientific renaissance, when those books first began to re-enter medieval Europe. 

During the Early Middle Ages, the only libraries still in existence in what had been the Western Roman Empire were those that existed in the Christian monasteries. Here we must once again dispose of two connected myths. The first more general one is the widespread myth that Christians deliberately destroyed pagan literature i.e., the texts of the Greeks and Romans. In fact, as Tim O’Neill points out in another excellent blog post, we have Christians to thank for those texts that did survive the general collapse of an urban civilisation. The second, closely related myth, spread by the “the Church is and always was anti-science brigade”, is that the Church deliberately abandoned Greek science because it was ant-Christian. Once again as Stephen McCluskey has documented in his excellent, Astronomies and Cultures in Early Medieval Europe, (CUP; 1998) it was the monasteries that keep the flame of the mathematical science burning during this period even if only on a low flame.

The manuscript collections of the medieval libraries were very small in comparison to the great Greek libraries such as Alexandria and Pergamum or the many public libraries of Rome, numbering in the best cases in the hundreds but often only in the tens. However, the guardians of these precious written documents did everything in their power to keep the books safe and in good condition and also endeavouring to acquire new manuscripts by copying those from other monastery libraries, often undertaking very arduous journeys to do so. 

Chained library in Hereford Cathedral Most of the books in the collection date to about 1100. Source: Wikimedia Commons

Things began to improve in the twelfth century with the scientific renaissance and the translation movement, which coincided with the founding of the European universities. The number of works available in manuscript increased substantially but they still had to be copied time and again to gradually spread throughout Europe. Like the monasteries the universities also began to collect books and to establish libraries but if we look at the figures for Cambridge University founded in 1209. The university library has its roots in the beginning of the fifteenth century, there would have been earlier individual college libraries earlier. The earliest surviving catalogue from c. 1424 list 122 volumes in the library. By 1473 a second catalogue lists 330 volumes. It is first in the sixteenth century that things really take off and the library begins to grow substantially. The equally famous Oxford University Bodleian Library was first founded in 1600 by the humanist scholar Thomas Bodley in 1600, replacing the earlier university library from 1444, which had been stripped and dissipated during the Reformation. 

Thomas Bodley Artist unknown Source: Wikimedia Commons 

We have of course now reached the Humanist Renaissance and it is here that the roots of the modern library were laid. The Humanist Renaissance was all about written texts. The humanists read texts, analysed the content of texts, annotated texts, translated texts, and applied philological analysis to texts to correct and/or eliminate errors introduced into texts by repeated copying and translations. The text was everything for the humanists, so they began to accumulate collections of manuscripts. Both humanist scholars and the various potentates, who sponsored the humanist movement began to create libraries, as new spaces of learning. 

The Malatestiana Library was founded by Malatesta Novello of Cesena (1418–1485) in 1454.

Malatestiana Library of Cesena, the first European civic library Source: Wikimedia Commons

The foundations of the Laurentian Library in Florence were laid by Cosimo de’ Medici (1389–1464), as one of a sequence of libraries that he funded.

Reading room of the Laurentian Library Source: Wikimedia Commons

Pope Nicholas V (1397–1455) brought the papal Greek and Latin collections together in separate libraries in Rome and they were then housed by Pope Sixtus IV (1414–1484), who appointed the humanist Bartolomeo Platina (1421–1481) librarian of the Bibliotheca Apostolica Vaticana.

Sixtus IV appointing Bartolomeo Platina librarian of the Bibliotheca Apostolica Vaticana. From left Giovanni della Rovere, Girolamo Riario, Bartolomeo Platina, later Julius II (Giuliano della Rovere), Raffaele Riario, Pope Sixtus IV Source: Wikimedia Commons

This was followed by the establishment of many private libraries both in Rome and in other Italian cities. As with other aspects of the Humanist Renaissance this movement spread outside of Italy to other European Countries. For example, the Bibliotheca Palatina was founded by Elector Ludwig III (1378–1436) in Heidelberg in the 1430s.

Elector Ludwig III. Contemporary image on the choir ceiling of the  Stiftskirche (Neustadt an der Weinstraße). Source: Wikimedia Commons

These new humanist libraries were not just book depositories but as stated above new spaces for learning. The groups of humanist scholars would meet regularly in the new libraries to discuss, debate or dispute over new texts, new translations, or new philological corrections to old, corrupted manuscripts. 

The (re)invention of movable type printing in about 1450 meant that libraries began to collect printed books as well as manuscripts. The first printer publishers in Italy concentrated on publishing the newly translated texts of the humanists even creating a new type face, Antiqua, which imitated the handwriting that had been developed and propagated by the first generations of humanist scholars. 

The spread of libraries during the Renaissance is a vast subject, too much to deal with in a blog post, but one can get a perspective on this development by looking at a sketch of the career of Johannes Müller (1436–1476) aka Regiomontanus or as he was known during his live time, Johannes de Monte Regio. 

Smithsonian “Print Artist: Braeht” (whereby the signature appears to be rather Brühl sculps[it] possibly Johann Benjamin Brühl (1691-1763) ) – Smithsonian Institution Libraries Digital Collection Source: Wikimedia Commons

Regiomontanus is, today, best known as the most significant European mathematician, astronomer, and astrologer of the fifteenth century, so it comes as something of a surprise to discover that he spent a substantial part of his life working as a librarian for various humanist book collectors. 

Regiomontanus graduated MA at the University of Vienna on his twenty-first birthday in 1457. He had actually completed the degree requirements much earlier, but university regulations required MA graduates to be at least twenty-one years old. He then joined his teacher Georg von Peuerbach as a teacher at the university, lecturing on optics amongst other things. Both Regiomontanus and Peuerbach were convinced humanists. In 1460 Basilios Bessarion (1403–1472) came to Vienna.

Basilios Bessarion Justus van Gent and Pedro Berruguete Source: Wikimedia Commons

He was a Greek Orthodox monk, who had converted to Catholicism, been elevated to Cardinal and was in Vienna as papal legate to negotiate with the Holy Roman Emperor Frederick III on behalf of Pope Pius II. Pius II, civil Aeneas Silvius Piccolomini (1405–1464), was a humanist scholar well acquainted with Frederick and Vienna from his own time as a papal legate. Bessarion, a Neo-Platonist, was a very active humanist, setting up and sponsoring humanist circles wherever his travels took him. In Vienna he sought out Peuerbach to persuade him to undertake a new Latin translation of Ptolemaeus’ Mathēmatikē Syntaxis from the original Greek. Peuerbach couldn’t read Greek but he, and after his death Regiomontanus, produced their Epitome of the Almagest, the story of which I have told elsewhere. Bessarion asked Peuerbach to return to Italy with him. Peuerbach agreed on the condition that Regiomontanus could also accompany them. Peuerbach died in 1461, so only Regiomontanus accompanied Bessarion back to Italy and it is here that his career as librarian began.

Bessarion was an avid book collector and Regiomontanus’ job in his personal entourage was to seek out and make copies of new manuscripts for Bessarion’s collection. A task that he fulfilled with esprit. Bessarion had in the meantime also taught him Greek. In 1468, Bessarion presented his personal library to the Senate of Venice in 1468 and the 482 Greek manuscripts and 264 Latin manuscripts today still form the core of the St. Mark’s Biblioteca Marciana.

Cardinal Bessarion’s letter to Doge Cristoforo Moro and the Senate of Venice, announcing the donation of his library. BNM Lat. XIV, 14 (= 4235), fol. 1r. Source: Wikimedia Commons

Regiomontanus left Bessarion’s entourage around 1465 and reappears in 1467 at the court of János Vitéz Archbishop of Esztergom (German, Gran) in Hungary. 

János Vitéz frontispiece of a manuscript Source: Wikimedia Commons

Vitéz, an old friend of Peuerbach, was a humanist scholar and an avid book collector. Although Regiomontanus served as court astrologer, his Tabulae Directionum, one of the most important Renaissance astrological texts was produced at Vitéz’s request, his main function at Vitéz’s court was as court librarian. From Esztergom he moved to the court of the Hungarian King, Matthias Corvinus (1443–1490), who had been educated by Vitéz.

Matthias Corvinus of Hungary portrait by Andrea Mantegna Source: Wikimedia Commons

Like his teacher, Corvinus was a humanist scholar and a major book collector. Once more, Regiomontanus served as a court librarian. The Bibliotheca Corviniana had become one of the largest libraries in Europe, second only to the Bibliotheca Apostolica Vaticana, when Corvinus died. Unfortunately, following his death, his library was dissipated. 

Long before Corvinus’ death, Regiomontanus had left Hungary for Nürnberg, with Corvinus’ blessing and a royal pension, to set up a programme to reform astronomy in order to improve astrological divination. During his travels, Regiomontanus had not only made copies of manuscripts for his patrons, but also for himself, so he arrived in Nürnberg with a large collection of manuscript in 1471. His aim was to set up a printing house and publish philologically corrected editions of a long list of Greek and Latin mathematical, astronomical, and astrological texts, which he advertised in a publisher’s list that he printed and published. Unfortunately, he died in 1476 having only published nine texts including his publishers list and to the shame of the city council of Nürnberg, his large manuscript collection was not housed in a library but dissipated. 

To close a last example of a lost and dissipated Renaissance library. The English mathematicus John Dee (1527–1609) hoped to establish a national library, but he failed to get the sponsorship he wished for.

John Dee artist unknown Source: Wikimedia Commons

Instead, he collected books and manuscripts in his own house in Mortlake, acquiring the largest library in England and one of the largest in Europe. In the humanist tradition, this became a research centre, with other scholars coming to Mortlake to consult the books and to discuss their research with Dee and other visitors. However, when Dee left England for the continent, in the 1580s with Edward Kelly, to try and find sponsors for his occult activities, his house was broken into, and his library pillaged and sold off. 

Despite the loss of some of the largest Renaissance book collections and libraries, the period saw the establishment of the library both public and private, as a centre for collecting books and a space for learning from them. 

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Filed under Book History, Early Scientific Publishing, Renaissance Science

A seventeenth century Jesuit, who constructed his own monument and designed the first(?) ‘auto-mobile’.

One of the world’s great tourist attractions is the Imperial Observatory in Beijing.

Source: Top 12 Best Places to go visiting Beijing

The man, who rebuilt it in its current impressive form was the seventeenth century Jesuit mathematician, astronomer, and engineer Ferdinand Verbiest (1623–1688).

Ferdinand Verbiest artist unknown Source: Wikimedia Commons

I have no idea how many Jesuits took part in the Chines mission in the seventeenth century[1]. A mission that is historically important because of the amount of cultural, scientific, and technological information that flowed between Europe and China in both directions. But Jean-Baptiste Du Halde’s print of the Jesuit Mission to China only shows the three most important missionaries, Matteo Ricci Johann Adam Schall von Bell and Ferdinand Verbiest.

Jesuit Mission to China, left to right  Matteo Ricci, Johann Adam Schall von Bell, Ferdinand Verbiest Source: Wikimedia

I have already written blog posts about Ricci and Schall von Bell and here, I complete the trilogy with a sketch of the life story of Ferdinand Verbiest and how, as the title states, he came to build his own monument in the form of one of the most splendid, surviving, seventeenth-century observatories. 

Ferdinand Verbiest was born 9 October 1623 in Pittem, a village about 25 km south of Bruges in the Spanish Netherlands, the fourth of seven children of the bailiff and tax collector, Judocus Verbiest and his wife Ann van Hecke. Initially educated in the village school, in 1635 was sent to school in Bruges. In 1636 he moved onto the Jesuit College in Kortrijk. In 1641 he matriculated in Lily College of the University of Leuven, the liberal arts faculty of the university. He entered the Society of Jesus 2 September 1641 and transferred to Mechelen for the next two years. In 1643 he returned to the University of Leuven for two years, where he had the luck to study mathematics under Andrea Tacquet (1612–1660) an excellent Jesuit mathematics pedagogue. 


In 1645, Verbiest became a mathematics teacher at the Jesuit College in Kortrijk, In the same year he applied to be sent to the Americas as a missionary, but his request was turned down.

One time Jesuit College now the Church of Saint Michael Kortrijk Source: Wikimedia Commons

In 1647 his third request was granted, and he was assigned to go to Mexico. However, in Spain the authorities refused him passage and he went instead to Brussels where he taught Greek and Latin from 1648 to 1652. He was now sent to the Gregorian University in Rome where he studied under Athanasius Kircher (1602–1680) and Gaspar Schott (1608–1666). In 1653, he was granted permission to become a missionary in the New Kingdom of Granada (now Columbia) but was first sent to Seville to complete his theological studies, which he did in 1655. Once again, the Spanish authorities refused him passage to the Americas, so he decided to go to China instead.

Whilst waiting for a passage to China he continued his studies of mathematics in Genoa. In 1656 he travelled to Lisbon; however, his plans were once again foiled when pirates hijacked the ship, he was due to sail on, whilst waiting for a new ship he taught mathematics at the Jesuit College in Coimbra. In 1657, he finally sailed from Lisbon eastwards with 37 missionaries of whom 17 were heading for China under the leadership of Martino Martini (1614–1661), a historian and cartographer of China, who provided the atlas of China for Joan Blaeu’s Atlas Maior, his Novus Atlas Sinensis.

Martino Martini Source: Wikimedia Commons
Frontpage of Novus Atlas sinensis, by Martino Martini, Amsterdam, 1655. Source: Wikimedia Commons

They arrived in Goa 30 January 1658 and sailed to Macao, which they reached 17 June. In the spring of 1659, now 37 years old, he finally entered China.

Verbiest was initially assigned to be a preacher in the Shaanxi province but in 1660 Johann Adam Schall von Bell (1591–1666), who was President of the Imperial Astronomical Institute and personal adviser to the Emperor Shunzhi (1638–1661), called him to Beijing to become his personal assistant. However, in 1664, following Shunzhi’s death in 1661, Schall von Bell fell foul of his political opponents at court and both he and Verbiest were thrown into jail. Because Schall von Bell had suffered a stroke, Verbiest functioned as his representative during the subsequent trial. Initially sentenced to death, they were pardoned and rehabilitated by the new young Kangxi Emperor Xuanye (1654–1722), Schall von Bell dying in 1666.  

Johann Adam Schall von Bell artist unknown Source: Wikimedia Commons

Yang Guangxian (1597–1669), Schall von Bell’s Chinese rival, took over the Directorship of the Imperial Observatory and the Presidency of the Imperial Astronomical Institute and although now free Verbiest had little influence at the court. However, he was able to demonstrate that Yang Guangxian’s calendar contained serious errors. Constructing an astronomical calendar, which was used for astrological and ritual purposes, was the principal function of the Imperial Astronomical Institute, so this was a serious problem. A contest was set up between Verbiest and Yang Guangxian to test their astronomical acumen, which Verbiest won with ease. Verbiest was appointed to replace Yang Guangxian in both of his positions and also became a personal advisor to the still young emperor.

Kangxi Emperor Xuanye (1654–1722) unknown artist Source: Wikimedia Commons

Verbiest tutored the Kangxi Emperor in geometry and a skilled linguist (he spoke Manchu, Latin, German, Dutch, Spanish, Italian, and Tartar) he translated the first six books of the Element of Euclid in Manchu for the Emperor. Matteo Ricci (1552–1610) together with Xu Guangqi (1562–1633) had translated them into Classical Chinese, the literal language of the educated elite, in 1607.

Matteo Ricci and Xu Guangqui (from Athanasius Kircher, China Illustrata, 1670). Source: Wikimedia Commons

Verbiest, like Schall von Bell before him, used his skills as an engineer to cast cannons for the imperial army,

A cannon made with technical guidance by Ferdinand Verbiest(Nan Huairen), in Hakozaki Shrine, Higashi Ward, Fukuoka City, Fukuoka, Japan. Source: Wikimedia Commons

but it was for the Imperial Observatory that he left his greatest mark as an engineer, when in 1673 he received the commission to rebuild it. 

Imperial Observatory Beijing Source: Wikimedia Commons

The Beijing Imperial Observatory was originally constructed in 1442 during the Ming dynasty. It was substantially reorganised by the Jesuits in 1644 but underwent its biggest restoration at the hands of Verbiest.

The emperor requested the priest to construct instruments like those of Europe, and in May, 1674, Verbiest was able to present him with six, made under his direction: a quadrant, six feet in radius; an azimuth compass, six feet in diameter; a sextant, eight feet in radius; a celestial globe, six feet in diameter; and two armillary spheres, zodiacal and equinoctial, each six feet in diameter. These large instruments, all of brass and with decorations which made them notable works of art, were, despite their weight, very easy to manipulate, and a credit to Verbiest’s mechanical skill as well as to his knowledge of astronomy and mathematics. They are still in a perfect state of preservation … Joseph Brucker, Ferdinand Verbiest, Catholic Encyclopedia (1913)

Childe, Thomas: Sternwarte, Peking. Observatory, Peking, c.1875. Terrace view. Source: Wikimedia Commons

Many secondary sources attribute the instrument designs to Verbiest

L0020841 Illustrations of astronomical instruments, Beijing, China Credit: Wellcome Library, London. via Wikimedia Commons

but they are, in fact, basically copies of the instruments that Tycho Brahe designed for his observatory on the island of Hven.

Tycho Brahe’s astronomical instruments from his Astronomiae instauratae progymnasmata 1572 Source:

The Jesuits were supporters of the Tychonic helio-geocentric model of the cosmos in the seventeenth century. Verbiest recreated Hven in Beijing.  

Ricci had already realised the utility of geography and cartography in gaining the interest and trust of the Chinese and using woodblocks had printed a world map with China in the centre, Kunyu Wanguo Quantu, at the request of the Wanli Emperor, Zhu Yijun, in 1602. He was assisted by the Mandarin Zhong Wentao and the technical translator Li Zhizao. It was the first western style Chinese map. 

Kunyu Wanguo Quantu Left panel Source Wikimedia Commons
Kunyu Wanguo Quantu Right panel Source: Wikimedia Commons

In 1674, Verbiest once again followed Ricci’s example and printed, using woodblocks, his own world map the Kunya Quantu, this time in the form of two hemispheres, with the Americas in the right-hand hemisphere and Asia, Africa, and Europe in the left-hand one, once again with China roughly at the centre where the two meet.

Kunyu Quantu Source: Wikimedia Commons

It was part of a larger geographical work the Kunyu tushuo as Joseph Brucker describes it in his Catholic Encyclopedia article (1907):

the map was part of a larger geographical work called ‘Kunyu tushuo’ (Illustrated Discussion of the Geography of the World), which included information on different lands as well as the physical map itself. Cartouches provide information on the size, climate, land-forms, customs and history of various parts of the world and details of natural phenomena such as eclipses and earthquakes.  Columbus’ discovery of America is also discussed.  Images of ships, real and imaginary animals and sea creatures pepper both hemispheres, creating a visually stunning as well as historically important object.

Due to his success at gaining access to the imperial court and the emperor, in 1677, Verbiest was appointed vice principle that is head of the Jesuit missions to China, a position that he held until his death.

Perhaps the most fascinating of all of Verbiest creations was his ‘auto-mobile’, which he built for Kangxi sometime tin the 1670s.

The steam ‘car’ designed by Verbiest in 1672 – from an 18th-century print Source: Wikimedia Commons

L. H. Weeks in his Automobile Biographies. An Account of the Lives and the Work of Those Who Have Been Identified with the Invention and Development of Self-Propelled Vehicles on the Common Roads (The Monograph Press, NY, 1904) describes it thus:

The Verbiest model was for a four-wheeled carriage, on which an aeolipile was mounted with a pan of burning coals beneath it. A jet of steam from the aeolipile impinged upon the vanes of a wheel on a vertical axle, the lower end of the spindle being geared to the front axle. An additional wheel, larger than the supporting wheels, was mounted on an adjustable arm in a manner to adapt the vehicle to moving in a circular path. Another orifice in the aeolipile was fitted with a reed, so that the steam going through it imitated the song of a bird.

The aeolipile was steam driving toy described in the Pneumatica of Hero of Alexandria and the De architectura of Vitruvius, both of which enjoyed great popularity in the sixteenth and seventeenth centuries in Europe. 

A modern replica of Hero’s aeolipile. Source: Wikimedia Commons

Having suffered a fall while out horse riding a year before, Verbiest died on 28 January 1688 and was buried with great ceremony in the same graveyard as Ricci and Schall von Bell. A man of great learning and talent he forged, for a time, a strong link between Europe and China. For example, Verbiest correspondence and publications were the source of much of Leibniz’s fascination with China. He was succeeded in his various positions by the Belgian Jesuits, mathematician and astronomer Antoine Thomas (1644–1709), whom he had called to Beijing to be his assistant in old age as Schall von Bell had called him three decades earlier. 

[1] According to research by David E. Mungello from 1552 (i.e., the death of St. Francis Xavier) to 1800, a total of 920 Jesuits participated in the China mission, of whom 314 were Portuguese, and 130 were French. Source: Wikipedia


Filed under Early Scientific Publishing, History of Astronomy, History of Mathematics, History of science

Renaissance Science – XVII

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

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

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

the Matthew Paris and Gough maps of Britain,

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

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

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

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

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

Macrobius zonal world map c. 1050 Source: British Library

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Oronce Fine World Map 1536 Source: Wikimedia Commons

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

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

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

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

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

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

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

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

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

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

Juan de la Cosa world map 1500

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

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

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

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

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

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

Waldseemüller globe gores of 1507 Source: Wikimedia Commons

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

Behaim Globe Germanisches Nationalmuseum Nürnberg

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

Schöner Terrestrial Globe 1515, Historisches Museum Frankfurt

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

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

Gemma Frisius globe 1536

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

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

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

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

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

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

Peter Apian cordiform world map 1530 Source: British Library

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

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

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

Saxton England and Wales proof map Source: British Library

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

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

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


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

Renaissance Science – XVI

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

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

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

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

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

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

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

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

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

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

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

Artist unknown Source: Wikimedia Commons

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


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

Willibald Pirckheimer portrait by Dürer Souce: Wikimedia Commons

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

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

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

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

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

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

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

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

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

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

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

Mercator the Frans Hogenberg portrait of 1574 Source: Wikimedia Commons

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

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

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


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

Renaissance Science – XII

There is a popular misconception that the emergence of modern science during the Renaissance, or proto-scientific revolution as we defined it in episode V of this series, and the scientific revolution proper includes a parallel rejection of the so-called occult sciences. Nothing could be further from the truth. This period sees a massive revival of all sorts of occult studies, covering a wide spectrum, we will look at this in more details in further episodes, but today I wish to deal with astrology. It is generally acknowledged that the period we know as the Renaissance was the golden age of astrology in Europe. There are multiple reasons for this rise of interest in and practice astrology in the period from roughly fourteen hundred and the middle of the seventeenth century.

As already explained in the previous episode, one reason for the rise in the status of the mathematical sciences during the Renaissance was the rise of astrological-medicine, or iatromathematics, within school medicine, something that we will look at in more detail when discussing Renaissance medicine. This rise in iatromathematics was, naturally, also a driving force in the increasing acceptance of astrology, but it was by no means the only one. This brings us to the important fact, that whereas most people on hearing the term astrology automatically think of natal astrology (also known as genethliacal astrology), that is birth horoscopes, but this is only one branch of the discipline and often in a given context not the most important one.

As well as natal astrology and iatromathematics there are also mundane astrology, electional astrology, horary astrology, locational astrology also called astrogeography, and meteorological astrology, each of which played a significant role in the world of astrology in the Renaissance. 

Mundane astrology is the application of astrology to world affairs and world events rather than to individuals and is generally acknowledged as the oldest form of astrology.

Electional astrology is the attempt to determine the most auspicious time to stage an event or undertake a venture, or even to show that no time would be auspicious for a given event of venture. The range of events or ventures can and did include, starting a war, or staging a battle, but also peaceful activities such as launching a diplomatic mission, simply going on a journey, or planning the date for an important, i.e., political, wedding.  

Horary astrology attempts to answer questions, interrogations, posed to the astrologer by casting a horoscope at the time that question is received and understood by the astrologer. The range of possible questions is entirely open, but few would waste the time of the astrologer or incur the costs that they might levy with trivial questions.

Locational astrology assumes that geographical locations play a specific role in astrological interpretation. For example, although time and latitude are the principle initial condition for casting a horoscope, two babies born at exactly the same time on the same day but in differing locations would have differing horoscopes, even if born at the same latitude, because of the influence of the geographical location.

Meteorological astrology, or astrometeorology, is the belief that the weather is caused by the position and motion of celestial objects, and it is therefor possible to predict or forecast the weather through astrological means.  

There are also special procedures such as lots of fortune and prorogation to determine special or important events in a subjects life, too detailed for this general survey. 

Mundane, natal, electional, horary and locational astrology are all grouped together under the term judicial astrology. Iatromathematics and astrometeorology are referred to as natural astrology. Those who objected to or rejected astrology, including at times the Catholic Church, usually rejected judicial astrology but accepted natural astrology as a branch of knowledge.

Western astrology has its origins in the omen astrology of the Babylonians, which was originally purely mundane astrology. Individual horoscope astrology emerged in Babylon around the sixth century BCE, and it was this that the ancient Greeks adopted and developed further. This is basically the astrology that was still in use in Renaissance Europe. After some reluctance the Romans adopted the Greek astrology and in the second century CE Ptolemaeus produced the most comprehensive text on the philosophy and practice of astrology, his Tetrabiblos, also known in Greek as Apotelesmatiká (Ἀποτελεσματικά) “Effects”, and in Latin as Quadripartitum. It should, however, be noted that this is by no means the only astrology text from antiquity. 

With the general collapse of learning in Europe in the Early Middle Ages from the fifth century onwards, astrology disappeared along with other scholarly disciplines. It was first revived by the Arabic, Islamic culture via the Persians in the eighth century. Arabic scholars developed and expanded the Greek astrology. Astrological texts were amongst the earliest ones translated into Arabic during the big translation movement in the eighth and ninth centuries. The same was true when European scholars began translating Arabic texts into Latin in the twelfth century. They translated both Greek and Arabic texts on astrology.

The Church could have rejected Greek astrology in the High Middle Ages as it was deterministic and as such contradicted the theological principle of free will, which is fundamental to Church doctrine. However, Albertus Magnus and Thomas Aquinas, who made Aristotelian philosophy acceptable to the Church also did the same for astrology reinterpreting it as contingent rather than determinist. By the thirteenth century all the forms of astrology had become established in Europe.

So, astrology in its various forms were well established in Europe in the High Middle Ages. This raises the question, why did it flourish and bloom during the Renaissance? As already stated above it was not just the rise of iatromathematics although this was a contributary factor.

One factor was the rise of the court astrologer, as a member of the retinue serving the ruler at court. Several Roman emperors had employed court astrologers, but the practice re-entered Europe in the Middle Ages via the Islamic culture. The Abbasid Caliphs, who started the major translation movement of Greek knowledge into Arabic, adopted the practice of employing a court astrologer from the Persians. In the Middle Ages, one of the first European potentates to adopt the practice was the Hohenstaufen Holy Roman Emperor, Frederick II (1194–1250), whose court was on the island of Sicily an exchange hub between North African Arabic-Islamic and European cultures. Frederick was a scholar, who not only traded goods with his Islamic neighbours but also knowledge. Following the Abbasid example, he installed an astrologer in his court. Both the prominent astrologers Michael Scot (1175–c. 1232) and Guido Bonatti (c. 1210–c. 1300) served in this function. The fashion spread and by the fifteenth century almost all rulers in Europe employed a court astrologer, either as a direct employee at court or when employed elsewhere on a consultant basis. The role of the court astrologer was that of a political advisor and whilst casting birth horoscopes, their main activities were in electional and horary astrology. Many notable mathematicians and astronomers served as court astrologers including Johannes Regiomontanus (1436–1476), Georg von Peuerbach (1423–1461), Peter Apian (1495–1552), Tycho Brahe (1546–1601), Michael Mästlin (1550–1631), and Johannes Kepler (1571–1630).

The upper echelons were thus firmly anchored in an astrological culture but what of the masses? Here, an important factor was the invention of movable type printing. This, of course, meant that the major Greek and Arabic astrological volumes became available in printed form. Ptolemaeus’ Tetrabiblos, translated from Arabic into Latin in the twelfth century, was first printed and published in Venice by Erhard Ratdolt (1442–1528) in 1484. However, much more important for the dissemination and popularisation of astrology were the astrological ephemera that began to appear from the very beginning of the age of print–wall calendars, prognostica, writing calendars and almanacs. The wall calendars, and Guttenberg printed a wall calendar to help finance the printing of his Bible, and writing calendars were a product of the iatromathematics, whereas the prognostica and almanacs dealt with astrometeorology and mundane astrology. These ephemera were comparatively cheap and were produced in print runs that often ran into the tens of thousands, making them very profitable for printer-publishers. Often containing editorial sections, the prognostica and almanacs came in a way to fulfil the function of the tabloid press today. For most households the annual almanac was the only print item that the purchased, apart perhaps from a Bible. 

But what of the Humanist Renaissance, did its basic philosophy or principles play a role in the rise of astrology? The answer is yes, very much so. Although the Tetrabiblos was translated into Latin comparatively early, the majority of important astrological texts in the Middle Ages were Arabic ones and these also found their way early into print editions. This circumstance kicked off a back to Greek purity–remove the Arabic influence debate amongst Renaissance astrologers. The humanists insisted that the only permissible astrological methods were those found in the Tetrabiblos and anything else was Arabic corruption. This meant they wanted to eliminate elections and interrogations, which Ptolemaeus does not deal with. Ironical both practices came into Arabic astrology via Persian astrology from Greek astrology that was older than Ptolemaeus’ work.

We don’t need to discuss the details of this debate but leading scholars, and the astrologers were leading mathematicians, astronomers and physicians were exchanging theoretical broadsides in print over decades. This, of course, raised the public perception and awareness of astrology and contributed to the Renaissance rise in astrology.

The Renaissance surge in astrology held well into the seventeenth century. With the notable exception of Copernicus, who apparently had little interest in astrology, all of the astronomers, who contributed to the so-called astronomical revolution including Tycho, Kepler and Galileo were practicing astrologers. Later in the seventeenth century, astrology went into decline but we don’t need to address that here.


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

An eighteenth-century cartographical community in Nürnberg

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


Fembohaus Source: Wikimedia Commons

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


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

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

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


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

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


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

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


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

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

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


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

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

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


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

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


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

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

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

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

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

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


Johann Hübner, engraving by Johann Kenckel Source: Wikimedia Commons

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


Kleiner Atlas scholasticus von 18 Charten

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


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

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


Johann Gottfried Gregorii Source: Wikimedia Commons

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

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


Johann Gabriel Doppelmayr Source: Wikimedia Commons

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


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

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


Georg Moriz Lowiz Source: Wikimedia Commons

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


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

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


Tobias Mayer Source: Wikimedia Commons

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

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


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

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Filed under Early Scientific Publishing, History of Astronomy, History of Cartography

Renaissance Science – IX

The part of mathematics that we most use in our lives is numbers, the building blocks of arithmetic. Today, we mostly use the Hindu-Arabic numerals and the associated place value decimal system, but this was not always the case. In fact, although this number system first entered Europe during the 12th century translation movement, it didn’t become truly established until well into the Renaissance.

First, we will briefly track the Hindu-Arabic place value decimal system from its origins till its advent in Europe. The system emerged in India sometime late in the sixth century CE. Āryabhaṭa (476–550) a leading mathematician and astronomer doesn’t mention them in his Aryasiddhanta. The earliest known source being in the Āryabhaṭīyabhāṣya of Bhāskara I (c. 600–c. 680) another leading astronomer mathematician. The full system, as we know it today, was described in the Brāhmasphuṭasiddhānta of Brahmagupta (c. 598–c. 668 n. Chr.). The only difference is that he allows division by zero, which as we all learnt in the school is not on.

The Brāhmasphuṭasiddhānta was translated into Arabic in about 770 by Ibrahim ibn Habib ibn Sulayman ibn Samura ibn Jundab al-Fazri (d. 777), Muhammad ibn Ibrahim ibn Habib ibn Sulayman ibn Samura ibn Jundab al-Fazri (d. c. 800) and Yaʿqūb ibn Ṭāriq (d. c. 796). The first two are father and son. Having teams doing scientific translations in the middle ages was actually very common. I won’t go into detail, but it should be noted that it took several hundred years for this system to replace the existing number systems in Arabic culture, many mathematicians preferring their own systems, which they considered superior.

The system first came into Europe in the 12th century through the translation of a work by Muhammad ibn Musa al-Khwārizmī (c. 780–c. 850) by an unknown translator. No Arabic manuscript of this work is known to exist, and it is only known by its Latin title Algoritmi de Numero Indorum, where Algoritmi is a corruption of al-Khwārizmī.

This translation only had a very limited impact. The new number system was adopted by the scholars at the universities as part of computus in order to calculate the date of Easter and the other moveable Church feasts. Leading scholars such as Sacrobosco wrote textbooks to teach the new discipline, which was Algorimus, another corruption of al-Khwārizmī. The other mostly university-based scholars, who used mathematics extensively, the astronomers, continued to use a sexagesimal i.e., base sixty, number system that they had inherited from both the Greek and the Arabic astronomers. This system would stay in use by astronomers down to Copernicus’ De revolutionibus (1543) and beyond.


This is the opening page of a 1490 manuscript copy of Johannes de Sacro Bosco’s Tractatus de Arte Numerandi, also referred to as his Algorismus Source:

What about the world outside of the universities? In the outside world the new number system was simply ignored. Which raises the question why? People generally believe that the base ten place value number system is vastly superior to the Roman numeral system that existed in Europe in the Middle ages, so why didn’t the people immediately adopt it? After all you can’t do arithmetic with Roman numerals. The thing is people didn’t do arithmetic with Roman numerals, although it would have been possible using different algorithm to the ones we use for the decimal place-value system. People did the calculations using either finger reckoning


of counting boards, also known as reckoning boards or abacuses. They only used the roman numerals to record the results.


Counting Board

In the hands of a skilled operator the counting board is a powerful instrument. It can be used very simply for addition and subtraction and using the halving and doubling algorithms, almost as simply for multiplication and division. A skilled operator can even extract roots using a counting board. The counting board also offers the possibility in a business deal for the reckoning masters of both parties to observe and control the calculations on the counting board.

The widespread use of counting boards over many centuries is still reflected in modern word usage. The serving surface in a shop is called a counter because it was originally the counting board on which the shop owner did their calculations. The English finance ministry is called the Exchequer after a special kind of counting board on which they did they calculations in the past. Nobody pays much attention to the strange term bankrupt, which also has its origins in the use of counting boards. The original medieval banks in Northern Italy were simply tables, Italian banca, on the marketplace, on which a printed cloth counting board was spread out. If the bankers were caught cheating their customers, then the authorities came and symbolically destroyed their table, in Italian, banca rotta, broken table.

Things first began to change slowly with the second introduction of Hindu-Arabic numerals by Leonardo from Pisa (c. 1175–c. 1250) in his Liber Abbaci (1202, 2nd edition 1227).


Leonardo from Pisa Liber Abbaci

This was basically a book on commercial arithmetic, following its Arabic origins. The Arabic/Islamic culture used different number systems for different tasks and used the Hindu-Arabic numerals and the decimal place-value system extensively in commercial arithmetic, in general account keeping, to calculate rates of interest, shares in business deals and the division of inheritance according to the complex Islamic inheritance laws. Leonardo’s father was a customs officer in North Africa, and it was here that Leonard learnt of the Hindu-Arabic numerals and the decimal place-value system from Arab traders in its usage as commercial arithmetic.

This new introduction saw the gradual spread in Norther Italy of Scuole or Botteghe D’abbaco (reckoning schools) lead by a Maestri D’abbaco (reckoning master), who taught this new commercial arithmetic to apprentice traders from Abbaco Libro (reckoning books), which he usually wrote himself. Many leading Renaissance mathematici, including Peter Apian (1495–1552, Niccolò Fontana Tartaglia (c. 1500–1557), Gerolamo Cardano (1501–1576), Gemma Frisius (1508–1555) and Robert Recorde (c. 1512–1558), wrote a published abbacus books. The very first printed mathematics book the Arte dell’Abbaco also known as the Treviso Arithmetic (1478) was , as the title clearly states, an abacus book.


Un maestro d’abaco. Filippo Calandri, De arimetricha opusculum, Firenze 1491

This practice began to accelerate with the introduction of double entry bookkeeping. This was part of the more general so-called commercial revolution, which included the founding of the first banks and the introduction of bills of exchange to eliminate the necessity of traders carrying large amounts of gold or silver. Developments in Europe that lead to the Renaissance. The earliest known example of double entry bookkeeping is the Messari Report of the Republic of Genoa, 1340. The earliest account of double entry bookkeeping is the Libro dell’arte di mercatura by Benedetto Cotrugli (1416–1469), which circulated in manuscript but was never printed. The first printed account was in the highly successful Summa de arithmetica, geometria, proportioni et proportionalita of Fra. Luca Bartolemeo Pacioli (c.1447–1517) published in 1494, which contain the twenty-seven-page introduction to double entry bookkeeping, Particularis de computis et scripturis.



Particularis de computis et scripturis, about double-entry bookkeeping.

Beginning with the Southern German trading centres of Augsburg, Regensburg and Nürnberg, which all traded substantially with the Northern Italian commercial centres, the new commercial arithmetic and double entry bookkeeping began to expand throughout Europe. This saw the fairly rapid establishment of reckoning schools and the printing of reckoning books throughout the continent. We can see the partial establishment of the Hindu-Arabic numerals some four hundred years after their first introduction, although they were used principally for recording, the reckoning continuing to be done on a counting board, in many cases down to the eighteenth century.

Already in the fifteenth century we can see the glimmer of the base ten system moving into other mathematical areas. Peuerbach and Regiomontanus started using circles with radii of 10,000 or 100,000, suggesting base ten, to calculate their trigonometrical tables instead of radii of 60,000, base sixty. The use of such large radii was to eliminate the need for fractional values.

By the end of the sixteenth century, the base ten positional value number system with Hindu-Arabic numerals had become well established across the whole spectrum of number use, throughout Europe. The Indian decimal system had no fractions and decimal fractions were first introduced into the Hindu-Arabic numerals by Abu’l Hasan Ahmad ibn Ibrahim Al-Uqlidisi in his Kitab al-Fusul fi al-Hisab al-Hindi around 952 and then again independently by Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (c. 1380–1429) in his Key to Arithmetic (1427). They first emerged in Europe in 1585 in Simon Stevin’s De Thiende also published in French as La Disme. The decimal point or comma was first used in Europe by Christoph Clavius (1538–1612) in the goniometric tables for his astrolabe in 1593. Its use became widespread through its adoption by John Napier in his Mirifici Logarithmorum Canonis Descriptio (1614).

However, at the end of the seventeenth century we still find both John Evelyn (1620–1706) and John Arbuthnot (1667–1735) discussing the transition from Roman to Hindu-Arabic numerals in their writings; the former somewhat wistfully, the later thankfully.

In the eighteenth century, Pierre-Simon Laplace reputedly said:

‘It is India that gave us the ingenious method of expressing all numbers by ten symbols, each receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.’

A very positive judgement, with hindsight, of the base ten place value number system with Hindu-Arabic numerals but one that was obviously not shared in the Early Modern period when the system was initially on offer in Europe.


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

The alchemist, who became a cosmographer

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

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


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

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

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

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

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


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

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


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


Source: The British Library

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


Source: Wikimedia Commons

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


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

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

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


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

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


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

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


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

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


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

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

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

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Filed under Early Scientific Publishing, History of Cartography, History of Navigation

The emergence of modern astronomy – a complex mosaic: Part XL

The event that would eventually lead to Isaac Newton writing and publishing his magnum opus, the Philosophiæ Naturalis Principia Mathematica (the Mathematical Principles of Natural Philosophy), took place in a London coffee house.


Title page of ‘Principia’, first edition (1687). Source: Wikimedia Commons

This is not quite as strange as it might at first appear, shortly after their first appearance in England around 1650 coffee houses became the favourite meeting places of the English scientific intelligentsia, the astronomers, mathematicians and natural philosophers. Here, these savants would meet up to exchange ideas, discuss the latest scientific theories and pose challenges to each other. These institutions also earned the appellation Penny Universities, as some of those savants, such as William Whiston, Francis Hauksbee and Abraham de Moivre, bettered their incomes by holding lectures or demonstrating experiments to willing audiences, who paid the price of a cup of coffee, a penny, for their intellectual entertainment. Later, after he had become Europe’s most famous living natural philosopher, Isaac Newton would come to hold court in a coffee shop, surrounded by his acolytes, the original Newtonians, distributing words of wisdom and handing round his unpublished manuscripts for scrutiny. However, all that still lay in the future.

One day in January 1684 Christopher Wren, Robert Hooke and Edmond Halley were discussing the actual astronomical theories over a cup of coffee. Wren, today better known as one of England most famous architects, was a leading mathematician and astronomers, who had served both as Gresham and Savilian professor of astronomy. Newton would name him along with John Wallis and William Oughtred as one of the three leading English mathematicians of the seventeenth century.


Wren, portrait c.1690 by John Closterman Source: Wikimedia Commons

Hooke was at the time considered to be the country’s leading experimental natural philosopher and Halley enjoyed an excellent reputation as a mathematician and astronomer.

NPG 4393; Edmond Halley by Richard Phillips

Portrait by Richard Phillips, before 1722 Source: Wikimedia Commons

The topic of discussion was Kepler’s elliptical, heliocentric astronomy and an inverse, squared law of gravity. All three men had arrived separately and independently at an inverse, squared law of gravity probably derived from Huygens’ formula for centrifugal force. Wren posed the question to the other two, whether they could demonstrate that such a law would lead to Kepler’s elliptical planetary orbits.

Hooke asserted that he already had such a demonstration but he would first reveal it to the others after they had admitted that they couldn’t solve the problem. Wren was sceptical of Hooke’s claim and offered a prize of a book worth forty shillings to the first to produce such a demonstration.  Hooke maintained his claim but didn’t deliver. It is worth noting that Hooke never did deliver such a demonstration. Halley, as already said no mean mathematician, tried and failed to solve the problem.

In August 1684 Halley was visiting Cambridge and went to see Newton in his chambers in Trinity College, who, as we know, he had met in 1682.


Trinity College Cambridge, David Loggan’s print of 1690 Source: Wikimedia Commons

According the Newton’s account as told to Abraham DeMoivre, Halley asked Newton, “what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of the distance from it. Sir Isaac replied immediately that it would be an Ellipse…” Here was Newton claiming to know the answer to Wren’s question. Halley asked Newton how he knew it and he replied, “I have calculated it…” Newton acted out the charade of looking for the supposed solution but couldn’t find it. However he promised Halley that he would send him the solution.

In November Edward Paget, a fellow of Trinity College, brought Halley a nine page thesis entitled De motu corporum in gyrum (On the Motion of Bodies in an Orbit).


Page of the De motu corporum in gyrum

When Halley read Newton’s little booklet he was immediately aware that he held something truly epoch making in the history of astronomy and physics in his hand. Newton had delivered up a mathematical proof that an elliptical orbit would be produced by an inverse square force situated at one of the foci of the ellipse, thus combining the inverse square law of gravity with Kepler’s first law. He went on to also derive Kepler’s second and third laws as well as laying down the beginnings of a mathematical theory of dynamics. Halley reported details of this extraordinary work to the Royal Society on 10 December 1684:

Mr Halley gave an account, that he had lately seen Mr. Newton at Cambridge, who had shewed him a curious treatise, De motu: which, upon Mr. Halley’s desire, was he said promised to be sent to the Society to be entered upon their register.

Mr. Halley was desired to put Mr. Newton in mind of his promise for securing his invention to himself till such time as he could be at leisure to publish it. Mr. Paget was desired to join with Mr. Halley.

The interest in and the demand to read Newton’s new production was very high but the author decided to improve and rewrite his first offering, triggering one of the most extraordinary episodes in his life.

Although he was Lucasian Professor and would turn forty-two on 25 December 1684, Newton remained a largely unknown figure in the intellectual world of the late seventeenth century. Following the minor debacle that resulted from the publication of his work in optics in the 1670s he had withdrawn into his shell, living in isolation within the walls of Cambridge University. He carried out his duties as Lucasian Professor but had almost no students to speak of and definitely no disciples. Thanks to the word of mouth propaganda of people like his predecessor as Lucasian Professor, Isaac Barrow, and above all the assiduous mathematics groupie, John Collins, it was rumoured that a mathematical monster slumbered in his chambers in Trinity College but he had done nothing to justify this bruited reputation. His chambers were littered with numerous unfinished scientific manuscripts, mostly mathematical but also natural philosophical and an even larger number of alchemical and theological manuscripts but none of them was in a fit state to publish and Newton showed no indication of putting them into a suitable state. Things now changed, Newton had found his vocation and his muse and the next two and a half years of his life were dedicated to creating the work that would make him into a history of science legend, the reworking of De motu into his Principia.

Over those two and a half years Newton turned his nine-page booklet into a major three-volume work of science. The modern English translation by I B Cohen runs to just over 560 large format pages, although this contains all the additions and alterations made in the second and third editions, so the original would have been somewhat shorter. Halley took over the editorship of the work, copyediting it and seeing it through the press. In 1685 the Royal Society had voted to take over the costs of printing and publishing Newton’s masterpiece, so everything seemed to be going smoothly and then disaster struck twice, firstly in the form of Robert Hooke and secondly in the form of a financial problem.

Hooke never slow to claim his priority in any matter of scientific discovery or invention stated that he alone had first discovered the inverse square law of gravity and that this fact should, indeed must, be acknowledged in full in the preface to Newton’s book. Halley, realising at once the potential danger of the situation, was the first to write to Newton outlining Hooke’s claim to priority, stating it, of course, as diplomatically as possible. Halley’s diplomacy did not work, Newton went ballistic. At first his reaction was comparatively mild, merely pointing out that he had had the inverse square law well before his exchanges with Hook in 1679 and had, in fact, discussed the matter with Wren in 1677, go ask him, Newton said. Then with more time to think about the matter and building up a head of steam, Newton wrote a new letter to Halley tearing into Hooke and his claim like a rabid dog. All of this ended with Newton declaring that he would no longer write volume three of his work. Halley didn’t know this at the time but this was in fact, as we shall see, the most important part of the entire work in which Newton presented his mathematical model of a Keplerian cosmos held together by the law of gravity. Halley remained calm and used all of his diplomatic skills to coax, flatter, persuade and cajole the prickly mathematician into delivering the book as finished. In the end Newton acquiesced and delivered but acknowledgements to Hooke were keep to a minimum and offered at the lowest level of civility.

The financial problem was of a completely different nature. In 1685 the Royal Society had taken over the cost of printing and publishing the deceased Francis Willughby’s Historia piscium as edited by John Ray.

This was an expensive project due to the large number plates that the book contained and the book was, at the time, a flop. This meant when it came time to print and publish Newton’s work the Royal Society was effectively bankrupt. One should note here that the popular ridicule poured out over Willughby’s volume, it having almost prevented Newton’s masterpiece appearing, is not justified. Historia piscium is an important volume in the history of zoology. Halley once again jumped into the breach and took over the costs of printing the volumes; on the 5 July 1687 Halley could write to Newton to inform him that the printing of his Philosophiæ Naturalis Principia Mathematica had been completed.









Filed under Early Scientific Publishing, History of Astronomy, History of Mathematics, History of science, Newton

The emergence of modern astronomy – a complex mosaic: Part XXXVI


From about 1630 onwards there were only two serious contenders under European astronomers, as the correct scientific description of the cosmos, on the one hand a Tychonic geo-heliocentric model, mostly with diurnal rotation and on the other Johannes Kepler’s elliptical heliocentric system; both systems had their positive points at that stage in the debate.


A 17th century illustration of the Hypothesis Tychonica from Hevelius’ Selenographia, 1647 page 163, whereby the Sun, Moon, and sphere of stars orbit the Earth, while the five known planets (Mercury, Venus, Mars, Jupiter, and Saturn) orbit the Sun. Source: Wikimedia Commons

A lot of the empirical evidence, or better said the lack of that empirical evidence spoke for a Tychonic geo-heliocentric model. The first factor, strangely enough spoke against diurnal rotation. If the Earth was truly rotating on its axis, then it was turning at about 1600 kilometres an hour at the equator, so why couldn’t one feel/detect it? If one sat on a galloping horse one had to hang on very tightly not to get blown off by the headwind and that at only 40 kilometres an hour or so. Copernicus had already seen this objection and had actually suggested the correct solution. He argued that the Earth carried its atmosphere with it in an all-enclosing envelope. Although this is, as already mentioned, the correct solution, proving or explaining it is a lot more difficult than hypothesising it. Parts of the physics that was first developed in the seventeenth century were necessary. We have already seen the first part, Pascal’s proof that air is a material that has weight or better said mass. Weight is the effect of gravity on mass and gravity is the other part of the solution and the discovery of gravity, in the modern sense of the word, still lay in the future. Copernicus’ atmospheric envelope is held in place by gravity, we literally rotate in a bubble.

In his Almagestum Novum (1651), Giovanni Battista Riccioli (1598–1671) brought a list of 126 arguments pro and contra a heliocentric system (49 pro, 77 contra) in which religious argument play a minor role and carefully argued scientific grounds a major one.


Frontispiece of Riccioli’s 1651 New Almagest. Mythological figures observe the heavens with a telescope and weigh the heliocentric theory of Copernicus in a balance against his modified version of Tycho Brahe’s geo-heliocentric system Source: Wikimedia Commons

Apart from the big star argument (see below) of particular interest is the argument against diurnal rotation based on what is now know as the Coriolis Effect, named after the French mathematician and engineer, Gaspard-Gustave de Coriolis (1792–1843), who described it in detail in his Sur les équations du mouvement relatif des systèmes de corps (On the equations of relative motion of a system of bodies) (1835). Put very simply the Coriolis Effect states that in a frame of reference that rotates with respect to an inertial frame projectile objects will be deflected. An Earth with diurnal rotation is such a rotating frame of reference.

Riccioli argued that if the Earth rotated on its axis then a canon ball fired from a canon, either northwards or southwards would be deflected by that rotation. Because such a deflection had never been observed Riccioli argued that diurnal rotation doesn’t exist. Once again with have a problem with dimensions because the Coriolis Effect is so small it is almost impossible to detect or observe in the case of a small projectile; it can however be clearly observed in the large scale movement of the atmosphere or the oceans, systems that Riccioli couldn’t observe. The most obvious example of the effect is the rotation of cyclones.


Illustration from Riccioli’s 1651 New Almagest showing the effect a rotating Earth should have on projectiles.[36] When the cannon is fired at eastern target B, cannon and target both travel east at the same speed while the ball is in flight. The ball strikes the target just as it would if the Earth were immobile. When the cannon is fired at northern target E, the target moves more slowly to the east than the cannon and the airborne ball, because the ground moves more slowly at more northern latitudes (the ground hardly moves at all near the pole). Thus the ball follows a curved path over the ground, not a diagonal, and strikes to the east, or right, of the target at G. Source: WIkimedia Commons

Riccioli was not alone in using the apparent absence of the Coriolis Effect to argue against diurnal rotation. The French Jesuit mathematician Claude François Milliet Deschales (1621–1678) in his Cursus seu Mundus Mathematicus (1674) brought a very similar argument against diurnal rotation.


Source: WIkimedia Commons


Image from Cursus seu Mundus Mathematicus (1674) of C.F.M. Dechales, showing how a cannonball should deflect to the right of its target on a rotating Earth, because the rightward motion of the ball is faster than that of the tower. Source: Wikimedia Commons

It was first 1749 that Euler derived the mathematical formula for Coriolis acceleration showing it to be two small to be detected in small projectiles.


A nearby star’s apparent movement against the background of more distant stars as the Earth revolves around the Sun is referred to as stellar parallax. Source:

The second empirical factor was the failure to detect stellar parallax. If the Earth is really orbiting the Sun then the position of prominent stars against the stellar background should appear to shift when viewed from opposite sides of the Earth’s orbit, six months apart so to speak. In the seventeenth century they didn’t. Once again supporters of heliocentricity had an ad hoc answer to the failure to detect stellar parallax, the stars are too far away so the apparent shift is too small to measure. This is, of course the correct answer and it would be another two hundred years before the available astronomical telescopes had evolved far enough to detect that apparent shift. In the seventeenth century, however, this ad hoc explanation meant that the stars were quite literally an unimaginable and thus unacceptable distance away. The average seventeenth century imagination was not capable of conceiving of a cosmos with such dimensions.

The distances that the fixed stars required in a heliocentric system produced a third serious empirical problem that has been largely forgotten today, star size.  This problem was first described by Tycho Brahe before the invention of the telescope. Tycho ascribed a size to the stars that he observed and calculating on the minimum distance that the fixed stars must have in order not to display parallax in a heliocentric system came to the result that stars must have a minimum size equal to Saturn’s orbit around the Sun in such a system. In a geo-heliocentric system, as proposed by Tycho, the stars would be much nearly to the Earth and respectively smaller.  This appeared to Tycho to be simply ridiculous and an argument against a heliocentric system. The problem was not improved by the invention of the telescope. Using the primitive telescopes of the time the stars appeared as a well-defined disc, as recorded by both Galileo and Simon Marius, thus confirming Tycho’s star size argument. Marius used this as an argument in favour of a geo-heliocentric theory; Galileo dodged the issue. In fact, we now know, that the star discs that the early telescope users observed were not real but an optical artefact, now known as an Airy disc. This solution was first hypothesised by Edmond Halley, at the end of the century and until then the star size problem occupied a central place in the astronomical system discussion.


With the eccentricity of the orbits exaggerated: Source

The arguments in favour of Kepler’s elliptical, heliocentric system were of a very different nature. The principle argument was the existence of the Rudolphine Tables. These planetary tables were calculated by Kepler using Tycho’s vast collection of observational data. The Rudolphine Tables possessed an, up till that time, unknown level of accuracy; this was an important aspect in the acceptance of Kepler’s system. Since antiquity, the principle function of astronomy had been to provide planetary tables and ephemerides for use by astrologers, cartographers, navigators etc. This function is illustrated, for example, by the fact that the tables from Ptolemaeus’ Mathēmatikē Syntaxis were issued separately as his so-called Handy Tables. Also the first astronomical texts translated from Arabic into Latin in the High Middle Ages were the zījes, astronomical tables.

The accuracy of the Rudolphine Tables were perceived by the users to be the result of Kepler using his elliptical, heliocentric model to calculate them, something that was not quite true, but Kepler didn’t disillusion them. This perception increased the acceptance of Kepler’s system. In the Middle Ages before Copernicus’ De revolutionibus, the astronomers’ mathematical models of the cosmos were judge on their utility for producing accurate data but their status was largely an instrumentalist one; they were not viewed as saying anything about the real nature of the cosmos. Determining the real nature of the cosmos was left to the philosophers. However, Copernicus regarded his system as being a description of the real cosmos, as indeed had Ptolemaeus his system before him, and by the middle of the seventeenth century astronomers had very much taken over this role from the philosophers, so the recognition of the utility of Kepler’s system for producing data was a major plus point in its acceptance as the real description of the cosmos.


The other major point in favour of Kepler’s system, as opposed to a Tychonic one was Kepler’s three laws of planetary motion. Their reception was, however, a complex and mixed one. Accepting the first law, that the planetary orbits were ellipses with the Sun at one focus of the ellipse, was for most people fairly easy to accept. An ellipse wasn’t the circle of the so-called Platonic axioms but it was a very similar regular geometrical figure. After Cassini, using a meridian line in the San Petronio Basilica in Bologna, had demonstrated that either the Earth’s orbit around the Sun or the Sun’s around the Earth, the experiment couldn’t differentiate, Kepler’s first law was pretty much universally accepted. Kepler’s third law being strictly empirical should have been immediately accepted and should have settled the discussion once and for all because it only works in a heliocentric system. However, although there was no real debate with people trying to refute it, it was Isaac Newton who first really recognised its true significance as the major game changer.

Strangely, the problem law turned out to be Kepler’s second law: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This seemingly obtuse relationship was not much liked by the early readers of Kepler’s Astronomia Nova. They preferred, what they saw, as the purity of the Platonic axiom, planetary motion is uniform circular motion and this despite all the ad hoc mechanism and tricks that had been used to make the anything but uniform circulation motion of the planets conform to the axiom. There was also the problem of Kepler’s proof of his second law. He divided the ellipse of a given orbit into triangles with the Sun at the apex and then determined the area covered in the time between two observations by using a form of proto-integration. The problem was, that because he had no concept of a limit, he was effectively adding areas of triangles that no longer existed having been reduced to straight lines. Even Kepler realised that his proof was mathematically more than dubious.


Ismaël Boulliau portrait by Pieter van Schuppen Source: Wikimedia Commons

The French astronomer and mathematician Ismaël Boulliau (1605–1694) was a convinced Keplerian in that he accepted and propagated Kepler’s elliptical orbits but he rejected Kepler’s mathematical model replacing it with his own Conical Hypothesis in his Astronomica philolaica published in 1645.


He criticised in particular Kepler’s area rule and replaced it in his work with a much simpler model.


Boulliau’s Conical Hypothesis [RA Hatch] Source: Wikimedia Commons

The Savilian Professor of astronomy at Oxford University, Seth Ward (1617–1689)

Greenhill, John, c.1649-1676; Seth Ward (1617-1689), Savilian Professor of Astronomy, Oxford (1649-1660), Bishop of Exeter and Salisbury

Bishop Seth Ward, portrait by John Greenhill Source: Wikimedia Commons

attacked Boulliau’s presentation in his In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis (1653), pointing out mathematical errors in the work and proposing a different alternative to the area law.

L0040222 Title Page of 'Astronomiae Philolacae Fundamenta'

Source: Wikimedia Commons

Boulliau responded to Ward’s criticisms in 1657, acknowledging the errors and correcting but in turn criticising Ward’s model.


Source: Wikimeda Commons

Ward in turn had already presented a fully version of his Keplerian system in his Astronomia geometrica (1656).


The whole episode is known as the Boulliau-Ward debate and although it reached no satisfactory conclusion, the fact that two high profile European astronomers were disputing publically over the Keplerian system very much raised the profile of that system. It is probable the Newton was first made aware of Kepler’s work through the Boulliau-Ward debate and he is known to have praised the Astronomica philolaica, which as Newton was later to acknowledge contained the first presentation of the inverse square law of gravity, which Boulliau personally rejected, although he was the one who proposed it.

The Boulliau-Ward debate was effectively brought to a conclusion and superseded by the work of the German mathematician Nikolaus Mercator (c. 1620–1687), whose birth name was Kauffman. His birthplace is not certain but he studied at the universities of Rostock and Leiden and was a lecturer for mathematics in Rostock (1642–1648) and then Copenhagen (1648–1654). From there he moved to Paris for two years before emigrating to England in 1657. In England unable to find a permanent position as lecturer he became a private tutor for mathematics. From 1659 to 1660 he corresponded with Boulliau on a range of astronomical topics. In 1664 he published his Hypothesis astronomica, a new presentation of the Keplerian elliptical system that finally put the area law on a sound mathematical footing. In 1676 he published a much-expanded version of his Keplerian astronomy in his two-volume Institutionum astronomicarum.


Mercator’s new mathematical formulation of Kepler’s second law ended the debate on the subject and was a major step in the eventual victory of Kepler’s system over its Tychonic rival.

Addendum: Section on Coriolis Effect added 21 May 2020













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