Category Archives: History of Astronomy

Internet Superstar, who are you, what do you think you are?

He’s back!

After his stupendously, mind-bogglingly, world shattering success rabbiting on about the history of astronomy on the History for Atheists YouTube channel, he can now be heard going on and on and on and on and on and on…  about the history of astronomy from Babylon to Galileo Galilei on the monumental, prodigious, phenomenal Subject to Change podcast, moderated by sensational Russell Hogg and available on so many different Internet channels you’ll need a week to decide where to listen. 


Filed under Autobiographical, History of Astrology, History of Astronomy

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

The seventeenth-century Chinese civil servant from Cologne 

From its very beginnings the Society of Jesus (the Jesuits) was set up as a missionary movement carrying the Catholic Religion to all corners of the world. It also had a very strong educational emphasis in its missions, carrying the knowledge of Europe to foreign lands and cultures and at the same time transmitting the knowledge of those cultures back to Europe. Perhaps the most well-known example of this is the seventeenth-century Jesuit mission to China, which famously in the history of science brought the latest European science to that far away and, for Europeans, exotic land. In fact, the Jesuits used their extensive knowledge of the latest European developments in astronomy to gain access to the, for foreigners, closed Chinese culture.

It was, initially, Christoph Clavius (1538–1612), who by introducing his mathematics programme into the Jesuits more general education system, ensured that the Jesuits were the best purveyors of mathematics in Europe in the early seventeenth century and it was Clavius’ student Matteo Ricci (1552–1610), who first breached the Chinese reserve towards strangers with his knowledge of the mathematical sciences.

The big question is what did the Chinese need the help of western astronomers for and why. Here we meet an interesting historical contradiction for the Jesuits. Unlike most people in the late sixteenth century and early seventeenth century, the Jesuits did not believe in or practice astrology. One should not forget that both Kepler and Galileo amongst many others were practicing astrologers. The Chinese were, however, very much practitioners of astrology at all levels and it was here that they found the assistance of the Jesuits desirable. The Chines calendar fulfilled important ritual and astrological functions, in particular the prediction of solar and lunar eclipses for which the emperor was personally responsible, and it had to be recalculated at the ascension to the throne of every new emperor. There was even an Imperial Astronomical Institute to carry out this task.

Although the Chinese had been practicing astronomy longer than the Europeans and, over the millennia, had developed a very sophisticated astronomy, in the centuries before the arrival of the Jesuits that knowledge had fallen somewhat into decay and had by that point not advanced as far as that of the Europeans. Before the arrival of the Jesuits, the Chinese had employed Muslim astronomers to aid them in this work, so the principle of employing foreigners for astronomical work had already been established. Through his work, Ricci had convinced the Chinese of his superior astronomical knowledge and abilities and thus established a bridgehead into the highest levels of Chinese society.

The man, who, for the Jesuits, made the greatest contribution to calendrical calculation in seventeenth century was the, splendidly named, Johann Adam Schall von Bell (1591–1666). Born, probably in Cologne, into a well-established aristocratic family, who trace their roots back to the twelfth century, Johann Adam was the second son of Heinrich Degenhard Schall von Bell zu Lüftelberg and his fourth wife Maria Scheiffart von Merode zu Weilerswist. He was initially educated at the Jesuit Tricoronatum Gymnasium in Cologne and then in 1607 sent to Rome to the Jesuit run seminary Pontificium Collegium Germanicum et Hungaricum de Urbe, where he concentrated on the study of mathematics and astronomy. It is thought that his parents sent him to Rome to complete his studies because of an outbreak of the plague in Cologne. In 1611 he joined the Jesuits and moved to the Collegio Romano, where he became a student of Christoph Grienberger

A portrait of German Jesuit Johann Adam Schall von Bell (1592–1666), Hand-colored engraving, artist unknown Source: Wikimedia Commons

He applied to take part in the Jesuit mission to China and in 1618 set sail for the East from Lisbon. He would almost certainly on his way to Lisbon have spent time at the Jesuit College in Coimbra, where the missionaries heading out to the Far East were prepared for their mission. Here he would probably have received instruction in the grinding of lenses and the construction of telescopes from Giovanni Paolo Lembo (c. 1570–1618), who taught these courses to future missionaries.

Schall von Bell set sail on 17 April 1618 in a group under the supervision of Dutch Jesuit Nicolas Trigault (1577–1628), Procurator of the Order’s Province of Japan and China.

Nicolas Trigault in Chinese costume, by Peter Paul Rubens, the Metropolitan Museum of Art Source: Wikimedia Commons
De Christiana expeditione apud Sinas, by Nicolas Trigault and Matteo Ricci, Augsburg, 1615. Source: Wikimedia Commons

Apart from Schall von Bell the group included the German, polymath Johannes Schreck (1576–1630), friend of Galileo and onetime member of the Accademia dei Lincei, and the Italian Giacomo Rho (1592–1638). They reached the Jesuit station in Goa 4 October 1618 and proceeded from there to Macau where they arrived on 22 July 1619. Here, the group were forced to wait four years, as the Jesuits had just been expelled from China. They spent to time leaning Chinese and literally fighting off an attempt by the Dutch to conquer Macau. 

In 1623 Schall von Bell and the others finally reached Peking. In 1628 Johann Schreck began work on a calendar reform for the Chinese. To aid his efforts Johannes Kepler sent a copy of the Rudolphine Tables to Peking in 1627. From 1627 to 1630 Schall von Bell worked as a pastor but when Schreck died he and Giacomo Rho were called back to Peking to take up the work on the calendar and Schall von Bell began what would become his life’s work.

He must first translate Latin textbooks into Chinese, establish a school for astronomical calculations and modernise astronomical instruments. In 1634 he constructed the first Galilean telescope in China, also writing a book in Chinese on the instrument. In 1635 he published his revised and modernised calendar, which still exists. 

Text on the utilisation and production of the telescope by Tang Ruowang (Chinese name of Johann Adam Schall von Bell) Source: Wikimedia Commons
Galilean telescope from Schall von Bell’s Chinese book Source: Wikimedia Commons

Scall von Bell used his influence to gain permission to build Catholic churches and establish Chinese Christian communities. This was actually the real aim of his work. He used his knowledge of mathematics and astronomy to win the trust of the Chinese authorities in order to be able to propagate his Christian mission.

In 1640 he produced a Chinese translation of Agricola’s De re metallica, which he presented to the Imperial Court. He followed this on a practical level by supervising the manufacture of a hundred cannons for the emperor. In 1644, the emperor appointed him President of the Imperial Astronomical Institute following a series of accurate astronomical prognostication. From 1651 to 1661 he was a personal advisor to the young Manchurian Emperor Shunzhi (1638–1661), who promoted Schall von Bell to Mandarin 1st class and 1st grade, the highest level of civil servant in the Chinese system.

Johann Adam Schall von Bell and Shunzhi Emperor Source: Wikimedia Commons

Following the death of Shunzhi, he initially retained his appointments and titles, which caused problems for him in Rome following a visitation in Peking by the Dominicans. The Vatican ruled that Jesuits should not take on mundane appointments. In 1664 Schall von Bell suffered a stroke, which left him vulnerable to attack from his rivals at court. He was accused of having provoked Shunzhi’s concubine’s death through having falsely calculated the place and time for the funeral of one of Shunzhi’s sons. 

The charges, that included other Jesuits, were high treason, membership of a religious order not compatible with right order and the spread of false astronomical teachings. Schall von Bell was imprisoned over the winter 1665/66 and Jesuits in Peking, who had not been charged were banned to Kanton. He was found guilty on 15 April 1665 and sentenced to be executed by Lingchi, death by a thousand cuts. However, according to legend, there was an earthquake shortly before the execution date and the judge interpreted it as a sign from the gods the Schall von Bell was innocent. On 15 May 1665 Schall von Bell was released from prison on the order of the Emperor Kangxi (1654–1722). He died 15 August 1666 and was rehabilitated by Kangxi, who ensured that he received a prominent gravestone that still exists. 

Jesuit astronomers with Kangxi Emperor by Philippe Behagle French tapestry weaver, 1641 – 1705 Source: Wikimedia Commons

Schall von Bell was represented at his trial by Flemish Jesuit Ferdinand Verbiest (1623–1688), who would later take up Schall von Bell’s work on the Chinese calendar but that’s a story for another day. Schall von Bell reached the highest ever level for a foreigner in the Chinese system of government but in the history of science it is his contributions to the modernisation of Chinese astronomy and engineering that are most important. 

Jesuit Mission to China, left to right Top: Matteo Ricci, Johann Adam Schall von Bell, Ferdinand Verbiest Artist: Jean-Baptiste Du Halde (1674 – 1743) French Jesuit historian Source: Wikimedia Commons


Filed under History of Astrology, History of Astronomy, History of Technology, Renaissance Science

The Renaissance Mathematicus tries his luck as YouTube Influencer

Some time back I had a late-night chat with medieval historian Tim O’Neill about all things Galileo Galilei; late night for me that is, early morning for him. Unbeknown to me the sneaky Aussie bugger recorded my ruminations on the Tuscan mathematicus; they’re like that those antipodeans, duplicitous. Now he’s gone and posted the whole affair on YouTube, for all the world to see.

 I may have to have plastic surgery and move to an unknown destination in South America.

However, if you have a strong stomach and like to watch train wrecks or are just curious what the Renaissance Mathematicus looks like in real life, then you can find the whole horrible mess on Tim’s History for Atheists YouTube channel in three obscenely long parts:

The Galileo Affair Part 1 

The Galileo Affair Part 2 

The Galileo Affair Part 3  

 Who knows, if enough people can be fooled into watching it, I might become the next Paris Hilton! 

WARNING: Not suitable for children or viewers with high moral standards: Expletives not deleted!


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

It’s Galileo time again!

An article in the Sunday Express, not a newspaper I would normally read in fact I would only ever use it as toilet paper in an emergency, starts thus:

Former Supreme Court Judge Lord Sumption has condemned attacks on scientists who challenge “official wisdom” on Covid, comparing their critics to the “persecutors of Galileo”.

A classic case of the Galileo fallacy or Galileo gambit. For anybody not aware of the Galileo fallacy:

Lucy Johnston, Health and social Affairs Editor of the Sunday Express tweeted this article with the following lede:

Lord Sumption: “Scientists behaving like the persecutors of Galileo….forgetting all scientific conclusions are provisional, including their own.

Lucy Johnston’s lede is in fact disingenuous, as she combines two half sentences that are in no way connected in the article, but we will examine it as if they were. Galileo’s persecutors were very well aware that scientific conclusions are provisional as stated very clearly by Roberto Bellarmino in his Foscarini Letter, I quote:

Third, I say that if there were a true demonstration that the sun is at the centre of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary; and say rather that we do not understand them than that what is demonstrated is false. But I will not believe that there is such a demonstration, until it is shown me. 

During the seventeenth century many Catholic astronomers and natural philosophers were involved in providing the necessary evidence to support a heliocentric world view. Many of them were Jesuits or Jesuit educated. They would not have done so if they did not believe that scientific conclusions are provisional. 

This is why I tweeted:

Sorry to introduce some real history into this thread but that is not what Galileo’s prosecutors did.

To which Helen O’Toole an Irish Early Years Educator (her description) replied with the following link:

One should note that the website, which is the website of the History television channel describes itself as “History #1 Factual Entertainment Brand” [my emphasis] History the television channel is notorious for it’s pseudo-documentaries of bullshit woo and the inaccuracies of its historical documentaries.

Here we can read the following: 

1633 April 12 Galileo is accused of heresy

This is in fact false. Galileo was not accused of heresy but of having breached the Church injunction, issued to him personally in 1616, not to hold or teach the heliocentric theory. Before somebody charges in saying, “they had no right to issue such an injunction”, I will point out, for the umpteenth time, that at the beginning of the seventeenth century the Catholic Church was an absolutist political and legal authority and had every right under the prevailing system to do so. 

It is also important to note, again for the umpteenth time, that when Galileo got himself into trouble with the Catholic authorities, the scientific situation was such that the available empirical evidence supported a geocentric or helio-geocentric system and not a heliocentric one, as there was absolutely no evidence that the Earth moved. Also, and this is very important, Galileo or anybody else, for that matter, was free to discuss a heliocentric system hypothetically but not to claim that it was factually true.

On April 12, 1633, chief inquisitor Father Vincenzo Maculani da Firenzuola, appointed by Pope Urban VIII, begins the inquisition of physicist and astronomer Galileo Galilei. Galileo was ordered to turn himself in to the Holy Office to begin trial for holding the belief that the Earth revolves around the sun, which was deemed heretical by the Catholic Church. Standard practice demanded that the accused be imprisoned and secluded during the trial.

Galileo was ordered to turn himself in for holding and teaching the heliocentric hypothesis as proven fact. The heliocentric theory was never formally declared heretical by the Catholic Church. The eleven Qualifiers, appointed by the Church to examine the heliocentric theory, came to the conclusion that the idea that the Sun is stationary is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture…” However, only the Pope can formally declare something heretical and in the case of the heliocentric theory no pope ever took this step.

This is followed by a wonderful case of false information by implication. “Standard practice demanded that the accused be imprisoned and secluded during the trial.” In Galileo’s case, due to his advanced age and his social status, on the one hand he was the most famous natural philosopher and astronomer in Europe and on the other he was a Medici courtier, Galileo was given his own three-room apartment, with servants, in the palace of the Inquisition. This is a somewhat different picture to the usual one, implied here, of Galileo being thrown into prison, or even a dungeon. Galileo even wrote a letter to his daughter saying how well he was being treated.

This was the second time that Galileo was in the hot seat for refusing to accept Church orthodoxy that the Earth was the immovable center of the universe: In 1616, he had been forbidden from holding or defending his beliefs. In the 1633 interrogation, Galileo denied that he “held” belief in the Copernican view but continued to write about the issue and evidence as a means of “discussion” rather than belief. The Church had decided the idea that the sun moved around the Earth was an absolute fact of scripture that could not be disputed, despite the fact that scientists had known for centuries that the Earth was not the center of the universe.

I do wish people wouldn’t in this context use the word belief. Galileo held it for a fact that the cosmos, as it was then known, was heliocentric and was convinced that he could prove it. The Church had not decided that “the idea that the sun moved around the Earth was an absolute fact of scripture that could not be disputed”. The Church said that scripture stated that the Sun revolves around the Earth and the best available empirical evidence at the beginning of the seventeenth century supported that hypothesis. The Church was quite happy to change that view if new evidence to support the heliocentric hypothesis should be found, which it did in the eighteenth century, when that evidence, stellar aberration, was in fact found. 

However, all the above I have gone through in various posts in the past, what drove me to write this new post was the last statement, “despite the fact that scientists had known for centuries that the Earth was not the center of the universe.” [my emphasis], I mean WHAT THE FUCK! It’s truly time for a bit of the HIST_SCI HULK

Can somebody please enlighten me, as to who these scientists were, who had known for centuries that the Earth was not the centre of the universe? 

Remember this was posted on “History #1 Factual Entertainment Brand” [my emphasis], so let us re-examine the actual historical facts. Copernicus published his De revolutionibus, containing his heliocentric hypothesis, in 1543, that’s ninety years before Galileo’s trial, not centuries. Copernicus had deferred the publication for a couple of decades because he couldn’t provide any empirical evidence to support his hypothesis. When he finally published his hypothesis was mathematically plausible but still lacked any empirical evidence. Over the next ninety years despite efforts by numerous astronomers at prove or refute Copernicus’ hypothesis nobody had found any empirical evidence to show that the Earth moved. The best evidence for a heliocentric system was Kepler’s three laws of planetary motion in particular his third law, which interestingly Galileo simply ignored. The other available evidence was the various observations, made by various astronomers, confirming the solar orbits of comets, which Galileo didn’t just ignore but actively rejected. Just for the record, in 1633, the available empirical evidence supported either a geocentric system or more likely a Tychonic helio-geocentric system with the Earth still firmly at the centre.

I find it simply depressing that an organisation with the worldwide reach of the History Channel (which actually just calls itself History these days) is propagating such inaccurate crap as factual history, which is being consumed and believed by such people as Helen O’Toole an Irish Early Years Educator, who drew my attention to this travesty. 


Filed under History of Astronomy, Myths of Science, Uncategorized

They also serve…

In 1610, Galileo published his Sidereus Nuncius, the first publication to make known the new astronomical discoveries made with the recently invented telescope.

Source: Wikimedia Commons

Although, one should also emphasise that although Galileo was the first to publish, he was not the first to use the telescope as an astronomical instrument, and during that early phase of telescopic astronomy, roughly 1609-1613, several others independently made the same discoveries. There was, as to be expected, a lot of scepticism within the astronomical community concerning the claimed discoveries. The telescopes available at the time were generally of miserable quality and Galileo’s discoveries proved difficult to replicate. It was the Jesuit mathematicians and astronomers in the mathematics department at the Collegio Romano, who would, after initial difficulties, provide the scientific confirmation that Galileo desperately needed. The man, who led the endeavours to confirm or refute Galileo’s claims was the acting head of the mathematics faculty Christoph Grienberger (the professor, Christoph Clavius, was old and infirm). Grienberger is one of those historical figures, who fades into the background because they made no major discoveries or wrote no important books, but he deserves to be better known, and so this brief sketch of the man and his contributions.

As is all too oft the case with Jesuit scholars in the Early Modern Period, we know almost nothing about Grienberger before he joined the Jesuit Order. There are no know portraits of him. The problems start with his name variously given as Bamberga, Bamberger, Banbergiera, Gamberger, Ghambergier, Granberger, Panberger and a total of nineteen variations, history has settled on Grienberger. He was born 2 July 1561 in Hall a small town in the Tyrol in the west of Austria. That’s all we know till he entered the Jesuit Order in 1580. He studied rhetoric and philosophy in Prague from 1583 to 1584. From 1587 he was a mathematics teacher at the Jesuit university in Olmütz. He began his theology studies, standard for a Jesuit, in Vienna in 1589, also teaching mathematics. His earliest surviving letter to Christoph Clavius, who he had never met but who he describes as his teacher, he had studied the mathematical sciences using Clavius’ books, is dated from 1590. In 1591 he moved to the Collegio Romano, where he became Clavius’ deputy. 

In 1595, Clavius went to Naples, the purpose of his journey is not clear, but he was away from Rome for somewhat more than a year. During his absence Grienberger took over direction of the mathematics department at the Collegio Romana. From the correspondence between the two mathematicians, during this period, it becomes very obvious that Grienberger does not enjoy being in the limelight. He complains to Clavius about having to give a commencement speech and also about having to give private tuition to the sons of aristocrats. Upon Clavius’ return he fades once more into the background, only emerging again with the commotion caused by the publication of Galileo’s Sidereus Nuncius.

Rumours of Galileo’s discoveries were already making the rounds before publication and, in fact on the day the Sidereus Nuncius appeared, the wealthy German, Humanist Markus Welser (1558–1614) from Augsburg wrote to Clavius asking him his opinion on Galileo’s claims.

Markus Welser artist unknown Source: Wikimedia Commons

We know from letters that the Jesuit mathematicians in the Collegio Romano already had a simple telescope and were making astronomical observations before the publication of the Sidereus Nuncius. They immediately took up the challenge of confirming or refuting Galileo’s discoveries. However, their telescope was not powerful enough to detect the four newly discovered moons of Jupiter. Grienberger was away in Sicily attending to problems at the Jesuit college there, so it was left to Giovanni Paolo Lembo (c. 1570–1618) to try and construct a telescope good enough to complete the task. We know that Lembo was skilled in this direction because between 1615 and 1617 he taught lens grinding and telescope construction to the Jesuits being trained as missionaries to East Asia at the University of Coimbra. 

Lembo’s initial attempts to construct a suitable instrument failed and it was only after Grienberger returned from Sicily that the two of them were able to make progress. At this point Galileo was corresponding with Clavius and urging the Jesuit astronomer on provide the confirmation of his discoveries that he so desperately needed, the general scepsis was very high, but he was not prepared to divulge any details on how to construct good quality telescopes. Eventually, Grienberger and Lembo succeeded in constructing a telescope with which they could observe the moons of Jupiter but only under very good observational conditions. They first observed three of the moons on 14 November 1610 and all four on 16 November. 

Clavius wrote to the merchant and mathematician Antonio Santini (1577–1662) in Venice, who had been to first to confirm the existence of the Jupiter moons in 1610, with a telescope that he constructed himself, detailing observation from 22, 23, 26, and 27 November but stating that they were still not certain as to the nature of the moons. Santini relayed this information to Galileo. On 17 December, Clavius wrote to Galileo:

…and so we have seen [the Medici Stars] here in Rome many times. At the end of the letter I will put some observations, from which it follows very clearly that they are not fixed but wandering stars, because they change position with respect to each other and Jupiter.

Much of what we know about the efforts of the Jesuit astronomers under the leadership of Grienberger to build an adequate telescope to confirm Galileo’s discoveries come from a letter that Grienberger wrote to Galileo in February 1611. One interesting aspect of Grienberger’s letter is that the Jesuit astronomers had also been observing Venus and there is good evidence that they discovered the phases of Venus independently at least contemporaneously if not earlier than Galileo. This was proof that Venus, and by analogy probably also Mercury, orbit the Sun and not the Earth. This was the death nell for a pure Ptolemaic geocentric system and the acceptance at a minimum of a Capellan system where the two inner planets orbit the Sun, which orbits the Earth, if not a full blown Tychonic system or even a heliocentric one. This was in 1611 troubling for the conservative leadership of the Jesuit Order, but would eventually lead to them adopting a Tychonic system at the beginning of the 1620s. 

Clavius died 6 February 1612 and Grienberger became his official successor as the professor for mathematics at the Collegio Romano, a position he retained until 1633, when he was succeeded in turn by Athanasius Kircher (1602–1680). The was a series of Rules of Modesty in Ignatius of Loyola’s rules for the Jesuit Order and individual Jesuits were expected to self-abnegate. The most extreme aspect of this was that many scientific works were published anonymously as a product of the Order and not the individual. Different Jesuit scholars reacted differently to this principle. On the one hand, Christoph Scheiner (1573–1650), Galileo’s rival in the sunspot dispute and author of the Rosa Ursina sive Sol(1626–1630) presented himself as a great astronomer, which did not endear him to his fellow Jesuits.

Christoph Scheiner artist unknown Source: Wikimedia Commons

On the other hand, Grienberger put his name on almost none of his own work preferring it to remain anonymous. There is only a star catalogue and a set of trigonometrical tables that bear his name.

However, as head of the mathematics department at the Collegio Romano he was responsible for controlling and editing all of the publications in the mathematical disciplines that went out from the Jesuit Order and it is know that he made substantial improvements to the works that he edited both in the theoretical parts and in the design of instruments. A good example is the heliotropic telescope, which enables the observer to track the movement of the Sun whilst observing sunspots, illustrated in Scheiner’s Rosa Ursina.

Heliotropic telescope on the left. On the right Scheiner’s acknowledgement that Grienberger was the inventor

This instrument is known to have been designed and constructed by Grienberger, who, however, explicitly declined Scheiner’s offer to add a text under his own name describing its operation. Grienberger also devised a system of gearing theoretical capable of lifting the Earth

Reconstruction of Grienberger’S Earth lifting gearing

Grienberger, admired Galileo and took his side, if only in the background, in Galileo’s dispute with the Aristotelians over floating bodies. He was, however, disappointed by Galileo’s unprovoked and vicious attacks on the Jesuit astronomer Orazio Grassi on the nature of comets and explicitly said that it had cost Galileo the support of the Jesuits in his later troubles. He also clearly stated that if Galileo had been content to propose heliocentricity as a hypothesis, its actual scientific status at the time, he could have avoided his confrontation with the Church.

Élie Diodati (1576–1661) the Calvinist, Genevan lawyer and friend of Galileo, who played a central role in the publication of the Discorsi, quoted Grienberger in a letter to Galileo from 25 July 1634, as having said, “If Galileo had recognised the need to maintain the favour of the Fathers of this College, then he would live gloriously in the world, and none of his misfortune would have occurred, and he could have written about any subject, as he thought fit, I say even about the movement of the Earth…”

Several popular secondary sources claim the Grienberger supported the Copernican system. However, there is only hearsay evidence for this claim and not actual proof. He might have but we will never know. 

Grienberger made no major discoveries and propagated no influential new theories, which would launch him into the forefront of the big names, big events style of the history of science. However, he played a pivotal role in the very necessary confirmation of Galileo’s telescopic discoveries. He also successfully helmed the mathematical department of the Collegio Romano for twenty years, which produced many excellent mathematicians and astronomers, who in turn went out to all corners of the world to teach others their disciplines. By the time Athanasius Kircher inherited Grienberger’s post there was a world-wide network of Jesuit astronomers, communicating data on important celestial events. One such was Johann Adam Schall von Bell (1591–1666), who studied under Grienberger and went on to lead the Jesuit mission in China.

Johann Adam Schall von Bell Source: Wikimedia Commons

Science is a collective endeavour and figures such as Grienberger, who serve inconspicuously in the background are as important to the progress of that endeavour as the shrill public figures, such as Galileo, hogging the limelight in the foreground. 


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

The deviser of the King’s horologes

There can’t be many Renaissance mathematici, whose existence was ennobled by a personal portrait by the master of the Renaissance portraits, Hans Holbein the younger. In fact, I only know of one, the German mathematicus, Nicolas Kratzer.

Nicolas Kratzer Portrait by Hans Holbein the younger

One might be excused for thinking that having received this singular honour that Kratzer had, in his lifetime, achieved something truly spectacular in the world of the Renaissance mathematical disciplines; however, almost the opposite is true. Kratzer appears to have produced nothing of any significance, was merely the designer and maker of sundials, and an elementary maths teacher, who was only portrayed by Holbein, because for a time they shared the same employers and were apparently mates. 

So, who was Kratzer and how did he and Holbein become mates? Here we find a common problem with minor scientific figures in the Renaissance, there are no biographies, no handy archives giving extensive details of his life. All we have are a few, often vague, sometimes contradictory, traces in the proverbial sands of time from which historians have attempted to reconstruct at least a bare outline of his existence. 

Kratzer was born in 1487 in Munich, the son of a saw-smith and it is probably that he learnt his metal working skills, as an instrument maker, from his father. He matriculated at the University of Köln 18 November 1506 and graduated BA 14 June 1509. He moved onto the University of Wittenberg, famous as the university of Martin Luther. However, this was before the Reformation and Wittenberg, a young university first founded in 1502, was then still Catholic. We now lose track of Kratzer, who is presumed to have then worked as an instrument maker. Sometime in the next years, probably in 1517, he copied some astronomical manuscripts at the Carthusian monastery of Maurbach, near Vienna. 

In January 1517, Pieter Gillis (1486–1533) wrote to his erstwhile teacher Erasmus (1466–1536) that the skilled mathematician Kratzer was on his way with astrolabes and spheres, and a Greek book.

HOLBEIN, Hans the Younger (b. 1497, Augsburg, d. 1543, London) Portrait of Erasmus of Rotterdam 1523 Wood, 76 x 51 cm National Gallery, London

This firmly places Kratzer in the circle of humanist scholars, most famously Erasmus and Thomas More (1478–1535) author of Utopia, who founded the English Renaissance on the court of Henry VIII (1491–1547). Holbein was also a member of this circle. Erasmus and Holbein had earlier both worked for the printer/publisher collective of Petri-Froben-Amerbach in Basel. Erasmus as a copyeditor and Holbein as an illustrator. Holbein produced the illustrations for Erasmus’ In Praise of Folly (written 1509, published by Froben 1511)

Holbein’s witty marginal drawing of Folly (1515), in the first edition, a copy owned by Erasmus himself

Kratzer entered England either at the end of 1517 or the beginning of 1518. His first identifiable employment was in the household of Thomas More as maths teacher for a tutorial group that included More’s children. It can be assumed that it was here that he got to know Holbein, who was also employed by More. 

Thomas More Portrait by Hans Holbein 1527

For his portraits, Holbein produced very accurate complete sketches on paper first, which he then transferred geometrically to his prepared wooden panels to paint them. Around 1527, Holbein painted a group portrait of the More family that is no longer extant, but the sketch is. The figures in the sketch are identified in writing and the handwriting has been identified as Kratzer’s. 

Like Holbein, Kratzer moved from More’s household to the court of Henry VIII, where he listed in the court accounts as the king’s astronomer with an income of £5 a quarter in 1529 and 1531. It is not very clear when he entered the King’s service but in 1520 Cuthbert Tunstall (1474–1559), later Prince-Bishop of Durham, wrote in a letter:

Met at Antwerp with [Nicolas Kratzer], an Almayn [German], devisor of the King’s horologes, who said the King had given him leave to be absent for a time.

Both Tunstall and Kratzer were probably in Antwerp for the coronation of Charles V (1500–1558) as King of Germany, which took place in Aachen. There are hints that Kratzer was there to negotiate with members of the German court on Henry’s behalf. Albrecht Dürer (1471–1528) was also in the Netherlands; he was hoping that Charles would continue the pension granted to him by Maximilian I, who had died in 1519. Dürer and Kratzer met in the house of Erasmus and Kratzer was present as Dürer sketched a portrait of Erasmus. He also drew a silver point portrait of Kratzer, which no longer exists. 


Dürer sketch of Erasmus 1520
Dürer engraved portrait of Erasmus based on 1520 sketch finished in 1526. Erasmus reportedly didn’t like the portrait

Back in England Kratzer spent some time lecturing on mathematical topics at Oxford University during the 1520s. Here once again the reports are confused and contradictory. Some sources say he was there at the behest of the King, others that he was there in the service of Cardinal Wolsey. There are later claims that Kratzer was appointed a fellow of Corpus Christi College, but the college records do not confirm this. However, it is from the Oxford records that we know of Kratzer’s studies in Köln and Wittenberg, as he was incepted in Oxford as BA and MA, on the strength of his qualifications from the German institutions, in the spring of 1523. 

During his time in Oxford, he is known to have erected two standing sundials in the college grounds, one of which bore an anti-Lutheran inscription.

Drawing of Kratzer’s sundial made for the garden of Corpus Christi College Oxford

Neither dial exists any longer and the only dial of his still there is a portable brass dial in the Oxford History of Science Museum, which is engraved with a cardinal’s hat on both side, which suggests it was made for Wolsey.

Kratzer polyhedral sundial presumably made for Cardinal Wolsey Museum for the History of Science Oxford

On 24 October 1524 Kratzer wrote the following to Dürer in Nürnberg

Dear Master Albert, I pray you to draw for me a model of the instrument that you saw at Herr Pirckheimer’s by which distances can be measured, and of which you spoke to me at Andarf [Antwerp], or that you will ask Herr Pirckheimer to send me a description of the said instrument… Also I desire to know what you ask for copies of all your prints, and if there is anything new at Nuremberg in my craft. I hear that our Hans, the astronomer, is dead. I wish you to write and tell me what he has left behind him, and about Stabius, what has become of his instruments and his blocks. Greet in my name Herr Pirckheimer. I hope shortly to make a map of England which is a great country, and was not known to Ptolemy; Herr Pirckheimer will be glad to see it. All who have written of it hitherto have only seen a small part of England, no more… I beg of you to send me the likeness of Stabius, fashioned to represent St. Kolman, and cut in wood…

Herr Pirckheimer is Willibald Pirckheimer (1470–1530), who was a lawyer, soldier, politician, and Renaissance humanist, who produced a new translation of Ptolemaeus’ Geographia from Greek into Latin.

Engraved portrait of Willibald Pirckheimer Dürer 1524

He was Dürer’s life-long friend, (they were born in the same house), patron and probably lover.  He was at the centre of the so-called Pirckheimer circle, a group of mostly mathematical humanists that included “Hans the astronomer, who was Johannes Werner (1468–1522), mathematician, astronomer, astrologer, geographer,

Johannes Werner artist unknown

and cartographer and Johannes “Stabius” (c.1468–1522) mathematician, astronomer, astrologer, and cartographer.

Johannes Stabius portrait by Dürer

Werner was almost certainly Dürer’s maths teacher and Stabius worked together with Dürer on various projects including his star maps. The two are perhaps best known for the Werner-Stabius heart shaped map projection. 

Dürer replied to Kratzer 5 December 1524 saying that Pirckheimer was having the required instrument made for Kratzer and that the papers and instruments of Werner and Stabius had been dispersed.

Here it should be noted that Dürer, in his maths bookUnderweysung der Messung mit dem Zirkel und Richtscheyt (Instruction in Measurement with Compass and Straightedge), published the first printed instructions in German on how to construct and orientate sundials. The drawing of one sundial in the book bears a very strong resemblance to the polyhedral sundial that Kratzer made for Cardinal Wolsey and presumably Kratzer was the original source of this illustration. 

Dürer drawing of a sundial

Kratzer is certainly the source of the mathematical instruments displayed on the top shelf of Holbein’s most famous painting the Ambassadors, as several of them are also to be seen in Holbein’s portrait of Kratzer.

in’s The AmbassadorsHolbe

Renaissance Mathematicus friend and guest blogger, Karl Galle, recently made me aware of a possible/probable indirect connection between Kratzer and Nicolas Copernicus (1473–1543). Georg Joachim Rheticus (1514–1574) relates that Copernicus’ best friend Tiedemann Giese (1480–1550) possessed his own astronomical instruments including a portable sundial sent to him from England. This was almost certainly sent to him by his brother Georg Giese (1497–1562) a prominent Hanseatic merchant trader, who lived in the Steelyard, the Hansa League depot in London, during the 1520s and 30s.

London’s Steelyard

He was one of a number of Hanseatic merchants, whose portraits were painted by Holbein, so it is more than likely that the sundial was one made by Kratzer. 

Georg Giese portrait by Hans Holbein 1532

Sometime after 1530, Kratzer fades into the background with only occasional references to his activities. After 1550, even these ceased, so it is assumed that he had died around this time. In the first half of the sixteenth century England lagged behind mainland Europe in the mathematical disciplines including instrument making, so it is a natural assumption that Kratzer with his continental knowledge was a welcome guest in the Renaissance humanist circles of the English court, as was his younger contemporary, the Flemish engraver and instrument maker, Thomas Gemini (1510–1562). Lacking homegrown skilled instrument makers, the English welcomed foreign talent and Kratzer was one who benefited from this. 

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Filed under History of Astronomy, History of Mathematics, History of science, History of Technology, 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 – VIII

In the last two episodes we have looked at developments in printing and art that, as we will see later played an important role in the evolving Renaissance sciences. Today, we begin to look at another set of developments that were also important to various areas of the newly emerging practical sciences, those in mathematics. It is a standard cliché that mathematisation played a central roll in the scientific revolution but contrary to popular opinion the massive increase in the use of mathematics in the sciences didn’t begin in the seventeenth century and certainly not as the myth has it, with Galileo.

Medieval science was by no means completely devoid of mathematics despite the fact that it was predominantly Aristotelian, and Aristotle thought that mathematics was not scientia, that is, it did not deliver knowledge of the natural world. However, the mathematical sciences, most prominent astronomy and optics, had a fairly low status within medieval university culture.

One mathematical discipline that only really became re-established in Europe during the Renaissance was trigonometry. This might at first seem strange, as trigonometry had its birth in Greek spherical astronomy, a subject that was taught in the medieval university from the beginning as part of the quadrivium. However, the astronomy taught at the university was purely descriptive if not in fact even prescriptive. It consisted of very low-level descriptions of the geocentric cosmos based largely on John of Sacrobosco’s (c. 1195–c. 1256) Tractatus de Sphera (c. 1230). Sacrobosco taught at the university of Paris and also wrote a widely used Algorismus, De Arte Numerandi. Because Sacrobosco’s Sphera was very basic it was complimented with a Theorica planetarum, by an unknown medieval author, which dealt with elementary planetary theory and a basic introduction to the cosmos. Mathematical astronomy requiring trigonometry was not hardy taught and rarely practiced.

Both within and outside of the universities practical astronomy and astrology was largely conducted with the astrolabe, which is itself an analogue computing device and require no knowledge of trigonometry to operate.

Before we turn to the re-emergence of trigonometry in the medieval period and its re-establishment during the Renaissance, it pays to briefly retrace its path from its origins in ancient Greek astronomy to medieval Europe.

The earliest known use of trigonometry was in the astronomical work of Hipparchus, who reputedly had a table of chords in his astronomical work. This was spherical trigonometry, which uses the chords defining the arcs of circles to measure angles. Hipparchus’ work was lost and the earliest actual table of trigonometrical chords that we know of is in Ptolemaeus’ Mathēmatikē Syntaxis or Almagest, as it is usually called today.


The chord of an angle subtends the arc of the angle. Source: Wikimedia Commons

When Greek astronomy was appropriated in India, the Indian astronomers replaced Ptolemaeus’ chords with half chords thus creating the trigonometrical ratios now known to us, as the sine and the cosine.

It should be noted that the tangent and cotangent were also known in various ancient cultures. Because they were most often associated with the shadow cast by a gnomon (an upright pole or post used to track the course of the sun) they were most often known as the shadow functions but were not considered part of trigonometry, an astronomical discipline. So-called shadow boxes consisting of the tangent and cotangent used for determine heights and depths are often found on the backs of astrolabes.


Shadow box in the middle of a drawing of the reverse of Astrolabium Masha’Allah Public Library Bruges [nl] Ms. 522. Basically the tangent and cotangent functions when combined with the alidade

  Islamic astronomers inherited their astronomy from both ancient Greece and India and chose to use the Indian trigonometrical half chord ratios rather than the Ptolemaic full cords. Various mathematicians and astronomers made improvements in the discipline both in better ways of calculating trigonometrical tables and producing new trigonometrical theorems. An important development was the integration of the tangent, cotangent, secant and cosecant into a unified trigonometry. This was first achieved by al-Battãnī (c.858–929) in his Exhaustive Treatise on Shadows, which as its title implies was a book on gnonomics (sundials) and not astronomy. The first to do so for astronomy was Abū al-Wafā (940–998) in his Almagest.


Image of Abū al-Wafā Source: Wikimedia Commons

It was this improved, advanced Arabic trigonometry that began to seep slowly into medieval Europe in the twelfth century during the translation movement, mostly through Spain. It’s reception in Europe was very slow.

The first medieval astronomers to seriously tackle trigonometry were the French Jewish astronomer, Levi ben Gershon (1288–1344), the English Abbot of St Albans, Richard of Wallingford (1292–1336) and the French monk, John of Murs (c. 1290–c. 1355) and a few others.


Richard of Wallingford Source: Wikimedia Commons

However, although these works had some impact it was not particularly widespread or deep and it would have to wait for the Renaissance and the first Viennese School of mathematics, Johannes von Gmunden (c. 1380­–1442), Georg von Peuerbach (1423–1461) and, all of whom were Renaissance humanist scholars, for trigonometry to truly establish itself in medieval Europe and even then, with some delay.

Johannes von Gmunden was instrumental in establishing the study of mathematics and astronomy at the University of Vienna, including trigonometry. His work in trigonometry was not especially original but displayed a working knowledge of the work of Levi ben Gershon, Richard of Wallingford, John of Murs as well as John of Lignères (died c. 1350) and Campanus of Novara (c. 200–1296). His Tractatus de sinibus, chordis et arcubus is most important for its probable influence on his successor Georg von Peuerbach.

Peuerbach produced an abridgement of Gmunden’s Tractatus and he also calculated a new sine table. This was not yet comparable with the sine table produced by Ulugh Beg (1394–1449) in Samarkand around the same time but set new standards for Europe at the time. It was Peuerbach’s student Johannes Regiomontanus, who made the biggest breakthrough in trigonometry in Europe with his De triangulis omnimodis (On triangles of every kind) in 1464. However, both Peuerbach’s sine table and Regiomontanus’ De triangulis omnimodis would have to wait until the next century before they were published. Regiomontanus’ On triangles did not include tangents, but he rectified this omission in his Tabulae Directionum. This is a guide to calculating Directions, a form of astrological prediction, which he wrote at the request for his patron, Archbishop Vitéz. This still exist in many manuscript copies, indicating its popularity. It was published posthumously in 1490 by Erhard Ratdolt and went through numerous editions, the last of which appeared in the early seventeenth century.


A 1584 edition of Regiomontanus’Tabulae Directionum Source

Peuerbach and Regiomontanus also produced their abridgement of Ptolemaeus’ Almagest, the Epitoma in Almagestum Ptolemae, published in 1496 in Venice by Johannes Hamman. This was an updated, modernised version of Ptolemaeus’ magnum opus and they also replaced his chord tables with modern sine tables. A typical Renaissance humanist project, initialled by Cardinal Basilios Bessarion (1403–1472), who was a major driving force in the Humanist Renaissance, who we will meet again later. The Epitoma became a standard astronomy textbook for the next century and was used extensively by Copernicus amongst others.


Title page Epitoma in Almagestum Ptolemae Source: Wikimedia Commons

Regiomontanus’ De triangulis omnimodis was edited by Johannes Schöner and finally published in Nürnberg in 1533 by Johannes Petreius, together with Peuerbach’s sine table, becoming a standard reference work for much of the next century. This was the first work published, in the European context, that treated trigonometry as an independent mathematical discipline and not just an aide to astronomy.

Copernicus (1473–1543,) naturally included modern trigonometrical tables in his De revolutionibus. When Georg Joachim Rheticus (1514–1574) travelled to Frombork in 1539 to visit Copernicus, one of the books he took with him as a present for Copernicus was Petreius’ edition of De triangulis omnimodis. Together they used the Regiomontanus text to improve the tables in De revolutionibus. When Rheticus took Copernicus’ manuscript to Nürnberg to be published, he took the trigonometrical section to Wittenberg and published it separately as De lateribus et angulis triangulorum (On the Sides and Angles of Triangles) in 1542, a year before De revolutionibus was published.


Rheticus’ action was the start of a career in trigonometry. Nine years later he published his Canon doctrinae triangvlorvmin in Leipzig. This was the first European publication to include all of the six standard trigonometrical ratios six hundred years after Islamic mathematics reached the same stage of development. Rheticus now dedicated his life to producing what would become the definitive work on trigonometrical tables his Opus palatinum de triangulis, however he died before he could complete and publish this work. It was finally completed by his student Valentin Otto (c. 1548–1603) and published in Neustadt and der Haardt in 1596.


Source: Wikimedia Commons

In the meantime, Bartholomäus Piticus (1561–1613) had published his own extensive work on both spherical and plane trigonometry, which coined the term trigonometry, Trigonometria: sive de solution triangulorum tractatus brevis et perspicuous, one year earlier, in 1595.


Source:. Wikimedia Commons

This work was republished in expanded editions in 1600, 1608 and 1612. The tables contained in Pitiscus’ Trigonometria were calculated to five or six places, whereas those of Rheticus were calculated up to more than twenty places for large angles and fifteenth for small ones. In comparison Peuerbach’s sine tables from the middle of the fifteenth century were only accurate to three places of decimals. However, on inspection, despite the years of effort that Rheticus and Otho had invested in the work, some of the calculations were found to be defective. Pitiscus recalculated them and republished the work as Magnus canon doctrinae triangulorum in 1607.


He published a second further improved version under the title Thesaurus mathematicus in 1613. These tables remained the definitive trigonometrical tables for three centuries only being replaced by Henri Andoyer’s tables in 1915–18.

In the seventeenth century a major change in trigonometry took place. Whereas throughout the Renaissance it had been handled as a branch of practical mathematics, used to solve spherical and plane triangles in astronomy, cartography, surveying and navigation, the various trigonometrical ratios now became mathematical functions in their own right, a branch of purely theoretical mathematics. This transition mirroring the general development in the sciences that occurred between the Renaissance and the scientific revolution, from practical to theoretical science.


Filed under History of Astronomy, History of Islamic Science, History of Mathematics, History of science, Renaissance Science

Alphabet of the stars

The brightest star in the night sky visible to the naked eye is Sirius the Dog Star. Its proper astronomical name is 𝛂 Canis Majoris. Historically for navigators in the northern hemisphere the most important star was the pole star, currently Polaris (the star designated the pole star changes over time due to the precession of the equinox), whose proper astronomical name is 𝛂 Ursae Minoris. The astronomical name of Sirius means that it is a star in the constellation in Canis Major, the greater dog, whilst Polaris’ name means that it is a star in Ursus Minor, the little bar. But what does the alpha that precedes each of these names mean and where does it come from?

A constellation consists of quite a large number of stars and this means that we need some sort of system of labelling or naming them for star catalogues, star maps or celestial atlases. The system that is used is the letters of the Greek alphabet. These are however not simply attached at random to some star or other but applied according to a system. That system was determined by apparent brightness.

Anybody who looks up into the night sky, when it is cloud free and there is no light pollution, will quickly realise that the various stars vary quite substantially in brightness. The ancient Greek astronomers were very much aware of this and divide up the stars into six categories, or as they are known magnitudes, according to their perceived or apparent brightness. Our unaided perception of the stars does not take into account their differing distances, so a very bright star that is very far away will appear less bright than not so bright star that is much nearer to the Earth. The earliest record of this six-magnitude scheme (one is the brightest, six the dimmest) is in Ptolemaeus’ Mathēmatikē Syntaxis, but it was probably older. The attribution, by some, to Hipparchus is purely speculative. Ptolemaeus also indicates intermediate values by writing greater than or less than magnitude X.

Using this basic framework inherited from Ptolemaeus, the early modern German astronomer Johann Bayer (1572–1625) labelled each of the stars in his maps of the constellations in his Uranometria (first published Augsburg, 1603) with a letter of the Greek alphabet, starting with alpha, in descending order of brightness, creating what is now known as the Bayer designation for stars. In this system the Greek letter is followed by a three-letter abbreviation of the constellation name. So, Aldebaran in the constellation Taurus is designated 𝛂 Tauri, abbreviated 𝛂 Tau. Who was Johann Bayer and what is the Uranometria?

Johann Bayer was born in Rain, a small town in Bavaria about forty kilometres north of Augsburg. He attended the Latin school in Rain and then probably a higher school in Augsburg.


Rain by Matthäus Merian 1665 Source: Wikimedia Commons

He entered the University of Ingolstadt in 1592, where, having completed the foundation course, he went on to study law, graduating with a master’s degree around sixteen hundred. Leaving the university, he settled in Augsburg, where he worked as a lawyer until his death in 1625. The University of Ingolstadt had a strong tradition of the mathematical science over the preceding century, home to notable mathematicians and astronomers such as Johannes Werner, Johannes Stabius and Andreas Stiborius at the end of the fifteenth century and father and son Peter and Phillip Apian in the middle of the sixteenth. It was certainly here that Bayer acquired his love for mathematics and astronomy. He also acquired an interest in archaeology and would later in life take part in excavation in the Via Nomentana during a visit to Rome.


Main building of the University of Ingolstadt 1571 Source: Wikimedia Comms

In 1603 Bayer’s Uranometria was published in Augsburg by Christophorus Mangus, or to give it its full title the Uranometria: omnium asterismorum continens schemata, nova methodo delineata, aereis laminis expressa. (Uranometria, containing charts of all the constellations, drawn by a new method and engraved on copper plates), that is a star atlas. The name derives from Urania the muse of astronomy, which in turn derives from the Greek uranos (oυρανός) meaning sky or heavens, it translates as “measuring the heavens” in analogy to “geometria”, measuring the earth.


Title page of Uranometria Source: Wikimedia Commons

The Uranometria contains fifty-one star-maps engraved on copper plates by Alexander Mair (c. 1562–1617). The first forty-eight carts contain the northern-hemisphere constellations listed and described by Ptolemaeus. For the northern constellations Bayer used Tycho Brahe’s star catalogue, which hadn’t been published yet but was available through various sources. He, however, added one thousand more stars.


Canis Major with Sirius very prominent on his nose Source


Ursa Mino with Polaris on the end of his tail Source:

The forty ninth chart contains twelve southern-hemisphere constellations unknown to Ptolemaeus. Bayer took the star positions and constellation names for this southern-hemisphere chart from the 1597 celestial globe created by Petrus Plancius (1552–1622) of the observations collected for him by the Dutch pilot Pieter Dirkszoon Keyser (c. 1540–1596), which was printed by Jodocus Hondius (1563–1612).


Chart of the Southern-Hemisphere ConstellationsSource

The final two charts are planispheres labelled Synopsis coeli superioris borea (Synopsis of the northern hemisphere) and Synopsis coeli inferioris austrina (Synopsis of the southern hemisphere).


Synopsis coeli superioris borea Source


Synopsis coeli inferioris austrina Source

For each star chart there is a star catalogue. In the first column the stars are listed according to their Ptolemaic number and then in their second column Bayer gives them the Bayer designation. Because the Greek alphabet only has twenty-four letters and some constellations have more than twenty-four stars, Bayer continues his list with the Latin alphabet using lower case letter except for the twenty-fifth star, which is designated with a capital A to avoid confusing a small with an alpha. The listing is not done strictly by order of brightness, listing the stars rather by the Ptolemaic magnitude classes. This means that by several constellations the star designated with an alpha is not actually the constellations brightest star.

Bayer was not the first astronomer to produce printed star maps in Europe (there are earlier printed Chinese star maps) that honour goes to the planispheres produced by Stabius, Dürer and Heinfogel in 1515.


Dürer Northern Hemisphere Star Map Source: Wikimedia Commons

His was also not the first printed star atlas that being the Sfera del mondo e De le stelle fisse (The sphere of the world and the fixed stars) of Alessandro Piccolomini (1508–1579), both published in 1540 and often together. Piccolomini was an Italian humanist, philosopher and astronomer best known for his popularisations of Greek and Latin scientific treatises, which he translated into the vernacular.


Portrait of Alessandro Piccolomini (1508-1579) engraving by Nicolas II de Larmessin Source: Wikimedia Commons

De le stelle fisse has charts of forty-seven of the Ptolemaic constellations, Equuleus (the little horse or foal) is missing. The book has a star catalogue organised by constellation, a series of woodblock plates of the constellations, tables indicating the stellar locations throughout the year and a section dealing with risings and settings of stars with reference to the constellations of the zodiac.


However, unlike the Dürer planispheres and Bayer’s Uranometria, Piccolomini’s De le stelle fisse doesn’t have constellation figures.


The book was very popular and went though, at least, fourteen editions during the sixteenth century. Piccolomini designated the stars in his catalogue with the letters of the Latin alphabet and there is the strong possibility that Bayer was inspired by Piccolomini in adopting his system of designation.

Bayer’s atlas was not free of problems. In the first edition the star catalogues were printed on the reverse of the constellation charts. This meant that it was not possible to consult the catalogue whilst viewing the chart. Also, the lettering of the catalogue showed through the page and spoiled the chart. To solve these problems the catalogue was printed separately in a smaller format under the title Explicatio charecterum aeneis Uranometrias in 1624, the year before Bayer’s death.


It was republished in 1640, 1654, 1697 and 1723. Unfortunately, the Explicatio was marred by printing errors from the start, which got progressively worse with each new edition.

The Uranometria was republished often, and editions are known from in 1624, 1639, 1641, 1648, 1655, 1661, 1666 and 1689. It set standards for star atlases and planispheres and continued to influence the work of other star cataloguers down into the eighteenth century.The next time that a popular science programme on the telly or a science fiction story starts on about Alpha Centauri, the next closest star to our solar system, then you will know that this is the Bayer designation for a magnitude one, possibly the brightest, star in the constellation Centaurus, a centaur being the half man half horse creature from Greek mythology. It’s actually slightly more complex than Bayer believed because Alpha Centauri is now known to be a triple star system and is now designated α Centauri A (officially Rigil Kentaurus), α Centauri B (officially Toliman), and α Centauri C (officially Proxima Centauri).


Uranometria Centaurus with Alpha Centauri on the near side front hoof Source


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