Category Archives: History of Astrology

The poetic astronomer


Regular readers of this blog will know that I can on occasion be a stroppy, belligerent, pedant, who gets rather riled up over people who spread myths of science and who has a tendency to give such people a public kicking on this blog. This tendency earned me the nickname, the HistSci_Hulk in earlier years. The subtitle to a podcast that I stumbled across yesterday on the BBC website provoked my inner Hist_Sci Hulk and has generated this post.

The podcast is a BBC Radio 4 “Radio 4 in Four” four minute documentary on the work of the Indian mathematician and astronomer, Aryabhata: Maths expressed as poetry. The subtitle was: In 5th century India, clever man Aryabhata wrote his definitive mathematical work entirely in verse and long before Galileo, argued the world was round [my emphasis]. It was that final clause that provoked my HistSci_Hulk moment.

I’ve lost count of how many times over the years I have explained patiently and oft not so patiently that educated society in European culture have known and accepted that the world is a sphere since at least the sixth century BCE. This is the most recent account here on the blog. Bizarrely in the podcast no mention is made of Aryabhata’s cosmological or astronomical views, so it is real puzzle as to why it’s mentioned in the subtitle. What is interesting is the fact that as a cosmologist Aryabhata held a fairly rare position, although he was a geocentrist he believed that the earth revolved around its own axis, i.e. geocentrism with diurnal rotation. You can read about the history of this theory here in an earlier blog post.

Statue of Aryabhata on the grounds of IUCAA, Pune. As there is no known information regarding his appearance, any image of Aryabhata originates from an artist’s conception.
Source: Wikimedia Commons

More interesting is the correct fact that Aryabhata wrote his astronomical/mathematical thesis in verse form. As the podcast points out this is because the culture in which he was writing was an oral one and complex facts are easier to remember in verse rather than in prose. What the podcast doesn’t say is that Aryabhata was not the only astronomer/mathematician to express his results in verse and was in this sense by no means unique. In fact he is part of a solid tradition of mathematical Sanskrit poetry.

India was not the only culture to use poetry to express scientific content. Probably the most famous example is the Latin poem De rerum natura by the first century BCE Roman poet Lucretius, which is the most extensive description of the physics of the ancient Greek atomists. The poem played a central role in the revival of atomism in the early modern period; a revival that several historians of science, such as David Lindberg, consider to be a key element in the so-called scientific revolution of the seventeenth century.

In astronomy/ astrology there is a poem from antiquity that played a significant role in the Renaissance. This is the Astronomica probably written by the poet Marcus Manilius in the first century CE; the first printed edition of this was published by Regiomontanus in Nürnberg in 1473.

Many people are not aware of some highly significant scientific poems from the eighteenth century written and published by Charles Darwin’s grandfather, Erasmus.

Joseph Wright of Derby, Erasmus Darwin (1770; Birmingham Museum and Art Gallery).
Source: Wikimedia Commons

Darwin’s The Loves of the Plants was the first work in English to popularise the botanical works of Linnaeus in English. The poem caused something of a scandal because it emphasised the explicit sexual nature of Linnaeus’ system of botanical nomenclature and was thus considered unsuitable for polite society. The Loves of the Plants was published together with another poem, The Economy of Vegetation, a more general poem on scientific progress and technological innovation, of which Darwin as a prominent member of the Lunar Society of Birmingham was very much aware. The Economy of Vegetation expresses an evolutionary view of progress. A footnote to The Loves of the Plants contains the first outlines of Darwin’s theory of biological evolution, which he would then expand upon in his prose work Zoonomia. Erasmus Darwin’s is an adaptive theory of evolution and is thus oft referred to as Lamarckian, although as Erasmus preceded Lamarck, maybe his theory should be referred to as Darwinian! A posthumous poem of Darwin’s, The Temple of Nature, contains a full description of his theory of evolution in verse.

Writing this led me to the thought that maybe editors of modern scientific journals should require their authors to submit their papers in iambic pentameters or in Shakespearean blank verse, with the abstracts written as sonnets. It would certainly make reading scientific papers more interesting.




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

An orb by any other name would circle as smoothly

Alan Stern, the principal investigator of the New Horizons Mission to Pluto is calling for a new definition for planets in order to return Pluto to, what he and other see as its former glory, the status of a planet. The so called demotion of Pluto caused the release of strong emotions amongst the distant planet’s fans and the stunning success of the New Horizons mission added fuel to the flames in the on going debate. Many of those participating seem to be somewhat unaware of the fact that the definition of what is a planet has changed down the centuries and I thought I would write a brief guide to the changing fortunes of the term planet since its inception in antiquity.

It should be made clear that I shall only be talking about European astronomy and not any other traditions such as Chinese, Indian, Mayan astronomies etc. European astronomy/astrology has its roots in ancient Babylon. The Babylonian tradition was most concerned with the Moon and the Sun but the Babylonians were aware of the planets Mercury, Venus, Mars, Jupiter and Saturn, which they like other ancient cultures regarded as divinities. They tracked their orbits over very long periods of time and developed algorithms to determine their appearances and disappearances for omen astrological purposes. They don’t appear to have been interested in the mechanism of the planetary orbits. I’m anything but an expert on Babylonian astronomy/astrology and I don’t know if they had a collective name for them.

The direct inheritors of the Babylonian celestial interests were the ancient Greeks and they were very much interested in orbital mechanics and they also coined the term planet. For the Greeks all illuminated objects in the heavens were stars (aster, astron), as I explained in an earlier post. The stars as we know them were the fixed stars because they appeared to remain in place relative to each other whilst the sphere of the fixed stars rotated about the celestial axis once every twenty-four hours. It was of course the Earth that rotated about its axis and not the stars but the Greeks were not aware of that. The illusion that the stars, visible to the naked-eye, are all equidistant to the Earth is easy to experience. Just go out into the countryside were there is no light pollution and look up at the night sky on a clear night. You will see the ‘sphere of the fixed stars’, as experienced by the ancient Greeks. Comets, much rarer and apparently random, were hairy stars, the word comet derives from the Greek aster kometes, literally long-haired star. The five planets known to the Babylonians and the Moon and the Sun were all present on a regular basis but unlike the fixed stars they appeared to wander around the heavens and so they became asteres planetai that is wandering stars, from planasthai to wander. The Greeks had seven wanderers Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn. The Earth was of course stationary at the middle of the whole system and so was not a planet.

16th-century representation of Ptolemy’s geocentric model in Peter Apian’s Cosmographia, 1524
Source: Wikimedia Commons

Subsequent European cultures and the Islamic Empire inherited the Greek model of the heavens with its seven wanderers and nothing of significance changed down the centuries until the Renaissance and the advent of Copernican heliocentrism in 1543. Copernicus’s new model was of course a major upheaval. The Sun became stationary and the Earth became a planet wandering through the heavens. The Moon acquired a strange new status, no longer orbiting the centre, now the Sun, but orbiting the Earth. Heliocentricity took more than one hundred years to become establish and Copernicus’ upheaval brought no immediate change of terminology.

The heliocentric order of the heavens from Copernicus’ De revolutionibus 1543

The first change came in 1610 with the telescopic discovery of the four largest moons of Jupiter by Galileo and Simon Marius. Here we have four new celestial bodies orbiting a planet, as with the Moon, and not the centre of the cosmos. At first Galileo referred to them as stars or planets, leading Kepler, who was at first not clear what the four new objects were, to panic and fear that Giordano Bruno was right and that all stars had planets. This conflicted with Kepler’s own finite universe cosmology. He was greatly relieved to discover that the new planets were in reality moons and coined the term satellite from the Latin satillitem meaning attendant, companion, courtier, accomplice or assistant. Kepler was very fond of creating new scientific terminology. The term was not adopted immediately but by the end of the seventeenth century astronomers differentiated between planets and satellites, around the same time as heliocentricity became firmly established and the Sun finally ceased to be a planet and the Earth finally became one. Around the same time astronomers became convinced that the Sun was actually one of the ‘fixed’ stars.

We entered the eighteenth century with six planets, Mercury, Venus, Earth, Mars, Jupiter and Saturn and so it remained until the musician and amateur astronomer William Herschel shocked the world with the discovery of a seventh one, Uranus on 13 March 1781. The first new planet discovered in about four thousand years of planetary astronomy.

William Herschel. Portrait by Lemuel Francis Abbott 1785, National Portrait Gallery, London
Source: Wikimedia Commons

In the middle of the eighteenth century Johann Elert Bode published what is now know as the Titus-Bode law in which the distance of the planets from the sun seemed to fit an arithmetical series with a gap in the series between Mars and Jupiter. Herschel’s discovery of Uranus beyond Saturn fit the Titus-Bode series, which led the German astronomer Baron Franz Xaver von Zach to organise a systematic search for that ‘missing planet’ between Mars and Jupiter. In fact the discovery was made by the Italian astronomer Giuseppe Piazzi, who was not part of Zach’s search team but discovered Ceres on 1 January 1801, exactly, where it should be according to the Titus-Bode law and then there were eight. Interestingly Piazzi lost Ceres and Carl Friedrich Gauss developed a new method of determining planetary orbits, which allowed astronomers to find it again. Very soon other astronomers discovered Pallas, Juno and Vesta and there were now eleven planets. It was not long before it became clear that the four new celestial bodies were somehow different to the other planets and Herschel coined the term ἀστεροειδής, or asteroeidēs, meaning ‘star-like, star-shaped’, in English asteroid. These smaller wanderers were also known as minor planets or planetoids although it was first in the later nineteenth century, by which time several more asteroids had been discovered that these terms became established and the number of planets was once again reduced, not to seven but to eight!

Piazzi’s book “Della scoperta del nuovo pianeta Cerere Ferdinandea” outlining the discovery of Ceres, dedicated the new “planet” to Ferdinand I of the Two Sicilies.
Source: Wikimedia Commons

It was eight because in the mean time both the English astronomer John Crouch Adams and the French astronomer Urbain Le Verrier had predicted the existence of an eighth planet based on gravitational anomalies in the orbit of Uranus and on 23 September 1846 the German observational astronomer discovered Neptune, the eighth planet, based on the predictions of Le Verrier.

Urbain Le Verrier
Source: Wikimedia Commons

In the late nineteenth century similar anomalies in the orbit of Neptune led Percival Lowell to predict the existence of a ninth planet and he set up his own observatory to search for it. In 1916 Lowell died without having found his predicted planet. However in 1929/30 the young Clyde Tombaugh discovered Pluto, the ninth planet.

From: O’Hara, Elva R. (2006). Clyde W. Tombaugh: Farm Boy Reached for the Stars. Borderlands 25.
Source: Wikimedia Commons

As with Ceres and the asteroids Pluto’s planetary status was challenged by the discovery of other orbiting objects in the Kuiper belt outside of the orbit of Neptune from the 1990s onward. The discovery of Eris in 2005 led to a serious reconsideration of Pluto’s planetary status and famously in 2006 the International Astronomical Union introduced a new formal definition of the term planet, which removed Pluto’s planetary status and according to Pluto’s fans demoted it to the status of a dwarf planet. At the moment there are five recognised dwarf planets Pluto, Ceres (the largest asteroid), Haumea, Makemake and Eris.

Eris (center) and Dysnomia (left of center), taken by the Hubble Space Telescope
Image NASA
Source: Wikimedia Commons

As I said at the beginning the Pluto fan club has not given up the fight and are now proposing a new definition of the term planet, which would not only return Pluto to its planetary status but also apparently the Moon. I hope I have shown that the term planet has gone through quite a lot of changes over the last two and a half thousand years or so since the ancient Greeks first coined it and we can, I think, assume that it will go through quite a few more in the future in particular with respect to the thousands of exoplanets that astronomers are busy discovering.


Filed under History of Astrology, History of Astronomy, History of science

Why Mathematicus?

“The Renaissance Mathematiwot?”

“Mathematicus, it’s the Latin root of the word mathematician.”

“Then why can’t you just write The Renaissance Mathematician instead of showing off and confusing people?”

“Because a mathematicus is not the same as a mathematician.”

“But you just said…”

“Words evolve over time and change their meanings, what we now understand as the occupational profile of a mathematician has some things in common with the occupational profile of a Renaissance mathematicus but an awful lot more that isn’t. I will attempt to explain.”

The word mathematician actually has its origins in the Greek word mathema, which literally meant ‘that which is learnt’, and came to mean knowledge in general or more specifically scientific knowledge or mathematical knowledge. In the Hellenistic period, when Latin became the lingua franca, so to speak, the knowledge most associated with the word mathematica was astrological knowledge. In fact the terms for the professors[1] of such knowledge, mathematicus and astrologus, were synonymous. This led to the famous historical error that St. Augustine rejected mathematics, whereas his notorious attack on the mathematici[2] was launched not against mathematicians, as we understand the term, but against astrologers.

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome Source: Wikimedia Commons

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome
Source: Wikimedia Commons

However St. Augustine lived in North Africa in the fourth century CE and we are concerned with the European Renaissance, which, for the purposes of this post we will define as being from roughly 1400 to 1650 CE.

The Renaissance was a period of strong revival for Greek astrology and the two hundred and fifty years that I have bracketed have been called the golden age of astrology and the principle occupation of our mathematicus is still very much the casting and interpretation of horoscopes. Mathematics had played a very minor role at the medieval universities but the Renaissance humanist universities of Northern Italy and Krakow in Poland introduced dedicated chairs for mathematics in the early fifteenth century, which were in fact chairs for astrology, whose occupants were expected to teach astrology to the medical students for their astro-medicine or as it was known iatro-mathematics. All Renaissance professors of mathematics down to and including Galileo were expected to and did teach astrology.

A Renaissance Horoscope Kepler's Horoskop für Wallenstein Source: Wikimedia Commons

A Renaissance Horoscope
Kepler’s Horoskop für Wallenstein
Source: Wikimedia Commons

Of course, to teach astrology they also had to practice and teach astronomy, which in turn required the basics of mathematics – arithmetic, geometry and trigonometry – which is what our mathematicus has in common with the modern mathematician. Throughout this period the terms Astrologus, astronomus and mathematicus – astrologer, astronomer and mathematician ­– were synonymous.

A Renaissance mathematicus was not just required to be an astronomer but to quantify and describe the entire cosmos making him a cosmographer i.e. a geographer and cartographer as well as astronomer. A Renaissance geographer/cartographer also covered much that we would now consider to be history, rather than geography.

The Renaissance mathematicus was also in general expected to produce the tools of his trade meaning conceiving, designing and manufacturing or having manufactured the mathematical instruments needed for astronomer, surveying and cartography. Many were not just cartographers but also globe makers.

Many Renaissance mathematici earned their living outside of the universities. Most of these worked at courts both secular and clerical. Here once again their primary function was usually court astrologer but they were expected to fulfil any functions considered to fall within the scope of the mathematical science much of which we would see as assignments for architects and/or engineers rather than mathematicians. Like their university colleagues they were also instrument makers a principle function being horologist, i.e. clock maker, which mostly meant the design and construction of sundials.

If we pull all of this together our Renaissance mathematicus is an astrologer, astronomer, mathematician, geographer, cartographer, surveyor, architect, engineer, instrument designer and maker, and globe maker. This long list of functions with its strong emphasis on practical applications of knowledge means that it is common historical practice to refer to Renaissance mathematici as mathematical practitioners rather than mathematicians.

This very wide range of functions fulfilled by a Renaissance mathematicus leads to a common historiographical problem in the history of Renaissance mathematics, which I will explain with reference to one of my favourite Renaissance mathematici, Johannes Schöner.

Joan Schonerus Mathematicus Source: Wikimedia Commons

Joan Schonerus Mathematicus
Source: Wikimedia Commons

Schöner who was a school professor of mathematics for twenty years was an astrologer, astronomer, geographer, cartographer, instrument maker, globe maker, textbook author, and mathematical editor and like many other mathematici such as Peter Apian, Gemma Frisius, Oronce Fine and Gerard Mercator, he regarded all of his activities as different aspects or facets of one single discipline, mathematica. From the modern standpoint almost all of activities represent a separate discipline each of which has its own discipline historians, this means that our historical picture of Schöner is a very fragmented one.

Because he produced no original mathematics historians of mathematics tend to ignore him and although they should really be looking at how the discipline evolved in this period, many just spring over it. Historians of astronomy treat him as a minor figure, whilst ignoring his astrology although it was this that played the major role in his relationship to Rheticus and thus to the publication of Copernicus’ De revolutionibus. For historians of astrology, Schöner is a major figure in Renaissance astrology although a major study of his role and influence in the discipline still has to be written. Historians of geography tend to leave him to the historians of cartography, these whilst using the maps on his globes for their studies ignore his role in the history of globe making whilst doing so. For the historians of globe making, and yes it really is a separate discipline, Schöner is a central and highly significant figure as the founder of the long tradition of printed globe pairs but they don’t tend to look outside of their own discipline to see how his globe making fits together with his other activities. I’m still looking for a serious study of his activities as an instrument maker. There is also, as far as I know no real comprehensive study of his role as textbook author and editor, areas that tend to be the neglected stepchildren of the histories of science and technology. What is glaringly missing is a historiographical approach that treats the work of Schöner or of the Renaissance mathematici as an integrated coherent whole.

Western hemisphere of the Schöner globe from 1520. Source: Wikimedia Commons

Western hemisphere of the Schöner globe from 1520.
Source: Wikimedia Commons

The world of this blog is at its core the world of the Renaissance mathematici and thus we are the Renaissance Mathematicus and not the Renaissance Mathematician.

[1] That is professor in its original meaning donated somebody who claims to possessing a particular area of knowledge.

[2] Augustinus De Genesi ad Litteram,

Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant. II, xvii, 37


Filed under History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, History of science, History of Technology, Renaissance Science

Another public service announcement

Marius Book Launch

In September 2014 a conference was held in Nürnberg, as the climax of a year dedicated to celebrating the life and work of the Franconian astronomer, astrologer and mathematician Simon Marius, whose magnum opus Mundus Iovialis was published four hundred years earlier in 1614.

The papers held at that conference together with some other contributions from people who could not attend in person have now been collected together in the book Simon Marius und Seine Forschung, eds. Hans Gaab and Pierre Leich (= Acta Historica Astronomiae, Band 57) which will be official launched in the Thalia bookshop in Nürnberg on this coming Thursday, 13 October at 18:30 MET.

This volume contains papers by a wide range of scholars and could/should be of interest to anybody studying the histories of astronomy, astrology and/or mathematics in the Early Modern Period. It can be purchased online, after Thursday, directly from the publishers, Leipziger Universitätsverlag


For those who would like to know more about the book including a table of contents (Inhaltsverzeichnis) they can inform themselves on the Marius Portal here.

For those who cannot read German, an English edition of the book is in planning for next year, for which further contributions on the life and work of Simon Marius would also be welcome. If anybody has any questions regarding this volume I would be happy to answer them.


P.S. For those waiting for blogging to resume here at the Renaissance Mathematicus I can report that there is light at the end of the tunnel!





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

The Astrolabe – an object of desire

Without doubt the astrolabes is one of the most fascinating of all historical astronomical instruments.

Astrolabe Renners Arsenius 1569 Source: Wikimedia Commons

Astrolabe Renners Arsenius 1569
Source: Wikimedia Commons

To begin with it is not simply one object, it is many objects in one:


  • An astronomical measuring device
  • A timepiece
  • An analogue computer
  • A two dimensional representation of the three dimensional celestial sphere
  • A work of art and a status symbol


This Medieval-Renaissance Swiss Army penknife of an astronomical instrument had according to one medieval Islamic commentator, al-Sufi writing in the tenth century, more than one thousand different functions. Even Chaucer in what is considered to be the first English language description of the astrolabe and its function, a pamphlet written for a child, describes at least forty different functions.

The astrolabe was according to legend invented by Hipparchus of Nicaea, the second century BCE Greek astronomer but there is no direct evidence that he did so. The oldest surviving description of the planisphere, that two-dimensional representation of the three-dimensional celestial sphere, comes from Ptolemaeus in the second century CE.

Modern Planisphere Star Chart c. 1900 Source: Wikimedia Commons

Modern Planisphere Star Chart c. 1900
Source: Wikimedia Commons

Theon of Alexandria wrote a thesis on the astrolabe, in the fourth century CE, which did not survive and there are dubious second-hand reports that Hypatia, his daughter invented the instrument. The oldest surviving account of the astrolabe was written in the sixth century CE by John Philoponus. However it was first the Islamic astronomers who created the instrument, as it is known today, it is said for religious purposes, to determine the direction of Mecca and the time of prayer. The earliest surviving dated instrument is dated 315 AH, which is 927/28 CE.

The Earliest  Dated Astrolabe Source: See Link

The Earliest Dated Astrolabe
Source: See Link

It is from the Islamic Empire that knowledge of the instrument found its way into medieval Europe. Chaucer’s account of it is based on that of the eight-century CE Persian Jewish astrologer, Masha’allah ibn Atharī, one of whom claim to fame is writing the horoscope to determine the most auspicious date to found the city of Baghdad.

So-called Chaucer Astrolabe dated 1326, similar to the one Chaucer describes, British Museum Source: Wikimedia Commons

So-called Chaucer Astrolabe dated 1326, similar to the one Chaucer describes, British Museum
Source: Wikimedia Commons

However this brief post is not about the astrolabe as a scientific instrument in itself but rather the last point in my brief list above the astrolabe as a work of art and a status symbol. One of the reasons for people’s interest in astrolabes is the fact that they are simply beautiful to look at. This is not a cold, functional scientific instrument but an object to admire, to cherish and desire. A not uncommon reaction of people being introduced to astrolabes for the first time is, oh that is beautiful; I would love to own one of those. And so you can there are people who make replica astrolabes but buying one will set you back a very pretty penny.

That astrolabes are expensive is not, however, a modern phenomenon. Hand crafted brass, aesthetically beautiful, precision instruments, they were always very expensive and the principal market would always have been the rich, often the patrons of the instrument makers. The costs of astrolabes were probably even beyond the means of most of the astronomers who would have used them professionally and it is significant that most of the well know astrolabe makers were themselves significant practicing astronomers; according to the principle, if you need it and can’t afford it then make it yourself. Other astronomers would probably have relied on their employers/patrons to supply the readies. With these thoughts in mind it is worth considering the claim made by David King, one of the world’s greatest experts on the astrolabe, that the vast majority of the surviving astrolabes, made between the tenth nineteenth centuries – about nine hundred – were almost certainly never actually used as scientific instruments but were merely owned as status symbols. This claim is based on, amongst other things, the fact that they display none of the signs of the wear and tear, which one would expect from regular usage.

Does this mean that the procession of astrolabes was restricted to a rich elite and their employees? Yes and no. When European sailors began to slowly extend their journeys away from coastal waters into the deep sea, in the High Middle Ages they also began to determine latitude as an element of their navigation. For this purpose they needed an instrument like the astrolabe to measure the elevation of the sun or of chosen stars. The astrolabe was too complex and too expensive for this task and so the so-called mariners astrolabe was developed, a stripped down, simplified, cheaper and more robust version of the astrolabe. When and where the first mariner’s astrolabe was used in not known but probably not earlier than the thirteenth century CE. Although certainly not cheap, the mariner’s astrolabe was without doubt to be had for considerably less money than its nobler cousin.


Mariner’s Astrolabe Francisco de Goes 1608 Source: Istituto e Museo di Storia della Scienza, Firenze

Another development came with the advent of printing in the fifteenth century, the paper astrolabe. At first glance this statement might seem absurd, how could one possibly make a high precision scientific measuring instrument out of something, as flexible, unstable and weak as paper? The various parts of the astrolabe, the planisphere, the scales, the rete star-map, etc. are printed onto sheets of paper. These are then sold to the customer who cuts them out and pastes them onto wooden forms out of which he then constructs his astrolabe, a cheap but serviceable instrument. One well-known instrument maker who made and sold printed-paper astrolabes and other paper instruments was the Nürnberger mathematician and astronomer Georg Hartmann. The survival rate of such cheap instruments is naturally very low but we do actually have one of Hartmann’s wood and paper astrolabes.

Hartmann Paper Astrolabe Source: Oxford Museum of History of Science

Hartmann Paper Astrolabe
Source: Oxford Museum of History of Science

In this context it is interesting to note that, as far as can be determined, Hartmann was the first instrument maker to develop the serial production of astrolabes. Before Hartmann each astrolabe was an unicum, i.e. a one off instrument. Hartmann standardised the parts of his brass astrolabes and produced them, or had them produced, in batches, assembling the finished product out of these standardised parts. To what extent this might have reduced the cost of the finished article is not known but Hartmann was obviously a very successful astrolabe maker as nine of those nine hundred surviving astrolabes are from his workshop, probably more than from any other single manufacturer.

Hartmann Serial Production Astrolabe Source: Museum Boerhaave

Hartmann Serial Production Astrolabe
Source: Museum Boerhaave


If this post has awoken your own desire to admire the beauty of the astrolabe then the biggest online collection of Medieval and Renaissance scientific instruments in general and astrolabes in particular is the Epact website, a collaboration between the Museum of the History of Science in Oxford, the British Museum, the Museum of the History of Science in Florence and the Museum Boerhaave in Leiden.

This blog post was partially inspired by science writer Philip Ball with whom I had a brief exchange on Twitter a few days ago, which he initiated, on our mutual desire to possess a brass astrolabe.






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

The Reformation, Astrology, and Mathematics in Schools and Universities.

It is one of the ironies of the medieval universities that mathematics played almost no role in undergraduate education. It is ironical because the curriculum was nominally based on the seven liberal arts of which the mathematical sciences – arithmetic, geometry, music and astronomy – formed one half, the quadrivium. Although the quadrivium was officially a large part of the curriculum in reality the four mathematical disciplines were paid little attention and hardly taught at all. This only began to change in the fifteenth century with the rise of astro-medicine or iatromathematics, to give it its formal name. With the rise of this astrology-based medicine the humanist universities of Northern Italy and Kraków introduced chairs of mathematics to teach astrology to their students of medicine. This of course entailed first teaching mathematics and then astronomy in order to be able to do astrology and thus mathematics gained a first foothold in the European universities. Ingolstadt became the first German university to introduce a chair for mathematics, also for teaching astrology to medical students, in the 1470s. It became an important centre for seeding new chairs at other universities with its graduates. Stabius and Stiborius going from there to Vienna with Celtis, for example. However there was no systematic introduction of mathematics into the university curriculum as of yet, this would first come as a result of the Reformation and the educational reforms of Philip Melanchthon.

Melanchthon in 1526: engraving by Albrecht Dürer Translation of Latin caption: «Dürer was able to draw Philip’s face, but the learned hand could not paint his spirit». Source: Wikimedia Commons

Melanchthon in 1526: engraving by Albrecht Dürer Translation of Latin caption: «Dürer was able to draw Philip’s face, but the learned hand could not paint his spirit».
Source: Wikimedia Commons

Melanchthon was born Philip Schwartzerdt in Bretten near Karlsruhe on 16 February 1497. A great nephew of Johann Reuchlin a leading humanist scholar Philip changed his name to Melanchthon, a literal Greek translation of his German name, which means black earth, at Reuchlin’s suggestion. Melanchthon was a child prodigy who would grow up to be Germany’s greatest humanist scholar. He studied at Heidelberg University where he was denied his master degree in 1512 on account of his youth. He transferred to Tübingen where he came under the influence of Johannes Stöffler, one of those Ingolstadt graduates, a leading and highly influential mathematician/astrologer.

Johannes Stöffler Source Wikimedia Commons

Johannes Stöffler
Source Wikimedia Commons

The cosmograph Sebastian Münster was another of Stöffler’s famous pupils. Stöffler also has a great influence on several of the Nürnberger mathematician-astronomers, especial Johannes Schöner and Georg Hartmann. Under Stöffler’s influence Melanchthon became a passionate supporter of astrology.

On Reuchlin’s recommendation Melanchthon became professor of Greek at Luther’s University of Wittenberg at the age of twenty-one and thus a central figure in the Reformation. One of the major problems faced by the reformers was the fact that the education system was totally in the hands of the Catholic Church, which meant that they had to start from scratch and create their own school and university system; this task was taken on by Melanchthon, who became Luther’s Preceptor Germania, Germany’s Schoolmaster.

Because of his own personal passion for astrology Melanchthon introduced mathematics into the curriculum of all the Lutheran schools and universities. He invented a new type of school on a level between the old Church Latin schools and the universities that were devised to prepare their pupils for a university education. The very first of these was the Eigidien Oberschule in Nürnberg, which opened in 1526 with Johannes Schöner, as its first professor for mathematics.


These type of school created by Melanchthon would become the Gymnasium, still today the highest level secondary schools in the German education system.

In Wittenberg he appointed Johannes Volmar (1480-1536) professor for the higher mathematic, music and astronomy, and Jakob Milich (1501- 1559) professor for the lower mathematic, arithmetic and geometry, in 1525. Their most famous students were Erasmus Reinhold, who followed Volmar on the chair for higher mathematics when he died in 1536, and Georg Joachim Rheticus, who followed Milich on the chair for lower mathematics, in the same year when Milich became professor for medicine. Schöner, Reinhold and Rheticus were not the only mathematicians supported by Melanchthon, who played an important role in the dissemination of the heliocentric astronomy. Although following Melanchthon’s lead these Protestant mathematicians treated the heliocentric hypothesis in a purely instrumentalist manner, i.e. it is not true but is mathematically useful, they taught it in their university courses alongside the geocentric astronomy.

As a result of Melanchthon’s passion for astrology the Lutheran Protestant schools and universities of Europe all had departments for the study of mathematics headed by qualified professors. The Catholic schools and universities would have to wait until the end of the sixteenth century before Christoph Clavius did the same for them, although his motivation was not astrology. Sadly Anglican England lagged well behind the continent with Oxford first appointing professors for geometry and astronomy in the 1620s at the bequest of Henry Savile, who had had to go abroad to receive his own mathematical education. Cambridge only followed suit with the establishment of the Lucasian Chair in 1663, whose first occupant was Isaac Barrow followed by that other Isaac, Newton. In 1705 John Arbuthnot could still complain in an essay that there was not one single school in England that taught mathematics.





Filed under History of Astrology, History of Astronomy, History of Mathematics, History of science, Renaissance Science, University History

The Arch-Humanist

The name Conrad Celtis is not one that you’ll find in most standard books on the history of mathematics, which is not surprising as he was a Renaissance humanist scholar best known in his lifetime as a poet. However, Celtis played an important role in the history of mathematics and is a good example of the fact that if you really wish to study the evolution of the mathematical sciences it is necessary to leave the narrow confines of the mathematics books.

Conrad Celtis: Gedächtnisbild von Hans Burgkmair dem Älteren, 1507 Source: Wikimedia Commons

Conrad Celtis: Gedächtnisbild von Hans Burgkmair dem Älteren, 1507
Source: Wikimedia Commons

Born Konrad Bickel or Pyckell, (Conrad Celtis was his humanist pseudonym) the son of a winemaker, in Franconian Wipfield am Main near Schweinfurt on 1 February 1459, he obtained his BA at the University of Cologne in 1497. Unsatisfied with the quality of tuition in Cologne he undertook the first of many study journeys, which typified his life, to Buda in 1482, where he came into contact with the humanist circle on the court of Matthias Corvinus, the earlier patron of Regiomontanus. 1484 he continued his studies at the University of Heidelberg specialising in poetics and rhetoric, learning Greek and Hebrew and humanism as a student of Rudolf Agricola, a leading Dutch early humanist scholar. Celtis obtained his MA in 1485. 1486 found him underway in Italy, where he continued his humanist studies at the leading Italian universities and in conversation with many leading humanist scholars. Returning to Germany he taught poetics at the universities of Erfurt, Rostock and Leipzig and on 18 April 1487 he was crowned Poet Laureate by Emperor Friedrich III in Nürnberg during the Reichstag. In Nürnberg he became part of the circle of humanists that produced the Nürnberger Chronicle to which he contributed the section on the history and geography of Nürnberg. It is here that we see the central occupation of Celtis’ life that brought him into contact with the Renaissance mathematical sciences.

During his time in Italy he suffered under the jibes of his Italian colleges who said that whilst Italy had perfect humanist credentials being the inheritors of the ancient Roman culture, Germany was historically a land of uncultured barbarians. This spurred Celtis on to prove them wrong. He set himself the task of researching and writing a history of Germany to show that its culture was the equal of Italy’s. Celtis’ concept of history, like that of his Renaissance contemporaries, was more a mixture of our history and geography the two disciplines being regarded as two sides of the same coin. Geography being based on Ptolemaeus’ Geographia (Geographike Hyphegesis), which of course meant cartography, a branch of the mathematical sciences.

Continuing his travels in 1489 Celtis matriculated at the University of Kraków specifically to study the mathematical sciences for which Kraków had an excellent reputation. A couple of years later Nicolaus Copernicus would learn the fundamentals of mathematics and astronomy there. Wandering back to Germany via Prague and Nürnberg Celtis was appointed professor of poetics and rhetoric at the University of Ingolstadt in 1491/92. Ingolstadt was the first German university to have a dedicated chair for mathematics, established around 1470 to teach medical students astrology and the necessary mathematics and astronomy to cast a horoscope. When Celtis came to Ingolstadt there were the professor of mathematics was Andreas Stiborius (born Stöberl 1464–1515) who was followed by his best student Johannes Stabius (born Stöberer before 1468­–1522) both of whom Celtis convinced to support him in his cartographic endeavours.

In 1497 Celtis received a call to the University of Vienna where he established a Collegium poetarum et mathematicorum, that is a college for poetry and mathematics, with Stiborius, whom he had brought with him from Ingolstadt, as the professor for mathematics. In 1502 he also brought Stabius, who had succeeded Stiborius as professor in Ingolstadt, and his star student Georg Tanstetter to Vienna. Stiborius, Stabius and Tanstetter became what is known, to historians of mathematics, as the Second Viennese School of Mathematics, the First Viennese School being Johannes von Gmunden, Peuerbach and Regiomontanus, in the middle of the fifteenth century. Under these three Vienna became a major European centre for the mathematical sciences producing many important mathematicians the most notable being Peter Apian.

Although not a mathematician himself Conrad Celtis, the humanist poet, was the driving force behind one of the most important German language centres for Renaissance mathematics and as such earns a place in the history of mathematics. A dedicated humanist, wherever he went on his travels Celtis would establish humanist societies to propagate humanist studies and it was this activity that earned him the German title of Der Erzhumanist, in English the Arch Humanist. Celtis died in 1508 but his Collegium poetarum et mathematicorum survived him by twenty-two years, closing first in 1530



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