Category Archives: Renaissance Science

Why, FFS! why?

On Twitter this morning physicist and science writer Graham Farmelo inadvertently drew my attention to a reader’s letter in The Guardian from Sunday by a Collin Moffat. Upon reading this load of old cobblers, your friendly, mild mannered historian of Renaissance mathematics instantly turned into the howling-with-rage HISTSCI_HULK. What could possibly have provoked this outbreak? I present for your delectation the offending object.

I fear Thomas Eaton (Weekend Quiz, 12 October) is giving further credence to “fake news” from 1507, when a German cartographer was seeking the derivation of “America” and hit upon the name of Amerigo Vespucci, an obscure Florentine navigator. Derived from this single source, this made-up derivation has been copied ever after.

The fact is that Christopher Columbus visited Iceland in 1477-78, and learned of a western landmass named “Markland”. Seeking funds from King Ferdinand of Spain, he told the king that the western continent really did exist, it even had a name – and Columbus adapted “Markland” into the Spanish way of speaking, which requires an initial vowel “A-”, and dropped “-land” substituting “-ia”.

Thus “A-mark-ia”, ie “America”. In Icelandic, “Markland” may be translated as “the Outback” – perhaps a fair description.

See Graeme Davis, Vikings in America (Birlinn, 2009).

Astute readers will remember that we have been here before, with those that erroneously claim that America was named after a Welsh merchant by the name of Richard Ap Meric. The claim presented here is equally erroneous; let us examine it in detail.

…when a German cartographer was seeking the derivation of “America” and hit upon the name of Amerigo Vespucci, an obscure Florentine navigator.

It was actually two German cartographers Martin Waldseemüller and Matthias Ringmann and they were not looking for a derivation of America, they coined the name. What is more, they give a clear explanation as to why and how the coined the name and why exactly they chose to name the newly discovered continent after Amerigo Vespucci, who, by the way, wasn’t that obscure. You can read the details in my earlier post. It is of interest that the supporters of the Ap Meric theory use exactly the same tactic of lying about Waldseemüller and Ringmann and their coinage.

The fact is that Christopher Columbus visited Iceland in 1477-78, and learned of a western landmass named “Markland”.

Let us examine what is known about Columbus’ supposed visit to Iceland. You will note that I use the term supposed, as facts about this voyage are more than rather thin. In his biography of Columbus, Felipe Fernandez-Armesto, historian of Early Modern exploration, writes:

He claimed that February 1477–the date can be treated as unreliable in such a long –deferred recollection [from 1495]–he sailed ‘a hundred leagues beyond’ Iceland, on a trip from Bristol…

In “Christopher Columbus and the Age of Exploration: An Encyclopedia”[1] edited by the American historian, Silvio A. Bedini, we can read:

The possibility of Columbus having visited Iceland is based on a passage in his son Fernando Colón’s biography of his father. He cites a letter from Columbus stating that in February 1477 he sailed “a hundred leagues beyond the island of Til” (i.e. Thule, Iceland). But there is no evidence to his having stopped in Iceland or spoken with anyone, and in any case it is unlikely that anyone he spoke to would have known about the the Icelandic discovery of Vinland.

This makes rather a mockery of the letter’s final claim:

Seeking funds from King Ferdinand of Spain, he told the king that the western continent really did exist, it even had a name – and Columbus adapted “Markland” into the Spanish way of speaking, which requires an initial vowel “A-”, and dropped “-land” substituting “-ia”.

Given that it is a well established fact that Columbus was trying to sail westward to Asia and ran into America purely by accident, convinced by the way that he had actually reached Asia, the above is nothing more than a fairly tale with no historical substance whatsoever.

To close I want to address the question posed in the title to this brief post. Given that we have a clear and one hundred per cent reliable source for the name of America and the two men who coined it, why oh why do people keep coming up with totally unsubstantiated origins of the name based on ahistorical fantasies? And no I can’t be bothered to waste either my time or my money on Graeme Davis’ book, which is currently deleted and only available as a Kindle.

[1] On days like this it pays to have one book or another sitting around on your bookshelves.

Felipe Fernández-Armesto, Columbus, Duckworth, London, ppb 1996, p. 18. Christopher Columbus and the Age of Exploration: An Encyclopedia, ed. Silvio A. Bedini, Da Capo Press, New York, ppb 1992, p. 314

4 Comments

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

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

A widespread myth in the popular history of astronomy is that Galileo Galilei (1564–1642) was the first or even the only astronomer to realise the potential of the newly invented telescope as an instrument for astronomy. This perception is very far from the truth. He was just one of a group of investigator, who realised the telescopes potential and all of the discoveries traditionally attributed to Galileo were actually made contemporaneously by several people, who full of curiosity pointed their primitive new instruments at the night skies. So why does Galileo usually get all of the credit? Quite simply, he was the first to publish.

Galileo_galilei,_telescopi_del_1609-10_ca.

Galileo’s “cannocchiali” telescopes at the Museo Galileo, Florence

Starting in the middle of 1609 various astronomers began pointing primitive Dutch telescopes at the night skies, Thomas Harriot (1560–1621) and his friend and student William Lower (1570–1615) in Britain, Simon Marius (1573–1625) in Ansbach, Johannes Fabricius (1587–1616) in Frisia, Odo van Maelcote (1572–1615) and Giovanni Paolo Lembo (1570–1618) in Rome, Christoph Scheiner (1573 or 1575–1650) in Ingolstadt and of course Galileo in Padua. As far as we can ascertain Thomas Harriot was the first and the order in which the others took up the chase is almost impossible to determine and also irrelevant, as it was who was first to publish that really matters and that was, as already stated, Galileo.

Harriot made a simple two-dimensional telescopic sketch of the moon in the middle of 1609.

harriot_moon1609_726

Thomas Harriot’s initial telescopic sketch of the moon from 1609 Source: Wikimedia Commons

Both Galileo and Simon Marius started making telescopic astronomical observations sometime late in the same year. At the beginning Galileo wrote his observation logbook in his Tuscan dialect and then on 7 January 1610 he made the discovery that would make him famous, his first observation of three of the four so-called Galilean moons of Jupiter.

Galileo_manuscript

It was on this page that Galileo first noted an observation of the moons of Jupiter. This observation upset the notion that all celestial bodies must revolve around the Earth. Source: Wikimedia Commons

Galileo realised at once that he had hit the jackpot and immediately changed to writing his observations in Latin in preparation for a publication. Simon Marius, who made the same discovery just one day later, didn’t make any preparations for immediate publication. Galileo kept on making his observations and collecting material for his publication and then on 12 March 1610, just two months after he first saw the Jupiter moons, his Sidereus Nuncius (Starry Messenger of Starry Message, the original Latin is ambiguous) was published in Padua but dedicated to Cosimo II de Medici, Fourth Grand Duke of Tuscany. Galileo had already negotiated with the court in Florence about the naming of the moons; he named them the Medicean Stars thus taking his first step in turning his discovery into personal advancement.

houghton_ic6-g1333-610s_-_sidereus_nuncius

Title page of Sidereus nuncius, 1610, by Galileo Galilei (1564-1642). *IC6.G1333.610s, Houghton Library, Harvard University Source: Wikimedia Commons

What exactly did Galileo discover with his telescope, who else made the same discoveries and what effect did they have on the ongoing astronomical/cosmological debate? We can start by stating quite categorically that the initial discoveries that Galileo published in his Sidereus Nuncius neither proved the heliocentric hypothesis nor did they refute the geocentric one,

The first discovery that the Sidereus Nuncius contains is that viewed through the telescope many more stars are visible than to the naked-eye. This was already known to those, who took part in Lipperhey’s first ever public demonstration of the telescope in Den Haag in September 1608 and to all, who subsequently pointed a telescope of any sort at the night sky. This played absolutely no role in the astronomical/cosmological debate but was worrying for the theologians. Christianity in general had accepted both astronomy and astrology, as long as the latter was not interpreted deterministically, because the Bible says  “And God said, Let there be lights in the firmament of the heaven to divide the day from night; and let them be for signs, and for seasons, and for days, and years:” (Gen 1:14). If the lights in the heavens are signs from God to be interpreted by humanity, what use are signs that can only be seen with a telescope?

Next up we have the fact that some of the nebulae, indistinct clouds of light in the heavens, when viewed with a telescope resolved into dense groups of stars. Nebulae had never played a major role in Western astronomy, so this discovery whilst interesting did not play a major role in the contemporary debate. Simon Marius made the first telescopic observations of the Andromeda nebula, which was unknown to Ptolemaeus, but which had already been described by the Persian astronomer, Abd al-Rahman al-Sufi (903–986), usually referred to simply as Al Sufi. It is historically interesting because the Andromeda nebula was the first galaxy to be recognised outside of the Milky Way.

m31alsufi

Al Sufi’s drawing of the constellation Fish with the Andromeda nebula in fount of it mouth

Galileo’s next discovery was that the moon was not smooth and perfect, as required of all celestial bodies by Aristotelian cosmology, but had geological feature, mountains and valleys, just like the earth i.e. the surface was three-dimensional and not two-dimensional, as Harriot had sketched it. This perception of Galileo’s is attributed to the fact that he was a trained painter used to creating light and shadows in paintings and he thus recognised that what he was seeing on the moons surface was indeed shadows cast by mountains.

As soon as he read the Sidereus Nuncius, Harriot recognised that Galileo was correct and he went on to produce the first real telescopic map of the moon.

harriot_lunar_map

Thomas Harriot’s 1611 telescopic map of the moon Source: Wikimedia Commons

Galileo’s own washes of the moon, the most famous illustrations in the Sidereus Nuncius, are in fact studies to illustrate his arguments and not accurate illustrations of what he saw.

1024px-Galileo's_sketches_of_the_moon

Galileo’s sketches of the Moon from Sidereus Nuncius. Source: Wikimedia Commons

That the moon was earth like and for some that the well-known markings on the moon, the man in the moon etc., are in fact a mountainous landscape was a view held by various in antiquity, such as Thales, Orpheus, Anaxagoras, Democritus, Pythagoras, Philolaus, Plutarch and Lucian. In particular Plutarch (c. 46–c. 120 CE) in his On the Face of the Moon in his Moralia, having dismissed other theories including Aristotle’s wrote:

Just as our earth contains gulfs that are deep and extensive, one here pouring in towards us through the Pillars of Herakles and outside the Caspian and the Red Sea with its gulfs, so those features are depths and hollows of the Moon. The largest of them is called “Hecate’s Recess,” where the souls suffer and extract penalties for whatever they have endured or committed after having already become spirits; and the two long ones are called “the Gates,” for through them pass the souls now to the side of the Moon that faces heaven and now back to the side that faces Earth. The side of the Moon towards heaven is named “Elysian plain,” the hither side, “House of counter-terrestrial Persephone.”

So Galileo’s discovery was not so sensational, as it is often presented. However, the earth-like, and not smooth and perfect, appearance of the moon was yet another hole torn in the fabric of Aristotelian cosmology.

Of course the major sensation in the Sidereus Nuncius was the discovery of the four largest moons of Jupiter.

Medicean_Stars

Galileo’s drawings of Jupiter and its Medicean Stars from Sidereus Nuncius. Image courtesy of the History of Science Collections, University of Oklahoma Libraries. Source: Wikimedia Commons

This contradicted the major premise of Aristotelian cosmology that all of the celestial bodies revolved around a common centre, his homo-centricity.  It also added a small modicum of support to a heliocentric cosmology, which had suffered from the criticism, if all the celestial bodies revolve around the sun, why does the moon continue to revolve around the earth. Now Jupiter had not just one but four moons, or satellites as Johannes Kepler called them, so the earth was no longer alone in having a moon. As already stated above Simon Marius discovered the moons of Jupiter just one day later than Galileo but he didn’t publish his discovery until 1614. A delay that would later bring him a charge of plagiarism from Galileo and ruin his reputation, which was first restored at the end of the nineteenth century when an investigation of the respective observation data showed that Marius’ observations were independent of those of Galileo.

The publication of the Sidereus Nuncius was an absolute sensation and the book quickly sold out. Galileo went, almost literally overnight, from being a virtually unknown, middle aged, Northern Italian, professor of mathematics to the most celebrated astronomer in the whole of Europe. However, not everybody celebrated or accepted the truth of his discoveries and that not without reason. Firstly, any new scientific discovery needs to be confirmed independently by other. If Simon Marius had also published early in 1610 things might have been different but he, for whatever reasons, didn’t publish his Mundus Jovialis (The World of Jupiter) until 1614. Secondly there was no scientific explanation available that explained how a telescope functioned, so how did anyone know that what Galileo and others were observing was real? Thirdly, and this is a very important point that often gets ignored, the early telescopes were very, very poor quality suffering from all sorts of imperfections and distortions and it is almost a miracle that Galileo et al discovered anything with these extremely primitive instruments.

As I stated in the last episode, the second problem was solved by Johannes Kepler in 1611 with the publication of his Dioptrice.

Kepler_dioptrice_titul

A book that Galileo, always rather arrogant, dismissed as unreadable. This was his triumph and nobody else was going to muscle in on his glory. The third problem was one that only time and improvements in both glass making and the grinding and polishing of lenses would solve. In the intervening years there were numerous cases of new astronomical discoveries that turned out to be artefacts produced by poor quality instruments.

The first problem was the major hurdle that Galileo had to take if he wanted his discoveries to be taken seriously. Upon hearing of Galileo discoveries, Johannes Kepler in Prague immediately put pen to paper and fired off a pamphlet, Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) congratulating Galileo, welcoming his discoveries and stating his belief in their correctness, which he sent off to Italy. Galileo immediately printed and distributed a pirate copy of Kepler’s work, without even bothering to ask permission, it was after all a confirmation from the Imperial Mathematicus and Kepler’s reputation at this time was considerably bigger than Galileo’s.

Johannes Kepler, Dissertatio cum Nuncio sidereo… (Frankfurt am Main, 1611)

A reprint of Kepler’s letter to Galileo, originally issued in Prague in 1610

However, Kepler’s confirmations were based on faith and not personal confirmatory observations, so they didn’t really solve Galileo’s central problem. Help came in the end from the Jesuit astronomers of the Collegio Romano.

Odo van Maelcote and Giovanni Paolo Lembo had already been making telescopic astronomical observations before the publication of Galileo’s Sidereus Nuncius. Galileo also enjoyed good relations with Christoph Clavius (1538–1612), the founder and head of the school of mathematics at the Collegio Romano, who had been instrumental in helping Galileo to obtain the professorship in Padua. Under the direction of Christoph Grienberger (1561–1636), soon to be Clavius’ successor as professor for mathematics at the Collegio, the Jesuit astronomers set about trying to confirm all of Galileo’s discoveries. This proved more than somewhat difficult, as they were unable, even with Galileo’s assistance via correspondence, to produce an instrument of sufficient quality to observe the moons of Jupiter. In the end Antonio Santini (1577–1662), a mathematician from Venice, succeeded in producing a telescope of sufficient quality for the task, confirmed for himself the existence of the Jupiter moons and then sent a telescope to the Collegio Romano, where the Jesuit astronomers were now also able to confirm all of Galileo’s discovery. Galileo could not have wished for a better confirmation of his efforts, nobody was going to doubt the word of the Jesuits.

In March 1611 Galileo travelled to Rome, where the Jesuits staged a banquet in his honour at which Odo van Maelcote held an oration to the Tuscan astronomer. Galileo’s strategy of dedicating the Sidereus Nuncius to Cosimo de Medici and naming the four moons the Medicean Stars paid off and he was appointed court mathematicus and philosophicus in Florence and professor of mathematics at the university without any teaching obligations; Galileo had arrived at the top of the greasy pole but what goes up must, as we will see, come down.

 

 

 

 

Leave a comment

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

Mathematical aids for Early Modern astronomers.

Since its very beginnings in the Fertile Crescent, European astronomy has always involved a lot of complicated and tedious mathematical calculations. Those early astronomers described the orbits of planets, lunar eclipses and other astronomical phenomena using arithmetical or algebraic algorithms. In order to simplify the complex calculations needed for their algorithms the astronomers used pre-calculated tables of reciprocals, squares, cubes, square roots and cube roots.

fcarc-may2012-MS3874r

Cuniform reciprocal table Source

The ancient Greeks, who inherited their astronomy from the Babylonians, based their astronomical models on geometry rather than algebra and so needed other calculation aids. They developed trigonometry for this work based on chords of a circle. The first chord tables are attributed to Hipparkhos (c. 190–c. 120 BCE) but they did not survive. The oldest surviving chord tables are in Ptolemaeus’ Mathēmatikē Syntaxis written in about 150 CE, which also contains a detailed explanation of how to calculate such a table in Chapter 10 of Book I.

chords001

Ptolemaeus’ Chord Table taken from Toomer’s Almagest translation. The 3rd and 6th columns are the interpolations necessary for angles between the given ones

Greek astronomy travelled to India, where the astronomers replaced Ptolemaeus’ chords with half chords, that is our sines. Islamic astronomers inherited their astronomy from the Indians with their sines and cosines and the Persian astronomer Abū al-Wafāʾ (940–998 CE) was using all six of the trigonometrical relations that we learnt at school (didn’t we!) in the tenth century.

Buzjani,_the_Persian

Abū al-Wafāʾ Source: Wikimedia Commons

Astronomical trigonometry trickled slowly into medieval Europe and Regiomontanus (1536–1576)  (1436–1476) was the first European to produce a comprehensive work on trigonometry for astronomers, his De triangulis omnimodis, which was only edited by Johannes Schöner and published by Johannes Petreius in 1533.

Whilst trigonometry was a great aid to astronomers calculating trigonometrical tables was time consuming, tedious and difficult work.

A new calculating aid for astronomers emerged during the sixteenth century, prosthaphaeresis, by which, multiplications could be converted into additions using a series of trigonometrical identities:

Prosthaphaeresis appears to have first been used by Johannes Werner (1468–1522), who used the first two formulas with both sides multiplied by two.

However Werner never published his discovery and it first became known through the work of the itinerant mathematician Paul Wittich (c. 1546–1586), who taught it to both Tycho Brahe (1546–1601) on his island of Hven and to Jost Bürgi (1552–1632) in Kassel, who both developed it further. It is not known if Wittich learnt the method from Werner’s papers on one of his visits to Nürnberg or rediscovered it for himself. Bürgi in turn taught it to Nicolaus Reimers Baer (1551–1600) in in exchange translated Copernicus’ De revolutionibus into German for Bürgi, who couldn’t read Latin. This was the first German translation of De revolutionibus. As can be seen the method of prosthaphaeresis spread throughout Europe in the latter half of the sixteenth century but was soon to be superceded by a superior method of simplifying astronomical calculations by turning multiplications into additions, logarithms.

As is often the case in the histories of science and mathematics logarithms were not discovered by one person but almost simultaneously, independently by two, Jost Bürgi and John Napier (1550–1617) and both of them seem to have developed the idea through their acquaintance with prosthaphaeresis. I have already blogged about Jost Bürgi, so I will devote the rest of this post to John Napier.

John_Napier

John Napier, artist unknown Source: Wikimedia Commons

John Napier was the 8th Laird of Merchiston, an independently owned estate in the southwest of Edinburgh.

Merchiston_castle

Merchiston Castle from an 1834 woodcut Source: Wikimedia Commons

His exact date of birth is not known and also very little is known about his childhood or education. It is assumed that he was home educated and he was enrolled at the University of St. Andrews at the age of thirteen. He appears not to have graduated at St. Andrews but is believed to have continued his education in Europe but where is not known. He returned to Scotland in 1571 fluent in Greek but where he had acquired it is not known. As a laird he was very active in the local politics. His intellectual reputation was established as a theologian rather than a mathematician.

It is not known how and when he became interested in mathematics but there is evidence that this interest was already established in the early 1570s, so he may have developed it during his foreign travels. It is thought that he learnt of prosthaphaeresis through John Craig (d. 1620) a Scottish mathematician and physician, who had studied and later taught at Frankfurt an der Oder, a pupil of Paul Wittich, who knew Tycho Brahe. Craig returned to Edinburgh in 1583 and is known to have had contact with Napier. The historian Anthony à Wood (1632–1695) wrote:

one Dr. Craig … coming out of Denmark into his own country called upon John Neper, baron of Murcheston, near Edinburgh, and told him, among other discourses, of a new invention in Denmark (by Longomontanus as ’tis said) to save the tedious multiplication and division in astronomical calculations. Neper being solicitous to know farther of him concerning this matter, he could give no other account of it than that it was by proportionable numbers. [Neper is the Latin version of his family name]

Napier is thought to have begum work on the invention of logarithms about 1590. Logarithms exploit the relation ship between arithmetical and geometrical series. In modern terminology, as we all learnt at school, didn’t we:

Am x An = Am+n

Am/An = Am-n

These relationships were discussed by various mathematicians in the sixteenth century, without the modern notation, in particularly by Michael Stefil (1487–1567) in his Arithmetica integra (1544).

Michael_Stifel

Michael Stifel Source: Wikimedia Commons

Michael_Stifel's_Arithmetica_Integra_(1544)_p225.tif

Michael Stifel’s Arithmetica Integra (1544) Source: Wikimedia Commons

What the rules for exponents show is that if one had tables to convert all numbers into powers of a given base then one could turn all multiplications and divisions into simple additions and subtractions of the exponents then using the tables to covert the result back into a number. This is what Napier did calling the result logarithms. The methodology Napier used to calculate his tables is too complex to deal with here but the work took him over twenty years and were published in his Mirifici logarithmorum canonis descriptio… (1614).

Logarithms_book_Napier

Napier coined the term logarithm from the Greek logos (ratio) and arithmos (number), meaning ratio-number. As well as the logarithm tables, the book contains seven pages of explanation on the nature of logarithms and their use. A secondary feature of Napier’s work is that he uses full decimal notation including the decimal point. He was not the first to do so but his doing so played an important role in the acceptance of this form of arithmetical notation. The book also contains important developments in spherical trigonometry.

Edward Wright  (baptised 1561–1615) produced an English translation of Napier’s Descriptio, which was approved by Napier, A Description of the Admirable Table of Logarithmes, which was published posthumously in 1616 by his son Samuel.

JohnNapier-EdwardWright-Logarithmes-1618-2

Gresham College was quick to take up Napier’s new invention and this resulted in Henry Briggs (1561–1630), the Gresham professor of geometry, travelling to Edinburgh from London to meet with Napier. As a result of this meeting Briggs, with Napier’s active support, developed tables of base ten logarithms, Logarithmorum chilias prima, which were publish in London sometime before Napier’s death in 1617.

page-0010

He published a second extended set of base ten tables, Arithmetica logarithmica, in 1624.

briggs_arith_log_title_1

Napier’s own tables are often said to be Natural Logarithms, that is with Euler’s number ‘e’ as base but this is not true. The base of Napierian logarithms is given by:

NapLog(x) = –107ln (x/107)

Natural logarithms have many fathers all of whom developed them before ‘e’ itself was discovered and defined; these include the Jesuit mathematicians Gregoire de Saint-Vincent (1584–1667) and Alphonse Antonio de Sarasa (1618–1667) around 1649, and Nicholas Mercator (c. 1620–1687) in his Logarithmotechnia (1688) but John Speidell (fl. 1600–1634), had already produced a table of not quite natural logarithms in 1619.

1927825(1)

Napier’s son, Robert, published a second work by his father on logarithms, Mirifici logarithmorum canonis constructio; et eorum ad naturales ipsorum numeros habitudines, posthumously in 1619.

4638

This was actually written earlier than the Descriptio, and describes the principle behind the logarithms and how they were calculated.

The English mathematician Edmund Gunter (1581–1626) developed a scale or rule containing trigonometrical and logarithmic scales, which could be used with a pair of compasses to solve navigational problems.

800px-Table_of_Trigonometry,_Cyclopaedia,_Volume_2

Table of Trigonometry, from the 1728 Cyclopaedia, Volume 2 featuring a Gunter’s scale Source: Wikimedia Commons

Out of two Gunter scales laid next to each other William Oughtred (1574–1660) developed the slide rule, basically a set of portable logarithm tables for carry out calculations.

Napier developed other aids to calculation, which he published in his Rabdologiae, seu numerationis per virgulas libri duo in 1617; the most interesting of which was his so called Napier’s Bones.

content

These are a set of multiplication tables embedded in rods. They can be used for multiplication, division and square root extraction.

1920px-An_18th_century_set_of_Napier's_Bones

An 18th century set of Napier’s bones Source: Wikimedia Commons

Wilhelm Schickard’s calculating machine incorporated a set of cylindrical Napier’s Bones to facilitate multiplication.

The Swiss mathematician Jost Bürgi (1552–1632) produced a set of logarithm tables independently of Napier at almost the same time, which were however first published at Kepler’s urging as, Arithmetische und Geometrische Progress Tabulen…, in 1620. However, unlike Napier, Bürgi delivered no explanation of the how his table were calculated.

csm_objekt_monat_2015_01_ee608568fa

Tables of logarithms became the standard calculation aid for all those making mathematical calculations down to the twentieth century. These were some of the mathematical tables that Babbage wanted to produce and print mechanically with his Difference Engine. When I was at secondary school in the 1960s I still carried out all my calculations with my trusty set of log tables, pocket calculators just beginning to appear as I transitioned from school to university but still too expensive for most people.

log-cover

Not my copy but this is the set of log tables that accompanied me through my school years

Later in the late 1980s at university in Germany I had, in a lecture on the history of calculating, to explain to the listening students what log tables were, as they had never seen, let alone used, them. However for more than 350 years Napier’s invention served all those, who needed to make mathematical calculations well.

 

 

 

 

 

 

 

 

 

 

 

 

6 Comments

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

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

It is not an exaggeration to say that the invention of telescope was a very major turning point in the general history of science and in particular the history of astronomy. Basic science is fundamentally empirical; people investigating the world make observations with their senses–taste, sight, touch, smell, hearing–then try to develop theories to describe and explain what has been observed and recorded. The telescope was the first ever instrument that was capable of expanding or strengthening one of those senses that of sight. The telescope made it possible to see things that had never been seen before.

The road to the telescope was a long one and one of the questions is why it wasn’t invented earlier. There are various legends or myths about devices to enable people to see things at a distance throughout antiquity and various lens shaped objects also from the distant past that might or might not have been lenses. Lenses in scientific literature in antiquity and the early middle ages were burning lenses used to focus sunlight to ignite fires. The first definite use of lenses to improve eyesight were the so-called reading stones, which emerged around 1000 CE, approximately hemispherical lenses, placed on documents to help those suffering from presbyopia, weakening of the ability of the eye to focus due to aging.

Reading-stone

Source: Zeiss

Reading glasses utilising plano-convex lenses first appeared around 1290.

Hugh_specs

The earliest pictorial evidence for the use of eyeglasses is Tommaso da Modena’s 1352 portrait of the cardinal Hugh de Provence reading in a scriptorium Source: Wikimedia Commons

The current accepted theory of the discovery of simple lenses is that in the Middle Ages monks cutting gems to decorate reliquary discovered the simple magnifying properties of the gemstones they were grinding and polishing.

800px-Reliquary_Cross_(French,_The_Cloisters)

Reliquary Cross, French, c. 1180 Source: Wikimedia Commons

By the middle of the fifteenth century eye glasses utilising both convex and concave lenses were being manufactured and traded, so why did it take until 1608 before somebody successfully combined a concave lens and convex lens to create a simple so-called Dutch telescope?

There are in fact earlier in the sixteenth century in the writings of Girolamo Fracastoro (ca. 1476–1553) and Giambattista della Porta (1532–1615) descriptions of the magnifying properties of such lens combinations but these are now thought to refer to special eyeglasses rather than telescopes.

Della Porta Telescope Sketch

The early lenses were spherical lenses, which were hand ground and polished and as a result were fairly inaccurate in their form tending to deviate from their ideal spherical form the further out one goes from the centre.  These deformations caused distortions in the images formed and combining lenses increased the level of distortion making such combinations next to useless. It is now thought that the breakthrough came through the use of a mask to stop down the diameter of the eyepiece lens cutting out the light rays from the periphery, restricting the image to the centre of the lens and thus massively reducing the distortion. So who made this discovery? Who first successfully developed a working telescope?

This question has been hotly discussed and various claims just as hotly disputed since at least the middle of the seventeenth century. However, there now exists a general consensus amongst historian of optics.

[To see the current stand on the subject read the bog post that I wrote at this time last year, which I don’t intend to repeat here]

Popular accounts of the early use of the telescope in astronomy almost always credit Galileo Galilei, at the time a relatively unknown professor for mathematics in Padua, with first recognising the potential of the telescope for astronomy; this is a myth.

As can be seen from the quote from the French newsletter AMBASSADES DV ROY DE SIAM ENVOYE’ A L’ECELence du Prince Maurice, arriué à la Haye le 10. Septemb.1608., recording the visit of the ambassador of the King of Siam (Thailand), who was also present at the first demonstration of the telescope the potential of this new instrument, as a tool for astronomy was recognised from the very beginning:

even the stars which normally are not visible for us, because of the scanty proportion and feeble sight of our eyes, can be seen with this instrument.

In fact the English polymath Thomas Harriot (1560–1621) made the earliest known telescopic, astronomical observations but, as with everything else he did, he didn’t publish, so outside of a small group of friends and acquaintances his work remained largely unknown. Also definitely contemporaneous with, if not earlier than, Galileo the Franconian court mathematicus, Simon Marius (1573–1625), began making telescopic observations in late 1609. However, unlike Galileo, who as we will see published his observations and discoveries as soon as possible, Marius didn’t publish until 1614, which would eventually bring the accusation of having plagiarised Galileo.  At the Collegio Romano, the Jesuit University in Rome, Odo van Maelcote (1572–1615) and Giovanni Paolo Lembo (1570–1618) were also making telescopic observations within the same time frame. There were almost certainly others, who didn’t make their observations public.

Before we turn to the observations and discoveries that these early telescopic observers made, we need to look at a serious technical problem that tends to get ignored by popular accounts of those discovery, how does a telescope work? In 1608 when the telescope first saw the light of day there existed absolutely no scientific explanation of how it worked. The group of early inventors almost certainly discovered its magnifying effect by accident and the first people to improve it and turn it into a viable scientific instrument, again almost certainly, did so by trial and error. At this point the problem is not to find the optical theory needed to develop better telescopes systematically but to find the optical theory necessary to justify the result the telescope produced. Using any sort of instrument in science requires a scientific explanation of how those results are achieved and as already stated at the beginning no such theory existed. The man, who came to the rescue, was Johannes Kepler in the second of his major contributions to the story of heliocentric astronomy.

Already in 1604 in his Ad Vitellionem Paralipomena Astronomiae pars optica, Kepler had published the first explanation of how lenses focus light rays and how eyeglasses work to compensate for short and long sightedness so he already had a head start on explaining how the telescope functions.

thumbnail-by-url.json

Source

Francesco Maurolico (1494–1575) had covered much of the same ground in his Theoremata de lumine et umbra earlier than Kepler but this work was only published posthumously in 1611, so the priority goes to Kepler.

Theoremata_de_lumine_et_umbra_[...]Maurolico_Francesco_bpt6k83058n

In 1611 Kepler published his very quickly written Dioptrice, in which he covered the path of light rays through single lenses and then through lens combinations. In this extraordinary work he covers the Dutch or Galilean telescope, convex objective–concave eyepiece, the astronomical or Keplerian telescope, convex objective–convex eyepiece, the terrestrial telescope, convex objective–convex eyepiece–convex–field–lens to invert image, and finally for good measure the telephoto lens! Galileo’s response to this masterpiece in the history of geometrical optics was that it was unreadable!

431px-Kepler_dioptrice_titul

Source: Wikimedia Commons

In the next section we will turn to the discoveries that the various early telescopic astronomical observers made and the roles that those various discoveries played in the debates on, which was the correct astronomical model of the cosmos. A much more complicated affair than it is often presented.

 

 

 

 

 

2 Comments

Filed under History of Astronomy, History of Optics, History of science, Renaissance Science

Revealing the secrets of the fire-using arts

During the Middle Ages it was common practice for those working in the crafts to keep the knowledge of their trades secret, masters passing on those secrets orally to new apprentices. This protection of trade secrets, perhaps, reached a peak during the Renaissance in the glassmaking centre of Venice, where anybody found guilty of revealing the secrets of the glassmaking was sentenced to death. Although there were in some crafts manuscripts, which made it into print, describing the work processes involved in the craft these were of very limited distribution. All of this began to change with the invention of moving type book printing. Over the sixteenth and seventeenth centuries printed books began to appear describing in detail the work processes of various crafts. I have already written a post about one such book, De re metallica by Georgius Agricola (1494–1555). However, Agricola’s book was not the first printed book on metallurgy that honour goes to the Pirotechnia of Vannoccio Biringuccio published posthumously in Italian in 1540. Agricola was well aware of Biringuccio’s book and even plagiarised sections of it in his own work.

800px-De_la_pirotechnia_1540_Title_Page_AQ1_(1)

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

Whereas Agricola was himself not a miner or metal worker but rather a humanist physician, whose knowledge of the medieval metallurgical industry was based on observation and questioning of those involved, Biringuccio, as we will see, spent his whole life engaged in one way or another in that industry and his book was based on his own extensive experiences.

Born in Siena 20 October 1480 the son of Lucrezia and Paolo Biringuccio, an architect.

16866

Siena 1568

As a young man Vannoccio travelled throughout Italy and Germany studying metallurgical operations. In Siena he was closely associated with the ruling Petrucci family and after having run an iron mine and forge for Pandolfo Petrucci, he was appointed to a public position at the arsenal and in 1513 director of the mint.

Petrucci_Coat_of_Arms

Petrucci coat of arms Source: Wikimedia Commons

He was exiled from Siena in 1516 after the Petruccis fell from power and undertook further travels throughout Italy and visited Sicily in 1517. In 1523 the Petruccis were reinstated and Vannoccio returned to Siena and to his position in the arsenal. In 1526 the Petruccis fell from power again and he was once again forced to leave his hometown. He worked in both the republics of Venice and Florence casting cannons and building fortifications. In 1531 in a period of political peace he returned once more to Sienna, where he was appointed a senator, and architect and director of building construction. Between 1531 and 1535 he cast cannons and constructed fortification in both Parma and Venice. In 1536 he was offered a job in Rome and after some hesitation accepted the post of head of the papal foundry and director of papal munitions. It is not known when or where he died but there is documentary evidence that he was already dead on 30 April 1539.

His Pirotechnia was first published posthumously in Venice in 1540, it was printed by Venturino Roffinello, published by Curtio Navo and dedicated to Bernardino di Moncelesi da Salo. Bernardino is mentioned both in the book’s preface as well as in the text. The Pirotechnia consists of ten books, each one dealing with a separate theme in the world of Renaissance metallurgy, transitioning from the wining of metal ores, over their smelting to the use of the thus produced materials in the manufacture of metal objects and dealing with a whole host of side topic on the way. Although by no means as lavishly illustrated as De re metallica, the book contains 84 line drawings** that are as important in imparting knowledge of the sixteenth century practices as the text.

Book I, is titled Every Kind of Mineral in General, after a general introduction on the location of ores it goes on the deal separately with the ores of gold, silver, copper, lead, tin and iron and closes with the practice of making steel and of making brass.

pirotechnia001

pirotechnia002

Book II continues the theme with what Biringuccio calls the semi-minerals an extensive conglomeration of all sorts of things that we wouldn’t necessarily call minerals. Starting with quicksilver he moves on to sulphur then antimony, marcasite (which includes all the sulphide minerals with a metallic luster), vitriol, rock alum, arsenic, orpiment and realgar.

pirotechnia003

pirotechnia004

This is followed by common salt obtained from mine or water and various other salts in general then calamine Zaffre and manganese. The book now takes a sharp turn as Biringuccio deals with the loadstone and its various effects and virtues. His knowledge in obviously not first hand as he repeats the standard myths about loadstones losing their power and virtue in the presence of diamonds, goat’s milk and garlic juice. He now move on to, ochre, bole, emery, borax, azure and green azure. Pointing out that many of the things he has dealt with are rocks rather than metals he now introduces rock crystal and all important gems in general before closing the book with glass.

pirotechnia005

Book III covers the assaying and smelting metal ores concentring on silver, gold and copper.

pirotechnia006

pirotechnia007

pirotechnia008

pirotechnia009

Book IV continues with a related theme, the various methods for separating gold from silver.

pirotechnia010

pirotechnia011

Having covered separation of gold and silver Book V covers the alloys of gold, silver, copper, lead and tin.

Following the extraction of metals, their assays, separation and alloys, Book VI turns to practical uses of metals: the art of casting in general and particular.

pirotechnia012

pirotechnia013.jpg

pirotechnia014

pirotechnia015

pirotechnia016

pirotechnia017

Book VII the various methods of melting metals.

pirotechnia018

pirotechnia019

pirotechnia020

pirotechnia021

pirotechnia022

pirotechnia023

Having dealt with the casting of bells and cannons in Book VII, Book VIII deals the small art of casting.

pirotechnia024

Book IX is a bit of a mixed bag titled, Concerning the Procedure of Various Operations of Fire. The book opens with a very short chapter on alchemy. Biringuccio has already dealt with alchemical transmutation fairy extensively in Book I when discussing the production of gold. He doesn’t believe in it: These men [alchemists] in order to arrive at such a port have equipped their vessels with sails and hard-working oarsmen and have sailed with guiding stars, trying every possible course, and, finally submerged in the impossible (according to my belief) not one of them to my knowledge has yet come to port. In Book XI he acknowledges that although transmutation doesn’t work, alchemists have developed many positive things: …it is surely a fine occupation, since in addition to being very useful to human need and convenience, it gives birth every day to new and splendid effects such as the extraction of medicinal substances, colours and perfumes, and an infinite number of compositions of things. It is known that many arts have issued solely from it; indeed, without it or its means it would have been impossible for them ever to have been discovered by man except through divine revelation.The next chapter deal briefly with sublimation and very extensively with distillation both of which he acknowledges are products of the alchemists.

pirotechnia025

pirotechnia026

pirotechnia027

He now takes a sharp turn left with a chapter on Discourse and Advice on How to Operate a Mint Honestly and with Profit. This is followed with chapters on goldsmith, coppersmith, ironsmith and pewterer work, leading on to chapters on wire drawing, preparing gold for spinning, removing gold from silver and other gilded objects, and the extraction of every particle of gold and silver from slags of ore.

pirotechnia028

pirotechnia029

The book closes with making mirrors from bell metal and three chapters on working with clay.

pirotechnia030.jpg

Book X closes out Biringuccio’s deliberations with essays on making saltpetre and gunpowder, then moving on to the uses of gunpowder in gunnery, military mining, and fireworks, the later in both military and civil circumstances.

pirotechnia031.jpg

pirotechnia032

Biringuccio’s efforts proved successful with Italian editions of the book appearing in 1540 (Sienna), 1550 (Venetia), 1558/9 (Venegia), 1559 (Venetia), 1678 (Bologna), and 1914 (Barese). French editions appeard in 1556 (Paris), 1572 (Paris), 1627 (Rouen), and 1856 (Paris). A German edition appeared in 1925 (Braunschweig). There were only partial translation into English in 1555 (London) and 1560 (London). The first full English translation was made by Martha Teach Gnudi & Cyril Stanley Smith with notes and an introduction in 1941 (New Haven), which was republished by Dover Books in New York in 1990. It is the Dover edition that forms the basis of this blog post.

Biringuccio’s Pirotechnia is an important publication in the histories of technology, metallurgy, inorganic chemistry and the crafts and trades in general and deserves to be much better known.

**I have only chosen a selection of the drawings. On some subjects such as the use of bellows Biringuccio brings wholes rows of illustrations to demonstrate the diverse methods used.

 

 

 

 

 

 

3 Comments

Filed under History of Chemistry, History of Technology, Renaissance Science

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

As I stated earlier in this series only a comparatively small number of astronomers accepted the whole of Copernicus’ theory, both cosmology and astronomy. More interestingly almost none of them had any lasting impact during the final decades of the sixteenth century on the gradual acceptance of heliocentrism. Although he appears to have abandoned Copernicus’ astronomy later in life, Rheticus did have a strong impact with his Narratio Prima(1540), which through its various editions was the first introduction to the heliocentric hypothesis for many readers. Two others, whose impact was principally in the seventeenth century, were Kepler and Galileo, who will be dealt with later. However, one astronomer who did play an important role in the sixteenth century was Michael Mästlin.

michaelis_mc3a4stlin_gemc3a4lde_1619

Michael Mästlin portrait 1619 artist unknown

Michael Mästlin (1550-1631) stood at the end of a long line of important Southern German astronomers and mathematicians. A graduate of the University of Tübingen he was a student of Philipp Apian (1531–1589),

hu_alt_-_philipp_apian_1590_mr

Philipp Apian, artist unknown Source: Wikimedia Commons

 

who was a student of his more famous father Peter Apian (1495–1552) in Ingolstadt. Peter Apian had studied under Georg Tannstetter (1482–1535) in Vienna, who had studied under Andreas Stiborius (c. 1464–1515) and Johannes Stabius (1450–1522) first in Ingolstadt then in Vienna. In 1584 Mästlin succeeded his teacher Philipp Apian as professor for astronomy and mathematics at Tübingen. An active astronomer since the beginning of the 1570s Mästlin was regarded as a leading German astronomer and consulted by the Protestant princes on matters astronomical, astrological and mathematical.

Mästlin represents the transitional nature of the times probably better than any other astronomer. His Epitome Astronomiae (1582), a university textbook, which went through a total of seven editions, was a standard Ptolemaic geocentric text that he continued to teach from until his death in 1631.

introimage

However, at the same time he taught selected students the fundaments of Copernican heliocentric astronomy. Earlier accounts claimed that he did this in secret but all of the available evidence suggests that he did so quite openly. This quasi revolutionary act of teaching famously produced one significant result in that Mästlin introduced Copernican astronomy to the young Johannes Kepler, who would go on to become the most important propagator of heliocentric astronomy in the early seventeenth century.

One subject on, which the German Protestant princes consulted Mästlin was the proposed Gregorian calendar reform from 1582. Mästlin launched a vitriolic polemic against it largely on religious grounds with his Gründtlicher Bericht von der allgemeinen und nunmehr bei 1600 Jahren von dem ersten Kaiser Julio bis jetzt gebrauchten jarrechnung oder kalender (Rigorous report on the general and up till now for 1600 years used calculation of years or calendar from the first Caesar Julio) (1583). The Protestant princes accepted his advice and as a result didn’t adopt the new calendar until 1700.

On the other side of the religious divide the man charged by the Pope to promote and defend the new calendar was the Jesuit professor of astronomy and mathematics at the Collegio Romano, Christoph Clavius (1538–1612).

christopher_clavius

Christoph Clavius. Engraving Francesco Villamena, 1606 Source: Wikimedia Commons

Although Clavius was a convinced defender of the Ptolemaic system until his death, he did play a central role in the developments that led to the eventual acceptance of the heliocentric system. The Catholic universities in the last quarter of the sixteenth century still didn’t really pay the mathematical disciplines much attention and their teaching of astronomy had not really progressed beyond the High Middle Ages. Clavius introduced modern mathematics and astronomy into the Jesuit educational reform programme, following the fundamental principle of that programme, if you want to win the debate with your non-Catholic opponents you need to be better educated than them. Many Jesuit and Jesuit educated mathematicians and astronomers, who came out of the pedagogical programme established by Clavius, would, as we shall see, make significant and important contributions to the developments in astronomy in the seventeenth century.

Clavius was also the author of a number of excellent up to date textbooks on a full range of mathematical topics. His astronomy textbook In Sphaeram Ioannis de Sacro Bosco commentarius, the first edition appearing in 1570 and further updated editions appearing in 1581, 1585, 1593, 1607, 1611 and posthumously in 1618, was the most widely read astronomy textbook in the last decades of the sixteenth and early decades of the seventeenth centuries. It was strictly Ptolemaic but he presented, described and commented upon Copernicus’ heliocentric hypothesis. Although he showed great respect for Copernicus as a mathematical astronomer, he of course rejected the hypothesis. However, anybody who read Clavius’ book would be informed of Copernicus work and could if interested go looking for more information. One should never underestimate the effect of informed criticism, and Clavius’ criticism was well informed, for disseminating a scientific hypothesis. Many people certainly had their first taste of the heliocentric hypothesis through reading Clavius.

Another group who had a positive impact on the propagation of the heliocentric hypothesis in the last quarter of the sixteenth century was the so-called English School of Mathematics. Whilst Robert Recorde (1510–1558) and John Dee (1527–c. 1608) were not committed supporters of Copernicus, they did much to spread knowledge of the heliocentric hypothesis. As we have already seen John Feild (c. 1520–1587) was a declared supporter of Copernicus but as his Copernican ephemerides proved no more accurate than the Ptolemaic ones his influence diminished. Not so Dee’s foster son Thomas Digges (c. 1546–1595).

His 1576 edition of his father’s A Prognostication everlastingcontained an appendix A Perfit Description of the Caelestiall Orbes according to the most aunciente doctrine of the Pythagoreans, latelye revived by Copernicus and by Geometricall Demonstrations approved, which is an annotated translation of part of the cosmological first book of De revolutionibus into English, which continued to have an impact on English readers long after Digges’ demise.

digges4

Source: Linda Hall Library

Thomas Harriot (c. 1560–1621) was another, who was committed to the heliocentric hypothesis.

thomasharriot

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

His biggest problem was that he published none of his scientific or mathematical work but he was well networked and contributed extensively to the debate through correspondence. The influence of this group would, as we will see, have an impact on the early acceptance of Kepler’s work inEngland.

Another figure in the last quarter of the sixteenth century, who, although not an astronomer, made a very important contribution to the cosmological debate, was the physician William Gilbert (1544–1603).

william_gilbert_45626i

William Gilbert (1544–1603) artist unknown. Source: Wellcome Library via Wikimedia Commons

Gilbert is well known in the history of science as the author of the first modern scientific investigation of magnetism in his De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth).

167203_0

Gilbert carried out many of his experiments with spherical magnets, which he called terella, from which he deduced his belief that the Earth itself is a spherical magnet. Based on his erroneous belief that a suspended terella rotates freely about its axis he came to accept and propagate diurnal rotation. Book VI of De magnete, the final book, is devoted to an analysis of the Earth as a spherical magnet based on the results of Gilbert’s experiments with his terella.

In Chapter III of Book VI, On the Daily Magnetic Revolution of the Globes, as Against the Time-Honoured Opinion of a primum mobile: A Probable Hypothesis, Gilbert gives a detailed review of the history of a geocentric system with diurnal rotation starting with Heraclides of Pontus and going through to Copernicus. Gilbert rejects the whole concept of celestial spheres, dismissing them as a human construction with no real existence. He brings the standard physical arguments that it is more logical that the comparatively small Earth rotates once in twenty-four hours rather than the vastly larger sphere of the fixed stars. In the following chapter he then argues that magnetism is the origin of this rotation. In Chapter V he discusses the arguments for and against movement of the Earth. At the end of Chapter III Gilbert writes, “I pass by the earth’s other movements, for here we treat only of the diurnal rotation…” so what he effectively promotes is a geocentric system with diurnal rotation. Later in his De Mundo Nostro Sublunari Philosophia Nova (New Philosophy about our Sublunary World), Gilbert propagated a full heliocentric system but this book was first published posthumously in 1651 and had no real influence on the astronomical discussion.

Demundo

Diagram of the cosmos De Mundo p. 202 Source: Wikimedia Commons

Gilbert’s De magnete was a widely read and highly influential book in the first half of the seventeenth century. Galileo praised it but criticised its lack of mathematics. As we shall see it had a massive influence on Kepler. Because of its status the book definitely had a major impact on the acceptance of geo-heliocentric systems with diurnal rotation rather than without later in the seventeenth century.

We will stop briefly and take stock in 1593, fifty years after the publication of De revolutionibus. We have seen that within Europe astronomers had already begun to question the inherited Ptolemaic system during the fifteenth century. In the sixteenth century a major debate developed about both the astronomical and cosmological models. The Aristotelian theories of comets, the celestial spheres and celestial immutability all came under attack and were eventually overturned. Alternative models–Aristotelian homocentricity, the Capellan system and geocentricity with diurnal rotation–were promoted.  With the publication of Copernicus’ De revolutionibus with its heliocentric hypothesis the debates went into overdrive. Only a comparatively small number of astronomers propagated the heliocentric system and an even smaller number of them actually went on to have a real impact on the discussion. A much larger number showed an initial strong interest in the mathematical models in De revolutionibus and the planetary tables and ephemerides based on them, in the hope they would generate better, more accurate data for applications such as astrology, cartography and navigation. This proved not to be the case as Copernicus’ work was based on the same inaccurate and corrupted ancient data, as Ptolemaic geocentric tables. Recognising this both Wilhelm IV in Kassel and Tycho Brahe on Hven began programmes of extensive new astronomical observations. However, this very necessary new data only became generally available well into the seventeenth century. Other astronomers partially convinced by Copernicus’ arguments turned to Capellan models with Mercury and Venus orbiting the Sun rather than the Earth and full geo-heliocentric models with the Moon and the Sun orbiting the Earth and all the other five planets orbiting the Sun. This was the situation at the beginning of the 1590s but a young Johannes Kepler (1571–1630), who would have a massive impact on the future astrological and cosmological models, was waiting in the wings.

 

 

 

 

 

5 Comments

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

Vienna and Astronomy the beginnings.

Vienna and its university played a very central role in introducing the study of mathematics, cartography and astronomy into Northern Europe in the fifteenth and sixteenth century. In early blog posts I have dealt with Georg von Peuerbach and Johannes Regiomontanus, Conrad Celtis and his Collegium poetarum et mathematicorum, Georg Tannstetter and the Apians, and Emperor Maximilian and his use of the Viennese mathematici. Today, I’m going to look at the beginnings of the University of Vienna and the establishment of the mathematical science as a key part of the university’s programme.

The University of Vienna was founded in 1365 by Rudolf IV, Duke of Austria (1339–1365) and his brothers Albrecht III, (c. 1349–1395) and Leopold III (1351–1386) both Dukes of Austria.

800px-Rudolf_IV

Rudolf IV, Duke of Austria Source: Wikimedia Commons

Like most young universities it’s early decades were not very successful or very stable. This began to change in 1384 when Heinrich von Langenstein (1325–1397) was appointed professor of theology.

langenstein_heinrich_von_1325-1397_in_rationale_divinorum_officiorum_des_wilhelmus_durandus_codex_2765_oenb_1385-1406_106.i.1840_0

Presumably Heinrich von Langenstein (1325-1397), Book miniature in Rationale divinorum officiorum of Wilhelmus Durandus, c. 1395

Heinrich von Langenstein studied from 1358 in Paris and in 1363 he was appointed professor for philosophy on the Sorbonne advancing to Vice Chancellor. He took the wrong side during the Western Schism (1378–1417) and was forced to leave the Sorbonne and Paris in 1382. Paris’ loss was Vienna’s gain. An excellent academic and experienced administrator he set the University of Vienna on the path to success. Most important from our point of view is the study of mathematics and astronomy at the university. We tend to think of the curriculum of medieval universities as something fixed: a lower liberal arts faculty teaching the trivium and quadrivium and three higher faculties teaching law, medicine and theology. However in their early phases new universities only had a very truncated curriculum that was gradually expanded over the early decades; Heinrich brought the study of mathematics and astronomy to the young university.

Heinrich was a committed and knowledgeable astronomer, who established a high level of tuition in mathematics and astronomy. When he died he left his collection of astronomical manuscripts and instruments to the university. Henry’s efforts to establish astronomy as a discipline in Vienna might well have come to nothing if a successor to teach astronomy had not been found. However one was found in the person of Johannes von Gmunden (c. 1380–1442).

Gmunden005

Initial from British Library manuscript Add. 24071 Canones de practica et utilitatibus tabularum by Johannes von Gmunden written 1437/38 by his student Georg Prunner Possibly a portrait of Johannes Source: Johannes von Gmunden (ca. 1384–1442) Astronom und Mathematiker Hg. Rudolf Simek und Kathrin Chlench, Studia Medievalia Septentrionalia 12

Unfortunately, as is often the case with medieval and Renaissance astronomers and mathematicians, we know almost nothing personal about Johannes von Gmunden. There is indirect evidence that he comes from Gmunden in Upper Austria and not one of the other Gmunden’s or Gmund’s. His date of birth is an estimate based on the dates of his studies at the University of Vienna and everything else we know about him is based on the traces he left in the archives of the university during his life. He registered as a student at the university in 1400, graduating BA in 1402 and MA in 1406.

His MA was his licence to teach and he held his first lecture in 1406 on the Theoricae planetarum by Gerhard de Sabbioneta (who might well not have been the author) a standard medieval astronomy textbook, establishing Johannes’ preference for teaching astronomy and mathematics. In 1407, making the reasonable assumption that Johannes Kraft is Johannes von Gmunden, thereby establishing that his family name was Kraft, he lectured on Euclid. 1408 to 1409 sees him lecturing on non-mathematical, Aristotelian texts and 1410 teaching Aristotelian logic using the Tractatus of Petrus Hispanus. In the same year he also taught Euclid again. 1411 saw a return to Aristotle but in 1412 he taught Algorismus de minutiis i.e. sexagesimal fractions. The Babylonian sexagesimal number system was used in European astronomy down to and including Copernicus in the sixteenth century, Aristotelian logic again in 1413 but John Pecham’s Perspectiva in 1414.

Gmunden006

Johannes von Gmunden Algorismus de minutiis printed by Georg Tannstetter 1515 Source: Johannes von Gmunden (ca. 1384–1442) Astronom und Mathematiker Hg. Rudolf Simek und Kathrin Chlench, Studia Medievalia Septentrionalia 12

Around this time Johannes took up the study of theology, although he never proceeded past BA, and 1415 and 16 see him lecturing on religious topics although he also taught Algorismus de minutiis again in 1416. From 1417 till 1434, with breaks, he lectured exclusively on mathematical and astronomical topics making him probably the first dedicated lecturer for the mathematical disciplines at a European university. Beyond his lectures he calculated and wrote astronomical tables, taught students how to use astronomical instruments (for which he also wrote instruction manuals), including the construction of cheap paper instruments.

Gmunden007

Johannes von Gmunden instructions for constructing an astrolabe rete Wiener Codex ÖNB 5296 fol. 6r Source: Johannes von Gmunden (ca. 1384–1442) Astronom und Mathematiker Hg. Rudolf Simek und Kathrin Chlench, Studia Medievalia Septentrionalia 12

He collected and also wrote extensive astronomical texts. As well as his teaching duties, Johannes served several times a dean of the liberal arts faculty and even for a time as vice chancellor of the university. His influence in his own time was very extensive; there are more than four hundred surviving manuscripts of Johannes Gmunden’s work in European libraries and archives.

When he died Johannes willed his comparatively large collection of mathematical and astronomical texts and instruments to the university establishing a proper astronomy department that would be inherited with very positive results by Georg von Peuerbach and Johannes Regiomontanus. Perhaps the most fascinating items listed in his will are an Albion and an instruction manual for it.

DDkqT54WsAEkGV9

Albion front side Source: Seb Falk’s Twitter feed

DDlDZSkW0AAKFCr

Albion rear Source: Seb Falk’s Twitter feed

The Albion is possibly the most fascinating of all medieval astronomical instruments. Invented by Richard of Wallingford (1292–1336), the Abbot of St Albans, mathematician, astronomer, horologist and instrument maker, most well known for the highly complex astronomical clock that he designed and had constructed for the abbey.

Richard_of_Wallingford

Richard of Wallingford Source: Wikimedia Commons

The Albion, ‘all by one’, was a highly complex and sophisticated, multi-functional astronomical instrument conceived to replace a whole spectrum of other instruments. Johannes’ lecture from 1431 was on the Albion.

Johannes von Gmunden did not stand alone in his efforts to develop the mathematical sciences in Vienna in the first half of fifteenth century; he was actively supported by Georg Müstinger (before 1400–1442), the Prior of the Augustinian priory of Klosterneuburg.

header_archiv-1920x552-c-default

Klosterneuburg

Müstinger became prior of Klosterneuburg in 1418 and worked to turn the priory into an intellectual centre. In 1421 he sent a canon of the priory to Padua to purchase books for over five hundred florins, a very large sum of money. The priory became a centre for producing celestial globes and cartography. It produced a substantial corpus of maps including a mappa mundi, of which only the coordinate list of 703 location still exist. Scholar who worked in the priory and university fanned out into the Southern German area carrying the knowledge acquired in Vienna to other universities and monasteries.

Johannes’ status and influence are nicely expressed in a poem about him and Georg von Peuerbach written by Christoph Poppenheuser in 1551:

The great Johannes von Gmunden, noble in knowledge, distinguished in spirit, and dignified in piety                                                                                                                                         And you Peuerbach, favourite of the muses, whose praise nobody can sing well enough                                                                                                                                           And Johannes, named after his home town, known as far away as the stars for his erudition

The tradition established in Vienna by Heinrich von Langenstein, Johannes von Gmunden and Georg Müstinger was successfully continued by Georg von Peuerbach (1423–1461), who contrary to some older sources was not a direct student of Johannes von Gmunden arriving in Vienna only in 1443 the year after Johannes death. However Georg did find himself in a readymade nest for the mathematical disciplines, an opportunity that he grasped with both hands developing further Vienna’s excellent reputation in this area.

 

 

 

 

 

3 Comments

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