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History of astronomy – reading the classics

Most non-specialists get their knowledge of the history of astronomy from general surveys of the subject or from even more general surveys of the history of science. The information contained in these on Ptolemaeus, Copernicus and the other boys in the history of astronomy band is often from secondary if not tertiary or even quaternary sources and as a result also often inaccurate if not completely false. The solution to this problem is of course to read the originals but not all of us are blessed with the linguistic abilities necessary to tackle second century Greek or Early Modern Latin, to say nothing of Galileo’s seventeenth century Tuscan. However, the current scholar interested in the classical texts from the history of astronomy is blessed with modern, annotated English translations of these and in this post I want to briefly present these and some secondary literature to assist in understanding them.

We start with the mother load lode, Ptolemaeus’ Mathēmatikē Syntaxis more commonly known by its Arabic name, the Almagest.


A imaginary portrait of Ptolemaeus from 1564 Source: Wikimedia Commons

This is by no means the earliest astronomical text in the European tradition but much of what we know about ancient Greek astronomy we only know through references by Ptolemaeus. He is of course preceded by the Babylonians and the ancient Egyptians but neither of these traditions has a comparable text to Mathēmatikē Syntaxis. Also Ptolemaeus stands patron for a tradition in astronomical observation, calculation and recording that remained largely unchanged for fifteen hundred years down to the work of the first Astronomer Royal, John Flamsteed. The methods were over the centuries refined but remained fundamentally the same. Even the invention of the telescope did not initially change much in the methodology of astronomy to be found in Ptolemaeus’ Great Treatise, a title for the work that is the origin of the Arabic name.

There is an excellent, annotated, English translation of Ptolemy’s Almagest by G.J. Toomer.[1] Even with Toomer’s excellent guidance the Almagest is not an easy text for non-specialists to comprehend so readers might find the following secondary literature useful. We start with Olaf Pedersen’s A Survey of the Almagest.[2] Pedersen (1920–1997) was one of the best historians of astronomy for antiquity and the Middle Ages and his opinions are always well founded. I would also recommend Liba Taub’s Ptolemy’s Universe: The Natural Philosophical and Ethical Foundations of Ptolemy’s Astronomy[3] for some solid background to Ptolemaeus’ work.

We now take a major jump of fourteen hundred years to CopernicusDe revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres), published in Nürnberg in 1543 by Johannes Petreius.

Copernicus followed the layout of Ptolemaeus’ Almagest and viewed his own volume as a modern version of the Ptolemaeus’ work, so to speak. There are several English translations but the one that I would recommend is quasi the official one. In 1973, the 500th anniversary of Copernicus’ birth, The Polish Academy of Sciences started a project to produce a uniform edition of Copernicus’ extant works. As well as publishing the Latin originals they published a set of authorised translations in the main modern European languages, the English translation is Edward Rosen’s On the Revolutions.[4] For various reasons I’m not a big fan of Rosen but as a historian he really knows his Copernicus and his commentaries are very good. A useful but specialist addition to understanding De revolutionibus is Swerdlow’s and Neugebauer’s Mathematical astronomy in Copernicus’ De revolutionibus,[5] which is justifiably regarded as a classic in the history of astronomy.

Next up is my personal favourite astronomer Johannes Kepler and here we have not just one but four books that we have to consider.


Portrait of Johannes Kepler 1610 by unknown artist. Source: Wikimedia Commons

We start with Kepler’s first ever publication the Mysterium Cosmographicum (1596). This book with its theory that the planets in their spheres are separated by the five Platonic solids appears totally bizarre to us today. However, if you want to understand Kepler’s astronomical thoughts then you should start here because its divine geometry remained Kepler’s leitmotif for all of his astronomical work. He published a second edition in 1621 following the publication of his magnum opus the Harmonice Mundi. There is an English translation of the second edition, Mysterium CosmographicumThe Secret of the Universe,[6] which is unfortunate no longer in print.


Kepler’s Platonic solid model of the Solar system from Mysterium Cosmographicum (1596) Source: Wikimedia Commons


From the point of view of modern astronomy, much more important is Kepler’s Astronomia nova, which contains his first two laws of planetary motion and the story of how he arrived at them. There is an excellent annotated English translation of this book from William Donahue.[7] I would also recommend James Voelkel’s The Composition of Kepler’s Astronomia nova potential readers,[8] which explains the strange narrative structure of Kepler’s book and why he employed it. Donahue has also published a short introduction to the Astronomia nova for students.[9]

Kepler regarded his Harmonice Mundi as his astronomical magnum opus. A big sprawling book it covers a wide range of topics that I sketched in a blog post here. It is of course most famous for containing his third law of planetary motion. There is an excellent, annotated English translation by E.J. Aiton, A.M. Duncan and J.V. Field.[10]

Our fourth astronomical book from Kepler book is his Epitome Astronomiae Copernicanae published in three sections 1618, 1620 and 1621. Unfortunately only a part of this book (Books VI & V of seven) is available in English translation.[11]

The counterpart to Kepler is of course Galileo Galilei and he has been much better served by his translators.


Galileo Galilei. Portrait by Leoni Source: Wikimedia Commons

We start with the book that established his reputation the Sidereus Nuncius. Here we have an excellent annotated translation by Albert van Helden.[12] Galileo is of course famously erudite and highly readable and so one doesn’t initially need any secondary literature to understand him. However, the reader is warned that Galileo is anything but honest in published works and one should check with the vast secondary Galileo literature before taking anything he say as true, in particular about supposed rivals. His infamous Dialogo has long been available in a standard English translation by Stillman Drake.[13]

For our final classic we spring to the end of the seventeenth century and Isaac Newton’s Principia.


This a copy of a painting by Sir Godfrey Kneller (1689). Source: Wikimedia Commons

The best English translation can be acquired in one volume with the best introduction to the text by one of its translators I. Bernard Cohen.[14] The two, guide and Principia, are available as separated volumes if you prefer. For those who find Newton heavy going despite Cohen’s assistance there is Chandrasekhar’s Newton’s Principia for the common reader.[15] Also recommended is The Cambridge Companion to Newton.[16]

I own most of the books that I have listed here but I won’t claim to have read them from cover to cover. (I have read the Harmonice Mundi from cover to cover!) However when reading about the history of astronomy I find it useful and informative to check what a particular scholar actually said rather than what somebody else thinks they said.

A couple of more general histories of astronomy that I would recommend for the wanna be historian of the subject as starting points and to provide a more general background into which to place the classics that I’ve listed above are John North’s Cosmos,[17] the Cambridge Illustrated History of Astronomy,[18] Linton’s From Eudoxus to Einstein,[19] and Crowe’s Theories of the World.[20]

By the time you’ve worked your way through that lot you can start your own history of astronomy blog – happy reading!

[1] Ptolemy’s Almagest, Translated and Annotated by G.J. Toomer, with a foreword by Owen Gingerich, Princeton University Press, Princeton, New Jersey, 1998

[2] Olaf Pedersen, A Survey of the Almagest, Odense University Press, 1974.

[3] Liba Taub, Ptolemy’s Universe: The Natural Philosophical and Ethical Foundations of Ptolemy’s Astronomy, Open Court Publishing Company, Chicago, 1993

[4] Nicolas Copernicus Complete Works, On the Revolutions, translation and commentary by Edward Rosen, The Johns Hopkins University Press, Baltimore & London, 1978

[5] Swerdlow, N.M., O. Neugebauer: Mathematical astronomy in Copernicus’ De revolutionibus, Springer, New York, 1984

[6] Johannes Kepler, Mysterium CosmographicumThe Secret of the Universe, (Facsimile of 2nd ed., 1621, and English translation on facing pages) translated by A.M. Duncan, introduction and commentary by E.J. Aiton, preface by I: Bernard Cohen, Abaris Books, New York, 1981

[7] Johannes Kepler, Astronomia Nova (New Revised Edition), translated by William H. Donahue, Green Lion Press, Santa Fe, 2015

[8] James Voelkel, The Composition of Kepler’s Astronomia nova, Princeton University Press, Princeton, 2001

[9] Selections from Kepler’s Astronomia Nova, A science Classics Module for Humanities Studies, Selected, translated, and annotated by William H. Donahue, Green Cat Books, Santa Fe, 2008

[10] The Harmony of the World by Johannes Kepler, Translated into English with an Introduction and Notes by E.J. Aiton, A.M. Duncan & J.V. Field, Memoirs of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge, Volume 209, 1997

[11] Johannes Kepler, Epitome of Copernican Astronomy & Harmonies of the World, Translated by Charles Glenn Wallis, Prometheus Books, New York, 1995

[12] Galileo Galilei, Sidereus Nuncius or The Sidereal Messenger, Translated with introduction, conclusion, and notes by Albert Van Helden, University of Chicago Press, Chicago and London, 1989

[13] Galileo, Dialogue Concerning the Two Chief World Systems, Translated with revised notes by Stillman Drake, University of California Press, Berkley, Los Angeles, London, 1967

[14] Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, A new translation by I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz, Preceded by A Guide to Newton’s Principia by I. Bernard Cohen.

[15] Subramanyan Chandrasekhar, Newton’s Principia for the Common Reader, Clarendon Press, Oxford, 1995

[16] The Cambridge Companion to Newton, 2nd edition, ed. Robert Iliffe and George E. Smith, Cambridge University Press, Cambridge, 2016

[17] John North, Cosmos: An Illustrated History of Astronomy and Cosmology, University of Chicago Press, Chicago & London, 2008

[18] The Cambridge Illustrated History of Astronomy, ed. Michael Hoskin, Cambridge University Press, Cambridge, 1997

[19] C.M. Linton, From Eudoxus to Einstein: A History of Mathematical Astronomy, CUP, Cambridge etc., 2004

[20] Michael J. Crowe, Theories of the World: From Antiquity to the Copernican Revolution, Dover Publication Ltd., New York, 2001



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Getting Hooke wrong!

I actually have a finished blog post lined up for this week but somebody on twitter linked to a website called ThoughtCo. and the post, Robert Hooke Biography (1635 – 1703), which I skim read. A couple of the statements about microscopes and telescopes brought out my inner Hist_Sci HulkTM and I couldn’t resist, so you are getting a bonus blog post to make up for the lack of one last week.

ThoughtCo. tells us that:

 He invented the compound microscope and Gregorian compound telescope.


Hooke’s microscope, from an engraving in Micrographia. Source: Wikimedia Commons

Now, long time readers of this blog will perhaps remember that I wrote a post celebrating Hooke’s Micrographia in which I outlined the history of the microscope in the seventeenth century. The very first microscopes that appeared in the second decade of the seventeenth century, more than twenty years before Hooke was born, were compound microscope and we don’t actually know who should be credited for its invention. I suggested that several people, like Galileo, accidentally looked through a Dutch or Galilean telescope the wrong way, noticed the diminution and went on from there to develop purpose built microscopes. We do know that the Keplerian microscope, two convex lenses, was invented by Cornelis Drebbel in 1621.

As far as the Gregorian (compound) telescope (I’m not sure what the word compound is doing in there) the name of the inventor might just possibly be deducible from the name of the telescope. It was of course not Hooke but James Gregory who first thought out this piece of optical hardware. Hooke apparently earns the honours for having constructed the first working model of a Gregorian telescope, something that its inventor had failed to do.


James Gregory artist unknown Source: Wikimedia Commons

Further on in the article ThoughtCo. informs us that:

In 1665, Hooke used his primitive compound microscope to examine the structure in a slice of cork. He was able to see the honeycomb structure of cell walls from the plant matter, which was the only remaining tissue since the cells were dead. He coined the word “cell” to describe the tiny compartments he saw. This was a significant discovery because prior to this, no one knew organisms consisted of cells. Hooke’s microscope offered a magnification of about 50x. The compound microscope opened up a whole new world to scientists and marked the beginning of the study of cell biology.

Hooke did indeed apply the word cell to the walled in empty spaces that he observed in a slice of cork because as he said they reminded him of monk’s cells in a monastery. To claim that he or anybody else deduced from this that organisms consisted of cells is a step too far. All Hooke showed was that a slice of cork has empty cell like structures; the study of cell biology didn’t take off until the nineteenth century long after Hooke gave the organic cell its name.


Schem. XI – Of the Schematisme or Texture of Cork, and of the Cells and Pores of some other such frothy Bodies. Source: National Library of Wales via Wikimedia Commons

The same paragraph continues as follows:

 In 1670, Anton van Leeuwenhoek, a Dutch biologist, first examined living cells using a compound microscope adapted from Hooke’s design.

Anton van Leeuwenhoek was a draper and amateur microscopist, calling him a biologist is not only incorrect but also misleading.


Portrait of Anthonie van Leeuwenhoek (1632-1723) by Jan Verkolje Source: Wikimedia Commons

Whatever else van Leeuwenhoek examined it is also incorrect and again somewhat misleading to say that he examined living cells. His main discoveries were bacteria and spermatozoa. The real hammer here is in the claims about van Leeuwenhoek’s choice of optical instrument. He definitely did not use a “compound microscope adapted from Hooke’s design.” Van Leeuwenhoek is famous for the fact that he made all of his ground-breaking discoveries uses high powered single lens microscopes that he designed and constructed himself. In fact when the Royal Society began to publish his discoveries in their Philosophical Transactions, it was Hooke who constructed single lens microscopes based on van Leeuwenhoek’s design.


A replica of a microscope by van Leeuwenhoek Source: Wikimedia Commons

ThoughCo. Writes the following about itself:

ThoughtCo, a Dotdash brand, is an education website that launched in March of 2017. Dotdash is a trusted media company that has been in operation since 1997 and is part of the IAC family of websites.

We take pride in the content that we create for our readers and strive to make our articles trustworthy and reliable.

They obviously don’t strive very hard or very successfully.



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My #histSTM Internet family

I came late to computers, no teenage Commodores or Ataris for me, which is slightly ironic as I was well versed in the history of computing and computers long before I owned one. I first launched myself into the murky waters of the Internet about twelve years ago. It was not long before I discovered that there were people on the Internet, who shared my love and fascination for the history and philosophy of mathematics and science. Almost exactly nine years ago I then launched this blog, see the blogiversary post next week, and officially joined the #histSTM Internet community. Over the years I have tried to hold to writing at least one substantive blog post a week, as a matter of self-imposed writing discipline. This is with the background thought that if I skip a week then I’ll probably skip two and finally, because of lack of inertia, grind to a halt. Knowing that I have a couple of loyal and regular readers I imagine that some of them might even have expectations and not wishing to disappoint them, when I know for some reason that I can’t post in the coming week or weeks, I usually announce the fact.

This was the case last week, as at very short notice I was ordered back into hospital for a second operation. The response to that short announcement on Twitter and Facebook was both mind-blowing and humbling. Over the years I have become an integral part of the large Internet #histSTM community and that community rose up to the occasion with friendliness and warmth on an extremely high level. Their kind words and well-wishes sustained and supported me through the hours and days in my hospital bed and left me feeling good despite everything.

I can’t really express in words the gratitude that I feel towards all the historians, philosophers, curators, scientists and just plain good people, who sent me their positive thoughts and wishes at this low point in my life. I’ll just say from the bottom of my heart that you are all wonderful and I love every single one of you. Thank you!



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Taking some time off!


Just spent a very tiring and frustrating day undergoing test and filling in forms in order to be admitted to hospital tomorrow morning at 6:30am! This means there will no blog post this week and possible not next week either, we’ll have to see.

To fill in the time you could read Karl Galle’s excellent Copernicus guest post if you have already done so, or my guest post on Forbidden Histories on astronomy & astrology.

In the mean time I wish all my readers a good time and promise that I will be back in the not too distant future.


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Publish and Perish

As I announced yesterday I am playing away this week with a tasty post on astrology and astronomy on the excellent Forbidden Histories blog site. However the substitute bank here at The Renaissance Mathematicus is filled with the finest from the fine. This week stepping up to the plate is mega historian of Early Modern science and Renaissance Mathematicus friend, Karl Galle, brought to you all the way from the sunny streets of Cairo (we are truly international here).

 Some time ago I realised that although I specialise in the history of Renaissance astronomy, I have up till now written no substantive biographical post about Nicolaus Copernicus. Now potted biography posts are one of my specialities and I have written them about almost everyone of significance in the Renaissance astronomy crew but not of the good old Nicky. Whilst I was pondering how I could best correct this omission, It occurred to me that my #histsci buddy Karl is currently engaged in researching and writing a modern biography of the Cannon of Frombork Cathedral. Knowing no shame, I immediately contacted Karl and suggested that he could take on the task in hand as a Renaissance Mathematicus guest blogger. With enough arm-twisting and the promise of an undisclosed number of free beers next time he is in Nürnberg he graciously agreed to write an authoritative blog post on Warmia’s most famous son. Read and enjoy!


 On May 24, 1543, Nicholas Copernicus achieved every writer’s great dream of finally holding in his hands a published copy of the book he had worked on for most of his life. Having done so, he then died that same day. Sadly, he was probably unconscious when the book was placed in his hands, as we learn from the only surviving account of his death in a letter from his best friend, Bishop Tiedemann Giese, to his only student, Georg Rheticus.

I’d like to thank Thony very much for inviting me to commemorate this year’s 475th anniversary of Copernicus’s death and the publication of his book De revolutionibus orbium coelestium (“On the Revolutions of the Heavenly Spheres”) with a guest post. While I won’t attempt to match Thony’s polymathic virtuosity on all things Mathematicus related, I thought I would try and channel a bit of the blog’s myth-busting spirit by using this opportunity to look at a few of the stories traditionally told in connection with Copernicus’s remarkable idea that the Earth, formerly assumed to be resting naturally at the center of the cosmos, is in fact both rotating on its axis and moving at high speed around the sun.


Figure 1: Copernicus’s manuscript diagram of the cosmos, showing the Sun at the center and the Earth and Moon in sphere #5, from the digitized autograph copy at the Jagiellonian University Library in Cracow.

Myth #1: Debates over the Copernican theory are central to understanding Copernicus’s own life and work.

It should be an obvious point given the timing of Copernicus’s death, but virtually the entire debate over the heliocentric theory took place posthumously and without further participation by the theory’s original author. The most famous episodes occurred more than half a century later. While many writers did discuss Copernicus’s mathematical models – usually with high praise – in the early years after De revolutionibus appeared, the next really detailed defense of the heliocentric theory didn’t appear in print until 1596 with Johannes Kepler’s Mysterium Cosmographicum. The Catholic Church only declared heliocentrism theologically heretical and suspended Copernicus’s book “until corrected” in 1616 (with a list of corrections approved in 1620), and Galileo’s trial for advocating the heliocentric theory took place in 1633.

All of these and many other less well-remembered episodes are fantastically interesting in their own right. For understanding the so-called Copernican revolution, however, they are the historiographical equivalent of studying the Bolshevik movement for insight into the composition of the Communist Manifesto. They provide useful lessons about the transformation and application of radical new ideas but are often profoundly misleading in regard to those ideas’ original contexts.

Kepler’s education and worldview were shaped by Protestant university reforms that had barely begun when Copernicus died, and Galileo’s trial took place under Counter-Reformation pressures dramatically different from the political and theological environment of 1543. This is before one even discusses the invention of the telescope, the huge observational programs of Tycho Brahe and others, and the extraordinary proliferation of mathematical texts and practitioners in the century after De revolutionibus, all of which were profoundly new developments from the time in which Copernicus lived and worked (1473-1543).


Figure 2: Statue of at the base of Frombork’s cathedral hill, where Copernicus lived for most of his professional life (author photograph).

Myth #2: We don’t know very much about Copernicus’s life.

One reason why historians have often spent more time examining posthumous debates over the heliocentric theory rather than Copernicus’s own era is the assumption that we don’t have much information about his life, and this is at least a moderately defensible point. Kepler, Galileo, and other canonical giants like Darwin all enjoyed the good fortune of having not just voluminous correspondence networks but great fame while they were still alive. When they died, the bulk of their manuscripts were gathered and preserved well enough to eventually become happy hunting grounds for generations of historians. By contrast, Copernicus’s posthumous renown arrived much later and after a good share of his books and personal papers had likely been dispersed. The Giese-Rheticus letter providing the date of Copernicus’s death was one of a few surviving manuscripts that were found and published by the Cracow professor Jan Brożek after he made a pilgrimage to Warmia in 1618 in search of information about Copernicus.

Nevertheless, when people say we know little about Copernicus’s life, what they really mean is we have few documents pertaining to his life as an astronomer, and therein lies one of the key differences between Copernicus and his successors. Brahe, Brożek, Galileo, Kepler, and other notable contemporaries like Christoph Clavius and Michael Maestlin occupied a diverse range of positions across universities, courts, and church institutions. What they all had in common, however, was an ability to earn a living working on subjects related to astronomy or mathematics for most of their professional careers and to have a large and technically accomplished peer group while they did so.

By contrast, as far as we know Copernicus never earned a single schilling specifically for his work in astronomy. His professional rank was as a canon serving the prince-bishopric of Warmia, and the largest portion of his surviving papers thus derive from administrative work for the church or correspondence with regional political figures. Surveying these materials, one gets the impression of a skilled but unpretentious professional who was frequently relied on to handle some of the chapter’s most challenging tasks. If you needed a contentious land dispute settled, a sensitive diplomatic communiqué drafted, or a castle’s defenses organized during a siege by invading Teutonic Knights, Copernicus was the guy who would get it done and probably not ask for a promotion when it was all over. While these documents therefore tell us almost nothing about his astronomy, they do hint at a rather rich and interesting life.


Figure 3: Remains of the castle at Olsztyn, where Copernicus organized the defenses during an invasion by the Teutonic Knights (author photograph).

Myth #3: We should still think of Copernicus as a professional astronomer.

Astronomy was unquestionably Copernicus’s main intellectual passion and the subject to which he devoted the bulk of his private study. Even when he was called on for scholarly rather than administrative tasks, however, it was probably not what his colleagues most valued. The oldest manuscript evidence of interest in his mathematical pursuits is a set of letters in 1510 from a spy who was attempting to steal one of Copernicus’s maps on behalf of the Teutonic Knights during a period of tense territorial negotiations in the years before their armies invaded and overran most of Warmia. (The fact that this spy later became Copernicus’s boss and effectively a head of state despite being a paid agent of a hostile foreign power is only one of the remarkable stories that virtually every Copernican biographer ignores simply because it doesn’t relate to astronomy.) This particular map doesn’t survive, but other non-espionage correspondence confirms that Copernicus’s map-making abilities were called on throughout his life for political and also economic purposes like delineating fishing rights.

Sometime around 1514, Copernicus wrote a now lost commentary on calendar reform, and in 1517 he finished a first draft of a treatise on currency reform that was later revised and submitted to Polish and Prussian authorities in late 1525 or early 1526. Throughout his career in Warmia he was also in demand as a personal physician to successive bishops and other patients. The point is not that any of these other responsibilities or pursuits eclipsed (so to speak) his interest in astronomy, but that if we are going to speak in anachronistic terms, it makes at least as much sense to think of Copernicus professionally not as an astronomer but as a government functionary who occasionally wore the hat of technical specialist or senior policy advisor, all while pursuing a longstanding intellectual hobby that was only indirectly relevant to his career.

Significantly, this is very much what most of his peer group looked like as well. To list only a few examples, a rare surviving letter that mentions Copernicus’s astronomical work is one from 1535 that accompanied a set of his planetary tables. The recipient of the tables, Sigismund von Herberstein, was a life-long Habsburg diplomat who published a lengthy geography and ethnography of Russia near the end of his life based on his travels to that country. The sender of the tables, Bernard Wapowski, is best remembered as a cartographer and therefore closer to Copernicus in having mathematical interests, but he served the Polish crown for most of his life and left behind a long unpublished manuscript on Polish history. Johannes Albrecht Widmanstetter, who discussed Copernicus’s theory in the Vatican gardens in 1533, spent much of his career as a papal secretary before publishing his magnum opus, a dictionary of the Syriac language, shortly before he died.

One could multiply these cases many times to illustrate how common it was for late medieval figures to produce major scholarly works while following varied careers as public officials or church leaders rather than solely university-based teachers. Even Albert de Brudzewo – frequently cited as a likely influence on Copernicus’s early astronomical studies – left his teaching post at Cracow University in order to take up a position with the Jagiellonian Grand Duke Alexander in Vilnius. The fact that Widmanstetter was invited by Pope Clement VII to explain Copernicus’s ideas, and then rewarded with a costly manuscript for doing so, also points toward one of the most persistent misperceptions about how the heliocentric theory was received during its earliest years.

Myth #4: Church leaders were unanimously horrified and opposed to Copernicus’s theory as soon as it appeared.

The 1543 letter between Rheticus and Bishop Giese also includes details about the only actual controversy that publication of Copernicus’s book sparked immediately, namely that both Giese and Rheticus were furious about an anonymous preface Andreas Osiander had attached to the work. The background behind this preface and the complaint that Giese made to the Nuremberg city council are a fascinating story of their own, but let’s pause for a moment just to consider the nature of the participants. You have on one side a Catholic bishop allying himself with a former professor from Wittenberg university (literally the birthplace of the Protestant Reformation) in a conflict with the copy editor of De revolutionibus (Osiander), a firebrand Protestant minister who had previously been reprimanded by Nuremberg’s council after publishing a pamphlet declaring the pope to be the anti-Christ. All of this was over a book that was dedicated to the pope, written by a Catholic church official, only came into existence because Wittenberg allowed one of their professors to take extended faculty leave to help bring it out, and was solicited and issued by one of the era’s greatest printers, a man renowned for publishing not just scientific but Protestant theological and musical works. One can argue all you like about the nature of Osiander’s preface, but short of throwing in a laudatory poem by Ulrich Zwingli or a posthumous endorsement by Jan Huss, it’s hard to imagine how Copernicus’s book could have featured a broader array of church figures who might have disagreed over certain aspects of the book’s merits but had very little problem supporting its appearance.

This is not to say there weren’t a few early rumblings of concern. Martin Luther is reputed to have made disparaging verbal remarks before De revolutionibus appeared about how certain people wanted to seem clever and turn astronomy upside down. However, this only counts as sharp criticism in Luther’s world if you’ve never read any of his published texts on Jews, Turks, papists, or pretty much anyone else he considered truly theologically dangerous. In Italy during the late 1540s, at least a couple of Dominican writers previewed some of the Catholic church’s later objections to Copernicus on the grounds of illogical physics and contradictions with scriptural passages, but these criticisms seem to have gained little traction at the time. As for Copernicus, other correspondence suggests that when he wrote of his fears that some people might mock his ideas, he was referencing not simply church authorities so much as “Peripatetics,” or Aristotelian philosophers whom he correctly feared might point out among other things that he hadn’t really answered all questions that would arise from the physics of a moving Earth.

The challenge of rewriting terrestrial physics to account for complex motions and then connect with the movements of the heavens would in fact occupy natural philosophers for the next century and a half. During that same period, much of Europe would tear itself apart in increasingly apocalyptic wars inflamed by religious tensions, and the potential grounds for heresy would expand to occupy philosophical domains including astronomy that had only occasionally been considered dangerous territory in centuries past. The condemnation of Galileo and the censorship of De revolutionibus were two consequences of this expanded politicization of knowledge, but this is not something that would have necessarily been predicted when Copernicus’s book first appeared in 1543. Ironically Nuremberg’s council seems to have been entirely unconcerned with the subject matter of heliocentrism, but they did investigate and censor another book that came out that same year because the Vatican’s Copernicus expert Widmanstetter wanted to publish a selection of Latin excerpts from the Qur’an. (See my comment above about episodes that are entirely ignored by Copernican biographers because anything that doesn’t explicitly mention astronomy is considered too boring to write about.)


Figure 4: Modern memorial to Copernicus in Frombork cathedral; his coffin is below the glass tile at the base (author photograph).

The afterlife of Copernicus

Copernicus died as a liked and well-respected figure to his colleagues, but not yet an unusually famous or controversial thinker among other scholars. As a new generation of astronomers worked through the lengthy text of De revolutionibus and began trying to fit its models to more accurate observations of the heavens, however, they also increasingly acclaimed Copernicus, hailing him repeatedly as “another Ptolemy” in recognition of his great mathematical abilities despite the fact that the heliocentric theory threatened to overturn Ptolemy’s old geocentric cosmos. A memorial plaque was belatedly erected in 1581 at Frombork cathedral, and Brożek copied out its text during his visit there in 1618. The exact location of Copernicus’s burial site was nevertheless forgotten until recent years when a research team located a set of remains and ingeniously matched them to Copernicus through genetic comparison with hairs found inside one of Copernicus’s former books now at Uppsala University. (Lesson to librarians – protect your rare books, but don’t clean them too well!) He was reburied beneath a tasteful modern monument in 2010, and I had the good fortune of visiting the site last fall.

One might justifiably ask why I’ve spent so much time harping about Copernicus’s era and social context rather than going into more detail about his astronomy and mathematics. There are indeed numerous interesting things to say on the latter subject, from the ongoing debates over exactly how Copernicus arrived at the heliocentric theory to the very tangible advantages his theory offered even during an era when astronomical observations were not yet precise enough to prove the empirical advantages of his individual planetary models over comparable models derived from Ptolemy.

As much as I enjoy the details of Copernicus’s astronomy, though, I think there’s a point at which exclusively focusing on the mathematics of De revolutionibus risks becoming the late medieval equivalent of writing a micro-history of free-return trajectories as if it’s the only subject worth talking about in regard to the US-Soviet space race. To say there are other topics worth discussing is not an either-or declaration of how to do history but a simple recognition that we need to understand more realistically how new knowledge takes shape and what transformations happen when it’s applied. Especially now, it’s worth resisting the regular incorporation of figures like Copernicus and Galileo into broader societal myths about how progress only happens when a tiny number of under-appreciated geniuses, working in isolation and free of interference from Big Government, acquire their wisdom through flashes of insight that spring fully formed like Athena from the head of Zeus, after which it only remains for the rest of us to appreciate their greatness rather than numbering among the benighted peasants and medieval reactionaries if we ask too many questions. If there is a lesson to be culled from the life of Copernicus and the period that followed, perhaps it is instead that understanding the cosmos is difficult, but sometimes even a few mild-mannered professionals who work well with their colleagues might get there in the end.

Karl Galle (@GalleKarl) is working on a new biography of Nicholas Copernicus that he hopes will be completed in less time than it took to write De revolutionibus. You can browse more photos from his Copernicus-related travels here.



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The German verb fremdgehen means to be unfaithful or to have a bit on the side in English. Regular visitors to this blog will know that the Renaissance Mathematicus is from time to time unfaithful and posts his scribblings in other places on the Internet. This has happened once again and I am actually pleased to announce that I have a post up on Andreas Sommer’s excellent blog Forbidden Histories. Andreas specialises in exposing the non-scientific underbelly of the history of science. Andreas asked me if I could write something on the history of astrology and I put together an overview of the common histories of astronomy and astrology: Astronomy and Astrology: The Siamese Twins of the Evolution of Science, which you can go over and read as of now. There is probably nothing new for those, who have read all of my previous astrology posts but I hope that what I have written is a short and informative introduction to the topic.


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400 Years of The Third Law–An overlooked and neglected revolution in astronomy

Four hundred years ago today Johannes Kepler rediscovered his most important contribution to the evolution of astronomy, his third law of planetary motion.


Portrait of Johannes Kepler 1610 by unknown artist. Source: Wikimedia Commons

He had originally discovered it two months earlier on 8 March but due to a calculation error rejected it. On 15 May he found it again and this time recognised that it was correct. He immediately added it to his Harmonices Mundi:


For when the true distances between the spheres were found, through the observations of Brahe, by continuous toil for a very long time, at last, at last, the genuine proportion of the periodic times to the proportion of the spheres –

Only at long last did she look back at him as she lay motionless,

But she look back and after a long time she came [Vergil, Eclogue I, 27 and 29.]

And if you want the exact moment in time, it was conceived mentally on the 8th of March in this year one thousand six hundred and eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labor of seventeen years on the observations of Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely exact that proportion between the periodic times of any two planets is precisely the sesquialterate[1] proportion of their mean distances, that is of the actual spheres, though with this in mind, that the arithmetic mean between the two diameters of the elliptical orbit is a little less than the longer diameter. Thus if one takes one third of the proportion from the period, for example, of the Earth, which is one year, and the same from the period of Saturn, thirty years, that is, the cube roots, and one double that proportion, by squaring the roots, he has in the resulting numbers the exactly correct proportion of the mean distances of the Earth and Saturn from the Sun.[2]

writing a few days later:

Now, because eighteen months ago the first dawn, three months ago the broad daylight, but a very few days ago the full sun of a most remarkable spectacle has risen, nothing holds me back. Indeed, I give myself up to a sacred frenzy.

He finished the book on 27 May although the printing would take a year.

In modern terminology:


The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit: i.e. for two planets with P = orbital period and R = semi-major axis P12/P22=R13/R23

Kepler’s third law is probably the most important discovery on the way to the establishment of a heliocentric astronomy but its importance was initially overlooked and its implications were somehow neglected until Isaac Newton displayed its significance in his Principia Mathematica, published in 1687 sixty-eight years after the third law first appeared in print.

What the third law gives us is a direct mathematical relationship between the size of the orbits of the planets and their duration, which only works in a heliocentric system. In fact as we will see later it’s actually equivalent to the law of gravity. There is nothing comparable for either a full geocentric system or for a geo-heliocentric Tychonic or semi-Tychonic system. It should have hit the early seventeenth-century astronomical community like a bomb but it didn’t, which raises the question why it didn’t.

The main answer lies in Kepler’s own writings. Although he viewed its discovery as the crowning glory of his work on the Harmonices Mundi Kepler didn’t give it any prominence in that work. The Harmonices Mundi is a vast sprawling book explicating Kepler’s version of the Pythagorean theory of the harmony of the spheres in five books. After four introductory books covering plane geometry, music theory and astrology Kepler gets down to harmonic planetary theory in the fifth and final book. Book V, 109 pages in the English translations, contains lots of musical relationships between various aspects of the planetary orbits, with the third law presented as just one amongst the many with no particular emphasis. The third law was buried in what is now regarded as a load of unscientific dross. Or as Carola Baumgardt puts it, somewhat more positively,  in her Johannes Kepler life and letters (Philosophical Library, 1951, p. 124):

Kepler’s aspirations, however, go even much higher than those of modern scientific astronomy. As he tried to do in his “Mysterium Cosmographicum” he coupled in his “Harmonice Mundi” the precise mathematical results of his investigations with an enormous wealth of metaphysical, poetical, religious and even historical speculations. 

Although most of Kepler’s contemporaries would have viewed his theories with more sympathy than his modern critics the chances of anybody recognising the significance of the harmony law for heliocentric astronomical theory were fairly minimal.

The third law reappeared in 1620 in the second part of Kepler’s Epitome Astronomiae Copernicanae, a textbook of heliocentric astronomy written in the form of a question and answer dialogue between a student and a teacher.

How is the ratio of the periodic times, which you have assigned to the mobile bodies, related to the aforesaid ratio of the spheres wherein, those bodies are borne?

The ration of the times is not equal to the ratio of the spheres, but greater than it, and in the primary planets exactly the ratio of the 3/2th powers. That is to say, if you take the cube roots of the 30 years of Saturn and the 12 years of Jupiter and square them, the true ration of the spheres of Saturn and Jupiter will exist in those squares. This is the case even if you compare spheres that are not next to each other. For example, Saturn takes 30 years; the Earth takes one year. The cube root of 30 is approximately 3.11. But the cube root of 1 is 1. The squares of these roots are 9.672 and 1. Therefore the sphere of Saturn is to the sphere of the Earth as 9.672 is to 1,000. And a more accurate number will be produced, if you take the times more accurately.[3]

Here the third law is not buried in a heap of irrelevance but it is not emphasised in the way it should be. If Kepler had presented the third law as a table of the values of the orbit radiuses and the orbital times and their mathematical relationship, as below[4], or as a graph maybe people would have recognised its significance. However he never did and so it was a long time before the full impact of the third law was felt in astronomical community.

third law001

The real revelation of the significance of the third law came first with Newton’s Principia Mathematica. By the time Newton wrote his great work the empirical truth of Kepler’s third law had been accepted and Newton uses this to establish the empirical truth of the law of gravity.

In Book I of Principia, the mathematics and physics section, Newton first shows, in Proposition 11[5], that for a body revolving on an ellipse the law of the centripetal force tending towards a focus of the ellipse is inversely as the square of the distance: i.e. the law of gravity but Newton is not calling it that at this point. In Proposition 14[6] he then shows that, If several bodies revolve about a common center and the centripetal force is inversely as the square of the distance of places from the center, I say that the principal latera recta of the orbits are as the squares of the areas which bodies describe in the same time by radii drawn to the center. And Proposition 15[7]: Under the same supposition as in prop. 14, I say the square of the periodic times in ellipses are as the cubes of the major axes. Thus Newton shows that his law of gravity and Kepler’s third law are equivalent, although in this whole section where he deals mathematically with Kepler’s three laws of planetary motion he never once mentions Kepler by name.

Having established the equivalence, in Book III of The Principia: The System of the World Newton now uses the empirical proof of Kepler’s third law to establish the empirical truth of the law of gravity[8]. Phenomena 1: The circumjovial planets, by radii drawn to the center of Jupiter, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their distances from that center. Phenomena 2: The circumsaturnian planets, by radii drawn to the center of Saturn, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their distances from that center. Phenomena 3: The orbits of the five primary planets—Mercury, Venus, Mars, Jupiter, and Saturn—encircle the sun. Phenomena 4: The periodic times of the five primary planets and of either the sun about the earth or the earth about the sun—the fixed stars being at rest—are as the 3/2 powers of their mean distances from the sun. “This proportion, which was found by Kepler, is accepted by everyone.”

Proposition 1: The forces by which the circumjovial planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the center of Jupiter and are inversely as the squares of the distances of their places from that center. “The same is to be understood for the planets that are Saturn’s companions.” As proof he references the respective phenomena from Book I. Proposition 2: The forces by which the primary planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the sun and are inversely as the squares of the distances of their places from its center. As proof he references the respective phenomenon from Book I:

One of the ironies of the history of astronomy is that the general acceptance of a heliocentric system by the time Newton wrote his Principia was largely as a consequence of Kepler’s Tabulae Rudolphinae the accuracy of which convinced people of the correctness of Kepler’s heliocentric system and not the much more important third taw of planetary motion.

[1] Sesquialterate means one and a half times or 3/2

[2] The Harmony of the World by Johannes Kepler, Translated into English with an Introduction and Notes by E.J. Aiton, A.M. Duncan & J.V. Field, Memoirs of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge, Volume 209, 1997 pp. 411-412

[3] Johannes Kepler, Epitome of Copernican Astronomy & Harmonies of the World, Translated by Charles Glenn Wallis, Prometheus Books, New York, 1995 p. 48

[4] Table taken from C.M. Linton, From Eudoxus to Einstein: A History of Mathematical Astronomy, CUP, Cambridge etc., 2004 p. 198

[5] Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, A New Translation by I: Bernard Cohen and Anne Whitman assisted by Julia Budenz, Preceded by A Guide to Newton’s Principia, by I. Bernard Cohen, University of California Press, Berkley, Los Angeles, London, 1999 p. 462

[6] Newton, Principia, 1999 p. 467

[7] Newton, Principia, 1999 p. 468

[8] Newton, Principia, 1999 pp. 797–802


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