I have become somewhat infamous for writing #histSTM blog posts that are a predominately negative take on the scientific achievements of Galileo Galilei. In fact I think I probably made my breakthrough as a #histsci blogger with my notorious Extracting the Stopper post, deflating Galileo’s popular reputation. I actually got commissioned to write a toned down version of that post for AEON several years later. In my opinion Galileo was an important figure in the evolution of science during the early seventeenth century but his reputation has been blown up out of all proportion, well beyond his actual contributions. To make a simple comparison, in the same period of time the contributions of Johannes Kepler were immensely greater and more significant than those made by Galileo but whereas Galileo is regarded as one of the giants of modern science and is probably one of the three most well known historical practitioners of the mathematical sciences, alongside Newton and Einstein, Kepler is at best an also ran, whose popular image is not even a fraction of that of Galileo’s. This of course raises the question, why? What does/did Galileo have that Kepler didn’t? I think the answer lies in Galileo’s undeniable talents as a writer.

Galileo was a master stylist, a brilliant polemicist and science communicator, whose major works are still a stimulating pleasure to read. If you ask people about Galileo they will more often than not quote one of his well-known turns of phrase rather than his scientific achievements. The two books trope with its ‘mathematics is the language of nature’, which in the original actually reads: Philosophy is written in this grand book, which stands continually open before our eyes (I say the ‘Universe’), but can not be understood without first learning to comprehend the language and know the characters as it is written. It is written in mathematical language, and its characters are triangles, circles and other geometric figures, without which it is impossible to humanly understand a word; without these one is wandering in a dark labyrinth. Or the much-loved, the Bible shows the way to go to heaven, not the way the heavens go, which again in the original reads: The intention of the Holy Ghost is to teach us how one goes to heaven, not how heaven goes. It is a trivial truth that Galileo had a way with words.

This cannot be said of Johannes Kepler. I shall probably bring the wrath of a horde of Kepler scholars on my head for saying this but even in translation, Johannes Kepler is anything but an easy read. Galileo even commented on this. When confronted with Kepler’s Dioptrice (1611), one of the most important books on optics ever written, Galileo complained that it was turgid and unreadable. Having ploughed my way through it in German translation, I sympathise with Galileo’s negative judgement. However, in his rejection Galileo failed to realise just how scientifically important the Dioptrice actually was. Nobody in their right mind would describe Kepler as a master stylist or a brilliant polemicist.

I think this contrast in literary abilities goes a long way to explaining the very different popular conceptions of the two men. People read Galileo’s major works or selections from them and are stimulated and impressed by his literary mastery, whereas Kepler’s major works are not even presented, as something to be read by anyone, who is not a historian of science. One just gets his three laws of planetary motion served up in modern guise, as a horribly mathematical side product of heliocentricity.

Of course, a serious factor in their respective notorieties is Galileo’s infamous trial by the Roman Inquisition. This was used to style him as a martyr for science, a process that only really began at the end of the eighteenth and beginning of the nineteenth centuries. Kepler’s life, which in many ways was far more spectacular and far more tragic than Galileo’s doesn’t have such a singular defining moment in it.

Returning to the literary theme I think that what has happened is that non-scientists and non-historians of science have read Galileo and impressed by his literary abilities, his skill at turning a phrase, his adroit, and oft deceitful, presentation of pro and contra arguments often fail to notice that they are being sold a pup. As I tried to make clear in the last episode of my continuing ‘the emergence of modern astronomy’ series although Galileo’s Dialogo has an awesome reputation in Early Modern history, its scientific value is, to put it mildly, negligible. To say this appears to most people as some form of sacrilege, “but the Dialogo is an important defence of science against the forces of religious ignorance” or some such they would splutter. But in reality it isn’t, as I hope I made clear the work contributed nothing new to the on going debate and all that Galileo succeeded in doing was getting up the Pope’s nose.

The same can be said of Il Saggiatore, another highly praised work of literature. As I commented in another post the, oft quoted line on mathematics, which had led to Galileo being praised as the man, who, apparently single handed, mathematized the physical science was actually, when he wrote it, old hat and others had been writing the book of nature in the language of mathematics for at least one hundred years before Galileo put pen to paper but none of them had taken the time to express what they were doing poetically. In fact it took historians of science a long time to correct this mistaken perception, as they also tended to suffer from a serious dose of Galileo adoration. The core of Il Saggiatore is as I have explained elsewhere is total rubbish, as Galileo is arguing against the scientific knowledge of his time with very spurious assertions merely so that he doesn’t have to acknowledge that Grassi is right and he is wrong. An admission that very few Galileo scholars are prepared to make in public, it might tarnish his reputation.

Interestingly one work that deserves its historical reputation Galileo’s Sidereus Nuncius, also suffers from serious scientific deficits that tend to get overlooked. Written and published in haste to avoid getting beaten to the punch by a potential, unknown rival the book actually reads more like an extended press release that a work of science. It might well be that Galileo intended to write a more scientific evaluation of his telescopic observations and discoveries once he had established his priority but somehow, having become something of a scientific superstar overnight, he never quite got round to it. This is once again a failing that most readers tend to overlook, over awed by the very impressive literary presentation.

Much of Galileo’s written work is actually more appearance than substance, or as the Germans say Mehr Schein als Sein, but ironically, there is one major work of Galileo’s that is both literarily brilliant and scientifically solid but which tends to get mostly overlooked, his Discorsi. The experiments on which part of it is based get described by the book itself remains for most people largely unknown. I shall be taking a closer look at it in a later post.

One of the central problems in the transition from the traditional geocentric astronomy/cosmology to a heliocentric one was that the system that the Early Modern astronomers inherited from their medieval predecessors was not just an uneasy amalgam of Aristotelian cosmology and Ptolemaic astronomy but it also included Aristotle’s (384–322 BCE) theories of terrestrial and celestial motion all tied together in a complete package. Aristotle’s theory of motion was part of his more general theory of change and differentiated between natural motion and unnatural or violent motion.

The celestial realm in Aristotle’s cosmology was immutable, unchanging, and the only form of motion was natural motion that consisted of uniform, circular motion; a theory that he inherited from Plato (c. 425 – c.347 BCE), who in turn had adopted it from Empedocles (c. 494–c. 434 BCE).

His theory of terrestrial motion had both natural and unnatural motion. Natural motion was perpendicular to the Earth’s surface, i.e. when something falls to the ground. Aristotle explained this as a form of attraction, the falling object returning to its natural place. Aristotle also claimed that the elapsed time of a falling body was inversely proportional to its weight. That is, the heavier an object the faster it falls. All other forms of motion were unnatural. Aristotle believed that things only moved when something moved them, people pushing things, draught animals pulling things. As soon as the pushing or pulling ceased so did the motion.  This produced a major problem in Aristotle’s theory when it came to projectiles. According to his theory when a stone left the throwers hand or the arrow the bowstring they should automatically fall to the ground but of course they don’t. Aristotle explained this apparent contradiction away by saying that the projectile parted the air through which it travelled, which moved round behind the projectile and pushed it further. It didn’t need a philosopher to note the weakness of this more than somewhat ad hoc theory.

If one took away Aristotle’s cosmology and Ptolemaeus’ astronomy from the complete package then one also had to supply new theories of celestial and terrestrial motion to replace those of Aristotle. This constituted a large part of the development of the new physics that took place during the so-called scientific revolution. In what follows we will trace the development of a new theory, or better-said theories, of terrestrial motion that actually began in late antiquity and proceeded all the way up to Isaac Newton’s (1642–1726) masterpiece Principia Mathematica in 1687.

The first person to challenge Aristotle’s theories of terrestrial motion was John Philoponus (c. 490–c. 570 CE). He rejected Aristotle’s theory of projectile motion and introduced the theory of impetus to replace it. In the impetus theory the projector imparts impetus to the projected object, which is used up during its flight and when the impetus is exhausted the projectile falls to the ground. As we will see this theory was passed on down to the seventeenth century. Philoponus also rejected Aristotle’s quantitative theory of falling bodies by apparently carrying out the simple experiment usually attributed erroneously to Galileo, dropping two objects of different weights simultaneously from the same height:

but this [view of Aristotle] is completely erroneous, and our view may be completely corroborated by actual observation more effectively than by any sort of verbal argument. For if you let fall from the same height two weights, one many times heavier than the other you will see that the ratio of the times required for the motion does not depend [solely] on the weights, but that the difference in time is very small. …

Philoponus also removed Aristotle’s distinction between celestial and terrestrial motion in that he attributed impetus to the motion of the planets. However, it was mainly his terrestrial theory of impetus that was picked up by his successors.

In the Islamic Empire, Ibn Sina (c. 980–1037), known in Latin as Avicenne, and Abu’l-Barakāt Hibat Allah ibn Malkā al-Baghdādī (c. 1080–1164) modified the theory of impetus in the eleventh century.

Avicenne Portrait (1271) Source: Wikimedia Commons

Nur ad-Din al-Bitruji (died c. 1204) elaborated it at the end of the twelfth century. Like Philoponus, al-Bitruji thought that impetus played a role in the motion of the planets.

Nur ad-Din al-Bitruji Source

Brought into European thought during the scientific Renaissance of the twelfth and thirteenth centuries by the translators it was developed by Jean Buridan  (c. 1301–c. 1360), who gave it the name impetus in the fourteenth century:

When a mover sets a body in motion he implants into it a certain impetus, that is, a certain force enabling a body to move in the direction in which the mover starts it, be it upwards, downwards, sidewards, or in a circle. The implanted impetus increases in the same ratio as the velocity. It is because of this impetus that a stone moves on after the thrower has ceased moving it. But because of the resistance of the air (and also because of the gravity of the stone) which strives to move it in the opposite direction to the motion caused by the impetus, the latter will weaken all the time. Therefore the motion of the stone will be gradually slower, and finally the impetus is so diminished or destroyed that the gravity of the stone prevails and moves the stone towards its natural place. In my opinion one can accept this explanation because the other explanations prove to be false whereas all phenomena agree with this one.

Jean Buridan Source

The impetus theory was now a part of medieval Aristotelian natural philosophy, which as Edward Grant pointed out was not Aristotle’s natural philosophy.

In the sixteenth century the self taught Italian mathematician Niccolò Fontana (c. 1500–1557), better known by his nickname, Tartaglia, who is best known for his dispute with Cardanoover the general solution of the cubic equation.

Niccolò Fontana Tartaglia Source: Wikimedia Commons

published the first mathematical analysis of ballistics his, Nova scientia (1537).

His theory of projectile trajectories was wrong because he was still using the impetus theory.

However, he was the first to demonstrate that an angle of 45° for a canon gives the widest range.

His book was massively influential in the sixteenth century and it also influenced Galileo, who owned a heavily annotated copy of the book.

We have traced the path of the impetus theory from its inception by John Philoponus up to the second half of the sixteenth century. Unlike the impetus theory Philoponus’ criticism of Aristotle’s theory of falling bodies was not taken up directly by his successors. However, in the High Middle Ages Aristotelian scholars in Europe did begin to challenge and question exactly those theories and we shall be looking at that development in the next section.

One of the most well known popular stories told about Galileo is how he dropped balls from the Leaning Tower of Pisa to disprove the Aristotelian hypothesis that balls of different weights would fall at different speeds; the heavier ball falling faster. This event probably never happened but it is related as a prelude to his brilliant experiments with balls and inclined planes, which he carried out to determine empirically the correct laws of fall and which really did take place and for which he is justifiably renowned as an experimentalist. What is very rarely admitted is that the investigation of the laws of fall had had a several-hundred-year history before Galileo even considered the problem, a history of which Galileo was well aware.

We saw in the last episode that John Philoponus had actually criticised Aristotle’s concept of fall in the sixth century and had even carried out the ball drop experiment. However, unlike his impulse concept for projectile motion, which was taken up by Islamic scholars and passed on by them into the European Middle Ages, his correct criticism of Aristotle’s fall theory appears not to have been taken up by later thinkers.

As far as we know the first people, after Philoponus, to challenge Aristotle’s concept was the so-called Oxford Calculatores.

Merton College in 1865 Source: Wikimedia Commons

This was a group of fourteenth-century, Aristotelian scholars at Merton College Oxford, who set about quantifying various theory of nature. These men–Thomas Bradwardine (c. 1300–1349), William of Heytesbury (c. 1313–c. 1372), Richard Swineshead (fl. c. 1340–1354) and John Dumbleton (c. 1310–c. 1349)–studied mechanics distinguishing between kinematics and dynamics, emphasising the former and investigating instantaneous velocity. They were the first to formulate the mean speed theorem, an achievement usually accredited to Galileo. The mean speed theorem states that a uniformly accelerated body, starting from rest, travels the same distance as a body with uniform speed, whose speed in half the final velocity of the accelerated body. The theory lies at the heart of the laws of fall.

The work of the Oxford Calculatores was quickly diffused throughout Europe and Nicole Oresme (c. 1320–1382), one of the so-called Parisian physicists,

Portrait of Nicole Oresme: Miniature from Oresme’s Traité de l’espère, Bibliothèque Nationale, Paris, France, fonds français 565, fol. 1r. Source: Wikimedia Commons

and Giovanni di Casali (c. 1320–after 1374) both produced graphical representation of the theory.

Oresme’s geometric verification of the Oxford Calculators’ Merton Rule of uniform acceleration, or mean speed theorem. Source: Wikimedia Commons

We saw in the last episode how Tartaglia applied mathematics to the problem of projectile motion and now we turn to a man, who for a time was a student of Tartaglia, Giambattista Benedetti (1530–1590). Like others before him Bendetti turned his attention to Aristotle’s concept of fall and wrote and published in total three works on the subject that went a long way towards the theory that Galileo would eventually publish. In his Resolutio omnium Euclidis problematum (1553) and his Demonstratio proportionum motuum localium (1554) he argued that speed is dependent not on weight but specific gravity and that two objects of the same material but different weights would fall at the same speed.

Source: Wikimedia Commons

However, in a vacuum, objects of different material would fall at different speed. Benedetti brought an early version of the thought experiment, usually attributed to Galileo, of viewing two bodies falling separately or conjoined, in his case by a cord.  Galileo considered a roof tile falling complete and then broken into two.

In a second edition of the Demonstratio (1554) he addressed surface area and resistance of the medium through which the objects are falling. He repeated his theories in his Demonstratio proportionum motuum localium (1554), where he explains his theories with respect to the theory of impetus. We know that Galileo had read his Benedetti and his own initial theories on the topic, in his unpublished De Motu, were very similar.

In the newly established United Provinces (The Netherlands) Simon Stevin (1548–1620) carried out a lot of work applying mathematics to various areas of physics. However in our contexts more interesting were his experiments in 1586, where he actually dropped lead balls of different weights from the thirty-foot-high church tower in Delft and determined empirically that they fell at the same speed, arriving at the ground at the same time.

Source: Wikimedia Commons

Some people think that because Stevin only wrote and published in Dutch that his mathematical physics remained largely unknown. However, his complete works published initially in Dutch were translated into both French and Latin, the latter translation being carried out by Willebrord Snell. As a result his work was well known in France, the major centre for mathematical physics in the seventeenth century.

In Italy the Dominican priest Domingo de Soto (1494–1560) correctly stated that a body falls with a constant, uniform acceleration. In his Opus novum, De Proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum. Item de aliza regula (1570) Gerolamo Cardano (1501–1576) demonstrates that two balls of different sizes will fall from a great height in the same time. The humanist poet and historian, Benedetto Varchi (c. 1502–1565) in 1544 and Giuseppe Moletti (1531–1588), Galileo’s predecessor as professor of mathematics in Padua, in 1576 both reported that bodies of different weights fall at the same speed in contradiction to Aristotle, as did Jacopo Mazzoni (1548–1598), a philosopher at Padua and friend of Galileo, in 1597. However none of them explained how they arrived at their conclusions.

Of particular relevance to Galileo is the De motu gravium et levium of Girolamo Borro (1512–1592) one of Galileo’s teachers in Pisa. In a dispute with his colleague Francesco Buonamici (1533–1603), another Pisan professor, Borro carried out experiments in which he threw objects of different material and the same weights out of a high window to test Aristotle’s theory, which he describes in his book. Borro’s work is known to have had a strong influence on Galileo’s early work in this area.

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When Galileo started his own extensive investigations into the problem of fall in the late sixteenth century he was tapping into an extensive stream of previous work on the subject of which he was well aware and which to some extent had already done much of the heavy lifting. This raises the question as to what extent Galileo deserves his reputation as the man, who solved the problem of fall.

Galileo Portrait by Ottavio Leoni Source: Wikimedia Commons

We saw in the last episode that his much praised Dialogo, his magnum opus on the heliocentricity contra geocentricity debate, not only contributed nothing new of substance to that debate but because of his insistence on retaining the Platonic axioms, his total rejection of the work of both Tycho Brahe and Kepler and his rejection of the strong empirical evidence for the supralunar nature of comets he actually lagged far behind the current developments in that debate. The result was that the Dialogo could be regarded as superfluous to the astronomical system debate. Can the same be said of the contribution of the Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences) (1638) to the debate on motion? The categorical answer is no; the Discorsi is a very important contribution to that debate and Galileo deserves his reputation as a mathematical physicist that this book gave him.

Source: Wikimedia Commons

What did Galileo contribute to the debate that was new? It not so much that he contributed much new to the debate but that he gave the debate the solid empirical and mathematical foundation, which it had lacked up till this point. Dropping weights from heights to examine the laws of fall suffers from various problems. It is extremely difficult to ensure that the object are both released at the same time, it is equally difficult to determine if they actually hit the ground at the same time and the whole process is so fast, that given the possibilities available at the time, it was impossible to measure the time taken for the fall. All of the previous experiments of Stevin et al were at best approximations and not really empirical proofs in a strict scientific sense. Galileo supplied the necessary empirical certainty.

Galileo didn’t drop balls he rolled them down a smooth, wooden channel in an inclined plane that had been oiled to remove friction. He argued by analogy the results that he achieved by slowing down the acceleration by using an inclined plane were equivalent to those that would be obtained by dropping the balls vertically. Argument by analogy is of course not strict scientific proof but is an often used part of the scientific method that has often, as in this case, led to important new discoveries and results.  He released one ball at a time and timed them separately thus eliminating the synchronicity problem. Also, he was able with a water clock to time the balls with sufficient accuracy to make the necessary mathematical calculations. He put the laws of falls on a sound empirical and mathematical footing. One should also not neglect the fact that Galileo’s undoubtable talent as a polemicist made the content of the Discorsi available in a way that was far more accessible than anything that had preceded it.

Galileo’s demonstration of the law of the space traversed in case of uniformly varied motion. It is the same demonstration that Oresme had made centuries earlier. Source: Wikimedia Commons

For those, who like to believe that Catholics and especially the Jesuits were anti-science in the seventeenth century, and unfortunately they still exist, the experimental confirmation of Galileo’s law of fall, using direct drop rather than an inclined plane, was the Jesuit, Giovanni Battista Riccioli(1598–1671).

Giovanni Battista Riccioli Source: Wikimedia Commons

The Discorsi also contains Galileo’s work on projectile motion, which again was important and influential. The major thing is the parabola law that states that anything projected upwards and away follows a parabolic path. Galileo was not the only natural philosopher, who determined this. The Englishman Thomas Harriot (c. 1560–1621) also discovered the parabola law and in fact his work on projectile motion went well beyond that of Galileo. Unfortunately, he never published anything so his work remained unknown.  One of Galileo’s acolytes, Bonaventura Cavalieri (1598–1647),

Bonaventura Cavalieri Source: Wikimedia Commons

was actually the first to publish the parabola law in his Lo Specchio Ustorio, overo, Trattato delle settioni coniche (The Burning Mirror, or a Treatise on Conic Sections) 1632.

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This brought an accusation of intellectual theft from Galileo and it is impossible to tell from the ensuing correspondence, whether Cavalieri discovered the law independently or borrowed it without acknowledgement from Galileo.

The only problem that remained was what exactly was impetus. What was imparted to bodies to keep them moving? The answer was nothing. The solution was to invert the question and to consider what makes moving bodies cease to move? The answer is if nothing does, they don’t. This is known as the principle of inertia, which states that a body remains at rest or continues to move in a straight line unless acted upon by a force. Of course, in the early seventeenth century nobody really knew what force was but they still managed to discover the basic principle of inertia. Galileo sort of got halfway there. Still under the influence of the Platonic axioms, with their uniform circular motion, he argued that a homogenous sphere turning around its centre of gravity at the earth’s surface forever were there no friction at its bearings or against the air. Because of this Galileo is often credited with provided the theory of inertia as later expounded by Newton but this is false.

The Dutch scholar Isaac Beeckman (1588–1637) developed the concept of rectilinear inertia, as later used by Newton but also believed, like Galileo, in the conservation of constant circular velocity. Beeckman is interesting because he never published anything and his writing only became known at the beginning of the twentieth century. However, Beeckman was in contact, both personally and by correspondence, with the leading French mathematicians of the period, Descartes, Gassendi and Mersenne. For a time he was Descartes teacher and much of Descartes physics goes back to Beeckman. Descartes learnt the principle of inertia from Beeckman and it was he who published and it was his writings that were Newton’s source. The transmission of Beeckman’s work is an excellent illustration that scientific information does not just flow over published works but also through personal, private channels, when scientists communicate with each other.

With the laws of fall, the parabola law and the principle of inertia the investigators in the early seventeenth century had a new foundation for terrestrial mechanics to replace those of Aristotle.

Thomas Paine (1736–1809) was an eighteenth-century political radical famous, or perhaps that should be infamous, for two political pamphlets, Common Sense (1776) and Rights of Man (1791) (he also wrote many others) and for being hounded out of England for his political views and taking part in both the French and American Revolutions.

Thomas Paine portrait of Laurent Dabos c. 1792 Source: Wikimedia Commons

So I was more than somewhat surprised when Michael Brooks, author of the excellent The Quantum Astrologer’s Handbook, posted the following excerpt from Paine’s The Age of Reason, praising trigonometry as the soul of science:

My first reaction to this beautiful quote was that he could be describing this blog, as the activities he names, astronomy, navigation, geometry, land surveying make up the core of the writings on here. This is not surprising as Ivor Grattan-Guinness in his single volume survey of the history of maths, The Rainbow of Mathematics: A History of the Mathematical Sciences, called the period from 1540 to 1660 (which is basically the second half of the European Renaissance) The Age of Trigonometry. This being the case I thought it might be time for a sketch of the history of trigonometry.

Trigonometry is the branch of mathematics that studies the relationships between the side lengths and the angles of triangles. Possibly the oldest trigonometrical function, although not regarded as part of the trigonometrical cannon till much later, was the tangent. The relationship between a gnomon (a fancy word for a stick stuck upright in the ground or anything similar) and the shadow it casts defines the angle of inclination of the sun in the heavens. This knowledge existed in all ancient cultures with a certain level of mathematical development and is reflected in the shadow box found on the reverse of many astrolabes.

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

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

With Greek astronomy, trigonometry moved from Greece to India, where the Hindu mathematicians halved the Greek chords and thus created the sine and also defined the cosine. The first recoded uses of theses function can be found in the Surya Siddhanta (late 4^th or early 5^th century CE) an astronomical text and the Aryabhatiya of Aryabhata (476–550 CE).

Statue depicting Aryabhata on the grounds of IUCAA, Pune (although there is no historical record of his appearance). Source: Wikimedia Commons

Medieval Islam in its general acquisition of mathematical knowledge took over trigonometry from both Greek and Indian sources and it was here that trigonometry in the modern sense first took shape.  Muḥammad ibn Mūsā al-Khwārizmī (c. 780–c. 850), famous for having introduced algebra into Europe, produced accurate sine and cosine tables and the first table of tangents.

Statue of al-Khwarizmi in front of the Faculty of Mathematics of Amirkabir University of Technology in Tehran Source: Wikimedia Commons

In 830 CE Ahmad ibn ‘Abdallah Habash Hasib Marwazi (766–died after 869) produced the first table of cotangents. Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī (c. 858–929) discovered the secant and cosecant and produced the first cosecant tables.

Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī (940–998) was the first mathematician to use all six trigonometrical functions.

Abū al-Wafā Source: Wikimedia Commons

Islamic mathematicians extended the use of trigonometry from astronomy to cartography and surveying. Muhammad ibn Muhammad ibn al-Hasan al-Tūsī (1201–1274) is regarded as the first mathematician to present trigonometry as a mathematical discipline and not just a sub-discipline of astronomy.

Iranian stamp for the 700th anniversary of Nasir al-Din Tusi’s death Source: Wikimedia Commons

Trigonometry came into Europe along with astronomy and mathematics as part the translation movement during the 11^th and 12^th centuries. Levi ben Gershon (1288–1344), a French Jewish mathematician/astronomer produced a trigonometrical text On Sines, Chords and Arcs in 1342. Trigonometry first really took off in Renaissance Europe with the translation of Ptolemaeus’ Geōgraphikḕ Hyphḗgēsis (Geographia) into Latin by Jacopo d’Angelo (before 1360–c. 1410) in 1406, which triggered a renaissance in cartography and astronomy.

The so-called first Viennese School of Mathematics made substantial contributions to the development of trigonometry in the sixteenth century. John of Gmunden (c. 1380–1442) produced a Tractatus de sinibus, chodis et arcubus. His successor, Georg von Peuerbach (1423–1461), published an abridgement of Gmunden’s work, Tractatus super propositiones Ptolemaei de sinibus et chordis together with a sine table produced by his pupil Regiomontanus (1436–1476) in 1541. He also calculated a monumental table of sines. Regiomontanus produced the first complete European account of all six trigonometrical functions as a separate mathematical discipline with his De Triangulis omnimodis (On Triangles) in 1464. To what extent his work borrowed from Arabic sources is the subject of discussion. Although Regiomontanus set up the first scientific publishing house in Nürnberg in 1471 he died before he could print De Triangulis. It was first edited by Johannes Schöner (1477–1547) and printed and published by Johannes Petreius (1497–1550) in Nürnberg in 1533.

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At the request of Cardinal Bessarion, Peuerbach began the Epitoma in Almagestum Ptolomei in 1461 but died before he could complete it. It was completed by Regiomontanus and is a condensed and modernised version of Ptolemaeus’ Almagest. Peuerbach and Regiomontanus replaced the table of chords with trigonometrical tables and modernised many of the proofs with trigonometry. The Epitoma was published in Venice in 1496 and became the standard textbook for Ptolemaic geocentric astronomy throughout Europe for the next hundred years, spreading knowledge of trigonometry and its uses.

In 1533 in the third edition of the Apian/Frisius Cosmographia, Gemma Frisius (1508–1555) published as an appendix the first account of triangulationin his Libellus de locorum describendum ratione. This laid the trigonometry-based methodology of both surveying and cartography, which still exists today. Even GPS is based on triangulation.

With the beginnings of deep-sea exploration in the fifteenth century first in Portugal and then in Spain the need for trigonometry in navigation started. Over the next centuries that need grew for determining latitude, for charting ships courses and for creating sea charts. This led to a rise in teaching trigonometry to seamen, as excellently described by Margaret Schotte in her Sailing School: Navigating Science and Skill, 1550–1800.

One of those students, who learnt their astronomy from the Epitoma was Nicolaus Copernicus (1473–1543). Modelled on the Almagest or more accurately the Epitoma, Copernicus’ De revolutionibus, published by Petreius in Nürnberg in 1543, also contained trigonometrical tables. WhenGeorg Joachim Rheticus (1514–1574) took Copernicus’ manuscript to Nürnberg to be printed, he also took the trigonometrical section home to Wittenberg, where he extended and improved it and published it under the title De lateribus et angulis triangulorum (On the Sides and Angles of Triangles) in 1542, a year before De revolutionibus was published. He would dedicate a large part of his future life to the science of trigonometry. In 1551 he published Canon doctrinae triangvlorvm in Leipzig. He then worked on what was intended to be the definitive work on trigonometry his Opus palatinum de triangulis, which he failed to finish before his death. It was completed by his student Valentin Otho (c. 1548–1603) and published in Neustadt an der Haardt in 1596.

Source: Wikimedia Commons

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

Source: Wikimedia Commons

This work was republished in expanded editions in 1600, 1608 and 1612. The tables contained in Pitiscus’ Trigonometria were calculated to five or six places, where as those of Rheticus were calculated up to more than twenty places for large angles and fifteenth for small ones. However, on inspection, despite the years of effort that Rheticus and Otho had invested in the work, some of the calculations were found to be defective. Pitiscus recalculated them and republished the work as Magnus canon doctrinae triangulorum in 1607. He published a second further improved version under the title Thesaurus mathematicus in 1613. These tables remained the definitive trigonometrical tables for three centuries only being replaced by Henri Andoyer’s tables in 1915–18.

Source

We have come a long way from ancient Greece in the second century BCE to Germany at the turn of the seventeenth century CE by way of Early Medieval India and the Medieval Islamic Empire. During the seventeenth century the trigonometrical relationships, which I have up till now somewhat anachronistically referred to as functions became functions in the true meaning of the term and through analytical geometry received graphical presentations completely divorced from the triangle. However, I’m not going to follow these developments here. The above is merely a superficial sketch that does not cover the problems involved in actually calculating trigonometrical tables or the discovery and development of the various relationships between the trigonometrical functions such as the sine and cosine laws. For a detailed description of these developments from the beginnings up to Pitiscus I highly recommend Glen van Brummelen’s The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton University Press, Princeton and Oxford, 2009.

[1] For a wonderful detailed description of spherical trigonometry and its history see Glen van Brummelen, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, Princeton and Oxford, 2013

Of all the discoveries made during the first phase of telescopic astronomical discoveries perhaps the more impactful was the discovery by various observers of the phases of Venus, which showed that Venus in fact orbited the Sun and not the Earth. This was the first real empirical proof that a pure geocentric system of astronomy was not possible. Because Mercury displayed the same behaviour as Venus in never moving more than a few degrees from the Sun as viewed from the Earth it was assumed, by analogy, that Mercury also orbited the Sun and not the Earth. This observed behaviour of Venus and Mercury had already led Martianus Capella (fl. c. 410–420) in late antiquity to hypothesise that both of them orbited the Sun and not the Earth. The Capellan system was widespread and well known in Europe during the Middle Ages. Unfortunately due to its comparatively small size and distance from the Earth, and the inadequacies of the most used Dutch or Galilean telescopes it would be almost three decades before anybody succeeded in observing the phases of Mercury.

Naboth’s representation of Martianus Capella’s geo-heliocentric astronomical model (1573) Source: Wikimedia Commons

The knowledge that Venus orbited the sun and the assumption that Mercury also did led to the possibility of observing a so-called transit of one or other of them, i.e. the passage of the planet across the face of the Sun, as observed from the Earth. What would appear to be simply simple is in fact complicated by various factors. Principally the orbits of the Earth and Venus and/or Mercury around the Sun do not actually lie in the same plane. Taken Venus, for example, its orbit is tilted with respect to the Earth’s this means that most times when Venus is between the Earth and the Sun, it mostly passes above or below it rather than in front of it. Transits of Mercury take place approximately 13 or 14 times per century. Transits of Venus are less frequent taking place over a 243 year-cycle, two transits separated by eight years followed by long gaps of 121.5 and 105.5 years.

In order to be able to observe transits of the inner planets an astronomer requires detailed, accurate planetary tables, which allow them to predict the occurrence of the transit. Following the discovery of the phases of Venus it was Johannes Kepler (1571–1630), who, with the Rudolphine Tables (1627), first provided a set of planetary tables accurate enough to predict a transit of either Venus or Mercury.

According to Kepler’s calculations there should have been transits of both Mercury and Venus in 1631. Kepler did his best to draw astronomers’ attention to these occurrences with his De raris mirisque Anni 1631 including anadmonitio ad astronomos (1629), because their observation would they would help astronomers to settle the question of the true size of the planetary orbits, which up till then known relative to the Earth’s distance from the Sun, an unknown distance, and to determine the angular sizes of Mercury and Venus.

Kepler died in 1630 but his son in law, the astronomer Jacob Bartsch (c. 1600–1633) published a printed pamphlet advising European astronomers of Kepler’s information.

Strangely there is no information that Bartsch observed the Transit of Mercury on 7 November 1631 but at least four other European astronomers did. The first was the German astronomer, astrologer, physician and calendar writer, Johann Rudrauf (1588–1654), known Johannes Remus Quietanus, a correspondent of Galileo, Kepler and Johannes Faber. Rudrauf observed the transit from Rufach in the Alsace border region between Germany and France, where he was town physician. The second was the Swiss Jesuit astronomer Johann Baptist Cysat (c. 1587–1657), who had been a student and assistant of Christoph Scheiner (c. 1573–1650) at the University of Ingolstadt and became his successor as professor of mathematics in 1618. Cysat observed the transit from Innsbruck in Austria.

Johann Baptist Cysat Source: Wikimedia Commons

The third observer was the French philosopher, astronomer and mathematician, Pierre Gassendi (1592–1655), who observed the transit from Paris. A fourth unknown astronomer observed the transit from Ingolstadt.

Pierre Gassendi after Louis-Édouard Rioult Source: Wikimedia Commons

Gassendi’s account of the transit was the most widely read and studied so he is usually credited with being the first to observe a transit of Mercury. On 6 December 1631 Gassendi tried to observe the transit of Venus that had been predicted by Kepler unaware that because it took place during the night it wasn’t visible from Europe.

Transit of Mercury on May 9, 2016 Source: Wikimedia Commons

Kepler’s tables predicted no further transits of either Mercury or Venus for the seventeenth century so theoretically nobody would have set out to observe one. However, a young, self taught, English astronomer, Jeremiah Horrocks (1618–1641)did something quite extraordinary. Studying Kepler’s Rudolphine Tables Horrocks’ realised there would be another transit of Venus on 24 November 1639 (os) (4 December (ns)). Horrocks and his friend and fellow amateur astronomer William Crabtree (1610–1644) both observed the transit that Horrocks had predicted, Crabtree from Manchester and Horrocks from Much Hoole by Preston about 40 miles north of Manchester.

Jeremiah Horrocks makes the first observation of the transit of Venus in 1639, as imagined by the artist W. R. Lavender in 1903 Source: Wikimedia Commons

Both of them made their observations by projecting the telescopic image on to a sheet of paper. Horrocks wrote an extensive report of their observations calculating both the size of Venus and the distance between the Earth and the Sun. Unfortunately Horrocks died in 1641 just 23 years old and his report of the first ever observation of a transit of Venus, Venus in sole visa, was first published was first published by the astronomer Johannes Hevelius (1611–1687)in Danzig in 1662.

In 1639 the Italian Jesuit astronomer Giovanni Battista Zupi (1589–1650) succeeded in observing the orbital phases of Mercury using an astronomical telescope (two convex lenses) constructed by the Neapolitan astronomer, mathematician and telescope maker Francesco Fontana (1585–c. 1656).

Zupi and Fontana often observed together and Zupi’s observations of the phases of Mercury were published in Fontana’s Novae Colestium in 1646.

The observations of the transits of Mercury and Venus, and the phases of Mercury was final empirical proof, if it was needed, that both of the inner planets orbited the Sun and not the Earth nailing down the lid on the coffin of a pure geocentric, astronomical system. However, by the time these observations were made the majority of the astronomical community had already decided that only Kepler’s elliptical system or a Tychonic system with diurnal rotation were acceptable as the true system. The observations were of course compatible with both systems, so a final decision was not yet possible.

There is a strong tendency to view the history of science and the people who produced it in a sort of vacuum, outside of everyday society–Copernicus published this, Kepler published that, Newton synthesised it all… In fact the so-called scientific revolution took place in one of the most troubled times in European history, the age of the religious wars, the main one of which the Thirty Years War is thought to have been responsible directly and indirectly for the death of between one third and two thirds of the entire population of middle Europe. Far from being isolated from this turbulence the figures, who created modern science, were right in the middle of it and oft deeply involved and affected by it.

The idea for this blog post sort of crept into my brain as I was writing my review, two weeks ago, of two books about female spies during the English Revolution and Interregnum that is the 1640s to the 1660s. Isaac Newton was born during this period and grew up during it and, as I will now sketch, was personally involved in the political turbulence that followed on from it.

Born on Christmas Day in 1642 (os) shortly after the outbreak of the first of the three wars between the King and Parliament, Britain’s religious wars, he was just nine years old when Charles I was executed at the end of the second war.

Portrait of Newton by Godfrey Kneller, 1689 Source: Wikimedia Commons

Newton was too young to be personally involved in the wars but others whose work would be important to his own later developments were. The Keplerian astronomer William Gascoigne (1612-1644), who invented the telescope micrometer, an important development in the history of the telescope, died serving in the royalist forces at the battle of Marston Moor. The mathematician John Wallis (1616–1703), whose Arithmetica Infinitorum (1656) strongly influenced Newton’s own work on infinite series and calculus, worked as a code breaker for Cromwelland later for Charles II after the restoration.

John Wallis by Sir Godfrey Kneller

Newton first went up to university after the restoration but others of an earlier generation suffered loss of university position for being on the wrong side at the wrong time. John Wilkins (1614–1672), a parliamentarian and Cromwell’s brother-in-law, was appointed Master of Trinity College Cambridge, Newton’s college, in 1659 and removed from this position at the restoration. Wilkins’ Mathematical Magick (1648) had been a favourite of Newton’s in his youth.

Greenhill, John; John Wilkins (1614-1672), Warden (1648-1659); Wadham College, University of Oxford;

Newton’s political career began in 1689 following the so-called Glorious Revolution, when James II was chased out of Britain by William of Orange, his son-in-law, invited in by the parliament out of fear that James could reintroduce Catholicism into Britain. Newton sat in the House of Commons as MP for the University of Cambridge in the parliament of 1689, which passed the Bill of Rights, effectively a new constitution for England. Newton was not very active politically but he identified as a Whig, the party of his student Charles Montagu (1661–1715), who would go on to become one of the most powerful politicians of the age. It was Montagu, who had Newton appointed to lead the Royal Mint and it was also Montagu, who had Newton knighted in 1705in an attempt to get him re-elected to parliament.

In the standard version of story Newton represents the end of the scientific revolution and Copernicus (1473–1543) the beginning. Religion, politics and war all played a significant role in Copernicus’ life.

Copernicus, the “Torun portrait” (anonymous, c. 1580), kept in Toruń town hall, Poland.

Copernicus spent the majority of his life living in the autonomous prince-bishopric of Warmia, where as a canon of the cathedral he was effectively a member of the government. Warmia was a Catholic enclave under the protection of the Catholic Crown of Poland but as the same time was geographically part of Royal Prussia ruled over by Duke Albrecht of Prussia (1490–1568), who had converted to Lutheran Protestantism in 1552. Ironically he was converted by Andreas Osiander (1498–1552), who would go on the author the controversial ad lectorum in Copernicus’ De revolutionibus. Relations between Poland and Royal Prussia were strained at best and sometimes spilled over into armed conflict. Between 1519 and 1521 there was a war between Poland and Royal Prussia, which took place mostly in Warmia. The Prussians besieged Frombork burning down the town, but not the cathedral, forcing Copernicus to move to Allenstein (Olsztyn), where he was put in charge of organising the defences during a siege from January to February 1521.  Military commander in a religious war in not a role usually associated with Copernicus. It is an interesting historical conundrum that, during this time of religious strife, De revolutionibus, the book of a Catholic cathedral canon, was published by a Protestant printer in a strongly Protestant city-state, Nürnberg.

The leading figure of the scientific revolution most affected by the religious wars of the age must be Johannes Kepler. A Lutheran Protestant he studied and graduated at Tübingen, one of the leading Protestant universities. However, he was despatched by the university authorities to become the mathematics teacher at the Protestant school in Graz in Styria, a deeply Catholic area in Austria in 1594. He was also appointed district mathematicus.

Johannes Kepler Source: Wikimedia Commons

In 1598, Archduke Ferdinand, who became ruler of Styria in 1596, expelled all Protestant teachers and pastors from the province. Kepler was initially granted an exception because he had proved his worth as district mathematicus but in a second wave of expulsion, he too had to go. After failing to find employment elsewhere, he landed in Prague as an assistant to Tycho Brahe, the Imperial Mathematicus.

Tycho Brahe Source: Wikimedia Commons

Once again he, like Tycho, was a Protestant in a Catholic city serving a Catholic Emperor, Rudolf II. Here he soon inherited Tycho’s position as Imperial Mathematicus. However, Rudolf was tolerant, more interested in Kepler’s abilities as an astrologer than in his religious beliefs. Apart from a substantial problem in getting paid in the permanently broke imperial court, Kepler now enjoyed a fairly quiet live for the next twelve years, then everything turned pear shaped once more.

In 1612, Rudolf’s younger brother Archduke Matthias deposed him and although Kepler was allowed to keep his title of Imperial Mathematicus, and theoretically at least, his salary but he was forced to leave Prague and become district mathematicus in Linz. In Linz Kepler, who openly propagated ecumenical ideas towards other Protestant communities, most notably the Calvinists, ran into conflict with the local Lutheran pastor. The pastor demanded that Kepler sign the Formula of Concord, basically a commitment to Lutheran theology and a rejection of all other theologies. Kepler refused and was barred from Holy Communion, a severe blow for the deeply religious astronomer. He appealed to the authorities in Tübingen but they up held the ban.

In 1618 the Thirty Years War broke out and in 1620 Linz was occupied by the Catholic army of Duke Maximilian of Bavaria, which caused problems for Kepler as a Lutheran. At the same time he was fighting for the freedom of his mother, Katharina, who had been accused of witchcraft. Although he won the court case against his mother, she died shortly after regaining her freedom. In 1625, the Counterreformation reach Linz and the Protestants living there were once again persecuted. Once more Kepler was granted an exception because of his status as Imperial Mathematicus but his library was confiscated making it almost impossible for him to work, so he left Linz.

Strangely, after two years of homeless wandering Kepler moved to Sagen in Silesia in 1628, the home of Albrecht von Wallenstein the commander of the Catholic forces in the war and for whom Kepler had interpreted a horoscope much earlier in life. Kepler never found peace or stability again in his life and died in Ulm in 1630. Given the turbulence in his life and the various forced moves, which took years rather than weeks, it is fairly amazing that he managed to publish eighty-three books and pamphlets between 1596 and his death in 1630.

A younger colleague of Kepler’s who also suffered during the Thirty Years’ War was Wilhelm Schickard, who Kepler had got to know during his time in Württemberg defending his mother. Schickard would go on to produce the illustrations both Kepler’s Epitome Astronomiae Copernicanae and his Harmonice Mundi, as well as inventing a calculating machine to help Kepler with his astronomical calculations. In 1632 Württemberg was invaded by the Catholic army, who brought the plague with them, by 1635 Schickard, his wife and his four living children, his sister and her three daughters had all died of the plague.

Wilhelm Schickard, artist unknown Source: Wikimedia Commons

As I have pointed out on numerous occasions Galileo’s initial problems in 1615-16 had less to do with his scientific views than with his attempts to tell the theologians how to interpret the Bible, not an intelligent move at the height of the Counterreformation. Also in 1632 his problems were very definitely compounded by the fact that he was perceived to be on the Spanish side in the conflict between the Spanish and French Catholic authorities to influence, control the Pope, Urban VIII.

Galileo Portrait by Ottavio Leoni Source: Wikimedia Commons

I will just mention in passing that René Descartes served as a soldier in the first two years of the Thirty Year’s War, at first in the Protestant Dutch States Army under Maurice of Nassau and then under the Catholic Duke of Bavaria, Maximilian. In 1620 he took part in the Battle of the White Mountain near Prague, which marked the end of Elector Palatine Frederick V’s reign as King of Bohemia. During his time in the Netherlands Descartes trained as a military engineer, which was his introduction to the works of Simon Stevin and Isaac Beeckman.

René Descartes Portrait after Frans Hals Source: Wikimedia Commons

We have now gone full circle and are almost back to Isaac Newton. One interesting aspect of these troubled times is that although the problems caused by the wars, the religious disputes and the associated politics caused major problems in the lives of the astronomers and mathematicians, who were forced to live through them, and certainly affected their ability to carry on with their work, I can’t somehow imagine Copernicus working on De revolutionibus during the siege of Allenstein, the scholars themselves communicated quite happily across the religious divide.

Rheticus was treated as an honoured guest in Catholic Warmia although he was a professor at the University of Wittenberg, home to both Luther and Melanchthon. Copernicus himself was personal physician to both the Catholic Bishop of Frombork and the Protestant Duke of Royal Prussia. As we have seen, Kepler spent a large part of his life, although a devoted Protestant, serving high-ranking Catholic employers. The Jesuits, who knew Kepler from Prague, even invited him to take the chair for mathematics at the Catholic University of Bologna following the death of Giovanni Antonio Magini in 1617, assuring him that he did not need to convert. Although it was a very prestigious university Kepler, I think wisely, declined the invitation. The leading mathematicians of the time all communicated with each other, either directly or through intermediaries, irrespective of their religious beliefs. Athanasius Kircher, professor for mathematics and astronomy at the Jesuit Collegio Romano, collected astronomical data from Jesuits all over the world, which he then distributed to astronomers all over Europe, Catholic and Protestant, including for example the Lutheran Leibniz. Christiaan Huygens, a Dutch Calvinist, spent much of his life working as an honoured guest in Catholic Paris, where he met and influenced the Lutheran Leibniz.

When we consider the lives of scientists we should always bear in mind that they are first and foremost human beings, who live and work, like all other human beings, in the real world with all of its social, political and religious problems and that their lives are just as affected by those problems as everybody else.

In the seventeenth century large parts of Europe were still Catholic; in 1616 the Catholic Church had placed De revolutionibus and all other texts promoting a heliocentric world-view on the Index of Forbidden Books and in 1632 they added Galileo’s Dialogo sopra i due massimi sistemi del mondo (Dialogue Concerning the Two Chief World Systems), so the question arises, how was knowledge of the heliocentric model disseminated? The answer is, somewhat surprisingly, that the dissemination of the heliocentric hypothesis was, even in Catholic countries, widespread and through diverse channels.

First off, although De revolutionibus was placed on the Index in 1616, it was only placed there until corrected. In fact, somewhat against the norm, it was actually corrected surprisingly quickly and, with a few rather minor changes, became freely available again for Catholic scholars by 1621. The astronomers within the Church had been able to convince the theologians of the importance of Copernicus’ work as an astronomy book even if one rejected the truth of the heliocentric hypothesis. The only changes were that any statements of the factual truth of the hypothesis were removed, so anybody with a censured copy could quite happily think those statements back into place for himself.

The Lutheran Protestant Church also rejected the heliocentric hypothesis but never formally banned it in anyway. In fact, from very early on, the astronomers and mathematicians at the Lutheran universities had begun teaching Copernicus’ work as a purely mathematical, instrumentalist thesis, whilst rejecting it as a true account of the cosmos. It was used, for example, by Erasmus Reinhold (1511–1553) using Copernicus’ data and mathematical models to calculate the Prutenicae Tabulae (1551), without however committing to heliocentricity. They maintained this instrumentalist approach throughout the seventeenth century utilising the most up to date books as they became available, without crediting the hypothesis with any truth. From about 1630 onwards, Kepler’s Epitome Astronomiae Copernicanae (3 Vols. 1617–1621) and his Tabulae Rudolphinae (1627) became the leading textbooks for teaching the heliocentric hypothesis. The latter was used both sides of the religious divide because it was quite simply vastly superior in its accuracy to any other volume of planetary tables on the market.

However, the mainstream pro heliocentricity texts were not the only published sources spreading the information of the heliocentric hypothesis and making the information available across Europe. One, perhaps surprising, source was the yearly astrological almanacs.

These annual pamphlets or booklets contained the astronomical and astrological data for the coming year, phases of the moon, hours of sunlight, any eclipse or planetary conjunctions etc. They also included basic horoscopes for the year covering political developments, weather forecasts, health issues and whatever. These were immensely popular and printed on cheap paper and not bound were reasonably cheap, so they sold in comparatively vast numbers, having much larger editions than any printed books. The market was fiercely contested so to make sure that their product was preferred by the potential customers, who came from all levels of society, the authors and/or publishers included editorials covering a wide range of topic. These editorials often contained medical issues but in the seventeenth century they also often contained popular expositions of the heliocentric hypothesis. Given the widespread consume of these publications it meant that basic knowledge of heliocentricity reached a large audience.

Another important source for the dissemination of the heliocentric hypothesis was in the writings of some of those who, nominally at least, opposed it. I will now take a brief look at two of those authors the Italian, Jesuit astronomer, mathematician and physicist Giovanni Battista Riccioli (1598–1671) and the French, priest, philosopher, astronomer and mathematician Pierre Gassendi (1592–1655) both of whom were highly influential and widely read scholars in the middle of the seventeenth century.

Pierre Gassendi is one of those figures in the history of science, who deserve to be better known than they are. Well known to historians of science and philosophy he remains largely unknown to those outside those disciplines. He was a central figure in the intellectual life of Europe in the middle of the seventeenth century part of the philosophical circle in Paris that included René Descartes, Marin Mersenne, Thomas Hobbes and Jean-Baptiste Morin amongst others. He also travelled to Holland and made the acquaintance of Isaac Beeckman. Probably his most important contribution to the evolution of science was his attempt to reconcile Epicurean atomism with Christian theology.

Pierre Gassendi after Louis-Édouard Rioult. Source: Wikimedia Commons

Throughout his life he actively promoted the work of both Kepler and Galileo. He wrote and published a biography of Nicolas-Claude Fabri de Peiresc (1580–1637), his patron, an astronomer and another supporter of the works of Galileo.  Shortly before the end of his life he published a collective biography of Tycho Brahe, Nicolaus Copernicus, Georg von Peuerbach and Johannes Regiomontanus: Tychonis Brahei, equitis Dani, astronomorum Coryphaei, vita; accessit Nicolai Copernici; Georgii Peurbachii, et Joannis Regiomontani, astronomorum celebrium vita (1654).

In 1645 Gassendi was appointed professor of mathematics at the Collège Royal in Paris and during his time there he wrote and published an astronomy textbook presenting both the Tychonic and heliocentric astronomical systems, Institvtio astronomica, iuxta hypothesis tam vetervm, qvam Copernici, et Tychonis. Dictata à Petro Gassendo … Eivsdem oratio inauguralis iteratò edita (1647).

Although, as a Catholic priest, he presented the Tychonic system as the correct one his treatment of heliocentricity was detailed, thorough and very sympathetic. Perhaps somewhat too sympathetic, as it led to him being investigated by the Inquisition, who however gave him a clean bill of health. Because of his excellent reputation his book was read widely and acted as a major source for the dissemination of the heliocentric hypothesis.

Like Gassendi, Riccioli was an important and influential figure in seventeenth century science. From 1636 he was professor in Bologna where did much important work in astronomy and physics as well as being the teacher of Giovanni Domenico Cassini (1625–1712), who we will meet later in this series.

Riccioli as portrayed in the 1742 Atlas Coelestis (plate 3) of Johann Gabriel Doppelmayer. Source: Wikimedia Commons

He is perhaps best known for his pioneering selenology together with his former student, Francesco Maria Grimaldi (1618–1663), which provided the nomenclature system for the moons geological features still in use today.  As stated earlier it was Riccioli, who provided the necessary empirical proof of Galileo’s laws of fall. He also hypothesised the existence of, what later became known as the Coriolis effect, if the Earth did in fact rotate.

If a ball is fired along a Meridian toward the pole (rather than toward the East or West), diurnal motion will cause the ball to be carried off [that is, the trajectory of the ball will be deflected], all things being equal: for on parallels of latitude nearer the poles, the ground moves more slowly, whereas on parallels nearer the equator, the ground moves more rapidly.

Having failed to detect it, it does exist but is too small to be measured using the methods available to Riccioli, he concluded that the Earth does not in fact rotate.

This was just one of many arguments pro and contra the heliocentric hypothesis that Riccioli presented in his Almagestum novum astronomiam veterem novamque complectens observationibus aliorum et propriis novisque theorematibus, problematibus ac tabulis promotam (Vol. I–III, 1651), a vast astronomical encyclopaedia that became a standard astronomical textbook throughout Europe. Although Riccioli rejected the heliocentric hypothesis his very detailed and thorough analysis of it with all its strengths and weaknesses meant that his book became a major source for those wishing to learn about it.

Frontispiece of Riccioli’s 1651 New Almagest. Source: Wikimedia Commons

This famous frontispiece shows a semi-Tychonic system being weighed against a heliocentric system and being found more substantial. Ptolemaeus lies on the ground under the scales obviously defeated but he is saying “I will rise again”.

As we have seen, although not provable at that stage and nominally banned by the Catholic Church, information on and details of the heliocentric hypothesis were widespread and easily accessible throughout the seventeenth century from multiple sources and thus knowledge of it and interest in it continued to spread throughout the century.

This is a writen version of the lecture that I was due to hold at the Science and the City conference in London on 7 April 2020. The conference has for obvious reasons been cancelled and will now take place on the Internet. You can view the revised conference program here.

The title of my piece is, of course, somewhat hyperbolic, as far as I know nobody has ever done a statistical analysis of the manufacture of and trade in scientific instruments in the sixteenth century. However, it is certain that in the period 1450-1550 Nürnberg was one of the leading European centres both the manufacture of and the trade in scientific instruments. Instruments made in Nürnberg in this period can be found in every major collection of historical instruments, ranging from luxury items, usually made for rich patrons, like the column sundial by Christian Heyden (1526–1576) from Hessen-Kassel

Column Sundial by Christian Heyden Source: Museumslandschaft Hessen-Kassel

to cheap everyday instruments like this rare (rare because they seldom survive) paper astrolabe by Georg Hartman (1489–1564) from the MHS in Oxford.

Paper and Wood Astrolabe Hartmann Source: MHS Oxford

I shall be looking at the reasons why and how Nürnberg became such a major centre for scientific instruments around 1500, which surprisingly have very little to do with science and a lot to do with geography, politics and economics.

Like many medieval settlements Nürnberg began simply as a fortification of a prominent rock outcrop overlooking an important crossroads. The first historical mention of that fortification is 1050 CE and there is circumstantial evidence that it was not more than twenty or thirty years old. It seems to have been built in order to set something against the growing power of the Prince Bishopric of Bamberg to the north. As is normal a settlement developed on the downhill slopes from the fortification of people supplying services to it.

A fairly accurate depiction of Nürnberg from the Nuremberg Chronicle from 1493. The castles (by then 3) at the top with the city spreading down the hill. Large parts of the inner city still look like this today

Initially the inhabitants were under the authority of the owner of the fortification a Burggraf or castellan. With time as the settlement grew the inhabitants began to struggle for independence to govern themselves.

In 1200 the inhabitants received a town charter and in 1219 Friedrich II granted the town of Nürnberg a charter as a Free Imperial City. This meant that Nürnberg was an independent city-state, which only owed allegiance to the king or emperor. The charter also stated that because Nürnberg did not possess a navigable river or any natural resources it was granted special tax privileges and customs unions with a number of southern German town and cities. Nürnberg became a trading city. This is where the geography comes into play, remember that important crossroads. If we look at the map below, Nürnberg is the comparatively small red patch in the middle of the Holy Roman Empire at the beginning of the sixteenth century. If your draw a line from Paris to Prague, both big important medieval cities, and a second line from the border with Denmark in Northern Germany down to Venice, Nürnberg sits where the lines cross almost literally in the centre of Europe. Nürnberg also sits in the middle of what was known in the Middle Ages as the Golden Road, the road that connected Prague and Frankfurt, two important imperial cities.

You can also very clearly see Nürnberg’s central position in Europe on Erhard Etzlaub’s  (c. 1460–c. 1531) pilgrimage map of Europe created for the Holy Year of 1500. Nürnberg, Etzlaub’s hometown, is the yellow patch in the middle. Careful, south is at the top.

Over the following decades and centuries the merchant traders of Nürnberg systematically expanded their activities forming more and more customs unions, with the support of various German Emperors, with towns, cities and regions throughout the whole of Europe north of Italy. Nürnberg which traded extensively with the North Italian cities, bringing spices, silk and other eastern wares, up from the Italian trading cities to distribute throughout Europe, had an agreement not to trade with the Mediterranean states in exchange for the Italians not trading north of their northern border.

As Nürnberg grew and became more prosperous, so its political status and position within the German Empire changed and developed. In the beginning, in 1219, the Emperor appointed a civil servant (Schultheis), who was the legal authority in the city and its judge, especially in capital cases. The earliest mention of a town council is 1256 but it can be assumed it started forming earlier. In 1356 the Emperor, Karl IV, issued the Golden Bull at the Imperial Diet in Nürnberg. This was effectively a constitution for the Holy Roman Empire that regulated how the Emperor was to be elected and, who was to be appointed as the Seven Prince-electors, three archbishops and four secular rulers. It also stipulated that the first Imperial Diet of a newly elected Emperor was to be held in Nürnberg. This stipulation reflects Nürnberg’s status in the middle of the fourteenth century.

The event is celebrated by the mechanical clock ordered by the town council to be constructed for the Frauenkirche, on the market place in 1506 on the 150^th anniversary of the Golden Bull, which at twelve noon displays the seven Prince-electors circling the Emperor.

Mechanical clock on the Frauenkirche overlooking the market place in Nürnberg. Ordered by the city council in 1506 to celebrate the 150th anniversary of the issuing of the Golden Bull at the Imperial Diet in 1356

Over time the city council had taken more and more power from the Schultheis and in 1385 they formally bought the office, integrating it into the councils authority, for 8,000 gulden, a small fortune. In 1424 Emperor, Sigismund appointed Nürnberg the permanent residence of the Reichskleinodien (the Imperial Regalia–crown, orb, sceptre, etc.).

The Imperial Regalia

This raised Nürnberg in the Imperial hierarchy on a level with Frankfurt, where the Emperor was elected, and Aachen, where he was crowned. In 1427, the Hohenzollern family, current holders of the Burggraf title, sold the castle, which was actually a ruin at that time having been burnt to the ground by the Bavarian army, to the town council for 120,000 gulden, a very large fortune. From this point onwards Nürnberg, in the style of Venice, called itself a republic up to 1806 when it was integrated into Bavaria.

In 1500 Nürnberg was the second biggest city in Germany, after Köln, with a population of approximately 40,000, about half of which lived inside the impressive city walls and the other half in the territory surrounding the city, which belonged to it.

Map of the city-state of Nürnberg by Abraham Ortelius 1590. the city itself is to the left just under the middle of the map. Large parts of the forest still exists and I live on the northern edge of it, Dormitz is a neighbouring village to the one where I live.

Small in comparison to the major Italian cities of the period but even today Germany is much more decentralised with its population more evenly distributed than other European countries. It was also one of the richest cities in the whole of Europe.

Nürnberg, Plan by Paul Pfinzing, 1594 Castles in the top left hand corner

Nürnberg’s wealth was based on two factors, trading, in 1500 at least 27 major trade routes ran through Nürnberg, which had over 90 customs unions with cities and regions throughout Europe, and secondly the manufacture of trading goods. It is now time to turn to this second branch of Nürnberg’s wealth but before doing so it is important to note that whereas in other trading centres in Europe individual traders competed with each other, Nürnberg function like a single giant corporation, with the city council as the board of directors, the merchant traders cooperating with each other on all levels for the general good of the city.

In 1363 Nürnberg had more than 1200 trades and crafts masters working in the city. About 14% worked in the food industry, bakes, butchers, etc. About 16% in the textile industry and another 27% working leather. Those working in wood or the building branch make up another 14% but the largest segment with 353 masters consisted of those working in metal, including 16 gold and silver smiths. By 1500 it is estimated that Nürnberg had between 2,000 and 3,000 trades and crafts master that is between 10 and 15 per cent of those living in the city with the metal workers still the biggest segment. The metal workers of Nürnberg produced literally anything that could be made of metal from sewing needles and nails to suits of armour. Nürnberg’s reputation as a producer rested on the quality of its metal wares, which they sold all over Europe and beyond. According to the Venetian accounts books, Nürnberg metal wares were the leading export goods to the orient. To give an idea of the scale of production at the beginning of the 16^th century the knife makers and the sword blade makers (two separate crafts) had a potential production capacity of 80,000 blades a week. The Nürnberger armourers filled an order for armour for 5,000 soldiers for the Holy Roman Emperor, Karl V (1500–1558).

The Nürnberger craftsmen did not only produce goods made of metal but the merchant traders, full blood capitalists, bought into and bought up the metal ore mining industry–iron, copper, zinc, gold and silver–of Middle Europe, and beyond, (in the 16th century they even owned copper mines in Cuba) both to trade in ore and to smelt and trade in metal as well as to ensure adequate supplies for the home production. The council invested heavily in the industry, for example, providing funds for the research and development of the world’s first mechanical wire-pulling mill, which entered production in 1368.

The wirepulling mills of Nürnberg by Albrecht Dürer

Wire was required in large quantities to make chainmail amongst other things. Around 1500 Nürnberg had monopolies in the production of copper ore, and in the trade with steel and iron.  Scientific instruments are also largely made of metal so the Nürnberger gold, silver and copper smiths, and toolmakers also began to manufacture them for the export trade. There was large scale production of compasses, sundials (in particular portable sundials), astronomical quadrants, horary quadrants, torquetum, and astrolabes as well as metal drawing and measuring instruments such as dividers, compasses etc.

The city corporation of Nürnberg had a couple of peculiarities in terms of its governance and the city council that exercised that governance. Firstly the city council was made up exclusively of members of the so-called Patrizier. These were 43 families, who were regarded as founding families of the city all of them were merchant traders. There was a larger body that elected the council but they only gave the nod to a list of the members of the council that was presented to them. Secondly Nürnberg had no trades and crafts guilds, the trades and crafts were controlled by the city council. There was a tight control on what could be produced and an equally tight quality control on everything produced to ensure the high quality of goods that were traded. What would have motivated the council to enter the scientific instrument market, was there a demand here to be filled?

It is difficult to establish why the Nürnberg city corporation entered the scientific instrument market before 1400 but by the middle of the 15^th century they were established in that market. In 1444 the Catholic philosopher, theologian and astronomer Nicolaus Cusanus (1401–1464) bought a copper celestial globe, a torquetum and an astrolabe at the Imperial Diet in Nürnberg. These instruments are still preserved in the Cusanus museum in his birthplace, Kues on the Mosel.

The Cusanus Museum in Kue

In fact the demand for scientific instrument rose sharply in the 15^th & 16^th centuries for the following reasons. In 1406 Jacopo d’Angelo produced the first Latin translation of Ptolemy’s Geographia in Florence, reintroducing mathematical cartography into Renaissance Europe. One can trace the spread of the ‘new’ cartography from Florence up through Austria and into Southern Germany during the 15^th century. In the early 16^th century Nürnberg was a major centre for cartography and the production of both terrestrial and celestial globes. One historian of cartography refers to a Viennese-Nürnberger school of mathematical cartography in this period. The availability of the Geographia was also one trigger of a 15^th century renaissance in astronomy one sign of which was the so-called 1^st Viennese School of Mathematics, Georg von Peuerbach (1423–1461) and Regiomontanus (1436–176), in the middle of the century. Regiomontanus moved to Nürnberg in 1471, following a decade wandering around Europe, to carry out his reform of astronomy, according to his own account, because Nürnberg made the best astronomical instruments and had the best communications network. The latter a product of the city’s trading activities. When in Nürnberg, Regiomontanus set up the world’s first scientific publishing house, the production of which was curtailed by his early death.

Another source for the rise in demand for instruments was the rise in interest in astrology. Dedicated chairs for mathematics, which were actually chairs for astrology, were established in the humanist universities of Northern Italy and Krakow in Poland early in the 15^th century and then around 1470 in Ingolstadt. There were close connections between Nürnberg and the Universities of Ingolstadt and Vienna. A number of important early 16th century astrologers lived and worked in Nürnberg.

The second half of the 15^th century saw the start of the so-called age of exploration with ships venturing out of the Iberian peninsular into the Atlantic and down the coast of Africa, a process that peaked with Columbus’ first voyage to America in 1492 and Vasco da Gama’s first voyage to India (1497–199). Martin Behaim(1459–1507), son of a Nürnberger cloth trading family and creator of the oldest surviving terrestrial globe, sat on the Portuguese board of navigation, probably, according to David Waters, to attract traders from Nürnberg to invest in the Portuguese voyages of exploration.  This massively increased the demand for navigational instruments.

The Erdapfel–the Behaim terrestial globe Germanische National Museum

Changes in the conduct of wars and in the ownership of land led to a demand for better, more accurate maps and the more accurate determination of boundaries. Both requiring surveying and the instruments needed for surveying. In 1524 Peter Apian (1495–1552) a product of the 2^nd Viennese school of mathematics published his Cosmographia in Ingolstadt, a textbook for astronomy, astrology, cartography and surveying.

The Cosmographia went through more than 30 expanded, updated editions, but all of which, apart from the first, were edited and published by Gemma Frisius (1508–1555) in Louvain. In 1533 in the third edition Gemma Frisius added an appendix Libellus de locorum describendum ratione, the first complete description of triangulation, the central method of cartography and surveying down to the present, which, of course in dependent on scientific instruments.

In 1533 Apian’s Instrumentum Primi Mobilis 

was published in Nürnberg by Johannes Petreius (c. 1497–1550) the leading scientific publisher in Europe, who would go on ten years later to publish, Copernicus’ De revolutionibus, which was a high point in the astronomical revival.

All of this constitutes a clear indication of the steep rise in the demand for scientific instruments in the hundred years between 1450 and 1550; a demand that the metal workers of Nürnberg were more than happy to fill. In the period between Regiomontanus and the middle of the 16^th century Nürnberg also became a home for some of the leading mathematici of the period, mathematicians, astronomers, astrologers, cartographers, instrument makers and globe makers almost certainly, like Regiomontanus, at least partially attracted to the city by the quality and availability of the scientific instruments.  Some of them are well known to historians of Renaissance science, Erhard Etzlaub, Johannes Werner, Johannes Stabius (not a resident but a frequent visitor), Georg Hartmann, Johannes Neudörffer and Johannes Schöner.**

There is no doubt that around 1500, Nürnberg was one of the major producers and exporters of scientific instruments and I hope that I have shown above, in what is little more than a sketch of a fairly complex process, that this owed very little to science but much to the general geo-political and economic developments of the first 500 years of the city’s existence.

One of the most beautiful sets on instruments manufactured in Nürnberg late 16th century. Designed by Johannes Pretorius (1537–1616), professor for astronomy at the Nürnberger University of Altdorf and manufactured by the goldsmith Hans Epischofer (c. 1530–1585) Germanische National Museum

**for an extensive list of those working in astronomy, mathematics, instrument making in Nürnberg (542 entries) see the history section of the Astronomie in Nürnberg website, created by Dr Hans Gaab.

In the previous episode of this series we looked into the academic literature that spread knowledge of the heliocentric system during the seventeenth century. However, there was another genre of literature during the century that was also partially dedicated to introducing and explaining the heliocentric system, fiction and popular literature and that is what we are going to look at now.

It should come as no surprise that the earliest author to produce a fictional account of the heliocentric system was Johannes Kepler with his posthumously published proto-science-fiction novel, Somnium (The Dream) (1634).

Source: Wikimedia Commons

Kepler first wrote the core of this book as a student dissertation, written for his teacher Michael Mästlin, explaining how the movement of the Earth, in a heliocentric system, would appear to somebody observing it from the Moon. Around 1605 he added a frame story to his student dissertation the dream of the title. Kepler relates that in 1608 he was reading a book on Bohemian legends when he fell asleep and began to dream. In his dream he takes down another book from the shelf and reads the story of Duracotus, an Icelander, and his mother Fiolxhilda, who is obviously a witch, although Kepler never explicitly states that. The boy open a herb charm that his mother has made to sell to sailors and removes the herbs making the charm useless. Outraged, his mother sells him instead to the ship’s captain, who takes him to Scandinavia, where he ends up on Hven with Tycho Brahe under whom he studies astronomy for five years. Returning to Iceland he reconciles himself with his mother, who reveals to him that she has magical knowledge of astronomy. Fiolxhilda summons a daemon, who tells Duracotus how they could travel to the moon and then holds a long discourse on the moon and its inhabitants, part science, part science fiction. To go into more detail would turn this post into book, however, because of the obvious autobiographical element Kepler thought that somebody had gained access to the manuscript and this was why his mother was charged with witchcraft; he was almost certainly mistaken in this belief.

Kepler did not publish his story but put it aside. Between 1620 and 1630 Kepler added 223 extensive endnotes, which elucidate the story, explaining his sources, his motivations and the content of the story itself. Even with these explanatory additions Kepler did not publish the book, leaving it unpublished at his death in 1630. Because his death had left his wife, Susanna, and his family in financial difficulties, his son in law, Jacob Bartsch (c. 1600–1633) edited the manuscript for publication with hope of generating an income for his mother-in-law. However, he too died before he could publish the book, which was then finally brought to press by Kepler’s son Ludwig (b. 1607).

Kepler’s Somnium was the first of a series of fictional books describing journeys to the moon in the seventeenth century nearly all of which promoted a heliocentric astronomy and it is to these that we now turn.

Our first author is the Anglican clergyman and natural philosopher, John Wilkins (1614–1672).

John Wilkins portrait attributed to John Greenhill Source: Wikimedia Commons

Although he produced no real new scientific discoveries or theories Wilkins was a highly influential figure in the scientific revolution in England. He published a series of popular and speculative science books and was a founding member of and a driving force behind the Royal Society. One of Wilkins’ popular science books, Mathematical Magick (1648) is said to have had a strong influence on a young Isaac Newton but it is two of his other books that interest us here, The Discovery of a World in the Moone (1638) and A Discourse Concerning a New Planet (1640), the second being a revised and expanded version of the first.

Cover and frontispiece. Note the heliocentric system diagram

Both books present a heliocentric astronomical system and, based on Galileo’s telescopic discoveries of the earth like nature of the moon, hypothesise an inhabited moon, as had Kepler’s Somnium, which however predated Galileo’s Sidereus Nuncius. Wilkins two books were a popular source for disseminating the heliocentric hypothesis in England.

Five months after the publication of The Discovery of a World in the Moone another journey to the moon fantasy by an Anglican clergyman was published, Francis Goodwin’s The Man in the Moone or A Discourse of a Voyage thither (1638), under the pseudonym Domingo Gonsales.

Francis Godwin artist unknown Source: Wikimedia Commons

Godwin (1562–1633) had died five years previously and although his book was published after Wilkins’ tome, it is thought to have been written in the 1620s and it is known to have influenced Wilkins’ book.

Source: Houghton Library via Wikimedia Commons

The ‘author’, Gonsales, a Spaniard on the run after killing a man in a duel, invents a flying machine powered by gansa, a species of wild swans, which after a series of adventures flies him to the moon, a twelve day journey. Here he discovers a utopian Christian society. After six months he returns to earth landing in China, where he has some more adventures. For our purposes what is important here is that like Wilkins, Godwin is a Copernican and although he only mentions Copernicus by name the influence of Kepler, Gilbert and Galileo is clearly discernable in his science fantasy.

Frontispiece and title page of the second edition (1657), now with the pseudonym replaced by “F.G. B. of H.” (“Francis Godwin, Bishop of Hereford”) Source: Wikimedia Commons

The books of Wilkins and Godwin were both best sellers and were translated into various other European languages including French, where they influenced another book in the genre, Cyrano de Bergerac’s L’Autre monde ou les états et empires de la Lune (The Other World: Comical History of the States and Empires of the Moon 1657), and his Les États et Empires du Soleil (The States and Empires of the Sun, 1662), both published posthumously.

Cyrano de Bergerac artist unknown Source: Wikimedia Commons

L’Autre monde is a satire on Godwin’s book and Cyrano’s hero, who is also called Cyrano, makes various failed attempts to reach the moon, including trying to rise up to the moon levitated by bottles of evaporating dew before he finally gets there.

Cyrano uses bottles of dew to float upwards. Illustration from the second volume of an edition of Cyrano de Bergerac’s complete works printed in Amsterdam in 1708 Source: Wikimedia Commons

When he does arrive on the moon one of the people he meets is Gonsales, with whom he has a religious debate. It might seem that Cyrano de Bergerac (1619–1655) as a literary author was just riffing off the success of Wilkins’ and Godwin’s works but he was a pupil of Pierre Gassendi (1592–1655) and so was well informed about the ongoing cosmology and astronomy debate.

Godwin’s The Man in the Moone and the English translation of Cyrano’s L’Autre monde inspired two later stage productions on the theme Aphra Behn’s (1640–1689) farce The Emperor of the Moon 1687, her second most successful play, and Elkanah Settle’s (1648–1724) opera The World in the Moon (1697).

Aphra Behn by the Anglo-Dutch artist Sir Peter Lely, Courtesy of the Yale Center for British Art, Yale University via Wikimedia Commons

All of the texts that we have looked at so far contain a common theme that emerged strongly during the seventeenth century, the possibility of life on other worlds, in this case the moon. Our final work, in this case not a fictional but a factual one, continues this theme, Bernard Le Bovier de Fontenelle’s popular presentation of the heliocentric hypothesis, Entretiens sur la pluralité des mondes (Conversations on the Plurality of Worlds, 1686). Bernard Le Bovier de Fontenelle (1657–1757) was an author and Cartesian philosopher, commentator rather than initiator, who was a member of both the Académie française and the Académie des sciences of which he was secretary for forty-two years beginning in 1697; in this function he wrote Histoire du renouvellement de l’Académie des Sciences (Paris, 3 vols., 1708, 1717, 1722).

Bernard Le Bovier de Fontenelle artist unknown Source: Wikimedia Commons

His Entretiens sur la pluralité des mondes was an early example of a popular science book written in French not Latin.

In the preface, Fontenelle addresses female readers and suggests that the offered explanation should be easily understood even by those without scientific knowledge. The book is presented as a dialogue between a philosopher and a marquise and elucidates the heliocentric system with a discussion of the possibility of extra-terrestrial life. The book is interesting in that Fontenelle explains that there is now only one system to consider because the Tychonic system was now considered to be too complex in comparison with the heliocentric system. This is one of the few real applications of Ockham’s razor in the history of science and comes long before there was any empirical proof for the heliocentric system. There was an English translation by John Glanville (c. 1664–1735) in 1687 and another by Aphra Behn A Discovery of New Worlds in 1688.

A Gentleman of the Inner Temple is John Glanville

This all too brief survey of the fictional and popular literature published in the seventeenth century demonstrates that the discussion on the cosmological/astronomical system had escaped the narrow confines of academia and entered the public forum.

The HISTSCI_HULK had just been settling down to the beautiful sunny morning and deciding, which of his Easter eggs he wanted to eat first (chocolate for breakfast on Easter is OK, isn’t it?), when he let out an ear shattering bellow of rage that signalled that he was about to go on the rampage. What could have so upset the valiant defender of truth and accuracy in the history of science? He had been casually perusing the website Today in Science History, a useful calendar of birth, deaths and events in #histSTM, when his eyes were drawn to the following brief statement:

“In 1633, Galileo Galilei’s second trial before the Inquisition began. At its conclusion his belief that the Earth was not the centre of the Universe was pronounced heretical”

What could possible have so enraged the HISTSCI monster in this apparently innocuous historical claim? Well, almost everything. The date and the name are correct but both substantive claims are simply false. Of course, there is the possibility that we have slipped into a parallel universe and are dealing with another Galileo Galilei about whom the stated facts are correct but Ockham’s razor would suggest that the simplest solution is that the facts are wrong.

We start with, “Galileo Galilei’s second trial before the Inquisition began,” Galileo only ever had one trial before the Inquisition so this could not have been the second. This is a wide spread misconception that occurs here not for this first time and it is worth explaining why it’s false. Galileo had to do with the Inquisition three times in his life. Three times, I hear you ask, when or what was the third time. Most people aren’t aware of Galileo’s first run in with the Inquisition, which took place when he was still a relatively unknown professor for mathematics in Padua in 1604.

Galileo was denounced to the Venetian Inquisition by a former amanuensis, Silvestro Pagnoni from Pesaro for practicing deterministic astrology. Yes, Galileo was a practicing astrologer and no, he didn’t just do it for the money. Greek astrology was deterministic, which meant that ones entire life was determined at the point of birth. This conflicted with the Christian belief in free will and was thus considered heretical. Quite why the Medieval Church didn’t just dump astrology is somewhat puzzling but in the thirteenth century Albertus Magnus and Thomas Aquinas redefined astrology, so that it was non-deterministic for human thought. You can read exactly how they did so in Darrel Rutkin’s excellent book, Sapientia Astrologica. Although the Church accepted astrology in the seventeenth century, deterministic astrology was definitely not acceptable. The Venetian Inquisition duly investigated the accusation and, having cleared Galileo of all suspicion, did not pursue the case any further. Galileo’s next brush with the Inquisition was the much more famous one in 1615/16 and it is this one that people mistakenly think was a trial with Galileo as the accused.

What actually happened was that the Church provoked by Galileo’s Letter to Benedetto Castelli and Paolo Antonio Foscarini’s Epistle concerning the Pythagorean and Copernican opinion of the Mobility of the Earth and the stability of the sun and of the new system or constitution of the World set up a commission to investigate and pass judgement on the heliocentric cosmological theory. The conclusion of the commission is generally well known.

The proposition that the Sun is stationary at the centre of the universe is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture”; the proposition that the Earth moves and is not at the centre of the universe “receives the same judgement in philosophy; and … in regard to theological truth it is at least erroneous in faith.”

Absurd in philosophy can be translated as scientifically false, a correct judgement based on the knowledge of the time, as the available empirical evidence solidly supported a geocentric or helio-geocentric system and not a heliocentric one.

As Galileo was the leading proponent of a heliocentric world view the Pope, Paul V, instructed Roberto Bellarmino, the Church’s leading theologian to inform Galileo of the commission’s findings and to instruct him that he could no longer hold or teach the heliocentric theory. Bellarmino did as instructed but at no point was Galileo on trail.

The astute reader will have already noticed that it was not at the end of his trial in 1633 that the “belief that the Earth was not the centre of the Universe was pronounced heretical” but already by the commission of investigation in 1616. In fact we now stumble upon a conundrum, the heliocentric theory was never actually officially pronounced heretical. The commission found that the proposition that the Sun is stationary at the centre of the universe is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture” but only a Pope can formally declare something heretical and no pope ever did.

I’m not going to address the trial itself and the factors leading up to it, as I fairly recently wrote a whole blog post on the topic, which you can read here.

This anniversary provoked an at times heated exchange on Twitter, yesterday and this morning, in which various people attacked the Catholic Church and/or the Inquisition, their attacks based largely on false or inaccurate information and I, as all too often, ended up trying my best to correct their mistaken utterances. I will now repeat some of the core insights from that exchange.

Galileo was during his interrogation and trial by the Roman Inquisition never imprisoned nor tortured and not even shown the instruments of torture, all of which claims are too often believed to represent the truth. He was, in fact, treated with care and respect as an honoured guest throughout his interrogation. He was housed in a luxury apartment with servants to see to his needs and during the breaks between the separate interrogations was even allowed to return to the apartment in Rome where he was staying before the interrogations began. Following the trial where he was found guilty of grave suspicion of heresy, and not heresy as if often falsely claimed, he was sentenced to life imprisonment, which was immediately commuted to house arrest. He spent the first weeks of his house arrest as the honoured guest of Archbishop Piccolomini in his palace in Sienna until it proved too much of a good thing and Urban ordered that he go home. He spent the rest of his house arrest in his own villa in Arceti near Florence, where he was cared for by servants. He was allowed visitors and now too old and too frail to travel anyway he devoted himself to writing the Discorsi, his most important scientific work, which despite a ban was published without the Church undertaking any action against it. The average European peasant in the period certainly lived a much worse life.

One topic that came up several times was that even if not tortured or threatened with torture, Galileo would have been scared of the Inquisition because of its reputation and especially because of what they did to Bruno. If there were a false facts about the Church and Galileo bingo game evoking Bruno would certainly occupy the centre square. These comment stimulated the following speculations on my part:

Actually, I don’t think Galileo was particularly concerned about the Inquisition; his self-opinionated arrogance protected him from such thoughts. He wasn’t a religious nutcase like Bruno, he was the greatest scientist in Europe, he was a Medicean courtier, he was a much admired and feted member of Roman high society, he counted princes and powerful cardinals amongst his best friends and supporters, Maffeo Barberini had been one of his best friends since 1612. When he became Pope Urban VIII, Barberini granted him several private audiences and praised his latest book, Il Saggiatore, it was Barberini who, as Pope, had commissioned him to write his book comparing the geocentric and heliocentric systems, what could he possibly have to fear?

This is of course, as I say, purely speculative but the way Galileo is known to have behaved during his interrogations would seem to support such a view.

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

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

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

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

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

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

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

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

Source: WIkimedia Commons

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

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

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

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

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

With the eccentricity of the orbits exaggerated: Source

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

Source

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

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

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

Ismaël Boulliau portrait by Pieter van Schuppen Source: Wikimedia Commons

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

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

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

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

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

Source: Wikimedia Commons

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

Source: Wikimeda Commons

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

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

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

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

Addendum: Section on Coriolis Effect added 21 May 2020

The ongoing astronomical/cosmological discussion on the nature of comets in the Early Modern Period has weaved its way continuously through our narrative. Starting with Toscanelli’s attempts to track the paths of comets, as if they were celestial objects in the mid fifteenth century, through the Europe wide discussion, amongst the leading astronomers of the period in the 1530s, leading up to the great comet of 1577 (usually called Tycho’s comet) and on to the great comet of 1618. The discussion was rekindled by two great comets in the 1660s, the great comets of 1664 (modern designation C/1644 W1)

The Great Comet of 1664: Johann Thomas Theyner (Frankfurt 1665) Source: Wikimedia Commons

and 1665 (modern designation C/1665 F1).

The Great Comet 1665 Sigismund Trew Source: Wikimedia Commons

It would not be an exaggeration to say that there was an outbreak of comet fever amongst European astronomers.

There are surviving observational reports on the appearance and path of these comets not just from Europe but also from China, Japan and North America. The earliest reported siting for C/1664 W1 was from Spain on 17 November. Samuel Pepys, who observed it together with Robert Hooke, mentions it in his famous diary and Daniel Defoe (1660–1731) included it in his fictional account of the bubonic plague in London, A Journal of the Plague Year (1722). This comet was, of course, regarded as the harbinger of both the plague and the Great Fire of London.

The Great Comet of 1664 from an anonymous pamphlet Source: Wikimedia Commons

Christiaan Huygens observed it in Leiden beginning on 2 December and his observations were included in a dissertation by the French astronomer, mathematician, physicist and instrument maker Pierre Petit (1594–1677). Giovanni Domenico Cassini (1625–1712), Geminiano Montanari (1633–1687) and Giovanni Borelli (1608-1679) all observed both comets in Italy, and Pierre Petit and Adrien Auzout (1622–1691) in Paris. Johannes Hevelius observed the comets in Danzig and published a report of his 1664 observations, Prodromus cometicus in 1665,

HEVELIUS, Joannes. Prodromus Cometicus, quo Historia Cometae anno 1664. Danzig: Simon Reiniger for the author, 1665. SourceSource

and then later a book on his observations of both comets, Cometographia (1668).

Source

The Polish theologian, historian and astronomer, Stanisław Lubieniecki (1623–1675) observed both comets from his house in Hamburg.

Source: The theatre of cosmic and human history

He corresponded with Ismäel Boulliau (1605–1694) in Paris and Henry Oldenburg (1618–1677), secretary of the Royal Society in London about the 1664 comet. In 1668 he published a three-part work on both comets, his Theatrum cometicum. Part one contained his correspondence on the topic with other European astronomers including Oldenburg, Hevelius and Athanasius Kircher (1602–1680), professor for mathematics and astronomy on the Jesuit University in Rome, including their observations. The first part also contained an impressive collection of copper plate prints of many historical comets.

Hevelius’ drawings go the Comet tails 1665 Source

The second part consisted of criticism by other scholars of his cometary theories and his answers to his critics, whilst the third part contained his astrological interpretations, including his opinion that the Great Fire of London was a punishment from God announced by the 1664 comet.

The French Jesuit, François-Joseph Le Mercier (1604–1690), reported observing the comet of 1664 for the first time in Québec on 29 November and continued observing it until 15 January 1665. He also observed the 1665 comet from 29 March until 17 April. In New England the Puritan minister and amateur astronomer Samuel Danforth (1626–1674) observed both comets. The author of three almanacs for the years 1647, 1648 and 1649, he wrote and published a book on the comets, which is considered one of the earliest printed astronomy publication in America.

Samuel Danforth Source

By the 1660s there was no doubt amongst astronomers that comets were supralunar bodies and that they were real solid objects and not some sort of optical phenomena. This being the case the debate that raged throughout Europe concerned the flight path that comets were thought to take. One reference work consulted by most of the participants in this discussion was Johannes Kepler’s De cometis libelli tres I. astronomicus, theoremata continens de motu cometarum … II. physicus, continens physiologiam cometarum novam … III. astrologicus, de significationibus cometarum annorum 1607 et 1618 / autore Iohanne Keplero … (1609), which was regarded as an authoritative work on the subject. Of interest is that Kepler expressed the opinion that the flight paths of comets were rectilinear and explained than any apparent curvature observed in the flight path was due to the movement of the Earth, the observation platform. Others argued that the fight paths were curved and began to reference Kepler’s laws of planetary motion to support this position.  Sir William Lower (1570–1615), friend and student of Thomas Harriot, had already suggested in a letter 1610, having read Kepler’s Astronomia Nova (1609) and based on his and Harriot’s observation of Comet Halley in 1607 that the flight path was elliptical.

Comet Halley 1607: David Herlitz, Von dem Cometen oder geschwentzten newen Stern, welcher sich im September dieses 1607. Pub. Johann Witten, Lubeck,1607 Source

The discussion about the flight paths of comets in the 1660s can be regarded as a defining moment, together with Nikolaus Mercator’s reformulation of Kepler’s second law in 1664, for the acceptance of Kepler’s elliptical heliocentric model of the cosmos over its rival the Tychonic geo-heliocentric model. This of course didn’t happen overnight but 1664 can be regarded as the turning point in the battle of the systems.

In the 1660s opinions varied. Some, such as Christopher Wren (1632–1723) Savillian Professor of astronomy at Oxford, and John Wallis (1616–1703) Savillian Professor of geometry at Oxford, stuck to the traditional rectilinear flight paths, whilst others suggested various curved flight paths ranging from circles over parabolas to ellipses. Cassini had already, in a work about comets from the 1650s, following the Tychonic theory, committed to circular orbits a view he maintained based on his observations of the 1664 comet. Auzout in Paris voted for ellipses, as did Hevelius. Borelli criticised both Cassini and Auzout and suggested that the flight paths were parabolas.

Danforth’s account is interesting because it comes very close to being the current accepted view of comets. In his An Astronomical Description of the Late Comet or Blazing Star; As it appeared in New-England in the 9th, 10th, 11th, and in the beginning of the 12th Moneth, 1664. Together with a Brief Theological Application thereof (1665) he states that comets are supralunar bodies, that the bright tail was sunlight reflected off exhalations from the head of the comet and the tail always points away from the sun. He thought that its flight path was possibly an ellipse but in this case he was wrong. Modern calculations suggest that both the 1664 and 1665 are either extremely long period elliptical comets or had parabolic flight paths and were thus not periodic. Although the proof that some comets were, in fact, periodical still lay in the future some astronomers already speculated in the 1660s that this was the case. Robert Hooke, for example, thought the 1664 comet was a return of the 1618 great comet, whilst Cassini speculated that the comets of 1577, 1665 and 1680 were periodical.

In 1664, Isaac Newton (1642–1726 os) was still an undergraduate student at Cambridge University. Up till then an indifferent student in 1664 he had embarked on a six-year period of study in mathematics and natural philosophy that would lay the foundations for his life’s work. To record the results of his reading in natural philosophy he started a notebook that he had titled, Questiones quaedam Philosophicae. On 29 December 1664 and on the following day he made and entered observations of a comet. On 31 August 1726, in a conversation with John Conduitt (1688-1737) he mentioned his extended observations of this comet. Another Cambridge student, Nicholas Wickins, who shared chambers with Newton at that time, told Conduitt, “He sate up so often long in the year 1664 to observe a comet that appeared then.” This is probably Newton’s first activity as an astronomer. As we shall see, comets and their orbits would come to play an important roll in Newton’s future theory of universal gravitation and in his magnum opus, the Principia.

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

One of the most often repeated false statements in the history of science is that Isaac Newton discovered gravity. Of course he didn’t discovery it, it’s all around us. You can observe gravity every time you drop something. Making the claim more precise, by saying Newton discovered the law of gravity, doesn’t really improve the situation much. What Newton did do was he proved the law of gravity and made the fairly rational assumption based on the available evidence that this law applies universally to all bodies in the cosmos. An assumption that is not written in stone and has been questioned in the present time for the general theory of relativity, the theory that replaced the Newtonian theory of universal gravity and of which the Newtonian theory of gravity is a very good approximation for local cases. However we don’t want to take the path to modern theories of cosmology and dark matter but want to stay firmly in the seventeenth century with Newton.

We can start with a brief survey of theories of gravity before Newton. Originally gravity was the Latin term applied to Aristotle’s explanation of why, when dropped, things fall to the ground. Aristotle thought that objects did so through a form of vital attraction, returning to their natural home, consisting predominantly of the elements earth and water. Fire and air rise up. This only applied to the Earth, as things beyond the Moon were made of a fifth element, aether, the quintessence, for which the natural form of motion was uniform circular motion.

This neat model wouldn’t work, however for Copernicus’ heliocentric model, which disrupted the division between the sublunar and supralunar worlds. To get around this problem Copernicus suggested that each planet had its own gravity, like the Earth. So we have terrestrial gravity, Saturnian gravity, Venusian gravity etc. This led Alexander von Humboldt, in the 19^th century, to claim that Copernicus should be honoured as the true originator of the universal theory of gravity, although it is by no means clear that Copernicus thought that he planetary gravities were all one and the same phenomenon.

The whole concept became even more questionable when the early telescopic astronomers, above all Galileo, showed that the Moon was definitely Earth like and by analogy probably the other planets too. At the end of a long line of natural philosophers stretching back to John Philoponus in the sixth century CE, Galileo also showed that gravity, whatever it might actually be, was apparently not a vitalist attraction but a force subject to mathematical laws, even if he did get the value for the acceleration due to gravity ‘g’ wrong and although he didn’t possess a clear concept of force.. Throughout the seventeenth century other natural philosophers, took up the trail and experimented with pendulums and dropped objects. A pendulum is of course an object, whose fall is controlled. Most notable were the Jesuit, natural philosopher Giovanni Battista Riccioli (1598–1671) and the Dutch natural philosopher Christiaan Huygens (1629–1695). Riccioli conducted a whole series of experiments, dropping objects inside a high tower, making a direct confirmation of the laws of fall. Both Riccioli and Huygens, who independently of each other corrected Galileo’s false value for ‘g’, experimented extensively with pendulums in particular determining the length of the one-second pendulum, i.e. a pendulum whose swing in exactly one second. As we will see later, the second pendulum played a central roll in an indirect proof of diurnal rotation. Huygens, of course, built the first functioning pendulum clock.

Turning to England, it was not Isaac Newton, who in the 1670s and 80s turned his attention to gravity but Robert Hooke (1635–1703), who was Curator of Experiments for the newly founded Royal Society. Like Riccioli and Huygens Hooke experimented extensively with dropping objects and pendulums to try and determine the nature of gravity. However his experiments were not really as successful as his continental colleagues. However, he did develop the idea that it was the force of gravity that controlled the orbits of the planets and, having accepted that comets were real solid objects and not optical phenomena, also the flight paths of comets. Although largely speculative at this point Hooke presented a theory of universal gravity, whilst Newton was still largely confused on the subject. Hooke turned to Newton in a letter with his theory in order to ask his opinion, an act that was to lead to a very heated priority dispute.

Before we handle that correspondence we need to go back to the beginnings of the 1670s and an earlier bitter dispute between the two.  In 1672 Newton announced his arrival on the European natural philosophy scene with his first publication, a letter in the Philosophical Transactions of the Royal Society (1671/72), A New Theory of Light and Colours, which described the experimental programme that he had carried out to demonstrate that white light actually consisted of the colours of the spectrum.

Newton’s original letter. Source: Royal Society

This brilliant piece of experimental optics did not receive the universal praise that, reading it today, we might have expected, in fact it was heavily criticised and attacked. Some critics were unable to reproduce Newton’s experimental results, probably because their prisms were of too poor quality. However, others, Hooke to the fore, criticised the content. Hooke and Huygens, the two current leaders in the field of optics both criticised Newton for interpreting his results within the framework of a particle theory of light, because they both propagated a wave theory of light. Newton actually wrote a paper that showed that his conclusions were just as valid under a wave theory of light, which, however, he didn’t publish. The harshest criticism came from Hooke alone, who dismissed the whole paper stating that he had already discovered anything of worth that it might contain . This did not make Newton very happy, who following this barrage of criticism announced his intention to resign from the Royal Society, to which he had only recently been elected.  Henry Oldenburg (c. 1619–1677), secretary of the Royal Society, offered to waive Newton’s membership fees if he would stay. Newton stayed but had little or nothing more to do with the society till after Hooke’s death in 1703. Newton did, however, write a very extensive paper on all of his optical work, which remained unpublished until 1704, when it formed a major part of his Opticks.

By  1679 tempers had cooled and Robert Hooke, now secretary of the Royal Society, wrote to Isaac Newton to enquire if he would be interested in reopening his dialogue with the Royal Society. In the same letter he asked Newton’s opinion on his own hypothesis that planetary motions are compounded of a tangential motion and “an attractive motion towards the centrall body…” Hooke is here referencing his Attempt to Prove the Motion of the Earth from Observations (1674, republished 1679),

which contains the following fascinating paragraph:

This depends on three Suppositions. First, That all Coelestial Bodies whatsoever, have an attractive or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from the, as we observe the earth to do, [here Hooke is obviously channelling Copernicus] but that they do also attract all other Coelestial Bodies that are within the sphere of their activity … The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual power deflected and bent into a Motion, describing a Circle, Ellipsis, or some other more compounded Curve Line. [the principle of inertia, as propounded by Descartes] The third supposition is, That these attractive powers are so much the more powerful in operating, by how much nearer the body wrought upon is to there own Centers. Now what these several degrees are I have not yet experimentally verified…

Whether or not this is truly a universal theory of gravity is a much-debated topic, but if not, it comes very close and was moving much more in that direction than anything Newton had produced at the time. As we shall see later this was to cause not a little trouble between the two rather prickly men.

Newton declined the offer of a regular exchange of ideas, claiming that he was moving away from (natural) philosophy to other areas of study. He also denied having read Hooke’s paper but referred to something else in it in a later letter to Flamsteed. However, in his reply he suggested an experiment to determine the existence of diurnal rotation involving the usually dropping of objects from high towers. Unfortunately for Newton, he made a fairly serious error in his descripting of the flight path of the falling object, which Hooke picked up on and pointed out to him, if unusually politely, in his reply. Newton of course took umbrage and ended the exchange but he did not forget it.

In our next episode we will deal with the events leading up to the writing and publication of Newton’s great masterpiece, Philosophiæ Naturalis Principia Mathematica (1687), which include the repercussions of this brief exchange between Hooke and its author.

The New Statesman recently had a review of Catherine Fletcher’s new book on the history of the Italian Renaissance, The Beauty and the Terror,[1] written by Rowan Williams under the title, Breaking the Renaissance myth.  For those, who might not know Rowan Williams is an ex Archbishop of Canterbury, who although ordained served as an academic rather than as a priest: However, he is/was a theologian and not a historian and very definitely not a historian of science.

Fletcher’s book is largely about what we might term the dark side of the Italian Renaissance and this is reflected in the title of Williams’ review.

I had no problems with the general tenor of what he had to say until I stumbled across the following two paragraphs in the middle of his review:

If we demythologise the Renaissance a little, we may learn to do more justice to what preceded it. Professor Fletcher has a brief discussion of scientific advances in the mid 16th century, especially in anatomy, navigational skills and botany – the latter two spurred on by the fresh stimulus of colonial travel and discovery. But the fact that this treatment is relatively brief and relates to a period rather later than the “high Renaissance” should give us pause if we are inclined to think of this as an epoch of spectacular scientific progress.

Many scholars have pointed out that the 15th and early 16th centuries are a rather stagnant period in many areas of natural science compared with some parts of the Middle Ages, when astronomy, mechanics and logic made substantial advances. The great 16th-century exception, Copernicus’s treatise of 1543 on the circulation of planets around the sun, was not a dramatic and total rejection of earlier astronomical method based on new scientific evidence, but a refinement designed to clear up the mathematics of charting the heavenly bodies. It was received with interest and some enthusiasm at the time, but was clearly not seen as a radical departure from the principles of Aristotle. Only with slightly later figures like Tycho Brahe (1546-1601) and Johannes Kepler (1571-1630) did actual observation of the heavens play a decisive part in the argument.

As somebody, who generally describes himself as a historian of Renaissance science I was, to say the least, more than somewhat discombobulated by the good Reverend Williams’ claims about my chosen discipline and I thought I might take a couple of minutes to examine them.

I’ll start with what Williams describes as Professor Fletcher’s brief discussion of scientific advances in the mid 16th century, especially in anatomy, navigational skills and botany. This is indeed extremely brief. The main text of the book is 350 pages long and there is a just-15-pages long chapter entitled, Art, Science and Reform of which only three pages deal with the scientific topics mentioned by Williams. This is principally a book of political history and the comment here have almost a throw away quality, something mentioned in passing. The anatomy mentioned is, of course, Vesalius’ De fabrica, which together with all the new developments in medicine, mainly in the North Italian universities, constitutes one of the largest revolutions in the entire history of medicine.  Fletcher does not discuss advances in the science of navigation, which were in fact very extensive in the 15^th and 16^th centuries, but the ‘navigations’ another term for the voyages of exploration and discovery undertaken in those centuries and their influence on developments back in Italy, as recorded by authors such as Giovanni Battista  Ramusio and Richard Hakluyt.

The botany refers to the establishment of botanical gardens at the universities of Padua and Pisa and the publications of herbaria (herbals) aimed at correcting such works as Pliny’s Natural History, as Vesalius had corrected Galen in medicine. What she doesn’t mention is that both the botanical gardens and the herbals were also part of the medical revolution, the scientific investigation of healing herbs being one of their central functions.

The last sentence of the first paragraph and the first of the second paragraph are a bit of a stunner. You know that I have a tendency to call myself a historian of Renaissance science and Williams is saying that I’m a historian of a bit of a damp squib. I’m used to people, who should know better, making rude and highly inaccurate statements about the history of medieval science, but to have somebody praise the vitality of medieval science, whilst at the same time putting the boot into Renaissance science is I think a first, at least as far as I’m concerned. This raises all sorts of problems, not least because the division between medieval science and Renaissance science is totally artificial and there is in reality continuity in European scientific activity that goes through from the translation movement in the twelfth century to at least the middle of the sixteenth century. Also I think to claim that medieval science made “substantial advances in astronomy, mechanics and logic” is a bit strong, as they were more involved in a game of catch up with antiquity and medieval Islam. On the other hand if you do try to identify a specifically Renaissance science, you first have to decide when it begins and when it ends. My own period definition of Renaissance science starts at the beginning of the fifteenth century and ends with the Thirty Years War. Kepler for all of his modernity is philosophically much more a Renaissance philosopher than a modern one, as is also Tycho. Galileo is more transitional but still has at least one foot in the Middle Ages.

Let us take stock and make an inventory of all the scientific activities that were developed and/or advanced in the period between 1400 and 1600. Regular readers will already have encountered much of what follows in various posts here over the years but it might prove of interest to see it laid out, if only in outline, all in one place.

We start with the first Latin translation of Ptolemaeus’ Geographia from the Greek by Jacobus Angelus in Florence in 1406. This is of course Renaissance culture in pure form, the translation from Greek into Latin of a major text from antiquity, above all because it was a text that had never been translated out of Arabic in the original translation movement. This text kicked off mathematical cartography in Renaissance Europe and with it revitalised astronomy, which was needed to determine latitude and longitude coordinates for this new form of cartography. The Ptolemaic world map, which very soon followed the translation both in manuscript and in print, was a totally new perception of the world in comparison to the medieval mappa mundi.

A mid-15th century Florentine map of the world based on Jacobus Angelus’s 1406 Latin translation of Maximus Planudes’s late-13th century rediscovered Greek manuscripts of Ptolemy’s 2nd-century Geography. Ptolemy’s 1st (modified conic) projection. Credited to Francesco di Antonio del Chierico – Ptolemy’s Geography (Harleian MS 7182, ff 58–59) Source: Wikimedia Commons

The new cartography spread northwards throughout Europe helping to trigger the First Viennese School of Mathematics. Here Gmunden, Peuerbach and Regiomontanus modernised Ptolemaic astronomy, integrating the newly developing trigonometry and many Arabic developments into Peurbach’s Theoricae Novae Plaetarum (1473) and the Peuerbach & Regiomontanus Epitoma in Almagestum Ptolemae (1496), which became the new textbooks for astronomy for the next one hundred plus years and were also the books Copernicus used to learn his astronomy.

Title page Epitoma in Almagestum Ptolemae Source: Wikimedia Commons

The Second Viennese School of Mathematics with Johannes Stabius, Andreas Stiborius, Georg Tannstetter and Peter Apian pushed the advances in cartography and astronomy further.

Apian’s copy of the Waldseemüller world map, naming the new fourth continent America Source: Wikimedia Commons

The Viennese mathematici stood in close contact with their colleagues in Nürnberg, where Johannes Schöner and Johannes Werner also made substantial contributions to theses advances. Schöner in particular was heavily involved in the activities that led to the publication of Copernicus’ De revolutionibus in Nürnberg in 1543. It was Schöner, who also kicked off the production of printed terrestrial and celestial globe pairs,

Celestial globe by Johann Schöner, c.1534 Source: Museum of the History of Science, Oxford

which was picked up by Gemma Frisius, who taught astronomy, cartography and mathematics to Gerhard Mercator, who in turn would go on to revolutionise both cartography and globe making triggering the golden age of both disciplines in the Netherlands in the seventeenth century.

Abraham Ortelius, who produced and published the first modern atlas, was also a member of the Frisius-Mercator circle along with numerous other important cartographical innovators.

Frisius, of course, introduced triangulation an important new tool in cartography, surveying and geodesy. New surveying instruments, such as the plain table, were also developed to carry out surveying using triangulation.

The early modern cartographers were not just simple mapmakers, their publications also contained much geographical information, much of it new, as well as historical, anthropological and ethnographical information about the areas mapped.

Another member of this European wide group of mathematici, Pedro Nunes, in Portugal was the discovery of the fact that a course of constant compass bearing on the globe is not part of a great circle but a loxodrome, a spiral.

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

This knowledge lies at the centre of the so-called Mercator map projection. Turning to navigation, the Portuguese and later Spanish explorations out into the Atlantic led to major developments such as the determination of latitude and the development of new instruments for this purpose such as the backstaff and the marine astrolabe. At the end of our period in 1600 to be exact, William Gilbert published his De Magnete, as well as being the definitive text up to that time on magnets and magnetism, it was also an important text on empirical, experimental science. Although published at the end of our period it relied on earlier work on magnetism and the magnet by such researchers as Robert Norman.

Coming back to astronomy, Copernicus’ De revolutionibus didn’t, as often presented, appear out of thin air but was part of a general movement to modernise astronomy and above all to make it more accurate that begins with Peuerbach and Regiomontanus and gains a lot of momentum in the sixteenth century particularly in the Europa wide debate in the 1530s, in which Copernicus also took an active part. I will address here Williams’ mindboggling statement about De revolutionibus:

The great 16th-century exception, Copernicus’s treatise of 1543 on the circulation of planets around the sun, was not a dramatic and total rejection of earlier astronomical method based on new scientific evidence, but a refinement designed to clear up the mathematics of charting the heavenly bodies. It was received with interest and some enthusiasm at the time, but was clearly not seen as a radical departure from the principles of Aristotle. [my emphasis]

As almost always we are dealing with someone whose knowledge of Renaissance cosmology and astronomy is obviously very minimal. The Peuerbachian geocentric system of the cosmos with which Copernicus was working was not Aristotelian astronomy but an uneasy mash up of Aristotelian cosmology and Ptolemaic astronomy. In fact there was a major attempt to return to Aristotelian homocentric astronomy, launched by Fracastoro amongst other, during those debates in the 1530s. Whilst, in a mathematical sense, Copernicus’ heliocentric astronomy didn’t stray far from Ptolemaic astronomy with its deferents and epicycles, but without its, for Copernicus, offensive equant points, it deviated radically from Aristotle’s cosmology and physics. Fundamental to Aristotelian cosmology is the fact that the Earth is immobile at the centre of the cosmos, to place the Sun there instead and the Earth in orbit around the Sun is a very a radical departure from the principles of Aristotle. Fundamental to Aristotelian physics is that the cosmos in divide into supralunar and sublunar areas. Above the Moon’s orbit natural motion is uniform and circular below it natural motion is perpendicular to the Earth’s surface. Upwards for fire and air, downwards for earth and water. Giving the Earth three additional motions–diurnal rotation, annual orbit around the Sun and a circulating of the poles– was a very radical departure from the principles of Aristotle.

Moving on from the mathematical sciences–astronomy, cartography, navigation, and surveying–to mathematics itself, the Renaissance saw a massive development in trigonometry and its applications. All four of the named mathematical sciences make extensive use of trigonometry. Regiomontanus wrote the first complete account of the six basic trigonometrical functions in Europe, this had been done much earlier in Arabic science, which also presented trigonometry as a separate mathematical discipline and not just a subsidiary of astronomy; this was published by Schöner in 1533.

Source

Rheticus published an expanded version of the trigonometry section of De revolutionibus as a separate work before De revolutionibus itself was published. The historian of mathematics, Grattan-Guinness, calls the Renaissance the age of trigonometry. We also have the transition of algebra from being merely commercial arithmetic to becoming a central mathematical discipline during the sixteenth century. This new analytical mathematics lay at the core of the so-called scientific revolution in the seventeenth century.

The fifteenth and sixteenth centuries also saw a renaissance in the mathematics and physics of Archimedes, in which Regiomontanus, once again, played a significant role. This renaissance peaked in 1544 when Thomas Venatorius published a bilingual, Greek and Latin, edition of the Works of Archimedes in Basel.

Archimedes, Opera omnia, Basel, 1544,

Galileo, who is often (falsely) called the founder of modern physics, explicitly took the work of Archimedes rather than that of Aristotle as reference point for his own work.

In the so-called natural sciences the Middle Ages were dominated by the Naturalis Historia of Gaius Plinius Secundus, or Pliny as he is know in English. This work is an encyclopaedia of everything that Pliny considered related to nature, astronomy, meteorology, geography, ethnography, anthropology, physiology, zoology, botany including agriculture and horticulture, pharmacology, magic, water, mining and mineralogy.  The work lacks originality and depth and is a ragbag of other sources thrown together under one concept, natural history; a term that we still use today. The Renaissance, especially after the invention of moving type book printing in the middle of the fifteenth century, saw the separating out and development of the individual disciplines as we known them today.

Vannoccio Biringuccio in his De la pirotechnia (1540) and Georgius Agricola in his De re metalica (1556) modernised and established metallurgy as an independent discipline. Agricola’s work together with his De natura fossilium also contributed substantially to the founding of geology and mineralogy as separate disciplines.

Zoology found its independence in the works of Ulisse Aldrovandi, who also contributed substantially to the foundations of geology, a word that he coined, and Conrad Gesner, who also published a fossil book. Aldrovandi was one of those who established a botanical garden and wrote and published a herbal. In zoology, some of the anatomists, who followed in the wake of Vesalius in the second half of sixteenth century, also instituted comparative anatomy, dissecting animal as well as human corpses.

Albrecht Dürer’s Rhinoceros from Conrad Gesner’s History Animalium

Herbals had already existed in the Middle Ages but following the invention of the printed book they took on a whole new dimension. The sixteenth century became the age of the great herbals of Otto Brunfels, Leonhart Fuchs, Hieronymus Bock, Rembert Dodoens, Carolus Clusius, Pietro Andrea Mattioli, Propero Alpino and others. Botanical gardens and herbariums, collections of dried plant specimens, were also established all over Europe and not just in university towns. Both the herbals and the botanical gardens served two purposes, on the one hand the study of botany and on the other the study of pharmacology. The authors of the herbals and the keepers of the botanical gardens and herbariums exchanged seeds, plants and dried specimens with their colleagues throughout Europe and even further afield. Researchers in the newly discovered lands (newly discovered for Europeans that is) sending specimens home from all over the world.

Leonhart Fuch’s Herbal

Williams emphasises that the little bit of scientific activity that he acknowledges took place during the Renaissance did so outside of the “high Renaissance”:

But the fact that this treatment is relatively brief and relates to a period rather later than the “high Renaissance” should give us pause if we are inclined to think of this as an epoch of spectacular scientific progress.

The expression “high Renaissance” is a highly dubious and rather meaningless historical concept, as it just basically means the short period when Leonardo, Raphael and Michelangelo were active, but is William’s implied claim that this period invoked no scientific progress really true?

The books on zoology and botany listed above were spectacularly illustrated, large format volumes and can even be viewed as the first printed coffee table books. What is interesting here is that they reflected and contributed to the development in fine art now labelled Naturalism. Many of the illustrators of those early coffee table books trained in the studios of the high Renaissance artists. Similarly the illustrations in the anatomical, medical works. This development lies at the heart of the so-called high Renaissance and alongside the realistic depiction of the natural world this included as a central element the development and use of linear perspective. Linear perspective is in fact a branch of applied or practical mathematics that developed in the Renaissance out of the medieval theories of optics. It developed further in the seventeenth century into projective geometry. The high Renaissance was not quite as devoid of scientific progress as Williams would have us believe.

Medicine also saw many new developments alongside the Vesalian revolution in anatomy. Many new drugs both botanical and mineral were sent back to Europe and investigated for their efficacy by those at home. With Paracelsus a whole new direction is medicine was established which grew and expanded following his death in 1541.

Paracelsus Source: Wikimedia Commons

This was a medicine based on alchemy and mineral rather than plant based medicines. The Paracelsian alchemy played a significant role in the transition from alchemy to modern chemistry and helped to establish the modern science of pharmacology. The first university chairs for chemistry at the beginning of the seventeenth century were chairs for Paracelsian medicine.

The sixteenth century also saw a restructuring of the medical industry in general with the physicians gaining prominence over the apothecaries, midwives and herbalist, creating a medical hierarchy that persists, with modifications, to the present day.

The above is merely a sketch of the scientific activity during the Renaissance and is by no means exhaustive. There are certainly other activities that I haven’t listed and even ones that I’m not aware of yet. However, I think I have outlined enough to show that the 15th and early 16th centuries are anything but a rather stagnant period in many areas of natural science compared with some parts of the Middle Ages. In fact those two centuries were rich in scientific developments and advances more than equal to anything produced in the earlier part of the Middle Ages. I would, however, once again emphasise that I think dividing the period between the twelfth and seventeenth centuries into Middle Ages and Renaissance with relation to the history of science is artificial and unproductive and we should look more at the continuities and less at the divisions.

[1] Catherine Fletcher, The Beauty and the Terror, The Bodley Head, London, 2020, As it is a book largely about political history I probably won’t be reviewing it here.

Giambattista della Porta (1535(?)–1615) is well known to historians of Renaissance science but for the general public he remains a largely unknown figure. If he is known at all,  he is often written off as an occultist, because of the title of his most well known work Magia Naturalis. In fact in the late sixteenth and early seventeenth centuries he was a highly respected and influential member of the Italian Renaissance scientific community. Although he wrote and published profusely over a wide range of scientific and related topics he made no really major discoveries and produced no major inventions and unlike his contemporaries, Kepler and Galileo, who were both well acquainted with his work, he has been largely forgotten.

Giambattista della Porta Source: Wikimedia Commons

Giambattista Della Porta were born at Vico Equense, Near Naples, probably sometime in 1535 (he created the confusion about his birth date), the third of four sons of the nobleman Nardo Antonio dell Porta of whom three survived childhood.  His parental home resembled an intellectual salon where the boys were continually exposed to and educated by visiting philosophers, mathematicians, poets and musicians. Their education was completed by private tutors, who also taught the boys the attributes of a gentleman, dancing, riding, skilled performance in tournaments and games and how to dress well. Della Porta never attended university but enjoyed life as a well educated polymathic, gentleman of leisure. If he can be considered to have had a profession, then it is that of a dramatist, he wrote more than twenty theatrical works, but it is his extensive activities in the sciences that interest us here.

Already in 1558, at the age of 23, he published the fist version of his most well known work, the Magia Naturalis in four books, a sort of encyclopaedia of the Renaissance sciences. From the beginning it was a bestseller running to five editions in Latin within the first ten years with translations into Italian (1560), French (1565), Dutch (1566) and English (1658). A vastly expanded version in twenty books was published in 1589. This final version covers a wide range of topics:

Source: Wikimedia Commons

Book 1: Of the Causes of Wonderful Things Book 2: Of the Generation of Animals Book 3: Of the Production of New Plants Book 4: Of Increasing Household-Stuff Book 5: Of Changing Metals Book 6: Of Counterfeiting Glorious StonesBook 7: Of the Wonders of the Load-Stone Book 8: Of Physical Experiments Book 9: Of Beautifying Women Book 10: Of Distillation Book 11: Of Perfuming Book 12: Of Artificial Fires Book 13: Of Tempering Steel Book 14: Of CookeryBook 15: Of Fishing, Fowling, Hunting, etc. Book 16: Of Invisible Writing Book 17: Of Strange Glasses Book 18: Of Static Experiments Book 19: Of Pneumatic Experiment Book 20: Of the Chaos

The contents range from fairly banal parlour tricks, over engineering, experimental science, horticulture and husbandry to every day things. At the very beginning della Porta is very careful to explain what exactly he mean by the term natural magic:

There are two sorts of Magick; the one is infamous, and unhappy, because it has to do with foul Spirits and consists of incantations and wicked curiosity; and this is called Socery; an art which all learned and good men detest; neither is it able to yield an truth of reason or nature, but stands merely upon fancies and imaginations, such as vanish presently away, and leave nothing behind them; as Jamblicus writes in his book concerning the mysteries of the Egyptians. The other Magick is natural; which all excellent wise men do admit and embrace, and worship with great applause; neither is there any thing more highly esteemed, or better thought of, by men of learning. The most noble Philosophers that ever were, Pythagorus, Empedocles, Democritus, and Plato forsook their own countries, and lived abroad as exiles and banished men, rather than as strangers; and all to search out and to attain this knowledge; and when they came home again, this was the Science which they professed, and this they esteemed a profound mystery. They that have been most skillful in dark and hidden points of learning, do call this knowledge the very highest point, and the perfection’s of Natural Sciences; inasmuch that if they could find out or devise amongst all Natural Sciences, any one thing more excellent or more wonderful then another, that they would still call by the name of  Magick. Others have named it the practical part of natural Philosophy, which produces her effects by the mutual and fit application of one natural thing unto another.

The association of Magick with natural philosophy is continued in della Porta’s definition of the Magician:

This is what is required to instruct a Magician, both what he must know, and what he must observe; that being sufficiently instructed in every way, he may bring very strange and wonderful things to us. Seeing Magick, as we showed before, as a practical part of natural Philosophy, it behooves a Magician and one that aspires to the dignity of the profession, to be an exact and very perfect Philosopher.

Despite the very diverse nature of the Magia Naturalis it does contain elements of genuine experimental science. For example, it contains the first experimental disproof of the widely held medieval belief that garlic disables magnets. He also experimented with the cooling properties of dissolving nitre in water. As described here by Andrea Sella (@SellaTheChemist)

As well as the Magia Naturalis della Porta wrote and published a large number of monographs on a very wide range of topics. Cryptography was a popular topic in Renaissance Europe, the most famous book being Johannes Trithemius’ Poligraphia, della Porta published his De Furtivis Literarum Notis (1563), which contain innovative cryptographical ideas.

In 1586 he published a work on physiognomy De humana physiognomonia libri IIII,

From De humana physiognomonia, 1586 Source: Wikimedia Commons

which was still being referenced in the nineteenth century, two years later a book on phytonomy (the science of the origin and growth of plants), Phytognomonica, which contains the first observations on fungal spores.

Phytognomonica, 1588 Source: Wikimedia Commons

These two books confirm della Porta’s adherence to the Renaissance doctrine of signatures. This theory claimed that it was possible to determine the nature of things based on their external appearances.

This was by no means the limit to della Porta’s publishing activities. He also wrote an agricultural encyclopaedia, separate volumes on various fruit bearing trees, books on mathematics, astronomy, meteorology, military engineering, distillation and in 1589 a book on optics, his De refractione optics. We shall return to the latter.

This incredible literary outpouring was just part of his scientific activity, in about 1560 he founded an academic society, Accademia dei Segreti (Academia Secratorum Naturae), the Academy of the Secrets of Nature, which is considered to be the earliest scientific society. The academy met regularly in della Porta’s home and membership was open to all but to become a member one had to present a new secret of nature that one had discovered. We know what some of those new secrets were as della Porta included them in the twenty volume version of his Magia Naturalis. In 1578 della Porta was summoned to Rome and investigated by the Pope. We do not know the exact grounds for this summons but he was forced to shut down his academy on suspicion of sorcery. This is to a certain extent ironic because della Porta was very careful in all his writing to avoid controversial topics particularly religious ones.

Although it was shut down the Accademia dei Segreti, would later have a major influence on another, much more renowned, early scientific academy, Federico Cesi’s Accademia dei Lincei. Cesi was a huge admirer of della Porta and as a young man travelled to Naples to visit the older natural philosopher. On his return home he founded his own academy, whose name was inspired by a line from the preface of the Magia Naturalis:

… with lynx like eyes, examining those things which manifest themselves, so that having observed them, he may zealously use them.

In 1610 della Porta became the fifth member of the Accademia dei Lincei, one year before Galileo.

Another important aspect of Renaissance science was the establishment of private natural philosophical museums also known as Wunderkammer, or cabinets of curiosity. Della Porta had, as to be expected, a particular fine cabinet of curiosity that would influence others to create their own, the Jesuit Athanasius Kircher for example.

Fold-out engraving from Ferrante Imperato’s Dell’Historia Naturale (Naples 1599), the earliest illustration of a natural history cabinet Source: Wikimedia Commons

Della Porta made minor contribution to the advance of science and engineering over a wide range of disciplines but I first ran into della Porta in the context of the history of optics and it his association with this history that I want to look at in somewhat more detail. The early seventeenth century saw both a significant turn in the theory of optics and independently of that the invention of the telescope, an instrument that would go one to revolutionise astronomy, della Porta played a minor roll in both of these things.

The invention of the telescope, by Hans Lipperhey, first became public in September 1608 and the role it would play in the future of astronomy became explosively obvious when Galileo published his Sidereus Nuncius in March 1610. Already in August 1609 della Porta wrote a letter to Federico Cesi claiming to have invented the telescope, he wrote:

I have seen the secret use of the eyeglass and it’s a load of balls [coglionaria] in any case it is taken from book 9 of my De Refractione.[1]

Here della Porta’s memory is faulty, he is after all over seventy years old, what he is referring to is not in the De Refractione but rather in Chapter 10 of Book 17 of Magia Naturalis (1589). Here we find the following suggestive description:

Concave Lenticulars will make one see most clearly things that are afar off.  But Convexes, things near at hand.  So you may use them as your sight requires.  With a Concave Lenticulars you shall see small things afar off very clearly.  With a Convex Lenticular, things nearer to be greater, but more obscurely.  If you know how to fit them both together, you shall see both things afar off, and things near hand, both greater and clearly.  I have much helped some of my friends, who saw things afar off, weakly, and what was near, confusedly, that they might see all things clearly.  If you will, you may.

The lens combination that della Porta describes here is indeed that of the Dutch or Galilean telescope but as van Helden say, and I agree with him, he is here describing some form of spectacles but not a telescope. Kepler, however, who owned a copy of Magia Naturalis credits him with being the inventor of the telescope in his Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) (1610), where he wrote that a recent Dutch invention had been made public years earlier in Magia Naturalis. In 1641 Pierre Gassendi stated that the actual invention had been made by chance by Metius [Jacob Metius (after 1571–1628), who applied for a patent for a telescope two weeks later than Lipperhey] the idea for a similar one had been published years earlier by della Porta.

Later della Porta would graciously admit that his fellow Lynx, Galileo, had achieved much more with his telescope that he, della Porta, could have ever have hoped to do, whilst not abandoning his claim to having first conceived of the telescope.

Della Porta also played a small role in the history of the camera obscura, describing the improvement to the image obtained by placing convex lens into the pinhole, something probably first suggested by Gerolamo Cardano. He also suggested, this time as the first to do so, using a concave mirror to project the image onto a sheet of paper to facilitate drawing it. The popularity of the Magia Naturalis did much to spread knowledge of the camera obscura and its utility as a drawing instrument. Interestingly della Porta compared his camera obscura with the human eye but, unlike Kepler, failed to make the connection that the lens focuses the image on the retina. He continued to believe like everybody before him that the image in perceived in the lens itself.

First published picture of camera obscura in Gemma Frisius’ 1545 book De Radio Astronomica et Geometrica Source: Wikimedia Commons

Della Porta’s role in the turn in the theory of optics is less disputed but not so widely discussed.  Ancient Greek optics was almost exclusively about theories of vision and when taken up and developed in the Islamic Middle Ages this too remained the emphasis. Ibn al-Haytham in his work on optics showed that one could combine an intromission theory of vision with the geometric optics of Euclid, Hero and Ptolemaeus, who had all propagated an extramission theory of vision. This was a major development in the history of optics. In the thirteenth century Robert Grosseteste introduced optics as a central element in both his vision of science and his theology, which led to it being established as a mathematical discipline on the medieval university. Shortly after Roger Bacon, John Peckham and Witelo introduced al-Haytham’s theories on optics into the medieval European mainstream founding what became known as the perspectivist school of optics. Strangely there were no real further developments in the theory of optics down to the end of the sixteenth century when Johannes Kepler, almost singlehandedly, turned the study of optics from one of theories of vision to one of theories of light, thereby ending the reign of the perspectivists. I say almost singlehandedly but he did have two predecessors, who made minor contributions to this turn, Francesco Maurolico (1494–1575) and della Porta.

One major flaw in the perspectivist theory was its treatment of spherical convex lenses and spherical concave mirrors, which said that the images created by them appeared at a single focus point; this is a fallacy. This flaw was in the theory from its inception in the thirteenth century and remained unchecked and uncorrected all the way down to the end of the sixteenth century. The fact that the don’t create their images at a single focal point is, of course, the cause of spherical aberration, something that would plague the construction of telescopes and microscopes well into the eighteenth century. The man who corrected this error in optical theory was della Porta.  Using a mixture of experiments and analytical light ray tracing he came very close to the correct solution an important step towards Kepler’s light ray based theory of optics.

Della Porta’s ray tracing analysis of the reflection of a spherical concave mirror A. Mark Smith, “From Sight to Light: The Passage from Ancient to Modern Optics”, Chicago University Press, 2015 p. 349

Giambattista della Porta is an interesting example of a widespread phenomenon in the history of science. In his own times he was highly respected and regarded, throughout Europe, as a leading natural Philosopher. His books, translated into many languages, were bestsellers and that even long after his death. Johannes Kepler was a fan and Galileo disliked him because he saw him as a serious rival for the position of top dog natural philosopher, a position that Galileo very much desired for himself. However, today most people have never even heard of him and if then he is largely dismissed as a minor irrelevance or even, because of the title of his major work, as some sort of anti-science occultist. But if historians really want to understand what was going on in the scientific community of Europe in the Early Modern Period then they have to take figures like della Porta seriously and not just focus on the ‘big names’ such as Kepler and Galileo.

[1] Quoted from David Freedberg, The Eye of the Lynx: Galileo, His Friends and the Beginnings of Modern Natural History, University of Chicago Press, Chicago and London, 2002, ppb. p. 101 Albert van Helden in his The Invention of the Telescope, American Philosophical Society, Philadelphia, 1977, Reprint, 2008, translates the phrase with coglionaria as …”it’s a hoax” pp. 44-45

The development of #histSTM in the early decades of the Dutch Republic, or Republic of the Seven United Netherlands, to give it its correct name, was quite extraordinary. Alongside the development of cartography and globe making, the most advanced in the whole of Europe, there were important figures such as the engineer, mathematician and physicist, Simon Stevin, the inventors of the telescope Hans Lipperhey and Jacob Metius, the mathematical father and son Rudolph and Willebrord Snel van Royan and Isaac Beeckman one of the founders of the mechanical philosophy in physics amongst others. However, one of the most strange and wonderful figures in the Netherlands during this period was, without doubt, the engineer, inventor, (al)chemist, optician and showman Cornelis Jacobszoon Drebbel (1571–1631).

Source: Wikimedia Commons

Drebbel is one of those larger than life historical figures, where it becomes difficult to separate the legends and the myths from the known facts, but I will try to keep to the latter. He was born to Jacob Drebbel an Anabaptist in Alkmaar in the province of North Holland. He seems not to have received much formal education but in about 1587 he started attending the Academy of the printmaker, draftsman and painter Hendrick Goltzius (1558–1617) in Haarlem also in North Holland.

Hendrick Goltzius – Self-Portrait, c. 1593-1594 – Google Art Project Source: Wikimedia Commons

Goltzius was regarded as the leading engraver in the Netherlands during the period and he was also an active alchemist. Drebbel became a skilled engraver under Goltzius’ instruction and also acquired an interest in alchemy. In 1595 he married Sophia Jansdochter Goltzius, Hendrick’s younger sister. They had at least six children of which four survived into adulthood. The legend says that Sophia’s prodigal life style drove Drebbel’s continual need to find better sources for earning money.

Drebbel’s town plan of Alkmaar 1597 Source: Wikimedia Commons

Drebbel initially worked as an engraver, cartographer and painter but somewhere down the line he began to work as an inventor and engineer.

Astronomy [from the series The Seven Liberal Arts]. Engraving by Drebbel Source: Wikimedia Commons

Also in 1598 he acquired a patent for Perpetuum mobile but which he, however, had not invented. The so-called Perpetuum mobile was a sort of clock, which was in reality powered in changes by the air temperature and air pressure had actually been invented by Jakob Dircksz de Graeff (1571–1638), an influential politician and natural philosopher, who was a friend of both Constantijn Huygens and René Descartes, and Dr Pieter Jansz Hooft (1574/5–1636) a politician, physician and schoolteacher.

Jakob Dircksz de Graeff Source: Wikimedia Commons

Pieter Jansz Hooft (1619), Attributed to Michiel van Mierevelt Source: Wikimedia Commons

Drebbel not only patented the Perpetuum mobile but also claimed to have invented it. His increasing reputation driven by this wonder machine earned his an invitation to the court of King James VI &I in London as the guest of the crown prince Henry in 1604. When on the court in London the Queen accidentally broke the Perpetuum mobile, Drebbel was unable to repair it.

The barometric clock of Cornelis Drebbel patented in 1598 and then known as “perpetuum mobile”. Print by Hiesserle von Choda (1557-1665) Source: Wikimedia Commons

At the court in London he was responsible for staging masques, a type of play with poetry, music, dance, and songs that was popular in the sixteenth and seventeenth centuries. He designed and built the stage sets and wonderful machines to enchant the audiences. Drebbel was by no means the only scientist-engineer to be employed to stage such entertainments during the Early Modern Period but he appears to have been very good at it. It was almost certainly Drebbel, who through his contacts imported from the Netherlands the first ever telescope to be seen in England, which was presented to James at the high point of a masque in 1609. He also built a magic lantern and a camera obscura with which he also entertained the members of the court.

Drebbel’s reputation grew to the point where he received an invitation to the court of the Holly Roman Empire, Rudolf II, in Prague in October 1610. Rudolf liked to surround himself with what might be termed wonder workers. Amongst those who had served in this capacity in Prague were Tycho Brahe, John Dee, Edward Kelley, Johannes Kepler and Jost Bürgi. There are no reports of any interactions between Drebbel and either Kepler or Bürgi, who were all on the court of Rudolf at the same time. In Prague he once again functioned as a court entertainer or showman.

AACHEN, Hans von – Portrait of Emperor Rudolf II Source: Wikimedia Commons

Rudolf was deposed by his brother Archduke Mathias in 1611and Drebbel was imprisoned for about a year. Following the death of Rudolf in 1612, Drebbel was released from prison and returned to London. Here, however, his situation was not as good as previously because Henry, his patron, had died in 1612. He kept his head above water as a lens grinder and instrument maker.

As a chemist Drebbel published his best-known written work Een kort Tractaet van de Natuere der Elemente (A short treatise of the nature of the elements) (Haarlem, 1621).

He was supposedly involved in the invention of the explosive mercury fulminate, Hg(CNO)₂, but this is disputed. He also developed other explosive mixtures. He invented a chicken incubator with a mercury thermostat to keep it at a constant, stable temperature. This is one of the earliest feedback controlled devices ever created. He also developed and demonstrated a functioning air conditioning system.

Error-controlled regulator using negative feedback, depicting Cornelius Drebbel’s thermostat-controlled incubator of circa 1600. Source: Wikimedia Commons

He didn’t himself exploit one of his most successful discoveries, one that he made purely by accident. He dropped a flask of aqua regia (a mixture of nitric and hydrochloric acid, normally used to dissolve gold) onto a tin windowsill and discovered that stannous chloride (SnCl₂) makes the colour of carmine (the red dye obtained from the cochineal insect) much brighter and more durable. Although Drebbel didn’t exploit this discovery his daughters Anna and Catherina and their husbands the brothers, Abraham and Johannes Sibertus Kuffler (a German inventor and chemist) did, setting up dye works originally in Leiden and then later in Bow in London. The colour was known as Colour Kuffler of Bow Dye and was very successful. Kuffler later continued his father-in-law’s development of self-regulating ovens that he demonstrated to the Royal Society.

In the early 1620s Constantijn Huygens, the father of Christiaan, came to London on a diplomatic mission. He made the acquaintance of Drebbel, who demonstrated his magic lantern and his camera obscura for the Dutch diplomat. Huygens was much impressed by his landsman and for a time became his pupil learning how to grind lenses, a skill that he might have passed onto his sons.

Constantijn Huygens (1596-1687), by Michiel Jansz van Mierevelt. Source: Wikimedia Commons

It is not known, who actually invented the microscope and it’s more than likely that the principle of the microscope was discovered by several people, all around the same time, who like Galileo looked through their Galilean or Dutch telescope the wrong way round. What, however, seems to be certain is that Drebbel is the first person known to have constructed a Keplerian telescope, that is with two convex lenses rather than a concave and a convex lens. As with all of his other optical instruments, Drebbel put on microscope demonstration introducing people to the microscopic world, as always the inventor as showman.

Drebbel’s most famous invention was without doubt his submarine. This is claimed to be the first-ever navigable submarine but has become the stuff of legends, how much of story is fact is difficult to assess. His submarine consisted of a wooden frame covered in leather, and one assumes waterproofed in someway; it was powered by oar.

Artistic representation of Drebbel’s submarine, artist unknown Source: Wikimedia Commons

It had bladders inside that were filled with water to enable the submarine to submerge; the bladders were emptied when the vessel was required to surface. In total between 1620 and 1624 Drebbel built three different vessels increasing in size. The final submarine had six oars and could carry up to sixteen passengers. Drebbel gave public demonstrations with this vessel on the river Thames. According to reports the vessel dived to a depth of four to five metres and remained submerged for three hours traveling from Westminster and Greenwich and back again. Assuming the reports to be true, there has been much speculation as to how fresh air was supplied inside the closed vessel. These speculations include a mechanical solution with some form of snorkel as well as chemical solutions with some sort of chemical apparatus to generate oxygen. It is also reported that Drebbel took King James on a dive under the Thames. Despite all of this Drebbel failed to find anybody, who would be prepared to finance a serious use of his submarine.

In the later 1620s Drebbel served the Duke of Buckingham as a military advisor but his various suggestions for weapons proved impractical and failed, the British blaming  the inventor and Drebbel blaming the English soldiers, finally ruining whatever reputation he still had. As already stated above towards the end of his life he was supposedly involved in a scheme to drain the Fens but the exact nature of his involvement remains obscure. Drebbel died in financial straights in 1633 in London, where he was scraping a living running a tavern on the banks of the Thames.

My Annus Mythologicus blog post was recently retweeted on Twitter in response to an inane tweet from Richard Dawkins and somebody questioned the reference in it that Newton was inspired to take up mathematics upon reading a book on astrology. This was not a nasty attack but a genuine statement on interest from somebody who had difficulty believing a man, who has been called the greatest mathematician ever, should have had anything to do with an astrology book. There is a sort of naïve belief that it is impossible for the people in the age of Newton, which is touted as the birth of the age of modern science and rationalism, could have had anything to do with the so-called occult sciences. This belief led many people, who should have known better, to try and sweep Newton’s very active engagement with alchemy under the carpet. During Newton’s lifetime astrology lost its status as a university discipline but was still all pervasive and permeated all aspects and levels of society. In what follows I will sketch some of the details of the role of astrology in the age of Newton.

Newton – 1677 Source: Wikimedia Commons

The Renaissance/Early Modern Period could with justification be called the golden age of astrology in Europe. This period was actually coming to an end during Newton’s lifetime, but astrology had by no means totally disappeared. That golden age began roughly with the beginning of the fifteenth century. During the first half of the century the humanist universities of Northern Italy and Poland created the first regular, dedicated chairs for mathematics and astronomy, which were in fact chairs for astrology, created to teach astrology to medical students. Teaching astrology to medical students was one of the principle obligations of the professors for mathematics at these universities and continued to be so well down into the seventeenth century. This trend continued with the creation of the first such chair in Germany, at the University of Ingolstadt, in the early 1470s. Astrological medicine, or iatromathematics to it is formal name was just one branch of astrology that flourished in this period.

Medical astrology was along with astrological meteorology considered to be a form of natural astrology and even those, who rejected natal astrology, for example, accepted the validity of natural astrology. Opposed to natural astrology was judicial astrology collective term for a group of other forms of astrology. Natal astrology, or genethliacal astrology, is the classic birth horoscope astrology that everybody thinks of, when they first hear the term astrology.  Other forms of judicial horoscope astrology are mundane astrology concerns the fate of nations etc., horary astrology answers question by casting a horoscope when the question is presented, and electional astrology, which is used to determine the most appropriate or auspicious time to carry out a planned action.

All these forms of astrology were widespread and considered valid by the vast majority during the fifteenth and sixteenth centuries. Astrology was firmly established in the fabric of European society and almost all of the active astronomers were also active astrologers right down to those astronomers, who were responsible for the so-called astronomical revolution. Georg Peuerbach, Regiomontanus, Tycho Brahe, Johannes Kepler and Galileo Galilei were all practicing astrologers and in fact owed much of the patronage that they received to their role as astrologer rather to that of astronomer, although the terms were interchangeable in this period. The terms Astrologus, Astronomus and Mathematicus were all synonym and all had astrologer in the modern sense as their principle meaning. Following the invention of moving type printing in about 1450, by far and away, the largest number of printed articles were astrological ephemera, almanacs, prognostica, and writing and single sheet wall calendars. A trend that continued all the way down to the eighteenth century.

During the fifteenth and sixteenth century efforts to give astrology a solid empirical footing were central to the activities of the astronomer-astrologers. Starting with Regiomontanus several astronomers believed that the inaccuracies in astrological forecasting were due to inaccuracies in the astronomy on which it was based. The reform of astronomy, for exactly this reason, was a principle motivation for the research programmes of Regiomontanus, Tycho Brahe and Wilhelm IV, Landgrave of Hessen-Kassel. Another approach was through astro-meteorology, with astronomer keeping weather diaries in which they noted the horoscope for the day and the actual weather on that day. They were looking for correlations, which they failed to find, but the practice led to the beginnings of modern weather forecasting. Notable weather diarists were Tycho Brahe and Johannes Werner. There were also attempts to find genuine correlations between birth charts and biographies of prominent people. Such biographical horoscope collections existed in manuscript before the invention of movable type printing. One of the largest, still extant, such manuscript collections is that of Erasmus Reinhold, a professor of mathematics at Wittenberg. The first such printed collection was that of Gerolamo Cardano, Libelli duo: De Supplemento Almanach; De Restitutione temporum et motuum coelestium; Item Geniturae LXVII insignes casibus et fortuna, cum expositione, printed and published by Johannes Petreius, specialist for astrological literature, in Nürnberg in 1543; the same year as he published Copernicus’ De revolutionibus.

During the first half of the seventeenth century the failures to find empirical evidence for astrology, a change in the philosophy underpinning science, astrology was justified with Aristotelian metaphysics, and changes in the ruling methodologies of mainstream medicine led to a decline in the academic status of astrology. Although a few universities continued teaching astrology for medical students into the eighteenth century, astrology as a university discipline largely ceased to exist by 1660. However, astrology was still very much woven into the fabric of European society.

Newton was born in 1642, which meant he grew up during the Civil War and the Interregnum. Astrology was used by both sides as propaganda during Civil War. Most famously William Lilly (1602–1681) publishing powerful pamphlets on behalf of the parliamentary side.

Portrait of Lilly, aged 45, now housed in the Ashmolean Museum at Oxford Source: Wikimedia Commons

This caused him major problem following the restitution. Lilly’s Christian Astrology (1647) was a highly influential book in the genre. Lilly was friends with many important figures of the age including Elias Ashmole (1617–1692) an antiquary who gave his name to the Ashmolean Museum of Art and Archaeology in Oxford, which was founded on his collection of books, manuscripts many objects. Ashmole was a passionate astrologer and a founding member of the London Society of Astrologers, which included many prominent intellectuals and existed from 1649 to 1658 and was briefly revived in 1682 by the astronomer, astrologer, printer and globemaker Joseph Moxon (1627–1691).

Joseph Moxon. Line engraving by F. H. van Hove, 1692. Source: Wikimedia Commons

Moxon successfully sold Ptolemaic globes in the last quarter of the seventeenth century, which were intended for astrologers not astronomers. Moxon’s Ptolemaic globes reflect an actual fashion in astrological praxis that could be described as back to the roots. In the middle of the seventeenth century many astrologers decide that astrology wasn’t working, as it should, because the methodology used had drifted to far from that described by Ptolemaeus in his Tetrabiblos. This movement was led by the Italian P. Placido de Titis (1603 – 1668) whose Physiomathematica sive coelestis philosophia published in 1650 with an improved 2^nd edition, 1675.

Alongside Moxon another English supporter of this back to the roots movement was John Partridge (1644–c. 1714), who published the first ever English translation of Ptolemaeus’ Tetrabiblos in 1704. Partridge was one of the most well-known astrologers of the age until he got skewered by Jonathan Swift in his infamous Isaac Bickerstaff letters beginning in 1708.

John Partridge. Line engraving by R. White, 1682 Credit: Wellcome Library, London. Wellcome Images Source: Wikimedia Commons http://wellcomeimages.org John Partridge. Line engraving by R. White, 1682, after himself. 1682 By: Robert WhitePublished: – Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0 http://creativecommons.org/licenses/by/4.0/

We always talk about the big names in the histories of astronomy and mathematics, but it is often more insignificant practitioners, who teach the next generation. In this Newton’s education in astronomy followed the norm and he learnt his astronomy from the books of Vincent Wing (1619–1668) Astronomia Britannica (1669)

Author portrait of Vincent Wing engraved by T. Cross (Frontispiece to the “Astronomia Britannica” of 1669) Source: Wikimedia Commons

and Thomas Streete (1621–1689) Astronomia Carolina, a new theorie of Coelestial Motions (1661).

They were the two leading astronomers in England during Newton’s youth and were both practicing astrologers. The two men were rivals and wrote polemics criticising the errors in the others work. Streete was friends with several other astronomers such as Flamsteed, who also used the Astronomia Carolina as his textbook, or Halley together with whom Streete made observation. Streete was Keplerian and it’s Kepler’s astronomy that he presents in his Astronomia Carolina , although he rejected Kepler’s second law and presented the theories of Boulliau and Ward instead. It is very probable that reading Streete was Newton’s introduction to Kepler’s theories.

Flamsteed, as already said, like Newton, a student of Steete, actually cast an electional horoscope for the laying of the foundation stone of the Royal Observatory in 1675 although he didn’t actually believe in astrology but was maintaining a well-established tradition.

Another example of this sort of half belief can be found in the attitude of Newton and Halley to comets. The two of them did far more than anybody else to establish comets as real celestial bodies affected by the same physical laws as all other celestial bodies and not some sort of message from the heavens. However, whilst neither of them believed in the truth of astrology both retained a belief that comets were indeed harbingers of doom.

As I said at the beginning Newton grew up and lived all of his life in a culture permeated with a belief in astrology. At the end of the seventeenth century astrological ephemera–almanacs, prognostica, etc.–were still a mass market phenomenon.

Zodiac man in EPB/61971/A: Goldsmith, 1679. An almanack for the year of our Lord God, 1679 (London: Printed by Mary Clark, for the Company of Stationers, 1679), leaf B2 recto. Image credit: Elma Brenner. Source:

A large annual fair such as Sturbridge in 1663, the largest annual fair in Europe, would have had a large selection of astrological literature on offer for the visitors; a public many of whose yearly almanac was the only printed book that they bought and read.

It is perfectly reasonable that a twenty-one year old Newton, just entering his second year at Cambridge university, stumbled across an astrological publication that awakened his mathematical curiosity as reported separately by both John Conduitt and Abraham DeMoirvre, in their memoirs based on conversations with Newton.

Eggolsheim is a small market town about twenty kilometres almost due north of Erlangen in the Fränkischen Schweiz (Franconian Switzerland).

Eggolsheim Source: Wikimedia Commons

The Fränkischen Schweiz is a hilly area with many rock faces and caves in Middle Franconia, to the north of Nürnberg that is very popular with tourists, day trippers, wanderers, rock-climbers and potholers. It also has lots of old churches and castles.

Fränkische Schweiz Source Wikimedia Commons

When I first moved to Middle Franconia the Fränkischen Schweiz had the highest density of private breweries of anywhere in the world. It also has many bierkeller that during the summer months attract large crowds of visitors at the weekend. Eggolsheim is these days probably best known for its bierkeller, but in the late fifteenth century it was the birthplace of the Renaissance mathematicus, Georg Hartmann, who would become one of the leading instrument makers in Renaissance Nürnberg in the early sixteenth century.

Georg Hartmann Source: Astronomie in Nürnberg

Hartmann was born on 9 February 1489. Unfortunately, as with so many Renaissance figures, we know nothing about his background or childhood. He matriculated at the university of Ingolstadt in 1503, which is where people from Franconia often studied as there were no University in either Nürnberg or Bamberg. Johannes Werner and Johannes Stabius, two other members of Nürnberg’s Renaissance mathematical community were graduates of Ingolstadt. In 1506, Hartmann transferred to the University of Köln, where he studied mathematics and theology, graduating in 1510. As was quite common during this period he completed his studies on a journey through Italy between 1510 and 1518. He spent several years in Rome, where he was friends with Andreas Copernicus, the older brother of Nicolas, who died in Rome, possibly of leprosy or syphilis in 1518.

In 1518 Hartmann arrived in Nürnberg, where he was appointed a vicar of the St. Sebaldus Church, one of the two parish churches of the city. Unlike the modern Anglican Church, where the vicar is the principal priest of a church, in the sixteenth century Catholic Church a vicar was a deputy or replacement priest with a special function appointed either permanently or temporarily. He might, for example, be appointed to sing a daily mass in the name of a rich deceased member of the parish, who left a stipend in his will to pay for this service, as another of Nürnberg’s mathematical community, Johannes Schöner, was appointed to do in Kirchehrenbach, also in the Fränkischen Schweiz, in 1523. We don’t know what Hartmann’s specific duties in the St. Sebaldus Church were. In 1522 he was also granted the prebend of the St. Walburga Chapel in Nürnberg.

St. Sebaldus in Nürnberg Source: Wikimedia Commons

This was a sinecure. It was not unusual for mathematici to receive sinecures from the Church to enable them to carry out their activities as mathematicians, instrument makers or cartographers in the service of the Church. This was certainly the case with Johannes Schöner, who was many years paid as a member of the St Joseph Beneficence in Bamberg but worked as mathematicus, printer and bookbinder for the Bishop. If this was actually so in Hartmann’s case is not known.

When he arrived in Nürnberg he became part of the, for the time, comparatively large community of mathematici, print makers, printer/publishers and instrument makers, which included both Werner and Stabius, the latter as a regular visitor, but both of whom died in 1522. I have written about this group before here and here. It also included Schöner, who only arrived in 1525, Erhard Etzlaub, Johann Neudörffer, Johannes Petreius and Albrecht Dürer.  Central to this group was Willibald Pirckheimer, who although not a mathematicus, was a powerful local figure–humanist scholar, merchant trader, soldier, politician, Dürer’s friend and patron–who had translated Ptolemaeus’ Geographia from Greek into Latin. Hartmann was friends with both Pirckheimer and Dürer, and acted as Schöner’s agent in Nürnberg, selling his globes in the city, during the time Schöner was still living in Kirchehrenbach. Like other members of this group Hartmann also stood in contact with and corresponded with many other scholars throughout Europe; the Nürnberger mathematici were integrated into the European network of mathematici.

Hartmann established himself as one of Nürnberg’s leading scientific instrument makers; he is known to have produced sundials, astrolabes, armillary spheres and globes. None of his armillary spheres or globes are known to have survived, although a few globe gores made by him are extant, an important factor when trying to assess the impact or range of an instrument maker, we can only work with that which endures the ravages of time. We know for example that Hartmann’s friend and colleague, Schöner, produced and sold large numbers of terrestrial and celestial globes but only a small handful of his globes are preserved.

A total of nine of Hartmann’s brass astrolabes are known to have survived and here Hartmann proved to be an innovator.

Hartmann astrolabe front

Hartmann astrolabe back

As far as is known, Hartmann was the earliest astrolabe maker to introduce serial production of this instrument. It is now assumed that he designed the instruments and then commissioned some of Nürnberg’s numerous metal workers to mass produce the separate parts of the astrolabe, which he them assembled and sold. Nine astrolabes might not seem a lot but compared to other known astrolabe makers, from whom often just one or two instruments are known, this is a comparatively large number. This survival rate suggests that Hartmann made and sold a large number of his mass-produced instruments.  

With his sundials the survival rate is much higher, there are seventy-five know Hartmann sundials in collection around the world. Hartmann made sundials of every type in brass, gold and ivory but is perhaps best known for his portable diptych sundials, a Nürnberg specialty. A diptych consists of two flat surfaces, usually made of ivory, connected by a hinge that fold flat to be put into a pocket. When opened the two surfaces are at the correct angle and joined by a thread, which functions as the dial’s gnomon. The lower surface contains a compass to help the user correctly orientate his dial during use.

Hartmann diptych sundial open

Hartmann diptych sundial closed

Open diptych sundial showing string gnomon and Hartmann’s name

Hartmann also made elaborate dials such as this ivory crucifix dial.

One thing that Hartmann is noted for is his paper instruments*. These are the elements for instrument printed on sheets of paper. These can be cut out and glued to thin wood backing to construct cheap but fully functioning instruments. Of course, the survival rates of such instruments are very low and in fact only one single paper astrolabe printed by Hartmann is known to have survived.

Hartmann paper astrolabe Source:History of Science Museum Oxford

However, we are lucky that several hundred sheets of Hartmann’s printed paper instruments have survived and are now deposited in various archives. There have been discussions, as to whether these were actually intended to be cut out and mounted onto wood to create real instruments or whether there are intended as sales archetypes, designed to demonstrate to customers the instruments that Hartmann would then construct out of ivory, brass or whatever.

Apart from designing and constructing instruments Hartman was obviously engaged in writing a book on how to design and construct instrument. Several partial manuscripts of this intended work exist but the book was never finished in his lifetime. The book however does reveal his debt as an instrument designer to Johannes Stöffler’s Elucidatio fabricae usuque astrolabii.

As a manufacturer of portable sun dials with built in compasses Hartmann also developed a strong interest in the magnetic compass. Whilst living in Rome he determined the magnetic declination of the city, i.e., how much a compass needle varies from true north in that location. Hartmann also appears to have been the first to discover magnetic dip or inclination, which information he shared with Duke Albrecht of Prussia in a letter in 1544, but he never published his discovery, so it is usually credited to the English mariner Robert Norman, who published the discovery in his The Newe Attractive, shewing The Nature, Propertie, and manifold Vertues of the Loadstone; with the declination of the Needle, Touched therewith, under the Plaine of the Horizon in 1581.

The only book that Hartmann did publish in his lifetime was an edition of John Peckham’s Perspectiva communis, the most widely used medieval optic textbook, which was printed by Johannes Petreius in 1542.

Hartmann died in Nürnberg in 1564 and was buried in the St Johannes graveyard, outside the city walls, where the graves of his friend Pirckheimer, Dürer and Petreius can also be found amongst many other prominent citizens of the Renaissance city.  

Hartmann’s grave Source: Astronomie in Nürnberg

Hartmann’s epitaph Source: Astronomie in Nürnberg

• For a detailed description of Hartmann’s printed paper instruments see: Suzanne Karr Schmidt, Interactive and Sculptural Printmaking in the Renaissance, Brill, 2017

Today is the winter solstice, which as I have explained on various occasions, in the past, is for me the natural New Year’s Eve/New Year’s Day rather than the arbitrary 31 December/1 January.

Obligatory Stonehenge winter solstice image

Today in also the occurrence of a so-called great conjunction in astronomy/astrology, which is when, viewed from the Earth, Jupiter and Saturn appear closest together in the night sky. Great conjunctions occur every twenty years but this one is one in which the two planets appear particularly close to each other.

Great conjunctions played a decisive role in the life of Johannes Kepler. As a youth Kepler received a state grant to study at the University of Tübingen. The course was a general-studies one to prepare the students to become Lutheran schoolteachers or village pastors in the newly converted Protestant state. Kepler, who was deeply religious, hoped to get an appointment as a pastor but when a vacancy came up for Protestant mathematics teacher in Graz, Michael Mästlin recommended Kepler and so his dream of becoming a pastor collapsed. He could have turned down the appointment but then he would have had to pay back his grant, which he was in no position to do so.

In 1594, Kepler thus began to teach the Protestant youths of Graz mathematics. He accepted his fate reluctantly, as he still yearned for the chance to serve his God as a pastor. Always interested in astronomy and converted to heliocentricity by Michael Mästlin, whilst still a student, he had long pondered the question as to why there were exactly six planets. Kepler’s God didn’t do anything by chance, so there had to be a rational reason for this. According to his own account, one day in class whilst explaining the cyclical nature of the great conjunctions in astronomy/astrology, which is when, viewed from the Earth, Jupiter and Saturn appear closest together in the night sky, he had a revelation.  Looking at the diagram that he had drawn on the board he asked himself, “What if his God’s cosmos was a geometrical construction and this was the determining factor in the number of planets?”

Kepler’s geometrical diagram of the cyclical nature of the great conjunctions in his Mysterium Cosmographicum Source: Linda Hall Library

Kepler determined from that point on in his life to serve his God as an astronomer by revealing the geometric structure of God’s cosmos. He first experimented with various regular polygons, inspired by the great conjunction diagram, but couldn’t find anything that fit, so he moved into three dimensions and polyhedra. Here he struck gold and decided that there were exactly six planets because their orbital spheres were separated by the five regular Platonic solids.

He published this theory in his first academic book, Mysterium Cosmographicum (lit. The Cosmographic Mystery, alternately translated as Cosmic Mystery, The Secret of the World) 1597. The book also contains his account of the revelation inspired by the great conjunction diagram. This was the start of his whole life’s work as a theoretical astronomer, which basically consisted of trying to fine tune this model.

In the early seventeenth century, Kepler was still deeply religious, a brilliant mathematician and theoretical astronomer, and a practicing astrologer. As an astrologer Kepler rejected the standard Ptolemaic sun sign i.e., Aquarius, Virgo, Gemini, etc., astrology. Normal horoscope astrology. Sun signs, or as most people call them star signs, are 30° segments of the circular ecliptic, the apparent path of the Sun around the Earth and not the asterisms or stellar constellations with the same names. Kepler developed his own astrology based entirely on planetary aspects, that is the angles subtended by the planets with each other on the ecliptic. (see the Wikipedia article Astrological aspect). Of course, in Kepler’s own astrology conjunctions play a major role.

Turning to the so-called Star of Bethlehem, the men from the east (no number is mentioned), who according to Matthew 2:2, followed the star were, in the original Greek, Magoi (Latin/English Magi) and this means they were astrologers and not the sanitised wise men or kings of the modern story telling. Kepler would have been very well aware of this. This led Kepler to speculate that what the Magoi followed was an important astrological occurrence and not a star in the normal meaning of the word. One should note that in antiquity all visible celestial objects were stars. Stars simple Asteres, planets (asteres) planētai wandering (stars) and a comet (aster) komētēs, literally long-haired (star), so interpreting the Star of Bethlehem as an astrological occurrence was not a great sketch.

His revelation in 1603 was that this astrological occurrence was a great conjunction and in fact a very special one, a so-called fiery trigon, one that links the three fire signs, Aries, Leo, Sagittarius.

Calculating backwards, Kepler the astronomer, determined that one such had occurred in 7 BCE and this was the star that the Magoi followed.

Whether Kepler’s theory was historically correct or an accepted view in antiquity is completely impossible to determine, is the Bible story of Jesus’ birth even true? In Kepler’s own time, nobody accepted his deviant astrology, so I very much doubt that many people accepted his Star of Bethlehem story, which he published in his De Stella Nova in Pede Serpentarii (On the New Star in the Foot of the Serpent Handler) in 1606.

I’m sure that a great conjunction on the date of the winter solstice has a very deep astrological significance but whether astrologers will look back and say, “Ah, that triggered this or that historical occurrence” only the future will tell.

I thank all of those who have read, digested and even commented upon my outpourings over the last twelve months and fully intend to do my best to keep you entertained over the next twelve. No matter which days you choose to celebrate during the next couple of weeks, in which way whatsoever and for what reasons, I wish all of my readers all the best and brace yourselves for another Renaissance Mathematicus Christmas Trilogy starting on 25 December.

We know that human beings have been traversing vast distances on the surface of the globe since Homo sapiens first emerged from Africa. However, in medieval Europe it would not have been uncommon for somebody born into a poor family never in their life to have journeyed more than perhaps thirty kilometres from their place of birth. Maybe a journey into the next larger settlement on market day or perhaps once a year to an even larger town for a fair on a public holiday. This might well have been Johannes Kepler’s fate, born as he was into an impoverished family, had it not been for his extraordinary intellectual abilities. Although he never left the Southern German speaking area of Europe (today, Southern Germany, Austria and the Czech Republic), he managed to clock up a large number of journey kilometres over the fifty-eight years of his life. In those days there was, of course, no public transport and in general we don’t know how he travelled. We can assume that for some of his longer journeys that he joined trader caravans. Traders often travelled in large wagon trains with hired guards to protect them from thieves and marauding bands and travellers could, for a fee, join them for protection. We do know that as an adult Kepler travelled on horseback but was often forced to go by foot due to the pain caused by his piles.[1]

It is estimated that in the Middle ages someone travelling on foot with luggage would probably only manage 15 km per day going up to perhaps 22 km with minimal luggage. A horse rider without a spare mount maybe as much as 40 km per day, with a second horse up to 60 km per day. I leave it to the reader to work out how long each of Kepler’s journeys might have taken him.

Johannes Kepler Source: Wikimedia Commons

Johannes’ first journey from home took place, when he attended the convent-school in Adelberg at the age of thirteen, which lies about 70 km due west of his birthplace, Weil der Stadt, and about 90 km, also due west of Ellmendigen, where his family were living at the time.

Adelberg Convent Source: Wikimedia Commons

His next journey took place a couple of years later when he transferred to the Cistercian monastery in Maulbronn about 50 km north of Weil der Stadt and 30 west of Ellmendingen.

Maulbronn Monastery Source: Wikimedia Commons

Finished with the lower schools in 1589, he undertook the journey to the University of Tübingen, where he was enrolled in the Tübinger Stift, about 40 km south of Weil der Stadt.

The Evangelical Tübinger Stift on the banks of the Neckar Source: WIkimedia Commons

Johannes’ first really long journey took place in 1594, when on 11 April he set out for Graz the capital city of Styria in Austria to take up the posts of mathematics teacher in the Lutheran academy, as well as district mathematicus, a distance of about 650 km. The young scholar would have been on the road for quite a few days.

Graz, Mur und Schloßberg, Georg Matthäus Vischer (1670) Source: Wikimedia Commons

Although he only spent a few years in Graz, Kepler manged at first to stabilise his life even marrying, Barbara Müller, and starting a family. However, the religious conflicts of the period intervened and Kepler, a Lutheran Protestant living in a heavily Catholic area became a victim of those conflicts. First, the Protestants of the area were forced to convert or leave, which led to the closing of the school where Kepler was teaching and his losing his job. Because of his success as astrologer, part of his duties as district mathematicus, Kepler was granted an exception to the anti-Protestant order, but it was obvious that he would have to leave. He appealed to Tübingen to give him employment, but his request fell on deaf ears. The most promising alternative seemed to be to go and work for Tycho Brahe, the Imperial Mathematicus, currently ensconced in the imperial capital, Prague, a mere 450 km distant.

Prague in the Nuremberg Chronicle 1493 Source: Wikimedia Commons

At first Kepler didn’t know how he would manage the journey to Prague to negotiate about possible employment with Tycho. However, an aristocratic friend was undertaking the journey and took Johannes along as a favour. After, several weeks of fraught and at times downright nasty negotiations with the imperious Dane, Kepler was finally offered employment and with this promise in his pocket he returned to Graz to settle his affairs, pack up his household and move his family to Prague. He made the journey between Graz and Prague three times in less than a year.

Not long after his arrival in Prague, with his family, Tycho died and Kepler was appointed his successor, as Imperial Mathematicus, the start of a ten year relatively stable period in his life. That is, if you can call being an imperial servant at the court of Rudolf II, stable. Being on call 24/7 to answer the emperor’s astrological queries, battling permanently with the imperial treasury to get your promised salary paid, fighting with Tycho’s heirs over the rights to his data. Kepler’s life in Prague was not exactly stress free.

1608 saw Johannes back on the road. First to Heidelberg to see his first major and possibly most important contribution to modern astronomy, his Astronomia Nova (1609), through the press and then onto the book fair in Frankfurt to sell the finished work, that had cost him several years of his life. Finally, back home to Prague from Frankfurt. A total round-trip of 1100 km, plus he almost certainly took a detour to visit his mother somewhere along his route.

Back in Prague things began to look rather dodgy again for Kepler and his family, as Rudolf became more and more unstable and Johannes began to look for a new appointment and a new place to live. His appeals to Tübingen for a professorship, not an unreasonable request, as he was by now widely acknowledged as Europe’s leading theoretical astronomer, once again fell on deaf ears. His search for new employment eventually led him to Linz the capital city of Upper Austria and the post of district mathematicus. 1612, found Johannes and his children once again on the move, his wife, Barbara, had died shortly before, this time transferring their household over the comparatively short distance of 250 km.

Linz anno 1594 Source: Wikimedia Commons

Settled in Linz, Kepler married his second wife, Susanna Reuttinger, after having weighed up the odds on various potential marriage candidates and the beginning of a comparative settled fourteen-year period in his life. That is, if you can call becoming embroiled in the Thirty Years War and having your mother arrested and charged with witchcraft settled. His mother’s witchcraft trial saw Johannes undertaking the journey from Linz to Tübingen and home again, to organise and conduct her defence, from October to December in 1617 and again from September 1620 to November 1621, a round trip each time of about 1,000 km, not to forget the detours to Leonberg, his mother’s home, 50 km from Tübingen, from where he took his mother, a feeble woman of 70, back to Linz on the first journey.

In 1624, Johannes set out once again, this time to Vienna, now the imperial capital, to try and obtain the money necessary to print the Rudolphine Tables from Ferdinand II the ruling emperor, just 200 km in one direction. Ferdinand refused to give Kepler the money he required, although the production of the Rudolphine Tables had been an imperial assignment. Instead, he ordered the imperial treasury to issues Kepler promissory notes on debts owed to the emperor by the imperial cities of Kempten, Augsburg and Nürnberg, instructing him to go and collect on the debts himself. Kepler returned to Linz more than somewhat disgruntled and it is not an exaggeration that his life went downhill from here.

Kepler set out from Linz to Augsburg, approximately 300 km, but the Augsburg city council wasn’t playing ball and he left empty handed for Kempten, a relatively short 100 km. In Kempten the authorities agreed to purchase and pay for the paper that he needed to print the Rudolphine Tables. From Kempten he travelled on to Nürnberg, another 250 km, which he left again empty handed, returning the 300 km to Linz, completing a nearly 1,000 km frustrating round trip that took four months.

In 1626, the War forced him once again to pack up his home and to leave Linz forever with his family. He first travelled to Regensburg where he found accommodation for his family before travelling on to Ulm where he had had the paper from Kempten delivered so that he could begin printing, a combined journey of about 500 km. When the printing was completed in 1627, having paid the majority of the printing costs out of his own pocket, Kepler took the entire print run to the bookfair in Frankfurt and sold it in balk to a book dealer to recoup his money, another journey of 300 km. He first travelled back to Ulm and then home to his family in Regensburg, adding another 550 km to his life’s total. Regensburg was visited by the emperor and Wallenstein, commander in chief of the Catholic forces, and Kepler presented the Tables to the Emperor, who received them with much praise for the author.

In 1628, he entered the service of Wallenstein, as his astrologer, moving from Regensburg to Wallenstein’s estates in the Dutchy of Sagan, yet another 500 km. In 1630, the emperor called a Reichstag in Regensburg and on 8 October Kepler set out on the last journey of his life to attend. Why he chose to attend is not very clear, but he did. He journeyed from Zagan to Leipzig and from there to Nürnberg before going on to Regensburg a total of 700 km. He fell ill on his arrival in Regensburg and died 15 November 1630.

Regensburg Nuremberg Chronicle 1493 Source: Wikimedia Commons

The mathematical abilities of the young boy born to an impoverish family in Weil der Stadt fifty-eight-years earlier had taken him on a long intellectual journey but also as we have seen on a long physical one, down many a road.

[1] I almost certainly haven’t included all of the journeys that Kepler made in his lifetime, but I think I’ve got most of the important ones. The distances are rounded up or down and are based on the modern distances by road connecting the places travelled to and from. The roads might have run differently in Kepler’s day.