Renaissance Science – VIII

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

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

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

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

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

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


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

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

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


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

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


Image of Abū al-Wafā Source: Wikimedia Commons

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

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


Richard of Wallingford Source: Wikimedia Commons

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

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

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


A 1584 edition of Regiomontanus’Tabulae Directionum Source

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


Title page Epitoma in Almagestum Ptolemae Source: Wikimedia Commons

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

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


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


Source: Wikimedia Commons

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


Source:. Wikimedia Commons

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


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

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

Leave a comment

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

The alchemist, who became a cosmographer

As an Englishman brought up on tales, myths and legends of Francis Drake, Walter Raleigh, Admiral Lord Nelson, the invincible Royal Navy and Britannia rules the waves, I tend not to think about the fact that Britain was not always a great seafaring nation. As an island there were, of course, always fisher boats going about their business in the coastal waters and archaeology has shown us that people have been crossing the strip of water between Britain and the continent, as long as the island has been populated. However, British sailors only really began to set out onto the oceans for distant lands in competition to their Iberian brethren during the Early Modern Period. Before the start of these maritime endeavours there was a political movement in England to get those in power to take up the challenge and compete with the Spanish and the Portuguese in acquiring foreign colonies, gold, silver and exotic spices. One, today virtually unknown, man, whose writings played a not insignificant role in this political movement was the alchemist Ricard Eden[1] (c. 1520–1576).

Richard Eden[2] was born into an East Anglian family of cloth merchants and clerics, the son of George Eden a cloth merchant. He studied at Christ’s College Cambridge (1534–1537) and then Queen’s College, where he graduated BA in 1538 and MA in 1544. He studied under Sir Thomas Smith (1533–1577) a leading classicist of the period, who was also politically active and a major supporter of colonialism, which possibly influenced Eden’s own later involvement in the topic.


A c. 19th-century line engraving of Sir Thomas Smith. Source: Wikimedia Commons

Through Smith, Eden was introduced to John Cheke (1514–1557), Roger Ascham (c. 1515–1568) and William Cecil (1520–1598), all of whom were excellent classicists and statesmen. Cecil would go on under Elizabeth I to become the most powerful man in England. From the beginning Eden moved in the highest intellectual and political circles.

After leaving Cambridge Eden was appointed first to a position in the Treasury and then distiller of waters to the royal household, already indicating an interest in and a level of skill in alchemy. Eden probably acquired his interest in alchemy from his influential Cambridge friends, who were all eager advocates of the art. However, he lost the post, probably given to someone else by Somerset following Henry VIII’s death in 1547 and so was searching for a new employer or patron.

Through a chance meeting he became acquainted with the rich landowner Richard Whalley, who shared his interest in alchemy. Whalley provided him with a house for his family and an income, so that he could devote himself to both medicinal and transmutational alchemy. His activities as an alchemist are not of interest here but one aspect of his work for Whalley is relevant, as it marked the beginning of his career as a translator.

Whalley was obviously also interested in mining for metal ores, because he commissioned Eden to translate the whole of Biringuccio’s Pirotechnia into English. Although he denied processing any knowledge of metal ores, Eden accepted the commission and by 1552 he had completed twenty-two chapters, that is to the end of Book 2. Unfortunately, he lent the manuscript to somebody, who failed to return it and so the project was never finished. In fact, there was no English translation of the Pirotechnia before the twentieth century. Later he produced a new faithful translation of the first three chapters dealing with gold, silver and copper ores, only omitting Biringuccio’s attacks on alchemy, for inclusion, as we shall see, in one of his later works.


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

In 1552, Eden fell out with Whalley and became a secretary to William Cecil. It is probable the Cecil employed him, as part of his scheme to launch a British challenge to the Iberian dominance in global trade. In his new position Eden now produced a translation of part of Book 5 of Sebastian Münster’s Cosmographia under the title A Treatyse of the New India in 1553. As I explained in an earlier blog post Münster’s Cosmographia was highly influential and one of the biggest selling books of the sixteenth century.


This first cosmographical publication was followed in 1555 by his The Decades of the newe worlde or west India, containing the nauigations and conquests of the Spanyardes… This was a compendium of various translations including those three chapters of Biringuccio, probably figuring that most explorers of the Americas were there to find precious metals. The main parts of this compendium were taken from Pietro Martire d’Anghiera’s De orbe novo decades and Gonzalo Fernández de Oviedo y Valdés’ Natural hystoria de las Indias.


Source: The British Library

Pietro Martire d’Anghiera (1457–1526) was an Italian historian in the service of Spain, who wrote the first accounts of the explorations of Central and South America in a series of letters and reports, which were published together in Latin. His De orbe novo (1530) describes the first contacts between Europeans and Native Americans.


Source: Wikimedia Commons

Gonzalo Fernández de Oviedo y Valdés (1478–1557) was a Spanish colonist, who arrived in the West Indies a few years after Columbus. His Natural hystoria de las Indias (1526) was the first text to introduce Europeans to the hammock, the pineapple and tobacco.


MS page from Oviedo’s La Natural hystoria de las Indias. Written before 1535, this MS page is the earliest known representation of a pineapple Source: Wikimedia Commons

Important as these writings were as propaganda to further an English involvement in the new exploration movement in competition to the Iberian explorers, it was probably Eden’s next translation that was the most important.

As Margaret Schotte has excellently documented in her Sailing School (Johns Hopkins University Press, 2019) this new age of deep-sea exploration and discovery led the authorities in Spain and Portugal to the realisation that an active education and training of navigators was necessary. In 1552 the Spanish Casa de la Contratación established a formal school of navigation with a cátedra de cosmografia (chair of cosmography). This move to a formal instruction in navigation, of course, needed textbooks, which had not existed before. Martín Cortés de Albacar (1510–1582), who had been teaching navigation in Cádiz since 1530, published his Breve compendio de la sphere y de la arte de navegar in Seville in 1551.


Retrato de Martín Cortés, ilustración del Breve compendio de la sphera y de la arte de navegar, Sevilla, 1556. Biblioteca Nacional de España via Wikimedia Commons

In 1558, an English sea captain from Dover, Stephen Borough (1525–1584), who was an early Artic explorer, visited Seville and was admitted to the Casa de la Contratación as an honoured guest, where he learnt all about the latest instruments and the instruction for on going navigators. On his return to England, he took with him a copy of Cortés’ Breve compendio, which he had translated into English by Richard Eden, as The Arte of Navigation in 1561. This was the first English manual of navigation and was immensely popular going through at least six editions in the sixteenth century.


In 1562, Eden became a companion to Jean de Ferrières, Vidame of Chartres, a Huguenot aristocrat, who raised a Protestant army in England to fight in the French religious wars. Eden, who was acknowledged as an excellent linguist, stayed with de Ferrières until 1573 travelling extensively throughout France and Germany. Following the St. Batholomew’s Day massacre, which began in the night of 23–24 August 1572, Eden together with de Ferrières party fled from France arriving in England on 7 September 1573. At de Ferrières request, Elizabeth I admitted Eden to the Poor Knights of Windsor, a charitable organisation for retired soldiers, where he remained until his death in 1576.

After his return to England Eden translated the Dutch musician and astrologer, Jean Taisnier’s Opusculum perpetua memoria dignissimum, de natura magnetis et ejus effectibus, Item de motu continuio, which was a plagiarism of Petrus Peregrinus de Maricourt’s (fl. 1269) Epistola de magnete and a treatise on the fall of bodies by Giambattista Benedetti (1530–1590) into English.


This was published posthumously together with his Arte of Navigation in 1579. His final translation was of Ludovico de Varthema’s (c. 1470–1517) Intinerario a semi-fictional account of his travels in the east. This was published by Richard Willes in The History of Travayle an enlarged version of his Decades of the newe worlde in 1577.

Eden’s translations and publications played a significant role in the intellectual life of England in the sixteenth century and were republished by Richard Hakluyt (1553–1616) in his The Principal Navigations, Voiages, Traffiques and Discoueries of the English Nation (1589, 1598, 1600), another publication intended as propaganda to promote English colonies in America.


Unlike Sebastian Münster or Richard Hakluyt, Eden has been largely forgotten but he made important and significant contributions to the history of cosmography and deserves to be better known.

[1] I want to thank Jenny Rampling, whose book The Experimental Fire, which I reviewed here, made me aware of Richard Eden, although, I have to admit, he turns up, managing to slip by unnoticed in other books that I own and have read.

[2] The biographical details on Eden are mostly taken from the ODNB article. I would like to thank the three wonderful people, who provided me with a pdf of this article literally within seconds of me asking on Twitter

Leave a comment

Filed under Early Scientific Publishing, History of Cartography, History of Navigation

Renaissance Science – VII

In the last post we looked at the European re-invention of moveable-type and the advent of the printed book, which played a highly significant role in the history of science in general and in Renaissance science in particular. I also emphasised the various print technologies developed for reproducing images, because they played a very important role in various areas of the sciences during the Renaissance, as we shall see in later posts in this series. Parallel to these technological developments there were two major developments in the arts, which would have a very major impact on the illustration in Renaissance science publications, the (re?)-discovery of linear perspective and the development of naturalism.

Linear perspective is the geometrical method required to reproduce three-dimensional objects realistically on a two-dimensional surface; the discovery or invention of linear perspective is usually attributed to the Renaissance artist-engineer and architect, Filippo Brunelleschi (1377–1446), about whom more below, but already in the Renaissance it was often referred to as a re-discovery. This Renaissance re-discovery trope was very much in line with the general Renaissance concept of a rebirth of classical knowledge. Here the belief that linear perspective was a re-discovery is based on the concept of skenographia in ancient Greek theatre, which consists of using painted flat panels on a stage to give the illusion of depth. This is mentioned in Aristotle’s Poetics (c. 335 BCE) a general work on drama. More importantly, from a Renaissance perspective, it is briefly described in Vitruvius’ De Architectura libri dicem (Ten Books on Architecture) from the first century BCE. Once again, as we shall see later, Vitruvius’ De Architectura played a central role in Renaissance thought. In his Book 7 On Finishing, Vitruvius wrote in the preface:

In Athens, when Aechylus was producing tragedies, Agathachus was the first to work for the theatre and wrote a treatise about it. Learning from this, Democritus and Anaxagoras wrote on the same subject, namely how the extension of rays from a certain established centre point ought to correspond in a natural ration to the eyes’ line of sight, so that they could represent the appearance of buildings in scene painting, no longer by some uncertain method, but precisely, both the surfaces that were depicted frontally, and those that seemed either to be receding or projecting[1].

Of course, ancient Greek theatre flats no longer exist, but some Greek and many more Roman wall paintings have survived, which very obviously display some degree of perspective. However, closer analysis of these paintings has shown that while they are in fact constructed on some sort of perspective scheme it is not the linear perspective that was developed in the Renaissance.


Villa of P. Fannius Synistor Cubiculum M alcove Panel with temple at east end of the alcove, the north end of the east wall Middle of the first century B.C. Boscoreale (Pompeii), Italy Source:

Although linear perspective was not strictly a re-discovery, it also didn’t emerge at the beginning of the fifteenth century out of thin air. Already, more than a century earlier the so-called proto-Renaissance artists, in particular Giotto (1267–1337), were producing paintings that displayed depth based on a mathematical model, when not quite that of linear perspective and not consistent.


‘Jesus Before the Caïf’, by Giotto (1305). The ceiling rafters show the Giotto’s introduction of convergent perspective. B. Detailed analysis, however, reveals that the ceiling has an inconsistent vanishing point and that the Caïf’s dais is in parallel perspective, with no vanishing point. Source

At the beginning of the fifteenth century, the Renaissance sculptor Lorenzo Ghiberti (1378–1455) used linear perspective in the panels of the second set of bronze doors he was commissioned to produce for the Florence Baptistry, dubbed the Gates of Paradise by Michelangelo.


A panel of Adam and Eve in Ghiberti’s “Gate’s of Paradise”. Photo by Thermos.Source: Wikimedia Commons

As already stated, Brunelleschi is credited with having invented linear perspective according to his biographer Antonio di Tuccio Manetti (1423–1497), he compared the reality of his painting using linear perspective of the Florence Baptistery with the building itself using mirrors.


Filippo Brunelleschi in an anonymous portrait of the 2nd half of the 15th century (Louvre, Paris) via Wikimedia Commons

According to Manetti, he used a grid or set of crosshairs to copy the exact scene square by square and produced a reverse image. The results were compositions with accurate perspective, as seen through a mirror. To compare the accuracy of his image with the real object, he made a small hole in his painting, and had an observer look through the back of his painting to observe the scene. A mirror was then raised, reflecting Brunelleschi’s composition, and the observer saw the striking similarity between the reality and painting. Both panels have since been lost. (Wikipedia)


Brunelleschi left no written account of how he constructed his painting and the first written account we have of the geometry of linear perspective is from another Renaissance humanist artist and architect, Leon Battista Alberti (1404–1472) in his book On painting, published in Tuscan dialect as Della Pittura in 1436/6 and in Latin as De pictura first in 1450, although the Latin edition was also written in 1435. The book contains a comparatively simple account of the geometrical rudiments of linear perspective.


Presumed self-portrait of Leon Battista Alberti Source: Wikimedia Commons


Figure from the 1804 edition of Della pittura showing the vanishing point Source: Wikimedia Commons

A much fuller written account of the mathematics of linear perspective was produced in manuscript by the painter Piero della Francesca (c. 1415–1492), De Prospectiva pingendi (On the Perspective of painting), around 1470-80.


An icosahedron in perspective from De Prospectiva pingendi Source: Wikimedia Commons

He never published this work, but his ideas on perspective were incorporated in his book Divina proportione by the mathematician Luca Pacioli (c. 1447–1517), written around 1498 but first published in 1509. Pacioli’s book also plagiarised another manuscript of della Francesca’s on perspective, his De quinque corporibus regularibus (The Five Regular Solids).


Piero della Francesca by Giorgio Vasari Source: Wikimedia Commons

Mathematicians and artists continued over the centuries to write books describing and investigating the geometrical principles of linear perspective the most notable of, which during the Renaissance was Albrecht Dürer’s Underweysung der Messung mit dem Zirckel und Richtscheyt (Instructions for Measuring with Compass and Ruler) published in 1525, which contains the first account of two point perspective. Dürer is credited with introducing linear perspective into the Northern Renaissance.


Dürer, draughtsman Making a Perspective Drawing of a Reclining Woman

Naturalism is, as its name would suggest, the development in art to depict things naturally i.e., as we see them with our own eyes. Linear perspective is actually one aspect of naturalism. In her The Body of the Artisan, Pamala H. Smith writes the following:

It is difficult to know where to begin a discussion of naturalism (which can encompass the striving for “verisimilitude,” “illusionism,” “realism,” and the “imitation of nature”) in the early modern period, for the secondary literature in art history alone is vast. David Summers has defined naturalism as the attempt to make the elements of the artwork (in his account primarily painting) coincide with the elements of the optical experience[2]. (Her endnote: Summers, The Judgement of Sense, p. 3)

Smith also quotes in this context Alberti, “[He] put it in about 1435, making a picture that was an “open window” through which the world was seen.[3]” There is no neat timeline of events for Naturalism, as I have recreated above for linear perspective. Smith gives as her first historical example of Naturalism the so-called Carrara Herbal produced in Padua around 1400, with till then unknown, for this type of literature, unprecedented naturalism in its illustrations.[4]


Violet plant – Carrara Herbal (c.1400), f.94 – BL Egerton MS 2020.jpg Source: Wikimedia Commons

As we will see in a later blog post it was in natural history, in particular in botany, that naturalism made a major impact in printed scientific illustrations.

Although, they still hadn’t really adopted the techniques of linear perspective it was the artists of the Northern Renaissance, rather than their Southern brethren, who first extensively adopted Naturalism, most notably Jan van Eyck (before 1390 – 1441). An attribute of the Naturalism of these painters was the use of mirrors in their paintings to symbolise the reflection of nature or reality.


Jan van Eyck Detail with mirror and signature; Arnolfini Portrait, 1434 Source: Wikimedia Commons

Once again, we meet here Albrecht Dürer, who is justifiably renowned for his lifelike reproduction of various aspects of nature in his artwork.


Albrecht Dürer Young Hare, (1502), Source: Wikimedia Commons


Albrecht Dürer Great Piece of Turf, 1503 Source: Wikimedia commons

It is important to note here that although this picture looks very realistic, when first viewed, it is actually an example of illusion or hyperrealism. There are none of the old or withered plants that such a scene in nature would inevitably have. Also none of the plants obscure other plants with their shadows, as they would in reality. What Dürer delivers up here is an idealised naturalism, almost a contradiction in terms. This conflict between real naturalism and the demands of clear to interpret illustrations would play a significant role in the illustrations of Renaissance books on natural history.

However, as we shall see in later posts both linear perspective and Naturalism made a massive impact on the scientific and technological book illustrations that were produced during the Renaissance.

[1] Vitruvius, Ten Books on Architecture, Eds. Ingrid D. Rowland & Thomas Noble Howe, CUP, 1999 p. 86

[2] Pamala H. Smith, The Body of the Artisan: Art and Experience in the Scientific Revolution, University of Chicago Press, 2004 p. 9

[3] Smith, p. 33

[4] Smith p. 33

1 Comment

Filed under Book History, History of science, Renaissance Science

One Thousand and One Blog Posts

Because evolution has given human beings ten fingers, most of the time, we use a ten based positional value number system, in which the positions are powers of ten. This also means that we have a strong tendency to note, to acknowledge and even to celebrate the points when lists or collections reach multiples or powers of ten. For example, we tend to think that somebody’s fortieth birthday is more significant than their thirty-ninth or forty-first. We also make a big deal with major celebrations when something reaches a ten to the power of two, that is a hundredth, anniversary and even more of a big deal by a ten to the power of three, that is a thousandth, anniversary. The only real exception to this, are legal anniversaries, coming of age for example, or multiples of twenty-five because these are viewed as the significant fractions of one hundred, one quarter, one half, etc.

Because I call myself a history of science storyteller, I have decided instead to borrow the title of what is perhaps the most famous collection of stories or tales, One Thousand and One Nights, and celebrate instead of the thousandth, the one thousand and first Renaissance Mathematicus blog post.


Having actually written the last sentence, I have to take a deep breath, have I really written one thousand blog posts? Is this really the one thousand and first? The answer to both questions is, according to the WordPress statistics for this blog, a definitive yes, although I don’t quite really believe it. As I have pointed out previously, although I have posted one thousand posts here, I didn’t actually write all of them, as several of them were guest posts. However, I have written more guest posts for other peoples’ blogs than there are guest posts here, so yes, I have actually written more than one thousand blog posts.

As I have also pointed out in the past, because I suffer from both adult AD(H)D and dysgraphia, I was functionally analphabet for most of my life, literally too scared to put pen to paper or fingers to keyboard. I started this blog as personal therapy to help myself to overcome that fear and teach myself to write; in this I think I have succeeded.

There was, however, a second reason or, better said, motivation for beginning this journey into the written word. I had spent the best part of half a century absorbing, contemplating and trying to apprehend the histories of mathematics and the mathematical sciences. I even spent ten years at university studying them. During that time, I had formulated my own ideas about numerous aspects of those histories and blogging would supply me with a medium to express those ideas in public if only to a very limited public. You might say, it was opening a safety valve to reduce the accumulated pressure. A sort of intellectual Primal Scream therapy.

Now, I didn’t just sit down, turn on the metaphorical tap in my brain and pour out finished history of science copy. When I conceive a potential theme for a blog post, I set out to refresh and to extend my knowledge of the topic in question, so writing this blog also became a learning process for me. Conceiving, researching and writing approximately fifteen hundred words on a history of science topic once a week is as good as any university education.

What I’m now going to say is one of the biggest clichés in the history of human thought, but clichés are very often clichés simply because they are true. The more that I have learnt over the years, writing this blog, the more I become aware of how little I actually know. Knowledge is a vast ocean and at best I have dabbled my toes in the ripples on one of its shores. The compulsion to maybe one day be able to swim in that ocean is what keeps me going. I don’t know where that compulsion comes from, it has simply always been there.


A desire to plunge right in

To close, I would just like to thank all of those who have been along for the ride. As I have stated in the past, I don’t write for you or anybody else, for that matter, I write for myself but I am truly grateful for the fact that you find my scribblings worth reading.


Filed under Autobiographical

Tracking the alchemical gospel through Medieval and Early Modern England

This is going to be yet another of those book reviews where I start by explaining how much the history of science has changed since I first became engaged in it, in my youth. Back in the not so good old days, the so-called occult sciences we not really considered part of the history of science by the mainstream of the discipline. In fact, they were often viewed as somehow dirty and degrading. When it first began to be suggested that Isaac Newton was an alchemist, Rupert Hall, then a leading historian of science, insisted that Newton’s activities had actually been chemistry, motivated by his work as boss of the Royal Mint and definitely not alchemy. I of course, not knowing better, stuck to the mainstream and avoided the occult sciences. Something, I now regard as rather strange given my very active advocacy for the history of astrology if one wishes to understand the history of astronomy.

As far as the history of alchemy is concerned, my eyes were opened by Betty Jo Teeter Dobbs’ The Foundations of Newtons Alchemy, or the Hunting of the Green Lyon (CUP; 1976), which I read with growing amazement and enthusiasm, sometime in the early 1980s. My memory tells me that the book caused a minor sensation in the history of science world, revealing as it did, for the first time with academic rigour, the extent of Newton’s involvement with this distinctly non-scientific discipline. The effect was even greater when Richard Westfall, Newton’s greatest biographer, gave more than tacit support to Dobbs’ views on Newton’s alchemical activities. Alchemy was now a serious subject for historians of science to pursue.

Over the succeeding decades the history of alchemy became an accepted part of the history of science with excellent publications from first class historians such as Bruce Moran, Tara Nummedal, Pamala H. Smith, as well as William R. R. Newman and Lawrence Principe both together and separately. For somebody new to the discipline I can recommend Lawrence Principe’s Secrets of Alchemy (University of Chicago Press, 2013), as an excellent general introduction. William Newman’s newest book is Newton the Alchemist: Science, Enigma, and the Quest for Nature’s Secret Fire (Princeton University Press, 2018). One of the stars of the new generation of historians of alchemy is Jennifer M. Rampling, whose latest book, The Experimental Fire: Inventing English Alchemy 1300–1700[1] is the subject of this book review.


Rampling’s book delivers exactly what the title promises. She takes her reader along the winding path that the study and practice of alchemy took in England from its early establishment during the reign of Edward III (1312–1377) up to end of the seventeenth century, when those stalwart founders of modern science, Robert Boyle and Isaac Newton were practicing alchemists.

Before she takes the reader through four hundred years of English alchemy history, Rampling prefaces the journey with a discussion of the multiple meanings, conflicting and oft contradictory meanings, shifting meanings and evolving meanings of various central alchemical terms, most notably mercury and the stone, as in the philosophers stone. Her careful analysis demonstrates the problems involved in trying to understand alchemical writings, not only for the modern reader or historian but also for the alchemical practitioners throughout history. This chapter also serves as an introduction to the central aspect of the book, what the author calls, ‘practical exegesis’. This is the process by which the practicing alchemists reads, interprets and attempts to convert into practice, the authoritative texts that allude and hint rather than instruct openly and clearly. Throughout her narrative Rampling shows how each generation of English alchemists made great efforts to produce a consistent, at least internally rational reading of the texts and authorities that they are working with.

Rampling distinguishes two main types of practicing alchemists. On the one hand we have the philosophical alchemist, who presents long complex interpretations of the authoritative texts to demonstrate his mastery of the secrets that they contain. Such alchemists oft preferred to avoid the term alchemist referring to themselves as philosophers, or natural philosophers, who rise above the mundane production of gold, although willing, when suitably induced, to do just that. On the other hand, there are the purely practical alchemists, who head straight for the laboratory with a recipe in hand and have little time for the high-flown philosophical speculations of their colleagues. Rampling deals predominantly with those of a philosophical cast.

Readers of this blog will know that I place a lot of emphasis in the history of science on a contextual narrative i.e., under which circumstances did the science in question take place, what were the external forces driving the science and how were the practitioners embedded in their cultural milieu. In this sense Rampling’s in exemplary. Her alchemists do not speculate in thin air devoid of any contact to society in general but are firmly embedded in the cultures of their times.

Rampling’s alchemists are real people, where the sources make this possible and unfortunately the sources are often meagre, she describes their life circumstances, their professions, their non-alchemical activities and their alchemical motivations. Financing was always important for alchemists and Rampling gives in depth analysis of the texts they wrote to attract wealthy, aristocratic and particularly royal sponsors for their alchemical endeavours. How these are formulated is particularly revealing, because for much of the period under discussion alchemy, or at least multiplication i.e., the alchemical production of gold or silver bullion was forbidden by law. On the other had the Crown was perpetually destitute and more than a bit interested in alchemists’ claims to able to covert base metals into gold and silver.

The English alchemy that Rampling traces down the centuries has its roots in the alchemical texts attributed to the Majorcan mathematician, philosopher and logician Ramon Llull (c. 1232–c. 1315). Attributed is here the correct term because none of texts were actually written by the Spanish polymath, which illustrates the common practice of attributing alchemical texts to eminent authors to increase their status. However, the medieval English alchemists believed the fake attribution and worked on understanding and interpreting the pseudo-Lllullian texts.

Having laid the foundations Rampling moves on to George Ripley (c. 1415–1490), who takes up a central position in the book. Ripley is the most important English medieval alchemist and Rampling takes the reader carefully through his main writings, explaining how he interpreted and balanced out the obscurities and contradictions he found in reading the pseudo-Llullian and other writings that informed his practice.


Have laid the basics, Rampling takes us down the years to 1700, showing how successive generations reworked the pseudo-Llullian and Ripleyian texts, creating new contributions to the alchemical canon, often reassigning known texts to new authors to give them more authority.  We learn how Henry VIII’s dissolution of the monasteries led to the loss of large quantities of manuscripts relevant to the study of alchemy making life difficult for the historian. However, Rampling shows how to reconstruct the alchemy of the period using literary archaeology on those texts that are still available.

Moving into the Elizabethan period we meet two new phenomena in the world of alchemy.  The English alchemist produced English translations of Latin texts making them available to a wider audience and at the same time creating a truly English school of alchemy. At the same time the English alchemists had to cope with foreign alchemists coming to their island and competing for the limited sources of sponsorship needed to set up alchemical laboratories and purchase the necessary starting materials.

Although it deals primarily with English alchemy, throughout the book the reader learns quite a lot about the continental developments, as there was, during the whole period, active exchange between the island and the mainland. Ripley is, for example, said to have travelled and studied on the continent the supposed source of much of his alchemical wisdom. The Elizabethan continental alchemists refreshed the English tradition with new continental developments in the discipline.

This exchange reached a high point in the life and work of Edward Kelley (1555–1597/8), who, better known as the scryer who mediated John Dee’s conversations with angels, was in his later life an acclaimed alchemist on the European mainland. Kelley originally travelled to Prague with Dee to try and find favour with the Holy Roman Emperor, Rudolf II, who was the biggest supporter and sponsor of the occult sciences in the whole of Europe. Dee failed to find favour on the continent and returned disappointed to England whereas Kelley remained and established himself as a leading alchemical authority. Rampling takes us skilfully through the twists and turns, and ups and downs of Kelley’s late career and yet another reworking of the pseudo-Llullian-Ripleyian canon, which found favour amongst continental practitioners


As is now well known to Newton scholars, alchemy didn’t disappear with the advent of the so-called scientific revolution but was still strong in England in the seventeenth century, with Newton, Boyle and Locke all practitioners. Here Rampling takes us through the work of figures such as Elias Ashmole (1617–1692), who created large collections of alchemical manuscripts and books in the final phase of English alchemy.

Rampling’s extensive survey of English alchemy is a masterclass in history of science research and serves as a model for anyone who wishes to undertake such a project. Although it meets the highest standards of academic research, she writes with a light touch and an accomplished literary style making a complex and technical topic accessible to the not necessarily specialist reader. The book is illustrated with grey in grey prints and, hallelujah, it has very extensive, high informative footnotes (not endnotes!). There is a wide-ranging bibliography of both primary and secondary sources and a comprehensive index.

The Experimental Fire is probably not recommended as an introductory text for somebody completely new to the history of alchemy, they should perhaps read Principe’s Secrets of Alchemy before attempting to tackle Rampling’s more advanced text. However, anybody with some basic knowledge of the history of alchemy, and an interest in developing that knowledge, could and should read her book. For those with a serious interest in the topic The Experimental Fire is an obligatory read and must already be considered a standard work in the genre.

[1] Jennifer M. Rampling, The Experimental Fire: Inventing English Alchemy 1300–1700, University of Chicago Press, Chicago and London, 2020.


Filed under History of Alchemy, History of science

Renaissance Science – VI

There is no doubt that the fifteenth and sixteenth century introduction of print technologies in Europe, making possible the advent of the printed book, was one of the most important developments in the history of not just Renaissance science, but the history of science in general. Many people go much further and list the invention of movable-type, as one of the most important or significant inventions in the whole of human history. The ‘in Europe’ is important, because two of those technologies, moveable-type and woodblock printing, were both known and used in Asia long before their introduction in Europe. It is also important to note that despite extensive research no evidence has ever been found of a technology transfer of moveable-type printing from Asia to Europe and the introduction into Europe appears to be a genuinely independent reinvention.

The Chinese artisan Bì Shēng (972–1051) invented the earliest systems of moveable-type around 1040 CE, one in ceramic materials the other using wood. Another wood-based system was invented by the mechanical engineer, Wang Zhen (fl. 1290–1333), in the fourteenth century. Metal moveable-type, made of bronze, definitely existed in China in the thirteenth century. Bronze moveable-type was also in use in Korea in the thirteenth century.


A revolving table typecase with individual movable type characters arranged primarily by rhyming scheme, from Wang Zhen’s Nong Shu, published 1313. Source: Wikimedia Commons

As already stated, there is no evidence of a technology transfer and moveable-type was independently invented in Europe in the fifteenth century. There were tentative experiments with moveable-type early in in the century that came to nothing and the European invention is generally attributed to Johannes Gensfleisch zur Laden zum Gutenberg (c.1400–1468), who is usually known simply as Johannes Gutenberg.


Gutenberg-Statue in Straßburg No portraits of the man are known to exist Source: Wikimedia Commons

Gutenberg was born sometime around 1400 in the city of Mainz, the youngest son of the patrician merchant Friele Gensfleisch zur Laden. Almost nothing is known about his early life, but he turns up living in Strasbourg working as a gold smith in 1434. He moved back to Mainz at some point. He was involved in various, possibly dubious, schemes to make money and it’s not really known how or why he developed his system of moveable-type printing. He supposedly announced his system of printing in 1440 but it wasn’t until around 1450 that his printing press was in operation.

Gutenberg’s real claim to fame is not just that he developed a system of metal moveable-type but that he created a complete system of mechanical printing. As well as the metal type, he modified a wine press to produce a printing press and developed a printing ink. Normal ink is too fluid to be used effectively in a printing press, so Gutenberg developed a more viscous, oil-based ink which stuck to the type, rather than running off.


In this woodblock from 1568, the printer at left is removing a page from the press while the one at right inks the text-blocks Source: Wikimedia Commons

For his press Gutenberg’s business partner was Johann Furst Fust, who lent Gutenberg 800 guilders for the enterprise. Also involved was Furst’s future son-in-law Peter Schöffler. Having conceived his legendary Bible project around 1451, Gutenberg borrowed another 800 guilders from Furst Fust, and printing began in 1452. The Bible began to appear around 1455. In 1456 Furst Fust sued Gutenberg for misappropriation of funds and Gutenberg Europe’s first printer-publisher became Europe’s first bankrupt printer-publisher. Furst Fust and Schöffler took over the publishing house.

Between the 1460s and 1470s Gutenberg’s invention spread rapidly, first throughout Germany and then over the borders into other European countries.


The rapid spread of moveable-type printing throughout Europe in the first fifty years Source: Wikimedia Commons

Gutenberg had nothing to do with the humanist Renaissance, although one of his first printed products was a wall calendar, which as we will see later was an integral part of Renaissance science. However, as his invention crossed the border into Italy it quickly became part of the humanist movement.

The first printer-publishers in Italy were Arnold Pannartz and Conrad Sweynheym, who set up a press in the Benedictine abbey of Subiaco in 1464. Their output was from the beginning humanist orientated. Their first book was by Aelius Donatus a Roman grammarian of which no copied survived. Next, they printed Cicero’s De oratore followed by religious books by Lactantius and Augustinus.

An important innovation was their typeface. German printers following Gutenberg used Blackletter or Gothic typefaces. The humanists had developed a new hand script based on capital Roman letters and Carolingian miniscule, which they mistakenly thought was original antique Latin script. This was modified to make the two different scripts compatible becoming Roman or Antiqua script. The Pannartz-Sweynheym type face was halfway between the German Blackletter typefaces and the humanist Roman script, as was expected from the humanists.


Specimen of a typeface by Pannartz and Sweinheim, considered to be the earliest form of Roman type, c. 1465. Source: Wikimedia Commons

n 1467 Pannartz & Sweynheym left Subiaco and set up a publishing house in Rome, where they continued to publish religious and humanist texts until 1472 when they, like Gutenberg before them, went bankrupt.

Very early, Venice established itself the centre of book printing in Italy and the Venetian printer-publishers, created full blown Roman or Antique type faces to print humanist literature. Most notable in this development were the type designer Nicholas Jensen (c. 1420–1480) and humanist scholar and publisher Aldus Manutius (c.1450–1515), who founded the Aldine Press, which specialised in printing classical Greek and Latin texts.

Aldus Pius Manutius, illustration in Vita di Aldo Pio Manuzio (1759) Source: Wikimedia Commons



The John Rylands Library copy of the Aldine Vergil of 1501, printed on vellum and hand-coloured Source: Wikimedia Commons

Johannes Regiomontanus (1436–1476), also a humanist scholar about whom we will have more to say later, and who established the worlds first scientific publishing house in Nürnberg in 1471, is credited with being the first printer-publisher to bring the Antiqua type faces back over the border into Germany.

Another humanist scholar Niccolò de’Niccoli (1364–1437) dissatisfied with the Roman script for writing humanist manuscripts developed the more flowing Italic script, which in turn generated the Italic type face.


Sample of Niccoli’s cursive script, which developed into Italic type. Source: Wikimedia Commons

Whilst the invention of moveable-type played the major role in the creation of the printed book, it is important to recognise that the possibility of generating reproduceable illustrations in printed books played a very major role in the production of science books, in particular in several areas of Renaissance knowledge, as we shall see later. Image reproduction was made possible by three different print technologies, woodblock printing, engraving and etching, and we will now take a brief look at the histories of each of these.

Woodblock printing was by a long way the oldest of these technologies and was in the early days of printed book productions the most frequently used method of illustration reproduction. In woodblock or woodcut printing the image to be printed in cut into the prepared flat surface of a block of wood, inked and then pressed onto the surface to be printed. It originated in China as a method of printing on textiles and later also to printing on paper, The earliest surviving examples of woodblock printing date to before 220 CE. The method spread throughout East Asia from China. Interestingly, despite its widespread use throughout Asia, it didn’t arrive in Europe until around the early of fourteenth century, when it was used to print textiles. Woodblock printing on paper began in Europe around the beginning of the fifteenth century with religious images and playing cards. During the first half of the fifteenth century woodblock prints became quite popular, but the quality of the prints declined steeply. With the advent of the printed book and the demand for woodblock illustrations grew the quality began to improve with, for example the painter and illustrator Michael Wolgemut (1434–1519) setting standards. Wolgemut’s most famous apprentice, Albrecht Dürer (1471–1528), became possibly the greatest ever creator of woodblock prints. A woodcut is usually produced by two craftsmen, the illustrator or artist, who draws the image on the block and the block cutter, who actually cuts it.


Block Cutter at Work woodcut by Jost Amman, 1568 Source: Wikimedia Commons

The oldest known printed book, the Chinese Dunhuang Diamond Sūtra dated to 868 CE, was entirely printed using woodcuts and not moveable-type.


The Chinese Diamond Sutra (868), the oldest existent woodblock printed book in the world. Source: Wikimedia Commons

The Buddhists were very fond of woodblock printing because they believed that objects with texts of the Buddha’s words are talismanic, so they mass produced leaflets with such texts using woodcuts to print them. A book like the Dunhuang Diamond Sūtra is known as a block-book. There was a brief period in the fifteenth century, mainly around 1460, 1470, when block-books were produced in Europe, usually with religious themes. Strangely it appears that none of the known surviving block-books predates the invention of moveable-type printing. It seems that they were offered as a cheaper alternative to moveable-type printed books but never really caught on.

The next technology for producing illustrations in printed books is engraving. Engraving is very similar to woodcut printing, but the image is cut, scratched or engraved into the surface of a sheet of metal, usually copper, rather than a block of wood. The earliest known printed objects produced in Europe using engraving are some German playing cards probably dating from the late 1430s. Engraving had long been used by gold and silver smiths to decorate metalwork, including amour musical instruments, jewellery etc. It is thought that the idea to use engraving as a print technology developed out of the process whereby goldsmiths filled the groves of an engraved pattern with chalk or similar to make an impression on paper, as a record of their work. It was also common practice when making an elaborate engraved breastplate, for example, to engrave one half of the pattern, left or right, then to make an impression to use to make the other half, thereby ensuring that the pattern was truly symmetrical.

The German artist Martin Schongauer (c.1450–1491) made the greatest early development in the art of producing engraved prints.


Martin Schongauer (German, Colmar ca. 1435/50–1491 Breisach) Griffin, 15th century German, Engraving; The Metropolitan Museum of Art, New York, Harris Brisbane Dick Fund, 1927 (27.54.5) via Wikimedia Commons

Of course, it was, once again, Albrecht Dürer, who became the great master of producing engraved prints. Although engraving allows the reproduction of much finer lines that woodcuts and so more delicate and accurate images, it is also more expensive that woodcuts and more difficult to integrate with moveable-type when printing. These factors led to a dominance from woodcuts over engraving in the early book production.


St. Jerome in His Study (1514), an engraving by Northern Renaissance master Albrecht Dürer Source: Wikimedia Commons

The final print technology for producing illustration is etching. Like engraving, etching uses metal sheets to hold the images to be reproduced but instead of the images being cut into the surface with a tool it is burnt in using acid. The basic technology of etching goes back into antiquity and was used, for example, to decorate jewellery. The earliest examples from the Indus valley date back to the third millennium BCE. Etching used by gold and silver smiths to decorate guns, armour and other metal objects was well-known in Europe in the Middle Ages. The application of etching to printing is thought to have been the work of the German artist and metalworker Daniel Hopfer (c. 1470–1536), who produced etched prints using iron plates.


Daniel Hopfer Three German Soldiers Armed with Halberds, c. 1510. An original etched iron plate from which prints would be made. National Gallery of Art via Wikimedia Commons

The oldest dated etching is by Albrecht Dürer from 1515. Dürer only produced six etchings before returning to engraving as his preferred technique. The move from iron to copper etching plates is thought to have been made by the Italians, once a suitable chemical agent had been found.

As a technology for printing illustrations in books, etching didn’t really become established until the eighteenth century. One major problem was the production of the etching fluids. These were often of very poor quality and contained contaminates, which cause damage during the etching process. In the first couple of centuries of book production, it was woodcuts that dominated illustration reproduction only very gradually being replaced by engraving.

As we shall see in later posts the printed book and especially the illustrated book played a very central role in the development of various areas of Renaissance knowledge. The ability to mechanically reproduce illustrations in large quantities playing a very central role. Before this, however, as I have briefly indicated above the early literary humanists were quick to adopt the new medium, creating their own distinctive typefaces to give themselves a clear identity in print and also from the beginning producing printed editions of the works of their classical role models such as Cicero and Quintillion, as well as printed editions of the first humanist scholars such as Plutarch.



Filed under Book History

Alphabet of the stars

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

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

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

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

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


Rain by Matthäus Merian 1665 Source: Wikimedia Commons

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


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

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


Title page of Uranometria Source: Wikimedia Commons

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


Canis Major with Sirius very prominent on his nose Source


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

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


Chart of the Southern-Hemisphere ConstellationsSource

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


Synopsis coeli superioris borea Source


Synopsis coeli inferioris austrina Source

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

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


Dürer Northern Hemisphere Star Map Source: Wikimedia Commons

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


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

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


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


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

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


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

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


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


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

Renaissance Science – V

According to the title, this series is supposed to be about Renaissance science but as we saw in the last episode the Renaissance started off as anything but scientific, so what exactly is Renaissance science, does it even exist, and does it actually have anything to do with the language and linguistics movement that kicked of the period that is now known as the Renaissance? I will start with the second of these questions and return later to the other two.

The history of science in its present form is actually a very young discipline, which really only came to fruition in the twentieth century. There are of course early elements of the discipline scattered around the past but the structured academic discipline as we know it only really began in the decades between the two world wars and came to maturity following the second world war. The early discipline was of course very euro-centric, and a major element was the so-called scientific revolution, which was initially seen as a single historical block. Maria Boas Hall (1919–2009) was, as far as I know, the first to divide that block into two parts, a sort of proto scientific revolution, her The Scientific Renaissance 1450–1630 (published, 1962), followed by the full scientific revolution. She was followed in this bifurcation by Peter Dear in his book Revolutionizing the Sciences: European Knowledge in Transition 1500–1700 (originally 2001, 3rd ed. 2019), who sees two phases, 1500-1600 and 1600-1700. These two books established, I think correctly, the idea of a separate Scientific Renaissance, which preceded the Scientific Revolution.

So, what is the nature of this Renaissance science, how did it differ from the existing medieval science and what changed and when going forward into the so-called scientific revolution? There is quite a lot to unpack here and the first thing we need to do is to stop talking about science and instead talk about knowledge, the more correct translation of the Latin term, scientia used in this period. Also, within the scope of scientia, what we might regard as the areas of hard science, which Aristotle called physics, meaning the study of nature, should more appropriately be referred to as natural philosophy. However, medieval natural philosophy was a very restricted area, it included cosmology but did not for example include astronomy, which was a mathematical discipline. Aristotle rejected mathematics as scientia, because its objects were not real. The mathematical disciplines, such as astronomy and optics, were not regarded as belonging to natural philosophy but were given a sort of halfway status. Natural philosophy also didn’t include any of what we would now call the life sciences.

Knowledge in the European medieval context was divided into two completely distinct areas, which didn’t intersect in anyway. On the one side there was the knowledge propagated by the medieval universities, which, as I explained in an earlier post, was almost totally theoretical book knowledge, with almost no practical aspects to it at all. This knowledge was not static, as it is often falsely presented, but evolved over time. However, this evolution was also a theoretical process. The knowledge progressed through debate and the application of argumentation and logic, not through the acquisition of new empirical facts.

The other area of knowledge was artisanal knowledge, that is the knowledge of the maker, the craftsman. This knowledge was empirical and practical, consisting of directions or instruction on how to complete a given task, how to achieve a given aim or fulfil a given assignment. It might, for example, be how to make bricks out of clay, or how to build a stone arch that would be stable and not collapse under load. This knowledge covered a vast range of activities and had been accumulated from a very wide range of sources over virtually the whole of human existence. This knowledge was, traditional, rarely written down but was usually passed on by word of mouth and direct training from master to apprentice, often from father to son over many generations. This knowledge was in general not viewed as knowledge by scholars within the university system.

Starting around fourteen hundred a process of what we would today call crossover began between these two previously distinct and separate areas of knowledge. Scholars began to write learned works about specific areas of artisanal knowledge, a classic example being Georgius Agricola’s De re metallica, published posthumously in 1556, and craftsmen began to write books explaining and elucidating their forms of knowledge, for example the goldsmith Lorenzo Ghiberti’s I commentarii, which remained unfinished in manuscript and unpublished at the time of his death in 1455. It should be noted that before the Renaissance the people we now call artists were regarded as craftsmen. Crossover is here perhaps the wrong term, as people didn’t just cross the boundary in both directions but the boundary itself began to dissolve producing a meld between the two types of knowledge that would over the next two and a half centuries lead to the modern concept of knowledge or science.

What provoked this move towards practical, empirical knowledge during the Renaissance? There are two major areas of development driving this shift in emphasis, as to what constitutes knowledge. The first is general social, political, economical and cultural developments. The rapid increase in long distant trade produced a demand for new methods of navigation and cartography. Changes in concepts of land ownership also drove developments in cartography and the closely associated surveying. Developments in warfare again drove developments in cartography but also in gunnery, a new discipline, and military tactics in general. The invention of gunpowder and with-it military gunnery drove developments in metallurgy, as did other areas where the use of metals increased, for example in the wider use of metal coinage. The greater demand for metals in turn drove the development of mining. Greater wealth in society in general and the perceived need for rulers to display their power through ostentatious display increased the demand for architecture and fine art. The introduction of gunpowder and gunnery also drove the development of architecture because of the need for better defences. These are just some examples of the growing demand for artisanal knowledge within an increasingly urban culture financed by long distance trade.

But what of the movement that gave the Renaissance its name, which we saw was initially language and linguistic based movement, how did this play a role in this move towards the elevation of the status of empirical and practical knowledge if at all? This is in fact our second area of development. Those early Renaissance scholars, who searched for Latin literature texts and orations in the monastic libraries also unearthed Greek and Latin texts on science, technology, mathematics and medicine and in the general renewal of the culture of antiquity also translated and made these texts available, often arguing for their purity in comparison to the texts from the same authors that had come into Europe through the filter of translation into Arabic and then back into Latin. Example of texts that became available for the first time are Vitruvius’ work on architecture De architectura and Ptolemaeus’ Geographia. The latter had been known to the Islamic cartographers but had not been translated into Latin from Arabic during the twelfth century translation movement. As well as bringing new original Greek and Latin manuscripts into circulation the Renaissance scholars introduced a strong empirical element through their philological work. This work was based on an empirical analysis of various copies of a given work as well as an investigation of the plausibility of a given word, phrase or sentence, which didn’t appear to make sense. Beyond this in some areas the Renaissance scholars, as we shall see in more detail later, began to try and understand what the scholars were referring to in specific instances. For example, which plants was Dioscorides referring to in his De meteria medica? The answer to such questions required real empirical research.

The Renaissance opened up a whole new world of practical, empirical knowledge alongside the theoretical book knowledge of the medieval university. The last question is how did this differ from the knowledge of the following period and when did this transition take place?

The emphasis on this Renaissance empirical knowledge was very much on the practical. How can we use it, where and how can it be applied? During the seventeenth century the emphasis changed to one of devising theoretical explanations for all of the freshly won empirical knowledge from the previous two hundred years. The transition is from how do we use or apply it, to how do we explain it. It is impossible to set a firm date for this transition as it was by its very nature a gradual one, so both Boas Hall and Dear are in a certain sense correct with their respective 1630 and 1600. The transition had definitely already begun by 1600 and probably wasn’t finished, yet by 1630. In my case I follow Francis Yates in choosing the end of the Thirty Year’s War in 1648, as I think the transition had been completed by then at the latest.


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

A flawed survey of science and the occult in the Early Modern Period

There is no shortage of good literature on the relationships between science and magic, or science and astrology, or science and alchemy during the Early Modern Period so what is new in Mark A. Waddell’s Magic, Science, and Religion in Early Modern Europe[1]? Nothing, because it is not Waddell’s aim to bring something new to this material but rather to present an introductory textbook on the theme aimed at university students. He sets out to demonstrate to the uninitiated how the seemingly contradictory regions of science, religion and magic existed in the Early Modern Period not just parallel to but interwoven and integrated with each other.  Waddell’s conception is a worthy one and would make for a positive addition to the literature, his book is however flawed in its execution.


Image with thanks from Brian Clegg

The book actually starts well, and our author sets out his planned journey in a lengthy but clear and informative introduction. The book itself is divided into clear sections each dealing with a different aspect of the central theme. The first section deals with the Renaissance discoveries of hermeticism and the cabala and the concept of natural magic, as a force to manipulate nature, as opposed to demonic magic. Although limited by its brevity, it provides a reasonable introduction to the topics dealt with. My only criticisms concerns, the usual presentation of John Dee as a magus, whilst downplaying his role as a mathematician, although this does get mentioned in passing. However, Waddell can’t resist suggesting that Dee was the role model for Marlowe’s Faustus, whereas Faustus is almost certainly modelled on Historia von D. Johann Faustus, a German book containing legends about the real Johann Georg Faust (c. 1480–c. 1541) a German itinerant alchemist, astrologer, and magician of the German Renaissance. A note for authors, not just for Waddell, Dee in by no means the only Renaissance magus and is not the role model for all the literary ones.

Waddell’s second section deals with demonic magic, that is magic thought to draw its power from communion with the Devil and other lesser demons. As far as I can tell this was the section that most interested our author whilst writing his book. He manages to present a clear and informative picture of the period of the European witch craze and the associated witch hunts. He deals really well with the interrelationship between the belief in demonic witchcraft and the Church and formal religion. How the Church created, propagated and increasingly expanded the belief in demonic magic and witches and how this became centred on the concept of heresy. Communion with the devil, which became the central theme of the witch hunts being in and of itself heretical.

Following this excellent ´section the book starts to go downhill. The third section of the book deals with magic, medicine and the microcosm. Compared with the good presentation of the previous section I can only call this one a mishmash. We get a standard brief introduction to medieval academic medicine, which Waddell labels premodern, with Hippocrates, Galen and a nod to Islamic medical writes, but with only Ibn Sīnā mentioned by name. This is followed by a brief description of the principles of humoral medicine. Waddell correctly points out the academic or learned doctors only represent one group offering medical assistance during this period and gives a couple of lines to the barber-surgeons. It is now that the quality of Waddell’s presentation takes a steep nosedive.

Having correctly pointed out that medieval academic medicine was largely theoretical he then, unfortunately, follows the myth of “and then came Andy”! That is, we jump straight into Andreas Vesalius and his De fabrica, as I quote, “the beginnings of what we would understand as a rigorous and empirical approach to the study of anatomy.” Strange, only two weeks ago I wrote a post pointing out that Vesalius didn’t emerge out of the blue with scalpel raised high but was one step, albeit a very major one, in a two-hundred-year evolution in the study of anatomy. Of course, Waddell dishes up the usual myth about how seldom dissection was before Vesalius and corpses to dissect were rare etc, etc. Whereas, in fact, dissection had become a regular feature of medical teaching at the European universities over that, previously mentioned two-hundred-year period. Waddell closes his Vesalius hagiography with the comment that Vesalius’ De fabrica “was a crucial step in the more widespread reform of medical theory and practice that took place over the next 150 years” and although his book goes up to the middle of the eighteenth century, we don’t get any more information on those reforms. One of his final comments on Vesalius perpetuates another hoary old myth. He writes, “Vesalius made it permissible to question the legacy of antiquity and, in some cases, to overturn ideas that had persisted for many hundred years.” Contrary to the image created here, people had been challenging the legacy of antiquity and overturning ideas since antiquity, as Edward Grant put it so wonderfully, medieval Aristotelian philosophy was not Aristotle’s philosophy. The same applies to all branches of knowledge inherited form antiquity.

Having dealt with Vesalius, Waddell moves on to the philosophy of microcosm-macrocosm and astro-medicine or as it was called iatromathematics, that is the application of astrology to medicine. His basic introduction to the microcosm-macrocosm theory is quite reasonable and he then moves onto astrology. He insists on explaining that, in his opinion, astrology is not a science but a system of non-scientific rules. This is all well and good but for the people he is dealing with in the Early Modern Period astrology was a science. We then get a guide to astrology for beginners which manages right from the start to make some elementary mistakes. He writes, “You might know what your “sign” is, based on when you were born […]. These refer to the twelve (or according to some, thirteen) signs of the Western zodiac, which is the band of constellations through which the Sun appears to move over the course of a year.” The bullshit with thirteen constellations was something dreamed up by some modern astronomers, who obviously know nothing about astrology, its history or the history of their own discipline for that matter, in order to discredit astrology and astrologers. The only people they discredited were themselves. The zodiac as originally conceived by the Babylonians a couple of millennia BCE, mapped the ecliptic, the apparent annual path of the Sun around the Earth, using seventeen constellations. These were gradually pared down over the centuries until the Western zodiac became defined around the fifth century BCE as twelve equal division of the ecliptic, that is each of thirty degrees, starting at the vernal or spring equinox and preceding clockwise around the ecliptic. The most important point is that these divisions, the “signs”, are not constellations. There are, perhaps unfortunately, named after the constellations that occupied those positions on the ecliptic a couple of millennia in the past but no longer do so because of the precession of the equinoxes.

Although, Waddell gives a reasonable account of the basics of astro-medicine and also how it was integrated with humoral medicine but then fails again when describing its actual application. A couple of examples:

There were cases of surgeons refusing to operate on a specific part of the body unless the heavens were aligned with the corresponding zodiac sign, and it was not uncommon for learned physicians to cast their patient’s horoscope as part of their diagnosis.


Though the use of astrology in premodern medicine was common, it is less clear how often physicians would have turned to astrological magic in order to treat patients. Some would have regarded it with suspicion and relied instead on genitures alone to dictate their treatment, using a patient’s horoscope as a kind of diagnostic tool that provided useful information about that person’s temperament and other influences on their health. Astrological magic was a different thing altogether, requiring the practitioner to harness the unseen forces and emanations of the planets to heal their patient rather than relying solely on a standard regimen of care.

This is a book about the interrelationships between magic, religion and science during the Early Modern period, but Waddell’s lukewarm statements here, “there were cases of surgeons refusing to operate…, not uncommon for learned physicians…” fail totally to capture the extent of astro-medicine and its almost total dominance of academic medicine during the Renaissance. Beginning in the early fifteenth century European universities established the first dedicated chairs for mathematics, with the specific assignment to teach astrology to medical students.

During the main period of astrological medicine, the most commonly produced printed products were wall and pocket calendars, in fact, Gutenberg printed a wall calendar long before his more famous Bible. These calendars were astronomical, astrological, medical calendars, which contained the astronomical-astrological data that enabled physicians and barber-surgeons to know when they should or should not apply a particular treatment. These calendars were universal, and towns, cities and districts appointed official calendar makers to produce new calendars, every year. Almost no physician or barber-surgeon would consider applying a treatment at an inappropriate time, not as Waddell says, “cases of surgeons refusing to operate.” Also, no learned physicians in this time would begin an examination without casting the patient’s horoscope, to determine the cause, course and cure for the existing affliction. The use of what Waddell calls astrological magic, by which he means astrological talismans, by learned physicians was almost non-existent. This is aa completely different area of both astrology and of medicine.

Within the context of the book, it is obvious that we now turn to Paracelsus. Here Waddell repeats the myth about the name Paracelsus, “The name by which he is best known, Paracelsus, is something of a mystery, but historians believe that it was inspired by the classical Roman medical writer Celsus (c. 25 BCE–c. 50 CE). The prefix “para-“ that he added to that ancient name has multiple meanings in Latin, including “beyond,” leading some to speculate that this was a not-so-modest attempt to claim a knowledge of medicine greater than that of Celsus.” This is once again almost certainly a myth. Nowhere in his voluminous writings does Paracelsus mention Celsus and there is no evidence that he even knew of his existence. Paracelsus is almost certainly a toponym for Hohenheim meaning ‘up high’, Hohenheim being German for high home. By the way, he only initially adopted Paracelsus for his alchemical writings. The rest of his account of Paracelsus is OK but fails to really come to grips with Paracelsus’ alchemy.

To close out his section on medicine, Waddell now brings a long digression on the history of the believe in weapon salve, a substance that supposedly cured wounds when smeared on the weapon that caused them, an interesting example of the intersection between magic and medicine. However, he misses the wonderful case of a crossover into science when Kenhelm Digby suggested that weapon salve could be used to determine longitude.


The next section A New Cosmos: Copernicus, Galileo, and the Motion of the Earth, takes us into, from my point of view, a true disaster area:

In this chapter, we explore how the European understanding of the cosmos changed in the sixteenth and seventeenth centuries. It was on the single greatest intellectual disruptions in European history, and in some ways we are still feeling its effects now, more than 450 years later. The claim that our universe was fundamentally different from what people had known for thousands of years led to a serious conflict between different sources of knowledge and forms of authority, and forced premodern Europe to grapple with a crucial question: Who has the right to define the nature of reality?

This particular conflict is often framed by historians and other commentators as a battle between science and religion in which the brave and progressive pioneers of the heliocentric cosmos were attacked unjustly by a tyrannical and old-fashioned Church. This is an exaggeration, but not by much. [my emphasis]

Waddell starts with a standard account of Aristotelian philosophy and cosmology, in which he like most other people exaggerates the continuity of Aristotle’s influence. This is followed by the usual astronomers only saved the phenomena story and an introduction to Ptolemy. Again, the continuity of his model is, as usual, exaggerated. Waddell briefly introduces the Aristotelian theory of the crystalline spheres and claims that it contradicted Ptolemy’s epicycle and deferent model, which is simply not true as Ptolemy combined them in his Planetary Hypothesis. The contradiction between the two models is between Aristotle’s astronomical mathematical homocentric spheres used to explain the moments of the planets (which Waddell doesn’t mention), which were imbedded in the crystalline spheres, and the epicycle-deferent model. Waddell then hypothesises a conflict between the Aristotelian and Ptolemaic system, which simply didn’t exist for the majority, people accepting a melange of Aristotle’s cosmology and Ptolemy’s astronomy. There were however over the centuries local revivals of Aristotle’s homocentric theory.

Now Copernicus enters stage right:

Copernicus had strong ties to the Catholic Church; he was a canon, which meant he was responsible for maintaining a cathedral (the seat of a bishop or archbishop), and some historians believe he was ordained as a priest as well.

If a student writes “some historians” in a paper they normally get their head torn off by their teachers. Which historians? Name them! In fact, I think Waddell would have a difficult time naming his “some historians”, as all the historians of astronomy that I know of, who have studied the question, say quite categorically that there is no evidence that Copernicus was ever ordained. Waddell delivers up next:

Most probably it [De revolutionibus] was completed by the mid-1530s, but Copernicus was reluctant to publish it right away because his work called into question some of the most fundamental assumptions about the universe held at the time.

It is now generally accepted that Copernicus didn’t published because he couldn’t provide any proofs for his heliocentric hypothesis. Waddell:

He did decide to circulate his ideas quietly among astronomers, however, and after seeing his calculations were not rejected outright Copernicus finally had his work printed in Nuremberg shortly before his death.

Here Waddell is obviously confusing Copernicus’ Commentariolus, circulated around 1510 and  Rheticus’ Narratio prima, published in two editions in Danzig and Basel, which I wouldn’t describe as circulated quietly. Also, neither book contained  calculations. Waddell now tries to push the gospel that nobody really read the cosmological part of De revolutionibus and were only interested in the mathematics. Whilst it is true that more astronomers were interested in the mathematical model, there was a complex and intensive discussion of the cosmology throughout the second half of the sixteenth century. Waddell also wants his reader to believe that Copernicus didn’t regard his model as a real model of the cosmos, sorry this is simply false. Copernicus very definitely believed his model was a real model.

 Moving on to Tycho Brahe and the geo-heliocentric system Waddell tells us that, “[Tycho] could not embrace a cosmology that so obviously conflicted with the Bible. It is not surprising, then, that the Tychonic system was adopted in the years following Brahe’s death in 1601”

At no point does Waddell acknowledge the historical fact that also the majority of astronomers in the early decades of the seventeenth century accepted a Tychonic system because it was the one that best fit the known empirical facts. This doesn’t fit his hagiographical account of Galileo vs the Church, which is still to come.

Next up Waddell presents Kepler and his Mysterium Cosmographicum and seems to think that Kepler’s importance lies in the fact that he was ac deeply religious and pious person embraced a heliocentric cosmos. We then get an absolute humdinger of a statement:

There is more that could be said about Kepler, including the fact that he improved upon the work of Copernicus by proposing three laws of planetary motion that are still taught in schools today. For the purpose of this chapter, however, Kepler is significant as someone who embraced heliocentricity and [emphasis in the original] faith.

With this statement Waddell disqualifies himself on the subject of the seventeenth century transition from a geocentric cosmos to a heliocentric one. Kepler didn’t propose his three laws he derived them empirically from Tycho’s observational data and they represent the single most important step in that transition.

We now have another Waddell and then came moment, this time with Galileo. We get a gabled version of Galileo’s vita with many minor inaccuracies, which I won’t deal with here because there is much worse to come. After a standard story of the introduction of the telescope and of Galileo’s improved model we get the following:

[Galileo] presented his device to the Doge (the highest official in Venice) and secured a truly impressive salary for life from the Venetian state. Mere weeks later he received word from the court of the Medici in Galileo’s home in Tuscany, that they wanted a telescope of their own. The Venetian leaders, however had ordered Galileo to keep his improved telescope a secret, to be manufactured only for Venetian use, and Galileo obliged, at least temporarily.

When they bought Galileo’s telescope they thought, erroneously, that they were getting exclusive use of a spectacular new instrument. However, it soon became very clear that telescopes were not particularly difficult to make and were freely available in almost all major European towns. They were more than slightly pissed off at the good Galileo but did not renege on their deal. The Medici court did not request a telescope of their own, but Galileo in his campaign to gain favour by the Medici, presented them with one and actually travelled to Florence to demonstrate it for them. We now move on to the telescopic discoveries in which Waddell exaggerates the discovery of the Jupiter moons. We skip over the Sidereus Nuncius and Galileo’s appointment as court philosophicus and mathematicus in Florence, which Waddell retells fairly accurately. Waddell now delivers up what he sees as the great coup:

The problem was that the moons of Jupiter, while important, did not prove the existence of a heliocentric cosmos. Galileo kept searching until he found something that did: the phases of Venus.

The discovery of the phases of Venus do indeed sound the death nell for a pure geocentric system à la Ptolemy but not for a Capellan geo-heliocentric system, popular throughout the Middle Ages, where Mercury and Venus orbit the Sun, which orbits the Earth, or a full Tychonic system with all five planets orbiting the Sun, which together with the Moon orbits the Earth. Neither here nor anywhere else does Waddell handle the Tychonic system, which on scientific, empirical grounds became the most favoured system in the early decades of the seventeenth century.

We then get Castelli getting into deep water with the Grand Duchess Christina and, according to Waddell, Galileo’s Letter to the Grand Duchess Christina. He never mentions the Letter to Castelli, of which the Letter to the Grand Duchess Christina was a later extended and improved version, although it was the Letter to Castelli, which got passed on to the Inquisition and caused Galileo’s problems in 1615. Waddell tells us:

In 1616 the Inquisition declared that heliocentrism was a formal heresy.

In fact, the eleven Qualifiers appointed by the Pope to investigate the status of the heliocentric theory delivered the following verdict:

( i ) The sun is the centre of the universe (“mundi”) and absolutely immobile in local motion.

( ii ) The earth is not the centre of the universe (“mundi”); it is not immobile but turns on itself with a diurnal movement.

All unanimously censure the first proposition as “foolish, absurd in philosophy [i.e. scientifically untenable] and formally heretical on the grounds of expressly contradicting the statements of Holy Scripture in many places according to the proper meaning of the words, the common exposition and the understanding of the Holy Fathers and learned theologians”; the second proposition they unanimously censured as likewise “absurd in philosophy” and theologically “at least erroneous in faith”.

However, the Qualifiers verdict was only advisory and the Pope alone can official name something a heresy and no Pope ever did.

Waddell gives a fairly standard account of Galileo’s meeting with Cardinal Roberto Bellarmino in 1616 and moves fairly rapidly to the Dialogo and Galileo’s trial by the Inquisition in 1633. However, on the judgement of that trial he delivers up this gem:

Ultimately, Galileo was found “vehemently suspect of heresy,” which marked his crime as far more serious than typical, run-of-the-mill heresy.

One really should take time to savour this inanity. The first time I read it, I went back and read it again, because I didn’t think anybody could write anything that stupid. and that I must have somehow misread it. But no, the sentence on page 131 of the book reads exactly as I have reproduced it here. Maybe I’m ignorant, but I never knew that to be suspected of a crime was actually “far more serious” than actually being found guilty of the same crime. One of my acquaintances, an excellent medieval historian and an expert for medieval astronomy asked, “WTF is run-of-the-mill heresy?” I’m afraid I can’t answer her excellent question, as I am as perplexed by the expression, as she obviously is.

Enough of the sarcasm, the complete sentence is, of course, total bollocks from beginning to end. Being found guilty of suspicion of heresy, vehement or not, is a much milder judgement than being found guilty of heresy. If Galileo had been found guilty of heresy, there is a very good chance he would have been sentenced to death. The expression “run-of-the-mill heresy” is quite simple total balderdash and should never, ever appear in any academic work.

Waddell now draws his conclusions for this section, and they are totally skewed because he has simple ignored, or better said deliberately supressed a large and significant part of the story. In the final part of this section, “Science versus Religion?”, he argues that the Church was defending its right to traditional truth against Galileo’s scientific truth. He writes:

This was not a fight between winners and losers, or between “right” and “wrong.” Instead, this is a story about power, tradition, and authority, about who gets to decide what is true and on what grounds.


Organised religion, exemplified here by the Catholic Church, had an interest in preserving the status quo [emphasis in original] for many reasons, some of which were undeniably self-serving.


The ideas of Aristotle and Ptolemy were still taught in virtually every European university well into the seventeenth century, making the Church’s allegiance to these ideas understandable. At the same time, the Church also recognised another source of authority, the Christian scriptures, which stated clearly that the Earth did not move. On both philosophical and theological grounds, then, the Church’s position on the immobility of the Earth was reasonable by the standards of the time.  

The above quotes have more relationship to a fairy tale than to the actual historical situation. Due to the astronomical discoveries made since about 1570, by1630 the Catholic Church had abandoned most of the Aristotelian cosmology and never adopted  Aristotelian astronomy. They fully accepted that the phases of Venus, almost certainly observed by the Jesuit astronomers of the Collegio Romano before Galileo did, refuted the Ptolemaic geocentric astronomy. Instead by 1620 the Church had officially adopted the Tychonic geo-heliocentric astronomy, not, as Waddell claims, on religious grounds but because it best fit the known empirical facts. Despite efforts since 1543, when Copernicus published De revolutionibus, nobody, not even Galileo, who had tried really hard, had succeeded in finding any empirical evidence to show that the Earth moves. Waddell’s attempt to portrait the Church as at best non-scientific or even anti.scientific completely ignores the fact that Jesuit and Jesuit educated mathematicians and astronomer were amongst the best throughout the seventeenth century. They made significant contributions to the development of modern astronomy before the invention of the telescope, during Galileo’s active period, in fact it was the Jesuits who provided the necessary scientific confirmation of Galileo’s telescopic discoveries, and all the way up to Newton’s Principia. Their record can hardly be described as anti-scientific.

The Church’s real position is best summed up by Roberto Bellarmino in his 1615 letter to Foscarini, which is also addressed to Galileo:

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

Put simple prove your theory and we the Church will then reinterpret the Bible as necessary, which they in fact did in the eighteenth century following Bradley’s first proof that the Earth does actually move.

Waddell then goes off on a long presentist defence of Galileo’s wish to separate natural philosophy and theology, which is all well and good but has very little relevance for the actual historical situation. But as already stated, Waddell is wrong to claim that the phases of Venus prove heliocentrism. Worse than this Galileo’s Dialogo is a con. In the 1630s the two chief world systems were not Ptolemy and Copernicus, the first refuted and the second with its epicycle-deferent models, which Galileo continues to propagate, abandoned, but the Tychonic system and Kepler’s ecliptical astronomy, which Waddell like Galileo simply chose to ignore.

One last comment before I move on. Somewhere Waddell claims that Galileo was the first to claim that the Copernicus’ heliocentric model represented reality rather than simply saving the phenomena. This is historically not correct, Copernicus, Tycho and Kepler all believed that their models represented reality and by 1615, when Galileo first came into confrontation with the Church it had become the norm under astronomers that they were trying to find a real model and not saving the phenomena.

Waddell’s account of the early period of the emergence of modern astronomy sails majestically past the current historical stand of our knowledge of this phase of astronomical history and could have been written some time in the first half of the twentieth century but should not be in a textbook for students in the year 2021.

With the next section we return to some semblance of serious state-of-the-art history. Waddell presents and contrasts the mechanical philosophies of Pierre Gassendi and René Descartes and their differing strategies to include their God within those philosophies. All pretty standard stuff reasonably well presented. The section closes with a brief, maybe too brief, discourse on Joseph Glanvill’s attempts to keep awareness of the supernatural alive against the rationalism of the emerging modern science.

The penultimate section deals with the transition from the Aristotelian concept of an experience-based explanation of the world to one based on experiments and the problems involved in conforming the truth of experimental results. In my opinion he, like most people, gives far too much attention/credit to Francis Bacon but that is mainstream opinion so I can’t really fault him for doing so. I can, however, fault him for presenting Bacon’s approach as something new and original, whereas Bacon was merely collating what had been widespread scientific practice for about two centuries before he wrote his main treatises. Specialist historians have been making this public for quite some time now and textbooks, like the one Waddell has written, should reflect these advances in our historical awareness.

Waddell moves on to alchemy as another source of experimentation that influenced the move to an experiment-based science in the seventeenth century. To be honest I found his brief account of alchemy as somewhat garbled and meandering, basically in need of a good editor. He makes one error, which I found illuminating, he writes:

Aristotle in particular had taught that all metals were composed of two principles: Mercury and Sulphur

Aristotle thought that metals were composed of two exhalations, one is dry and smoky, the other wet and steamy. These first became widely labeled as Mercury and Sulphur in the ninth century writings of the Arabic alchemist Jābir ibn-Hayyān, who took it from the mid-ninth century work, the Book of the Secrets of Creation by Balīnūs. I find this illuminating because I don’t know things like this off by heart, I just knew that Mercury-Sulphur was not from Aristotle, and so have to look them up. To do so I turned to Principe’s The Secrets of Alchemy. Now, according to Waddell’s bibliographical essays at the end of the book, Principe is his main source for the history of alchemy, which means he read the same paragraph as I did and decided to shorten it thus producing a fake historical statement. When writing history facts and details matter!

Having introduced alchemy we now, of course, get Isaac Newton. Waddell points out that Newton is hailed as the epitome of the modern scientist, whereas in fact he was a passionate exponent of alchemy and devoted vast amounts of time and effort to his heterodox religious studies. The only thing that I have to criticise here is that Waddell allocates Newton and his Principia to the mechanical philosophy, whereas his strongest critics pointed out that gravity is an occult force and is anything but conform with the mechanical philosophy. Waddell makes no mention of this here but strangely, as we will see does so indirectly later.

The final section of the book is a discussion of the enlightenment, which I found quite good.  Waddell points out that many assessments of the enlightenment and what supposedly took place are contradicted by the historical facts of what actually happened in the eighteenth century.

Waddell draws to a close with a five-page conclusion that rather strangely suddenly introduces new material that is not in the main text of the book, such as Leibniz’s criticism that Newton’s theory of gravity is not mechanical. It is in fact more a collection of after thoughts than a conclusion.

The book ends with a brief but quite extensive bibliographical essay for each section of the book, and it was here that I think I found the reason for the very poor quality of the A New Cosmos section, he writes at the very beginning:

Two important studies on premodern astronomy and the changes it experienced in early modern Europe are Arthur Koestler’s The Sleepwalkers: A History of Man’s Changing Vision of the Universe (Penguin Books, 1990) and Thomas Kuhn’s The Copernican Revolution: Planetary Astronomy in the Development of Western Thought (Harvard University Press, 1992)

The Sleepwalkers was originally published in 1959 and The Copernican Revolution in 1957, both are horribly outdated and historically wildly inaccurate and should never be recommended to students in this day and age.

All together Waddell’s tome  has the makings of a good and potentially useful textbook for students on an important set of themes but it is in my opinion it is spoilt by some sloppy errors and a truly bad section on the history of astronomy in the early modern period and the conflict between Galileo and the Catholic Church.

[1] Mark A. Waddell, Magic, Science, and Religion in Early Modern Europe, Cambridge University Press, Cambridge & London, 2021


Filed under Book Reviews, History of Alchemy, History of Astrology, History of Astronomy, History of medicine, History of science, Renaissance Science

Renaissance Science – IV

We have now reached the period of history that the majority of people automatically think of when the hear or read the name, The Renaissance. The majority probably also think, when the hear the term, of a period in European art history, often called the Italian Renaissance, doing which the great artists Leonardo, Michelangelo, Raphael et al flourished. This is one aspect of the Renaissance that won’t be dealt with directly in this series but, of which some aspects do turn up on the fringes a couple of time. For a long time, the Renaissance was simply called the Renaissance, but because historians began to use the term for the other renaissances that we have already looked at–the Carolingian Renaissance, the Ottonian Renaissance and the Scientific Renaissance–it became common practice, at least amongst historians, to qualify the name as the Humanist Renaissance and it is here that we meet our first problem. Both the term Humanist and the term Renaissance were actually first coined in the nineteenth century. Somebody in the Early Modern period would not have recognised this name. So, what was it called then? It wasn’t. Although, as we will see the people, who kicked off the Renaissance distanced themselves from the Middle Ages, a term that they created, they gave their movement a name, but didn’t give their period one. Who were theses people, when were they active and what did they set out to do?

Before we examine the true origins of the Renaissance, we need to first dispel an oft repeated false statement. It is very common to read that the Renaissance started with the final collapse of the Eastern Roman Empire, when the Ottoman Turks captured Constantinople in 1453, with images of Greek scholars fleeing to Western Europe with bundles of Greek manuscript clutched under their arms. This is a myth. In fact, the Renaissance had its beginnings more than a hundred years earlier centred on Florence in Northern Italy.


The final siege of Constantinople, contemporary 15th-century French miniature. Bertrandon de la Broquière in Voyages d’Outremer – Source: Wikimedia Commons

The earliest phase of the Renaissance is attributed to the writers Dante Alighieri (c. 1265–1321), Giovanni Boccaccio (1313–1375) and Francesco Petrarca (1304–1374), better known in English as Petrarch, who are considered to have launched a new wave of literature in the fourteenth century.


Dante Alighieri, attributed to Giotto, in the chapel of the Bargello palace in Florence. This oldest picture of Dante was painted just prior to his exile and has since been heavily restored. Source: Wikimedia Commons

In its initial phase their Renaissance was a literary and linguistic movement. Led by Petrarch, the notary Coluccio Salutati (1331–1406) famous for his skills as a writer and orator, and the scholars Niccolò de’ Niccoli (1364–1437) and Poggio Bracciolini (1380–1459), this literary movement turned to classical Rome, as its model in literature and oratory.


Petrarch portrait by Altichiero Source: Wikimedia Commons

In particular these men praised and tried to emulate the works of Marcus Tullius Cicero (106–43 BCE) and Marcus Fabius Quintilianus (c. 35–c. 100 CE), usually simple known as Cicero and Quintilian, both regarded as masters of oratory.


First-century AD bust of Cicero in the Capitoline Museums, Rome via Wikimedia Commons

Their late medieval admirers regarded both the literary style and their classical Latin as exemplary and considered both style and language worthy of emulation. It is here that we witness the first rupture with the Middle Ages. The literary scholars of Northern Italy regarded the medieval Latin of the Church and universities as degenerate and barbaric and strove to replace it with, what they perceived to be, the pure uncorrupted classical Latin of Cicero. How successful they were can be seen in the fact that the Latin taught in schools and to archaeology and history undergraduates at universities in my youth in the 1970s was classical Latin and only classical Latin, medieval Latin still being regarded as somehow inferior, so that the medieval archaeologists and historians had to then subsequently learn medieval Latin. Of course, medieval Latin is not degenerate and corrupt, languages evolve and more than one thousand years separate Cicero and the twelfth century medieval university. Medieval Latin had evolved out of so-called Late Latin, the Latin that had developed between approximately the third and sixth centuries CE, influenced by both Christianity and the non-Latin languages spoken on the borders of the empire. Medieval Latin began to evolve around the seventh century heavily influenced by the Church and is also referred to as Ecclesiastical Latin. Compared to classical Latin, medieval Latin had a much larger vocabulary, because it needed terms not available in classical Latin, but also significant changes in grammar, syntax and orthography.

Having denigrated the medieval language those founders of the Renaissance, also dismissed the period itself, labelling it the Middle Ages, the period in-between the glory that was the classical period of Rome and their own almost as glorious revival of it. They didn’t actually label their own period but did refer to it in Italian, as rinascimento, a rebirth, which is of course the origin of the modern term Renaissance. They referred to their own activities as studia humanitatis, from the Latin humanitas meaning education befitting a cultivated man. Once again, the origin of the modern words: humanism, humanist, and the name, the humanities. These student of humanitas devoted themselves to searching out manuscripts in monastic libraries in Latin but also in Greek that fulfilled their concept of such an education, history, music, art, literature and poetry predominating. Poggio Bracciolini was particularly zealous finding many such manuscripts including Lucretius’ De rerum natura, Vitruvius’ De architectura and lost orations by Cicero and Quintilian.


Frontispiece of a 1720 edition of the Institutio Oratoria, showing Quintilan teaching rhetoric Copper engraving by F. Bleyswyk. Source: Wikimedia Commons

These scholars also began to apply philological principles to the study of the manuscripts they recovered. The word itself is a fourteenth century coinage philologie meaning love of literature; personification of linguistics and literary knowledge. Aware that the oft copied manuscripts of ancient knowledge were corrupted by scribal errors and slips, they began to compare and analyse manuscripts, to discovery and irradicate those error and in so doing attempting to recreate the texts in their original state.

The initial impact of this movement on the medieval university was relatively small, although as we’ll see in later episode it did set other greater changes in motion. In this early phase the humanist scholars succeeded in reshaping the trivium removing logic so it was now grammar, rhetoric, history, moral philosophy and above all poetics. Impact of the latter can be clearly seen in later times. Georg von Peuerbach (1423–1461) a central figure in the history of astronomy, as a member of the First Viennese School of Mathematics, who was himself an accomplished poet, actually lectured on poetics at the university; his astronomy was, so to speak, an unofficial activity. Conrad Celtis (1459–1508), instrumental in introducing and spreading humanism north of the Alps and known in German as the Arch-Humanist, a crowned poet laureate and founder of the Second Viennese School of Mathematics, when called to the University of Vienna in 1497 founded a Collegium poetarum et mathematicorum, that is a college for poetry and mathematics.


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

A question remains open, is it correct to name an entire epoch or period of history after what was initially a small, rather local movement within a limited academic sphere? The answer is yes, because that movement created waves that spread through time and space outwards from Florence to encompass the whole of Europe and influence the intellectual and academic development over the next two hundred plus years. In later posts we shall be looking at those developments with regard to their impact on the evolution of the sciences. Another open question is when did the Renaissance end? This is hotly debated, and I shall, for my purposes, follow Francis Yates, who takes the end of the Thirty Years War as the end of the Renaissance, which I will explain, or justify in my next post. A closing important comment is that there is actually a very high level of continuity rather than disruption from the High Middle Ages through the Renaissance and one can regard the Renaissance both as a phase of the Middle Ages but also of the Early Modern Period; all historical periodisations are of course artificial and also to some extent arbitrary.



1 Comment

Filed under Mediaeval Science, Renaissance Science