OHMS or everything you wanted to know about the history of trigonometry and didn’t know who to ask

When I was a kid, letters from government departments came in buff, manila envelopes with OHMS printed on the front is large, black, capital letters. This acronym stood for, On Her Majesty’s Service and earlier during Liz’s father’s reign (and no I’m not that old, although I was just born in his reign), On His Majesty’s Service, implying that civil servants worked directly for the monarch.  This was, of course, the origin of the title of Ian Fleming’s eleventh James Bond novel, On Her Majesty’s Secret Service

When I started learning trigonometry at school this acronym took on a whole new meaning as a mnemonic for the sine relation in right angle triangles, Opposite over Hypotenuse Means Sine. Recently it occurred to me that we had no mnemonic for the other trigonometric relations. Now in those days or even later when the trigonometry I was taught got more complex, I wasn’t aware of the fact that this mathematical discipline had a history. Now, a long year historian of mathematics, I am very much aware of the fact that trigonometry has a very complex, more than two-thousand-year history, winding its way from ancient Greece over India, the Islamic Empire and Early Modern Europe down to the present day. 

The Canadian historian of mathematics, Glen van Brummelen has dedicated a large part of his life to researching, writing up and publishing that history of trigonometry. The results of his labours have appeared in three volumes, over the years, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton University Press, Princeton and Oxford, 2009, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, Princeton and Oxford, 2013 and most recently The Doctrine of TrianglesA History of Modern Trigonometry, Princeton University Press, Princeton and Oxford, 2021. He describes himself as the “best trigonometry historian, and the worst trigonometry historian”, as he is the only one[1]

A review of these three volumes could be written in one sentence, if you are interested in the history of trigonometry, then these three masterful volumes are essential. One really doesn’t need to say more, but in what follows I will give a brief sketch of each of the books. 

The Mathematics of the Heavens and the Earth: The Early History of Trigonometry delivers exactly what it says on the cover. The book opens with a brief but detailed introduction to the basics of spherical astronomy, because for a large part of the period covered, what we have is not the history of plane trigonometry, that’s the stuff we all learnt at school, but spherical trigonometry, that is the geometry of triangles on the surface of a sphere, which was developed precisely to do spherical astronomy. 

A friendly warning for potential readers this is not popular history but real, hardcore history of mathematics with lots of real mathematical examples worked through in detail. However, given the way Van Brummelen structures his narrative, it is possible to skip the worked examples and still get a strong impression of the historical evolution of the discipline. This is possible because Van Brummelen gives a threefold description of every topic that he elucidates. First comes a narrative, fairly non-technical, description of the topic he is discussing. This is followed by an English translation of a worked example from the historical text under discussion, followed in turn by a technical explication of the text in question in modern terminology. Van Brummelen’s narrative style is clear and straightforward meaning that the non-expert reader can get good understanding of the points being made, without necessarily wading through the intricacies of the piece of mathematics under discussion. 

The book precedes chronologically. The first chapter, Precursors, starts by defining what trigonometry is and also what it isn’t. Having dealt with the definitions, Van Brummelen moves onto the history proper dealing with things that preceded the invention of trigonometry, which are closely related but are not trigonometry. 

Moving on to Alexandrian Greece, Van Brummelen takes the reader through the beginnings of trigonometry starting with Hipparchus, who produced the first chord table linking angles to chords and arcs of circles, Moving on through Theodosius of Bithynia and Menelaus of Alexandria and the emergence of spherical trigonometry. He then arrives at Ptolemy his astronomy and geography. Ptolemy gets the longest section of the book, which given that everything that follows in some way flows from his work in logical. Here we also get two defining features of the book. The problem of calculating trigonometrical tables and what each astronomer or mathematician contributed to this problem and the trigonometrical formulas that each of them developed to facilitate calculations. 

From Greece we move to India and the halving of Hipparchus’ and Ptolemy’s chords to produce the sine function and later the cosine that we still use today. Van Brummelen takes his reader step for step and mathematician for mathematician through the developments of trigonometry in India. 

The Islamic astronomers took over the baton from the Indians and continued the developments both in astronomy and geography. It was Islamic mathematicians, who developed the plane trigonometry that we know today rather than the spherical trigonometry. As with much other mathematics and science, trigonometry came into medieval Europe through the translation movement out of Arabic into Latin. Van Brummelen traces the development in medieval Europe down to the first Viennese School of mathematics, John of Gmunden, Peuerbach, and Regiomontanus. This volume closes with Johannes Werner and Copernicus, with a promise of a second volume. 

In the book itself, the brief sketch above is filled out in incredible detail covering all aspects of the evolution of the discipline, the problems, the advances, the stumbling stones and the mathematicians and astronomers, who discovered each problem, solved, or failed to solve them. To call Van Brummelen comprehensive would almost be an understatement. Having finished this first volume, I eagerly awaited the promised second volume, but something else came along instead.

Having made clear in his first book that the emphasis is very much on spherical trigonometry rather than plane trigonometry, in his second book Van Brummelen sets out to explain to the modern reader what exactly spherical trigonometry is, as it ceased to be part of the curriculum sometime in the modern period. What we have in Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry is a spherical trigonometry textbook written from a historical perspective. The whole volume is written in a much lighter and more accessible tone than The Mathematics of the Heavens and the Earth. After a preface elucidating the purpose of the book there follow two chapters, Heavenly Mathematics and Exploring the Sphere, which lay out and explain the basics in clear and easy to follow steps.

Next up, we have the historical part of the book with one chapter each on The Ancient Approach and The Medieval Approach. These chapters could be used as an aid to help understand the relevant sections of the authors first book. But fear not the reader must not don his medieval personality to find their way around the complexities of spherical trigonometry because following this historical guide we are led into the modern textbook.

The bulk of the book consists of five chapters, each of which deals in a modern style with an aspect of spherical trigonometry: Right Angle Triangles, Oblique Triangles, Areas, Angles and Polyhedra, Stereographic Projection, and finally Navigation by the Stars. The chapter on stereographic projection is particularly interesting for those involved with astrolabes and/or cartography. 

The book closes with three useful appendices. The first is on Ptolemy’s determination of the position of sun. The second is a bibliography of textbooks on or including spherical trigonometry with the very helpful indication, which of them are available on Google Books. The final appendix is a chapter by chapter annotated list of further reading on each topic. 

If you wish to up your Renaissance astrology game and use the method of directions to determine your date of death, which require spherical trigonometry to convert from one celestial coordinate system to another, then this is definitely the book for you. It is of course also a brilliant introduction for anybody, who wishes to learn the ins and outs of spherical trigonometry. 

I bought Van Brummelen’s first book when it was published, in 2009, and read it with great enthusiasm, but experienced a sort of coitus interruptus, when in stopped in the middle of the Renaissance, the period that interested me most. I was consoled by the author’s declaration that a second volume would follow, which I looked forward to with great expectations. Over the years those expectations dimmed, and I began to fear that the promised second volume would never appear, so I was overjoyed when the publication of The Doctrine of Triangles was announced this year and immediately placed an advanced order. I was not disappointed. 

The modern history of trigonometry continues where the early history left off, tracing the developments of trigonometry in Europe from Regiomontanus down to Clavius and Gunter in the early seventeenth century. There then follows a major change of tack, as Van Brummelen delves into the origins of logarithms.

Today in the age of the computer and the pocket calculator, logarithmic tables are virtually unknown, a forgotten relic of times past. I, however, grew up using my trusty four figure log tables to facilitate calculations in maths, physics, and chemistry. Now, school kids only know logarithms as functions in analysis. One thing that many, who had the pleasure of using log tables, don’t know is that Napier’s first tables were of the logarithms of trigonometrical factions in order to turn the difficult multiplications and divisions of sines, cosines et al in spherical trigonometry into much simpler additions and subtractions and therefore Van Brummelen’s detailed presentation of the topic.

Moving on, in his third chapter, Van Brummelen now turns to the transition of trigonometry as a calculation aid in spherical and plane triangles to trigonometrical functions in calculus. There where they exist in school mathematics today. Starting in the period before Leibniz and Newton, he takes us all the way through to Leonard Euler in the middle of the eighteenth century. 

The book now undergoes a truly major change of tack, as Van Brummelen introduces a comparative study of the history of trigonometry in Chinese mathematics. In this section he deals with the Indian and Islamic introduction of trigonometry into China and its impact. How the Chinese dealt with triangles before they came into contact with trigonometry and then the Jesuit introductions of both trigonometry and logarithms into China and to what extent this influenced Chinese geometry of the triangle. A fascinating study and an enrichment of his already excellent book.

The final section of the book deals with a potpourri of developments in trigonometry in Europe post Euler. To quote Van Brummelen, “A collection of short stories is thus more appropriate here than a continuous narrative.” The second volume of Van Brummelen’s history is just as detailed and comprehensive as the first. 

All three of the books display the same high level of academic rigour and excellence. The two history volumes have copious footnotes, very extensive bibliographies, and equally extensive indexes. The books are all richly illustrated with many first-class explanatory diagrams and greyscale prints of historical title pages and other elements of the books that Van Brummelen describes. All in all, in his three volumes Van Brummelen delivers a pinnacle in the history of mathematics that sets standards for all other historians of the discipline. He really does live up to his claim to be “the best historian of trigonometry” and not just because he’s the only one.

Coda: If the potential reader feels intimidated by the prospect of the eight hundred and sixty plus pages of the three volumes described here, they could find a gentle entry to the topic in Trigonometry: A Very Short Introduction (OUP, 2020), which is also authored by Van Brummelen, a sort of Van Brummelen light or Van Brummelen’s greatest hits.

In this he covers a wide range of trigonometrical topics putting them into their historical context. But beware, reading the Very Short Introduction could well lead to further consumption of Van Brummelen’s excellent work. 


[1] This is not strictly true as Van Brummelen has at least two predecessors both of who he quotes in his works. The German historian Anton von Braunmühl, who wrote several articles and a two volume Vorlesung über Geschichte der Trigonometrie (Leipzig, 1900/1903) and the American Sister Mary Claudia Zeller, The Development of Trigonometry from Regiomontanus to Pitiscus (Ann Arbor 1944)

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Filed under History of Astronomy, History of Cartography, History of Islamic Science, History of Mathematics, History of Navigation

We plumb the depths of boundless history of science stupidity 

Late on Friday evening, Renaissance mathematicus friend and star historian of medieval science, Seb Falk, posted a couple of paragraphs from an Oberserver newspaper interview with the physicist and self-appointed science communicator Michio Kaku, from April this year. The history of science content of those paragraphs was so utterly, mindbogglingly ludicrous that it had me tossing and turning all night and woke from his deep winter sleep the HISTSCI_HULK, who is now raging through my humble abode like a demented behemoth on speed. What was it that set the living history of science bullshit detector in such a state of apoplexy? I offer up the evidence:

How much, do you think, would Isaac Newton understand of your book?
I think he would appreciate it. In 1666 we had the great plague. Cambridge University was shut down and a 23-year-old boy was sent home, and he saw an apple fall on his estate. And then he realised that the laws that control an apple are the same laws that control the moon. So the epidemic gave Isaac Newton an opportunity to sit down and follow the mathematics of falling apples and falling moons. But of course there was no mathematics at that time. He couldn’t solve the problem so he created his own mathematics. That’s what we are doing now. We, too, are being hit by the plague. We, too, are confined to our desks. And we, too, are creating new mathematics.

This paragraph is, of course, the tired old myth of Newton’s Annus mirabilis, which got continually recycled in the early months of the current pandemic and, which I demolished in a blog post back in April 2020, so I won’t bore you with a rehash here. However, Kaku has managed to add a dimension of utter mind shattering ignorance

But of course there was no mathematics at that time. He couldn’t solve the problem so he created his own mathematics.

Just limiting myself to the Early Modern Period, Tartaglia, Cardano, Ferrari, Bombelli, Stiefel, Viète, Harriot, Napier, Kepler, Galileo, Cavalieri, Fermat, Descartes, Pascal, Gregory, Barrow, Wallis and many others are all not just turning in their graves, but spinning at high speed, whilst screaming WHAT THE FUCK! at 140 decibels.

The real irony is that not only did Newton not codify the calculus during his non-existent Annus mirabilis–he didn’t create it, it evolved over a period of approximately two thousand years–but when he wrote his Principia twenty years later, he used a modernised version of Euclidian geometry, which was created some two thousand years earlier, and not the calculus!  

There is more to come:

There are many brilliant scientists whose contributions you discuss in the book. Which one, for you, stands out above the rest?
Newton is at number one, because, almost out of nothing, out of an era of witchcraft and sorcery, he comes up with the mathematics of the universe, he comes up with a theory of almost everything. That’s incredible. Einstein piggybacked on Newton, using the calculus of Newton to work out the dynamics of curved spacetime and general relativity. They are like supernovas, blindingly brilliant and illuminating the entire landscape and changing human destiny. Newton’s laws of motion set into motion the foundation for the Industrial Revolution. A person like that comes along once every several centuries.

Where to start? To describe the late seventeenth and early nineteenth centuries as “an era of witchcraft and sorcery” is simply bizarre. This is the highpoint of the so-called Scientific Revolution, it is the Augustan age of literature that in Britain alone produced Swift, Pope, Defoe, and many others, it is the age of William Hogarth, it is the age in which modern capitalism was born and, and, and… Yes, some people still believed in witchcraft and sorcery, some still do today, but it was by no means a central factor of the social, political, or cultural life of the period. This was the dawn of the Enlightenment, for fuck’s sake, the period of Spinosa, Locke, Hume and, once again, many others. 

The “Newton is at number one, because, almost out of nothing” produces howls of protest echoing down the centuries from Kepler, Stevin, Galileo, Torricelli, Descartes, Pascal, Huygens et al

With respect to Steven Strogatz, I will grant him his hyperbolic “mathematics of the universe”, but Newton’s physics covers just a very small area of the entire world of knowledge and is in no way a “theory of almost everything.” 

I should leave the comments on Einstein, to those better qualified to condemn them than I. However, I find the claim that “Einstein piggybacked on Newton” simply grotesque. Also, the calculus that Newton and Leibniz codified, which became the mathematics of Newtonian physics, although Newton himself did not use it, is a very different beast to the tensor calculus used in the general relativity theory. In fact, the only thing they have in common is the word calculus, I would expect someone with a doctorate in physics to know that.

One is tempted to ask if the Guardian has fired all of its science editors and replaced them with failed door to door vacuum cleaner salesmen. It’s the only rational explanation as to why the science pages of the Observer were adorned with such unfathomably dumb history of science. It is supposed to be a quality newspaper!

The HISTSCI_HULK has in the meantime thrown himself off the balcony into the snowstorm and was last seen stomping off into the woods muttering, The horror! The horror!

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Filed under History of science, Myths of Science

Renaissance Science – XXIV

It might be considered rational to assume that during the period that is viewed as the precursor to the so-called scientific revolution, which is itself viewed as the birth of modern science, that the level of esotericism and the importance of the occult sciences would decline. However, the exact opposite is true, the Renaissance saw a historical highpoint in the popularity and practice of esotericism and the occult sciences. We have already seen how astro-medicine or iatromathematics came to dominate the practice of medicine in this period and horoscope astrology continued to be practiced by almost all astronomers till well into the seventeenth century. We also saw how, not just due to the efforts of Paracelsus, the practice and status of alchemy also reached a high point during this period. Now, I would like to take a look at the emergence of natural magic during this period and the processes that drove it.

There was nothing new about the supposed existence of magic in the Renaissance, but throughout the Christian era magic was associated with demonic forces. It was thought that people, who practiced magic, were calling on the power of the devil. Augustinus, who had been a practicing astrologer and believed that astrology worked, thought it could only do so through demonic forces thus his famous condemnation of the mathematici, by which he meant astrologers and not mathematicians. What was new in the Renaissance was the concept of a magic, natural magic, that was not dependent on demonic forces. This is the origin of the concept of the distinction between black magic and white magic, to use the more modern terms for it. Various groups of texts that found prominence in the Renaissance humanist search for authentic texts from antiquity were instrumental in this development. In roughly the order of there emergence they were the philosophy of Plato and in particular the work of the Neoplatonists from the third century CE, the Hermetic Corpus, and the Jewish Kabbalah. In the first two of these the humanist scholar Marsilio Ficino (1433–1499) played a pivotal role. 

Marsilio Ficino from a fresco painted by Domenico Ghirlandaio in the Tornabuoni Chapel, Santa Maria Novella, Florence Source: Wikimedia Commons

Ficino was the son of Diotifeci d’Angolo a physician whose patron was Cosimo de’ Medici (1389–1464) a major supporter of the humanist Renaissance. Ficino became a member of the Medici household and Cosimo remained his patron for his entire life, even appointing him tutor to his grandson Lorenzo de’ Medici (1449–1492).

Cosimo de’ Medici portrait by Jacopo Pontormo Source: Wikimedia Commons

At the Council of Florence (1438-1444), an attempt to heal the schism between the Orthodox and Catholic Churches, Cosimo de’ Medici became acquainted and enamoured with the Greek Neoplatonic philosopher Georgius Gemistus Pletho (C. 1355–c. 1450), who was also the teacher of Basileios Bessarion (1403–1472) another highly influential Renaissance scholar.

Portrait of Gemistus Pletho, detail of a fresco by Benozzo Gozzoli, Palazzo Medici Riccardi, Florence Source: Wikimedia Commons 

Returning home Cosimo decided to refound Plato’s Academy and appointed Ficino to head it, who then proceeded to learn Greek from Ioannis Argyropoulus (c. 1415–1487), another Greek, who came to Italy during the Council of Florence.

Ioannis Argyropoulos as depicted by Domenico Ghirlandaio Source: Wikimedia Commons

Today Plato is regarded as one of the greatest and most important of all Western philosophers, there is a saying that Plato is just footnotes to Socrates and Alfred North Whitehead (1861–1947) once quipped that Western philosophy is just footnotes to Plato, so it might seem strange to us that during the Renaissance Plato was virtually unknown in Europe. In the Early Middle Ages, the only one of Plato’s worked that was known in Latin was the Timaeus (c. 360 BCE) his speculations on the nature of the physical world, about which George Sarton infamously wrote in his A History of Science (Harvard University Press, 1959):

The influence of Timaeus upon later times was enormous and essentially evil. A large portion of Timaeus had been translated into Latin by Chalcidius, and that translation remained for over eight centuries the only Platonic text known in the Latin West. Yet the fame of Plato had reached them, and thus the Latin Timaeusbecame a kind of Platonic evangel which many scholars were ready to interpret literally. The scientific perversities of Timaeus were mistaken for scientific truths. I cannot mention any other work whose influence was more mischievous, except the Revelations of John the Devine. The apocalypse, however, was accepted as a religious book, the Timaeus as a scientific one; errors and superstition are never more dangerous than when offered to us under the cloak of science. 

George Sarton  A History of Science (Harvard University Press, 1959)

Strong stuff! Somehow Plato got ignored during the so-called Scientific Renaissance and unlike Aristotle his works were not translated into Latin at this time. In 1462 Cosimo de’ Medici supplied Ficino with Greek manuscripts of Plato’s work and commissioned him to translate them into into Latin, a task that he carried out by 1468-69, the works being published in 1484. Ficino also translated the work of many of the Neoplatonist in particular the work of Porphyry (c. 234–c. 305) and Plotinus (c. 204–270 CE). 

So, what does this revival in the philosophy of Plato have to do with magic, natural or otherwise? The answer lies in that which Sarton found so abhorrent in Plato’s philosophy of science. Plato’s philosophy of scienced is heavily laced with what can be simply described as a heavy dose of mysticism and it is this aspect of Plato’s philosophy that is strongly emphasised by the third century Neoplatonists. I’m not going to go into great detail as this blog post would rapidly turn into a monster, there have been numerous thick books written about the Timaeus alone but will only present a very brief sketch of the relevant concepts.

According to Plato the cosmos was created by the demiurge, the divine craftsman, as a single living entity, which he then endowed with a world soul. It was this concept of the Oneness of the cosmos that was at the core of the philosophy of the third century Neoplatonists and in Ficino’s own personal interpretation of Platonic thought. How this relates to natural magic, I will explain later after we have looked at Ficino’s translation of the Hermetic Corpus. 

In 1460, Leonardo de Candia Pistola, one of the agents Cosimo de’ Medici had sent out to search European monasteries for ancient manuscripts, returned to Tuscany with the so-called Corpus Hermeticum. This is a collection of seventeen Greek texts supposedly of great antiquity and written by Hermes Trismegistus a legendary Hellenistic creation combining elements of the Egyptian god Thoth and his Greek counterpart Hermes. Ficino interrupted his translation of Plato and immediately began translating the texts of the Corpus Hermeticum into Latin; he translated the first fourteen of the texts and Lodovico Lazzarelli (1447–1500) translated the other three.

Lodovico Lazzarelli (via his muse) presents the manuscript of Fasti christianae religionis to Ferdinand I of Aragon, king of Naples and Sicily. (Beinecke MS 391, f.6v) Source: Wikimedia Commons

There are other Hermetic texts most notably the Emerald Tablet an Arabic text first known in the eight or early nine century and the Asclepius already know in Latin during the Middle Ages. 

Once again, the subject is far to extensive for an analysis in a blog post, so I will only sketch a brief outline of the salient points. The hermetic texts are a complex mix of religious-philosophical magic texts, astrological texts, and alchemical texts. The religious-philosophical aspect has a strong similarity to the Platonic theory of the One, the cosmos as a single living entity. In hermeticism, God and the cosmos are one and the same thing. God is the All and at the same time the creator of the All. Hermeticists also believed in the principle of a prisca theologica, that there is a single true, original theology, which for Christian Hermeticists originates with Moses. They believed Hermes had his knowledge direct from Moses. A central tenet of Hermeticism was the macrocosm-microcosm theory, as above so below. Meaning the Earth is a copy of the heavens, astrology and alchemy are instances of the forces of the heavens working on the Earth. 

Macrocosm-Microcosm Lucas Jemnnis Museum Hermeticum (1625)

Combining Neoplatonic philosophy and Hermeticism, Renaissance humanists developed the concept of natural magic. Rather than a magic based on demonic influence, natural magic works by tapping directly into the forces of the cosmos that are the source of astrology and alchemy. 

The Kabbalah is a school of Jewish esoteric teaching that is supposed to explain the relationship between the unchanging, infinite, eternal God and the mortal, finite cosmos, God’s creation. Renaissance humanist believed in the ideal of the tres linguæ sacræ (the three holy languages)–Latin, Greek, and Hebrew–the languages needed for Biblical studies. The scholars of Hebrew stumbled across the Jewish Kabbalah and began to incorporate it into the Renaissance mysticism. Giovanni Pico della Mirandola (1463–1494) an Italian Renaissance nobleman and student of Ficino

Giovanni Pico della Mirandola portrait by Cristofano dell’Altissimo (c. 1525–1605) Source: Wikimedia Commons

founded or created a Christian Kabbalah, which he wove together with Platonism, Neoplatonism, Aristotelianism, and Hermeticism. A heady brew! Given his own personal philosophy, which included a form of natural magic that he called Theurgy, operation of the gods, I find it more than somewhat ironic that Pico is hailed as an early rejecter of astrology.

The Christian Kabbalah was developed by Pico’s most noted follower in this area, the German humanist, Johannes Reuchlin (1455–1522), who not only propagated the Christian Kabbalah but fiercely defended Jewish literature against the strong Anti-Semitic movement to ban and burn it in the early sixteenth century.

Johann Reuchlin, woodcut depiction from 1516 Source: Wikimedia Commons

He was a highly influential teacher of Hebrew and became professor for Hebrew at the University of Ingolstadt. Amongst his most notable students were his nephew Philip Melanchthon (1497–1560) (it was Reuchlin who suggested that Philip adopt the humanist name Melanchthon a Greek translation of his birth name, Schwartzerdt) and the Nürnberger reformer, Andreas Osiander (1498­–1522), who famously authored the Ad lectorum at the beginning of Copernicus’ De revolutionibus. Even Martin Luther consulted Reuchlin on Hebrew and read his texts on the Kabbalah, whilst disagreeing with him.

Hermeticism was adopted by many leading thinkers in the Early Modern Period including Giordano Bruno (1548–1600), Francesco Patrizi (1529–1597) (an influential and much discussed philosopher in the period, who is largely forgotten today except by specialists), and Robert Fludd (1574–1637), who notoriously disputed with Johannes Kepler, rejecting Kepler’s mathematics-based science for one based on what might be described as hermetic mandalas. Even Isaac Newton (1642–1727) processed a substantial collection of hermetic literature. 

The English Renaissance historian Frances Yates (1899–1981) argued in, her much praised, Giordano Bruno and the Hermetic Tradition (1964) that hermeticism played a central role in the emergence of heliocentric astronomy in the Early Modern Period. Even Copernicus appears to quote Hermes Trismegistus in his De revolutionibus in his hymn of praise of the Sun to justify its central position of the cosmos:

At rest, however, in the middle of everything is the sun. For in this most beautiful temple, who would place this lamp in another or better position than that from which it can light up the whole thing at the same time? For, the sun is not inappropriately called by some people the lantern of the universe, its mind by others, and its ruler by still others. [Hermes] Trismegistus labels it a visible god and Sophocles’ Electra, the all-seeing. 

Yates’ thesis is now largely rejected by historians of astronomy, but her book is still praised for making people aware of the extent of hermeticism in the Early Modern Period. It is difficult to assess if hermeticism had any direct or indirect influence on the development of science during the period, but it was certainly very present in the intellectual atmosphere of the period.

Before I turn to natural magic it is interesting to note that the highly influential, humanist scholar Isaac Casaubon (1559–1614), who through the much-propagated philological analysis of texts was able to show, at the beginning of the seventeenth century, that the Corpus Hermeticum was not as ancient as its supporters claimed but was created in the early centuries of the common era and was thus contemporaneous with the Neoplatonic texts. Casaubon’s analysis was largely ignored by the supporters of hermeticism in the seventeenth century.

Isaac Casaubon artist unknown Source: Wikimedia Commons

 As already stated above natural magic was the belief into the possibility to directly tap into the forces within the single, living, cosmic organism, of the Neoplatonists and Hermeticists, that were present in astrology and alchemy. One of the strongest propagators of natural magic was the German polymath Heinrich Cornelius Agrippa von Nettesheim (1486–1535).

Heinrich Cornelius Agrippa von Nettesheim Source: Wikimedia Commons

He presented his views on the topic in his widely read De Occulta Philosophia libri III (Three Books of Occult Philosophy) the first volume of which was published in Paris in 1531 and the full three volumes in Cologne in 1533.

Man inscribed in a pentagram, from Heinrich Cornelius Agrippa’s De Occulta Philosophia libri III . The signs on the perimeter represent the 5 visible planets in astrology. Source: Wikipedia Commons

In an earlier work, De incertitudine et vanitate scientiarum atque artium declamatio invectiva (Declamation Attacking the Uncertainty and Vanity of the Sciences and the Arts, Cologne 1527) he wrote the following explanation of natural magic:

Natural magic is that which having contemplated the virtues of all natural and celestial and carefully studied their order proceeds to make known the hidden and secret powers of nature in such a way that inferior and superior things are joined by an interchanging application of each to each: thus incredible miracles are often accomplished not so much by art as by nature, to whom this art is a servant when working at these things. For this reason magicians are careful explorers of nature, only directing what nature has formally prepared, uniting actives to passives and often succeeding in anticipating results; so that these things are popularly held to be miracles when they are really no more than anticipations of natural operations … therefore those who believe the operations of magic to be above or against nature are mistaken because they are only derived from nature and in harmony with it.

The other major figure of natural magic was the Italian polymath Giambattista della Porta (1535(?)–1615), a respected figure in the Renaissance scientific community, who authored the Magia Naturalis, first published as a single volume in 1558, which grew to twenty volumes by 1589.

Giambattista della Porta artist unknown Source: Wikimedia Commons

I have written an extensive blog post on della Porta and his book here, so I won’t add more here. He describes natural magic thus:

Magick is nothing else but the knowledge of the whole course of Nature. For, whilst we consider the Heavens, the Stars, the Elements, how they moved, and how they changed, by this means we find out the hidden secrecies of living creatures, of plants, of metals, and of their generation and corruption; so that this whole science seems merely to depend upon the view of Nature … This Art, I say, is full of much virtue, of many secret mysteries; it openeth unto us the properties and qualities of hidden thins, and the knowledge of the whole course of Nature; and it teacheth us by the agreement and the disagreement of things, either so to sunder them, or else to lay them so together by the mutual and fit applying of one thing to another, as thereby we do strange works, such as the vulgar sort call miracles, and such men can neither well conceive, nor sufficiently admire … Wherefore, as many of you as come to behold Magic, must be perswaded that the works of Magick are nothing else but the works of Nature, whose dutiful hand-maid magick is.

Both Agrippa and della Porta were widely read and important parts of the philosophical debates around science in the Renaissance but it is difficult to say whether their concept of natural magic any influence on the development of science in this period. It can and has been argued that because natural magic was inductive by nature that it influenced the adoption of induction in the scientific method in the seventeenth century. There exists a debate amongst historians to what extent Francis Bacon was or was not influenced by hermeticism and natural magic. Others such as Bruno and John Dee certainly were. Dee included magic as one of the mathematical disciplines in his Mathematicall Praeface to Henry Billingsley’s English translation of The Elements of Euclid.

It probably seems strange to include a long essay on what is basically occult philosophy in a series on Renaissance science, but one can’t ignore the fact that Neoplatonism, hermeticism and natural magic were all separately and in various combinations an integral part of the intellectual debate of the period between fourteen and seventeen hundred.

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Filed under History of Alchemy, History of Astrology, History of science, Renaissance Science

The astronomical librarian 

I’m continuing my look at the French mathematician astronomers of the seventeenth century with some of those, who were both members of Nicolas-Claude Fabri de Peiresc’s group of telescopic, astronomical observers, as well as Marin Mersenne’s informal Academia Parisiensis, starting with Ismael Boulliau (1605–1694), who like Peiresc and Mersenne was also a prominent member of the Republic of Letters with about 5000 surviving letters. 

Ismael Boulliau Source: Wikimedia Commons

Boulliau was born in Loudun, France the second son of Ismael Boulliau a notary and amateur astronomer and Susanne Motet on 28 September 1605. The first son had been born a year earlier and was also named Ismael, but he died and so the name was transferred to their second son. Both of his parents were Calvinists. His father introduced him to astronomy and in his Astronomia philolaica (1645) Ismael junior tells us that his father observed both Halley’s comet in 1607 and the great comet of 1618. The later was when Boulliau was thirteen years old, and one can assume that he observed together with his father. 

Probably following in his father’s footsteps, he studied law but at the age of twenty-one he converted to Catholicism and in 1631, aged twenty-six, he was ordained a priest. In 1632 he moved to Paris and began to work for Pierre Dupuy (1582–1651) and his brother Jacques (1591–1656), who were keepers of the Bibliothèque du Roi, today the Bibliothèque nationale de France. Boulliau held this position until the death of the Dupuy brothers and during that time travelled widely in Europe collecting books and manuscripts for the library. 

Pierre Dupuy Source: Wikimedia Commons

Boulliau also enjoyed the patronage of the powerful and influential de Trou family, who were closely connected with the library and who financed his book collecting travels. Following the death of the Dupuy brothers he became employed by the French ambassador to the United Provinces, a member of the de Trou family, a secretary and librarian. In 1666, following a dispute with his employer, he became librarian at the Collège de Laon in Paris. For the last five years of his live he returned to the priesthood in the Abbey St Victor near Paris where he died aged 89. Although Boulliau was an active member of Mersenne’s Academia Parisiensis he never became a member of the Académie des sciences, but he was elected one of the first foreign associates of the Royal Society on 4 April 1667. 

Abbey of St. Victor, 1655 Source: Wikimedia Commons

 Like Peiresc, Boulliau was a polymath with extensive knowledge of a wide range of humanities topics, which was useful in his work as a librarian, but, as with Peiresc, it is scientific activities that are of interest here. He continued to make astronomical observations throughout his life, which were of a high level of accuracy. In his Principia, Newton puts him on a level with Kepler for his determination of the planetary orbits. In Book 3 Phenomenon 4 of Principia Newton writes: 

But of all astronomers, Kepler and Boulliau have determined the magnitude of the orbits from observations with the most diligence. 

Boulliau’s first significant scientific publication was, however, not in astronomy but in optics, his De natura lucis (On the Nature of Light) (1638) based on the discussions he was having with Gassendi on the topic. This work is not particular important in the history of optics but it does contain his discussion of Kepler’s inverse square law for the propagation of light.

Source: Wikimedia Commons

His first astronomical work Philolaus (1639), which places him firmly in the Copernican heliocentric camp but not, yet a Keplerian was next. 

He now changed tack once again with a historical mathematical work. In 1644, he translated and published the first printed edition of Theon of Smyrna’s Expositio rerum mathematicarum ad legendum Platonem utilium a general handbook for students of mathematics of no real significance. Continuing with his mathematical publications. In 1657, he published De lineis spiralibus (On Spirals) related to the work of Archimedes and Pappus on the topic.

Source: Wikimedia Commons

Much later in 1682, he published Opus novum ad arithmeticam infinitorum, which he claimed clarified the Arithmetica infinitorum(1656) of John Wallis (1616–1703).

Source: Wikimedia Commons

All of Boulliau’s work was old fashioned and geometrical. He rejected the new developments in analytical mathematics and never acknowledged Descartes’ analytical geometry. As we shall see, his astronomy was also strictly geometrical. He even criticised Kepler for being a bad geometer. 

Boulliau’s most important publication was his second astronomical text Astronomia philolaica (1645).

Source: Wikimedia Commons

In this highly influential work, he fully accepted Kepler’s elliptical orbits but rejects almost all of the rest of Kepler’s theories. As stated above his planetary hypothesis is strictly geometrical and centres round his conical hypothesis:

“The Planets, according to that astronomer [Boulliau], always revolve in circles; for that being the most perfect figure, it is impossible they should revolve in any other. No one of them, however, continues to move in any one circle, but is perpetually passing from one to another, through an infinite number of circles, in the course of each revolution; for an ellipse, said he, is an oblique section of a cone, and in a cone, betwixt the vertices of the ellipse there is an infinite number of circles, out of the infinitely small portions of which the elliptical line is compounded. The Planet, therefore, which moves in this line, is, in every point of it, moving in an infinitely small portion of a certain circle. The motion of each Planet, too, according to him, was necessarily, for the same reason, perfectly equable. An equable motion being the most perfect of all motions. It was not, however, in the elliptical line, that it was equable, but in any one of the circles that were parallel to the base of that cone, by whose section this elliptical line had been formed: for, if a ray was extended from the Planet to any one of those circles, and carried along by its periodical motion, it would cut off equal portions of that circle in equal times; another most fantastical equalizing circle, supported by no other foundation besides the frivolous connection betwixt a cone and an ellipse, and recommended by nothing but the natural passion for circular orbits and equable motions,” (Adam Smith, History of Astronomy, IV.55-57).

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

Boulliau’s theory replaces Kepler’s second law, and this led to the Boulliau-Ward debate on the topic with the English astronomer Seth Ward (1617–1689), the Savilian Professor of astronomy at Oxford University.

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

Ward criticised Boulliau’s theory in his In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis (1653), also pointing out mathematical errors in Boulliau’s work. 

Boulliau responded to Ward’s criticisms in 1657, acknowledging the errors and correcting but in turn criticising Ward’s model in his De lineis spiralibus. A year earlier Ward had published his own version of Keplerian astronomy in his Astronomia geometrica (1656).

Source: Wikimedia Commons

This exchange failed to find a resolution but this very public debate between two of Europe’s leading astronomers very much raised awareness of Kepler’s work and was factor in its eventual acceptance of Kepler’s elliptical heliocentric astronomy. 

It was in his Astronomia philolaica that Boulliau was the first to form an inverse squared theory of attraction between the sun and the planets. 

As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances that is, 1/d2 ​.

Here we see the influence of Kepler’s theory of light propagation, which as noted Boulliau discussed in his De natura lucis. However, having set up this hypothesis Boulliau goes on to reject it. 

… I say that the Sun is moved by its own form around its axis, by which form it was ignited and made light, indeed I say that no kind of motion presses upon the remaining planets … indeed [I say] that the individual planets are driven round by individual forms with which they were provided …

Despite Boulliau’s rejection of his own hypothesis, during Newton’s dispute with Hooke over who should get credit for the theory of gravity, he gives Boulliau the credit in a letter to Edmond Halley.

…so Bullialdus [i.e., Boulliau] wrote that all force respecting ye Sun as its center & depending on matter must be reciprocally in a duplicate ratio of ye distance from ye center, & used that very argument for it by wch you, Sr, in the last Transactions have proved this ratio in gravity. Now if Mr Hook from this general Proposition in Bullialdus might learn ye proportion in gravity, why must this proportion here go for his invention?

In 1667, Boulliau published a final astronomy book, Ad astronomos monita duo in which he was the first to establish the periodicity of the variable star, Mira Ceti.

Source:

His estimate of the period 333 days was only out by a one day. Mira had first been recognised as a variable star by David Fabricius beginning 3 August 1596.

Apart from his publications Boulliau kept Mersenne’s correspondence network alive for another thirty years after Mersenne’s death, communicating with Leopoldo de’ Medici (1617–1675) in Italy, Johannes Hevelius (1611–1687) in Danzig and Christiaan Huygens (1629–1695). Huygens first imparted his discovery of the rings of Saturn to Boulliau and Boulliau distributed Huygens’ System sarturnium (1658) in Paris. Boulliau also distributed Pascal’s Letters D’Amos Dettonville (1658–1659) to English and Dutch mathematicians, his challenge on the mathematics of the cycloid, an important publication in the development of calculus.

Ismael Boulliau is a prime example of a scholar, who didn’t make any major discoveries or develop any major theories himself but still had a very significant influence on the development of science.

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Filed under History of Astronomy, History of Mathematics, History of Optics, History of science

Renaissance Science – XXIII

Without doubt, one of the most eccentric and certainly one of the most controversial figures of the entire Early Modern period was the iconoclastic Swiss physician Theophrastus von Hohenheim (c. 1493–1541), more popularly known as Paracelsus. Trying to write about Paracelsus is complicated by the fact that he is the source of numerous myths and legends. Even if one resorts to the old maxim of Sergeant Joe Friday in the 1950s American radio series Dragnet, “just the facts ma’am”,* you run into problems. Every fact presented by one Paracelsus researcher has been disputed by at least one other Paracelsus researcher, so I shall just give a sketch of the generally accepted facts about his life then concentrate on his medical theories and their impact in the Early Modern Period.

He was born Theophrastus von Hohenheim the son of Wilhelm Bombast von Hohenheim, an illegitimate descendent of a Swabian aristocratic family, and his wife a bondswoman of the local Benedictine monastery in Einsiedeln in the canton of Schwyz in Switzerland, probably in 1493 or 94. Wilhelm held a Master’s degree in medicine and was physician to the mining community in Einsiedeln. Following the early death of his mother, probably around 1502, his father moved to Villach in Austria, another mining community. 

Aureoli Theophrasti ab Hohenheim. Reproduction, 1927, of etching by A. Hirschvogel, 1538. Source: Wikimedia Commons

It is probable that Theophrastus received his early education from his father in medicine, mining, minerology, botany, and alchemy. Almost nothing in known about his further education other than that he was registered as a Artzney Doctor(Doctor of Medicine) in Strasbourg in 1525 and a year later in Basel he testified that his doctorate was from the University of Ferrara. There is, however, no other evidence to support this claim. He seems to have travelled widely throughout Europe in his youth but, once again, there are no real details of this part of his life. 

In 1525 he settled in Salzburg as a physician, but probably because of the unrest caused by the German Peasant’s War he moved to Strasbourg in 1526. In 1527, he received what should have been a major boost in his career when he was called to Basel to treat the leading humanist publisher Johann Froben (c. 1460–1527), who had been written off by his own doctors, apparently because of a gangrenous foot. During six weeks of treatment in early 1527 Theophrastus succeeded in bringing relief to the publisher and for his efforts was richly rewarded and appointed town physician of Basel. This appointment included not just the right but the obligation to hold lectures at the university. Although he probably didn’t realise it at the time, Theophrastus had reached the apex of his formal career as physician.

1493 woodcut of Basle, from the Nuremberg Chronicle Source: Wikimedia Commons

During his time in Basel, Theophrastus came into contact with many leading humanist scholars, including Erasmus, who had worked for Froben and with whom he carried out a correspondence on theological issues.

Theophrastus’ time in Basel was to put it mildly stormy. He clashed head on with the local medical establishment and began his career as medical iconoclast declaring war on the conventional university medical teachings. He held his lectures in German instead of Latin to make them accessible to everyman and rejected the authority of the standard medical texts, preferring experience and empiricism to book learning. This behaviour reached a high point when he burnt a copy of Avicenna’s Canon of Medicine, probably the most important university medical textbook, on the Basel marketplace in the St John’s Eve fire on 23 June 1527. In February 1528 his brief career as an establishment physician came to an end and Theophrastus left Basel for what would turn out to be a life as an itinerant physician until his death in 1541. 

In 1529, Theophrastus moved to the city of Nürnberg, in the early sixteenth century, one of the richest cities in Europe and a major centre for both the mathematical science including astrology and medicine. His aim was to establish himself in the thriving and lucrative market for medical books. Here he decided to enter the rumbling syphilis debate. The disease had first appeared in Europe in the late fifteenth century and in fact only obtained the name, syphilis, from Girolamo Fracastoro (c. 1477–1553) in 1530. In 1529, there were two competing “cures” for syphilis, mercury, and guaiac wood. Theophrastus took up arms for mercury and against guaiac wood. He published one short pamphlet and a longer text on the topic with success. Unfortunately, the import from guaiacum wood from Brazil was financed by the Fugger banking house and the influential Leipziger physician Heinrich Stromer von Auerbach, a Fugger client, persuaded the Nürnberger medical establishment to block a planned major work from Theophrastus on the subject. Stromer’s influence throughout the German medical establishment served to effectively end Theophrastus’ medical publishing career before it had really started.

Heinrich Stromer von Auerbach Source: Wikimedia Commons

This medical publishing block led to Theophrastus adopting the name Paracelsus, a toponym for Hohenheim, for his future publication. In late 1529, he published an astrological pamphlet under the name Theophrastus Paracelsus and a short tract on the Comet of 1531 simply under the name Paracelsus. He proved to be a fairly successful astrological author and the majority of his publication up till his death were astrological.

From now on Theophrastus, blocked by the medical establishment was forced to live from treating rich private patient. He had a brief change of fortune in 1536, when he succeeded in getting his Die große Wundarzney (Great Book of Surgery) published by Heinrich Steiner (before 1500–1548) in Augsburg. The book was a success with, to Theophrastus’ annoyance, pirate editions appearing in both Ulm and Frankfurt in the same year. It remained a much-read reference work for more than a century. Theophrastus’ live continued to go downhill until his relatively early death in 1541.

Title page from ‘Der grossen Wundartzney’ (Great Surgery Book, 1536) by the Swiss alchemist and physician Paracelsus (1493-1541). Source

By the time of his death Theophrastus could be regarded as a failure. He had manged to publish little in the way of medical literature and apart from his brief time in Basel had held no important medical positions. He had succeeded in antagonising and alienating the medical establishment and was better known for his scandals than for any contributions to medicine. If his story had ended there, he would have become a mere footnote in the history of medicine as the man, who had publicly burnt a medical textbook on St John’s Eve in Basel in 1527. However, his story experienced a remarkable posthumous renaissance, which began about twenty years after his death.

Theophrastus had written a large number of books and tracts outlining his heterodox medical philosophy, none of which were published in his lifetime. Beginning in 1560, what might be termed his fan club–Adam von Bodenstein (1528–1577), Michael Toxites (1514–1581), Gerhard Dorn (c. 1530–1584), all of them physicians and alchemists–began to publish these texts, a process that culminated in the publication of a ten-volume edition of his medicinal and philosophical treatises under the title Bucher und Schriften by Johann Huser (c. 1545–1600) in Basel from 1598 to 1591. Huser’s edition of Theophrastus’ surgical publications appeared posthumously in 1605. It is in the last third of the sixteenth century that Paracelsian medicine became a serious discipline but what was it?

Paracelsus’ medical philosophy was a complex melange of religion, astrology, alchemy, and straight forward weirdness. He was first and foremost deeply religious and fundamentally Christian. He regarded himself, above everything else, as a religious reformer and a prophet. His religious stance was at the core of his rejection of the medicine taught at the European medieval universities. Greek and Islamic medicine were both heathen and thus to be rejected. Paracelsus insisted that his medicine was one hundred percent Christian. His rejection of Greek knowledge, of course, cost him any support he might have received from the humanists, who completely rejected him. 

At the centre of his philosophy was the macrocosm/microcosm, as above so below, concept that lay at the heart of the justification for astrology. This viewed the human body as a miniature model of the cosmos, the one affecting the other. Paracelsus took this one step further believing that all the minerals found in the world were found in another form within the human body.  This tied up with his concept of alchemy.

Paracelsus’ alchemy was not the alchemy of transmuting base metals into gold and silver but a medical alchemy. This was not a new thing, The Franciscan alchemist Jean de Roquetaillade, also known as John of Rupescissa (c. 1310–c. 1368) had emphasised the use of distillation to produce medicinal elixirs in his De Consideratione Quintae Essentiae (On the Consideration of the Quintessence of all Things).

Manuscript of Rupescissa c. 1350

This very popular text was reworked and integrated into the Pseudo-Lullian Liber de secretis naturae (Book of the Secrets of Nature). Paracelsus knew both works well. Believing like cures like, Paracelsus developed alchemical mineral cures that would act upon the minerals he believed to be in the body. He also believed that the organs of the body were organic alchemical apparatuses, there being an alchemical furnace at the centre of the body. Philosophically, borrowing from the Aristotelian belief that all metals originated from two principles present in different quantities, which Abu Mūsā Jābir ibn Hayyān named Mercury and Sulphur, in the eighth century. He believed that all matter consisted of three principles, his tria prima, Mercury, Sulphur, and Salt. A tripartite concept mirroring the Holy Trinity. I’m not going to go any deeper into this aspect of his alchemy or how it related to the traditional four element matter theory, but I will point out that it eventually led to the phlogiston theory in the seventeenth century. 

It was Paracelsus’ medical alchemy that his followers took up during the posthumous renaissance of his work, rechristening it chymiatria or iatrochemistry. This renaissance mostly took place not in the universities, the university professors of medicine rejecting the book burning iconoclast, but on the courts of various European rulers. First and foremost, Ernst of Bayern (1554­–1611), archbishop of Cologne, who was Johan Huser’s patron. Earlier the elector Palatine Ottheinrich (1502–1559) had been an enthusiastic supporter of Paracelsus. Later the Holy Roman Emperor Rudolf II (1552–1612), Wolfgang II von Hohenlohe (1546–1610), and Moritz von Hessen-Kassel (1572–1632) were all important patrons of Paracelsian alchemy. The University of Marburg boasts that they have the world’s first professorship for chemistry, but, in fact, the chair founded by Moritz von Hessen-Kassel, with the appointment of Johannes Hartmann (1561–1638) in 1609, was for Paracelsian iatrochemistry. 

Johannes Hartmann Source: Wikimedia Commons

The chair in Marburg was followed in the seventeenth century by several other new chairs all of them being chymiatria, and closely connected with the medical departments, rather than what is now known as chemistry. However, this adoption of Paracelsian chymiatria marks two different developments. Firstly, it is the beginning of pharmacology, of which Paracelsus is often called the founder. In Germany many pharmacies are still named after him. Secondly, it is an important development in the transition from alchemy to modern chemistry, a process that took place throughout the seventeenth and eighteenth centuries, with chemists, in the modern sense, in the eighteenth century strongly denying that their discipline ever had anything to do with alchemy. 

There were notable cases of scholars in the seventeenth century adopting and contributing to these developments in chymiatria, whilst stridently distancing themselves from Paracelsus and his “magic”. One notable example is Andreas Libavius (c.1550–1616), whose Alchymia (1597 is often cited as the first chemistry textbook.

Source: Wikimedia Commons

In his rejection of Paracelsus, he refers back to Pseudo-Lull and other medieval sources, claiming that Paracelsus was merely derivative. Another chemically inclined rejector of Paracelsus was Jan Baptist van Helmont (1580–1644). The heated debates between the Paracelsians, the convention physicians who rejected his alchemical medicine and those who accepted it, but vehemently rejected the man actually helped to spread his ideas. 

L0003194 Portrait of J.B. van Helmont, Aufgang…1683 Credit: Wellcome Library, London. Wellcome Images images@wellcome.ac.uk http://wellcomeimages.org Portrait of J.B. van Helmont. Engraving Aufgang der Artzney-Kunst… Jean Baptiste van Helmont Published: 1683 Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0 http://creativecommons.org/licenses/by/4.0/

One highly influential Paracelsian, who should get a brief mention, is the Dane Peder Sørensen (1542–1602), better known as Petrus Severinus, who became chancellor of Denmark. In 1571 he published his Idea medicinae philosophicae (Ideal of Philosophical Medicine) (1571), which asserted the superiority of the ideas of Paracelsus to those of Galen and was highly influential, above all because it was written in Latin, the language of the learned rather than Paracelsus’ preferred German.

Source:

The German physician Daniel Sennert (1572–1637) author of De chymicorum cum Aristotelicis et Galenicis consensu ac dissensu (On the Agreements and Disagreements of the Chymists with the Aristotelians and Galenists) (1619), who became professor of medicine in Wittenberg, was highly influenced by Severinus, although he was one of those, who rejected Paracelsus the man. It was Sennert, who was most important in introducing the concept of atomism taken from the medieval alchemist Paul of Taranto (13th century) into the seventeenth century scientific debate exercising a major influence on Robert Boyle (1527–1691).

Source:Wikimedia Commons

Another important scholar influenced by Severinus was the Frenchman Guy de La Brosse (1586–1641) physician to King Louis XII and director of the first botanical garden in Paris Le Jardin du Roi founded in 1635. His support of Paracelsian medicine was particularly significant as the medical faculty of the university in Paris was vehemently anti-Paracelsus.

Le Jardin du Roi Paris

Perhaps Severinus’ most interesting follower was the astronomer, Tycho Brahe (1546–1601). It was Severinus, as Denmark’s most powerful politician, who persuaded the king to set up Tycho’s astronomical observatory on Hven, where Tycho also built a laboratory to produce Paracelsian medicines. 

To close a brief look at Paracelsus the physician beyond his chymiatria. Shut out by the medical establishment from the universities and the lucrative medical book market, Paracelsus must have been a successful physician, as he survived over the years on his reputation for healing wealthy private patients. In his polemics on the study of medicine, Paracelsus rejected book learning in favour of empirical observation and experience. He very much favoured hands on artisanal knowledge over, what he considered, the intellectual posturing of the university physicians. All of this places him very much in line with the general trends in Renaissance science, although he was certainly more radical than most of his contemporaries. His insistence on empirical observation is most notable in two areas where he made fairly novel contributions.

Paracelsus is credited with making one of the first studies of occupational diseases. His work in this direction is based on his observations of the typical diseases of the miners working in the areas where his father was employed and where he also worked from time to time. The second area where Paracelsus distinguished himself is in his analysis of mental illness. Although his writings on the subject are to a certain extent confused and complex, he does present some remarkable insights. He clearly distinguishes between genetic mental deficiency and mental illness. He diagnosed what we would now call manic-depression and was probably the first physician to recognise the existence of psychosomatic illnesses. Lastly, his suggested treatments for the mentally ill were positively humane compared to most of his contemporaries. All of this was very much based on clear-eyed empirical observation.

Theophrastus von Hohenheim is a very complex historical figure and it is almost impossible to do him justice in a brief blog post, but, however one views him, there is no denying that he had a major influence during the Renaissance both in the promotion of iatrochemistry and the turn away from book learning towards empirical investigation, perhaps the principle distinguishing feature of Renaissance science.

*Like many an oft quoted catch phrase, Sergeant Joe Friday never actually said “just the facts ma’am”. It only turns up in Stan Freburg’s brilliant Dragnet parody “St. George and the Dragonet” (1953), which is where I know it from, never actually having heard the original Dragnet.

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

Would you like a new body for that brain, sir?

Brain transplants are the subject of science fiction and Gothic horror, right? One of the most famous Gothic horror stories, Mary Shelley’s Frankenstein; or, The Modern Prometheus features a brain transplant, of which much is made in the various film versions. But in real life, a fantasy not a reality, or? Wrong, the American neurosurgeon Robert White (1926–2010) devoted most of his working life to the dream of transplanting a human brain, experimenting, and working towards fulfilment of this dream. I’m a voracious reader consuming, particularly in my youth, vast amounts of scientific and related literature, but I had never come across the work of Robert White, which took place during my lifetime. Thanks to Brandy Schillace, this lacuna in my knowledge has been more than filled, through her fascinating and disturbing book Mr. Humble and Dr. ButcherA Monkey’s Head, the Pope’s Neuroscientist, and the Quest to transplant the Soul[1], which tells in great detail the story of Robert White’s dream and his attempts to fulfil it.

The title is of course a play on the title of Robert Louis Stevenson’s notorious Gothic novella Strange Case of Dr Jekyll and Mr Hyde, the story of a medically induced split personality, with a good persona and an evil one. Here, Mr Humble refers to the neurosurgeon Bob White, deeply religious, Catholic family father and brain surgeon, who always engaged 150% for his patients. A saint of a man, who everybody looked up to and admired.

Mr Humble

Dr. Butcher refers to the research scientist Dr White, who carried out a, at times truly brutal, programme of animal experimentation on the way to his ultimate goal, the transplantation of a human brain.

Schillace takes us through Robert White’s entire life in detail, illustrating both sides of his personality, at the same time demonstrating that it is not so simple to separate the supposedly contradictory aspect of that personality into the neat division suggested by the title. White both a neurosurgeon and a theoretical neurologists regarded his dream of becoming the first man to carry out a brain transplant, as his greatest medical contribution to the welfare of humanity. Just think what it would mean to a quadriplegic with a healthy and creative brain, trapped in a degenerating body to have their life revitalised by having their brain transferred to the healthy body of a car crash victim, he argued. 

Schillace’s book not only tells the life story of the good Doctor Bob, but embeds it deeply in the medical, social, ethical, and political contexts in which it evolved. For example, the reader might justifiably ask how White managed to get research financing, which he did, for what at first glance looks like the script for a Hollywood horror movie. The answer is as surprising as it is simple, the Cold War. We tend to think of the Cold War in terms of nuclear weapons and the space race, but the rivalry between the two superpowers, as they were called, in the post Second World War period covered almost all human activities, including, as it turns out, brain transplants. 

A Russian researcher, Vladimir Demikhov, had carried out numerous experiments on dogs in the post war periods, including transplanting the head of one dog onto the body of a second dog creating a two headed monster that did not live very long. When pictures of Demikhov’s two headed dog appeared in the West, it had a similar impact in the US, as when the Russians launched Sputnik I, panic! “My God, the Russkis are light years ahead of us in their medical research, throw some money at it!” So, Bob White got his brain transplant research generously financed by a US government, firmly convinced that they had to catch up with the commie competition. It would later turn out that Demikhov’s research, dressed up for the Western media, was by no means as revolutionary as it first appeared, and the US didn’t actually have any catching up to do.

Transplant and replacement surgery has become a normal part of our medical world, with kidney transplants or artificial knee joint replacement, for example, now regarded as everyday medical procedures. This was, however, not the case when Bob White started out on his long year research programme, so Schillace also includes as background in her book a fairly detailed sketch of the history of transplant surgery, in particular the problem of organ rejection and the path to its solution. 

At the centre of White’s story is his long intensive programme of experiments leading to the transplantation of the head of one monkey onto the body of a second monkey whilst keeping the brain of the transplanted head alive and ticking. Schillace’s detailed descriptions of these crucial experiments are brilliantly written, fascinating, gripping accounts that leave nothing to the imagination and if they don’t leave you feeling queasy, then maybe you should think seriously about your emotive responses. This is the first book review I have ever written that includes a warning to the reader. If you react badly to vivid descriptions of brutal animal experiments, then you should approach this book with caution.

White’s animal experiments led inevitably to confrontations with the animal rights movement, which in the form that we now know it was coming into being in White’s heyday. White met these confrontations head on, even taking part in television debates with his most virulent and articulate critics from the animal rights movement. His arguments were the standard ones of medical researchers, who do experiments on animals, that the benefits to humanity won through such research justifies the suffering to the animals. White’s main opponents on the animal cruelty front were Ingrid Newkirk and Alex Pacheco the couple who founded PETA (People for the Ethical Treatment of Animals), so Schillace delivers not just a general history of the animal rights movement but a fairly detailed one on the origins of PETA. Their debate with White was one of the cases that helped them from being “five people in a basement” (their own description) to becoming a major voice in animal welfare.

Dr Butcher

Animal rights and animal welfare were not the only ethical or philosophical themes that White had to deal with in his endeavours to become the first man to transplant a human brain. There were two major ones, the first of which was a question for all transplant surgeons and the second one of which was very central to White’s specific undertaking. 

Put simply, the more general problem is when exactly do we die? In terms of transplant surgery, when can the transplant surgeon begin plundering one body to supply spare parts to repair another body and be sure on the one hand that they didn’t kill the donor by taking the parts and on the other hand ensure that those parts are still fresh enough to be used? This is, of course, a complex ongoing debate and one that Schillace deals with more than adequately in her book.

The question specific to White’s work is an even more complex one. If, as most Christian claim, the human body is merely a mortal shell that we abandon when we die, where or what is the real person? What does the real person consist of and where is it situated? Where is the human mind situated and more importantly for believers, where the soul? These questions, and especially the second one, were vitally important to Bob White, who was a devout Catholic. Were the mind and soul both fully contained in the brain, meaning that if one were to transplant a brain, one would transplant a complete human being from one empty shell to another? This is what White wished to believe and a great deal of his research with monkeys was dedicated to trying to prove just this. However, a scientific proof was not enough for White, who needed the blessing of the Catholic Church. In what is a truly fascinating segment of the book, Schillace describes White’s taking up contact with the Church, his meeting with the Pope and his attempt to convince the Church to actively support him in his belief, as to what constitutes real human existence. This contact between the neurosurgeon and the Church led to him becoming a scientific advisor to the Vatican.

Although he never really came near to realising his lifelong ambition, White’s research into transplant surgery did lead to one very important development in transplant and severe injury surgery. During such surgery there are two main problems, one is the need for high speed because if, for example, you cut off the blood supply you need to restore it very fast if you want to keep your patient alive. The second is the need to be very quick to prevent the deterioration of and further damage to the organs. One method that is used extensively these days is radical cooling, hypothermia, of the affected body parts or the whole body to slow the metabolism and decelerate the any tissue deterioration. This was one of White’s discoveries and it brought him, late in life, a justifiable Nobel Prize nomination. He didn’t win.

The book has endnotes that mostly just record the numerous sources that Schillace consulted in writing this very well research volume. There is, however, no separate bibliography. There is an extensive and useful index. The book is rounded out with a selection of both black and white and colour photos.

Schillace, who is a world class story teller pulling the reader along with her pulsating narrative, has written a truly excellent book. A straightforward account of Bob White’s life and work would make for a fascinating narrative but the amount of context in which Schillace has embedded her narrative make this book so much more. She takes her readers down numerous intriguing rabbit holes, leaving this reader at least with the desire to read up on a dozen random topics.

This is a book for anybody who likes good quality, stimulating, informative history that will leave the reader with a hat full of philosophical conundrums about life and what exactly it is. Don’t take my word for it, get hold of a copy and read it!


[1] Brandy Schillace, Mr. Humble and Dr. ButcherA Monkey’s Head, the Pope’s Neuroscientist, and the Quest to transplant the Soul, Simon & Schuster, New York, London, Toronto, Sydney, New Delhi, 2021

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Renaissance Science – XXII

Perhaps surprisingly, land surveying as we know it today, a mathematical discipline utilising complex technological measuring instruments is very much a product of the practical mathematics of the Renaissance. Why surprisingly? Surveying is an ancient discipline that has its origins in humanity becoming settled many thousands of years ago. Ancient monuments such as the pyramids or Stonehenge definitely required some level of surveying in their construction and there are surviving documents from all literate ancient societies that refer to methods or the practice of surveying. 

All surveying uses some aspects of geometry and as Herodotus famously claimed geometry (Greek: geōmetría from geōmétrēs), which literally means measurement of earth or land, had its origins in Egyptian surveying for tax purposes. According to his account, King Sesostris divided all the lands in Egypt amongst its inhabitants in return for an annual rent. However, every year the Nile floods washing away the parts of the plots:

The country is converted into a sea, and nothing appears but the cities, which looked like islands in the Aegean. 

Those whose land had been lost objected to paying the rent, so Sesostris summoned those affected to appear before him.

Upon which, the king sent persons to examine, and determine by measurement the exact extent of the loss: and thenceforth only such a rent was demanded of him as was proportionate to the reduced size of his land. From this practice, I think, geometry first came to be known in Egypt, whence it passed into Greece.

According to legend, both Thales and Pythagoras, are reputed to have learnt their geometry in Egypt.

In all early cultures surveying was fairly primitive with measurements being made with ropes and measuring rods. In Egypt, surveyors were known as rope stretchers (harpedonaptai), the ropes used for measuring being stretched to avoid sagging.

A rope being used to measure fields. Taken from the Tomb of Menna, TT69. (c. 1500–1200 BCE) Source: Wikimedia Commons

Longer distances were either measured by estimation or by pacing. In ancient Egypt and Greece Bematistae (step measurer) where trained to walk with equal length paces and the historical records of Alexander the Great’s campaigns suggest that they were indeed highly accurate. This measuring of distances by pacing in reflected in our word mile, which is the Latin word for a thousand, mille, meaning a thousand paces.

The Latin for surveyor was agrimensores, meaning field measurers. They were also called gromatici after the groma a surveyor’s pole, an early instrument for determining lines at right angles to each other. 

The groma or gruma was a Roman surveying instrument. It comprised a vertical staff with horizontal cross-pieces mounted at right angles on a bracket. Each cross piece had a plumb line hanging vertically at each end. It was used to survey straight lines and right angles, thence squares or rectangles. They were stabilized on the high ground and pointed in the direction it was going to be used. The helper would step back 100 steps and place a pole. The surveyor would tell him where to move the pole and the helper would set it down.

(Lewis, M. J. T., Surveying instruments of Greece and Rome, McGraw Hill Professional, 2001, p. 120)
Staking out a right angle using a groma

Another instrument used for the same purpose was the dioptra. The dioptra was a sighting tube or, alternatively an alidade, that is a rod with a sight at each end, attached to a stand. If fitted with protractors, it could be used to measure angles. Hero from Alexandria wrote a whole book on this instrument and its use but there are doubts that the dioptra in the complex form described by Hero was actually used in field surveying.

Dioptra as described by Hero of Alexandria Source: Wikimedia Commons

The methods used by the Romans in field surveying were described in the works of technical authors such as Sextus Julius Frontinus (c. 40–103 CE) and Gaius Julius Hyginus (c. 64 BCE–17 CE).

All of the surveying described in antiquity was fairly small scale–measuring fields, determining boundaries, laying out military camps, etc–and geometrically centred on squares and rectangles. Cartography was done using astronomical determinations of latitude and longitude, whereby the latter was difficult, and distances estimated or paced. Nothing really changed in Europe during the medieval period. The surveying that was done was carried out using the same methods that the Romans had used. However, during the fifteenth century things began to change substantially and the first question is why?

The rediscovery of Ptolemaeus’ Geographia at the beginning of the fifteenth century, as described here, and the subsequent substantial increase in cartographical activity, as described here, played a major role, but as already stated above Ptolemaic cartography relied almost exclusively on astronomical methods and did not utilise field surveying. However, there was an increased demand for internal accuracy in maps that astronomical methods could not supply. Secondly, changes in land ownership led to an increased demand for accurate field surveying of estates that required more sophisticated methods than those of the agrimensores. Lastly, we have a good example of the knowledge crossover, typical for the Renaissance, as described in Episode V of this series. The surveyors of antiquity were artisans producing practical knowledge for everyday usage. In the Renaissance, university educated scholars began to interest themselves for this practical knowledge and make contributions to its development and it is these developments that we will now look at. 

The biggest change in surveying was the introduction of the simple geometrical figure the triangle into surveying, as Sebastian Münster, one of the most influential cosmographers (today we would say geographer) of the period, wrote in a German edition of his Cosmographia. Beschreibung aller Lender durch Sebastianum Münsterum in 1550:

Every thing you measure must be measured in triangles.

Actually, the theory of similar triangles, as explained in Euclid’s Elements, had been used in surveying in antiquity, in particular to determine the height of things or for example the width of a river. A method that I learnt as a teenager in the Boy Scouts.

What was new as we will see was the way that triangles were being used in surveying and that now it was the angles of the triangles that were measured and not the length of the sides, as in the similar triangles’ usage. We are heading towards the invention and usage of triangulation in surveying and cartography, a long-drawn-out process.

In his Ludi rerum mathematicarum (c. 1445), the architect Leon Battista Alberti describes a method of surveying by taking angular bearings of prominent points in the area he is surveying using a self-made circular protractor to create a network of triangles. He concludes by explaining that one only needs to the length of one side of one triangle to determine all the others. What we have here is an early description of a plane table surveying (see below) and step towards triangulation that, however, only existed in manuscript 

Alberti Ludi rerum mathematicarum 

Münster learnt his geometry from Johannes Stöffler (1452–1531), professor for mathematics in Tübingen, who published the earliest description of practical geometry for surveyors. In his De geometricis mensurationibus rerum (1513),

Johannes Stöffler Engraving from the workshop of Theodor de Brys, Source: Wikimedia Commons

Stöffler explained how inaccessible distances could be measured by measuring one side of a triangle using a measuring rod (pertica) and then observing the angles from either end of the measured stretch. However, most of the examples in his book are still based on the Euclidian concept of similar triangles rather than triangulation. In 1522, the printer publisher Joseph Köbel, who had published the Latin original, published a German version of Stöffler’s geometry book. 

Joseph Köbel Source: Wikimedia Commons

Both Peter Apian in his Cosmographia (1524) and Oronce Fine in his De geometria practica (1530) give examples of using triangles to measure distances in the same way as Stöffler.

Source

Fine indicating that he knew of Stöffler’s book. Apian explicitly uses trigonometry to resolve his triangles rather than Euclidian geometry. Trigonometry had already been known in Europe in the Middle Ages but hadn’t been used before the sixteenth century in surveying. Fine, however, still predominantly used Euclidian methods in his work, although he also, to some extent, used trigonometry.

A very major development was the publication in 1533 of Libellus de locorum describendum ratione (Booklet concerning a way of describing places) by Gemma Frisius as an appendix to the third edition of Apian’s Cosmographia, which he edited, as he would all edition except the first. Here we have a full technical description of triangulation published for the first time. It would be included in all further editions in Latin, Spanish, French, Flemish, in what was the most popular and biggest selling manual on mapmaking and instrument making in the sixteenth and seventeenth centuries.

Source: Wikimedia Commons

1533 also saw the publication in Nürnberg by Johannes Petreius (c. 1497–1550) of Regiomontanus’s De triangulis omnimodis (On triangles of every kind) edited by the mapmaker and globe maker, Johannes Schöner (1477–1547).

Source:

This volume was originally written in 1464 but Regiomontanus died before he could print and publish it himself, although he had every intention of doing so. This was the first comprehensive work on trigonometry in Europe in the Early Modern Period, although it doesn’t cover the tangent, which Regiomontanus handled in his Tabula directionum (written 1467, published 1490), an immensely popular and oft republished work on astrology. 

Regiomontanus built on previous medieval works on trigonometry and the publication of his book introduces what Ivor Grattan Guinness has termed The Age of Trigonometry. In the sixteenth century it was followed by Rheticus’ separate publication of the trigonometrical section of Copernicus’s De revolutionibus, as De lateribus et angulis triangulorium in 1542. Rheticus (1514–1574) followed this in 1551 with his own Canon doctrinae triangulorum. This was the first work to cover all six trigonometric functions and the first to relate the function directly to triangles rather than circular arcs.

Source: Wikimedia Commons

Rheticus spent the rest of his life working on his monumental Opus Palatinum de Triangulis, which was, however, first published posthumously by his student Lucius Valentin Otho in 1596. Rheticus and Otho were pipped at the post by Bartholomaeus Pitiscus (1561–1613), whose Trigonometriasive de solutione triangulorum tractatus brevis et perspicuous was published in 1595 and gave the discipline its name.

Source: Wikimedia Commons

Pitiscus’ work went through several edition and he also edited and published improved and corrected editions of Rheticus’ trigonometry volumes. 

Through Gemma Frisius’ detailed description of triangulation and sixteenth century works on trigonometry, Renaissance surveyors and mapmakers now had the mathematical tools for a new approach to surveying. What they now needed were the mathematical instruments to measure distances and angles in the field and they were not slow in coming.

The measure a straight line of a given distance as a base line in triangulation surveyors still relied on the tools already used in antiquity the rope and the measuring rod. Ropes were less accurate because of elasticity and sagging if used for longer stretches. In the late sixteenth century, they began to be replaced by the surveyor’s chain, made of metal links but this also suffered from the problem of sagging due to its weight, so for accuracy wooden rods were preferred. 

A Gunter chain photographed at Campus Martius Museum. Source: Wikimedia Commons

In English the surveyor’s chain is usually referred to as Gunter’s chain after the English practical mathematician Edmund Gunter (1581–1626) and he is also often referred to erroneously as the inventor of the surveyor’s chain but there are references to the use of the surveyor’s chain in 1579, when Gunter was still a child. 

He did, however, produce what became a standardised English chain of 100 links, 66 feet or four poles, perches, or rods long, as John Ogilby (1600–1676) wrote in his Britannia Atlas in 1675:

…a Word or two of Dimensurators or Measuring Instruments, whereof the mosts usual has been the Chain, and the common length for English Measures 4 Poles, as answering indifferently to the Englishs Mile and Acre, 10 such Chains in length making a Furlong, and 10 single square Chains an Acre, so that a square Mile contains 640 square Acres…’

An English mile of 5280 feet was thus 80 chains in length and there are 10 chains to a furlong. An acre was 10 square chains. I actually learnt this antiquated system of measurement whilst still at primary school. The name perch is a corruption of the Roman name for the surveyor’s rod the pertica. 

To measure angles mapmakers and surveyors initially adopted the instruments developed and used by astronomers, the Jacob staff, the quadrant, and the astrolabe. An instrument rarely still used in astronomy but popular in surveying was the triquetum of Dreistab. The surveyors triquetum consists of three arms pivoted at two points with circular protractors added at the joints to measure angles and with a magnetic compass on the side to determine bearings. 

Surveyors then began to develop variants of the dioptra. The most notable of these, that is still in use today albeit highly modernised, was the theodolite, an instrument with sights capable of measuring angles both vertically and horizontally. The name first occurs in the surveying manual A geometric practice named Pantometria by Leonard Digges (c. 1515–c. 1559) published posthumously by his son Thomas (c. 1546–1595) in 1571.

Leonard Digges  A geometric practice named Pantometria Source

However, Digges’ instrument of this name could only measure horizontal angles. He described another instrument that could measure both vertical and horizontal angles that he called a topographicall instrument. Josua Habermehl, about whom nothing is known, but who was probably a relative of famous instrument maker Erasmus Habermehl (c. 1538–1606), produced the earliest known instrument similar to the modern theodolite, including a compass and tripod, in 1576. In 1725, Jonathan Sisson (1690–1747) constructed the first theodolite with a sighting telescope.

Theodolite 1590 Source:

A simpler alternative to the theodolite for measuring horizontal angles was the circumferentor. This was a large compass mounted on a plate with sights, with which angles were measured by taking their compass bearings.

18th century circumferentor

Instruments like the triquetum and the circumferentor were most often used in conjunction of another new invention, the plane table. Gemma Frisius had already warned in his Libellus de locorum describendum rationeof the difficulties of determining the lengths of the sides of the triangles in triangulation using trigonometry and had described a system very similar to the plane table in which the necessity for these calculation is eliminated. 

Surveying with plane table and surveyor’s chain

The plane table is a drawing board mounted on a tripod, with an alidade. Using a plumb bob, the table is centred on one end of a baseline, levelled by eye or after its invention (before 1661) with a spirit level, and orientated with a compass. The alidade is placed on the corresponding end of the scaled down baseline on the paper on the table and bearings are taken of various prominent features in the area, the sight lines being drawn directly on the paper. This procedure is repeated at the other end of the baseline creating triangles locating the prominent figures on the paper without having to calculate.

Philippe Danfrie (c.1532–1606) Surveying with a plane table

As with the theodolite there is no certain knowledge who invented the plane table. Some sources attribute the invention of the plane table to Johannes Praetorius (1537–1616), professor for mathematics at the University of Altdorf, as claimed by his student Daniel Schwentner (1585–1636). However, there was already a description of the plane table in “Usage et description de l’holomètre”, by Abel Foullon (c. 1514–1563) published in Paris in 1551. It is obvious from his description that Foullon hadn’t invented the plane table himself. 

The plane table is used for small surveys rather than mapmaking on a large scale and is not triangulation as described by Gemma Frisius. Although the Renaissance provided the wherewithal for full triangulation, it didn’t actually get used much for mapping before the eighteenth century. At the end of the sixteenth century Tycho Brahe carried out a triangulation of his island of Hven, but the results were never published. The most notable early use was by Willebrord Snel (1580–1626) to measure one degree of latitude in order to determine the size of the earth in 1615. He published the result in his Eratosthenes batavus in Leiden in 1617. He then extended his triangulation to cover much of the Netherlands.

Snel’s Triangulation of the Dutch Republic from 1615 Source: Wikimedia Commons

In the late seventeenth century Jean Picard (1620–1682) made a much longer meridian measurement in France using triangulation. 

Picard’s triangulation and his instruments

In fourteen hundred European surveyors were still using the same methods of surveying as the Romans a thousand years earlier but by the end of the seventeenth century when Jean-Dominique Cassini (1625–1712) began the mapping of France that would occupy four generations of the Cassini family for most of the eighteenth century, they did so with the fully developed trigonometry-based triangulation that had been developed over the intervening three hundred years. 

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The amateur, astronomical, antiquarian aristocrat from Aix

In a recent blog post about the Minim friar, Marin Mersenne (1588–1648), I mentioned that when Mersenne arrived in Paris in 1619 he was introduced to the intellectual elite of the city by Nicolas-Claude Fabri de Peiresc (1580-1637). In another recent post on the Republic of Letters I also mentioned that Peiresc was probably, the periods most prolific correspondent, with more than ten thousand surviving letters. So, who was this champion letter writer and what role did he play in the European scientific community in the first third of the seventeenth century?

Nicolas-Claude Fabri de Peiresc by Louis Finson Source: Wikimedia Commons

Nicolas-Claude Fabri was born, into a family of lawyers and politicians, in the town Belgentier near Toulon on 1 December in 1580, where his parents had fled to from their hometown of Aix-en-Provence to escape the plagues. He was educated at Aix-en-Provence, Avignon, and the Jesuit College at Tournon. Having completed his schooling, he set off to Padua in Italy, nominally to study law, but he devoted the three years, 1600–1602, to a wide-ranging, encyclopaedic study of the history of the world and everything in it. 

In this he was aided in that he became a protégé of Gian Vincenzo Pinelli (1535–1601) a humanist scholar and book collector, his library numbered about 8,500 printed works, with all-embracing intellectual interests, whose main areas were botany, optics, and mathematical instruments.

Gian Vincènzo Pinelli Source: Rijksmuseum via Wikimedia Commons

Pinelli introduced Fabri to many leading scholars including Marcus Welser (1558–1614), Paolo Sarpi (1552–1623) and indirectly Joseph Scaliger (1540–1609). Pinelli also introduced him to another of his protégés, Galileo Galilei (1564–1642). One should always remember that although he was thirty-eight years old in 1602, Galileo was a virtually unknown professor of mathematics in Padua. When Pinelli died, Fabri was living in his house and became involved in sorting his papers.

In 1602, Fabri returned to Aix-en-Provence and completed his law degree, graduating in 1604. In the same year he assumed the name Peiresc, it came from a domain in the Alpes-de-Haute-Provence, which he had inherited from his father. He never actually visited Peiresc, now spelt Peyresq.

Village of Peyresq Source: Wikimedia Commons

Following graduation Peiresc travelled to the Netherlands and England via Paris, where he made the acquaintance of other notable scholars, including actually meeting Scaliger and also meeting the English antiquarian and historian William Camden (1551–1623).

Returning to Provence, in 1607, he took over his uncle’s position as conseiller to the Parliament of Provence under his patron Guillaume du Vair (1556–1621), cleric, lawyer, humanist scholar and president of the parliament.

Guillaume-du-Vair Source: Wikimedia Commons

In 1615 he returned to Paris with du Vair as his secretary, as du Vair was appointed keeper of the seals during the regency of Marie de’ Medici (1575–1642). Peiresc continued to make new contacts with leading figures from the world of scholarship, and the arts, including Peter Paul Rubens (1577–1640).

Peter Paul Rubens self-portrait 1623

Peiresc acted as a go between in the negotiations between Reubens and the French court in the commissioning of his Marie de’ Medici Cycle. Just one of Peiresc’s many acts of patronage in the fine arts.

Marie de’ Medici Cycle in the Richelieu wing of the Louvre Source: Wikimedia Commons

In 1621 de Vair died and in 1623 Peiresc returned to Provence, where he continued to serve in the parliament until his death in 1637.

Peiresc was an active scholar and patron over a wide range of intellectual activities, corresponding with a vast spectrum of Europe’s intellectual elite, but we are interested here in his activities as an astronomer. Having developed an interest for astronomical instruments during his time as Pinelli’s protégé, Peiresc’s astronomical activities were sparked by news of Galileo’s telescopic discoveries, which reached him before he got a chance to read the Sidereus Nuncius. He rectified this lack of direct knowledge by ordering a copy from Venice and borrowing one from a friend until his own copy arrived.

Source: Wikimedia Commons

He immediately began trying to construct a telescope to confirm or refute Galileo’s claims, in particular the discovery of the first four moons of Jupiter. At this point in his life Peiresc was still a geocentrist, later he became a convinced heliocentrist. We know very little about where and how he acquired his lenses, but we do know that he had various failures before he finally succeeded in observing the moons of Jupiter for himself, in November 1610. In this he was beaten to the punch by his fellow Provencal astronomer Joseph Gaultier de la Valette (1564–1647), vicar general of Aix. At this point it is not clear whether the two were competing or cooperating, as they would then later do with Gaultier de la Valette becoming a member of Peiresc’s Provencal astronomical observation group. Shortly thereafter, Peiresc became the first astronomer to make telescopic observations of the Orion Nebular and Gaultier de la Valette the second. This is rather strange as the Orion Nebular is visible to the naked eye. However, apparently none of the telescopic astronomy pioneers had turned their telescopes to it before Peiresc.

In one of the most detailed astronomical images ever produced, NASA/ESA’s Hubble Space Telescope captured an unprecedented look at the Orion Nebula. … This extensive study took 105 Hubble orbits to complete. All imaging instruments aboard the telescope were used simultaneously to study Orion. Source: Wikimedia Commons

Peiresc, like Galileo, realised that the moons of Jupiter could be used as a clock to determine longitude and began an observation programme of the moons, viewing them every single day that the weather conditions permitted, well into 1612. Having compiled tables of his observations he sent one of his own protégés Jean Lombard, about whom little is known, equipped with suitable instruments on a tour of the Mediterranean. Lombard observed the satellites at Marseille in November 1611 and then proceeded to Malta, Cyprus and to Tripoli observing as he went, until May 1612. Meanwhile, Peiresc made parallel observation in Aix and Paris, he hoped by comparing the time differences in the two sets of observations to be able to accurately determine the longitude differences. Unfortunately, the observations proved to be not accurate enough for the purpose and the world would have to wait for Giovanni Domenico Cassini (1625–1712) to become the first to successfully utilise this method of determining longitude. Peiresc’s own observation were, however, the longest continuous series of observations of the Jupiter moons made in the seventeenth century and displayed a high level of accuracy even when compared with this of Galileo.

I mentioned, above, Peiresc’s Provencal astronomical observing group. Peiresc employed/sponsored young astronomers to help him with his observation programmes, supplying them with instruments and instructions on how to use them. This group included such notable, future astronomers, as Jean-Baptiste Morin (1583–1556),

Jean-Baptiste Morin Source: Wikimedia Commons

Ismaël Boulliau (1605–1694),

Ismaël Boulliau Source: Wikimedia Commons

and Pierre Gassendi (1592–1655). Peiresc’s patronage extended well beyond this. Gassendi had held the chair of philosophy at the University of Aix-en-Provence since 1617 but in 1623 the university was taken over by the Jesuits and Gassendi was replaced by a Jesuit and became unemployed.

Portrait of Pierre Gassendi by Louis-Édouard Rioult Source: Wikimedia Commons

From then until he again found regular employment in 1634, Peiresc provided him with a home base in his own house and financed his travels and research. Similarly, Peiresc, having introduced Mersenne to Parisian intellectual circles in 1619, continued to support him financially, Mersenne as a Minim friar had no income, supplying him with instruments and financing his publications. 

Marin Mersenne Source: Wikimedia Commons

Patronage played a central role in Peiresc’s next venture into astronomy and another attempt to solve the longitude problem. There has been much talk in recent decades about so-called citizen science, in which members of the public are invited to participate in widespread scientific activities. Annual counts of the birds in one’s garden is a simple example of this. Citizen science is mostly presented as a modern phenomenon, but there are examples from the nineteenth century. Peiresc had already launched a variation on citizen science in the seventeenth century.

In order to determine longitude Peiresc further developed a method that had been in use since antiquity. Two astronomers situated in different location would observe a lunar or solar eclipse and then by comparing their observations they could determine the local time difference between their observations and thus the longitude difference between the locations. By the seventeenth century predicting eclipses had become a fairly accurate science and Peiresc thought that if he could organise and coordinated a world spanning network of observers to accurately observe and record an eclipse, he could then calculate a world spanning network of longitude measurements. The idea was good in theory but failed in practice.

Most of Peiresc’s team of observers were amateurs–missionaries, diplomats, traders, travellers–whom he supplied with astronomical instruments and written instructions on how to use them, even paying travelling expenses, where necessary. Peiresc organised mass observations for lunar eclipses in 1628, 1634, and 1635 and a solar eclipse in 1633. Unfortunately, many of his observers proved to be incompetent and the results of their observations were too inaccurate to be usable. One positive result was that Peiresc was able to correct the value for the length of the Mediterranean. Before one is too hard on Peiresc’s amateur observers, one should remember that in the middle of the eighteenth century the world’s professional astronomical community basically failed in their attempt to use the transits of Venus to determine the astronomical unit, despite being equipped with much better instruments and telescopes.

Although, Peiresc’s various astronomical activities and their results were known throughout Europe by word of mouth through his various colleagues and his correspondence, he never published any of his work. Quite why, is not really known although there are speculations.

Peiresc was a high ranking and highly influential Catholic and he applied that influence in attempts to change the Church’s treatment of astronomers he saw as being persecuted. He interceded on behalf Tommaso Campanella (1568–1639), actively supporting him when he fled to France in 1634.

Tommaso Campanella portrait by Francesco Cozza Source: Wikimedia Commons

More famously he personally interceded with the Church on behalf of Galileo, without any great success.

Nicolas-Claude Fabri de Peiresc’s career is, like that of his friend Mersenne, a good illustration that the evolution of science is a product of widespread cooperation of a community of practitioners and not the result of the genial discoveries of a handful of big names, as it is unfortunately too often presented. Morin, Boulliau, Gassendi and Mersenne, who all made serious contributions to the evolution of science in the seventeenth century, did so with the encouragement, guidance, and very active support of Peiresc.

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Renaissance Science – XXI

One of the products of the Republic of Letters during the Humanist Renaissance was the beginning or the foundation of the modern European library. Naturally they didn’t invent libraries; the concept of the library goes back quite a long way into antiquity. To a great extent, libraries are a natural consequence of the invention of writing. When you have writing, then you have written documents. If you preserve those written documents then at some point you have a collection of written documents and when that collection becomes big enough, then you start to think about storage, sorting, classification, listing, cataloguing and you have created an archive or a library. I’m not going try and sort out the difference between an archive and a library and will from now on only use the term library, meaning a collection of books, without answering the question, what constitutes a book?

The oldest know libraries are the collections of clay tablets found in the temples of Sumer, some of which date back to the middle of the third millennium BCE. There were probably parallel developments in ancient Egypt but as papyrus doesn’t survive as well as clay tablets there is less surviving evidence for early Egyptian libraries. There is evidence of a library in the Sumerian city of Nippur around two thousand BCE and a library with a classification system in the Assyrian city of Nineveh around seven hundred BCE. The Library of Ashurbanipal in Nineveh contained more than thirty thousand clay tablets containing literary, religious, administrative, and scientific works. Other ancient cultures such as China and India also developed early libraries.

Library of Ashurbanipal Mesopotamia 1500-539 BC Gallery, British Museum, Source: Wikimedia Commons

The most well-known ancient library is the legendary Library of Alexandria, which is clouded in layers of myth. The library was part of the of the Mouseion, a large research institute, which was probably conceived by Ptolemy I Soter (c. 367–282 BCE) but first realised by his son Ptolemy II Philadelphus (309–246 BCE). Contrary to popular myth it was neither destroyed by Christian zealots nor by Muslim ones but suffered a steady decline over a number of centuries. For the full story read Tim O’Neill’s excellent blog post on the subject, which also deals with a number of the other myths. As Tim points out, Alexandria was by no means the only large library during this period, its biggest rival being the Library of Pergamum founded around the third century BCE. The Persian Empire is known to have had large libraries as did the Roman Empire.

Artistic rendering of the Library of Alexandria, based on some archaeological evidence Source: Wikimedia Commons

With the gradual decline of the Western Roman Empire, libraries disappeared out of Europe but continued to thrive in the Eastern Empire, the future Byzantium. The Islamic Empire became the major inheritor of the early written records of ancient Greece, Egypt, Persia, and Rome creating in turn their own libraries throughout their territories. These libraries became to source of the twelfth century translation movement, also known as the scientific renaissance, when those books first began to re-enter medieval Europe. 

During the Early Middle Ages, the only libraries still in existence in what had been the Western Roman Empire were those that existed in the Christian monasteries. Here we must once again dispose of two connected myths. The first more general one is the widespread myth that Christians deliberately destroyed pagan literature i.e., the texts of the Greeks and Romans. In fact, as Tim O’Neill points out in another excellent blog post, we have Christians to thank for those texts that did survive the general collapse of an urban civilisation. The second, closely related myth, spread by the “the Church is and always was anti-science brigade”, is that the Church deliberately abandoned Greek science because it was ant-Christian. Once again as Stephen McCluskey has documented in his excellent, Astronomies and Cultures in Early Medieval Europe, (CUP; 1998) it was the monasteries that keep the flame of the mathematical science burning during this period even if only on a low flame.

The manuscript collections of the medieval libraries were very small in comparison to the great Greek libraries such as Alexandria and Pergamum or the many public libraries of Rome, numbering in the best cases in the hundreds but often only in the tens. However, the guardians of these precious written documents did everything in their power to keep the books safe and in good condition and also endeavouring to acquire new manuscripts by copying those from other monastery libraries, often undertaking very arduous journeys to do so. 

Chained library in Hereford Cathedral Most of the books in the collection date to about 1100. Source: Wikimedia Commons

Things began to improve in the twelfth century with the scientific renaissance and the translation movement, which coincided with the founding of the European universities. The number of works available in manuscript increased substantially but they still had to be copied time and again to gradually spread throughout Europe. Like the monasteries the universities also began to collect books and to establish libraries but if we look at the figures for Cambridge University founded in 1209. The university library has its roots in the beginning of the fifteenth century, there would have been earlier individual college libraries earlier. The earliest surviving catalogue from c. 1424 list 122 volumes in the library. By 1473 a second catalogue lists 330 volumes. It is first in the sixteenth century that things really take off and the library begins to grow substantially. The equally famous Oxford University Bodleian Library was first founded in 1600 by the humanist scholar Thomas Bodley in 1600, replacing the earlier university library from 1444, which had been stripped and dissipated during the Reformation. 

Thomas Bodley Artist unknown Source: Wikimedia Commons 

We have of course now reached the Humanist Renaissance and it is here that the roots of the modern library were laid. The Humanist Renaissance was all about written texts. The humanists read texts, analysed the content of texts, annotated texts, translated texts, and applied philological analysis to texts to correct and/or eliminate errors introduced into texts by repeated copying and translations. The text was everything for the humanists, so they began to accumulate collections of manuscripts. Both humanist scholars and the various potentates, who sponsored the humanist movement began to create libraries, as new spaces of learning. 

The Malatestiana Library was founded by Malatesta Novello of Cesena (1418–1485) in 1454.

Malatestiana Library of Cesena, the first European civic library Source: Wikimedia Commons

The foundations of the Laurentian Library in Florence were laid by Cosimo de’ Medici (1389–1464), as one of a sequence of libraries that he funded.

Reading room of the Laurentian Library Source: Wikimedia Commons

Pope Nicholas V (1397–1455) brought the papal Greek and Latin collections together in separate libraries in Rome and they were then housed by Pope Sixtus IV (1414–1484), who appointed the humanist Bartolomeo Platina (1421–1481) librarian of the Bibliotheca Apostolica Vaticana.

Sixtus IV appointing Bartolomeo Platina librarian of the Bibliotheca Apostolica Vaticana. From left Giovanni della Rovere, Girolamo Riario, Bartolomeo Platina, later Julius II (Giuliano della Rovere), Raffaele Riario, Pope Sixtus IV Source: Wikimedia Commons

This was followed by the establishment of many private libraries both in Rome and in other Italian cities. As with other aspects of the Humanist Renaissance this movement spread outside of Italy to other European Countries. For example, the Bibliotheca Palatina was founded by Elector Ludwig III (1378–1436) in Heidelberg in the 1430s.

Elector Ludwig III. Contemporary image on the choir ceiling of the  Stiftskirche (Neustadt an der Weinstraße). Source: Wikimedia Commons

These new humanist libraries were not just book depositories but as stated above new spaces for learning. The groups of humanist scholars would meet regularly in the new libraries to discuss, debate or dispute over new texts, new translations, or new philological corrections to old, corrupted manuscripts. 

The (re)invention of movable type printing in about 1450 meant that libraries began to collect printed books as well as manuscripts. The first printer publishers in Italy concentrated on publishing the newly translated texts of the humanists even creating a new type face, Antiqua, which imitated the handwriting that had been developed and propagated by the first generations of humanist scholars. 

The spread of libraries during the Renaissance is a vast subject, too much to deal with in a blog post, but one can get a perspective on this development by looking at a sketch of the career of Johannes Müller (1436–1476) aka Regiomontanus or as he was known during his live time, Johannes de Monte Regio. 

Smithsonian “Print Artist: Braeht” (whereby the signature appears to be rather Brühl sculps[it] possibly Johann Benjamin Brühl (1691-1763) ) – Smithsonian Institution Libraries Digital Collection Source: Wikimedia Commons

Regiomontanus is, today, best known as the most significant European mathematician, astronomer, and astrologer of the fifteenth century, so it comes as something of a surprise to discover that he spent a substantial part of his life working as a librarian for various humanist book collectors. 

Regiomontanus graduated MA at the University of Vienna on his twenty-first birthday in 1457. He had actually completed the degree requirements much earlier, but university regulations required MA graduates to be at least twenty-one years old. He then joined his teacher Georg von Peuerbach as a teacher at the university, lecturing on optics amongst other things. Both Regiomontanus and Peuerbach were convinced humanists. In 1460 Basilios Bessarion (1403–1472) came to Vienna.

Basilios Bessarion Justus van Gent and Pedro Berruguete Source: Wikimedia Commons

He was a Greek Orthodox monk, who had converted to Catholicism, been elevated to Cardinal and was in Vienna as papal legate to negotiate with the Holy Roman Emperor Frederick III on behalf of Pope Pius II. Pius II, civil Aeneas Silvius Piccolomini (1405–1464), was a humanist scholar well acquainted with Frederick and Vienna from his own time as a papal legate. Bessarion, a Neo-Platonist, was a very active humanist, setting up and sponsoring humanist circles wherever his travels took him. In Vienna he sought out Peuerbach to persuade him to undertake a new Latin translation of Ptolemaeus’ Mathēmatikē Syntaxis from the original Greek. Peuerbach couldn’t read Greek but he, and after his death Regiomontanus, produced their Epitome of the Almagest, the story of which I have told elsewhere. Bessarion asked Peuerbach to return to Italy with him. Peuerbach agreed on the condition that Regiomontanus could also accompany them. Peuerbach died in 1461, so only Regiomontanus accompanied Bessarion back to Italy and it is here that his career as librarian began.

Bessarion was an avid book collector and Regiomontanus’ job in his personal entourage was to seek out and make copies of new manuscripts for Bessarion’s collection. A task that he fulfilled with esprit. Bessarion had in the meantime also taught him Greek. In 1468, Bessarion presented his personal library to the Senate of Venice in 1468 and the 482 Greek manuscripts and 264 Latin manuscripts today still form the core of the St. Mark’s Biblioteca Marciana.

Cardinal Bessarion’s letter to Doge Cristoforo Moro and the Senate of Venice, announcing the donation of his library. BNM Lat. XIV, 14 (= 4235), fol. 1r. Source: Wikimedia Commons

Regiomontanus left Bessarion’s entourage around 1465 and reappears in 1467 at the court of János Vitéz Archbishop of Esztergom (German, Gran) in Hungary. 

János Vitéz frontispiece of a manuscript Source: Wikimedia Commons

Vitéz, an old friend of Peuerbach, was a humanist scholar and an avid book collector. Although Regiomontanus served as court astrologer, his Tabulae Directionum, one of the most important Renaissance astrological texts was produced at Vitéz’s request, his main function at Vitéz’s court was as court librarian. From Esztergom he moved to the court of the Hungarian King, Matthias Corvinus (1443–1490), who had been educated by Vitéz.

Matthias Corvinus of Hungary portrait by Andrea Mantegna Source: Wikimedia Commons

Like his teacher, Corvinus was a humanist scholar and a major book collector. Once more, Regiomontanus served as a court librarian. The Bibliotheca Corviniana had become one of the largest libraries in Europe, second only to the Bibliotheca Apostolica Vaticana, when Corvinus died. Unfortunately, following his death, his library was dissipated. 

Long before Corvinus’ death, Regiomontanus had left Hungary for Nürnberg, with Corvinus’ blessing and a royal pension, to set up a programme to reform astronomy in order to improve astrological divination. During his travels, Regiomontanus had not only made copies of manuscripts for his patrons, but also for himself, so he arrived in Nürnberg with a large collection of manuscript in 1471. His aim was to set up a printing house and publish philologically corrected editions of a long list of Greek and Latin mathematical, astronomical, and astrological texts, which he advertised in a publisher’s list that he printed and published. Unfortunately, he died in 1476 having only published nine texts including his publishers list and to the shame of the city council of Nürnberg, his large manuscript collection was not housed in a library but dissipated. 

To close a last example of a lost and dissipated Renaissance library. The English mathematicus John Dee (1527–1609) hoped to establish a national library, but he failed to get the sponsorship he wished for.

John Dee artist unknown Source: Wikimedia Commons

Instead, he collected books and manuscripts in his own house in Mortlake, acquiring the largest library in England and one of the largest in Europe. In the humanist tradition, this became a research centre, with other scholars coming to Mortlake to consult the books and to discuss their research with Dee and other visitors. However, when Dee left England for the continent, in the 1580s with Edward Kelly, to try and find sponsors for his occult activities, his house was broken into, and his library pillaged and sold off. 

Despite the loss of some of the largest Renaissance book collections and libraries, the period saw the establishment of the library both public and private, as a centre for collecting books and a space for learning from them. 

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Putting women back into the history of science

Readers who have been around here for a long time will know that for several years I was editor in chief of On Giants’ Shoulders the monthly history of science blog carnival. They will also know that I buried it when its time had come and replaced it with Whewell’s Gazette Your weekly digest of all the best of Internet history of science, technology and medicine Editor in Chief: The Ghost of William Whewell, which I edited for three years until it became just too much, closing it down in July 2017. Since then, I have maintained a more casual but fairly comprehensive interest in the history of science content on the Internet. All of this means that I probably have an at least as great awareness of the history of science cyberspace activity as anybody alive.

Without any doubt whatsoever, one of the most important and significant online contributions to the history of science, in all the time that I’ve been monitoring it, has been Lady Science. Originally set up seven years ago by Anna Reser and Leila McNeill, as a blog dedicated to emphasising the role of women in the history of science it became so much more. A magazine with features, essays, commentaries, ideas, reviews, and podcasts, which describes itself as A magazine for the history and popular culture of science. We publish a variety of voices & work on women and gender across the sciences, written by an ever-expanding group of authors, who maintain an impressively high standard of expression. 

 Sadly, last week Anna and Leila announced that they were closing down Lady Science at the end of 2021 and you can read their explanation why here. They are moving on to new projects and I wish them all the best, whilst shedding a silent tear for the loss of Lady Science

However, for all fans and supporters of their work, Reser and McNeill published an encyclopaedical collection of their work this year under the title, Forces of NatureThe Women Who Changed Science.[1]

 Following an introduction, that sets out the Lady Science approach to investigating the role that women have played in science, the book is divided into five sections: I Antiquity to the Middle Ages, II The Renaissance & The Enlightenment, III The Long Nineteenth Century, IV The Twentieth Century, Pre-World War II, and V Twentieth Century, Post-World War II. Each section is in turn divided thematically into the numerous areas where women made their contributions to the development of science. So, in section II we have a section on women calculators in astronomy and one on the wives and sisters of scientific partnership. In section III one on women science writers and popularisers and in section IV one on women archaeologists and anthropologists. These are just examples, to illustrate the width of the authors’ presentation. 

Both authors excellent narrators and the individual essays are written in an attractive, easy to read style and are richly illustrated; the whole book has an attractive graphic design. Following the main section there is an afterword titled Other women to inspire, containing thumbnail portraits of other women scientists not included in the main-text.

This is followed by an index of names, endnotes referring to the sources and a bibliography of those sources presented chapter for chapter. 

 Regular readers of my reviews are probably expecting comments on the historical accuracy of the individual essays; there are not going to be any. This is not because the book is perfect, I have found historical errors, but here this is not so essential, as in other contexts. This book is intended to serve a very different purpose. That purpose consists of a broad sweep to illustrate the roles that women have played in the evolution of science throughout the ages. It’s a wakeup call! Most history of science writing simply ignores the roles that women have played, and this should and indeed must change. To give a simple example out of my own area of expertise. Neither Johannes Hevelius (1611–1687) nor William Herschel (1738–1822), both very important and significant astronomers, could have achieved that which they achieved without the active involvement and support of their respective wife, Elisabeth (1647–1693) and sister Caroline (1750–1848), who were very much more than just housewives, but skilled and active astronomers in their own right. 

As well as a wakeup call for historians, this book should serve as an inspiration for any young woman contemplating a career or a life in one of the sciences. This book should be available in every American high school and college library and in the libraries of the equivalent educational institutions of other lands. Teachers should place this book in the hands of any girl interested in STEM subjects, to show them that not all scientists are male and there are plenty of female role models that they could aspire to emulating. Also, the book should finally make clear that Hypatia, Ada Lovelace, and Marie Curie are not the only female scientists that four thousand years of science have thrown up. Lastly if you are a parent with a daughter, who displays an interest in science, do yourself a favour and buy them a copy of this excellent book. 


[1] Anna Reser and Leila McNeill, Forces of NatureThe Women Who Changed Science, Frances Lincoln Publishing, London, 2021

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